%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWW298+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 09:05:02 AM UTC 2026
% Result : Theorem 76.45s 76.73s
% Output : Proof 76.58s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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_triple__valid__Suc,axiom,
! [V_t,V_n,T_a] :
( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t)
=> c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ),
file('theBenchmark.p',fact_triple__valid__Suc) ).
fof(fact_hoare__valids__def,axiom,
! [V_tsa_2,V_G_2,T_b] :
( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_G_2,V_tsa_2)
<=> ! [B_n] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_G_2))
=> c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) )
=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
=> c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) ) ) ),
file('theBenchmark.p',fact_hoare__valids__def) ).
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_of__nat__aux_Osimps_I2_J,axiom,
! [V_i_2,V_na_2,V_inc_2,T_b] :
( class_Rings_Osemiring__1(T_b)
=> c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,hAPP(c_Nat_OSuc,V_na_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,V_na_2,hAPP(V_inc_2,V_i_2)) ),
file('theBenchmark.p',fact_of__nat__aux_Osimps_I2_J) ).
fof(fact_power_Opower_Opower__Suc,axiom,
! [V_na_2,V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_na_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),V_na_2)),
file('theBenchmark.p',fact_power_Opower_Opower__Suc) ).
fof(fact_nat__case__Suc,axiom,
! [V_nat_2,V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2),
file('theBenchmark.p',fact_nat__case__Suc) ).
fof(fact_nat__rec__Suc,axiom,
! [V_nat_2,V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(hAPP(V_f2_2,V_nat_2),hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),V_nat_2)),
file('theBenchmark.p',fact_nat__rec__Suc) ).
fof(fact_INFI__bool__eq,axiom,
! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b),
file('theBenchmark.p',fact_INFI__bool__eq) ).
fof(fact_mono__Suc,axiom,
c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),
file('theBenchmark.p',fact_mono__Suc) ).
fof(fact_mono__iff__le__Suc,axiom,
! [V_f_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,T_b,V_f_2)
<=> ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n)))) ) ),
file('theBenchmark.p',fact_mono__iff__le__Suc) ).
fof(fact_def__nat__rec__Suc,axiom,
! [V_na_2,V_h_2,V_c_2,T_b,V_f_2] :
( ! [B_n] : hAPP(V_f_2,B_n) = hAPP(c_Nat_Onat_Onat__rec(T_b,V_c_2,V_h_2),B_n)
=> hAPP(V_f_2,hAPP(c_Nat_OSuc,V_na_2)) = hAPP(hAPP(V_h_2,V_na_2),hAPP(V_f_2,V_na_2)) ),
file('theBenchmark.p',fact_def__nat__rec__Suc) ).
fof(fact_of__nat__aux_Osimps_I1_J,axiom,
! [V_i_2,V_inc_2,T_b] :
( class_Rings_Osemiring__1(T_b)
=> c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ),
file('theBenchmark.p',fact_of__nat__aux_Osimps_I1_J) ).
fof(fact_power_Opower_Opower__0,axiom,
! [V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2,
file('theBenchmark.p',fact_power_Opower_Opower__0) ).
fof(fact_nat__rec__0,axiom,
! [V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2,
file('theBenchmark.p',fact_nat__rec__0) ).
fof(fact_nat__case__0,axiom,
! [V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2,
file('theBenchmark.p',fact_nat__case__0) ).
fof(fact_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_strict__mono__mono,axiom,
! [V_f_2,T_b,T_c] :
( ( class_Orderings_Oorder(T_b)
& class_Orderings_Oorder(T_c) )
=> ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
=> c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2) ) ),
file('theBenchmark.p',fact_strict__mono__mono) ).
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_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_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_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_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_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_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_neq0__conv,axiom,
! [V_na_2] :
( V_na_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_na_2)) ),
file('theBenchmark.p',fact_neq0__conv) ).
fof(fact_nat__neq__iff,axiom,
! [V_na_2,V_m_2] :
( V_m_2 != V_na_2
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ),
file('theBenchmark.p',fact_nat__neq__iff) ).
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_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_le__0__eq,axiom,
! [V_na_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_le__0__eq) ).
fof(fact_nat__less__le,axiom,
! [V_na_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
<=> ( V_m_2 != V_na_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ),
file('theBenchmark.p',fact_nat__less__le) ).
fof(fact_le__eq__less__or__eq,axiom,
! [V_na_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
<=> ( V_m_2 = V_na_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ),
file('theBenchmark.p',fact_le__eq__less__or__eq) ).
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_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_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_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_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_nat__less__cases,axiom,
! [V_P_2,V_na_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
=> hBOOL(hAPP(hAPP(V_P_2,V_na_2),V_m_2)) )
=> ( ( V_m_2 = V_na_2
=> hBOOL(hAPP(hAPP(V_P_2,V_na_2),V_m_2)) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
=> hBOOL(hAPP(hAPP(V_P_2,V_na_2),V_m_2)) )
=> hBOOL(hAPP(hAPP(V_P_2,V_na_2),V_m_2)) ) ) ),
file('theBenchmark.p',fact_nat__less__cases) ).
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_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_b,T_c] :
( class_Orderings_Oord(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ),
file('theBenchmark.p',fact_le__funE) ).
fof(fact_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_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_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__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_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_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_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_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__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_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_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_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_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__antisym__conv,axiom,
! [V_x_2,V_y_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> ( V_x = V_y
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ),
file('theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__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_le__funD,axiom,
! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
( class_Orderings_Oord(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ),
file('theBenchmark.p',fact_le__funD) ).
fof(fact_linorder__antisym__conv2,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_order__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__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_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_leD,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ),
file('theBenchmark.p',fact_leD) ).
fof(fact_order__less__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_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_b] :
( class_Orderings_Olinorder(T_b)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_linorder__antisym__conv3,axiom,
! [V_x_2,V_y_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_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_strict__monoD,axiom,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Oorder(T_b)
& class_Orderings_Oorder(T_c) )
=> ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ),
file('theBenchmark.p',fact_strict__monoD) ).
fof(fact_strict__mono__less__eq,axiom,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Olinorder(T_b)
& class_Orderings_Oorder(T_c) )
=> ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_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)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_strict__mono__less__eq) ).
fof(fact_strict__mono__less,axiom,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Olinorder(T_b)
& class_Orderings_Oorder(T_c) )
=> ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_strict__mono__less) ).
fof(fact_strict__mono__eq,axiom,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Olinorder(T_b)
& class_Orderings_Oorder(T_c) )
=> ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_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_strict__mono__eq) ).
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_order__le__less,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> ( V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_order__le__less) ).
fof(fact_order__eq__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( V_x_2 = V_y_2
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_order__eq__iff) ).
fof(fact_less__le__not__le,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Opreorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_less__le__not__le) ).
fof(fact_order__less__le,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
<=> ( V_x_2 != V_y_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_order__less__le) ).
fof(fact_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_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_le__fun__def,axiom,
! [V_g_2,V_f_2,T_b,T_c] :
( class_Orderings_Oord(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
<=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ),
file('theBenchmark.p',fact_le__fun__def) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
<=> ( V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ),
file('theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_linorder__neq__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( V_x_2 != V_y_2
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_linorder__not__le,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_linorder__not__le) ).
fof(fact_linorder__not__less,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_linorder__not__less) ).
fof(fact_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_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_na_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2)))
<=> V_na_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_na_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_na_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ),
file('theBenchmark.p',fact_Suc__le__eq) ).
fof(fact_less__Suc__eq__le,axiom,
! [V_na_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ),
file('theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_less__eq__Suc__le,axiom,
! [V_m_2,V_na_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) ),
file('theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_less__Suc__eq__0__disj,axiom,
! [V_na_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
<=> ( ? [B_j] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_na_2))
& V_m_2 = hAPP(c_Nat_OSuc,B_j) )
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_less__Suc__eq__0__disj) ).
fof(fact_less__Suc0,axiom,
! [V_na_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_less__Suc0) ).
fof(fact_gr0__conv__Suc,axiom,
! [V_na_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2))
<=> ? [B_m] : V_na_2 = hAPP(c_Nat_OSuc,B_m) ),
file('theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_INF__subset,axiom,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2))) ) ),
file('theBenchmark.p',fact_INF__subset) ).
fof(fact_monoD,axiom,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Oorder(T_b)
& class_Orderings_Oorder(T_c) )
=> ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ),
file('theBenchmark.p',fact_monoD) ).
fof(fact_not__less__eq,axiom,
! [V_na_2,V_m_2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) ),
file('theBenchmark.p',fact_not__less__eq) ).
fof(fact_less__Suc__eq,axiom,
! [V_na_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
<=> ( V_m_2 = V_na_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ),
file('theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_Suc__less__eq,axiom,
! [V_na_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_na_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ),
file('theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_not__less__less__Suc__eq,axiom,
! [V_m_2,V_na_2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2)))
<=> V_na_2 = V_m_2 ) ),
file('theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_less__antisym,axiom,
! [V_m,V_n] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
=> V_m = V_n ) ),
file('theBenchmark.p',fact_less__antisym) ).
fof(fact_less__SucI,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ),
file('theBenchmark.p',fact_less__SucI) ).
fof(fact_Suc__lessI,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> ( hAPP(c_Nat_OSuc,V_m) != V_n
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ),
file('theBenchmark.p',fact_Suc__lessI) ).
fof(fact_less__trans__Suc,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ),
file('theBenchmark.p',fact_less__trans__Suc) ).
fof(fact_less__SucE,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> V_m = V_n ) ),
file('theBenchmark.p',fact_less__SucE) ).
fof(fact_Suc__lessD,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
file('theBenchmark.p',fact_Suc__lessD) ).
fof(fact_Suc__less__SucD,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ),
file('theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_Suc__n__not__le__n,axiom,
! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)),
file('theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_not__less__eq__eq,axiom,
! [V_na_2,V_m_2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) ),
file('theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_le__Suc__eq,axiom,
! [V_na_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
<=> ( V_m_2 = hAPP(c_Nat_OSuc,V_na_2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ),
file('theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_Suc__le__mono,axiom,
! [V_m_2,V_na_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),hAPP(c_Nat_OSuc,V_m_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_m_2)) ),
file('theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_le__SucI,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ),
file('theBenchmark.p',fact_le__SucI) ).
fof(fact_le__SucE,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> V_m = hAPP(c_Nat_OSuc,V_n) ) ),
file('theBenchmark.p',fact_le__SucE) ).
fof(fact_Suc__leD,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ),
file('theBenchmark.p',fact_Suc__leD) ).
fof(fact_Zero__not__Suc,axiom,
! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m),
file('theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_nat_Osimps_I2_J,axiom,
! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H),
file('theBenchmark.p',fact_nat_Osimps_I2_J) ).
fof(fact_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_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_of__nat__0__less__iff,axiom,
! [V_na_2,T_b] :
( class_Rings_Olinordered__semidom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) ),
file('theBenchmark.p',fact_of__nat__0__less__iff) ).
fof(fact_gr0__implies__Suc,axiom,
! [V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> ? [B_m] : V_n = hAPP(c_Nat_OSuc,B_m) ),
file('theBenchmark.p',fact_gr0__implies__Suc) ).
fof(fact_lift__Suc__mono__less__iff,axiom,
! [V_m_2,V_na_2,V_f_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_na_2)),hAPP(V_f_2,V_m_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) ) ) ),
file('theBenchmark.p',fact_lift__Suc__mono__less__iff) ).
fof(fact_lift__Suc__mono__less,axiom,
! [V_n_H_2,V_na_2,V_f_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_n_H_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_na_2)),hAPP(V_f_2,V_n_H_2))) ) ) ),
file('theBenchmark.p',fact_lift__Suc__mono__less) ).
fof(fact_power__eq__imp__eq__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> V_a = V_b ) ) ) ) ),
file('theBenchmark.p',fact_power__eq__imp__eq__base) ).
fof(fact_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_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_zero__reorient,axiom,
! [V_x_2,T_b] :
( class_Groups_Ozero(T_b)
=> ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
<=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_zero__reorient) ).
fof(fact_strict__monoI,axiom,
! [V_f_2,T_b,T_c] :
( ( class_Orderings_Oorder(T_b)
& class_Orderings_Oorder(T_c) )
=> ( ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),B_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) )
=> c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2) ) ),
file('theBenchmark.p',fact_strict__monoI) ).
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_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__square,axiom,
! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))),
file('theBenchmark.p',fact_le__square) ).
fof(fact_le__cube,axiom,
! [V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)))),
file('theBenchmark.p',fact_le__cube) ).
fof(fact_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_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_mult__le__mono1,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))) ),
file('theBenchmark.p',fact_mult__le__mono1) ).
fof(fact_mult__le__mono2,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))) ),
file('theBenchmark.p',fact_mult__le__mono2) ).
fof(fact_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_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_less__fun__def,axiom,
! [V_g_2,V_f_2,T_b,T_c] :
( class_Orderings_Oord(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) ) ),
file('theBenchmark.p',fact_less__fun__def) ).
fof(fact_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_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_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_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_of__nat__eq__iff,axiom,
! [V_na_2,V_m_2,T_b] :
( class_Nat_Osemiring__char__0(T_b)
=> ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)
<=> V_m_2 = V_na_2 ) ),
file('theBenchmark.p',fact_of__nat__eq__iff) ).
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_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_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__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_power__Suc,axiom,
! [V_n,V_a,T_a] :
( class_Power_Opower(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
file('theBenchmark.p',fact_power__Suc) ).
fof(fact_power__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_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_mult__zero__right,axiom,
! [V_a,T_a] :
( class_Rings_Omult__zero(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mult__zero__right) ).
fof(fact_mult__eq__0__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Oring__no__zero__divisors(T_b)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_mult__eq__0__iff) ).
fof(fact_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_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_of__nat__le__iff,axiom,
! [V_na_2,V_m_2,T_b] :
( class_Rings_Olinordered__semidom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ),
file('theBenchmark.p',fact_of__nat__le__iff) ).
fof(fact_mult__cancel2,axiom,
! [V_na_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_na_2),V_k_2)
<=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_na_2 ) ),
file('theBenchmark.p',fact_mult__cancel2) ).
fof(fact_mult__cancel1,axiom,
! [V_na_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_na_2)
<=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_na_2 ) ),
file('theBenchmark.p',fact_mult__cancel1) ).
fof(fact_mult__is__0,axiom,
! [V_na_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_na_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_mult__is__0) ).
fof(fact_mult__0__right,axiom,
! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_mult__0__right) ).
fof(fact_mult__0,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_mult__0) ).
fof(fact_Suc__mult__cancel1,axiom,
! [V_na_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_na_2)
<=> V_m_2 = V_na_2 ),
file('theBenchmark.p',fact_Suc__mult__cancel1) ).
fof(fact_Suc__mult__le__cancel1,axiom,
! [V_na_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_na_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ),
file('theBenchmark.p',fact_Suc__mult__le__cancel1) ).
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_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_zero__le__mult__iff) ).
fof(fact_mult__le__0__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_mult__le__0__iff) ).
fof(fact_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_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_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_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_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_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_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__pos) ).
fof(fact_mult__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_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__neg) ).
fof(fact_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_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_power__eq__0__iff,axiom,
! [V_na_2,V_a_2,T_b] :
( ( class_Rings_Ozero__neq__one(T_b)
& class_Rings_Ono__zero__divisors(T_b)
& class_Rings_Omult__zero(T_b)
& class_Power_Opower(T_b) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_na_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_power__eq__0__iff) ).
fof(fact_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_mult__le__cancel__left__pos,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_mult__le__cancel__left__pos) ).
fof(fact_mult__le__cancel__left__neg,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ),
file('theBenchmark.p',fact_mult__le__cancel__left__neg) ).
fof(fact_mult__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_power__Suc__0,axiom,
! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_power__Suc__0) ).
fof(fact_nat__power__eq__Suc__0__iff,axiom,
! [V_m_2,V_x_2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
fof(fact_nat__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_nat__power__less__imp__less,axiom,
! [V_n,V_m,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ),
file('theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(fact_nat__zero__less__power__iff,axiom,
! [V_na_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_na_2)))
<=> ( V_na_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_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_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_mult__eq__1__iff,axiom,
! [V_na_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_na_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( V_na_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_one__le__mult__iff,axiom,
! [V_na_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_na_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_na_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_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_na_2,V_m_2,T_b] :
( class_Rings_Olinordered__semidom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ),
file('theBenchmark.p',fact_of__nat__less__iff) ).
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_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__le__cancel2,axiom,
! [V_na_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_na_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_na_2)) ) ),
file('theBenchmark.p',fact_mult__le__cancel2) ).
fof(fact_mult__le__cancel1,axiom,
! [V_na_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_na_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_na_2)) ) ),
file('theBenchmark.p',fact_mult__le__cancel1) ).
fof(fact_mult__less__cancel2,axiom,
! [V_na_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_na_2),V_k_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_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__cancel1,axiom,
! [V_na_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_na_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_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_nat__0__less__mult__iff,axiom,
! [V_na_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_na_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_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_Suc__mult__less__cancel1,axiom,
! [V_na_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_na_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ),
file('theBenchmark.p',fact_Suc__mult__less__cancel1) ).
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__inject__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> V_a = V_b ) ) ) ),
file('theBenchmark.p',fact_power__inject__base) ).
fof(fact_power__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_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_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_nat__mult__le__cancel1,axiom,
! [V_na_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_na_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ),
file('theBenchmark.p',fact_nat__mult__le__cancel1) ).
fof(fact_nat__mult__eq__cancel1,axiom,
! [V_na_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_na_2)
<=> V_m_2 = V_na_2 ) ),
file('theBenchmark.p',fact_nat__mult__eq__cancel1) ).
fof(fact_nat__mult__less__cancel1,axiom,
! [V_na_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_na_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ),
file('theBenchmark.p',fact_nat__mult__less__cancel1) ).
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_equalityI,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> V_A_2 = V_B_2 ) ),
file('theBenchmark.p',fact_equalityI) ).
fof(fact_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_nat__mult__eq__cancel__disj,axiom,
! [V_na_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_na_2)
<=> ( V_m_2 = V_na_2
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
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_zero__less__int__conv,axiom,
! [V_na_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_na_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ),
file('theBenchmark.p',fact_zero__less__int__conv) ).
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_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_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_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_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_int__power,axiom,
! [V_n,V_m] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n),
file('theBenchmark.p',fact_int__power) ).
fof(fact_zpower__int,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m)),V_n) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)),
file('theBenchmark.p',fact_zpower__int) ).
fof(fact_int__int__eq,axiom,
! [V_na_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_na_2)
<=> V_m_2 = V_na_2 ),
file('theBenchmark.p',fact_int__int__eq) ).
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__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__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_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_int__0,axiom,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_int__0) ).
fof(fact_int__eq__0__conv,axiom,
! [V_na_2] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_na_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_int__eq__0__conv) ).
fof(fact_int__le__0__conv,axiom,
! [V_na_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_na_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_int__le__0__conv) ).
fof(fact_zless__int,axiom,
! [V_na_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_na_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ),
file('theBenchmark.p',fact_zless__int) ).
fof(fact_subset__refl,axiom,
! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2)),
file('theBenchmark.p',fact_subset__refl) ).
fof(fact_psubset__eq,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
<=> ( V_A_2 != V_B_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_psubset__eq) ).
fof(fact_set__eq__subset,axiom,
! [T_b,V_B_2,V_A_2] :
( V_A_2 = V_B_2
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_set__eq__subset) ).
fof(fact_subset__iff__psubset__eq,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
<=> ( V_A_2 = V_B_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_subset__iff__psubset__eq) ).
fof(fact_equalityD1,axiom,
! [T_b,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_equalityD1) ).
fof(fact_equalityD2,axiom,
! [T_b,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
file('theBenchmark.p',fact_equalityD2) ).
fof(fact_psubset__imp__subset,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_psubset__imp__subset) ).
fof(fact_psubset__subset__trans,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
file('theBenchmark.p',fact_psubset__subset__trans) ).
fof(fact_subset__psubset__trans,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
file('theBenchmark.p',fact_subset__psubset__trans) ).
fof(fact_subset__trans,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
file('theBenchmark.p',fact_subset__trans) ).
fof(fact_equalityE,axiom,
! [T_b,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ),
file('theBenchmark.p',fact_equalityE) ).
fof(fact_zle__int,axiom,
! [V_na_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_na_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ),
file('theBenchmark.p',fact_zle__int) ).
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_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_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_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_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_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_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_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_transfer__int__nat__quantifiers_I1_J,axiom,
! [V_P_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_P_2,B_x)) )
<=> ! [B_x] : hBOOL(hAPP(V_P_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_P_2] :
( ? [B_x] :
( hBOOL(hAPP(V_P_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_P_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__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_of__int__less__0__iff,axiom,
! [V_z_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('theBenchmark.p',fact_of__int__less__0__iff) ).
fof(fact_of__int__0__less__iff,axiom,
! [V_z_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ),
file('theBenchmark.p',fact_of__int__0__less__iff) ).
fof(fact_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_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_psubset__trans,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ),
file('theBenchmark.p',fact_psubset__trans) ).
fof(fact_zle__linear,axiom,
! [V_w,V_z] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) ),
file('theBenchmark.p',fact_zle__linear) ).
fof(fact_zle__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_zmult__commute,axiom,
! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z),
file('theBenchmark.p',fact_zmult__commute) ).
fof(fact_zmult__assoc,axiom,
! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)),
file('theBenchmark.p',fact_zmult__assoc) ).
fof(fact_of__int__eq__iff,axiom,
! [V_z_2,V_w_2,T_b] :
( class_Int_Oring__char__0(T_b)
=> ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
<=> V_w_2 = V_z_2 ) ),
file('theBenchmark.p',fact_of__int__eq__iff) ).
fof(fact_of__int__le__iff,axiom,
! [V_z_2,V_w_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ),
file('theBenchmark.p',fact_of__int__le__iff) ).
fof(fact_of__int__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__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_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_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_b] :
( class_Int_Oring__char__0(T_b)
=> ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
<=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_of__int__0__eq__iff) ).
fof(fact_of__int__eq__0__iff,axiom,
! [V_z_2,T_b] :
( class_Int_Oring__char__0(T_b)
=> ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_of__int__eq__0__iff) ).
fof(fact_of__int__less__iff,axiom,
! [V_z_2,V_w_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ),
file('theBenchmark.p',fact_of__int__less__iff) ).
fof(fact_of__int__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__0__le__iff,axiom,
! [V_z_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ),
file('theBenchmark.p',fact_of__int__0__le__iff) ).
fof(fact_of__int__le__0__iff,axiom,
! [V_z_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('theBenchmark.p',fact_of__int__le__0__iff) ).
fof(fact_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_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
! [V_n,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_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_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_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_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_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_one__less__power,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ),
file('theBenchmark.p',fact_one__less__power) ).
fof(fact_power__le__imp__le__exp,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ),
file('theBenchmark.p',fact_power__le__imp__le__exp) ).
fof(fact_power__increasing__iff,axiom,
! [V_y_2,V_x_2,V_b_2,T_b] :
( class_Rings_Olinordered__semidom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_power__increasing__iff) ).
fof(fact_power__decreasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ) ),
file('theBenchmark.p',fact_power__decreasing) ).
fof(fact_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__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_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_one__reorient,axiom,
! [V_x_2,T_b] :
( class_Groups_Oone(T_b)
=> ( c_Groups_Oone__class_Oone(T_b) = V_x_2
<=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ),
file('theBenchmark.p',fact_one__reorient) ).
fof(fact_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_int__1,axiom,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint),
file('theBenchmark.p',fact_int__1) ).
fof(fact_transfer__int__nat__numerals_I2_J,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('theBenchmark.p',fact_transfer__int__nat__numerals_I2_J) ).
fof(fact_of__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_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_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_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_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_mult_Ocomm__neutral,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_mult_Ocomm__neutral) ).
fof(fact_mult__1__right,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_mult__1__right) ).
fof(fact_mult__1,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ),
file('theBenchmark.p',fact_mult__1) ).
fof(fact_mult__1__left,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ),
file('theBenchmark.p',fact_mult__1__left) ).
fof(fact_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_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_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_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_nat__mult__1,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n,
file('theBenchmark.p',fact_nat__mult__1) ).
fof(fact_nat__1__eq__mult__iff,axiom,
! [V_na_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_na_2)
<=> ( V_na_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__1__eq__mult__iff) ).
fof(fact_nat__mult__1__right,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
file('theBenchmark.p',fact_nat__mult__1__right) ).
fof(fact_nat__mult__eq__1__iff,axiom,
! [V_na_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_na_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( V_na_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_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_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_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__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_P_2] :
( ! [B_x1] : hBOOL(hAPP(V_P_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_P_2,hAPP(c_Int_Onat,B_x))) ) ),
file('theBenchmark.p',fact_all__nat) ).
fof(fact_ex__nat,axiom,
! [V_P_2] :
( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
<=> ? [B_x] :
( hBOOL(hAPP(V_P_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_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_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_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_na_2,V_m_2,V_a_2,T_b] :
( class_Rings_Olinordered__semidom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_na_2)
<=> V_m_2 = V_na_2 ) ) ),
file('theBenchmark.p',fact_power__inject__exp) ).
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_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_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_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_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_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__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_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_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_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_mult__left__le__one__le,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)),V_x)) ) ) ) ),
file('theBenchmark.p',fact_mult__left__le__one__le) ).
fof(fact_mult__right__le__one__le,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_x)) ) ) ) ),
file('theBenchmark.p',fact_mult__right__le__one__le) ).
fof(fact_power__less__power__Suc,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ),
file('theBenchmark.p',fact_power__less__power__Suc) ).
fof(fact_power__gt1__lemma,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ),
file('theBenchmark.p',fact_power__gt1__lemma) ).
fof(fact_power__0__left,axiom,
! [V_n,T_a] :
( ( class_Rings_Osemiring__0(T_a)
& class_Power_Opower(T_a) )
=> ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ) ),
file('theBenchmark.p',fact_power__0__left) ).
fof(fact_power__gt1,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)))) ) ),
file('theBenchmark.p',fact_power__gt1) ).
fof(fact_power__strict__increasing__iff,axiom,
! [V_y_2,V_x_2,V_b_2,T_b] :
( class_Rings_Olinordered__semidom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_power__strict__increasing__iff) ).
fof(fact_power__less__imp__less__exp,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ),
file('theBenchmark.p',fact_power__less__imp__less__exp) ).
fof(fact_power__strict__increasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ),
file('theBenchmark.p',fact_power__strict__increasing) ).
fof(fact_power__increasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ),
file('theBenchmark.p',fact_power__increasing) ).
fof(fact_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_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_pos__zmult__eq__1__iff,axiom,
! [V_na_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_na_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( V_na_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_power__power__power,axiom,
! [T_b] :
( class_Power_Opower(T_b)
=> c_Power_Opower__class_Opower(T_b) = c_Power_Opower_Opower(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Otimes__class_Otimes(T_b)) ),
file('theBenchmark.p',fact_power__power__power) ).
fof(fact_zero__less__nat__eq,axiom,
! [V_z_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,V_z_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ),
file('theBenchmark.p',fact_zero__less__nat__eq) ).
fof(fact_nat__less__eq__zless,axiom,
! [V_z_2,V_w_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),hAPP(c_Int_Onat,V_z_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ),
file('theBenchmark.p',fact_nat__less__eq__zless) ).
fof(fact_transfer__nat__int__relations_I2_J,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_transfer__nat__int__relations_I2_J) ).
fof(fact_nat__eq__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__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__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_P_2] :
( hBOOL(hAPP(V_P_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_P_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_P_2,B_n)) ) ) ),
file('theBenchmark.p',fact_split__nat) ).
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_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_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_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_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_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_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_sgn__pos,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_sgn__pos) ).
fof(fact_sgn__1__pos,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
file('theBenchmark.p',fact_sgn__1__pos) ).
fof(fact_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_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_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_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_negative__zle,axiom,
! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))),
file('theBenchmark.p',fact_negative__zle) ).
fof(fact_negative__zless,axiom,
! [V_m,V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,V_n)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m))),
file('theBenchmark.p',fact_negative__zless) ).
fof(fact_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_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_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_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_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_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_add__number__of__diff1,axiom,
! [V_c,V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_c)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w))),V_c) ),
file('theBenchmark.p',fact_add__number__of__diff1) ).
fof(fact_add__number__of__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__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_eq__number__of,axiom,
! [V_y_2,V_x_2,T_b] :
( ( class_Int_Oring__char__0(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_eq__number__of) ).
fof(fact_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_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_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__reorient,axiom,
! [V_x_2,V_w_2,T_b] :
( class_Int_Onumber(T_b)
=> ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
<=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ),
file('theBenchmark.p',fact_number__of__reorient) ).
fof(fact_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_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_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__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_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_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_number__of__diff,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
file('theBenchmark.p',fact_number__of__diff) ).
fof(fact_number__of__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_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_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_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_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_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_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_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_right__minus,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_right__minus) ).
fof(fact_eq__neg__iff__add__eq__0,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Ogroup__add(T_b)
=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
fof(fact_left__minus,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_left__minus) ).
fof(fact_ab__left__minus,axiom,
! [V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_ab__left__minus) ).
fof(fact_minus__unique,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ),
file('theBenchmark.p',fact_minus__unique) ).
fof(fact_diff__cancel2,axiom,
! [V_n,V_k,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),
file('theBenchmark.p',fact_diff__cancel2) ).
fof(fact_diff__cancel,axiom,
! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n),
file('theBenchmark.p',fact_diff__cancel) ).
fof(fact_diff__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__diff__left,axiom,
! [V_k,V_j,V_i] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),V_j)),V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_k)),
file('theBenchmark.p',fact_diff__diff__left) ).
fof(fact_diff__add__inverse,axiom,
! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_n) = V_m,
file('theBenchmark.p',fact_diff__add__inverse) ).
fof(fact_diff__add__inverse2,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m,
file('theBenchmark.p',fact_diff__add__inverse2) ).
fof(fact_diff__eq__diff__eq,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Groups_Oab__group__add(T_b)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_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_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_b] :
( class_Groups_Ocancel__semigroup__add(T_b)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_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_b] :
( class_Groups_Ocancel__semigroup__add(T_b)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_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__diff__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = V_a ),
file('theBenchmark.p',fact_add__diff__cancel) ).
fof(fact_diff__add__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_b) = V_a ),
file('theBenchmark.p',fact_diff__add__cancel) ).
fof(fact_minus__add__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_neg__equal__iff__equal,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Ogroup__add(T_b)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
<=> V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_neg__equal__iff__equal) ).
fof(fact_minus__equation__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Ogroup__add(T_b)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
<=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ),
file('theBenchmark.p',fact_minus__equation__iff) ).
fof(fact_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_equation__minus__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Ogroup__add(T_b)
=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
<=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ),
file('theBenchmark.p',fact_equation__minus__iff) ).
fof(fact_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_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__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_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_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__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_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_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_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_eq__add__iff2,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( class_Rings_Oring(T_b)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
<=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ),
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_b] :
( class_Rings_Oring(T_b)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2 ) ),
file('theBenchmark.p',fact_eq__add__iff1) ).
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_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_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_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_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_diff__diff__right,axiom,
! [V_i,V_j,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_k)),V_j) ),
file('theBenchmark.p',fact_diff__diff__right) ).
fof(fact_le__diff__conv,axiom,
! [V_i_2,V_k_2,V_j_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))) ),
file('theBenchmark.p',fact_le__diff__conv) ).
fof(fact_le__add__diff,axiom,
! [V_m,V_n,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_k))) ),
file('theBenchmark.p',fact_le__add__diff) ).
fof(fact_le__add__diff__inverse,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)) = V_m ),
file('theBenchmark.p',fact_le__add__diff__inverse) ).
fof(fact_add__diff__assoc,axiom,
! [V_i,V_j,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_k) ),
file('theBenchmark.p',fact_add__diff__assoc) ).
fof(fact_le__diff__conv2,axiom,
! [V_i_2,V_j_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ),
file('theBenchmark.p',fact_le__diff__conv2) ).
fof(fact_le__add__diff__inverse2,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ),
file('theBenchmark.p',fact_le__add__diff__inverse2) ).
fof(fact_le__imp__diff__is__add,axiom,
! [V_k_2,V_j_2,V_i_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
<=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ),
file('theBenchmark.p',fact_le__imp__diff__is__add) ).
fof(fact_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_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__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_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__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_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_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_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_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_of__int__number__of__eq,axiom,
! [V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ),
file('theBenchmark.p',fact_of__int__number__of__eq) ).
fof(fact_of__int__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_le__add__iff1,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( class_Rings_Oordered__ring(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ),
file('theBenchmark.p',fact_le__add__iff1) ).
fof(fact_le__add__iff2,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( class_Rings_Oordered__ring(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ),
file('theBenchmark.p',fact_le__add__iff2) ).
fof(fact_less__add__iff1,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( class_Rings_Oordered__ring(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ),
file('theBenchmark.p',fact_less__add__iff1) ).
fof(fact_less__add__iff2,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( class_Rings_Oordered__ring(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ),
file('theBenchmark.p',fact_less__add__iff2) ).
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_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_nat__diff__split,axiom,
! [V_b_2,V_a_2,V_P_2] :
( hBOOL(hAPP(V_P_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_P_2,B_d)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
=> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('theBenchmark.p',fact_nat__diff__split) ).
fof(fact_nat__diff__split__asm,axiom,
! [V_b_2,V_a_2,V_P_2] :
( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
<=> ~ ( ? [B_d] :
( ~ hBOOL(hAPP(V_P_2,B_d))
& V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
| ( ~ hBOOL(hAPP(V_P_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_diff__Suc__diff__eq2,axiom,
! [V_m,V_j,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))),V_m) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_j)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k),V_m)) ),
file('theBenchmark.p',fact_diff__Suc__diff__eq2) ).
fof(fact_diff__Suc__diff__eq1,axiom,
! [V_m,V_j,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_k)),hAPP(c_Nat_OSuc,V_j)) ),
file('theBenchmark.p',fact_diff__Suc__diff__eq1) ).
fof(fact_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_nat__le__add__iff1,axiom,
! [V_na_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_na_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_na_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_na_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_na_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_na_2 ) ),
file('theBenchmark.p',fact_nat__eq__add__iff1) ).
fof(fact_nat__le__add__iff2,axiom,
! [V_na_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_na_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_na_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_na_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_na_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_na_2) ) ),
file('theBenchmark.p',fact_nat__eq__add__iff2) ).
fof(fact_diff__eq__diff__less__eq,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__less__eq) ).
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_b] :
( class_Groups_Oab__group__add(T_b)
=> ( V_a_2 = V_b_2
<=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_eq__iff__diff__eq__0) ).
fof(fact_right__minus__eq,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Ogroup__add(T_b)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_right__minus__eq) ).
fof(fact_diff__eq__diff__less,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__less) ).
fof(fact_le__minus__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ),
file('theBenchmark.p',fact_le__minus__iff) ).
fof(fact_minus__le__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ),
file('theBenchmark.p',fact_minus__le__iff) ).
fof(fact_neg__le__iff__le,axiom,
! [V_a_2,V_b_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_neg__le__iff__le) ).
fof(fact_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_minus__zero,axiom,
! [T_a] :
( class_Groups_Ogroup__add(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_minus__zero) ).
fof(fact_neg__0__equal__iff__equal,axiom,
! [V_a_2,T_b] :
( class_Groups_Ogroup__add(T_b)
=> ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
<=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ),
file('theBenchmark.p',fact_neg__0__equal__iff__equal) ).
fof(fact_equal__neg__zero,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_equal__neg__zero) ).
fof(fact_neg__equal__0__iff__equal,axiom,
! [V_a_2,T_b] :
( class_Groups_Ogroup__add(T_b)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_neg__equal__0__iff__equal) ).
fof(fact_neg__equal__zero,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_neg__equal__zero) ).
fof(fact_less__minus__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ),
file('theBenchmark.p',fact_less__minus__iff) ).
fof(fact_minus__less__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ),
file('theBenchmark.p',fact_minus__less__iff) ).
fof(fact_neg__less__iff__less,axiom,
! [V_a_2,V_b_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_neg__less__iff__less) ).
fof(fact_minus__mult__right,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ),
file('theBenchmark.p',fact_minus__mult__right) ).
fof(fact_minus__mult__left,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ),
file('theBenchmark.p',fact_minus__mult__left) ).
fof(fact_minus__mult__commute,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ),
file('theBenchmark.p',fact_minus__mult__commute) ).
fof(fact_minus__mult__minus,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ),
file('theBenchmark.p',fact_minus__mult__minus) ).
fof(fact_square__eq__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Oidom(T_b)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2)
<=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
| V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_square__eq__iff) ).
fof(fact_add__le__cancel__right,axiom,
! [V_b_2,V_c_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__le__cancel__left,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_add__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__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__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__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__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__0__left,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ),
file('theBenchmark.p',fact_add__0__left) ).
fof(fact_add__0,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ),
file('theBenchmark.p',fact_add__0) ).
fof(fact_double__zero__sym,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_double__zero__sym) ).
fof(fact_add__0__right,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_add__0__right) ).
fof(fact_add_Ocomm__neutral,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_add__0__iff,axiom,
! [V_a_2,V_b_2,T_b] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
=> ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_add__0__iff) ).
fof(fact_double__eq__0__iff,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_add__less__cancel__right,axiom,
! [V_b_2,V_c_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__cancel__left,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_add__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_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_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_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_b] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
=> ( ( V_c_2 != V_d_2
& V_a_2 != V_b_2 )
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)) ) ),
file('theBenchmark.p',fact_crossproduct__noteq) ).
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_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_crossproduct__eq,axiom,
! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2))
<=> ( V_y_2 = V_z_2
| V_w_2 = V_x_2 ) ) ),
file('theBenchmark.p',fact_crossproduct__eq) ).
fof(fact_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_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_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__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_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_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_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_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_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_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_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_diff__le__mono2,axiom,
! [V_l,V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ),
file('theBenchmark.p',fact_diff__le__mono2) ).
fof(fact_diff__le__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__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_eq__diff__iff,axiom,
! [V_na_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_na_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_na_2),V_k_2)
<=> V_m_2 = V_na_2 ) ) ),
file('theBenchmark.p',fact_eq__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_le__diff__iff,axiom,
! [V_na_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_na_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_na_2),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ),
file('theBenchmark.p',fact_le__diff__iff) ).
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_zadd__0,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z,
file('theBenchmark.p',fact_zadd__0) ).
fof(fact_zadd__0__right,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z,
file('theBenchmark.p',fact_zadd__0__right) ).
fof(fact_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_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_na_2,V_m_2] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( V_na_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__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_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__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_add__Suc__shift,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)),
file('theBenchmark.p',fact_add__Suc__shift) ).
fof(fact_add__Suc,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),
file('theBenchmark.p',fact_add__Suc) ).
fof(fact_add__Suc__right,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),
file('theBenchmark.p',fact_add__Suc__right) ).
fof(fact_Suc__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_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_termination__basic__simps_I1_J,axiom,
! [V_z,V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ),
file('theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [V_y,V_z,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ),
file('theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_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_na_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_na_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_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_zadd__left__mono,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_i)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_j))) ),
file('theBenchmark.p',fact_zadd__left__mono) ).
fof(fact_zadd__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_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_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_le__iff__add,axiom,
! [V_na_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
<=> ? [B_k] : V_na_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__add__left__cancel__le,axiom,
! [V_na_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_na_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ),
file('theBenchmark.p',fact_nat__add__left__cancel__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_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_termination__basic__simps_I4_J,axiom,
! [V_y,V_z,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ),
file('theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [V_z,V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ),
file('theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_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_add__mult__distrib,axiom,
! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
file('theBenchmark.p',fact_add__mult__distrib) ).
fof(fact_add__mult__distrib2,axiom,
! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
file('theBenchmark.p',fact_add__mult__distrib2) ).
fof(fact_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_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_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_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_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_nat__less__add__iff1,axiom,
! [V_na_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_na_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_na_2)) ) ),
file('theBenchmark.p',fact_nat__less__add__iff1) ).
fof(fact_nat__less__add__iff2,axiom,
! [V_na_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_na_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_na_2))) ) ),
file('theBenchmark.p',fact_nat__less__add__iff2) ).
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__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_sgn__if,axiom,
! [V_x,T_a] :
( class_Groups_Osgn__if(T_a)
=> ( ( V_x != c_Groups_Ozero__class_Ozero(T_a)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) ) )
& ( V_x = c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sgn__if) ).
fof(fact_sgn__1__neg,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_sgn__1__neg) ).
fof(fact_sgn__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_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__0__0,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_sgn__0__0) ).
fof(fact_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_le__iff__diff__le__0,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_le__iff__diff__le__0) ).
fof(fact_less__iff__diff__less__0,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_less__iff__diff__less__0) ).
fof(fact_neg__0__le__iff__le,axiom,
! [V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_neg__0__le__iff__le) ).
fof(fact_le__minus__self__iff,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_le__minus__self__iff) ).
fof(fact_neg__le__0__iff__le,axiom,
! [V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
file('theBenchmark.p',fact_neg__le__0__iff__le) ).
fof(fact_minus__le__self__iff,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
file('theBenchmark.p',fact_minus__le__self__iff) ).
fof(fact_neg__0__less__iff__less,axiom,
! [V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_neg__0__less__iff__less) ).
fof(fact_less__minus__self__iff,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_less__minus__self__iff) ).
fof(fact_neg__less__0__iff__less,axiom,
! [V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
file('theBenchmark.p',fact_neg__less__0__iff__less) ).
fof(fact_neg__less__nonneg,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
file('theBenchmark.p',fact_neg__less__nonneg) ).
fof(fact_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_le__number__of__eq__not__less,axiom,
! [V_w_2,V_v_2,T_b] :
( ( class_Orderings_Olinorder(T_b)
& class_Int_Onumber(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2))) ) ),
file('theBenchmark.p',fact_le__number__of__eq__not__less) ).
fof(fact_square__eq__1__iff,axiom,
! [V_x_2,T_b] :
( class_Rings_Oring__1__no__zero__divisors(T_b)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
<=> ( V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
| V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ),
file('theBenchmark.p',fact_square__eq__1__iff) ).
fof(fact_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_zero__le__double__add__iff__zero__le__single__add,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
file('theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_add__nonneg__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))) ) ) ),
file('theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Groups_Oordered__comm__monoid__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ),
file('theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_add__increasing,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
file('theBenchmark.p',fact_add__increasing) ).
fof(fact_add__increasing2,axiom,
! [V_a,V_b,V_c,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
file('theBenchmark.p',fact_add__increasing2) ).
fof(fact_add__nonpos__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_le__number__of,axiom,
! [V_y_2,V_x_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_le__number__of) ).
fof(fact_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_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_zero__less__double__add__iff__zero__less__single__add,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
file('theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [V_a_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_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_pos__add__strict,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c))) ) ) ),
file('theBenchmark.p',fact_pos__add__strict) ).
fof(fact_add__neg__neg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_add__neg__neg) ).
fof(fact_even__less__0__iff,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_less__number__of,axiom,
! [V_y_2,V_x_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_less__number__of) ).
fof(fact_sum__squares__eq__zero__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_b)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
fof(fact_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_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_number__of__mult,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
file('theBenchmark.p',fact_number__of__mult) ).
fof(fact_arith__simps_I32_J,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ),
file('theBenchmark.p',fact_arith__simps_I32_J) ).
fof(fact_mult__number__of__left,axiom,
! [V_z,V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z) ),
file('theBenchmark.p',fact_mult__number__of__left) ).
fof(fact_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__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_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_diff__less,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_m)) ) ),
file('theBenchmark.p',fact_diff__less) ).
fof(fact_zero__less__diff,axiom,
! [V_m_2,V_na_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_na_2),V_m_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ),
file('theBenchmark.p',fact_zero__less__diff) ).
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_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_na_2,V_m_2] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_na_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_na_2)) ),
file('theBenchmark.p',fact_diff__is__0__eq) ).
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_less__diff__iff,axiom,
! [V_na_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_na_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_na_2),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ) ),
file('theBenchmark.p',fact_less__diff__iff) ).
fof(fact_diff__less__mono,axiom,
! [V_c,V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a),V_c)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_b),V_c))) ) ),
file('theBenchmark.p',fact_diff__less__mono) ).
fof(fact_negative__eq__positive,axiom,
! [V_m_2,V_na_2] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_na_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_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_negative__eq__positive) ).
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_one__is__add,axiom,
! [V_na_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_na_2)
<=> ( ( V_na_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_na_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_na_2,V_m_2] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( V_na_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_na_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_na_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_na_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_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__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_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_na_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
<=> ? [B_k] : V_na_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_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_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_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_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_zle__add1__eq__le,axiom,
! [V_z_2,V_w_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ),
file('theBenchmark.p',fact_zle__add1__eq__le) ).
fof(fact_add1__zle__eq,axiom,
! [V_z_2,V_w_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ),
file('theBenchmark.p',fact_add1__zle__eq) ).
fof(fact_zless__imp__add1__zle,axiom,
! [V_z,V_w] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_w),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_z)) ),
file('theBenchmark.p',fact_zless__imp__add1__zle) ).
fof(fact_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_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_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_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_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_of__int__of__nat,axiom,
! [V_k,T_a] :
( class_Rings_Oring__1(T_a)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_k)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)))) ) ) ),
file('theBenchmark.p',fact_of__int__of__nat) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__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_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_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__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__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__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__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_sum__squares__le__zero__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_b)))
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_sum__squares__le__zero__iff) ).
fof(fact_sum__squares__ge__zero,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))) ),
file('theBenchmark.p',fact_sum__squares__ge__zero) ).
fof(fact_sum__squares__gt__zero__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Rings_Olinordered__ring__strict(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))))
<=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
fof(fact_not__sum__squares__lt__zero,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))),c_Groups_Ozero__class_Ozero(T_a))) ),
file('theBenchmark.p',fact_not__sum__squares__lt__zero) ).
fof(fact_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_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_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_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_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_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_int__zle__neg,axiom,
! [V_m_2,V_na_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_na_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_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_int__zle__neg) ).
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_sgn__greater,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ),
file('theBenchmark.p',fact_sgn__greater) ).
fof(fact_sgn__less,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ),
file('theBenchmark.p',fact_sgn__less) ).
fof(fact_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_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__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_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_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_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_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_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_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_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_compl__le__compl__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Lattices_Oboolean__algebra(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_compl__le__compl__iff) ).
fof(fact_nat__add__right__cancel,axiom,
! [V_na_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_na_2),V_k_2)
<=> V_m_2 = V_na_2 ),
file('theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [V_na_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_na_2)
<=> V_m_2 = V_na_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_Compl__subset__Compl__iff,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
file('theBenchmark.p',fact_Compl__subset__Compl__iff) ).
fof(fact_Compl__anti__mono,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ),
file('theBenchmark.p',fact_Compl__anti__mono) ).
fof(fact_Diff__subset,axiom,
! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
file('theBenchmark.p',fact_Diff__subset) ).
fof(fact_Diff__mono,axiom,
! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ),
file('theBenchmark.p',fact_Diff__mono) ).
fof(fact_double__diff,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ),
file('theBenchmark.p',fact_double__diff) ).
fof(fact_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_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_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_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_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_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_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_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_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_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_minus__apply,axiom,
! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
( class_Groups_Ominus(T_b)
=> hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ),
file('theBenchmark.p',fact_minus__apply) ).
fof(fact_compl__eq__compl__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Lattices_Oboolean__algebra(T_b)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_compl__eq__compl__iff) ).
fof(fact_uminus__apply,axiom,
! [V_x_2,V_A_2,T_c,T_b] :
( class_Groups_Ouminus(T_b)
=> hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ),
file('theBenchmark.p',fact_uminus__apply) ).
fof(fact_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_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_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_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_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_zdiff__int__split,axiom,
! [V_y_2,V_x_2,V_P_2] :
( hBOOL(hAPP(V_P_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_P_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_P_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_power__nat__number__of__number__of,axiom,
! [V_w,V_v] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w)) ) ),
file('theBenchmark.p',fact_power__nat__number__of__number__of) ).
fof(fact_power__nat__number__of,axiom,
! [V_n,V_v] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),V_n)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) ) ),
file('theBenchmark.p',fact_power__nat__number__of) ).
fof(fact_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_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_ex__least__nat__less,axiom,
! [V_na_2,V_P_2] :
( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(V_P_2,V_na_2))
=> ? [B_k] :
( hBOOL(hAPP(V_P_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_P_2,B_i)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_na_2)) ) ) ),
file('theBenchmark.p',fact_ex__least__nat__less) ).
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_eq__number__of__eq,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
<=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ),
file('theBenchmark.p',fact_eq__number__of__eq) ).
fof(fact_Diff__idemp,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
file('theBenchmark.p',fact_Diff__idemp) ).
fof(fact_Compl__eq__Compl__iff,axiom,
! [V_B_2,V_A_2,T_b] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)
<=> V_A_2 = V_B_2 ),
file('theBenchmark.p',fact_Compl__eq__Compl__iff) ).
fof(fact_double__complement,axiom,
! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = V_A_2,
file('theBenchmark.p',fact_double__complement) ).
fof(fact_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__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_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_div__0,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_div__0) ).
fof(fact_div__by__0,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_div__by__0) ).
fof(fact_div__by__1,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_div__by__1) ).
fof(fact_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__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_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_b] :
( class_Rings_Osemiring__1(T_b)
=> ( c_Int_Oiszero(T_b,V_z_2)
<=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_iszero__def) ).
fof(fact_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_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_pos__imp__zdiv__neg__iff,axiom,
! [V_a_2,V_b_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('theBenchmark.p',fact_pos__imp__zdiv__neg__iff) ).
fof(fact_neg__imp__zdiv__neg__iff,axiom,
! [V_a_2,V_b_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ),
file('theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).
fof(fact_div__neg__pos__less0,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('theBenchmark.p',fact_div__neg__pos__less0) ).
fof(fact_zdiv__self,axiom,
! [V_a] :
( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('theBenchmark.p',fact_zdiv__self) ).
fof(fact_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__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__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__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__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__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_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_zdiv__eq__0__iff,axiom,
! [V_k_2,V_i_2] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) )
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_zdiv__eq__0__iff) ).
fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
! [V_a_2,V_b_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ),
file('theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).
fof(fact_pos__imp__zdiv__pos__iff,axiom,
! [V_i_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ),
file('theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).
fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
! [V_b_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) ) ) ),
file('theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).
fof(fact_zdiv__mono2,axiom,
! [V_b,V_b_H,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H))) ) ) ),
file('theBenchmark.p',fact_zdiv__mono2) ).
fof(fact_div__nonneg__neg__le0,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('theBenchmark.p',fact_div__nonneg__neg__le0) ).
fof(fact_div__pos__pos__trivial,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_div__pos__pos__trivial) ).
fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
! [V_a_2,V_b_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_2),V_b_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).
fof(fact_div__nonpos__pos__le0,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('theBenchmark.p',fact_div__nonpos__pos__le0) ).
fof(fact_zdiv__mono2__neg,axiom,
! [V_b,V_b_H,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b_H)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ) ),
file('theBenchmark.p',fact_zdiv__mono2__neg) ).
fof(fact_div__neg__neg__trivial,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_div__neg__neg__trivial) ).
fof(fact_zdiv__mono1,axiom,
! [V_b,V_a_H,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b))) ) ),
file('theBenchmark.p',fact_zdiv__mono1) ).
fof(fact_zdiv__mono1__neg,axiom,
! [V_b,V_a_H,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_H),V_b)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))) ) ),
file('theBenchmark.p',fact_zdiv__mono1__neg) ).
fof(fact_int__div__less__self,axiom,
! [V_k,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_k)),V_x)) ) ),
file('theBenchmark.p',fact_int__div__less__self) ).
fof(fact_zdiv__zmult2__eq,axiom,
! [V_b,V_a,V_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),V_c) ),
file('theBenchmark.p',fact_zdiv__zmult2__eq) ).
fof(fact_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__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__add__self1,axiom,
! [V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ),
file('theBenchmark.p',fact_div__add__self1) ).
fof(fact_div__add__self2,axiom,
! [V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),c_Groups_Oone__class_Oone(T_a)) ) ),
file('theBenchmark.p',fact_div__add__self2) ).
fof(fact_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_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_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_split__zdiv,axiom,
! [V_k_2,V_na_2,V_P_2] :
( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_na_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_na_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_P_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_na_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_P_2,B_i)) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(V_P_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_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_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_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_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_decr__mult__lemma,axiom,
! [V_k_2,V_P_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_P_2,B_x))
=> hBOOL(hAPP(V_P_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_P_2,B_x))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ),
file('theBenchmark.p',fact_decr__mult__lemma) ).
fof(fact_incr__mult__lemma,axiom,
! [V_k_2,V_P_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_P_2,B_x))
=> hBOOL(hAPP(V_P_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_P_2,B_x))
=> hBOOL(hAPP(V_P_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_div__pos__neg__trivial,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ),
file('theBenchmark.p',fact_div__pos__neg__trivial) ).
fof(fact_split__neg__lemma,axiom,
! [V_na_2,V_P_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_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_na_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_na_2,V_k_2)))
<=> ! [B_i,B_j] :
( ( V_na_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_P_2,B_i),B_j)) ) ) ),
file('theBenchmark.p',fact_split__neg__lemma) ).
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_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_zmod__minus1__right,axiom,
! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_zmod__minus1__right) ).
fof(fact_mod__0,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mod__0) ).
fof(fact_mod__by__0,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_mod__by__0) ).
fof(fact_mod__self,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mod__self) ).
fof(fact_mod__add__self2,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ),
file('theBenchmark.p',fact_mod__add__self2) ).
fof(fact_mod__add__self1,axiom,
! [V_a,V_b,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ),
file('theBenchmark.p',fact_mod__add__self1) ).
fof(fact_mod__add__right__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ),
file('theBenchmark.p',fact_mod__add__right__eq) ).
fof(fact_mod__add__left__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ),
file('theBenchmark.p',fact_mod__add__left__eq) ).
fof(fact_mod__add__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ),
file('theBenchmark.p',fact_mod__add__eq) ).
fof(fact_zmod__simps_I2_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ),
file('theBenchmark.p',fact_zmod__simps_I2_J) ).
fof(fact_zmod__simps_I1_J,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) ),
file('theBenchmark.p',fact_zmod__simps_I1_J) ).
fof(fact_mod__add__cong,axiom,
! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
=> ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c) ) ) ),
file('theBenchmark.p',fact_mod__add__cong) ).
fof(fact_mod__mult__right__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ),
file('theBenchmark.p',fact_mod__mult__right__eq) ).
fof(fact_mod__mult__left__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ),
file('theBenchmark.p',fact_mod__mult__left__eq) ).
fof(fact_mod__mult__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ),
file('theBenchmark.p',fact_mod__mult__eq) ).
fof(fact_mod__mult__mult1,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ),
file('theBenchmark.p',fact_mod__mult__mult1) ).
fof(fact_mod__mult__mult2,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_c) ),
file('theBenchmark.p',fact_mod__mult__mult2) ).
fof(fact_zmod__simps_I4_J,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ),
file('theBenchmark.p',fact_zmod__simps_I4_J) ).
fof(fact_mod__mult__cong,axiom,
! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
=> ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b_H),V_c) ) ) ),
file('theBenchmark.p',fact_mod__mult__cong) ).
fof(fact_mod__diff__cong,axiom,
! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
( class_Divides_Oring__div(T_a)
=> ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
=> ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_H),V_b_H),V_c) ) ) ),
file('theBenchmark.p',fact_mod__diff__cong) ).
fof(fact_mod__diff__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Oring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ),
file('theBenchmark.p',fact_mod__diff__eq) ).
fof(fact_mod__diff__left__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Oring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_c)),V_b),V_c) ),
file('theBenchmark.p',fact_mod__diff__left__eq) ).
fof(fact_mod__diff__right__eq,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Oring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c) ),
file('theBenchmark.p',fact_mod__diff__right__eq) ).
fof(fact_mod__minus__cong,axiom,
! [V_a_H,V_b,V_a,T_a] :
( class_Divides_Oring__div(T_a)
=> ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_H),V_b) ) ),
file('theBenchmark.p',fact_mod__minus__cong) ).
fof(fact_mod__minus__eq,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Oring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a),V_b) = c_Divides_Odiv__class_Omod(T_a,hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) ),
file('theBenchmark.p',fact_mod__minus__eq) ).
fof(fact_div__le__dividend,axiom,
! [V_n,V_m] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)),
file('theBenchmark.p',fact_div__le__dividend) ).
fof(fact_div__le__mono,axiom,
! [V_k,V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_k)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),V_k))) ),
file('theBenchmark.p',fact_div__le__mono) ).
fof(fact_div__mult2__eq,axiom,
! [V_c,V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_a),V_b)),V_c),
file('theBenchmark.p',fact_div__mult2__eq) ).
fof(fact_zmod__self,axiom,
! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_zmod__self) ).
fof(fact_zmod__zero,axiom,
! [V_b] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_zmod__zero) ).
fof(fact_rel__simps_I24_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
file('theBenchmark.p',fact_rel__simps_I24_J) ).
fof(fact_rel__simps_I7_J,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
file('theBenchmark.p',fact_rel__simps_I7_J) ).
fof(fact_zmod__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_zdiff__zmod__right,axiom,
! [V_m,V_y,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y,V_m)),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m),
file('theBenchmark.p',fact_zdiff__zmod__right) ).
fof(fact_zdiff__zmod__left,axiom,
! [V_y,V_m,V_x] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_m)),V_y),V_m) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y),V_m),
file('theBenchmark.p',fact_zdiff__zmod__left) ).
fof(fact_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_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_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__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,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ),
file('theBenchmark.p',fact_mod__mult__self2) ).
fof(fact_mod__mult__self1,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Divides_Odiv__class_Omod(T_a,V_a,V_b) ),
file('theBenchmark.p',fact_mod__mult__self1) ).
fof(fact_mod__by__1,axiom,
! [V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mod__by__1) ).
fof(fact_mod__div__trivial,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_mod__div__trivial) ).
fof(fact_div__1,axiom,
! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = V_m,
file('theBenchmark.p',fact_div__1) ).
fof(fact_div__less,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_div__less) ).
fof(fact_nat__mult__div__cancel__disj,axiom,
! [V_n,V_m,V_k] :
( ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) )
& ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__mult__div__cancel__disj) ).
fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y))) ) ),
file('theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_zmod__le__nonneg__dividend,axiom,
! [V_k,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_k)),V_m)) ),
file('theBenchmark.p',fact_zmod__le__nonneg__dividend) ).
fof(fact_neg__mod__bound,axiom,
! [V_a,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ),
file('theBenchmark.p',fact_neg__mod__bound) ).
fof(fact_pos__mod__bound,axiom,
! [V_a,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b)) ),
file('theBenchmark.p',fact_pos__mod__bound) ).
fof(fact_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_zmod__eq__0__iff,axiom,
! [V_d_2,V_m_2] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ),
file('theBenchmark.p',fact_zmod__eq__0__iff) ).
fof(fact_bin__less__0__simps_I2_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('theBenchmark.p',fact_bin__less__0__simps_I2_J) ).
fof(fact_zmod__zminus2__not__zero,axiom,
! [V_l,V_k] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('theBenchmark.p',fact_zmod__zminus2__not__zero) ).
fof(fact_zmod__zminus1__not__zero,axiom,
! [V_l,V_k] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k),V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('theBenchmark.p',fact_zmod__zminus1__not__zero) ).
fof(fact_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_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_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_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_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_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_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_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__less__dividend,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),V_m)) ) ),
file('theBenchmark.p',fact_div__less__dividend) ).
fof(fact_mult__minus1__right,axiom,
! [V_z,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ),
file('theBenchmark.p',fact_mult__minus1__right) ).
fof(fact_mult__minus1,axiom,
! [V_z,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_z) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_z) ),
file('theBenchmark.p',fact_mult__minus1) ).
fof(fact_mod__neg__neg__trivial,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ),
file('theBenchmark.p',fact_mod__neg__neg__trivial) ).
fof(fact_neg__mod__conj,axiom,
! [V_a,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
file('theBenchmark.p',fact_neg__mod__conj) ).
fof(fact_neg__mod__sign,axiom,
! [V_a,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('theBenchmark.p',fact_neg__mod__sign) ).
fof(fact_mod__pos__pos__trivial,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ),
file('theBenchmark.p',fact_mod__pos__pos__trivial) ).
fof(fact_pos__mod__conj,axiom,
! [V_a,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)),V_b))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ) ),
file('theBenchmark.p',fact_pos__mod__conj) ).
fof(fact_pos__mod__sign,axiom,
! [V_a,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b))) ),
file('theBenchmark.p',fact_pos__mod__sign) ).
fof(fact_number__of__Min,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ),
file('theBenchmark.p',fact_number__of__Min) ).
fof(fact_arith__simps_I31_J,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ),
file('theBenchmark.p',fact_arith__simps_I31_J) ).
fof(fact_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__eq__1__iff,axiom,
! [V_na_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_na_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( ( V_na_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_na_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_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_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_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_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_na_2,V_P_2] :
( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_na_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_na_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_P_2,B_i)) ) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('theBenchmark.p',fact_split__div) ).
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_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_div__eq__minus1,axiom,
! [V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),V_b) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ),
file('theBenchmark.p',fact_div__eq__minus1) ).
fof(fact_le__div__geq,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n)) ) ),
file('theBenchmark.p',fact_le__div__geq) ).
fof(fact_split__div__lemma,axiom,
! [V_m_2,V_q_2,V_na_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_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_na_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_na_2),V_q_2)),V_m_2)) )
<=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_na_2) ) ),
file('theBenchmark.p',fact_split__div__lemma) ).
fof(fact_split__div_H,axiom,
! [V_na_2,V_m_2,V_P_2] :
( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_na_2)))
<=> ( ? [B_q] :
( hBOOL(hAPP(V_P_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_na_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_na_2),B_q)),V_m_2)) )
| ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('theBenchmark.p',fact_split__div_H) ).
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_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_na_2,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_na_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_na_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_P_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_na_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_P_2,B_j)) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(V_P_2,V_na_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__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_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_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_split__pos__lemma,axiom,
! [V_na_2,V_P_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_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_na_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_na_2,V_k_2)))
<=> ! [B_i,B_j] :
( ( V_na_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_P_2,B_i),B_j)) ) ) ),
file('theBenchmark.p',fact_split__pos__lemma) ).
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_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_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_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_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_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_eq__special_I1_J,axiom,
! [V_y_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
<=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ),
file('theBenchmark.p',fact_eq__special_I1_J) ).
fof(fact_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__ge__self,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ),
file('theBenchmark.p',fact_abs__ge__self) ).
fof(fact_abs__le__D1,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ),
file('theBenchmark.p',fact_abs__le__D1) ).
fof(fact_abs__zero,axiom,
! [T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_abs__zero) ).
fof(fact_abs__eq__0,axiom,
! [V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add__abs(T_b)
=> ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_abs__eq__0) ).
fof(fact_abs__add__abs,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ),
file('theBenchmark.p',fact_abs__add__abs) ).
fof(fact_abs__mult,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__minus__commute,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b),V_a)) ),
file('theBenchmark.p',fact_abs__minus__commute) ).
fof(fact_abs__one,axiom,
! [T_a] :
( class_Rings_Olinordered__idom(T_a)
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_abs__one) ).
fof(fact_abs__minus__cancel,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) ),
file('theBenchmark.p',fact_abs__minus__cancel) ).
fof(fact_power__abs,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n) ),
file('theBenchmark.p',fact_power__abs) ).
fof(fact_abs__of__nat,axiom,
! [V_n,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),V_n) ),
file('theBenchmark.p',fact_abs__of__nat) ).
fof(fact_mod__Suc__eq__Suc__mod,axiom,
! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n),
file('theBenchmark.p',fact_mod__Suc__eq__Suc__mod) ).
fof(fact_mod__less,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ),
file('theBenchmark.p',fact_mod__less) ).
fof(fact_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_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_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__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_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_Pls__def) ).
fof(fact_rel__simps_I19_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
file('theBenchmark.p',fact_rel__simps_I19_J) ).
fof(fact_rel__simps_I2_J,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
file('theBenchmark.p',fact_rel__simps_I2_J) ).
fof(fact_add__Pls__right,axiom,
! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k,
file('theBenchmark.p',fact_add__Pls__right) ).
fof(fact_add__Pls,axiom,
! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k,
file('theBenchmark.p',fact_add__Pls) ).
fof(fact_mult__Pls,axiom,
! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls,
file('theBenchmark.p',fact_mult__Pls) ).
fof(fact_diff__bin__simps_I1_J,axiom,
! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k,
file('theBenchmark.p',fact_diff__bin__simps_I1_J) ).
fof(fact_minus__Pls,axiom,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
file('theBenchmark.p',fact_minus__Pls) ).
fof(fact_rel__simps_I37_J,axiom,
c_Int_OPls != c_Int_OMin,
file('theBenchmark.p',fact_rel__simps_I37_J) ).
fof(fact_rel__simps_I40_J,axiom,
c_Int_OMin != c_Int_OPls,
file('theBenchmark.p',fact_rel__simps_I40_J) ).
fof(fact_abs__ge__zero,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ),
file('theBenchmark.p',fact_abs__ge__zero) ).
fof(fact_abs__le__zero__iff,axiom,
! [V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add__abs(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_abs__le__zero__iff) ).
fof(fact_abs__of__nonneg,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ),
file('theBenchmark.p',fact_abs__of__nonneg) ).
fof(fact_abs__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_zero__less__abs__iff,axiom,
! [V_a_2,T_b] :
( class_Groups_Oordered__ab__group__add__abs(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)))
<=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_zero__less__abs__iff) ).
fof(fact_abs__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_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_b] :
( class_Groups_Oordered__ab__group__add__abs(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_abs__le__iff) ).
fof(fact_abs__ge__minus__self,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ),
file('theBenchmark.p',fact_abs__ge__minus__self) ).
fof(fact_abs__less__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_abs__less__iff) ).
fof(fact_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_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__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__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_abs__zmult__eq__1,axiom,
! [V_n,V_m] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('theBenchmark.p',fact_abs__zmult__eq__1) ).
fof(fact_number__of__Pls,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_number__of__Pls) ).
fof(fact_semiring__norm_I112_J,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ),
file('theBenchmark.p',fact_semiring__norm_I112_J) ).
fof(fact_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_add__numeral__0,axiom,
! [V_a,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)),V_a) = V_a ),
file('theBenchmark.p',fact_add__numeral__0) ).
fof(fact_add__numeral__0__right,axiom,
! [V_a,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = V_a ),
file('theBenchmark.p',fact_add__numeral__0__right) ).
fof(fact_abs__sgn,axiom,
! [V_k,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ),
file('theBenchmark.p',fact_abs__sgn) ).
fof(fact_mult__sgn__abs,axiom,
! [V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)) = V_x ),
file('theBenchmark.p',fact_mult__sgn__abs) ).
fof(fact_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_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_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_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_zero__is__num__zero,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
file('theBenchmark.p',fact_zero__is__num__zero) ).
fof(fact_rel__simps_I23_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('theBenchmark.p',fact_rel__simps_I23_J) ).
fof(fact_rel__simps_I20_J,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
file('theBenchmark.p',fact_rel__simps_I20_J) ).
fof(fact_rel__simps_I3_J,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
file('theBenchmark.p',fact_rel__simps_I3_J) ).
fof(fact_rel__simps_I6_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('theBenchmark.p',fact_rel__simps_I6_J) ).
fof(fact_eq__number__of__Pls__Min,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
file('theBenchmark.p',fact_eq__number__of__Pls__Min) ).
fof(fact_not__neg__number__of__Pls,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
file('theBenchmark.p',fact_not__neg__number__of__Pls) ).
fof(fact_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_succ__Min,axiom,
c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
file('theBenchmark.p',fact_succ__Min) ).
fof(fact_abs__mult__pos,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_y)),V_x) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ),
file('theBenchmark.p',fact_abs__mult__pos) ).
fof(fact_abs__eq__mult,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__ring__abs(T_a)
=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) )
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)) ) ),
file('theBenchmark.p',fact_abs__eq__mult) ).
fof(fact_abs__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__minus__le__zero,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))),c_Groups_Ozero__class_Ozero(T_a))) ),
file('theBenchmark.p',fact_abs__minus__le__zero) ).
fof(fact_abs__of__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__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__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_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_zabs__less__one__iff,axiom,
! [V_z_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('theBenchmark.p',fact_zabs__less__one__iff) ).
fof(fact_zabs__def,axiom,
! [V_i] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) ),
file('theBenchmark.p',fact_zabs__def) ).
fof(fact_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_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_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_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_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_eq__number__of__0,axiom,
! [V_v_2] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ),
file('theBenchmark.p',fact_eq__number__of__0) ).
fof(fact_eq__0__number__of,axiom,
! [V_v_2] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ),
file('theBenchmark.p',fact_eq__0__number__of) ).
fof(fact_number__of2,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
file('theBenchmark.p',fact_number__of2) ).
fof(fact_less__nat__number__of,axiom,
! [V_v_H_2,V_v_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) ) ),
file('theBenchmark.p',fact_less__nat__number__of) ).
fof(fact_le__nat__number__of,axiom,
! [V_v_H_2,V_v_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H_2)))
<=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ),
file('theBenchmark.p',fact_le__nat__number__of) ).
fof(fact_abs__number__of,axiom,
! [V_x,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a)))
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)),c_Groups_Ozero__class_Ozero(T_a)))
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x)) ) ) ),
file('theBenchmark.p',fact_abs__number__of) ).
fof(fact_abs__power__minus__one,axiom,
! [V_n,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),V_n)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_abs__power__minus__one) ).
fof(fact_split__mod,axiom,
! [V_k_2,V_na_2,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_na_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_na_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_P_2,B_j)) ) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hBOOL(hAPP(V_P_2,V_na_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_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_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_zero__less__zpower__abs__iff,axiom,
! [V_na_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_na_2)))
<=> ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_zero__less__zpower__abs__iff) ).
fof(fact_le__special_I1_J,axiom,
! [V_y_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ),
file('theBenchmark.p',fact_le__special_I1_J) ).
fof(fact_le__special_I3_J,axiom,
! [V_x_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ),
file('theBenchmark.p',fact_le__special_I3_J) ).
fof(fact_less__special_I1_J,axiom,
! [V_y_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ),
file('theBenchmark.p',fact_less__special_I1_J) ).
fof(fact_less__special_I3_J,axiom,
! [V_x_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ),
file('theBenchmark.p',fact_less__special_I3_J) ).
fof(fact_less__0__number__of,axiom,
! [V_v_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ),
file('theBenchmark.p',fact_less__0__number__of) ).
fof(fact_add__nat__number__of,axiom,
! [V_v_H,V_v] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_v_H)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_H) ) ),
file('theBenchmark.p',fact_add__nat__number__of) ).
fof(fact_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_eq__special_I3_J,axiom,
! [V_x_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) ) ),
file('theBenchmark.p',fact_eq__special_I3_J) ).
fof(fact_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_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_eq__special_I2_J,axiom,
! [V_y_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
<=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) ) ),
file('theBenchmark.p',fact_eq__special_I2_J) ).
fof(fact_eq__special_I4_J,axiom,
! [V_x_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
<=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) ) ),
file('theBenchmark.p',fact_eq__special_I4_J) ).
fof(fact_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_int__val__lemma,axiom,
! [V_k_2,V_f_2,V_na_2] :
( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_na_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_na_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_na_2)) ) ) ) ),
file('theBenchmark.p',fact_int__val__lemma) ).
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_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_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_less__int__code_I16_J,axiom,
! [V_k2_2,V_k1_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
file('theBenchmark.p',fact_less__int__code_I16_J) ).
fof(fact_rel__simps_I17_J,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
file('theBenchmark.p',fact_rel__simps_I17_J) ).
fof(fact_rel__simps_I39_J,axiom,
! [V_l] : c_Int_OPls != c_Int_OBit1(V_l),
file('theBenchmark.p',fact_rel__simps_I39_J) ).
fof(fact_rel__simps_I46_J,axiom,
! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
file('theBenchmark.p',fact_rel__simps_I46_J) ).
fof(fact_Bit1__Min,axiom,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
file('theBenchmark.p',fact_Bit1__Min) ).
fof(fact_rel__simps_I43_J,axiom,
! [V_l_2] :
( c_Int_OMin = c_Int_OBit1(V_l_2)
<=> c_Int_OMin = V_l_2 ),
file('theBenchmark.p',fact_rel__simps_I43_J) ).
fof(fact_rel__simps_I47_J,axiom,
! [V_k_2] :
( c_Int_OBit1(V_k_2) = c_Int_OMin
<=> V_k_2 = c_Int_OMin ),
file('theBenchmark.p',fact_rel__simps_I47_J) ).
fof(fact_succ__pred,axiom,
! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
file('theBenchmark.p',fact_succ__pred) ).
fof(fact_bin__less__0__simps_I4_J,axiom,
! [V_w_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('theBenchmark.p',fact_bin__less__0__simps_I4_J) ).
fof(fact_rel__simps_I22_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
file('theBenchmark.p',fact_rel__simps_I22_J) ).
fof(fact_rel__simps_I12_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
file('theBenchmark.p',fact_rel__simps_I12_J) ).
fof(fact_Bit1__def,axiom,
! [V_k] : c_Int_OBit1(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)),V_k),
file('theBenchmark.p',fact_Bit1__def) ).
fof(fact_rel__simps_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_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_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_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_iszero__number__of__Bit1,axiom,
! [V_w,T_a] :
( ( class_Int_Oring__char__0(T_a)
& class_Int_Onumber__ring(T_a) )
=> ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ),
file('theBenchmark.p',fact_iszero__number__of__Bit1) ).
fof(fact_succ__Pls,axiom,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
file('theBenchmark.p',fact_succ__Pls) ).
fof(fact_le__iff__pred__less,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ),
file('theBenchmark.p',fact_le__iff__pred__less) ).
fof(fact_pred__Pls,axiom,
c_Int_Opred(c_Int_OPls) = c_Int_OMin,
file('theBenchmark.p',fact_pred__Pls) ).
fof(fact_pred__def,axiom,
! [V_k] : c_Int_Opred(V_k) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('theBenchmark.p',fact_pred__def) ).
fof(fact_add__Min__right,axiom,
! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k),
file('theBenchmark.p',fact_add__Min__right) ).
fof(fact_add__Min,axiom,
! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k),
file('theBenchmark.p',fact_add__Min) ).
fof(fact_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__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_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_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_I29_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
file('theBenchmark.p',fact_rel__simps_I29_J) ).
fof(fact_rel__simps_I5_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
file('theBenchmark.p',fact_rel__simps_I5_J) ).
fof(fact_one__is__num__one,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
file('theBenchmark.p',fact_one__is__num__one) ).
fof(fact_Numeral1__eq1__nat,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
file('theBenchmark.p',fact_Numeral1__eq1__nat) ).
fof(fact_nat__numeral__1__eq__1,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('theBenchmark.p',fact_nat__numeral__1__eq__1) ).
fof(fact_diff__bin__simps_I4_J,axiom,
! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)),
file('theBenchmark.p',fact_diff__bin__simps_I4_J) ).
fof(fact_minus__Min,axiom,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
file('theBenchmark.p',fact_minus__Min) ).
fof(fact_not__iszero__Numeral1,axiom,
! [T_a] :
( class_Int_Onumber__ring(T_a)
=> ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ),
file('theBenchmark.p',fact_not__iszero__Numeral1) ).
fof(fact_numeral__1__eq__Suc__0,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_numeral__1__eq__Suc__0) ).
fof(fact_numeral__3__eq__3,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
file('theBenchmark.p',fact_numeral__3__eq__3) ).
fof(fact_power3__eq__cube,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),V_a) ),
file('theBenchmark.p',fact_power3__eq__cube) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
fof(fact_Suc3__eq__add__3,axiom,
! [V_n] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n),
file('theBenchmark.p',fact_Suc3__eq__add__3) ).
fof(fact_transfer__int__nat__numerals_I4_J,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
file('theBenchmark.p',fact_transfer__int__nat__numerals_I4_J) ).
fof(fact_transfer__nat__int__numerals_I4_J,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
file('theBenchmark.p',fact_transfer__nat__int__numerals_I4_J) ).
fof(fact_le__special_I4_J,axiom,
! [V_x_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ),
file('theBenchmark.p',fact_le__special_I4_J) ).
fof(fact_le__special_I2_J,axiom,
! [V_y_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ),
file('theBenchmark.p',fact_le__special_I2_J) ).
fof(fact_less__special_I4_J,axiom,
! [V_x_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ),
file('theBenchmark.p',fact_less__special_I4_J) ).
fof(fact_less__special_I2_J,axiom,
! [V_y_2,T_b] :
( ( class_Rings_Olinordered__idom(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ),
file('theBenchmark.p',fact_less__special_I2_J) ).
fof(fact_add__special_I3_J,axiom,
! [V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),c_Int_OBit1(c_Int_OPls))) ),
file('theBenchmark.p',fact_add__special_I3_J) ).
fof(fact_add__special_I2_J,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w)) ),
file('theBenchmark.p',fact_add__special_I2_J) ).
fof(fact_Suc__diff__eq__diff__pred,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),V_n))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ),
file('theBenchmark.p',fact_Suc__diff__eq__diff__pred) ).
fof(fact_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_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__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_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_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_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_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_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_zmod__number__of__Bit1,axiom,
! [V_v,V_w] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
file('theBenchmark.p',fact_zmod__number__of__Bit1) ).
fof(fact_neg__zmod__mult__2,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_a))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
file('theBenchmark.p',fact_neg__zmod__mult__2) ).
fof(fact_pos__zdiv__mult__2,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_a) ),
file('theBenchmark.p',fact_pos__zdiv__mult__2) ).
fof(fact_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_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_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_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_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_less__eq__int__code_I13_J,axiom,
! [V_k2_2,V_k1_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ),
file('theBenchmark.p',fact_less__eq__int__code_I13_J) ).
fof(fact_rel__simps_I31_J,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
file('theBenchmark.p',fact_rel__simps_I31_J) ).
fof(fact_rel__simps_I14_J,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
file('theBenchmark.p',fact_rel__simps_I14_J) ).
fof(fact_less__int__code_I13_J,axiom,
! [V_k2_2,V_k1_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
file('theBenchmark.p',fact_less__int__code_I13_J) ).
fof(fact_rel__simps_I44_J,axiom,
! [V_k_2] :
( c_Int_OBit0(V_k_2) = c_Int_OPls
<=> V_k_2 = c_Int_OPls ),
file('theBenchmark.p',fact_rel__simps_I44_J) ).
fof(fact_rel__simps_I38_J,axiom,
! [V_l_2] :
( c_Int_OPls = c_Int_OBit0(V_l_2)
<=> c_Int_OPls = V_l_2 ),
file('theBenchmark.p',fact_rel__simps_I38_J) ).
fof(fact_Bit0__Pls,axiom,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
file('theBenchmark.p',fact_Bit0__Pls) ).
fof(fact_rel__simps_I50_J,axiom,
! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l),
file('theBenchmark.p',fact_rel__simps_I50_J) ).
fof(fact_rel__simps_I49_J,axiom,
! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l),
file('theBenchmark.p',fact_rel__simps_I49_J) ).
fof(fact_add__Bit0__Bit0,axiom,
! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)),
file('theBenchmark.p',fact_add__Bit0__Bit0) ).
fof(fact_Bit0__def,axiom,
! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k),
file('theBenchmark.p',fact_Bit0__def) ).
fof(fact_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_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_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_bin__less__0__simps_I3_J,axiom,
! [V_w_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('theBenchmark.p',fact_bin__less__0__simps_I3_J) ).
fof(fact_rel__simps_I21_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
file('theBenchmark.p',fact_rel__simps_I21_J) ).
fof(fact_rel__simps_I27_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
file('theBenchmark.p',fact_rel__simps_I27_J) ).
fof(fact_rel__simps_I32_J,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
file('theBenchmark.p',fact_rel__simps_I32_J) ).
fof(fact_less__eq__int__code_I14_J,axiom,
! [V_k2_2,V_k1_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ),
file('theBenchmark.p',fact_less__eq__int__code_I14_J) ).
fof(fact_rel__simps_I10_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
file('theBenchmark.p',fact_rel__simps_I10_J) ).
fof(fact_rel__simps_I4_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
file('theBenchmark.p',fact_rel__simps_I4_J) ).
fof(fact_less__int__code_I15_J,axiom,
! [V_k2_2,V_k1_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
file('theBenchmark.p',fact_less__int__code_I15_J) ).
fof(fact_rel__simps_I16_J,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
file('theBenchmark.p',fact_rel__simps_I16_J) ).
fof(fact_add__Bit1__Bit0,axiom,
! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)),
file('theBenchmark.p',fact_add__Bit1__Bit0) ).
fof(fact_add__Bit0__Bit1,axiom,
! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)),
file('theBenchmark.p',fact_add__Bit0__Bit1) ).
fof(fact_diff__bin__simps_I3_J,axiom,
! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),V_l)),
file('theBenchmark.p',fact_diff__bin__simps_I3_J) ).
fof(fact_diff__bin__simps_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_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_rel__simps_I28_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ),
file('theBenchmark.p',fact_rel__simps_I28_J) ).
fof(fact_rel__simps_I8_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ),
file('theBenchmark.p',fact_rel__simps_I8_J) ).
fof(fact_zdiv__number__of__Bit0,axiom,
! [V_w,V_v] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),
file('theBenchmark.p',fact_zdiv__number__of__Bit0) ).
fof(fact_neg__number__of__Bit0,axiom,
! [V_w_2] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ),
file('theBenchmark.p',fact_neg__number__of__Bit0) ).
fof(fact_pred__Bit0,axiom,
! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)),
file('theBenchmark.p',fact_pred__Bit0) ).
fof(fact_pred__Bit1,axiom,
! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k),
file('theBenchmark.p',fact_pred__Bit1) ).
fof(fact_pred__Min,axiom,
c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
file('theBenchmark.p',fact_pred__Min) ).
fof(fact_iszero__number__of__Bit0,axiom,
! [V_w_2,T_b] :
( ( class_Int_Oring__char__0(T_b)
& class_Int_Onumber__ring(T_b) )
=> ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
<=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ),
file('theBenchmark.p',fact_iszero__number__of__Bit0) ).
fof(fact_succ__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_number__of__Bit0,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
file('theBenchmark.p',fact_number__of__Bit0) ).
fof(fact_rel__simps_I15_J,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
file('theBenchmark.p',fact_rel__simps_I15_J) ).
fof(fact_less__int__code_I14_J,axiom,
! [V_k2_2,V_k1_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ),
file('theBenchmark.p',fact_less__int__code_I14_J) ).
fof(fact_rel__simps_I33_J,axiom,
! [V_l_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
file('theBenchmark.p',fact_rel__simps_I33_J) ).
fof(fact_less__eq__int__code_I15_J,axiom,
! [V_k2_2,V_k1_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
file('theBenchmark.p',fact_less__eq__int__code_I15_J) ).
fof(fact_mult__Bit1,axiom,
! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(V_k)),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l))),V_l),
file('theBenchmark.p',fact_mult__Bit1) ).
fof(fact_rel__simps_I25_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ),
file('theBenchmark.p',fact_rel__simps_I25_J) ).
fof(fact_rel__simps_I11_J,axiom,
! [V_k_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ),
file('theBenchmark.p',fact_rel__simps_I11_J) ).
fof(fact_diff__bin__simps_I5_J,axiom,
! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)),
file('theBenchmark.p',fact_diff__bin__simps_I5_J) ).
fof(fact_diff__bin__simps_I6_J,axiom,
! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)),
file('theBenchmark.p',fact_diff__bin__simps_I6_J) ).
fof(fact_diff__bin__simps_I8_J,axiom,
! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(V_k)),V_l)),
file('theBenchmark.p',fact_diff__bin__simps_I8_J) ).
fof(fact_add__Bit1__Bit1,axiom,
! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_Osucc(V_l))),
file('theBenchmark.p',fact_add__Bit1__Bit1) ).
fof(fact_double__number__of__Bit0,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) ),
file('theBenchmark.p',fact_double__number__of__Bit0) ).
fof(fact_number__of1,axiom,
! [V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_n))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_n)))) ) ),
file('theBenchmark.p',fact_number__of1) ).
fof(fact_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__power2,axiom,
! [T_a] :
( class_Rings_Osemiring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_zero__power2) ).
fof(fact_zero__eq__power2,axiom,
! [V_a_2,T_b] :
( class_Rings_Oring__1__no__zero__divisors(T_b)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_b)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_zero__eq__power2) ).
fof(fact_semiring__norm_I115_J,axiom,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('theBenchmark.p',fact_semiring__norm_I115_J) ).
fof(fact_numeral__2__eq__2,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_numeral__2__eq__2) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(fact_power2__eq__square,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ),
file('theBenchmark.p',fact_power2__eq__square) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
fof(fact_add__2__eq__Suc_H,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)),
file('theBenchmark.p',fact_add__2__eq__Suc_H) ).
fof(fact_add__2__eq__Suc,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)),
file('theBenchmark.p',fact_add__2__eq__Suc) ).
fof(fact_one__power2,axiom,
! [T_a] :
( class_Rings_Osemiring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_one__power2) ).
fof(fact_power2__minus,axiom,
! [V_a,T_a] :
( class_Rings_Oring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('theBenchmark.p',fact_power2__minus) ).
fof(fact_nat__mult__2,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_zero__le__power2,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
file('theBenchmark.p',fact_zero__le__power2) ).
fof(fact_power2__le__imp__le,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ),
file('theBenchmark.p',fact_power2__le__imp__le) ).
fof(fact_power2__eq__imp__eq,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> V_x = V_y ) ) ) ),
file('theBenchmark.p',fact_power2__eq__imp__eq) ).
fof(fact_power2__less__0,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))) ),
file('theBenchmark.p',fact_power2__less__0) ).
fof(fact_zero__less__power2,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
<=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_zero__less__power2) ).
fof(fact_sum__power2__eq__zero__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_b)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_sum__power2__eq__zero__iff) ).
fof(fact_power2__eq__square__number__of,axiom,
! [V_w,T_b] :
( ( class_Int_Onumber(T_b)
& class_Groups_Omonoid__mult(T_b) )
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)) ),
file('theBenchmark.p',fact_power2__eq__square__number__of) ).
fof(fact_less__2__cases,axiom,
! [V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
=> ( V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_less__2__cases) ).
fof(fact_nat__2,axiom,
hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_nat__2) ).
fof(fact_power2__eq__1__iff,axiom,
! [V_a_2,T_b] :
( class_Rings_Oring__1__no__zero__divisors(T_b)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_b)
<=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
| V_a_2 = c_Groups_Oone__class_Oone(T_b) ) ) ),
file('theBenchmark.p',fact_power2__eq__1__iff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
! [V_n,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
fof(fact_power__minus__even,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Oring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) ),
file('theBenchmark.p',fact_power__minus__even) ).
fof(fact_power2__less__imp__less,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ),
file('theBenchmark.p',fact_power2__less__imp__less) ).
fof(fact_sum__power2__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_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_b)))
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_sum__power2__le__zero__iff) ).
fof(fact_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_sum__power2__gt__zero__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
<=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_sum__power2__gt__zero__iff) ).
fof(fact_power2__sum,axiom,
! [V_y,V_x,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ),
file('theBenchmark.p',fact_power2__sum) ).
fof(fact_zero__le__even__power_H,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))) ),
file('theBenchmark.p',fact_zero__le__even__power_H) ).
fof(fact_power__odd__eq,axiom,
! [V_n,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('theBenchmark.p',fact_power__odd__eq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
! [V_n,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) ).
fof(fact_power__minus1__even,axiom,
! [V_n,T_a] :
( class_Rings_Oring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_power__minus1__even) ).
fof(fact_zdiv__number__of__Bit1,axiom,
! [V_v,V_w] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_v))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) ),
file('theBenchmark.p',fact_zdiv__number__of__Bit1) ).
fof(fact_mod2__gr__0,axiom,
! [V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
<=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
file('theBenchmark.p',fact_mod2__gr__0) ).
fof(fact_div__2__gt__zero,axiom,
! [V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
file('theBenchmark.p',fact_div__2__gt__zero) ).
fof(fact_power2__diff,axiom,
! [V_y,V_x,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ),
file('theBenchmark.p',fact_power2__diff) ).
fof(fact_odd__0__le__power__imp__0__le,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ),
file('theBenchmark.p',fact_odd__0__le__power__imp__0__le) ).
fof(fact_odd__power__less__zero,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)))),c_Groups_Ozero__class_Ozero(T_a))) ) ),
file('theBenchmark.p',fact_odd__power__less__zero) ).
fof(fact_power__minus1__odd,axiom,
! [V_n,T_a] :
( class_Rings_Oring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ),
file('theBenchmark.p',fact_power__minus1__odd) ).
fof(fact_power__m1__even,axiom,
! [V_n,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_power__m1__even) ).
fof(fact_power__m1__odd,axiom,
! [V_n,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n))) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin) ),
file('theBenchmark.p',fact_power__m1__odd) ).
fof(fact_int__of__code,axiom,
! [V_k] :
( ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> ( ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_k,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Code__Numeral_Oint__of,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_k),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ) )
& ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_int__of__code) ).
fof(fact_one__code__numeral__code,axiom,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)),
file('theBenchmark.p',fact_one__code__numeral__code) ).
fof(fact_half__gt__zero,axiom,
! [V_r,T_a] :
( ( class_Int_Onumber__ring(T_a)
& class_Fields_Olinordered__field__inverse__zero(T_a) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_r),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
file('theBenchmark.p',fact_half__gt__zero) ).
fof(fact_half__gt__zero__iff,axiom,
! [V_r_2,T_b] :
( ( class_Int_Onumber__ring(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ),
file('theBenchmark.p',fact_half__gt__zero__iff) ).
fof(fact_nat0__intermed__int__val,axiom,
! [V_k_2,V_f_2,V_na_2] :
( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_na_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_na_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_na_2)) ) ) ) ),
file('theBenchmark.p',fact_nat0__intermed__int__val) ).
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_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_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_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_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_add__divide__distrib,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ),
file('theBenchmark.p',fact_add__divide__distrib) ).
fof(fact_times__divide__eq__right,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ),
file('theBenchmark.p',fact_times__divide__eq__right) ).
fof(fact_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_diff__divide__distrib,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)) ),
file('theBenchmark.p',fact_diff__divide__distrib) ).
fof(fact_divide__1,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
file('theBenchmark.p',fact_divide__1) ).
fof(fact_minus__divide__left,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b) ),
file('theBenchmark.p',fact_minus__divide__left) ).
fof(fact_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_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_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_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
! [V_y,V_x] :
( c_Nat__Transfer_Ois__nat(V_x)
=> ( c_Nat__Transfer_Ois__nat(V_y)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
! [V_y,V_x] :
( c_Nat__Transfer_Ois__nat(V_x)
=> ( c_Nat__Transfer_Ois__nat(V_y)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J) ).
fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
! [V_y,V_x] :
( c_Nat__Transfer_Ois__nat(V_x)
=> ( c_Nat__Transfer_Ois__nat(V_y)
=> c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ),
file('theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I2_J) ).
fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
! [V_y,V_x] :
( c_Nat__Transfer_Ois__nat(V_x)
=> ( c_Nat__Transfer_Ois__nat(V_y)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ),
file('theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I1_J) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
! [V_n,V_x] :
( c_Nat__Transfer_Ois__nat(V_x)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) ).
fof(fact_divide__right__mono__neg,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c))) ) ) ),
file('theBenchmark.p',fact_divide__right__mono__neg) ).
fof(fact_divide__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ),
file('theBenchmark.p',fact_divide__right__mono) ).
fof(fact_divide__le__0__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_divide__le__0__iff) ).
fof(fact_zero__le__divide__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_zero__le__divide__iff) ).
fof(fact_divide__strict__right__mono__neg,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ),
file('theBenchmark.p',fact_divide__strict__right__mono__neg) ).
fof(fact_divide__strict__right__mono,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c))) ) ) ),
file('theBenchmark.p',fact_divide__strict__right__mono) ).
fof(fact_divide__neg__neg,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
file('theBenchmark.p',fact_divide__neg__neg) ).
fof(fact_divide__neg__pos,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_divide__neg__pos) ).
fof(fact_divide__pos__neg,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_divide__pos__neg) ).
fof(fact_divide__pos__pos,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
file('theBenchmark.p',fact_divide__pos__pos) ).
fof(fact_divide__less__0__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_divide__less__0__iff) ).
fof(fact_zero__less__divide__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_zero__less__divide__iff) ).
fof(fact_nonzero__eq__divide__eq,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Rings_Odivision__ring(T_b)
=> ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ),
file('theBenchmark.p',fact_nonzero__eq__divide__eq) ).
fof(fact_nonzero__divide__eq__eq,axiom,
! [V_a_2,V_b_2,V_c_2,T_b] :
( class_Rings_Odivision__ring(T_b)
=> ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
<=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ),
file('theBenchmark.p',fact_nonzero__divide__eq__eq) ).
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_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_eq__divide__eq,axiom,
! [V_c_2,V_b_2,V_a_2,T_b] :
( class_Fields_Ofield__inverse__zero(T_b)
=> ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
<=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ) ),
file('theBenchmark.p',fact_eq__divide__eq) ).
fof(fact_divide__eq__eq,axiom,
! [V_a_2,V_c_2,V_b_2,T_b] :
( class_Fields_Ofield__inverse__zero(T_b)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
<=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ) ),
file('theBenchmark.p',fact_divide__eq__eq) ).
fof(fact_mult__divide__mult__cancel__right,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ),
file('theBenchmark.p',fact_mult__divide__mult__cancel__right) ).
fof(fact_mult__divide__mult__cancel__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_c != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ),
file('theBenchmark.p',fact_mult__divide__mult__cancel__left) ).
fof(fact_frac__eq__eq,axiom,
! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
( class_Fields_Ofield(T_b)
=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2) ) ) ) ),
file('theBenchmark.p',fact_frac__eq__eq) ).
fof(fact_right__inverse__eq,axiom,
! [V_a_2,V_b_2,T_b] :
( class_Rings_Odivision__ring(T_b)
=> ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
<=> V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_right__inverse__eq) ).
fof(fact_divide__self,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_divide__self) ).
fof(fact_divide__self__if,axiom,
! [V_a,T_a] :
( class_Rings_Odivision__ring__inverse__zero(T_a)
=> ( ( V_a != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) )
& ( V_a = c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_divide__self__if) ).
fof(fact_nonzero__minus__divide__divide,axiom,
! [V_a,V_b,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ),
file('theBenchmark.p',fact_nonzero__minus__divide__divide) ).
fof(fact_nonzero__minus__divide__right,axiom,
! [V_a,V_b,T_a] :
( class_Rings_Odivision__ring(T_a)
=> ( V_b != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) ) ),
file('theBenchmark.p',fact_nonzero__minus__divide__right) ).
fof(fact_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_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_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_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_divide__nonpos__neg,axiom,
! [V_y,V_x,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
file('theBenchmark.p',fact_divide__nonpos__neg) ).
fof(fact_divide__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_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_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__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_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_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__strict__left__mono__neg,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ),
file('theBenchmark.p',fact_divide__strict__left__mono__neg) ).
fof(fact_divide__strict__left__mono,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_c),V_b))) ) ) ) ),
file('theBenchmark.p',fact_divide__strict__left__mono) ).
fof(fact_neg__divide__less__eq,axiom,
! [V_a_2,V_b_2,V_c_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ),
file('theBenchmark.p',fact_neg__divide__less__eq) ).
fof(fact_neg__less__divide__eq,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ),
file('theBenchmark.p',fact_neg__less__divide__eq) ).
fof(fact_mult__imp__less__div__pos,axiom,
! [V_x,V_z,V_y,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ),
file('theBenchmark.p',fact_mult__imp__less__div__pos) ).
fof(fact_mult__imp__div__pos__less,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z)) ) ) ),
file('theBenchmark.p',fact_mult__imp__div__pos__less) ).
fof(fact_pos__divide__less__eq,axiom,
! [V_a_2,V_b_2,V_c_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ),
file('theBenchmark.p',fact_pos__divide__less__eq) ).
fof(fact_pos__less__divide__eq,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ),
file('theBenchmark.p',fact_pos__less__divide__eq) ).
fof(fact_divide__less__eq,axiom,
! [V_a_2,V_c_2,V_b_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ),
file('theBenchmark.p',fact_divide__less__eq) ).
fof(fact_less__divide__eq,axiom,
! [V_c_2,V_b_2,V_a_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_less__divide__eq) ).
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_add__num__frac,axiom,
! [V_x,V_z,V_y,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_y != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ),
file('theBenchmark.p',fact_add__num__frac) ).
fof(fact_add__divide__eq__iff,axiom,
! [V_y,V_x,V_z,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ),
file('theBenchmark.p',fact_add__divide__eq__iff) ).
fof(fact_add__frac__num,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_y != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ),
file('theBenchmark.p',fact_add__frac__num) ).
fof(fact_divide__add__eq__iff,axiom,
! [V_y,V_x,V_z,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ),
file('theBenchmark.p',fact_divide__add__eq__iff) ).
fof(fact_add__frac__eq,axiom,
! [V_w,V_x,V_z,V_y,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_y != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ),
file('theBenchmark.p',fact_add__frac__eq) ).
fof(fact_diff__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_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__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_eq__divide__eq__number__of1,axiom,
! [V_w_2,V_b_2,V_a_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Ofield__inverse__zero(T_b) )
=> ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
<=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_b_2 ) ) ) ),
file('theBenchmark.p',fact_eq__divide__eq__number__of1) ).
fof(fact_eq__divide__eq__number__of,axiom,
! [V_c_2,V_b_2,V_w_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Ofield__inverse__zero(T_b) )
=> ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
<=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
=> hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) = V_b_2 ) ) ) ),
file('theBenchmark.p',fact_eq__divide__eq__number__of) ).
fof(fact_divide__eq__eq__number__of,axiom,
! [V_w_2,V_c_2,V_b_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Ofield__inverse__zero(T_b) )
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
<=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
=> hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) ) ) ) ),
file('theBenchmark.p',fact_divide__eq__eq__number__of) ).
fof(fact_divide__eq__eq__number__of1,axiom,
! [V_a_2,V_w_2,V_b_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Ofield__inverse__zero(T_b) )
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_a_2
<=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ) ),
file('theBenchmark.p',fact_divide__eq__eq__number__of1) ).
fof(fact_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_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_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_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_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_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__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_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_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_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_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_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_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_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_pos__divide__le__eq,axiom,
! [V_a_2,V_b_2,V_c_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ),
file('theBenchmark.p',fact_pos__divide__le__eq) ).
fof(fact_pos__le__divide__eq,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Fields_Olinordered__field(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ),
file('theBenchmark.p',fact_pos__le__divide__eq) ).
fof(fact_divide__le__eq,axiom,
! [V_a_2,V_c_2,V_b_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ),
file('theBenchmark.p',fact_divide__le__eq) ).
fof(fact_le__divide__eq,axiom,
! [V_c_2,V_b_2,V_a_2,T_b] :
( class_Fields_Olinordered__field__inverse__zero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_le__divide__eq) ).
fof(fact_less__divide__eq__number__of1,axiom,
! [V_w_2,V_b_2,V_a_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_less__divide__eq__number__of1) ).
fof(fact_less__divide__eq__number__of,axiom,
! [V_c_2,V_b_2,V_w_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_less__divide__eq__number__of) ).
fof(fact_divide__less__eq__number__of,axiom,
! [V_w_2,V_c_2,V_b_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) ) ) ),
file('theBenchmark.p',fact_divide__less__eq__number__of) ).
fof(fact_divide__less__eq__number__of1,axiom,
! [V_a_2,V_w_2,V_b_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) ) ) ),
file('theBenchmark.p',fact_divide__less__eq__number__of1) ).
fof(fact_power__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_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_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_divide__le__eq__number__of1,axiom,
! [V_a_2,V_w_2,V_b_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) ) ) ),
file('theBenchmark.p',fact_divide__le__eq__number__of1) ).
fof(fact_divide__le__eq__number__of,axiom,
! [V_w_2,V_c_2,V_b_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) ) ) ),
file('theBenchmark.p',fact_divide__le__eq__number__of) ).
fof(fact_le__divide__eq__number__of,axiom,
! [V_c_2,V_b_2,V_w_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_le__divide__eq__number__of) ).
fof(fact_le__divide__eq__number__of1,axiom,
! [V_w_2,V_b_2,V_a_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Fields_Olinordered__field__inverse__zero(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_le__divide__eq__number__of1) ).
fof(fact_nat__of__aux__code,axiom,
! [V_n,V_i] :
( ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> c_Code__Numeral_Onat__of__aux(V_i,V_n) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,V_n)) )
& ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) ),
file('theBenchmark.p',fact_nat__of__aux__code) ).
fof(fact_code__numeral_Osize_I1_J,axiom,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_code__numeral_Osize_I1_J) ).
fof(fact_code__numeral_Osize_I3_J,axiom,
hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_code__numeral_Osize_I3_J) ).
fof(fact_code__numeral_Osimps_I4_J,axiom,
! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2,
file('theBenchmark.p',fact_code__numeral_Osimps_I4_J) ).
fof(fact_mod__induct__0,axiom,
! [V_i_2,V_P_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_P_2,B_i))
=> hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
=> ( hBOOL(hAPP(V_P_2,V_i_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
=> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('theBenchmark.p',fact_mod__induct__0) ).
fof(fact_nat__intermed__int__val,axiom,
! [V_k_2,V_f_2,V_na_2,V_m_2] :
( ! [B_i] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_na_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_na_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_na_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_na_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_code__numeral_Osize_I4_J,axiom,
! [V_code__numeral] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_code__numeral_Osize_I4_J) ).
fof(fact_code__numeral_Osize_I2_J,axiom,
! [V_code__numeral] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_code__numeral_Osize_I2_J) ).
fof(fact_log_Osimps,axiom,
! [V_i,V_b] :
( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
=> c_Random_Olog(V_b,V_i) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(V_b,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_i),V_b))) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
=> c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) ),
file('theBenchmark.p',fact_log_Osimps) ).
fof(fact_mod__div__decomp,axiom,
! [V_b,V_a,T_a] :
( class_Divides_Osemiring__div(T_a)
=> V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b)) ),
file('theBenchmark.p',fact_mod__div__decomp) ).
fof(fact_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_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_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_I2_J,axiom,
! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H),
file('theBenchmark.p',fact_code__numeral_Osimps_I2_J) ).
fof(fact_code__numeral_Osimps_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_I5_J,axiom,
! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2),
file('theBenchmark.p',fact_code__numeral_Osimps_I5_J) ).
fof(fact_Suc__code__numeral__minus__one,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_n)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = V_n,
file('theBenchmark.p',fact_Suc__code__numeral__minus__one) ).
fof(fact_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__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_negDivAlg__eqn__1__number__of,axiom,
! [V_w] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))
=> c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))
=> c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ) ),
file('theBenchmark.p',fact_negDivAlg__eqn__1__number__of) ).
fof(fact_nat_Osize_I2_J,axiom,
! [V_nat] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_nat_Osize_I2_J) ).
fof(fact_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_code__numeral_Orecs_I2_J,axiom,
! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(hAPP(V_f2_2,V_code__numeral_2),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,V_code__numeral_2)),
file('theBenchmark.p',fact_code__numeral_Orecs_I2_J) ).
fof(fact_INF__less__iff,axiom,
! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
( ( class_Orderings_Olinorder(T_b)
& class_Complete__Lattice_Ocomplete__lattice(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_f_2)),V_a_2))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_INF__less__iff) ).
fof(fact_less__eq__nat_Osimps_I2_J,axiom,
! [V_na_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_na_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_na_2)) ),
file('theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).
fof(fact_INT__subset__iff,axiom,
! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ),
file('theBenchmark.p',fact_INT__subset__iff) ).
fof(fact_le__INF__iff,axiom,
! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_M_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ),
file('theBenchmark.p',fact_le__INF__iff) ).
fof(fact_INFI__apply,axiom,
! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ),
file('theBenchmark.p',fact_INFI__apply) ).
fof(fact_INF__commute,axiom,
! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ),
file('theBenchmark.p',fact_INF__commute) ).
fof(fact_fun__Compl__def,axiom,
! [V_x_2,V_A_2,T_c,T_b] :
( class_Groups_Ouminus(T_b)
=> hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ),
file('theBenchmark.p',fact_fun__Compl__def) ).
fof(fact_fun__diff__def,axiom,
! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
( class_Groups_Ominus(T_b)
=> hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ),
file('theBenchmark.p',fact_fun__diff__def) ).
fof(fact_less__eq__Suc__le__raw,axiom,
! [V_na_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),
file('theBenchmark.p',fact_less__eq__Suc__le__raw) ).
fof(fact_diff__Suc,axiom,
! [V_na_2,V_m_2] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_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_na_2)),
file('theBenchmark.p',fact_diff__Suc) ).
fof(fact_nat__number__of__Bit0,axiom,
! [V_w_2] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
file('theBenchmark.p',fact_nat__number__of__Bit0) ).
fof(fact_nat_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_power__number__of__even,axiom,
! [V_w_2,V_z_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ),
file('theBenchmark.p',fact_power__number__of__even) ).
fof(fact_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_power__number__of__even__number__of,axiom,
! [V_w_2,V_v_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ),
file('theBenchmark.p',fact_power__number__of__even__number__of) ).
fof(fact_diff__nat__eq__if,axiom,
! [V_z_2,V_z_H_2] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),V_z_H_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(c_Int_Onat,V_z_2) ) ),
file('theBenchmark.p',fact_diff__nat__eq__if) ).
fof(fact_negDivAlg__div__mod,axiom,
! [V_l,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
=> c_Divides_OnegDivAlg(V_k,V_l) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l)) ) ),
file('theBenchmark.p',fact_negDivAlg__div__mod) ).
fof(fact_negDivAlg__minus1,axiom,
! [V_b] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('theBenchmark.p',fact_negDivAlg__minus1) ).
fof(fact_semiring__1__class_Oof__nat__code,axiom,
! [V_na_2,T_b] :
( class_Rings_Osemiring__1(T_b)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_Groups_Oone__class_Oone(T_b)),V_na_2,c_Groups_Ozero__class_Ozero(T_b)) ),
file('theBenchmark.p',fact_semiring__1__class_Oof__nat__code) ).
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_eq__number__of__Suc,axiom,
! [V_na_2,V_v_2] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_na_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_na_2))))) ),
file('theBenchmark.p',fact_eq__number__of__Suc) ).
fof(fact_Suc__eq__number__of,axiom,
! [V_v_2,V_na_2] :
( hAPP(c_Nat_OSuc,V_na_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_na_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_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat))),
file('theBenchmark.p',fact_nat__case__number__of) ).
fof(fact_nat__rec__number__of,axiom,
! [V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),c_Int_Onat)))),
file('theBenchmark.p',fact_nat__rec__number__of) ).
fof(fact_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_less__Suc__number__of,axiom,
! [V_v_2,V_na_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_na_2)),c_Int_Onat))))) ),
file('theBenchmark.p',fact_less__Suc__number__of) ).
fof(fact_less__number__of__Suc,axiom,
! [V_na_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_na_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_na_2)))) ),
file('theBenchmark.p',fact_less__number__of__Suc) ).
fof(fact_le__number__of__Suc,axiom,
! [V_na_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_na_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_na_2)))) ),
file('theBenchmark.p',fact_le__number__of__Suc) ).
fof(fact_le__Suc__number__of,axiom,
! [V_v_2,V_na_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_na_2)),c_Int_Onat))))) ),
file('theBenchmark.p',fact_le__Suc__number__of) ).
fof(fact_nat__case__add__eq__if,axiom,
! [V_na_2,V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_na_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,V_na_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_na_2)))),
file('theBenchmark.p',fact_nat__case__add__eq__if) ).
fof(fact_nat__rec__add__eq__if,axiom,
! [V_na_2,V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_na_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),V_na_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_na_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_na_2))))),
file('theBenchmark.p',fact_nat__rec__add__eq__if) ).
fof(fact_power__number__of__odd,axiom,
! [V_z_2,V_w_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2))),c_COMBI(T_b))) ) ) ),
file('theBenchmark.p',fact_power__number__of__odd) ).
fof(fact_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_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_power__number__of__odd__number__of,axiom,
! [V_v_2,V_w_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)))),c_COMBI(T_b))) ) ) ),
file('theBenchmark.p',fact_power__number__of__odd__number__of) ).
fof(fact_code__numeral_Orecs_I1_J,axiom,
! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2,
file('theBenchmark.p',fact_code__numeral_Orecs_I1_J) ).
fof(fact_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_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_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_posDivAlg__eqn,axiom,
! [V_a,V_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
=> c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
=> c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) ) ) ),
file('theBenchmark.p',fact_posDivAlg__eqn) ).
fof(fact_posDivAlg__eqn__number__of,axiom,
! [V_w,V_v] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
=> c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) ) ) ),
file('theBenchmark.p',fact_posDivAlg__eqn__number__of) ).
fof(fact_negDivAlg_Opsimps,axiom,
! [V_b_2,V_a_2] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a_2),V_b_2)))
=> ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) )
=> c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(c_Divides_Oadjust(V_b_2),c_Divides_OnegDivAlg(V_a_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b_2))) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2))) )
=> c_Divides_OnegDivAlg(V_a_2,V_b_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_negDivAlg_Opsimps) ).
fof(fact_accp_Osimps,axiom,
! [V_a_2,V_r_2,T_b] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ),
file('theBenchmark.p',fact_accp_Osimps) ).
fof(fact_accp_Oequations,axiom,
! [V_a_2,V_r_2,T_b] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ),
file('theBenchmark.p',fact_accp_Oequations) ).
fof(fact_accp__downward,axiom,
! [V_a_2,V_b_2,V_r_2,T_b] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ),
file('theBenchmark.p',fact_accp__downward) ).
fof(fact_accp__subset,axiom,
! [V_R2_2,V_R1_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_R1_2),V_R2_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_b,V_R2_2)),c_Wellfounded_Oaccp(T_b,V_R1_2))) ),
file('theBenchmark.p',fact_accp__subset) ).
fof(fact_posDivAlg__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__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_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_of__int__num,axiom,
! [V_k_2,T_b] :
( class_Rings_Oring__1(T_b)
=> ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),T_b),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),tc_Int_Oint),c_COMBB(tc_fun(T_b,T_b),T_b,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,T_b),T_b),tc_Int_Oint),c_HOL_OLet(T_b,T_b)),c_Int_Oring__1__class_Oof__int(T_b)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,T_b)),tc_Int_Oint),c_COMBS(T_b,T_b,T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),tc_Int_Oint),c_COMBB(T_b,tc_fun(T_b,T_b),T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Oplus__class_Oplus(T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b)))),c_Groups_Oone__class_Oone(T_b))))),c_Divides_Odivmod__int(V_k_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2))) ) ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_of__int__num) ).
fof(fact_negDivAlg_Opinduct,axiom,
! [V_P_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_P_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_P_2,B_a),B_b)) ) )
=> hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
file('theBenchmark.p',fact_negDivAlg_Opinduct) ).
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_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_zmult2__lemma,axiom,
! [V_c,V_r,V_q,V_b,V_a] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
=> ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_q),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_q,V_c))),V_r)))) ) ) ),
file('theBenchmark.p',fact_zmult2__lemma) ).
fof(fact_divmod__int__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_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_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_self__quotient,axiom,
! [V_r,V_q,V_a] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
=> ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_self__quotient) ).
fof(fact_divmod__int__rel__mod,axiom,
! [V_r,V_q,V_b,V_a] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
=> ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ),
file('theBenchmark.p',fact_divmod__int__rel__mod) ).
fof(fact_divmod__int__rel__div,axiom,
! [V_r,V_q,V_b,V_a] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
=> ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ),
file('theBenchmark.p',fact_divmod__int__rel__div) ).
fof(fact_negDivAlg__correct,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ),
file('theBenchmark.p',fact_negDivAlg__correct) ).
fof(fact_divmod__int__rel__div__mod,axiom,
! [V_a,V_b] :
( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)))) ),
file('theBenchmark.p',fact_divmod__int__rel__div__mod) ).
fof(fact_posDivAlg__correct,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ),
file('theBenchmark.p',fact_posDivAlg__correct) ).
fof(fact_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_zadd1__lemma,axiom,
! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_aq),V_ar)))
=> ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_bq),V_br)))
=> ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br),V_c)))) ) ) ),
file('theBenchmark.p',fact_zadd1__lemma) ).
fof(fact_zminus1__lemma,axiom,
! [V_r_2,V_q_2,V_b_2,V_a_2] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a_2,V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)))
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b_2),V_r_2))))) ),
file('theBenchmark.p',fact_zminus1__lemma) ).
fof(fact_divmod__int__relI,axiom,
! [V_r,V_q,V_b,V_a] :
( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)
=> ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) ) ) )
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ) ),
file('theBenchmark.p',fact_divmod__int__relI) ).
fof(fact_zmult1__lemma,axiom,
! [V_a,V_r,V_q,V_c,V_b] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
=> ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_r),V_c)))) ) ),
file('theBenchmark.p',fact_zmult1__lemma) ).
fof(fact_divmod__int__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_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_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_posDivAlg_Opinduct,axiom,
! [V_P_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_P_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_P_2,B_a),B_b)) ) )
=> hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
file('theBenchmark.p',fact_posDivAlg_Opinduct) ).
fof(fact_split__twice,axiom,
! [V_p_2,V_g_2,T_f,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,tc_prod(T_c,T_d)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(T_f,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_f),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2))),V_g_2)),V_p_2),
file('theBenchmark.p',fact_split__twice) ).
fof(fact_split__eta,axiom,
! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_d),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_d,T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c))) = V_f_2,
file('theBenchmark.p',fact_split__eta) ).
fof(fact_splitI,axiom,
! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
file('theBenchmark.p',fact_splitI) ).
fof(fact_prod__caseI,axiom,
! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
file('theBenchmark.p',fact_prod__caseI) ).
fof(fact_splitD,axiom,
! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
=> hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ),
file('theBenchmark.p',fact_splitD) ).
fof(fact_splitD_H,axiom,
! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_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_apsnd__conv,axiom,
! [V_y_2,V_x_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),hAPP(V_f_2,V_y_2)),
file('theBenchmark.p',fact_apsnd__conv) ).
fof(fact_negateSnd__def,axiom,
c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
file('theBenchmark.p',fact_negateSnd__def) ).
fof(fact_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_c,T_b] :
( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2)
<=> ( V_b_2 = V_b_H_2
& V_a_2 = V_a_H_2 ) ),
file('theBenchmark.p',fact_Pair__eq) ).
fof(fact_split__paired__All,axiom,
! [T_c,T_b,V_P_2] :
( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
<=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ),
file('theBenchmark.p',fact_split__paired__All) ).
fof(fact_split__weak__cong,axiom,
! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
( V_p_2 = V_q_2
=> hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_q_2) ),
file('theBenchmark.p',fact_split__weak__cong) ).
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__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_split__conv,axiom,
! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2),
file('theBenchmark.p',fact_split__conv) ).
fof(fact_prod_Osimps_I2_J,axiom,
! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
file('theBenchmark.p',fact_prod_Osimps_I2_J) ).
fof(fact_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_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_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_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__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_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_split__def,axiom,
! [V_p_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)),
file('theBenchmark.p',fact_split__def) ).
fof(fact_split__comp__eq,axiom,
! [V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),tc_prod(T_b,T_c)),V_f_2),hAPP(hAPP(c_COMBB(T_b,T_e,tc_prod(T_b,T_c)),V_g_2),c_Product__Type_Ofst(T_b,T_c)))),c_Product__Type_Osnd(T_b,T_c)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),T_b),V_f_2),V_g_2)),
file('theBenchmark.p',fact_split__comp__eq) ).
fof(fact_split__beta,axiom,
! [V_z_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_P_2),V_z_2) = hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)),
file('theBenchmark.p',fact_split__beta) ).
fof(fact_prod__case__beta,axiom,
! [V_p_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)),
file('theBenchmark.p',fact_prod__case__beta) ).
fof(fact_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__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_Pair__fst__snd__eq,axiom,
! [T_c,T_b,V_t_2,V_s_2] :
( V_s_2 = V_t_2
<=> ( hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2)
& hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) ) ),
file('theBenchmark.p',fact_Pair__fst__snd__eq) ).
fof(fact_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__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__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_fst__eqD,axiom,
! [V_a,V_y,V_x,T_b,T_a] :
( hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) = V_a
=> V_x = V_a ),
file('theBenchmark.p',fact_fst__eqD) ).
fof(fact_fst__conv,axiom,
! [V_b,V_a,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b)) = V_a,
file('theBenchmark.p',fact_fst__conv) ).
fof(fact_snd__eqD,axiom,
! [V_a,V_y,V_x,T_a,T_b] :
( hAPP(c_Product__Type_Osnd(T_b,T_a),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x),V_y)) = V_a
=> V_y = V_a ),
file('theBenchmark.p',fact_snd__eqD) ).
fof(fact_snd__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_fst__apsnd,axiom,
! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_b,T_d),V_x_2),
file('theBenchmark.p',fact_fst__apsnd) ).
fof(fact_snd__apsnd,axiom,
! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)),
file('theBenchmark.p',fact_snd__apsnd) ).
fof(fact_apsnd__eq__conv,axiom,
! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
( hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2)
<=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) ),
file('theBenchmark.p',fact_apsnd__eq__conv) ).
fof(fact_fst__def,axiom,
! [V_p_2,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_b),c_COMBK(T_b,T_c)),V_p_2),
file('theBenchmark.p',fact_fst__def) ).
fof(fact_snd__def,axiom,
! [V_p_2,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_b),hAPP(c_COMBK(tc_fun(T_b,T_b),T_c),c_COMBI(T_b))),V_p_2),
file('theBenchmark.p',fact_snd__def) ).
fof(fact_mod__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__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_div__int__def,axiom,
! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)),
file('theBenchmark.p',fact_div__int__def) ).
fof(fact_mod__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_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__base,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
=> c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m) ),
file('theBenchmark.p',fact_divmod__nat__base) ).
fof(fact_divmod__nat__div__mod,axiom,
! [V_n,V_m] : c_Divides_Odivmod__nat(V_m,V_n) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),
file('theBenchmark.p',fact_divmod__nat__div__mod) ).
fof(fact_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_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_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_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_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_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_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_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_divmod__nat__if,axiom,
! [V_m_2,V_na_2] :
( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
| V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> c_Divides_Odivmod__nat(V_m_2,V_na_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_na_2),V_na_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
| V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> c_Divides_Odivmod__nat(V_m_2,V_na_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_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_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_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_prod__size__simp,axiom,
! [V_p_2,V_g_2,V_f_2,T_c,T_b] : c_Product__Type_Oprod_Oprod__size(T_b,T_c,V_f_2,V_g_2,V_p_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_prod__size__simp) ).
fof(fact_conjI__realizer,axiom,
! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_P_2] :
( hBOOL(hAPP(V_P_2,V_p_2))
=> ( hBOOL(hAPP(V_Q_2,V_q_2))
=> ( hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2))))
& hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) ) ) ),
file('theBenchmark.p',fact_conjI__realizer) ).
fof(fact_exI__realizer,axiom,
! [T_b,T_c,V_x_2,V_y_2,V_P_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
=> hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)))) ),
file('theBenchmark.p',fact_exI__realizer) ).
fof(fact_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_min__Suc__number__of,axiom,
! [V_na_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_na_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_na_2)))),
file('theBenchmark.p',fact_min__Suc__number__of) ).
fof(fact_min__number__of__Suc,axiom,
! [V_v_2,V_na_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_na_2)),c_Int_Onat)))),
file('theBenchmark.p',fact_min__number__of__Suc) ).
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_min__max_Oinf_Oidem,axiom,
! [V_a,T_a] :
( class_Orderings_Olinorder(T_a)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ),
file('theBenchmark.p',fact_min__max_Oinf_Oidem) ).
fof(fact_min__max_Oinf_Ocommute,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Olinorder(T_a)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_a) ),
file('theBenchmark.p',fact_min__max_Oinf_Ocommute) ).
fof(fact_min__max_Oinf__commute,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x) ),
file('theBenchmark.p',fact_min__max_Oinf__commute) ).
fof(fact_min__max_Oinf_Oleft__idem,axiom,
! [V_b,V_a,T_a] :
( class_Orderings_Olinorder(T_a)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b) ),
file('theBenchmark.p',fact_min__max_Oinf_Oleft__idem) ).
fof(fact_min__max_Oinf__left__idem,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) ),
file('theBenchmark.p',fact_min__max_Oinf__left__idem) ).
fof(fact_min__max_Oinf_Oleft__commute,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Orderings_Olinorder(T_a)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ),
file('theBenchmark.p',fact_min__max_Oinf_Oleft__commute) ).
fof(fact_min__max_Oinf__left__commute,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ),
file('theBenchmark.p',fact_min__max_Oinf__left__commute) ).
fof(fact_min__max_Oinf_Oassoc,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Olinorder(T_a)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b),V_c)) ),
file('theBenchmark.p',fact_min__max_Oinf_Oassoc) ).
fof(fact_min__max_Oinf__assoc,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) ),
file('theBenchmark.p',fact_min__max_Oinf__assoc) ).
fof(fact_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__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_Ole__iff__inf,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ),
file('theBenchmark.p',fact_min__max_Ole__iff__inf) ).
fof(fact_min__max_Ole__inf__iff,axiom,
! [V_z_2,V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_y_2),V_z_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_min__max_Ole__inf__iff) ).
fof(fact_min__max_Ole__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__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_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_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_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__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_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_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__le__iff__disj,axiom,
! [V_z_2,V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ),
file('theBenchmark.p',fact_min__le__iff__disj) ).
fof(fact_min__max_Oless__infI2,axiom,
! [V_a,V_x,V_b,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ),
file('theBenchmark.p',fact_min__max_Oless__infI2) ).
fof(fact_min__max_Oless__infI1,axiom,
! [V_b,V_x,V_a,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ),
file('theBenchmark.p',fact_min__max_Oless__infI1) ).
fof(fact_min__less__iff__disj,axiom,
! [V_z_2,V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) ) ) ),
file('theBenchmark.p',fact_min__less__iff__disj) ).
fof(fact_min__less__iff__conj,axiom,
! [V_y_2,V_x_2,V_z_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) ) ) ),
file('theBenchmark.p',fact_min__less__iff__conj) ).
fof(fact_min__add__distrib__left,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ),
file('theBenchmark.p',fact_min__add__distrib__left) ).
fof(fact_min__diff__distrib__left,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)) ),
file('theBenchmark.p',fact_min__diff__distrib__left) ).
fof(fact_min__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_min__Suc__Suc,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)),
file('theBenchmark.p',fact_min__Suc__Suc) ).
fof(fact_min__diff,axiom,
! [V_n,V_i,V_m] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_i)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_i)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m),V_n)),V_i),
file('theBenchmark.p',fact_min__diff) ).
fof(fact_min__of__mono,axiom,
! [V_na_2,V_m_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Olinorder(T_b)
& class_Orderings_Olinorder(T_c) )
=> ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,V_na_2)) = hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_m_2),V_na_2)) ) ),
file('theBenchmark.p',fact_min__of__mono) ).
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_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_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_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_divmod__nat__rel__def,axiom,
! [V_qr_2,V_na_2,V_m_2] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_na_2),V_qr_2))
<=> ( ( V_na_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_na_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_na_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_na_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_na_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_na_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_na_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_min__Suc2,axiom,
! [V_na_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_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_na_2)),V_m_2),
file('theBenchmark.p',fact_min__Suc2) ).
fof(fact_min__Suc1,axiom,
! [V_m_2,V_na_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_na_2)),V_m_2),
file('theBenchmark.p',fact_min__Suc1) ).
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_min__ord__min,axiom,
! [T_b] :
( class_Orderings_Oord(T_b)
=> c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ),
file('theBenchmark.p',fact_min__ord__min) ).
fof(fact_prod_Orecs,axiom,
! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Product__Type_Oprod_Oprod__rec(T_c,T_d,T_b,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
file('theBenchmark.p',fact_prod_Orecs) ).
fof(fact_max__number__of__Suc,axiom,
! [V_v_2,V_na_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_na_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_na_2)),c_Int_Onat)))),
file('theBenchmark.p',fact_max__number__of__Suc) ).
fof(fact_max__Suc__number__of,axiom,
! [V_na_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_na_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_na_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_na_2)))),
file('theBenchmark.p',fact_max__Suc__number__of) ).
fof(fact_apsnd__apfst,axiom,
! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_e,T_d),V_x_2))),
file('theBenchmark.p',fact_apsnd__apfst) ).
fof(fact_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_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_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_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_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_le__max__iff__disj,axiom,
! [V_y_2,V_x_2,V_z_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2)) ) ) ),
file('theBenchmark.p',fact_le__max__iff__disj) ).
fof(fact_min__max_Ole__supE,axiom,
! [V_x,V_b,V_a,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ),
file('theBenchmark.p',fact_min__max_Ole__supE) ).
fof(fact_min__max_Osup__mono,axiom,
! [V_d,V_b,V_c,V_a,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_c),V_d))) ) ) ),
file('theBenchmark.p',fact_min__max_Osup__mono) ).
fof(fact_min__max_Osup__least,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x)) ) ) ),
file('theBenchmark.p',fact_min__max_Osup__least) ).
fof(fact_min__max_Ole__supI,axiom,
! [V_b,V_x,V_a,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) ) ) ),
file('theBenchmark.p',fact_min__max_Ole__supI) ).
fof(fact_min__max_Osup__absorb1,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ),
file('theBenchmark.p',fact_min__max_Osup__absorb1) ).
fof(fact_min__max_Osup__absorb2,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ),
file('theBenchmark.p',fact_min__max_Osup__absorb2) ).
fof(fact_min__max_Ole__supI2,axiom,
! [V_a,V_b,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ),
file('theBenchmark.p',fact_min__max_Ole__supI2) ).
fof(fact_min__max_Ole__supI1,axiom,
! [V_b,V_a,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ),
file('theBenchmark.p',fact_min__max_Ole__supI1) ).
fof(fact_min__max_Ole__sup__iff,axiom,
! [V_z_2,V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ),
file('theBenchmark.p',fact_min__max_Ole__sup__iff) ).
fof(fact_min__max_Ole__iff__sup,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ),
file('theBenchmark.p',fact_min__max_Ole__iff__sup) ).
fof(fact_le__maxI2,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Olinorder(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ),
file('theBenchmark.p',fact_le__maxI2) ).
fof(fact_le__maxI1,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ),
file('theBenchmark.p',fact_le__maxI1) ).
fof(fact_less__max__iff__disj,axiom,
! [V_y_2,V_x_2,V_z_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) ) ) ),
file('theBenchmark.p',fact_less__max__iff__disj) ).
fof(fact_max__less__iff__conj,axiom,
! [V_z_2,V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) ) ) ),
file('theBenchmark.p',fact_max__less__iff__conj) ).
fof(fact_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_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_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_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_max__0R,axiom,
! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n,
file('theBenchmark.p',fact_max__0R) ).
fof(fact_max__0L,axiom,
! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n,
file('theBenchmark.p',fact_max__0L) ).
fof(fact_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_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__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__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_max__of__mono,axiom,
! [V_na_2,V_m_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Olinorder(T_b)
& class_Orderings_Olinorder(T_c) )
=> ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,V_na_2)) = hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_m_2),V_na_2)) ) ),
file('theBenchmark.p',fact_max__of__mono) ).
fof(fact_apfst__conv,axiom,
! [V_y_2,V_x_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_x_2)),V_y_2),
file('theBenchmark.p',fact_apfst__conv) ).
fof(fact_apfst__eq__conv,axiom,
! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
( hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2)
<=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) ),
file('theBenchmark.p',fact_apfst__eq__conv) ).
fof(fact_fst__apfst,axiom,
! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)),
file('theBenchmark.p',fact_fst__apfst) ).
fof(fact_snd__apfst,axiom,
! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_d,T_b),V_x_2),
file('theBenchmark.p',fact_snd__apfst) ).
fof(fact_max__number__of,axiom,
! [V_v,V_u,T_b] :
( ( class_Orderings_Oord(T_b)
& class_Int_Onumber(T_b) )
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_u)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v) ) ) ),
file('theBenchmark.p',fact_max__number__of) ).
fof(fact_min__max_Odistrib__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_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__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_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_apsnd__apfst__commute,axiom,
! [V_p_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,V_g_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_e,V_f_2),V_p_2)),
file('theBenchmark.p',fact_apsnd__apfst__commute) ).
fof(fact_max__Suc1,axiom,
! [V_m_2,V_na_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_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_na_2)),V_m_2),
file('theBenchmark.p',fact_max__Suc1) ).
fof(fact_max__Suc2,axiom,
! [V_na_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_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_na_2)),V_m_2),
file('theBenchmark.p',fact_max__Suc2) ).
fof(fact_apfst__apsnd,axiom,
! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2))),
file('theBenchmark.p',fact_apfst__apsnd) ).
fof(fact_dual__min,axiom,
! [T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Orderings_Oord_Omin(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omax(T_b) ),
file('theBenchmark.p',fact_dual__min) ).
fof(fact_max__ord__max,axiom,
! [T_b] :
( class_Orderings_Oord(T_b)
=> c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ),
file('theBenchmark.p',fact_max__ord__max) ).
fof(fact_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_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_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_iterate_Osimps,axiom,
! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_b,tc_prod(T_c,T_b)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_c,T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_f_2)) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2) ) ),
file('theBenchmark.p',fact_iterate_Osimps) ).
fof(fact_scomp__scomp,axiom,
! [V_h_2,V_g_2,V_f_2,T_g,T_f,T_c,T_e,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_e,T_c),hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,tc_prod(T_d,T_e)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,T_c),V_f_2),hAPP(hAPP(c_COMBC(T_f,tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_g,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),T_f),c_Product__Type_Oscomp(T_g,T_d,T_e,T_c)),V_g_2)),V_h_2)),
file('theBenchmark.p',fact_scomp__scomp) ).
fof(fact_scomp__Pair,axiom,
! [V_x_2,T_d,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,tc_prod(T_c,T_d)),V_x_2),c_Product__Type_OPair(T_c,T_d)) = V_x_2,
file('theBenchmark.p',fact_scomp__Pair) ).
fof(fact_Pair__scomp,axiom,
! [V_f_2,V_x_2,T_c,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_b,T_c),hAPP(c_Product__Type_OPair(T_d,T_b),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2),
file('theBenchmark.p',fact_Pair__scomp) ).
fof(fact_scomp__apply,axiom,
! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)),
file('theBenchmark.p',fact_scomp__apply) ).
fof(fact_scomp__def,axiom,
! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)),
file('theBenchmark.p',fact_scomp__def) ).
fof(fact_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_dual__max,axiom,
! [T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Orderings_Oord_Omax(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omin(T_b) ),
file('theBenchmark.p',fact_dual__max) ).
fof(fact_scomp__unfold,axiom,
! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_e),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_d,T_e),hAPP(V_f_2,V_x_2))),
file('theBenchmark.p',fact_scomp__unfold) ).
fof(fact_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_norm__frac_Opinduct,axiom,
! [V_P_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_P_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_P_2,B_a),B_b)) ) )
=> hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
file('theBenchmark.p',fact_norm__frac_Opinduct) ).
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_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_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_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_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_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_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_INF1__iff,axiom,
! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ),
file('theBenchmark.p',fact_INF1__iff) ).
fof(fact_rev__predicate1D,axiom,
! [V_Q_2,T_b,V_x_2,V_P_2] :
( hBOOL(hAPP(V_P_2,V_x_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
=> hBOOL(hAPP(V_Q_2,V_x_2)) ) ),
file('theBenchmark.p',fact_rev__predicate1D) ).
fof(fact_predicate1D,axiom,
! [V_x_2,V_Q_2,V_P_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
=> ( hBOOL(hAPP(V_P_2,V_x_2))
=> hBOOL(hAPP(V_Q_2,V_x_2)) ) ),
file('theBenchmark.p',fact_predicate1D) ).
fof(fact_rev__predicate2D,axiom,
! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_P_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2))
=> hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_rev__predicate2D) ).
fof(fact_predicate2D,axiom,
! [V_y_2,V_x_2,V_Q_2,V_P_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2))
=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_predicate2D) ).
fof(fact_nat__gcd_Opinduct,axiom,
! [V_P_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_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
=> hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
=> hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
file('theBenchmark.p',fact_nat__gcd_Opinduct) ).
fof(fact_Nitpick_Oplus__frac__def,axiom,
! [V_r_2,V_q_2,T_b] : c_Nitpick_Oplus__frac(T_b,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_b),V_q_2),hAPP(c_Nitpick_Odenom(T_b),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_b),tc_Int_Oint),c_Nitpick_Ofrac(T_b)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_q_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_q_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_r_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_r_2)))))),c_COMBI(tc_Int_Oint))),
file('theBenchmark.p',fact_Nitpick_Oplus__frac__def) ).
fof(fact_internal__split__def,axiom,
! [T_d,T_c,T_b] : c_Product__Type_Ointernal__split(T_b,T_c,T_d) = c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),
file('theBenchmark.p',fact_internal__split__def) ).
fof(fact_bool_Osize_I2_J,axiom,
c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_bool_Osize_I2_J) ).
fof(fact_bool_Osize_I1_J,axiom,
c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_bool_Osize_I1_J) ).
fof(fact_internal__split__conv,axiom,
! [V_b_2,V_a_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2),
file('theBenchmark.p',fact_internal__split__conv) ).
fof(fact_Nitpick_Otimes__frac__def,axiom,
! [V_r,V_q,T_a] : c_Nitpick_Otimes__frac(T_a,V_q,V_r) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_r))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Odenom(T_a),V_r))),
file('theBenchmark.p',fact_Nitpick_Otimes__frac__def) ).
fof(fact_Nitpick_Oof__frac__def,axiom,
! [V_q,T_a,T_b] :
( ( class_Rings_Oring__1(T_b)
& class_Rings_Oinverse(T_b) )
=> c_Nitpick_Oof__frac(T_a,T_b,V_q) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Nitpick_Odenom(T_a),V_q))) ),
file('theBenchmark.p',fact_Nitpick_Oof__frac__def) ).
fof(fact_Nitpick_Oinverse__frac__def,axiom,
! [V_q,T_a] : c_Nitpick_Oinverse__frac(T_a,V_q) = hAPP(hAPP(c_Nitpick_Ofrac(T_a),hAPP(c_Nitpick_Odenom(T_a),V_q)),hAPP(c_Nitpick_Onum(T_a),V_q)),
file('theBenchmark.p',fact_Nitpick_Oinverse__frac__def) ).
fof(fact_Nitpick_Ouminus__frac__def,axiom,
! [V_q,T_a] : c_Nitpick_Ouminus__frac(T_a,V_q) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Nitpick_Odenom(T_a),V_q))),
file('theBenchmark.p',fact_Nitpick_Ouminus__frac__def) ).
fof(fact_Nitpick_Oless__frac__def,axiom,
! [V_r_2,V_q_2,T_b] :
( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('theBenchmark.p',fact_Nitpick_Oless__frac__def) ).
fof(fact_Nitpick_Oless__eq__frac__def,axiom,
! [V_r_2,V_q_2,T_b] :
( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('theBenchmark.p',fact_Nitpick_Oless__eq__frac__def) ).
fof(fact_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_pair__box_Osize_I1_J,axiom,
! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__size(T_b,T_c,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_pair__box_Osize_I1_J) ).
fof(fact_The__split,axiom,
! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))),
file('theBenchmark.p',fact_The__split) ).
fof(fact_Random_Osimps,axiom,
! [V_size_2,V_g_2,T_b,V_nrandom_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
=> c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(V_g_2,V_size_2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_b,V_g_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_size_2))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_b)),c_Product__Type_Ofst(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
=> c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) ) ),
file('theBenchmark.p',fact_Random_Osimps) ).
fof(fact_pair__box_Oinject,axiom,
! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
( c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2)
<=> ( V_b_2 = V_b_H_2
& V_a_2 = V_a_H_2 ) ),
file('theBenchmark.p',fact_pair__box_Oinject) ).
fof(fact_The__split__eq,axiom,
! [V_y_2,V_x_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2),
file('theBenchmark.p',fact_The__split__eq) ).
fof(fact_split__paired__The,axiom,
! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_P_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))),
file('theBenchmark.p',fact_split__paired__The) ).
fof(fact_divmod__nat__def,axiom,
! [V_na_2,V_m_2] : c_Divides_Odivmod__nat(V_m_2,V_na_2) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(V_m_2,V_na_2)),
file('theBenchmark.p',fact_divmod__nat__def) ).
fof(fact_Random__Sequence_Oempty__def,axiom,
! [V_size_2,V_nrandom_2,T_b] : c_Random__Sequence_Oempty(T_b,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)),
file('theBenchmark.p',fact_Random__Sequence_Oempty__def) ).
fof(fact_Random__Sequence_Osingle__def,axiom,
! [V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_b),V_x_2),V_nrandom_2),V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_b),V_x_2)),
file('theBenchmark.p',fact_Random__Sequence_Osingle__def) ).
fof(fact_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_Osimps_I2_J,axiom,
! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__case(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
file('theBenchmark.p',fact_pair__box_Osimps_I2_J) ).
fof(fact_pair__box_Orecs,axiom,
! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__rec(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
file('theBenchmark.p',fact_pair__box_Orecs) ).
fof(fact_the__eq__trivial,axiom,
! [V_a_2,T_b] : c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2,
file('theBenchmark.p',fact_the__eq__trivial) ).
fof(fact_the__sym__eq__trivial,axiom,
! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2,
file('theBenchmark.p',fact_the__sym__eq__trivial) ).
fof(fact_exE__realizer,axiom,
! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_P_2] :
( hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2)))
=> ( ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(V_P_2,B_y),B_x))
=> hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
=> hBOOL(hAPP(V_Q_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2))) ) ),
file('theBenchmark.p',fact_exE__realizer) ).
fof(fact_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_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_Code__Numeral_Oof__nat__inject,axiom,
! [V_m_2,V_na_2] :
( hAPP(c_Code__Numeral_Oof__nat,V_na_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
<=> V_na_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_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_zero__code__numeral__def,axiom,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_zero__code__numeral__def) ).
fof(fact_one__code__numeral__def,axiom,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('theBenchmark.p',fact_one__code__numeral__def) ).
fof(fact_less__code__numeral__code,axiom,
! [V_m_2,V_na_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_na_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) ),
file('theBenchmark.p',fact_less__code__numeral__code) ).
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_na_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_na_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_m_2)) ),
file('theBenchmark.p',fact_less__eq__code__numeral__code) ).
fof(fact_subtract__code__numeral__code,axiom,
! [V_m,V_n] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),
file('theBenchmark.p',fact_subtract__code__numeral__code) ).
fof(fact_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_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_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_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_New__DSequence_Opos__decr__bind__def,axiom,
! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
( ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) )
& ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_b) ) ),
file('theBenchmark.p',fact_New__DSequence_Opos__decr__bind__def) ).
fof(fact_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_nat__of__of__nat,axiom,
! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n,
file('theBenchmark.p',fact_nat__of__of__nat) ).
fof(fact_of__nat__nat__of,axiom,
! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k,
file('theBenchmark.p',fact_of__nat__nat__of) ).
fof(fact_nat__of__inverse,axiom,
! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x,
file('theBenchmark.p',fact_nat__of__inverse) ).
fof(fact_less__code__numeral__def,axiom,
! [V_m_2,V_na_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_na_2),V_m_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_na_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) ),
file('theBenchmark.p',fact_less__code__numeral__def) ).
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_less__eq__code__numeral__def,axiom,
! [V_m_2,V_na_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_na_2),V_m_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_na_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_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_New__Random__Sequence_Opos__decr__bind__def,axiom,
! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Opos__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
file('theBenchmark.p',fact_New__Random__Sequence_Opos__decr__bind__def) ).
fof(fact_New__DSequence_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_New__DSequence_Opos__bind__def,axiom,
! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Opos__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)),
file('theBenchmark.p',fact_New__DSequence_Opos__bind__def) ).
fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
( ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)) )
& ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_b) ) ),
file('theBenchmark.p',fact_New__DSequence_Oneg__decr__bind__def) ).
fof(fact_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_pos__empty__def,axiom,
! [V_seed_2,V_size_2,V_nrandom_2,T_b] : c_New__Random__Sequence_Opos__empty(T_b,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_b),
file('theBenchmark.p',fact_pos__empty__def) ).
fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Oneg__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
file('theBenchmark.p',fact_New__Random__Sequence_Oneg__decr__bind__def) ).
fof(fact_pos__bind__def,axiom,
! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
file('theBenchmark.p',fact_pos__bind__def) ).
fof(fact_New__DSequence_Oneg__bind__def,axiom,
! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Oneg__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)),
file('theBenchmark.p',fact_New__DSequence_Oneg__bind__def) ).
fof(fact_curry__def,axiom,
! [V_y_2,V_x_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_c_2),V_x_2),V_y_2) = hAPP(V_c_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),
file('theBenchmark.p',fact_curry__def) ).
fof(fact_curryI,axiom,
! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
=> hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ),
file('theBenchmark.p',fact_curryI) ).
fof(fact_curryE,axiom,
! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
=> hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
file('theBenchmark.p',fact_curryE) ).
fof(fact_curryD,axiom,
! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
=> hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
file('theBenchmark.p',fact_curryD) ).
fof(fact_curry__conv,axiom,
! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_f_2),V_a_2),V_b_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),
file('theBenchmark.p',fact_curry__conv) ).
fof(fact_split__curry,axiom,
! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),c_Product__Type_Ocurry(T_b,T_c,T_d,V_f_2)) = V_f_2,
file('theBenchmark.p',fact_split__curry) ).
fof(fact_curry__split,axiom,
! [V_f_2,T_d,T_c,T_b] : c_Product__Type_Ocurry(T_b,T_c,T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)) = V_f_2,
file('theBenchmark.p',fact_curry__split) ).
fof(fact_neg__bind__def,axiom,
! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
file('theBenchmark.p',fact_neg__bind__def) ).
fof(fact_Powp__def,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
=> hBOOL(hAPP(V_A_2,B_x)) ) ),
file('theBenchmark.p',fact_Powp__def) ).
fof(fact_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__mult__cancel1,axiom,
! [V_na_2,V_m_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_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_na_2)),V_m_2))
<=> V_na_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel1) ).
fof(fact_dvd__mult__cancel2,axiom,
! [V_na_2,V_m_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_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_na_2),V_m_2)),V_m_2))
<=> V_na_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel2) ).
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__abs__iff,axiom,
! [V_k_2,V_m_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ),
file('theBenchmark.p',fact_dvd__abs__iff) ).
fof(fact_abs__dvd__iff,axiom,
! [V_k_2,V_m_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ),
file('theBenchmark.p',fact_abs__dvd__iff) ).
fof(fact_dvd__if__abs__eq,axiom,
! [V_k,V_l,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k)) ) ),
file('theBenchmark.p',fact_dvd__if__abs__eq) ).
fof(fact_div__dvd__div,axiom,
! [V_c_2,V_b_2,V_a_2,T_b] :
( class_Divides_Osemiring__div(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_c_2),V_a_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2)) ) ) ) ),
file('theBenchmark.p',fact_div__dvd__div) ).
fof(fact_one__dvd,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) ),
file('theBenchmark.p',fact_one__dvd) ).
fof(fact_dvd__minus__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Rings_Ocomm__ring__1(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_dvd__minus__iff) ).
fof(fact_minus__dvd__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Rings_Ocomm__ring__1(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_minus__dvd__iff) ).
fof(fact_dvd__mod__iff,axiom,
! [V_m_2,V_na_2,V_k_2,T_b] :
( class_Divides_Osemiring__div(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_na_2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_na_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ),
file('theBenchmark.p',fact_dvd__mod__iff) ).
fof(fact_mod__mod__cancel,axiom,
! [V_a,V_b,V_c,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
=> c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,V_a,V_c) ) ),
file('theBenchmark.p',fact_mod__mod__cancel) ).
fof(fact_dvd__mod,axiom,
! [V_n,V_m,V_k,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ),
file('theBenchmark.p',fact_dvd__mod) ).
fof(fact_dvd__mod__imp__dvd,axiom,
! [V_n,V_m,V_k,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ),
file('theBenchmark.p',fact_dvd__mod__imp__dvd) ).
fof(fact_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_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(fact_dvd_Oless__asym_H,axiom,
! [V_b,V_a] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) )
=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ),
file('theBenchmark.p',fact_dvd_Oless__asym_H) ).
fof(fact_dvd_Oless__le__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_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__le__trans) ).
fof(fact_dvd_Oord__less__eq__trans,axiom,
! [V_c,V_b,V_a] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) )
=> ( V_b = V_c
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ),
file('theBenchmark.p',fact_dvd_Oord__less__eq__trans) ).
fof(fact_dvd_Oless__imp__not__eq2,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)) )
=> V_y != V_x ),
file('theBenchmark.p',fact_dvd_Oless__imp__not__eq2) ).
fof(fact_dvd_Oless__imp__not__eq,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)) )
=> V_x != V_y ),
file('theBenchmark.p',fact_dvd_Oless__imp__not__eq) ).
fof(fact_dvd_Oless__imp__not__less,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__imp__not__less) ).
fof(fact_dvd_Oless__imp__le,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)) ),
file('theBenchmark.p',fact_dvd_Oless__imp__le) ).
fof(fact_dvd_Oless__not__sym,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__not__sym) ).
fof(fact_dvd_Oless__imp__neq,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)) )
=> V_x != V_y ),
file('theBenchmark.p',fact_dvd_Oless__imp__neq) ).
fof(fact_dvd_Ole__less__trans,axiom,
! [V_z,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_Ole__less__trans) ).
fof(fact_dvd_Oord__eq__less__trans,axiom,
! [V_c,V_b,V_a] :
( V_a = V_b
=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c)) )
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ),
file('theBenchmark.p',fact_dvd_Oord__eq__less__trans) ).
fof(fact_dvd_Oorder__trans,axiom,
! [V_z,V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ),
file('theBenchmark.p',fact_dvd_Oorder__trans) ).
fof(fact_dvd_Oantisym,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
=> V_x = V_y ) ),
file('theBenchmark.p',fact_dvd_Oantisym) ).
fof(fact_dvd__antisym,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
=> V_m = V_n ) ),
file('theBenchmark.p',fact_dvd__antisym) ).
fof(fact_dvd_Oord__le__eq__trans,axiom,
! [V_c,V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
=> ( V_b = V_c
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ),
file('theBenchmark.p',fact_dvd_Oord__le__eq__trans) ).
fof(fact_dvd_Oord__eq__le__trans,axiom,
! [V_c,V_b,V_a] :
( V_a = V_b
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ),
file('theBenchmark.p',fact_dvd_Oord__eq__le__trans) ).
fof(fact_dvd_Ole__neq__trans,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
=> ( V_a != V_b
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_dvd_Ole__neq__trans) ).
fof(fact_dvd_Ole__imp__less__or__eq,axiom,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
=> ( V_x = V_y
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ),
file('theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).
fof(fact_dvd_Oantisym__conv,axiom,
! [V_x_2,V_y_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_dvd_Oantisym__conv) ).
fof(fact_dvd_Oeq__refl,axiom,
! [V_y,V_x] :
( V_x = V_y
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
file('theBenchmark.p',fact_dvd_Oeq__refl) ).
fof(fact_dvd_Oneq__le__trans,axiom,
! [V_b,V_a] :
( V_a != V_b
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_dvd_Oneq__le__trans) ).
fof(fact_dvd_Oless__le,axiom,
! [V_y_2,V_x_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
<=> ( V_x_2 != V_y_2
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_dvd_Oless__le) ).
fof(fact_dvd_Ole__less,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
<=> ( V_x_2 = V_y_2
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_dvd_Ole__less) ).
fof(fact_dvd_Oeq__iff,axiom,
! [V_y_2,V_x_2] :
( V_x_2 = V_y_2
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_dvd_Oeq__iff) ).
fof(fact_dvd__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__diff,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Rings_Ocomm__ring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z))) ) ) ),
file('theBenchmark.p',fact_dvd__diff) ).
fof(fact_dvd__add,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),V_c))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ),
file('theBenchmark.p',fact_dvd__add) ).
fof(fact_dvd__power__same,axiom,
! [V_n,V_y,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))) ) ),
file('theBenchmark.p',fact_dvd__power__same) ).
fof(fact_dvd__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__reduce,axiom,
! [V_na_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_na_2)) ),
file('theBenchmark.p',fact_dvd__reduce) ).
fof(fact_dvd__diff__nat,axiom,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))) ) ),
file('theBenchmark.p',fact_dvd__diff__nat) ).
fof(fact_nat__dvd__1__iff__1,axiom,
! [V_m_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
<=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
file('theBenchmark.p',fact_nat__dvd__1__iff__1) ).
fof(fact_dvd__mult__cancel__left,axiom,
! [V_b_2,V_a_2,V_c_2,T_b] :
( class_Rings_Oidom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
| V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel__left) ).
fof(fact_dvd__mult__cancel__right,axiom,
! [V_b_2,V_c_2,V_a_2,T_b] :
( class_Rings_Oidom(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
| V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel__right) ).
fof(fact_dvd__eq__mod__eq__0,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Divides_Osemiring__div(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
<=> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_dvd__eq__mod__eq__0) ).
fof(fact_dvd__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_div__add,axiom,
! [V_y,V_x,V_z,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_z)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_y),V_z)) ) ) ),
file('theBenchmark.p',fact_div__add) ).
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__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_le__imp__power__dvd,axiom,
! [V_a,V_n,V_m,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
file('theBenchmark.p',fact_le__imp__power__dvd) ).
fof(fact_dvd__power__le,axiom,
! [V_m,V_n,V_y,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m))) ) ) ),
file('theBenchmark.p',fact_dvd__power__le) ).
fof(fact_power__le__dvd,axiom,
! [V_m,V_b,V_n,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_b))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_b)) ) ) ),
file('theBenchmark.p',fact_power__le__dvd) ).
fof(fact_div__power,axiom,
! [V_n,V_x,V_y,T_a] :
( class_Divides_Osemiring__div(T_a)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)) ) ),
file('theBenchmark.p',fact_div__power) ).
fof(fact_dvd__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_nat__dvd__not__less,axiom,
! [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),V_m),V_n))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) ) ),
file('theBenchmark.p',fact_nat__dvd__not__less) ).
fof(fact_nat__mult__dvd__cancel__disj,axiom,
! [V_na_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_na_2)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_na_2))
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
fof(fact_dvd__diffD,axiom,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ),
file('theBenchmark.p',fact_dvd__diffD) ).
fof(fact_dvd__diffD1,axiom,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ),
file('theBenchmark.p',fact_dvd__diffD1) ).
fof(fact_unity__coeff__ex,axiom,
! [V_l_2,V_P_2,T_b] :
( ( class_Rings_Osemiring__0(T_b)
& class_Rings_Odvd(T_b) )
=> ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
<=> ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b)))) ) ) ),
file('theBenchmark.p',fact_unity__coeff__ex) ).
fof(fact_inf__period_I3_J,axiom,
! [V_t_2,V_D_2,V_d_2,T_b] :
( ( class_Rings_Odvd(T_b)
& class_Rings_Ocomm__ring(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
=> ! [B_x,B_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ),
file('theBenchmark.p',fact_inf__period_I3_J) ).
fof(fact_inf__period_I4_J,axiom,
! [V_t_2,V_D_2,V_d_2,T_b] :
( ( class_Rings_Odvd(T_b)
& class_Rings_Ocomm__ring(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
=> ! [B_x,B_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ),
file('theBenchmark.p',fact_inf__period_I4_J) ).
fof(fact_dvd__eq__mod__eq__0__number__of,axiom,
! [V_y_2,V_x_2,T_b] :
( ( class_Int_Onumber(T_b)
& class_Divides_Osemiring__div(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
<=> c_Divides_Odiv__class_Omod(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_dvd__eq__mod__eq__0__number__of) ).
fof(fact_dvd__div__eq__mult,axiom,
! [V_c_2,V_b_2,V_a_2,T_b] :
( class_Divides_Osemiring__div(T_b)
=> ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
=> ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_c_2
<=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),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_b] :
( class_Divides_Osemiring__div(T_b)
=> ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_c_2),V_d_2))
=> ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_c_2)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) ) ) ) ) ) ),
file('theBenchmark.p',fact_dvd__div__div__eq__mult) ).
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_na_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_na_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_na_2)) ) ),
file('theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
fof(fact_Powp__mono,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_b,V_A_2)),c_Predicate_OPowp(T_b,V_B_2))) ),
file('theBenchmark.p',fact_Powp__mono) ).
fof(fact_dvd__power,axiom,
! [V_x,V_n,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( ( V_x = c_Groups_Oone__class_Oone(T_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_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ) ),
file('theBenchmark.p',fact_dvd__power) ).
fof(fact_dvd_Ostrict__monoD,axiom,
! [V_y_2,V_x_2,V_f_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ),
file('theBenchmark.p',fact_dvd_Ostrict__monoD) ).
fof(fact_dvd_OmonoD,axiom,
! [V_y_2,V_x_2,V_f_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ),
file('theBenchmark.p',fact_dvd_OmonoD) ).
fof(fact_nat__dvd__iff,axiom,
! [V_m_2,V_z_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_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_z_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_z_2))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) ) ) ),
file('theBenchmark.p',fact_nat__dvd__iff) ).
fof(fact_int__dvd__iff,axiom,
! [V_z_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)))) ),
file('theBenchmark.p',fact_int__dvd__iff) ).
fof(fact_dvd__int__iff,axiom,
! [V_m_2,V_z_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2))),V_m_2)) ),
file('theBenchmark.p',fact_dvd__int__iff) ).
fof(fact_zdvd__zdiffD,axiom,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),V_n)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ),
file('theBenchmark.p',fact_zdvd__zdiffD) ).
fof(fact_uminus__dvd__conv_I2_J,axiom,
! [V_t_2,V_d_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_t_2))) ),
file('theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).
fof(fact_uminus__dvd__conv_I1_J,axiom,
! [V_t_2,V_d_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d_2)),V_t_2)) ),
file('theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).
fof(fact_zdvd__zmod,axiom,
! [V_n,V_m,V_f] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_m))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_n))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))) ) ),
file('theBenchmark.p',fact_zdvd__zmod) ).
fof(fact_zdvd__zmod__imp__zdvd,axiom,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m)) ) ),
file('theBenchmark.p',fact_zdvd__zmod__imp__zdvd) ).
fof(fact_zdvd__antisym__abs,axiom,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_b),V_a))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_a) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_b) ) ),
file('theBenchmark.p',fact_zdvd__antisym__abs) ).
fof(fact_zdvd__antisym__nonneg,axiom,
! [V_n,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_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
=> V_m = V_n ) ) ) ),
file('theBenchmark.p',fact_zdvd__antisym__nonneg) ).
fof(fact_zdvd__not__zless,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_m),V_n))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) ) ),
file('theBenchmark.p',fact_zdvd__not__zless) ).
fof(fact_zdvd__mult__cancel,axiom,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n)))
=> ( V_k != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n)) ) ),
file('theBenchmark.p',fact_zdvd__mult__cancel) ).
fof(fact_zdvd__mono,axiom,
! [V_t_2,V_m_2,V_k_2] :
( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2))) ) ),
file('theBenchmark.p',fact_zdvd__mono) ).
fof(fact_zdvd__period,axiom,
! [V_c_2,V_t_2,V_x_2,V_d_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2))
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),V_t_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_c_2),V_d_2))),V_t_2))) ) ),
file('theBenchmark.p',fact_zdvd__period) ).
fof(fact_zdvd__reduce,axiom,
! [V_m_2,V_na_2,V_k_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_na_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2))))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_na_2)) ),
file('theBenchmark.p',fact_zdvd__reduce) ).
fof(fact_zdvd__int,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) ),
file('theBenchmark.p',fact_zdvd__int) ).
fof(fact_transfer__int__nat__relations_I4_J,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ),
file('theBenchmark.p',fact_transfer__int__nat__relations_I4_J) ).
fof(fact_zdvd__mult__div__cancel,axiom,
! [V_m,V_n] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_m),V_n)) = V_m ),
file('theBenchmark.p',fact_zdvd__mult__div__cancel) ).
fof(fact_zmod__eq__dvd__iff,axiom,
! [V_y_2,V_na_2,V_x_2] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,V_na_2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y_2,V_na_2)
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_na_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x_2),V_y_2))) ),
file('theBenchmark.p',fact_zmod__eq__dvd__iff) ).
fof(fact_zdvd1__eq,axiom,
! [V_x_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('theBenchmark.p',fact_zdvd1__eq) ).
fof(fact_abs__div,axiom,
! [V_x,V_y] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_y),V_x))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)) ),
file('theBenchmark.p',fact_abs__div) ).
fof(fact_dvd_Ostrict__mono__mono,axiom,
! [V_f_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)
=> c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ),
file('theBenchmark.p',fact_dvd_Ostrict__mono__mono) ).
fof(fact_zdvd__imp__le,axiom,
! [V_n,V_z] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z),V_n))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_n)) ) ),
file('theBenchmark.p',fact_zdvd__imp__le) ).
fof(fact_zdvd__iff__zmod__eq__0__number__of,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_y_2)))
<=> c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_x_2)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('theBenchmark.p',fact_zdvd__iff__zmod__eq__0__number__of) ).
fof(fact_dvd__imp__le__int,axiom,
! [V_d,V_i] :
( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d),V_i))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_d)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i))) ) ),
file('theBenchmark.p',fact_dvd__imp__le__int) ).
fof(fact_transfer__nat__int__relations_I4_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_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_transfer__nat__int__relations_I4_J) ).
fof(fact_zdvd__mult__cancel1,axiom,
! [V_na_2,V_m_2] :
( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_na_2)),V_m_2))
<=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_na_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_zdvd__mult__cancel1) ).
fof(fact_dvd_Ostrict__monoI,axiom,
! [V_f_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( ! [B_x,B_y] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_y),B_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) )
=> c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2) ) ),
file('theBenchmark.p',fact_dvd_Ostrict__monoI) ).
fof(fact_dvd_OmonoI,axiom,
! [V_f_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) )
=> c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ),
file('theBenchmark.p',fact_dvd_OmonoI) ).
fof(fact_arith__series__int,axiom,
! [V_na_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_na_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_na_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_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))),
file('theBenchmark.p',fact_arith__series__int) ).
fof(fact_mod__eqD,axiom,
! [V_r,V_d,V_m] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_d) = V_r
=> ? [B_q] : V_m = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B_q),V_d)) ),
file('theBenchmark.p',fact_mod__eqD) ).
fof(fact_nat__mod__eq__iff,axiom,
! [V_y_2,V_na_2,V_x_2] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,V_na_2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y_2,V_na_2)
<=> ? [B_q1,B_q2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_na_2),B_q1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_na_2),B_q2)) ),
file('theBenchmark.p',fact_nat__mod__eq__iff) ).
fof(fact_setsum__abs,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( class_Groups_Oordered__ab__group__add__abs(T_b)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ),
file('theBenchmark.p',fact_setsum__abs) ).
fof(fact_setsum__abs__ge__zero,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( class_Groups_Oordered__ab__group__add__abs(T_b)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ),
file('theBenchmark.p',fact_setsum__abs__ge__zero) ).
fof(fact_of__nat__setsum,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( class_Rings_Osemiring__1(T_b)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ),
file('theBenchmark.p',fact_of__nat__setsum) ).
fof(fact_setsum__commute,axiom,
! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_b),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))),V_A_2)),V_B_2) ),
file('theBenchmark.p',fact_setsum__commute) ).
fof(fact_setsum__lessThan__Suc,axiom,
! [V_na_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_2))),hAPP(V_f_2,V_na_2)) ),
file('theBenchmark.p',fact_setsum__lessThan__Suc) ).
fof(fact_of__int__setsum,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( class_Rings_Oring__1(T_b)
=> hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ),
file('theBenchmark.p',fact_of__int__setsum) ).
fof(fact_lessThan__eq__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_lessThan__eq__iff) ).
fof(fact_setsum__0,axiom,
! [V_A_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ),
file('theBenchmark.p',fact_setsum__0) ).
fof(fact_setsum__addf,axiom,
! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ),
file('theBenchmark.p',fact_setsum__addf) ).
fof(fact_setsum__product,axiom,
! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
( class_Rings_Osemiring__0(T_b)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_b),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,T_b)),T_c),c_COMBB(T_b,T_b,T_d)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ),
file('theBenchmark.p',fact_setsum__product) ).
fof(fact_setsum__left__distrib,axiom,
! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
( class_Rings_Osemiring__0(T_b)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_r_2)),V_A_2) ),
file('theBenchmark.p',fact_setsum__left__distrib) ).
fof(fact_setsum__right__distrib,axiom,
! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
( class_Rings_Osemiring__0(T_b)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2)),V_f_2)),V_A_2) ),
file('theBenchmark.p',fact_setsum__right__distrib) ).
fof(fact_setsum__subtractf,axiom,
! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
( class_Groups_Oab__group__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ),
file('theBenchmark.p',fact_setsum__subtractf) ).
fof(fact_setsum__negf,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( class_Groups_Oab__group__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) ),
file('theBenchmark.p',fact_setsum__negf) ).
fof(fact_setsum__divide__distrib,axiom,
! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
( class_Fields_Ofield(T_b)
=> hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_r_2)),V_A_2) ),
file('theBenchmark.p',fact_setsum__divide__distrib) ).
fof(fact_abs__setsum__abs,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( class_Groups_Oordered__ab__group__add__abs(T_b)
=> hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ),
file('theBenchmark.p',fact_abs__setsum__abs) ).
fof(fact_lessThan__subset__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_lessThan__subset__iff) ).
fof(fact_lessThan__strict__subset__iff,axiom,
! [V_na_2,V_m_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_na_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_na_2)) ) ),
file('theBenchmark.p',fact_lessThan__strict__subset__iff) ).
fof(fact_arith__series__general,axiom,
! [V_na_2,V_d_2,V_a_2,T_b] :
( class_Rings_Ocomm__semiring__1(T_b)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_b)),c_Nat_Osemiring__1__class_Oof__nat(T_b))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ),
file('theBenchmark.p',fact_arith__series__general) ).
fof(fact_arith__series__nat,axiom,
! [V_na_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_na_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_na_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_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_d_2)))),
file('theBenchmark.p',fact_arith__series__nat) ).
fof(fact_setsum__natinterval__difff,axiom,
! [V_f_2,V_na_2,V_m_2,T_b] :
( class_Groups_Oab__group__add(T_b)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_2)) = c_Groups_Ozero__class_Ozero(T_b) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
file('theBenchmark.p',fact_setsum__natinterval__difff) ).
fof(fact_gauss__sum,axiom,
! [V_na_2,T_b] :
( class_Rings_Ocomm__semiring__1(T_b)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_na_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)),c_Groups_Oone__class_Oone(T_b))) ),
file('theBenchmark.p',fact_gauss__sum) ).
fof(fact_geometric__sum,axiom,
! [V_na_2,V_x_2,T_b] :
( class_Fields_Ofield(T_b)
=> ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_Power_Opower__class_Opower(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),V_na_2)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_x_2),c_Groups_Oone__class_Oone(T_b))) ) ),
file('theBenchmark.p',fact_geometric__sum) ).
fof(fact_setsum__ub__add__nat,axiom,
! [V_p_2,V_f_2,V_na_2,V_m_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),V_p_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),V_p_2)))) ) ),
file('theBenchmark.p',fact_setsum__ub__add__nat) ).
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_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_atLeastLessThan__inj_I2_J,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_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_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_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_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_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_atLeast0LessThan,axiom,
! [V_na_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_2),
file('theBenchmark.p',fact_atLeast0LessThan) ).
fof(fact_atLeastatMost__subset__iff,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_atLeastatMost__subset__iff) ).
fof(fact_atLeastLessThan__subset__iff,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ),
file('theBenchmark.p',fact_atLeastLessThan__subset__iff) ).
fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
! [V_na_2,V_m_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_na_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_na_2)) ),
file('theBenchmark.p',fact_setsum__shift__bounds__Suc__ivl) ).
fof(fact_setsum__shift__bounds__nat__ivl,axiom,
! [V_na_2,V_k_2,V_m_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_na_2)) ),
file('theBenchmark.p',fact_setsum__shift__bounds__nat__ivl) ).
fof(fact_ivl__diff,axiom,
! [V_m_2,V_na_2,V_i_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_na_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_na_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_na_2),V_m_2) ) ),
file('theBenchmark.p',fact_ivl__diff) ).
fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
! [V_na_2,V_m_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_na_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_2)) ),
file('theBenchmark.p',fact_setsum__shift__bounds__cl__Suc__ivl) ).
fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
! [V_na_2,V_k_2,V_m_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_2)) ),
file('theBenchmark.p',fact_setsum__shift__bounds__cl__nat__ivl) ).
fof(fact_int__setsum,axiom,
! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2),
file('theBenchmark.p',fact_int__setsum) ).
fof(fact_setsum__add__nat__ivl,axiom,
! [V_f_2,V_p_2,V_na_2,V_m_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_p_2))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_na_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_na_2),V_p_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)) ) ) ),
file('theBenchmark.p',fact_setsum__add__nat__ivl) ).
fof(fact_setsum__diff__nat__ivl,axiom,
! [V_f_2,V_p_2,V_na_2,V_m_2,T_b] :
( class_Groups_Oab__group__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_p_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_na_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_na_2),V_p_2)) ) ) ),
file('theBenchmark.p',fact_setsum__diff__nat__ivl) ).
fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)),
file('theBenchmark.p',fact_transfer__nat__int__sum__prod2_I1_J) ).
fof(fact_atLeastatMost__psubset__iff,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ),
file('theBenchmark.p',fact_atLeastatMost__psubset__iff) ).
fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
! [V_k_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ),
file('theBenchmark.p',fact_setsum__shift__lb__Suc0__0__upt) ).
fof(fact_setsum__head__upt__Suc,axiom,
! [V_f_2,V_na_2,V_m_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_na_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_na_2))) ) ),
file('theBenchmark.p',fact_setsum__head__upt__Suc) ).
fof(fact_setsum__head__Suc,axiom,
! [V_f_2,V_na_2,V_m_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_na_2))) ) ),
file('theBenchmark.p',fact_setsum__head__Suc) ).
fof(fact_setsum__op__ivl__Suc,axiom,
! [V_f_2,V_m_2,V_na_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_na_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_na_2))),hAPP(V_f_2,V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_na_2))) = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_setsum__op__ivl__Suc) ).
fof(fact_setsum__cl__ivl__Suc,axiom,
! [V_f_2,V_m_2,V_na_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_na_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_na_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_na_2))) = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_setsum__cl__ivl__Suc) ).
fof(fact_all__nat__less,axiom,
! [V_P_2,V_na_2] :
( ! [B_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_na_2))
=> hBOOL(hAPP(V_P_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_na_2)))
=> hBOOL(hAPP(V_P_2,B_x)) ) ),
file('theBenchmark.p',fact_all__nat__less) ).
fof(fact_ex__nat__less,axiom,
! [V_P_2,V_na_2] :
( ? [B_m] :
( hBOOL(hAPP(V_P_2,B_m))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_na_2)) )
<=> ? [B_x] :
( hBOOL(hAPP(V_P_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_na_2))) ) ),
file('theBenchmark.p',fact_ex__nat__less) ).
fof(fact_all__nat__less__eq,axiom,
! [V_P_2,V_na_2] :
( ! [B_m] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_na_2))
=> hBOOL(hAPP(V_P_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_na_2)))
=> hBOOL(hAPP(V_P_2,B_x)) ) ),
file('theBenchmark.p',fact_all__nat__less__eq) ).
fof(fact_ex__nat__less__eq,axiom,
! [V_P_2,V_na_2] :
( ? [B_m] :
( hBOOL(hAPP(V_P_2,B_m))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_na_2)) )
<=> ? [B_x] :
( hBOOL(hAPP(V_P_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_na_2))) ) ),
file('theBenchmark.p',fact_ex__nat__less__eq) ).
fof(fact_sum__diff__distrib,axiom,
! [V_na_2,V_P_2,V_Q_2] :
( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_P_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_P_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Q_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_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_P_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_2)) ),
file('theBenchmark.p',fact_sum__diff__distrib) ).
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_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_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_periodic__finite__ex,axiom,
! [V_P_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_P_2,B_x))
<=> hBOOL(hAPP(V_P_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_P_2,B_x1))
<=> ? [B_x] :
( hBOOL(hAPP(V_P_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_bset_I9_J,axiom,
! [V_t_2,V_B_2,V_D_2,V_d_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),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_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ),
file('theBenchmark.p',fact_bset_I9_J) ).
fof(fact_aset_I9_J,axiom,
! [V_t_2,V_A_2,V_D_2,V_d_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),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_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ),
file('theBenchmark.p',fact_aset_I9_J) ).
fof(fact_bset_I10_J,axiom,
! [V_t_2,V_B_2,V_D_2,V_d_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),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_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ),
file('theBenchmark.p',fact_bset_I10_J) ).
fof(fact_aset_I10_J,axiom,
! [V_t_2,V_A_2,V_D_2,V_d_2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),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_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2))) ) ) ),
file('theBenchmark.p',fact_aset_I10_J) ).
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_image__mono,axiom,
! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ),
file('theBenchmark.p',fact_image__mono) ).
fof(fact_subset__image__iff,axiom,
! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
<=> ? [B_AA] :
( V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) ) ),
file('theBenchmark.p',fact_subset__image__iff) ).
fof(fact_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_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_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_image__image,axiom,
! [V_A_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_d,T_b,hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_f_2),V_g_2)),V_A_2),
file('theBenchmark.p',fact_image__image) ).
fof(fact_INT__simps_I10_J,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)),
file('theBenchmark.p',fact_INT__simps_I10_J) ).
fof(fact_INT__extend__simps_I10_J,axiom,
! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2),
file('theBenchmark.p',fact_INT__extend__simps_I10_J) ).
fof(fact_image__diff__subset,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))),
file('theBenchmark.p',fact_image__diff__subset) ).
fof(fact_image__uminus__atLeastAtMost,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__atLeastAtMost) ).
fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
! [V_A_2,V_f_2,T_b] :
( ( class_Groups_Ocomm__monoid__mult(T_b)
& class_Groups_Ocomm__monoid__add(T_b) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ),
file('theBenchmark.p',fact_transfer__nat__int__sum__prod_I1_J) ).
fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
! [V_na_2,V_m_2] :
( c_Nat__Transfer_Ois__nat(V_m_2)
=> ( c_Nat__Transfer_Ois__nat(V_na_2)
=> c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_m_2,V_na_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_na_2))) ) ),
file('theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__functions) ).
fof(fact_setsum__head,axiom,
! [V_P_2,V_na_2,V_m_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_na_2))) ) ),
file('theBenchmark.p',fact_setsum__head) ).
fof(fact_setsum__SucD,axiom,
! [V_na_2,V_A_2,V_f_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_na_2)
=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_setsum__SucD) ).
fof(fact_setsum__ivl__cong,axiom,
! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] :
( ( class_Orderings_Oord(T_b)
& class_Groups_Ocomm__monoid__add(T_c) )
=> ( V_a_2 = V_c_2
=> ( V_b_2 = V_d_2
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
=> hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) ) ) ) ),
file('theBenchmark.p',fact_setsum__ivl__cong) ).
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_image__uminus__greaterThan,axiom,
! [V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__greaterThan) ).
fof(fact_greaterThan__eq__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_greaterThan__eq__iff) ).
fof(fact_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_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_image__add__atLeastLessThan,axiom,
! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)),
file('theBenchmark.p',fact_image__add__atLeastLessThan) ).
fof(fact_image__add__atLeastAtMost,axiom,
! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_i_2,V_j_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)),
file('theBenchmark.p',fact_image__add__atLeastAtMost) ).
fof(fact_card__eq__setsum,axiom,
! [V_A_2,T_b] : hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2),
file('theBenchmark.p',fact_card__eq__setsum) ).
fof(fact_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_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_greaterThan__subset__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_greaterThan__subset__iff) ).
fof(fact_setsum__constant,axiom,
! [V_A_2,V_y_2,T_c,T_b] :
( class_Rings_Osemiring__1(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))),V_y_2) ),
file('theBenchmark.p',fact_setsum__constant) ).
fof(fact_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_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
! [V_na_2,V_m_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_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_na_2))),
file('theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I2_J) ).
fof(fact_image__uminus__atLeastLessThan,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__atLeastLessThan) ).
fof(fact_image__uminus__greaterThanAtMost,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__greaterThanAtMost) ).
fof(fact_image__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_image__uminus__lessThan,axiom,
! [V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__lessThan) ).
fof(fact_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_transfer__int__nat__sum__prod_I1_J,axiom,
! [V_f_2,V_A_2,T_b] :
( ( class_Groups_Ocomm__monoid__mult(T_b)
& class_Groups_Ocomm__monoid__add(T_b) )
=> ( c_Nat__Transfer_Onat__set(V_A_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ),
file('theBenchmark.p',fact_transfer__int__nat__sum__prod_I1_J) ).
fof(fact_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__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_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
! [V_na_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_na_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_na_2))),
file('theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I1_J) ).
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__eq__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_atMost__eq__iff) ).
fof(fact_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_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_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_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_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_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_atLeast0AtMost,axiom,
! [V_na_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_na_2) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_na_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_image__uminus__greaterThanLessThan,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__greaterThanLessThan) ).
fof(fact_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_atMost__subset__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_atMost__subset__iff) ).
fof(fact_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_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_Compl__atMost,axiom,
! [V_k_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2) ),
file('theBenchmark.p',fact_Compl__atMost) ).
fof(fact_Compl__greaterThan,axiom,
! [V_k_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2) ),
file('theBenchmark.p',fact_Compl__greaterThan) ).
fof(fact_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_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_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_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_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_setsum__atMost__Suc,axiom,
! [V_na_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_na_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_na_2))) ),
file('theBenchmark.p',fact_setsum__atMost__Suc) ).
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_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__cong_I1_J,axiom,
! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
( ( class_Groups_Ocomm__monoid__mult(T_b)
& class_Groups_Ocomm__monoid__add(T_b) )
=> ( V_A_2 = V_B_2
=> ( c_Nat__Transfer_Onat__set(V_B_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
=> hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ),
file('theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I1_J) ).
fof(fact_ivl__disj__un_I19_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I19_J) ).
fof(fact_ivl__disj__un_I18_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I18_J) ).
fof(fact_dvd_OatLeastatMost__psubset__iff,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_d_2))
& ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_d_2),V_b_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_c_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) ) )
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_dvd_OatLeastatMost__psubset__iff) ).
fof(fact_upto_Opinduct,axiom,
! [V_P_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_P_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_P_2,B_i),B_j)) ) )
=> hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
file('theBenchmark.p',fact_upto_Opinduct) ).
fof(fact_sup1E,axiom,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
=> ( ~ hBOOL(hAPP(V_A_2,V_x_2))
=> hBOOL(hAPP(V_B_2,V_x_2)) ) ),
file('theBenchmark.p',fact_sup1E) ).
fof(fact_sup1CI,axiom,
! [T_b,V_A_2,V_x_2,V_B_2] :
( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
=> hBOOL(hAPP(V_A_2,V_x_2)) )
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
file('theBenchmark.p',fact_sup1CI) ).
fof(fact_image__Un,axiom,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)),
file('theBenchmark.p',fact_image__Un) ).
fof(fact_Un__Diff,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
file('theBenchmark.p',fact_Un__Diff) ).
fof(fact_Un__Diff__cancel2,axiom,
! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2),
file('theBenchmark.p',fact_Un__Diff__cancel2) ).
fof(fact_Un__Diff__cancel,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
file('theBenchmark.p',fact_Un__Diff__cancel) ).
fof(fact_sup__max,axiom,
! [T_b] :
( ( class_Orderings_Olinorder(T_b)
& class_Lattices_Osemilattice__sup(T_b) )
=> c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ),
file('theBenchmark.p',fact_sup__max) ).
fof(fact_Un__absorb,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2,
file('theBenchmark.p',fact_Un__absorb) ).
fof(fact_Un__commute,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2),
file('theBenchmark.p',fact_Un__commute) ).
fof(fact_Un__left__absorb,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
file('theBenchmark.p',fact_Un__left__absorb) ).
fof(fact_Un__left__commute,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
file('theBenchmark.p',fact_Un__left__commute) ).
fof(fact_Un__assoc,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
file('theBenchmark.p',fact_Un__assoc) ).
fof(fact_bex__Un,axiom,
! [V_P_2,V_B_2,V_A_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
<=> ( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
| ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_bex__Un) ).
fof(fact_ball__Un,axiom,
! [V_P_2,V_B_2,V_A_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hBOOL(hAPP(V_P_2,B_x)) )
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
=> hBOOL(hAPP(V_P_2,B_x)) )
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(V_P_2,B_x)) ) ) ),
file('theBenchmark.p',fact_ball__Un) ).
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_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_c,T_b] :
( class_Lattices_Olattice(T_b)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ),
file('theBenchmark.p',fact_sup__apply) ).
fof(fact_sup__fun__def,axiom,
! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
( class_Lattices_Olattice(T_b)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ),
file('theBenchmark.p',fact_sup__fun__def) ).
fof(fact_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_sup1I1,axiom,
! [V_B_2,T_b,V_x_2,V_A_2] :
( hBOOL(hAPP(V_A_2,V_x_2))
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
file('theBenchmark.p',fact_sup1I1) ).
fof(fact_sup1I2,axiom,
! [V_A_2,T_b,V_x_2,V_B_2] :
( hBOOL(hAPP(V_B_2,V_x_2))
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
file('theBenchmark.p',fact_sup1I2) ).
fof(fact_le__supE,axiom,
! [V_x,V_b,V_a,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ),
file('theBenchmark.p',fact_le__supE) ).
fof(fact_sup__mono,axiom,
! [V_d,V_b,V_c,V_a,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_c),V_d))) ) ) ),
file('theBenchmark.p',fact_sup__mono) ).
fof(fact_sup__least,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x)) ) ) ),
file('theBenchmark.p',fact_sup__least) ).
fof(fact_le__supI,axiom,
! [V_b,V_x,V_a,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)) ) ) ),
file('theBenchmark.p',fact_le__supI) ).
fof(fact_sup__absorb1,axiom,
! [V_x,V_y,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ),
file('theBenchmark.p',fact_sup__absorb1) ).
fof(fact_sup__absorb2,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ),
file('theBenchmark.p',fact_sup__absorb2) ).
fof(fact_le__supI2,axiom,
! [V_a,V_b,V_x,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ),
file('theBenchmark.p',fact_le__supI2) ).
fof(fact_le__supI1,axiom,
! [V_b,V_a,V_x,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ),
file('theBenchmark.p',fact_le__supI1) ).
fof(fact_le__sup__iff,axiom,
! [V_z_2,V_y_2,V_x_2,T_b] :
( class_Lattices_Osemilattice__sup(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2)),V_z_2))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ),
file('theBenchmark.p',fact_le__sup__iff) ).
fof(fact_le__iff__sup,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Lattices_Osemilattice__sup(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ),
file('theBenchmark.p',fact_le__iff__sup) ).
fof(fact_sup__ge2,axiom,
! [V_x,V_y,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ),
file('theBenchmark.p',fact_sup__ge2) ).
fof(fact_inf__sup__ord_I4_J,axiom,
! [V_x,V_y,T_a] :
( class_Lattices_Olattice(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ),
file('theBenchmark.p',fact_inf__sup__ord_I4_J) ).
fof(fact_sup__ge1,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Osemilattice__sup(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ),
file('theBenchmark.p',fact_sup__ge1) ).
fof(fact_inf__sup__ord_I3_J,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ),
file('theBenchmark.p',fact_inf__sup__ord_I3_J) ).
fof(fact_Un__upper1,axiom,
! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),
file('theBenchmark.p',fact_Un__upper1) ).
fof(fact_Un__upper2,axiom,
! [V_A_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),
file('theBenchmark.p',fact_Un__upper2) ).
fof(fact_subset__Un__eq,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
<=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ),
file('theBenchmark.p',fact_subset__Un__eq) ).
fof(fact_Un__absorb1,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ),
file('theBenchmark.p',fact_Un__absorb1) ).
fof(fact_Un__absorb2,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ),
file('theBenchmark.p',fact_Un__absorb2) ).
fof(fact_Un__least,axiom,
! [V_B_2,V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ),
file('theBenchmark.p',fact_Un__least) ).
fof(fact_Un__mono,axiom,
! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ),
file('theBenchmark.p',fact_Un__mono) ).
fof(fact_mono__Un,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_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)),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ),
file('theBenchmark.p',fact_mono__Un) ).
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_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_INT__simps_I7_J,axiom,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
file('theBenchmark.p',fact_INT__simps_I7_J) ).
fof(fact_INT__simps_I6_J,axiom,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
file('theBenchmark.p',fact_INT__simps_I6_J) ).
fof(fact_INT__extend__simps_I7_J,axiom,
! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
file('theBenchmark.p',fact_INT__extend__simps_I7_J) ).
fof(fact_Un__INT__distrib,axiom,
! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)),
file('theBenchmark.p',fact_Un__INT__distrib) ).
fof(fact_INT__extend__simps_I6_J,axiom,
! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)),
file('theBenchmark.p',fact_INT__extend__simps_I6_J) ).
fof(fact_Un__INT__distrib2,axiom,
! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))),
file('theBenchmark.p',fact_Un__INT__distrib2) ).
fof(fact_mono__sup,axiom,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
( ( class_Lattices_Osemilattice__sup(T_b)
& class_Lattices_Osemilattice__sup(T_c) )
=> ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_A_2),V_B_2)))) ) ),
file('theBenchmark.p',fact_mono__sup) ).
fof(fact_ivl__disj__un_I17_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I17_J) ).
fof(fact_Diff__partition,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ),
file('theBenchmark.p',fact_Diff__partition) ).
fof(fact_Diff__subset__conv,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) ),
file('theBenchmark.p',fact_Diff__subset__conv) ).
fof(fact_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_ivl__disj__un_I20_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I20_J) ).
fof(fact_Compl__Diff__eq,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2),
file('theBenchmark.p',fact_Compl__Diff__eq) ).
fof(fact_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_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_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_min__max_Omono__sup,axiom,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Olinorder(T_b)
& class_Lattices_Osemilattice__sup(T_c) )
=> ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_A_2),V_B_2)))) ) ),
file('theBenchmark.p',fact_min__max_Omono__sup) ).
fof(fact_ivl__disj__un_I21_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I21_J) ).
fof(fact_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_ivl__disj__un_I8_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I8_J) ).
fof(fact_ivl__disj__un_I22_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I22_J) ).
fof(fact_ivl__disj__un_I9_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I9_J) ).
fof(fact_ivl__disj__un_I11_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I11_J) ).
fof(fact_ivl__disj__un_I15_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I15_J) ).
fof(fact_ivl__disj__un_I16_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I16_J) ).
fof(fact_ivl__disj__un_I10_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I10_J) ).
fof(fact_ivl__disj__un_I7_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I7_J) ).
fof(fact_dvd_OatLeastatMost__subset__iff,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_dvd_OatLeastatMost__subset__iff) ).
fof(fact_ivl__disj__un_I12_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I12_J) ).
fof(fact_ivl__disj__un_I13_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I13_J) ).
fof(fact_UN__le__eq__Un0,axiom,
! [V_M_2,V_na_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_na_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_na_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_coinduct3__mono__lemma,axiom,
! [V_B_2,V_X_2,V_f_2,T_c,T_b] :
( class_Orderings_Oorder(T_b)
=> ( c_Orderings_Oorder__class_Omono(T_b,tc_fun(T_c,tc_HOL_Obool),V_f_2)
=> c_Orderings_Oorder__class_Omono(T_b,tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_f_2)),V_X_2))),V_B_2)) ) ),
file('theBenchmark.p',fact_coinduct3__mono__lemma) ).
fof(fact_image__ident,axiom,
! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2,
file('theBenchmark.p',fact_image__ident) ).
fof(fact_SUP1__iff,axiom,
! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_SUP1__iff) ).
fof(fact_SUPR__apply,axiom,
! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ),
file('theBenchmark.p',fact_SUPR__apply) ).
fof(fact_UN__UN__flatten,axiom,
! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)),
file('theBenchmark.p',fact_UN__UN__flatten) ).
fof(fact_UN__simps_I9_J,axiom,
! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)),
file('theBenchmark.p',fact_UN__simps_I9_J) ).
fof(fact_UN__extend__simps_I9_J,axiom,
! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2),
file('theBenchmark.p',fact_UN__extend__simps_I9_J) ).
fof(fact_SUP__commute,axiom,
! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ),
file('theBenchmark.p',fact_SUP__commute) ).
fof(fact_ball__UN,axiom,
! [V_P_2,V_B_2,V_A_2,T_c,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hBOOL(hAPP(V_P_2,B_x)) )
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
=> hBOOL(hAPP(V_P_2,B_xa)) ) ) ),
file('theBenchmark.p',fact_ball__UN) ).
fof(fact_atLeast__eq__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_atLeast__eq__iff) ).
fof(fact_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_UN__subset__iff,axiom,
! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)) ) ),
file('theBenchmark.p',fact_UN__subset__iff) ).
fof(fact_UN__simps_I10_J,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)),
file('theBenchmark.p',fact_UN__simps_I10_J) ).
fof(fact_image__UN,axiom,
! [V_B_2,V_A_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Oimage(T_c,T_b,V_f_2)),V_B_2)),
file('theBenchmark.p',fact_image__UN) ).
fof(fact_UN__extend__simps_I10_J,axiom,
! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2),
file('theBenchmark.p',fact_UN__extend__simps_I10_J) ).
fof(fact_UN__Un,axiom,
! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)),
file('theBenchmark.p',fact_UN__Un) ).
fof(fact_UN__Un__distrib,axiom,
! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)),
file('theBenchmark.p',fact_UN__Un__distrib) ).
fof(fact_UN__extend__simps_I6_J,axiom,
! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)),
file('theBenchmark.p',fact_UN__extend__simps_I6_J) ).
fof(fact_UN__simps_I6_J,axiom,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
file('theBenchmark.p',fact_UN__simps_I6_J) ).
fof(fact_INT__simps_I9_J,axiom,
! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)),
file('theBenchmark.p',fact_INT__simps_I9_J) ).
fof(fact_INT__extend__simps_I9_J,axiom,
! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2),
file('theBenchmark.p',fact_INT__extend__simps_I9_J) ).
fof(fact_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_SUP__le__iff,axiom,
! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_M_2)),V_u_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ),
file('theBenchmark.p',fact_SUP__le__iff) ).
fof(fact_less__SUP__iff,axiom,
! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
( ( class_Orderings_Olinorder(T_b)
& class_Complete__Lattice_Ocomplete__lattice(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_f_2)))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_less__SUP__iff) ).
fof(fact_UN__simps_I7_J,axiom,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
file('theBenchmark.p',fact_UN__simps_I7_J) ).
fof(fact_UN__extend__simps_I7_J,axiom,
! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
file('theBenchmark.p',fact_UN__extend__simps_I7_J) ).
fof(fact_Compl__UN,axiom,
! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
file('theBenchmark.p',fact_Compl__UN) ).
fof(fact_Compl__INT,axiom,
! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
file('theBenchmark.p',fact_Compl__INT) ).
fof(fact_SUP__subset,axiom,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_B_2),V_f_2))) ) ),
file('theBenchmark.p',fact_SUP__subset) ).
fof(fact_atLeast__subset__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_atLeast__subset__iff) ).
fof(fact_Compl__lessThan,axiom,
! [V_k_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2) ),
file('theBenchmark.p',fact_Compl__lessThan) ).
fof(fact_Compl__atLeast,axiom,
! [V_k_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2) ),
file('theBenchmark.p',fact_Compl__atLeast) ).
fof(fact_UN__le__add__shift,axiom,
! [V_k_2,V_M_2,V_na_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_na_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat),V_M_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),V_k_2))),V_M_2),
file('theBenchmark.p',fact_UN__le__add__shift) ).
fof(fact_ivl__disj__un_I14_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I14_J) ).
fof(fact_image__uminus__atMost,axiom,
! [V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__atMost) ).
fof(fact_image__uminus__atLeast,axiom,
! [V_x_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ),
file('theBenchmark.p',fact_image__uminus__atLeast) ).
fof(fact_lessThan__Suc__eq__insert__0,axiom,
! [V_na_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_na_2))),
file('theBenchmark.p',fact_lessThan__Suc__eq__insert__0) ).
fof(fact_setsum__diff__nat,axiom,
! [V_f_2,V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2)) ) ),
file('theBenchmark.p',fact_setsum__diff__nat) ).
fof(fact_coinduct,axiom,
! [V_X_2,V_f_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))) ) ) ),
file('theBenchmark.p',fact_coinduct) ).
fof(fact_coinduct__lemma,axiom,
! [V_f_2,V_X_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))))
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))))) ) ) ),
file('theBenchmark.p',fact_coinduct__lemma) ).
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_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__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_finite__lessThan,axiom,
! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))),
file('theBenchmark.p',fact_finite__lessThan) ).
fof(fact_finite__atMost,axiom,
! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))),
file('theBenchmark.p',fact_finite__atMost) ).
fof(fact_finite__atLeastLessThan__int,axiom,
! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,V_l_2),V_u_2))),
file('theBenchmark.p',fact_finite__atLeastLessThan__int) ).
fof(fact_finite__greaterThanAtMost,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_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_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_Un__insert__right,axiom,
! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
file('theBenchmark.p',fact_Un__insert__right) ).
fof(fact_Un__insert__left,axiom,
! [V_C_2,V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
file('theBenchmark.p',fact_Un__insert__left) ).
fof(fact_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_image__insert,axiom,
! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)),
file('theBenchmark.p',fact_image__insert) ).
fof(fact_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_insert__absorb2,axiom,
! [V_A_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2),
file('theBenchmark.p',fact_insert__absorb2) ).
fof(fact_insert__commute,axiom,
! [V_A_2,V_y_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),
file('theBenchmark.p',fact_insert__commute) ).
fof(fact_insert__code,axiom,
! [V_x_2,V_A_2,V_y_2,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
<=> ( hBOOL(hAPP(V_A_2,V_x_2))
| V_y_2 = V_x_2 ) ),
file('theBenchmark.p',fact_insert__code) ).
fof(fact_subset__insertI,axiom,
! [V_a_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
file('theBenchmark.p',fact_subset__insertI) ).
fof(fact_subset__insertI2,axiom,
! [V_b_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ),
file('theBenchmark.p',fact_subset__insertI2) ).
fof(fact_insert__mono,axiom,
! [V_a_2,V_D_2,V_C_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2))) ),
file('theBenchmark.p',fact_insert__mono) ).
fof(fact_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_INT__simps_I5_J,axiom,
! [V_B_2,V_a_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
file('theBenchmark.p',fact_INT__simps_I5_J) ).
fof(fact_INT__extend__simps_I5_J,axiom,
! [V_B_2,V_C_2,T_c,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)),
file('theBenchmark.p',fact_INT__extend__simps_I5_J) ).
fof(fact_gfp__upperbound,axiom,
! [V_f_2,V_X_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,V_X_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))) ) ),
file('theBenchmark.p',fact_gfp__upperbound) ).
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_gfp__unfold,axiom,
! [V_f_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2) = hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)) ) ),
file('theBenchmark.p',fact_gfp__unfold) ).
fof(fact_def__gfp__unfold,axiom,
! [V_f_2,V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> V_A_2 = hAPP(V_f_2,V_A_2) ) ) ),
file('theBenchmark.p',fact_def__gfp__unfold) ).
fof(fact_setsum__infinite,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ),
file('theBenchmark.p',fact_setsum__infinite) ).
fof(fact_setsum_Oinfinite,axiom,
! [V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ),
file('theBenchmark.p',fact_setsum_Oinfinite) ).
fof(fact_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_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_setsum__eq__0__iff,axiom,
! [V_f_2,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
=> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('theBenchmark.p',fact_setsum__eq__0__iff) ).
fof(fact_UN__insert,axiom,
! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
file('theBenchmark.p',fact_UN__insert) ).
fof(fact_setsum_Odistrib,axiom,
! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Oplus__class_Oplus(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_A_2)) ) ),
file('theBenchmark.p',fact_setsum_Odistrib) ).
fof(fact_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_gfp__lemma3,axiom,
! [V_f_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))) ) ),
file('theBenchmark.p',fact_gfp__lemma3) ).
fof(fact_gfp__lemma2,axiom,
! [V_f_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))) ) ),
file('theBenchmark.p',fact_gfp__lemma2) ).
fof(fact_atLeastAtMostSuc__conv,axiom,
! [V_na_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
=> c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_na_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_2)) ),
file('theBenchmark.p',fact_atLeastAtMostSuc__conv) ).
fof(fact_setsum__eq__Suc0__iff,axiom,
! [V_f_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ? [B_x] :
( ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
=> ( B_x != B_xa
=> hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_setsum__eq__Suc0__iff) ).
fof(fact_setsum__eq__1__iff,axiom,
! [V_f_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ? [B_x] :
( ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
=> ( B_x != B_xa
=> hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_setsum__eq__1__iff) ).
fof(fact_setsum__diff,axiom,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Oab__group__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_setsum__diff) ).
fof(fact_def__coinduct,axiom,
! [V_X_2,V_f_2,V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),V_A_2))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_def__coinduct) ).
fof(fact_finite__INT,axiom,
! [V_A_2,T_c,V_I_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))) ),
file('theBenchmark.p',fact_finite__INT) ).
fof(fact_card__psubset,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_card__psubset) ).
fof(fact_diff__card__le__card__Diff,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ),
file('theBenchmark.p',fact_diff__card__le__card__Diff) ).
fof(fact_card__Diff__subset,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ),
file('theBenchmark.p',fact_card__Diff__subset) ).
fof(fact_finite_OinsertI,axiom,
! [V_a_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ),
file('theBenchmark.p',fact_finite_OinsertI) ).
fof(fact_finite__imageI,axiom,
! [V_h_2,T_c,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ),
file('theBenchmark.p',fact_finite__imageI) ).
fof(fact_finite__Diff,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_finite__Diff) ).
fof(fact_finite,axiom,
! [V_A_2,T_b] :
( class_Finite__Set_Ofinite(T_b)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('theBenchmark.p',fact_finite) ).
fof(fact_finite__code,axiom,
! [V_A_2,T_b] :
( class_Finite__Set_Ofinite(T_b)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('theBenchmark.p',fact_finite__code) ).
fof(fact_finite__insert,axiom,
! [V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('theBenchmark.p',fact_finite__insert) ).
fof(fact_rev__finite__subset,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
file('theBenchmark.p',fact_rev__finite__subset) ).
fof(fact_finite__subset,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
file('theBenchmark.p',fact_finite__subset) ).
fof(fact_finite__Un,axiom,
! [V_G_2,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ),
file('theBenchmark.p',fact_finite__Un) ).
fof(fact_finite__UnI,axiom,
! [V_G_2,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2))) ) ),
file('theBenchmark.p',fact_finite__UnI) ).
fof(fact_finite__Diff2,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
file('theBenchmark.p',fact_finite__Diff2) ).
fof(fact_finite__UN,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ),
file('theBenchmark.p',fact_finite__UN) ).
fof(fact_finite__surj,axiom,
! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ),
file('theBenchmark.p',fact_finite__surj) ).
fof(fact_finite__Diff__insert,axiom,
! [V_B_2,V_a_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_finite__Diff__insert) ).
fof(fact_card__infinite,axiom,
! [V_A_2,T_b] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_card__infinite) ).
fof(fact_card__ge__0__finite,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('theBenchmark.p',fact_card__ge__0__finite) ).
fof(fact_card__insert__le,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)))) ),
file('theBenchmark.p',fact_card__insert__le) ).
fof(fact_card__seteq,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
=> V_A_2 = V_B_2 ) ) ),
file('theBenchmark.p',fact_card__seteq) ).
fof(fact_card__mono,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ),
file('theBenchmark.p',fact_card__mono) ).
fof(fact_card__image__le,axiom,
! [V_f_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ),
file('theBenchmark.p',fact_card__image__le) ).
fof(fact_psubset__card__mono,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ),
file('theBenchmark.p',fact_psubset__card__mono) ).
fof(fact_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_setsum__mono3,axiom,
! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
( ( class_Groups_Oordered__ab__semigroup__add(T_c)
& class_Groups_Ocomm__monoid__add(T_c) )
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ),
file('theBenchmark.p',fact_setsum__mono3) ).
fof(fact_card__Plus__conv__if,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
=> hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
=> hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ),
file('theBenchmark.p',fact_card__Plus__conv__if) ).
fof(fact_card_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ),
file('theBenchmark.p',fact_card_Oinsert__remove) ).
fof(fact_finite_OemptyI,axiom,
! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_finite_OemptyI) ).
fof(fact_empty__subsetI,axiom,
! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
file('theBenchmark.p',fact_empty__subsetI) ).
fof(fact_finite_Oequations_I1_J,axiom,
! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_finite_Oequations_I1_J) ).
fof(fact_empty__not__insert,axiom,
! [V_A_2,V_a_2,T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2),
file('theBenchmark.p',fact_empty__not__insert) ).
fof(fact_insert__not__empty,axiom,
! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_insert__not__empty) ).
fof(fact_doubleton__eq__iff,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
<=> ( ( V_b_2 = V_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_singleton__inject,axiom,
! [V_b_2,V_a_2,T_b] :
( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
=> V_a_2 = V_b_2 ),
file('theBenchmark.p',fact_singleton__inject) ).
fof(fact_Diff__cancel,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Diff__cancel) ).
fof(fact_Diff__empty,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2,
file('theBenchmark.p',fact_Diff__empty) ).
fof(fact_empty__Diff,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_empty__Diff) ).
fof(fact_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__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_subset__empty,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_subset__empty) ).
fof(fact_image__is__empty,axiom,
! [V_A_2,V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_image__is__empty) ).
fof(fact_image__empty,axiom,
! [V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_image__empty) ).
fof(fact_empty__is__image,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_empty__is__image) ).
fof(fact_ball__empty,axiom,
! [V_P_2,T_b,B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
=> hBOOL(hAPP(V_P_2,B_x)) ),
file('theBenchmark.p',fact_ball__empty) ).
fof(fact_bot__apply,axiom,
! [V_x_2,T_c,T_b] :
( class_Orderings_Obot(T_b)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ),
file('theBenchmark.p',fact_bot__apply) ).
fof(fact_bot__fun__def,axiom,
! [V_x_2,T_c,T_b] :
( class_Orderings_Obot(T_b)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ),
file('theBenchmark.p',fact_bot__fun__def) ).
fof(fact_Un__empty,axiom,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_Un__empty) ).
fof(fact_Un__empty__right,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2,
file('theBenchmark.p',fact_Un__empty__right) ).
fof(fact_Un__empty__left,axiom,
! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2,
file('theBenchmark.p',fact_Un__empty__left) ).
fof(fact_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_not__psubset__empty,axiom,
! [V_A_2,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_not__psubset__empty) ).
fof(fact_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_SUP__const,axiom,
! [V_M_2,T_b,V_A_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ),
file('theBenchmark.p',fact_SUP__const) ).
fof(fact_UNION__empty__conv_I1_J,axiom,
! [V_B_2,V_A_2,T_c,T_b] :
( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_UNION__empty__conv_I1_J) ).
fof(fact_UN__empty2,axiom,
! [V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_UN__empty2) ).
fof(fact_UN__constant,axiom,
! [V_c_2,T_c,T_b,V_A_2] :
( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_UN__constant) ).
fof(fact_UNION__empty__conv_I2_J,axiom,
! [V_B_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_UNION__empty__conv_I2_J) ).
fof(fact_INF__const,axiom,
! [V_M_2,T_b,V_A_2,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ),
file('theBenchmark.p',fact_INF__const) ).
fof(fact_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_b] :
( class_Lattices_Obounded__lattice__bot(T_b)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
<=> ( V_y_2 = c_Orderings_Obot__class_Obot(T_b)
& V_x_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ),
file('theBenchmark.p',fact_sup__eq__bot__iff) ).
fof(fact_finite__Plus__iff,axiom,
! [V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
file('theBenchmark.p',fact_finite__Plus__iff) ).
fof(fact_finite__Plus,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ) ),
file('theBenchmark.p',fact_finite__Plus) ).
fof(fact_finite__PlusD_I1_J,axiom,
! [V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('theBenchmark.p',fact_finite__PlusD_I1_J) ).
fof(fact_finite__PlusD_I2_J,axiom,
! [V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ),
file('theBenchmark.p',fact_finite__PlusD_I2_J) ).
fof(fact_setsum__empty,axiom,
! [V_f_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ),
file('theBenchmark.p',fact_setsum__empty) ).
fof(fact_setsum_Oempty,axiom,
! [V_g_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ),
file('theBenchmark.p',fact_setsum_Oempty) ).
fof(fact_subset__singletonD,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
=> ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_subset__singletonD) ).
fof(fact_insert__is__Un,axiom,
! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_A_2),
file('theBenchmark.p',fact_insert__is__Un) ).
fof(fact_atLeastatMost__empty__iff2,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_atLeastatMost__empty__iff2) ).
fof(fact_atLeastatMost__empty__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_atLeastatMost__empty__iff) ).
fof(fact_atLeastatMost__empty,axiom,
! [V_a_2,V_b_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
=> c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_atLeastatMost__empty) ).
fof(fact_Diff__insert,axiom,
! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_Diff__insert) ).
fof(fact_Diff__insert2,axiom,
! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2),
file('theBenchmark.p',fact_Diff__insert2) ).
fof(fact_insert__Diff__single,axiom,
! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2),
file('theBenchmark.p',fact_insert__Diff__single) ).
fof(fact_atLeastLessThan__empty,axiom,
! [V_a_2,V_b_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
=> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_atLeastLessThan__empty) ).
fof(fact_card_Oempty,axiom,
! [T_b] : hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_card_Oempty) ).
fof(fact_atLeastLessThan__empty__iff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_atLeastLessThan__empty__iff) ).
fof(fact_atLeastLessThan__empty__iff2,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_atLeastLessThan__empty__iff2) ).
fof(fact_atLeastAtMost__singleton_H,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( V_a_2 = V_b_2
=> c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ),
file('theBenchmark.p',fact_atLeastAtMost__singleton_H) ).
fof(fact_atLeastAtMost__singleton__iff,axiom,
! [V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,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_b] :
( class_Orderings_Oorder(T_b)
=> c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_atLeastAtMost__singleton) ).
fof(fact_subset__Compl__self__eq,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_subset__Compl__self__eq) ).
fof(fact_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_greaterThanAtMost__empty,axiom,
! [V_k_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
=> c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_greaterThanAtMost__empty) ).
fof(fact_greaterThanAtMost__empty__iff,axiom,
! [V_l_2,V_k_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ),
file('theBenchmark.p',fact_greaterThanAtMost__empty__iff) ).
fof(fact_greaterThanAtMost__empty__iff2,axiom,
! [V_l_2,V_k_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2)
<=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ),
file('theBenchmark.p',fact_greaterThanAtMost__empty__iff2) ).
fof(fact_greaterThanLessThan__empty,axiom,
! [V_k_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
=> c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_greaterThanLessThan__empty) ).
fof(fact_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_image__constant__conv,axiom,
! [V_c_2,T_c,T_b,V_A_2] :
( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_image__constant__conv) ).
fof(fact_UN__extend__simps_I1_J,axiom,
! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ),
file('theBenchmark.p',fact_UN__extend__simps_I1_J) ).
fof(fact_UN__singleton,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2,
file('theBenchmark.p',fact_UN__singleton) ).
fof(fact_UN__simps_I1_J,axiom,
! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_UN__simps_I1_J) ).
fof(fact_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_UN__extend__simps_I2_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) ),
file('theBenchmark.p',fact_UN__extend__simps_I2_J) ).
fof(fact_UN__extend__simps_I3_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) ),
file('theBenchmark.p',fact_UN__extend__simps_I3_J) ).
fof(fact_UN__simps_I2_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_UN__simps_I2_J) ).
fof(fact_UN__simps_I3_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_UN__simps_I3_J) ).
fof(fact_card__eq__0__iff,axiom,
! [V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_card__eq__0__iff) ).
fof(fact_single__Diff__lessThan,axiom,
! [V_k_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_single__Diff__lessThan) ).
fof(fact_image__eq__UN,axiom,
! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Set_Oinsert(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_image__eq__UN) ).
fof(fact_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_INT__extend__simps_I4_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) ),
file('theBenchmark.p',fact_INT__extend__simps_I4_J) ).
fof(fact_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_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_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_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_card__gt__0__iff,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
& V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_card__gt__0__iff) ).
fof(fact_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__un_I2_J,axiom,
! [V_u_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ),
file('theBenchmark.p',fact_ivl__disj__un_I2_J) ).
fof(fact_atLeastLessThanSuc,axiom,
! [V_na_2,V_m_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
=> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_na_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_na_2))
=> hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_na_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_na_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_na_2)) ) ),
file('theBenchmark.p',fact_atLeastLessThanSuc) ).
fof(fact_ivl__disj__un_I1_J,axiom,
! [V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ),
file('theBenchmark.p',fact_ivl__disj__un_I1_J) ).
fof(fact_card__Plus,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ),
file('theBenchmark.p',fact_card__Plus) ).
fof(fact_setsum_Oinsert__remove,axiom,
! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
file('theBenchmark.p',fact_setsum_Oinsert__remove) ).
fof(fact_card__insert,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ),
file('theBenchmark.p',fact_card__insert) ).
fof(fact_card__Diff1__le,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ),
file('theBenchmark.p',fact_card__Diff1__le) ).
fof(fact_ivl__disj__un_I6_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I6_J) ).
fof(fact_ivl__disj__un_I5_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I5_J) ).
fof(fact_ivl__disj__un_I3_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I3_J) ).
fof(fact_ivl__disj__un_I4_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ),
file('theBenchmark.p',fact_ivl__disj__un_I4_J) ).
fof(fact_the__elem__def,axiom,
! [V_X_2,T_b] : c_Set_Othe__elem(T_b,V_X_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),
file('theBenchmark.p',fact_the__elem__def) ).
fof(fact_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_the__elem__eq,axiom,
! [V_x_2,T_b] : c_Set_Othe__elem(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2,
file('theBenchmark.p',fact_the__elem__eq) ).
fof(fact_Plus__eq__empty__conv,axiom,
! [V_B_2,V_A_2,T_c,T_b] :
( c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))
<=> ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
& V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_Plus__eq__empty__conv) ).
fof(fact_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_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_card__Diff__singleton,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
file('theBenchmark.p',fact_card__Diff__singleton) ).
fof(fact_card__Diff__singleton__if,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
file('theBenchmark.p',fact_card__Diff__singleton__if) ).
fof(fact_folding__one_Oinsert__remove,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_folding__one_Oinsert__remove) ).
fof(fact_equalityCE,axiom,
! [V_c_2,T_b,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) )
=> ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_equalityCE) ).
fof(fact_INF2__E,axiom,
! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
=> ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_INF2__E) ).
fof(fact_INF2__D,axiom,
! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ),
file('theBenchmark.p',fact_INF2__D) ).
fof(fact_SUP2__I,axiom,
! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ),
file('theBenchmark.p',fact_SUP2__I) ).
fof(fact_emptyE,axiom,
! [V_a_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_emptyE) ).
fof(fact_insertE,axiom,
! [V_A_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
=> ( V_a_2 != V_b_2
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_insertE) ).
fof(fact_insertCI,axiom,
! [V_b_2,V_B_2,V_a_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
=> V_a_2 = V_b_2 )
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ),
file('theBenchmark.p',fact_insertCI) ).
fof(fact_subsetD,axiom,
! [V_c_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
file('theBenchmark.p',fact_subsetD) ).
fof(fact_image__eqI,axiom,
! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
( V_b_2 = hAPP(V_f_2,V_x_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ),
file('theBenchmark.p',fact_image__eqI) ).
fof(fact_UnE,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),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_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_UnCI) ).
fof(fact_DiffI,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
file('theBenchmark.p',fact_DiffI) ).
fof(fact_DiffE,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
file('theBenchmark.p',fact_DiffE) ).
fof(fact_ComplI,axiom,
! [V_A_2,V_c_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ),
file('theBenchmark.p',fact_ComplI) ).
fof(fact_UN__I,axiom,
! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
file('theBenchmark.p',fact_UN__I) ).
fof(fact_SUP1__I,axiom,
! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
=> hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ),
file('theBenchmark.p',fact_SUP1__I) ).
fof(fact_INF1__D,axiom,
! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ),
file('theBenchmark.p',fact_INF1__D) ).
fof(fact_INF1__E,axiom,
! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
=> ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_INF1__E) ).
fof(fact_INT__D,axiom,
! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ),
file('theBenchmark.p',fact_INT__D) ).
fof(fact_INT__E,axiom,
! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_INT__E) ).
fof(fact_mem__splitI,axiom,
! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)))) ),
file('theBenchmark.p',fact_mem__splitI) ).
fof(fact_pair__imageI,axiom,
! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_d),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),V_A_2))) ),
file('theBenchmark.p',fact_pair__imageI) ).
fof(fact_all__not__in__conv,axiom,
! [V_A_2,T_b] :
( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_all__not__in__conv) ).
fof(fact_ex__in__conv,axiom,
! [V_A_2,T_b] :
( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
<=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ex__in__conv) ).
fof(fact_empty__iff,axiom,
! [V_c_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_empty__iff) ).
fof(fact_equals0D,axiom,
! [V_a_2,T_b,V_A_2] :
( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
file('theBenchmark.p',fact_equals0D) ).
fof(fact_Diff__iff,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
<=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ),
file('theBenchmark.p',fact_Diff__iff) ).
fof(fact_DiffD1,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
file('theBenchmark.p',fact_DiffD1) ).
fof(fact_DiffD2,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ),
file('theBenchmark.p',fact_DiffD2) ).
fof(fact_insert__absorb,axiom,
! [V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ),
file('theBenchmark.p',fact_insert__absorb) ).
fof(fact_insertI2,axiom,
! [V_b_2,V_B_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ),
file('theBenchmark.p',fact_insertI2) ).
fof(fact_insert__ident,axiom,
! [V_B_2,V_A_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
=> ( hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)
<=> V_A_2 = V_B_2 ) ) ),
file('theBenchmark.p',fact_insert__ident) ).
fof(fact_insert__iff,axiom,
! [V_A_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_insert__iff) ).
fof(fact_insertI1,axiom,
! [V_B_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
file('theBenchmark.p',fact_insertI1) ).
fof(fact_ComplE,axiom,
! [V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
file('theBenchmark.p',fact_ComplE) ).
fof(fact_ComplD,axiom,
! [V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
file('theBenchmark.p',fact_ComplD) ).
fof(fact_Compl__iff,axiom,
! [V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
<=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
file('theBenchmark.p',fact_Compl__iff) ).
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_rev__image__eqI,axiom,
! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_b_2 = hAPP(V_f_2,V_x_2)
=> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ),
file('theBenchmark.p',fact_rev__image__eqI) ).
fof(fact_imageI,axiom,
! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ),
file('theBenchmark.p',fact_imageI) ).
fof(fact_image__iff,axiom,
! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
<=> ? [B_x] :
( V_z_2 = hAPP(V_f_2,B_x)
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_image__iff) ).
fof(fact_mem__def,axiom,
! [V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
<=> hBOOL(hAPP(V_A_2,V_x_2)) ),
file('theBenchmark.p',fact_mem__def) ).
fof(fact_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_eqset__imp__iff,axiom,
! [V_x_2,T_b,V_B_2,V_A_2] :
( V_A_2 = V_B_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_eqset__imp__iff) ).
fof(fact_eqelem__imp__iff,axiom,
! [V_A_2,T_b,V_y_2,V_x_2] :
( V_x_2 = V_y_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ),
file('theBenchmark.p',fact_eqelem__imp__iff) ).
fof(fact_eq__mem__trans,axiom,
! [V_A_2,T_b,V_b_2,V_a_2] :
( V_a_2 = V_b_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_eq__mem__trans) ).
fof(fact_pred__equals__eq,axiom,
! [V_S_2,V_R_2,T_b] :
( hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)
<=> V_R_2 = V_S_2 ),
file('theBenchmark.p',fact_pred__equals__eq) ).
fof(fact_eq__mem,axiom,
! [V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
<=> V_x_2 = V_y_2 ),
file('theBenchmark.p',fact_eq__mem) ).
fof(fact_in__mono,axiom,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_in__mono) ).
fof(fact_set__rev__mp,axiom,
! [V_B_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_set__rev__mp) ).
fof(fact_set__mp,axiom,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_set__mp) ).
fof(fact_weak__coinduct,axiom,
! [V_f_2,V_X_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,V_X_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))) ) ),
file('theBenchmark.p',fact_weak__coinduct) ).
fof(fact_UnI2,axiom,
! [V_A_2,V_B_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_UnI2) ).
fof(fact_UnI1,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_UnI1) ).
fof(fact_Un__iff,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ),
file('theBenchmark.p',fact_Un__iff) ).
fof(fact_psubsetD,axiom,
! [V_c_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
file('theBenchmark.p',fact_psubsetD) ).
fof(fact_bot__empty__eq,axiom,
! [V_x_2,T_b] :
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_bot__empty__eq) ).
fof(fact_ord_OatLeastAtMost__iff,axiom,
! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_b,V_less__eq_2,V_l_2,V_u_2)))
<=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
& hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) ) ),
file('theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).
fof(fact_pred__equals__eq2,axiom,
! [V_S_2,V_R_2,T_c,T_b] :
( hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)
<=> V_R_2 = V_S_2 ),
file('theBenchmark.p',fact_pred__equals__eq2) ).
fof(fact_sup__Un__eq2,axiom,
! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ),
file('theBenchmark.p',fact_sup__Un__eq2) ).
fof(fact_bot__empty__eq2,axiom,
! [V_y_2,V_x_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_bot__empty__eq2) ).
fof(fact_pred__subset__eq,axiom,
! [V_S_2,V_R_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ),
file('theBenchmark.p',fact_pred__subset__eq) ).
fof(fact_sup__Un__eq,axiom,
! [V_x_2,V_S_2,V_R_2,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ),
file('theBenchmark.p',fact_sup__Un__eq) ).
fof(fact_UN__iff,axiom,
! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_UN__iff) ).
fof(fact_INT__iff,axiom,
! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ),
file('theBenchmark.p',fact_INT__iff) ).
fof(fact_folding__one_Oinsert,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_folding__one_Oinsert) ).
fof(fact_singleton__iff,axiom,
! [V_a_2,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
<=> V_b_2 = V_a_2 ),
file('theBenchmark.p',fact_singleton__iff) ).
fof(fact_singletonE,axiom,
! [V_a_2,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
=> V_b_2 = V_a_2 ),
file('theBenchmark.p',fact_singletonE) ).
fof(fact_insert__subset,axiom,
! [V_B_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
file('theBenchmark.p',fact_insert__subset) ).
fof(fact_subset__insert,axiom,
! [V_B_2,V_A_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_subset__insert) ).
fof(fact_insert__image,axiom,
! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ),
file('theBenchmark.p',fact_insert__image) ).
fof(fact_weak__coinduct__image,axiom,
! [V_f_2,V_g_2,T_c,V_X_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_X_2)),hAPP(V_f_2,hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_X_2))))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_g_2,V_a_2)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_c,tc_HOL_Obool),V_f_2))) ) ),
file('theBenchmark.p',fact_weak__coinduct__image) ).
fof(fact_insert__Diff__if,axiom,
! [V_A_2,V_B_2,V_x_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ),
file('theBenchmark.p',fact_insert__Diff__if) ).
fof(fact_insert__Diff1,axiom,
! [V_A_2,V_B_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ),
file('theBenchmark.p',fact_insert__Diff1) ).
fof(fact_lessThan__iff,axiom,
! [V_k_2,V_i_2,T_b] :
( class_Orderings_Oord(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ),
file('theBenchmark.p',fact_lessThan__iff) ).
fof(fact_ord_OgreaterThanLessThan__iff,axiom,
! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_b,V_less_2,V_l_2,V_u_2)))
<=> ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
& hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) ) ),
file('theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).
fof(fact_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_atMost__iff,axiom,
! [V_k_2,V_i_2,T_b] :
( class_Orderings_Oord(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ),
file('theBenchmark.p',fact_atMost__iff) ).
fof(fact_atLeast__iff,axiom,
! [V_k_2,V_i_2,T_b] :
( class_Orderings_Oord(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ),
file('theBenchmark.p',fact_atLeast__iff) ).
fof(fact_greaterThan__iff,axiom,
! [V_k_2,V_i_2,T_b] :
( class_Orderings_Oord(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ),
file('theBenchmark.p',fact_greaterThan__iff) ).
fof(fact_gfp__fun__UnI2,axiom,
! [V_X_2,V_a_2,V_f_2,T_b] :
( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))))) ) ),
file('theBenchmark.p',fact_gfp__fun__UnI2) ).
fof(fact_le__SUPI,axiom,
! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_M_2))) ) ),
file('theBenchmark.p',fact_le__SUPI) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_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_INF__leI,axiom,
! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ),
file('theBenchmark.p',fact_INF__leI) ).
fof(fact_folding__one_Oremove,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_F_2,V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_folding__one_Oremove) ).
fof(fact_UN__insert__distrib,axiom,
! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_UN__insert__distrib) ).
fof(fact_UN__upper,axiom,
! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_UN__upper) ).
fof(fact_UN__absorb,axiom,
! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ),
file('theBenchmark.p',fact_UN__absorb) ).
fof(fact_INT__insert__distrib,axiom,
! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_INT__insert__distrib) ).
fof(fact_INT__lower,axiom,
! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ),
file('theBenchmark.p',fact_INT__lower) ).
fof(fact_pred__subset__eq2,axiom,
! [V_S_2,V_R_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) ),
file('theBenchmark.p',fact_pred__subset__eq2) ).
fof(fact_Diff__insert__absorb,axiom,
! [V_A_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2 ),
file('theBenchmark.p',fact_Diff__insert__absorb) ).
fof(fact_insert__Diff,axiom,
! [V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = V_A_2 ),
file('theBenchmark.p',fact_insert__Diff) ).
fof(fact_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_setsum__delta_H,axiom,
! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
file('theBenchmark.p',fact_setsum__delta_H) ).
fof(fact_setsum__delta,axiom,
! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
file('theBenchmark.p',fact_setsum__delta) ).
fof(fact_coinduct__set,axiom,
! [V_X_2,V_a_2,V_f_2,T_b] :
( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))) ) ) ),
file('theBenchmark.p',fact_coinduct__set) ).
fof(fact_def__coinduct__set,axiom,
! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_A_2))))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_def__coinduct__set) ).
fof(fact_image__constant,axiom,
! [V_c_2,T_c,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_image__constant) ).
fof(fact_folding__one_Osingleton,axiom,
! [V_x_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
file('theBenchmark.p',fact_folding__one_Osingleton) ).
fof(fact_setsum_Oinsert,axiom,
! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)) ) ) ),
file('theBenchmark.p',fact_setsum_Oinsert) ).
fof(fact_setsum__insert,axiom,
! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_F_2)) ) ) ),
file('theBenchmark.p',fact_setsum__insert) ).
fof(fact_diff__single__insert,axiom,
! [V_B_2,V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) ),
file('theBenchmark.p',fact_diff__single__insert) ).
fof(fact_subset__insert__iff,axiom,
! [V_B_2,V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) ) ) ),
file('theBenchmark.p',fact_subset__insert__iff) ).
fof(fact_card__insert__if,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ),
file('theBenchmark.p',fact_card__insert__if) ).
fof(fact_card__insert__disjoint,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ),
file('theBenchmark.p',fact_card__insert__disjoint) ).
fof(fact_card_Oinsert,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ),
file('theBenchmark.p',fact_card_Oinsert) ).
fof(fact_psubset__insert__iff,axiom,
! [V_B_2,V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_psubset__insert__iff) ).
fof(fact_setsum__diff1__nat,axiom,
! [V_f_2,V_A_2,V_a_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ),
file('theBenchmark.p',fact_setsum__diff1__nat) ).
fof(fact_setsum__diff1_H,axiom,
! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ),
file('theBenchmark.p',fact_setsum__diff1_H) ).
fof(fact_setsum_Oremove,axiom,
! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ),
file('theBenchmark.p',fact_setsum_Oremove) ).
fof(fact_setsum__diff1__ring,axiom,
! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
( class_Rings_Oring(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ),
file('theBenchmark.p',fact_setsum__diff1__ring) ).
fof(fact_setsum__diff1,axiom,
! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
( class_Groups_Oab__group__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_setsum__diff1) ).
fof(fact_card__Suc__Diff1,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ),
file('theBenchmark.p',fact_card__Suc__Diff1) ).
fof(fact_card__Diff2__less,axiom,
! [V_y_2,V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ),
file('theBenchmark.p',fact_card__Diff2__less) ).
fof(fact_card__Diff1__less,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ),
file('theBenchmark.p',fact_card__Diff1__less) ).
fof(fact_card__Diff__insert,axiom,
! [V_B_2,V_a_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
file('theBenchmark.p',fact_card__Diff__insert) ).
fof(fact_card_Oremove,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
file('theBenchmark.p',fact_card_Oremove) ).
fof(fact_in__rel__def,axiom,
! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_R_2)) ),
file('theBenchmark.p',fact_in__rel__def) ).
fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
! [V_f_2,V_A_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ),
file('theBenchmark.p',fact_transfer__int__nat__sum__prod2_I1_J) ).
fof(fact_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_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_sup2E,axiom,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
=> ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_sup2E) ).
fof(fact_sup2CI,axiom,
! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
file('theBenchmark.p',fact_sup2CI) ).
fof(fact_bot2E,axiom,
! [V_y_2,V_x_2,T_c,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)),
file('theBenchmark.p',fact_bot2E) ).
fof(fact_less__by__empty,axiom,
! [V_B_2,T_b,V_A_2] :
( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_less__by__empty) ).
fof(fact_SUP2__iff,axiom,
! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_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_b),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_SUP2__iff) ).
fof(fact_sup2I1,axiom,
! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
file('theBenchmark.p',fact_sup2I1) ).
fof(fact_sup2I2,axiom,
! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
file('theBenchmark.p',fact_sup2I2) ).
fof(fact_INF2__iff,axiom,
! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ),
file('theBenchmark.p',fact_INF2__iff) ).
fof(fact_Nitpick_Orefl_H__def,axiom,
! [V_r_2,T_b] :
( c_Nitpick_Orefl_H(T_b,V_r_2)
<=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ),
file('theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
fof(fact_dvd_OgreaterThan__iff,axiom,
! [V_k_2,V_i_2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2)))
<=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ),
file('theBenchmark.p',fact_dvd_OgreaterThan__iff) ).
fof(fact_dvd_OlessThan__iff,axiom,
! [V_k_2,V_i_2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2)))
<=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ),
file('theBenchmark.p',fact_dvd_OlessThan__iff) ).
fof(fact_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_ord_OlessThan__iff,axiom,
! [V_k_2,V_less_2,V_i_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
<=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ),
file('theBenchmark.p',fact_ord_OlessThan__iff) ).
fof(fact_ord_OgreaterThan__iff,axiom,
! [V_k_2,V_less_2,V_i_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
<=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ),
file('theBenchmark.p',fact_ord_OgreaterThan__iff) ).
fof(fact_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_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_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_in__measure,axiom,
! [V_f_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ),
file('theBenchmark.p',fact_in__measure) ).
fof(fact_dvd_OatLeast__iff,axiom,
! [V_k_2,V_i_2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ),
file('theBenchmark.p',fact_dvd_OatLeast__iff) ).
fof(fact_dvd_OatMost__iff,axiom,
! [V_k_2,V_i_2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2)))
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ),
file('theBenchmark.p',fact_dvd_OatMost__iff) ).
fof(fact_ord_OatMost__iff,axiom,
! [V_k_2,V_less__eq_2,V_i_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
<=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ),
file('theBenchmark.p',fact_ord_OatMost__iff) ).
fof(fact_ord_OatLeast__iff,axiom,
! [V_k_2,V_less__eq_2,V_i_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
<=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ),
file('theBenchmark.p',fact_ord_OatLeast__iff) ).
fof(fact_folding__image__simple_Oremove,axiom,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ),
file('theBenchmark.p',fact_folding__image__simple_Oremove) ).
fof(fact_fold__graph_H_Ointros_I2_J,axiom,
! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_y_2)
=> c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_fold__graph_H_Ointros_I2_J) ).
fof(fact_setsum__mono2,axiom,
! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
( class_Groups_Oordered__comm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( ! [B_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ),
file('theBenchmark.p',fact_setsum__mono2) ).
fof(fact_flat__lub__def,axiom,
! [V_b_2,V_A_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
=> c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
=> c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 ) ),
file('theBenchmark.p',fact_flat__lub__def) ).
fof(fact_folding__image__simple_Oempty,axiom,
! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ),
file('theBenchmark.p',fact_folding__image__simple_Oempty) ).
fof(fact_fold__graph_H_Ointros_I1_J,axiom,
! [V_z_2,V_f_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_z_2),
file('theBenchmark.p',fact_fold__graph_H_Ointros_I1_J) ).
fof(fact_fold__graph_H_Oequations_I1_J,axiom,
! [V_a2_2,V_a1_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),
file('theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).
fof(fact_folding__image__simple_Oinsert,axiom,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ) ),
file('theBenchmark.p',fact_folding__image__simple_Oinsert) ).
fof(fact_folding__image__simple_Oinsert__remove,axiom,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ),
file('theBenchmark.p',fact_folding__image__simple_Oinsert__remove) ).
fof(fact_mlex__leq,axiom,
! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ),
file('theBenchmark.p',fact_mlex__leq) ).
fof(fact_mlex__less,axiom,
! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ),
file('theBenchmark.p',fact_mlex__less) ).
fof(fact_Least__mono,axiom,
! [V_S_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Oorder(T_b)
& class_Orderings_Oorder(T_c) )
=> ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
=> ( ? [B_x] :
( ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_S_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) )
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
=> c_Orderings_Oord__class_OLeast(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2))) = hAPP(V_f_2,c_Orderings_Oord__class_OLeast(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))) ) ) ),
file('theBenchmark.p',fact_Least__mono) ).
fof(fact_def__coinduct3,axiom,
! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),V_A_2)))))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_def__coinduct3) ).
fof(fact_lfp__const,axiom,
! [V_t_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> c_Inductive_Ocomplete__lattice__class_Olfp(T_b,hAPP(c_COMBK(T_b,T_b),V_t_2)) = V_t_2 ),
file('theBenchmark.p',fact_lfp__const) ).
fof(fact_LeastI__ex,axiom,
! [V_P_2,T_b] :
( class_Orderings_Owellorder(T_b)
=> ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
=> hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))) ) ),
file('theBenchmark.p',fact_LeastI__ex) ).
fof(fact_LeastI,axiom,
! [V_k_2,V_P_2,T_b] :
( class_Orderings_Owellorder(T_b)
=> ( hBOOL(hAPP(V_P_2,V_k_2))
=> hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))) ) ),
file('theBenchmark.p',fact_LeastI) ).
fof(fact_lfp__lowerbound,axiom,
! [V_A_2,V_f_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_A_2)),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_A_2)) ) ),
file('theBenchmark.p',fact_lfp__lowerbound) ).
fof(fact_lfp__unfold,axiom,
! [V_f_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2) = hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)) ) ),
file('theBenchmark.p',fact_lfp__unfold) ).
fof(fact_def__lfp__unfold,axiom,
! [V_f_2,V_h_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( V_h_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> V_h_2 = hAPP(V_f_2,V_h_2) ) ) ),
file('theBenchmark.p',fact_def__lfp__unfold) ).
fof(fact_Least__le,axiom,
! [V_k_2,V_P_2,T_b] :
( class_Orderings_Owellorder(T_b)
=> ( hBOOL(hAPP(V_P_2,V_k_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Orderings_Oord__class_OLeast(T_b,V_P_2)),V_k_2)) ) ),
file('theBenchmark.p',fact_Least__le) ).
fof(fact_not__less__Least,axiom,
! [V_P_2,V_k_2,T_b] :
( class_Orderings_Owellorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),c_Orderings_Oord__class_OLeast(T_b,V_P_2)))
=> ~ hBOOL(hAPP(V_P_2,V_k_2)) ) ),
file('theBenchmark.p',fact_not__less__Least) ).
fof(fact_lfp__lemma2,axiom,
! [V_f_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2))),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2))) ) ),
file('theBenchmark.p',fact_lfp__lemma2) ).
fof(fact_lfp__lemma3,axiom,
! [V_f_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)))) ) ),
file('theBenchmark.p',fact_lfp__lemma3) ).
fof(fact_Least__Suc,axiom,
! [V_na_2,V_P_2] :
( hBOOL(hAPP(V_P_2,V_na_2))
=> ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_OSuc))) ) ),
file('theBenchmark.p',fact_Least__Suc) ).
fof(fact_coinduct3__lemma,axiom,
! [V_f_2,V_X_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))))))
=> ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))))) ) ),
file('theBenchmark.p',fact_coinduct3__lemma) ).
fof(fact_coinduct3,axiom,
! [V_X_2,V_a_2,V_f_2,T_b] :
( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))))))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))) ) ) ),
file('theBenchmark.p',fact_coinduct3) ).
fof(fact_setsum__bounded,axiom,
! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
( ( class_Rings_Osemiring__1(T_c)
& class_Groups_Oordered__ab__semigroup__add(T_c) )
=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_K_2))) ) ),
file('theBenchmark.p',fact_setsum__bounded) ).
fof(fact_card__Suc__eq,axiom,
! [V_k_2,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
<=> ? [B_b,B_B] :
( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
& ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
& V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) ) ),
file('theBenchmark.p',fact_card__Suc__eq) ).
fof(fact_ord_OatLeastLessThan__iff,axiom,
! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
<=> ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
& hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) ) ),
file('theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).
fof(fact_ord_OgreaterThanAtMost__iff,axiom,
! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
<=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
& hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) ) ),
file('theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).
fof(fact_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_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__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_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__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__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_Nats__number__of,axiom,
! [V_w_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ),
file('theBenchmark.p',fact_Nats__number__of) ).
fof(fact_Ints__odd__less__0,axiom,
! [V_a_2,T_b] :
( class_Rings_Olinordered__idom(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ),
file('theBenchmark.p',fact_Ints__odd__less__0) ).
fof(fact_Sup__fin_Oremove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oremove) ).
fof(fact_Max_Oremove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_Max_Oremove) ).
fof(fact_Max_Osingleton,axiom,
! [V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
file('theBenchmark.p',fact_Max_Osingleton) ).
fof(fact_Sup__fin_Osingleton,axiom,
! [V_x_2,T_b] :
( class_Lattices_Olattice(T_b)
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
file('theBenchmark.p',fact_Sup__fin_Osingleton) ).
fof(fact_Ints__0,axiom,
! [T_b] :
( class_Rings_Oring__1(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ),
file('theBenchmark.p',fact_Ints__0) ).
fof(fact_Ints__add,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Oring__1(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ),
file('theBenchmark.p',fact_Ints__add) ).
fof(fact_Ints__mult,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Oring__1(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ),
file('theBenchmark.p',fact_Ints__mult) ).
fof(fact_Ints__diff,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Oring__1(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ),
file('theBenchmark.p',fact_Ints__diff) ).
fof(fact_Ints__number__of,axiom,
! [V_w_2,T_b] :
( class_Int_Onumber__ring(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Int_Oring__1__class_OInts(T_b))) ),
file('theBenchmark.p',fact_Ints__number__of) ).
fof(fact_Ints__1,axiom,
! [T_b] :
( class_Rings_Oring__1(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ),
file('theBenchmark.p',fact_Ints__1) ).
fof(fact_Ints__minus,axiom,
! [V_a_2,T_b] :
( class_Rings_Oring__1(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Int_Oring__1__class_OInts(T_b))) ) ),
file('theBenchmark.p',fact_Ints__minus) ).
fof(fact_Ints__power,axiom,
! [V_na_2,V_a_2,T_b] :
( class_Rings_Oring__1(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_na_2)),c_Int_Oring__1__class_OInts(T_b))) ) ),
file('theBenchmark.p',fact_Ints__power) ).
fof(fact_Ints__of__nat,axiom,
! [V_na_2,T_b] :
( class_Rings_Oring__1(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)),c_Int_Oring__1__class_OInts(T_b))) ),
file('theBenchmark.p',fact_Ints__of__nat) ).
fof(fact_Ints__of__int,axiom,
! [V_z_2,T_b] :
( class_Rings_Oring__1(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Int_Oring__1__class_OInts(T_b))) ),
file('theBenchmark.p',fact_Ints__of__int) ).
fof(fact_Max__ge,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))) ) ) ),
file('theBenchmark.p',fact_Max__ge) ).
fof(fact_Max__in,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ),
file('theBenchmark.p',fact_Max__in) ).
fof(fact_Sup__fin_Oin__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oin__idem) ).
fof(fact_Max_Oin__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ),
file('theBenchmark.p',fact_Max_Oin__idem) ).
fof(fact_Nats__0,axiom,
! [T_b] :
( class_Rings_Osemiring__1(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ),
file('theBenchmark.p',fact_Nats__0) ).
fof(fact_Nats__add,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Osemiring__1(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ),
file('theBenchmark.p',fact_Nats__add) ).
fof(fact_Nats__mult,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Rings_Osemiring__1(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ),
file('theBenchmark.p',fact_Nats__mult) ).
fof(fact_Nats__1,axiom,
! [T_b] :
( class_Rings_Osemiring__1(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ),
file('theBenchmark.p',fact_Nats__1) ).
fof(fact_of__nat__in__Nats,axiom,
! [V_na_2,T_b] :
( class_Rings_Osemiring__1(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ),
file('theBenchmark.p',fact_of__nat__in__Nats) ).
fof(fact_Ints__double__eq__0__iff,axiom,
! [V_a_2,T_b] :
( class_Int_Oring__char__0(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
file('theBenchmark.p',fact_Ints__double__eq__0__iff) ).
fof(fact_Max__mono,axiom,
! [V_N_2,V_M_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
=> ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2))) ) ) ) ),
file('theBenchmark.p',fact_Max__mono) ).
fof(fact_Sup__fin_Oinsert__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oinsert__idem) ).
fof(fact_Sup__fin_Osubset__idem,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Osubset__idem) ).
fof(fact_Max__insert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ),
file('theBenchmark.p',fact_Max__insert) ).
fof(fact_Sup__fin_Ounion__idem,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Ounion__idem) ).
fof(fact_Max_Osubset__idem,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ) ),
file('theBenchmark.p',fact_Max_Osubset__idem) ).
fof(fact_Max__Un,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ),
file('theBenchmark.p',fact_Max__Un) ).
fof(fact_Ints__odd__nonzero,axiom,
! [V_a_2,T_b] :
( class_Int_Oring__char__0(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) ),
file('theBenchmark.p',fact_Ints__odd__nonzero) ).
fof(fact_Sup__fin_Oinsert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oinsert) ).
fof(fact_Max_Oinsert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Max_Oinsert) ).
fof(fact_Sup__fin_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oinsert__remove) ).
fof(fact_Max_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_Max_Oinsert__remove) ).
fof(fact_Max_Oclosed,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Max_Oclosed) ).
fof(fact_Sup__fin_Oclosed,axiom,
! [V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oclosed) ).
fof(fact_Min_Oremove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_Min_Oremove) ).
fof(fact_fold__graph_H_Oequations_I2_J,axiom,
! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
( c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))
<=> ( ? [B_x,B_y] :
( c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),B_y)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
& hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) )
| ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2
& V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ),
file('theBenchmark.p',fact_fold__graph_H_Oequations_I2_J) ).
fof(fact_Min_Osingleton,axiom,
! [V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
file('theBenchmark.p',fact_Min_Osingleton) ).
fof(fact_Min__le,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_x_2)) ) ) ),
file('theBenchmark.p',fact_Min__le) ).
fof(fact_Min__in,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ),
file('theBenchmark.p',fact_Min__in) ).
fof(fact_Min_Oin__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ),
file('theBenchmark.p',fact_Min_Oin__idem) ).
fof(fact_Min__antimono,axiom,
! [V_N_2,V_M_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
=> ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_M_2))) ) ) ) ),
file('theBenchmark.p',fact_Min__antimono) ).
fof(fact_Min__insert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ),
file('theBenchmark.p',fact_Min__insert) ).
fof(fact_Min_Osubset__idem,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ) ),
file('theBenchmark.p',fact_Min_Osubset__idem) ).
fof(fact_Min__Un,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ),
file('theBenchmark.p',fact_Min__Un) ).
fof(fact_Min_Oinsert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Min_Oinsert) ).
fof(fact_Min_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_Min_Oinsert__remove) ).
fof(fact_minus__Min__eq__Max,axiom,
! [V_S_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ),
file('theBenchmark.p',fact_minus__Min__eq__Max) ).
fof(fact_minus__Max__eq__Min,axiom,
! [V_S_2,T_b] :
( class_Groups_Olinordered__ab__group__add(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ),
file('theBenchmark.p',fact_minus__Max__eq__Min) ).
fof(fact_Min_Oclosed,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Min_Oclosed) ).
fof(fact_in__lex__prod,axiom,
! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_b_H_2)),V_s_2))
& V_a_2 = V_a_H_2 )
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_in__lex__prod) ).
fof(fact_in__finite__psubset,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_b)))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_in__finite__psubset) ).
fof(fact_min__max_OSup__fin_Oremove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oremove) ).
fof(fact_min__max_OSup__fin_Oin__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oin__idem) ).
fof(fact_min__max_OSup__fin_Osingleton,axiom,
! [V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
file('theBenchmark.p',fact_min__max_OSup__fin_Osingleton) ).
fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert__idem) ).
fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Osubset__idem) ).
fof(fact_min__max_Oinf__Sup__absorb,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = V_a_2 ) ) ),
file('theBenchmark.p',fact_min__max_Oinf__Sup__absorb) ).
fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Ounion__idem) ).
fof(fact_min__max_OSup__fin_Oinsert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert) ).
fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert__remove) ).
fof(fact_same__fstI,axiom,
! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_P_2] :
( hBOOL(hAPP(V_P_2,V_x_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2))) ) ),
file('theBenchmark.p',fact_same__fstI) ).
fof(fact_min__max_OSup__fin_Oclosed,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oclosed) ).
fof(fact_min__max_OInf__le__Sup,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__le__Sup) ).
fof(fact_min__max_OInf__fin_Oremove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oremove) ).
fof(fact_min__max_OInf__fin_Oin__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oin__idem) ).
fof(fact_min__max_OInf__fin_Osingleton,axiom,
! [V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
file('theBenchmark.p',fact_min__max_OInf__fin_Osingleton) ).
fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert__idem) ).
fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Osubset__idem) ).
fof(fact_min__max_Osup__Inf__absorb,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = V_a_2 ) ) ),
file('theBenchmark.p',fact_min__max_Osup__Inf__absorb) ).
fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Ounion__idem) ).
fof(fact_min__max_OInf__fin_Oinsert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert) ).
fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert__remove) ).
fof(fact_min__max_OInf__fin_Oclosed,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oclosed) ).
fof(fact_folding__one_Oclosed,axiom,
! [V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_folding__one_Oclosed) ).
fof(fact_fun__upd__image,axiom,
! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
file('theBenchmark.p',fact_fun__upd__image) ).
fof(fact_setprod__gen__delta,axiom,
! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ) ),
file('theBenchmark.p',fact_setprod__gen__delta) ).
fof(fact_fun__upd__triv,axiom,
! [V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,hAPP(V_f_2,V_x_2)) = V_f_2,
file('theBenchmark.p',fact_fun__upd__triv) ).
fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
! [V_A_2,V_f_2,T_b] :
( ( class_Groups_Ocomm__monoid__mult(T_b)
& class_Groups_Ocomm__monoid__add(T_b) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2)) ),
file('theBenchmark.p',fact_transfer__nat__int__sum__prod_I2_J) ).
fof(fact_fun__upd__def,axiom,
! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
( ( V_x_2 != V_a_2
=> hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = hAPP(V_f_2,V_x_2) )
& ( V_x_2 = V_a_2
=> hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2 ) ),
file('theBenchmark.p',fact_fun__upd__def) ).
fof(fact_fun__upd__idem__iff,axiom,
! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
( c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2
<=> hAPP(V_f_2,V_x_2) = V_y_2 ),
file('theBenchmark.p',fact_fun__upd__idem__iff) ).
fof(fact_fun__upd__upd,axiom,
! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_z_2),
file('theBenchmark.p',fact_fun__upd__upd) ).
fof(fact_fun__upd__same,axiom,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2),V_x_2) = V_y_2,
file('theBenchmark.p',fact_fun__upd__same) ).
fof(fact_fun__upd__apply,axiom,
! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
( ( V_z_2 != V_x_2
=> hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) )
& ( V_z_2 = V_x_2
=> hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2 ) ),
file('theBenchmark.p',fact_fun__upd__apply) ).
fof(fact_fun__upd__twist,axiom,
! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] :
( V_a_2 != V_c_2
=> c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_a_2,V_b_2),V_c_2,V_d_2) = c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,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_c,T_b,V_x_2,V_z_2] :
( V_z_2 != V_x_2
=> hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ),
file('theBenchmark.p',fact_fun__upd__other) ).
fof(fact_fun__upd__idem,axiom,
! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
( hAPP(V_f_2,V_x_2) = V_y_2
=> c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2 ),
file('theBenchmark.p',fact_fun__upd__idem) ).
fof(fact_setprod__timesf,axiom,
! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__mult(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),V_A_2)) ),
file('theBenchmark.p',fact_setprod__timesf) ).
fof(fact_of__int__setprod,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( ( class_Rings_Oring__1(T_b)
& class_Groups_Ocomm__monoid__mult(T_b) )
=> hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ),
file('theBenchmark.p',fact_of__int__setprod) ).
fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)),
file('theBenchmark.p',fact_transfer__nat__int__sum__prod2_I2_J) ).
fof(fact_of__nat__setprod,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( ( class_Rings_Osemiring__1(T_b)
& class_Groups_Ocomm__monoid__mult(T_b) )
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ),
file('theBenchmark.p',fact_of__nat__setprod) ).
fof(fact_int__setprod,axiom,
! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2),
file('theBenchmark.p',fact_int__setprod) ).
fof(fact_setprod__1,axiom,
! [V_A_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__mult(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Oone__class_Oone(T_b))),V_A_2) = c_Groups_Oone__class_Oone(T_b) ),
file('theBenchmark.p',fact_setprod__1) ).
fof(fact_abs__setprod,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( class_Fields_Olinordered__field(T_b)
=> hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ),
file('theBenchmark.p',fact_abs__setprod) ).
fof(fact_setprod__zero__iff,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( ( class_Rings_Ono__zero__divisors(T_c)
& class_Rings_Ocomm__semiring__1(T_c) )
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
<=> ? [B_x] :
( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_setprod__zero__iff) ).
fof(fact_setprod__zero,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Rings_Ocomm__semiring__1(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ? [B_x] :
( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ),
file('theBenchmark.p',fact_setprod__zero) ).
fof(fact_setprod_Oempty,axiom,
! [V_g_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__mult(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ),
file('theBenchmark.p',fact_setprod_Oempty) ).
fof(fact_setprod__empty,axiom,
! [V_f_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__mult(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ),
file('theBenchmark.p',fact_setprod__empty) ).
fof(fact_setprod_Oinfinite,axiom,
! [V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ),
file('theBenchmark.p',fact_setprod_Oinfinite) ).
fof(fact_setprod__infinite,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ),
file('theBenchmark.p',fact_setprod__infinite) ).
fof(fact_setprod__eq__1__iff,axiom,
! [V_f_2,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
=> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ),
file('theBenchmark.p',fact_setprod__eq__1__iff) ).
fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
! [V_f_2,V_A_2,T_b] :
( ( class_Groups_Ocomm__monoid__mult(T_b)
& class_Groups_Ocomm__monoid__add(T_b) )
=> ( c_Nat__Transfer_Onat__set(V_A_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)) ) ),
file('theBenchmark.p',fact_transfer__int__nat__sum__prod_I2_J) ).
fof(fact_setprod_Odistrib,axiom,
! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_A_2)) ) ),
file('theBenchmark.p',fact_setprod_Odistrib) ).
fof(fact_setprod__dividef,axiom,
! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
( class_Fields_Ofield__inverse__zero(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Rings_Oinverse__class_Odivide(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ),
file('theBenchmark.p',fact_setprod__dividef) ).
fof(fact_dvd__setprod,axiom,
! [V_f_2,V_i_2,V_A_2,T_b,T_c] :
( class_Rings_Ocomm__semiring__1(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,V_i_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ),
file('theBenchmark.p',fact_dvd__setprod) ).
fof(fact_setprod__pos__nat__iff,axiom,
! [V_f_2,V_S_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ),
file('theBenchmark.p',fact_setprod__pos__nat__iff) ).
fof(fact_setprod__dvd__setprod__subset,axiom,
! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
( ( class_Rings_Odvd(T_c)
& class_Groups_Ocomm__monoid__mult(T_c) )
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))) ) ) ),
file('theBenchmark.p',fact_setprod__dvd__setprod__subset) ).
fof(fact_setprod__delta_H,axiom,
! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
file('theBenchmark.p',fact_setprod__delta_H) ).
fof(fact_setprod__delta,axiom,
! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) ) ) ) ),
file('theBenchmark.p',fact_setprod__delta) ).
fof(fact_setprod__constant,axiom,
! [V_y_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_COMBK(T_c,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_y_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ),
file('theBenchmark.p',fact_setprod__constant) ).
fof(fact_setprod__insert,axiom,
! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)) ) ) ),
file('theBenchmark.p',fact_setprod__insert) ).
fof(fact_setprod_Oinsert,axiom,
! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ),
file('theBenchmark.p',fact_setprod_Oinsert) ).
fof(fact_setprod_Oinsert__remove,axiom,
! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
file('theBenchmark.p',fact_setprod_Oinsert__remove) ).
fof(fact_setprod_Oremove,axiom,
! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ),
file('theBenchmark.p',fact_setprod_Oremove) ).
fof(fact_setprod__diff1,axiom,
! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
( class_Fields_Ofield(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ) ),
file('theBenchmark.p',fact_setprod__diff1) ).
fof(fact_setsum__nonneg__leq__bound,axiom,
! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ),
file('theBenchmark.p',fact_setsum__nonneg__leq__bound) ).
fof(fact_setsum__nonneg__0,axiom,
! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
( class_Groups_Oordered__ab__group__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
=> hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ),
file('theBenchmark.p',fact_setsum__nonneg__0) ).
fof(fact_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_min__max_OSup__fin_Ohom__commute,axiom,
! [V_N_2,V_h_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Ohom__commute) ).
fof(fact_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_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__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_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_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_smin__emptyI,axiom,
! [V_X_2] :
( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict)) ),
file('theBenchmark.p',fact_smin__emptyI) ).
fof(fact_wmin__insertI,axiom,
! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__weak))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__weak)) ) ) ),
file('theBenchmark.p',fact_wmin__insertI) ).
fof(fact_wmax__insertI,axiom,
! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omax__weak))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)),V_YS_2)),c_FunDef_Omax__weak)) ) ) ),
file('theBenchmark.p',fact_wmax__insertI) ).
fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
! [V_f_2,V_A_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ),
file('theBenchmark.p',fact_transfer__int__nat__sum__prod2_I2_J) ).
fof(fact_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_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_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_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ),
file('theBenchmark.p',fact_max__ext__additive) ).
fof(fact_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_b] :
( c_Wellfounded_Omax__extp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_R_2),V_x_2,V_xa_2)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ),
file('theBenchmark.p',fact_max__extp__max__ext__eq) ).
fof(fact_less__than__iff,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ),
file('theBenchmark.p',fact_less__than__iff) ).
fof(fact_intrel__iff,axiom,
! [V_v_2,V_u_2,V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2))),c_Int_Ointrel))
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2) ),
file('theBenchmark.p',fact_intrel__iff) ).
fof(fact_rp__inv__image__rp,axiom,
! [V_f_2,T_c,V_P_2,T_b] :
( c_FunDef_Oreduction__pair(T_b,V_P_2)
=> c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_P_2),V_f_2)) ),
file('theBenchmark.p',fact_rp__inv__image__rp) ).
fof(fact_pair__less__def,axiom,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
file('theBenchmark.p',fact_pair__less__def) ).
fof(fact_mlex__prod__def,axiom,
! [V_R_2,V_f_2,T_b] : c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_b),T_b),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_b,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(tc_Nat_Onat,T_b)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_prod(tc_Nat_Onat,T_b)),T_b),c_Product__Type_OPair(tc_Nat_Onat,T_b)),V_f_2)),c_COMBI(T_b))),
file('theBenchmark.p',fact_mlex__prod__def) ).
fof(fact_rp__inv__image__def,axiom,
! [T_c,T_b] : c_FunDef_Orp__inv__image(T_b,T_c) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBS(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(T_c,T_b)),c_Product__Type_OPair(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),c_Relation_Oinv__image(T_b,T_c))))),c_Relation_Oinv__image(T_b,T_c))),
file('theBenchmark.p',fact_rp__inv__image__def) ).
fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
! [V_N_2,V_h_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Ohom__commute) ).
fof(fact_Max_Ohom__commute,axiom,
! [V_N_2,V_h_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
file('theBenchmark.p',fact_Max_Ohom__commute) ).
fof(fact_measure__def,axiom,
! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than),
file('theBenchmark.p',fact_measure__def) ).
fof(fact_in__inv__image,axiom,
! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) ),
file('theBenchmark.p',fact_in__inv__image) ).
fof(fact_Min_Ohom__commute,axiom,
! [V_N_2,V_h_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
file('theBenchmark.p',fact_Min_Ohom__commute) ).
fof(fact_Sup__fin_Ohom__commute,axiom,
! [V_N_2,V_h_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Ohom__commute) ).
fof(fact_irrefl__def,axiom,
! [V_r_2,T_b] :
( c_Relation_Oirrefl(T_b,V_r_2)
<=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ),
file('theBenchmark.p',fact_irrefl__def) ).
fof(fact_Field__insert,axiom,
! [V_r_2,V_b_2,V_a_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_b),V_r_2)),
file('theBenchmark.p',fact_Field__insert) ).
fof(fact_setprod__mono__one__left,axiom,
! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
=> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) ) ) ) ),
file('theBenchmark.p',fact_setprod__mono__one__left) ).
fof(fact_Field__empty,axiom,
! [T_b] : hAPP(c_Relation_OField(T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Field__empty) ).
fof(fact_mono__Field,axiom,
! [V_s_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2))) ),
file('theBenchmark.p',fact_mono__Field) ).
fof(fact_Field__Un,axiom,
! [V_s_2,V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2)),
file('theBenchmark.p',fact_Field__Un) ).
fof(fact_finite__Field,axiom,
! [V_r_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ),
file('theBenchmark.p',fact_finite__Field) ).
fof(fact_setprod__mono__one__right,axiom,
! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
=> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) ) ) ) ),
file('theBenchmark.p',fact_setprod__mono__one__right) ).
fof(fact_setsum__mono__zero__left,axiom,
! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
=> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) ) ) ) ),
file('theBenchmark.p',fact_setsum__mono__zero__left) ).
fof(fact_setsum__mono__zero__right,axiom,
! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
=> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) ) ) ) ),
file('theBenchmark.p',fact_setsum__mono__zero__right) ).
fof(fact_card__Pow,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ),
file('theBenchmark.p',fact_card__Pow) ).
fof(fact_finite__empty__induct,axiom,
! [V_P_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(V_P_2,V_A_2))
=> ( ! [B_a,B_A] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
=> ( hBOOL(hAPP(V_P_2,B_A))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) )
=> hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ),
file('theBenchmark.p',fact_finite__empty__induct) ).
fof(fact_folding__one__idem_Ounion__idem,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ),
file('theBenchmark.p',fact_folding__one__idem_Ounion__idem) ).
fof(fact_PowI,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ),
file('theBenchmark.p',fact_PowI) ).
fof(fact_finite__Pow__iff,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('theBenchmark.p',fact_finite__Pow__iff) ).
fof(fact_Cantors__paradox,axiom,
! [V_A_2,T_b] :
~ ? [B_f] : hAPP(c_Set_Oimage(T_b,tc_fun(T_b,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_b),V_A_2),
file('theBenchmark.p',fact_Cantors__paradox) ).
fof(fact_image__Pow__surj,axiom,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
=> hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2)) = hAPP(c_Set_OPow(T_b),V_B_2) ),
file('theBenchmark.p',fact_image__Pow__surj) ).
fof(fact_folding__one__idem_Oidem,axiom,
! [V_x_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
=> hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ),
file('theBenchmark.p',fact_folding__one__idem_Oidem) ).
fof(fact_PowD,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_PowD) ).
fof(fact_Pow__iff,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_Pow__iff) ).
fof(fact_Pow__top,axiom,
! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_A_2))),
file('theBenchmark.p',fact_Pow__top) ).
fof(fact_Pow__not__empty,axiom,
! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),
file('theBenchmark.p',fact_Pow__not__empty) ).
fof(fact_Pow__bottom,axiom,
! [V_B_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Set_OPow(T_b),V_B_2))),
file('theBenchmark.p',fact_Pow__bottom) ).
fof(fact_Pow__empty,axiom,
! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))),
file('theBenchmark.p',fact_Pow__empty) ).
fof(fact_Pow__insert,axiom,
! [V_A_2,V_a_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_b),V_a_2)),hAPP(c_Set_OPow(T_b),V_A_2))),
file('theBenchmark.p',fact_Pow__insert) ).
fof(fact_Pow__INT__eq,axiom,
! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2)),
file('theBenchmark.p',fact_Pow__INT__eq) ).
fof(fact_Pow__mono,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))) ),
file('theBenchmark.p',fact_Pow__mono) ).
fof(fact_Un__Pow__subset,axiom,
! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))),
file('theBenchmark.p',fact_Un__Pow__subset) ).
fof(fact_UN__Pow__subset,axiom,
! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))),
file('theBenchmark.p',fact_UN__Pow__subset) ).
fof(fact_Powp__Pow__eq,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Predicate_OPowp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ),
file('theBenchmark.p',fact_Powp__Pow__eq) ).
fof(fact_image__Pow__mono,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2))),hAPP(c_Set_OPow(T_b),V_B_2))) ),
file('theBenchmark.p',fact_image__Pow__mono) ).
fof(fact_folding__one__idem_Oin__idem,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ),
file('theBenchmark.p',fact_folding__one__idem_Oin__idem) ).
fof(fact_folding__one__idem_Oinsert__idem,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ),
file('theBenchmark.p',fact_folding__one__idem_Oinsert__idem) ).
fof(fact_folding__one__idem_Osubset__idem,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ),
file('theBenchmark.p',fact_folding__one__idem_Osubset__idem) ).
fof(fact_finite__subset__induct,axiom,
! [V_P_2,V_A_2,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
=> ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
=> ( ! [B_a,B_F] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
=> ( hBOOL(hAPP(V_P_2,B_F))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
=> hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ),
file('theBenchmark.p',fact_finite__subset__induct) ).
fof(fact_setsum__strict__mono,axiom,
! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
( ( class_Groups_Oordered__cancel__ab__semigroup__add(T_c)
& class_Groups_Ocomm__monoid__add(T_c) )
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2))) ) ) ) ),
file('theBenchmark.p',fact_setsum__strict__mono) ).
fof(fact_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_Image__UN,axiom,
! [V_B_2,V_A_2,T_d,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)),
file('theBenchmark.p',fact_Image__UN) ).
fof(fact_Image__Un,axiom,
! [V_B_2,V_A_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)),
file('theBenchmark.p',fact_Image__Un) ).
fof(fact_Image__empty,axiom,
! [V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Image__empty) ).
fof(fact_Image__mono,axiom,
! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ),
file('theBenchmark.p',fact_Image__mono) ).
fof(fact_Un__Image,axiom,
! [V_A_2,V_S_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_S_2),V_A_2)),
file('theBenchmark.p',fact_Un__Image) ).
fof(fact_Image__INT__subset,axiom,
! [V_B_2,V_A_2,T_d,V_r_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)))),
file('theBenchmark.p',fact_Image__INT__subset) ).
fof(fact_rev__ImageI,axiom,
! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ),
file('theBenchmark.p',fact_rev__ImageI) ).
fof(fact_Image__iff,axiom,
! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_Image__iff) ).
fof(fact_Image__eq__UN,axiom,
! [V_B_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Relation_OImage(T_c,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),
file('theBenchmark.p',fact_Image__eq__UN) ).
fof(fact_Image__singleton__iff,axiom,
! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) ),
file('theBenchmark.p',fact_Image__singleton__iff) ).
fof(fact_of__int,axiom,
! [V_j_2,V_i_2,T_b] :
( class_Rings_Oring__1(T_b)
=> hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_i_2),V_j_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_j_2)) ),
file('theBenchmark.p',fact_of__int) ).
fof(fact_One__int__def,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('theBenchmark.p',fact_One__int__def) ).
fof(fact_mult,axiom,
! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_v_2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_u_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('theBenchmark.p',fact_mult) ).
fof(fact_Rep__Integ__inverse,axiom,
! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2,
file('theBenchmark.p',fact_Rep__Integ__inverse) ).
fof(fact_minus,axiom,
! [V_y_2,V_x_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_y_2),V_x_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('theBenchmark.p',fact_minus) ).
fof(fact_Zero__int__def,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('theBenchmark.p',fact_Zero__int__def) ).
fof(fact_int__def,axiom,
! [V_m_2] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('theBenchmark.p',fact_int__def) ).
fof(fact_add,axiom,
! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),V_v_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('theBenchmark.p',fact_add) ).
fof(fact_nat,axiom,
! [V_y_2,V_x_2] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2),
file('theBenchmark.p',fact_nat) ).
fof(fact_minus__int__def,axiom,
! [V_z_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_2) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
file('theBenchmark.p',fact_minus__int__def) ).
fof(fact_less,axiom,
! [V_v_2,V_u_2,V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ),
file('theBenchmark.p',fact_less) ).
fof(fact_le,axiom,
! [V_v_2,V_u_2,V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ),
file('theBenchmark.p',fact_le) ).
fof(fact_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_quotient__def,axiom,
! [V_r_2,V_A_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)))),
file('theBenchmark.p',fact_quotient__def) ).
fof(fact_ImageE,axiom,
! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
=> ~ ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_ImageE) ).
fof(fact_quotient__empty,axiom,
! [V_r_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),
file('theBenchmark.p',fact_quotient__empty) ).
fof(fact_quotient__is__empty2,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_quotient__is__empty2) ).
fof(fact_quotient__is__empty,axiom,
! [V_r_2,V_A_2,T_b] :
( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
<=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_quotient__is__empty) ).
fof(fact_quotientI,axiom,
! [V_r_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ),
file('theBenchmark.p',fact_quotientI) ).
fof(fact_singleton__quotient,axiom,
! [V_r_2,V_x_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))),
file('theBenchmark.p',fact_singleton__quotient) ).
fof(fact_subset__equiv__class,axiom,
! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ),
file('theBenchmark.p',fact_subset__equiv__class) ).
fof(fact_quotientE,axiom,
! [V_r_2,V_A_2,V_X_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
=> ~ ! [B_x] :
( V_X_2 = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_quotientE) ).
fof(fact_Id__on__def,axiom,
! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),
file('theBenchmark.p',fact_Id__on__def) ).
fof(fact_Id__on__def_H,axiom,
! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),c_fequal))),V_A_2)),
file('theBenchmark.p',fact_Id__on__def_H) ).
fof(fact_Id__on__empty,axiom,
! [T_b] : c_Relation_OId__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),
file('theBenchmark.p',fact_Id__on__empty) ).
fof(fact_Id__on__eqI,axiom,
! [V_A_2,T_b,V_b_2,V_a_2] :
( V_a_2 = V_b_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId__on(T_b,V_A_2))) ) ),
file('theBenchmark.p',fact_Id__on__eqI) ).
fof(fact_Id__on__iff,axiom,
! [V_A_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
& V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_Id__on__iff) ).
fof(fact_equiv__class__self,axiom,
! [V_a_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
file('theBenchmark.p',fact_equiv__class__self) ).
fof(fact_equiv__class__eq,axiom,
! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
=> hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_equiv__class__eq) ).
fof(fact_quotient__eq__iff,axiom,
! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
=> ( V_X_2 = V_Y_2
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_quotient__eq__iff) ).
fof(fact_quotient__eqI,axiom,
! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
=> V_X_2 = V_Y_2 ) ) ) ) ) ),
file('theBenchmark.p',fact_quotient__eqI) ).
fof(fact_eq__equiv__class,axiom,
! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
=> ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ),
file('theBenchmark.p',fact_eq__equiv__class) ).
fof(fact_eq__equiv__class__iff,axiom,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
=> ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ),
file('theBenchmark.p',fact_eq__equiv__class__iff) ).
fof(fact_equiv__class__eq__iff,axiom,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
<=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
& hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ),
file('theBenchmark.p',fact_equiv__class__eq__iff) ).
fof(fact_equiv__class__subset,axiom,
! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
file('theBenchmark.p',fact_equiv__class__subset) ).
fof(fact_eq__equiv__class__iff2,axiom,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
=> ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ),
file('theBenchmark.p',fact_eq__equiv__class__iff2) ).
fof(fact_UN__equiv__class,axiom,
! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2) ) ) ),
file('theBenchmark.p',fact_UN__equiv__class) ).
fof(fact_UN__equiv__class2,axiom,
! [V_a2_2,V_a1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
=> ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
=> ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2) ) ) ) ) ),
file('theBenchmark.p',fact_UN__equiv__class2) ).
fof(fact_equiv__class__nondisjoint,axiom,
! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_equiv__class__nondisjoint) ).
fof(fact_inf1E,axiom,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
=> ~ ( hBOOL(hAPP(V_A_2,V_x_2))
=> ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ),
file('theBenchmark.p',fact_inf1E) ).
fof(fact_inf1I,axiom,
! [T_b,V_B_2,V_x_2,V_A_2] :
( hBOOL(hAPP(V_A_2,V_x_2))
=> ( hBOOL(hAPP(V_B_2,V_x_2))
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ),
file('theBenchmark.p',fact_inf1I) ).
fof(fact_IntE,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
file('theBenchmark.p',fact_IntE) ).
fof(fact_IntI,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
file('theBenchmark.p',fact_IntI) ).
fof(fact_finite__Int,axiom,
! [V_G_2,V_F_2,T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2))
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2))) ),
file('theBenchmark.p',fact_finite__Int) ).
fof(fact_Int__UN__distrib2,axiom,
! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))),
file('theBenchmark.p',fact_Int__UN__distrib2) ).
fof(fact_UN__extend__simps_I4_J,axiom,
! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)),
file('theBenchmark.p',fact_UN__extend__simps_I4_J) ).
fof(fact_Int__UN__distrib,axiom,
! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)),
file('theBenchmark.p',fact_Int__UN__distrib) ).
fof(fact_UN__extend__simps_I5_J,axiom,
! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
file('theBenchmark.p',fact_UN__extend__simps_I5_J) ).
fof(fact_UN__simps_I4_J,axiom,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
file('theBenchmark.p',fact_UN__simps_I4_J) ).
fof(fact_UN__simps_I5_J,axiom,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
file('theBenchmark.p',fact_UN__simps_I5_J) ).
fof(fact_Pow__Int__eq,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2)),
file('theBenchmark.p',fact_Pow__Int__eq) ).
fof(fact_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_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_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_inf1D2,axiom,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
=> hBOOL(hAPP(V_B_2,V_x_2)) ),
file('theBenchmark.p',fact_inf1D2) ).
fof(fact_inf1D1,axiom,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
=> hBOOL(hAPP(V_A_2,V_x_2)) ),
file('theBenchmark.p',fact_inf1D1) ).
fof(fact_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_inf__fun__def,axiom,
! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
( class_Lattices_Olattice(T_b)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ),
file('theBenchmark.p',fact_inf__fun__def) ).
fof(fact_inf__apply,axiom,
! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
( class_Lattices_Olattice(T_b)
=> hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ),
file('theBenchmark.p',fact_inf__apply) ).
fof(fact_inf__assoc,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ),
file('theBenchmark.p',fact_inf__assoc) ).
fof(fact_inf__sup__aci_I2_J,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) ),
file('theBenchmark.p',fact_inf__sup__aci_I2_J) ).
fof(fact_inf_Oassoc,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ),
file('theBenchmark.p',fact_inf_Oassoc) ).
fof(fact_inf__left__commute,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ),
file('theBenchmark.p',fact_inf__left__commute) ).
fof(fact_inf__sup__aci_I3_J,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ),
file('theBenchmark.p',fact_inf__sup__aci_I3_J) ).
fof(fact_inf_Oleft__commute,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_c)) ),
file('theBenchmark.p',fact_inf_Oleft__commute) ).
fof(fact_inf__left__idem,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ),
file('theBenchmark.p',fact_inf__left__idem) ).
fof(fact_inf__sup__aci_I4_J,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) ),
file('theBenchmark.p',fact_inf__sup__aci_I4_J) ).
fof(fact_inf_Oleft__idem,axiom,
! [V_b,V_a,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) ),
file('theBenchmark.p',fact_inf_Oleft__idem) ).
fof(fact_inf__commute,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ),
file('theBenchmark.p',fact_inf__commute) ).
fof(fact_inf__sup__aci_I1_J,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x) ),
file('theBenchmark.p',fact_inf__sup__aci_I1_J) ).
fof(fact_inf_Ocommute,axiom,
! [V_b,V_a,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b),V_a) ),
file('theBenchmark.p',fact_inf_Ocommute) ).
fof(fact_inf__idem,axiom,
! [V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ),
file('theBenchmark.p',fact_inf__idem) ).
fof(fact_inf_Oidem,axiom,
! [V_a,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ),
file('theBenchmark.p',fact_inf_Oidem) ).
fof(fact_Int__assoc,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
file('theBenchmark.p',fact_Int__assoc) ).
fof(fact_Int__left__commute,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
file('theBenchmark.p',fact_Int__left__commute) ).
fof(fact_Int__left__absorb,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
file('theBenchmark.p',fact_Int__left__absorb) ).
fof(fact_Int__commute,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2),
file('theBenchmark.p',fact_Int__commute) ).
fof(fact_Int__absorb,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2,
file('theBenchmark.p',fact_Int__absorb) ).
fof(fact_inf__min,axiom,
! [T_b] :
( ( class_Orderings_Olinorder(T_b)
& class_Lattices_Osemilattice__inf(T_b) )
=> c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ),
file('theBenchmark.p',fact_inf__min) ).
fof(fact_Diff__Int2,axiom,
! [V_B_2,V_C_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2),
file('theBenchmark.p',fact_Diff__Int2) ).
fof(fact_Diff__Int__distrib2,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
file('theBenchmark.p',fact_Diff__Int__distrib2) ).
fof(fact_Int__Diff,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
file('theBenchmark.p',fact_Int__Diff) ).
fof(fact_Diff__Int__distrib,axiom,
! [V_B_2,V_A_2,V_C_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
file('theBenchmark.p',fact_Diff__Int__distrib) ).
fof(fact_le__infE,axiom,
! [V_b,V_a,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)))
=> ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ),
file('theBenchmark.p',fact_le__infE) ).
fof(fact_inf__mono,axiom,
! [V_d,V_b,V_c,V_a,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_c),V_d))) ) ) ),
file('theBenchmark.p',fact_inf__mono) ).
fof(fact_inf__greatest,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))) ) ) ),
file('theBenchmark.p',fact_inf__greatest) ).
fof(fact_le__infI,axiom,
! [V_b,V_a,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) ) ) ),
file('theBenchmark.p',fact_le__infI) ).
fof(fact_inf__absorb2,axiom,
! [V_x,V_y,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ),
file('theBenchmark.p',fact_inf__absorb2) ).
fof(fact_inf__absorb1,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ),
file('theBenchmark.p',fact_inf__absorb1) ).
fof(fact_le__infI2,axiom,
! [V_a,V_x,V_b,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ),
file('theBenchmark.p',fact_le__infI2) ).
fof(fact_le__infI1,axiom,
! [V_b,V_x,V_a,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ),
file('theBenchmark.p',fact_le__infI1) ).
fof(fact_le__inf__iff,axiom,
! [V_z_2,V_y_2,V_x_2,T_b] :
( class_Lattices_Osemilattice__inf(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_y_2),V_z_2)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_le__inf__iff) ).
fof(fact_le__iff__inf,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Lattices_Osemilattice__inf(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
<=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ),
file('theBenchmark.p',fact_le__iff__inf) ).
fof(fact_inf__le2,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ),
file('theBenchmark.p',fact_inf__le2) ).
fof(fact_inf__sup__ord_I2_J,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ),
file('theBenchmark.p',fact_inf__sup__ord_I2_J) ).
fof(fact_inf__le1,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Osemilattice__inf(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ),
file('theBenchmark.p',fact_inf__le1) ).
fof(fact_inf__sup__ord_I1_J,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ),
file('theBenchmark.p',fact_inf__sup__ord_I1_J) ).
fof(fact_Int__lower1,axiom,
! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
file('theBenchmark.p',fact_Int__lower1) ).
fof(fact_Int__lower2,axiom,
! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)),
file('theBenchmark.p',fact_Int__lower2) ).
fof(fact_Int__absorb2,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ),
file('theBenchmark.p',fact_Int__absorb2) ).
fof(fact_Int__absorb1,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ),
file('theBenchmark.p',fact_Int__absorb1) ).
fof(fact_Int__greatest,axiom,
! [V_B_2,V_A_2,V_C_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
file('theBenchmark.p',fact_Int__greatest) ).
fof(fact_Int__mono,axiom,
! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ),
file('theBenchmark.p',fact_Int__mono) ).
fof(fact_INT__Int__distrib,axiom,
! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)),
file('theBenchmark.p',fact_INT__Int__distrib) ).
fof(fact_inf__Int__eq,axiom,
! [V_x_2,V_S_2,V_R_2,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ),
file('theBenchmark.p',fact_inf__Int__eq) ).
fof(fact_IntD2,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ),
file('theBenchmark.p',fact_IntD2) ).
fof(fact_IntD1,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
file('theBenchmark.p',fact_IntD1) ).
fof(fact_Int__iff,axiom,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ),
file('theBenchmark.p',fact_Int__iff) ).
fof(fact_sup__inf__distrib2,axiom,
! [V_x,V_z,V_y,T_a] :
( class_Lattices_Odistrib__lattice(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_z),V_x)) ),
file('theBenchmark.p',fact_sup__inf__distrib2) ).
fof(fact_inf__sup__distrib2,axiom,
! [V_x,V_z,V_y,T_a] :
( class_Lattices_Odistrib__lattice(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_x)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_z),V_x)) ),
file('theBenchmark.p',fact_inf__sup__distrib2) ).
fof(fact_sup__inf__distrib1,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Odistrib__lattice(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ),
file('theBenchmark.p',fact_sup__inf__distrib1) ).
fof(fact_inf__sup__distrib1,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Odistrib__lattice(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z)) ),
file('theBenchmark.p',fact_inf__sup__distrib1) ).
fof(fact_sup__inf__absorb,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = V_x ),
file('theBenchmark.p',fact_sup__inf__absorb) ).
fof(fact_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_Un__Int__crazy,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),
file('theBenchmark.p',fact_Un__Int__crazy) ).
fof(fact_Un__Int__distrib2,axiom,
! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),
file('theBenchmark.p',fact_Un__Int__distrib2) ).
fof(fact_Int__Un__distrib2,axiom,
! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),
file('theBenchmark.p',fact_Int__Un__distrib2) ).
fof(fact_Un__Int__distrib,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
file('theBenchmark.p',fact_Un__Int__distrib) ).
fof(fact_Int__Un__distrib,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
file('theBenchmark.p',fact_Int__Un__distrib) ).
fof(fact_Int__empty__left,axiom,
! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Int__empty__left) ).
fof(fact_Int__empty__right,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Int__empty__right) ).
fof(fact_disjoint__iff__not__equal,axiom,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
=> B_x != B_xa ) ) ),
file('theBenchmark.p',fact_disjoint__iff__not__equal) ).
fof(fact_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_insert__inter__insert,axiom,
! [V_B_2,V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
file('theBenchmark.p',fact_insert__inter__insert) ).
fof(fact_distrib__sup__le,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)))) ),
file('theBenchmark.p',fact_distrib__sup__le) ).
fof(fact_distrib__inf__le,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Lattices_Olattice(T_a)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)))) ),
file('theBenchmark.p',fact_distrib__inf__le) ).
fof(fact_compl__inf__bot,axiom,
! [V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_x) = c_Orderings_Obot__class_Obot(T_a) ),
file('theBenchmark.p',fact_compl__inf__bot) ).
fof(fact_inf__compl__bot,axiom,
! [V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = c_Orderings_Obot__class_Obot(T_a) ),
file('theBenchmark.p',fact_inf__compl__bot) ).
fof(fact_diff__eq,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
file('theBenchmark.p',fact_diff__eq) ).
fof(fact_compl__sup,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
file('theBenchmark.p',fact_compl__sup) ).
fof(fact_compl__inf,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
file('theBenchmark.p',fact_compl__inf) ).
fof(fact_Int__insert__right,axiom,
! [V_B_2,V_A_2,V_a_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_Int__insert__right) ).
fof(fact_Int__insert__left,axiom,
! [V_B_2,V_C_2,V_a_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ) ),
file('theBenchmark.p',fact_Int__insert__left) ).
fof(fact_Int__insert__right__if0,axiom,
! [V_B_2,V_A_2,V_a_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ),
file('theBenchmark.p',fact_Int__insert__right__if0) ).
fof(fact_Int__insert__left__if0,axiom,
! [V_B_2,V_C_2,V_a_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) ),
file('theBenchmark.p',fact_Int__insert__left__if0) ).
fof(fact_Int__insert__right__if1,axiom,
! [V_B_2,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_Int__insert__right__if1) ).
fof(fact_Int__insert__left__if1,axiom,
! [V_B_2,V_C_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ),
file('theBenchmark.p',fact_Int__insert__left__if1) ).
fof(fact_mono__inf,axiom,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
( ( class_Lattices_Osemilattice__inf(T_b)
& class_Lattices_Osemilattice__inf(T_c) )
=> ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2)))) ) ),
file('theBenchmark.p',fact_mono__inf) ).
fof(fact_image__Int__subset,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)))),
file('theBenchmark.p',fact_image__Int__subset) ).
fof(fact_Diff__triv,axiom,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ),
file('theBenchmark.p',fact_Diff__triv) ).
fof(fact_Diff__disjoint,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Diff__disjoint) ).
fof(fact_Un__Int__assoc__eq,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ),
file('theBenchmark.p',fact_Un__Int__assoc__eq) ).
fof(fact_Un__Diff__Int,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2,
file('theBenchmark.p',fact_Un__Diff__Int) ).
fof(fact_Diff__Un,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
file('theBenchmark.p',fact_Diff__Un) ).
fof(fact_Diff__Int,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
file('theBenchmark.p',fact_Diff__Int) ).
fof(fact_ivl__disj__int_I11_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I11_J) ).
fof(fact_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_Compl__disjoint,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Compl__disjoint) ).
fof(fact_Compl__disjoint2,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Compl__disjoint2) ).
fof(fact_Image__Int__subset,axiom,
! [V_B_2,V_A_2,V_R_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)))),
file('theBenchmark.p',fact_Image__Int__subset) ).
fof(fact_Compl__Int,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
file('theBenchmark.p',fact_Compl__Int) ).
fof(fact_Compl__Un,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
file('theBenchmark.p',fact_Compl__Un) ).
fof(fact_Diff__Compl,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
file('theBenchmark.p',fact_Diff__Compl) ).
fof(fact_Diff__eq,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
file('theBenchmark.p',fact_Diff__eq) ).
fof(fact_ivl__disj__int_I14_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I14_J) ).
fof(fact_mono__Int,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2)))) ),
file('theBenchmark.p',fact_mono__Int) ).
fof(fact_Image__Id__on,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
file('theBenchmark.p',fact_Image__Id__on) ).
fof(fact_INT__absorb,axiom,
! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ),
file('theBenchmark.p',fact_INT__absorb) ).
fof(fact_INT__extend__simps_I1_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) ),
file('theBenchmark.p',fact_INT__extend__simps_I1_J) ).
fof(fact_INT__extend__simps_I2_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) ),
file('theBenchmark.p',fact_INT__extend__simps_I2_J) ).
fof(fact_INT__insert,axiom,
! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
file('theBenchmark.p',fact_INT__insert) ).
fof(fact_INT__Un,axiom,
! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)),
file('theBenchmark.p',fact_INT__Un) ).
fof(fact_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_congruent2__implies__congruent,axiom,
! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
=> ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ),
file('theBenchmark.p',fact_congruent2__implies__congruent) ).
fof(fact_inf__Sup__absorb,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = V_a_2 ) ) ),
file('theBenchmark.p',fact_inf__Sup__absorb) ).
fof(fact_min__max_Omono__inf,axiom,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Olinorder(T_b)
& class_Lattices_Osemilattice__inf(T_c) )
=> ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2)))) ) ),
file('theBenchmark.p',fact_min__max_Omono__inf) ).
fof(fact_disjoint__eq__subset__Compl,axiom,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) ),
file('theBenchmark.p',fact_disjoint__eq__subset__Compl) ).
fof(fact_ivl__disj__int_I15_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I15_J) ).
fof(fact_lfp__induct,axiom,
! [V_P_2,V_f_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_P_2))),V_P_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_P_2)) ) ) ),
file('theBenchmark.p',fact_lfp__induct) ).
fof(fact_def__lfp__induct,axiom,
! [V_P_2,V_f_2,V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
=> ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_A_2),V_P_2))),V_P_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_A_2),V_P_2)) ) ) ) ),
file('theBenchmark.p',fact_def__lfp__induct) ).
fof(fact_Int__atLeastAtMost,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__atLeastAtMost) ).
fof(fact_Int__atLeastLessThan,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__atLeastLessThan) ).
fof(fact_ivl__disj__int_I4_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I4_J) ).
fof(fact_ivl__disj__int_I2_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I2_J) ).
fof(fact_ivl__disj__int_I16_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I16_J) ).
fof(fact_ivl__disj__int_I13_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I13_J) ).
fof(fact_ivl__disj__int_I12_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I12_J) ).
fof(fact_Int__greaterThanAtMost,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__greaterThanAtMost) ).
fof(fact_ivl__disj__int_I9_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I9_J) ).
fof(fact_Int__greaterThanLessThan,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__greaterThanLessThan) ).
fof(fact_Int__atLeastAtMostR1,axiom,
! [V_d_2,V_c_2,V_b_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__atLeastAtMostR1) ).
fof(fact_Int__atLeastAtMostL1,axiom,
! [V_d_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
file('theBenchmark.p',fact_Int__atLeastAtMostL1) ).
fof(fact_ivl__disj__int_I8_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I8_J) ).
fof(fact_ivl__disj__int_I7_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I7_J) ).
fof(fact_Int__atLeastAtMostR2,axiom,
! [V_d_2,V_c_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_d_2) ),
file('theBenchmark.p',fact_Int__atLeastAtMostR2) ).
fof(fact_Int__atLeastAtMostL2,axiom,
! [V_c_2,V_b_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_b_2) ),
file('theBenchmark.p',fact_Int__atLeastAtMostL2) ).
fof(fact_ivl__disj__int_I3_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I3_J) ).
fof(fact_ivl__disj__int_I1_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I1_J) ).
fof(fact_ivl__disj__int_I10_J,axiom,
! [V_u_2,V_m_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I10_J) ).
fof(fact_ivl__disj__int_I6_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I6_J) ).
fof(fact_ivl__disj__int_I5_J,axiom,
! [V_u_2,V_l_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_ivl__disj__int_I5_J) ).
fof(fact_folding__image__simple_Ounion__inter,axiom,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
file('theBenchmark.p',fact_folding__image__simple_Ounion__inter) ).
fof(fact_setsum__Un__Int,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_setsum__Un__Int) ).
fof(fact_setprod__Un__Int,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_setprod__Un__Int) ).
fof(fact_setprod_Ounion__inter,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_setprod_Ounion__inter) ).
fof(fact_card_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ),
file('theBenchmark.p',fact_card_Ounion__inter) ).
fof(fact_card__Un__Int,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
file('theBenchmark.p',fact_card__Un__Int) ).
fof(fact_card__Diff__subset__Int,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
file('theBenchmark.p',fact_card__Diff__subset__Int) ).
fof(fact_setsum__restrict__set,axiom,
! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ),
file('theBenchmark.p',fact_setsum__restrict__set) ).
fof(fact_quotient__disj,axiom,
! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| V_X_2 = V_Y_2 ) ) ) ),
file('theBenchmark.p',fact_quotient__disj) ).
fof(fact_atMost__Int__atLeast,axiom,
! [V_na_2,T_b] :
( class_Orderings_Oorder(T_b)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_na_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_na_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_na_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_atMost__Int__atLeast) ).
fof(fact_folding__image__simple_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_folding__image__simple_Ounion__disjoint) ).
fof(fact_folding__one_Ounion__inter,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_folding__one_Ounion__inter) ).
fof(fact_folding__one_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_folding__one_Ounion__disjoint) ).
fof(fact_congruent__def,axiom,
! [V_f_2,V_r_2,T_c,T_b] :
( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2))),V_f_2)),B_x)) ) ),
file('theBenchmark.p',fact_congruent__def) ).
fof(fact_setsum__Un__disjoint,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_setsum__Un__disjoint) ).
fof(fact_setsum__Un,axiom,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Oab__group__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
file('theBenchmark.p',fact_setsum__Un) ).
fof(fact_setprod_Ounion__disjoint,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_setprod_Ounion__disjoint) ).
fof(fact_setprod__Un__disjoint,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_setprod__Un__disjoint) ).
fof(fact_card__Un__disjoint,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ),
file('theBenchmark.p',fact_card__Un__disjoint) ).
fof(fact_Sup__fin_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Ounion__disjoint) ).
fof(fact_Sup__fin_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Ounion__inter) ).
fof(fact_Min_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_Min_Ounion__disjoint) ).
fof(fact_Min_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_Min_Ounion__inter) ).
fof(fact_Max_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_Max_Ounion__inter) ).
fof(fact_Max_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_Max_Ounion__disjoint) ).
fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Ounion__disjoint) ).
fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Ounion__inter) ).
fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Ounion__inter) ).
fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Ounion__disjoint) ).
fof(fact_congruent2D,axiom,
! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_d,T_c,T_b] :
( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y1_2),V_z1_2)),V_r1_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y2_2),V_z2_2)),V_r2_2))
=> hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ),
file('theBenchmark.p',fact_congruent2D) ).
fof(fact_setsum__Un__nat,axiom,
! [V_f_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
file('theBenchmark.p',fact_setsum__Un__nat) ).
fof(fact_congruentD,axiom,
! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_r_2))
=> hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ),
file('theBenchmark.p',fact_congruentD) ).
fof(fact_congruent2__implies__congruent__UN,axiom,
! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
=> ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
=> ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
=> c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_d,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) ) ) ) ),
file('theBenchmark.p',fact_congruent2__implies__congruent__UN) ).
fof(fact_UN__equiv__class__inject,axiom,
! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
=> ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_Y_2),V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
=> ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) ) ) )
=> V_X_2 = V_Y_2 ) ) ) ) ) ),
file('theBenchmark.p',fact_UN__equiv__class__inject) ).
fof(fact_UN__equiv__class__type2,axiom,
! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
=> ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
=> ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A1_2),V_r1_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A2_2),V_r2_2)))
=> ( ! [B_x1] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
=> ! [B_x2] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_UN__equiv__class__type2) ).
fof(fact_UN__equiv__class__type,axiom,
! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_UN__equiv__class__type) ).
fof(fact_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_inf__Int__eq2,axiom,
! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ),
file('theBenchmark.p',fact_inf__Int__eq2) ).
fof(fact_card_Ounion__inter__neutral,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ),
file('theBenchmark.p',fact_card_Ounion__inter__neutral) ).
fof(fact_setprod__Un,axiom,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( class_Fields_Ofield(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ),
file('theBenchmark.p',fact_setprod__Un) ).
fof(fact_setprod__Un__one,axiom,
! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
=> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2)) ) ) ) ),
file('theBenchmark.p',fact_setprod__Un__one) ).
fof(fact_inf2E,axiom,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
=> ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
=> ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_inf2E) ).
fof(fact_inf2I,axiom,
! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_inf2I) ).
fof(fact_inf2D2,axiom,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ),
file('theBenchmark.p',fact_inf2D2) ).
fof(fact_inf2D1,axiom,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ),
file('theBenchmark.p',fact_inf2D1) ).
fof(fact_setprod_Ounion__inter__neutral,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_setprod_Ounion__inter__neutral) ).
fof(fact_setsum__Un__zero,axiom,
! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
=> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2)) ) ) ) ),
file('theBenchmark.p',fact_setsum__Un__zero) ).
fof(fact_setsum_Ounion__inter__neutral,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_setsum_Ounion__inter__neutral) ).
fof(fact_refl__on__def_H,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),B_x)) ) ) ),
file('theBenchmark.p',fact_refl__on__def_H) ).
fof(fact_Inf__fin_Oremove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 ) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oremove) ).
fof(fact_equiv__imp__dvd__card,axiom,
! [V_k_2,V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),B_x))) )
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ),
file('theBenchmark.p',fact_equiv__imp__dvd__card) ).
fof(fact_refl__on__Id__on,axiom,
! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)),
file('theBenchmark.p',fact_refl__on__Id__on) ).
fof(fact_Inf__fin_Osingleton,axiom,
! [V_x_2,T_b] :
( class_Lattices_Olattice(T_b)
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
file('theBenchmark.p',fact_Inf__fin_Osingleton) ).
fof(fact_refl__on__empty,axiom,
! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),
file('theBenchmark.p',fact_refl__on__empty) ).
fof(fact_refl__on__Un,axiom,
! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
=> c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
file('theBenchmark.p',fact_refl__on__Un) ).
fof(fact_refl__on__Int,axiom,
! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
=> c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
file('theBenchmark.p',fact_refl__on__Int) ).
fof(fact_sup__Inf__absorb,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = V_a_2 ) ) ),
file('theBenchmark.p',fact_sup__Inf__absorb) ).
fof(fact_Inf__fin_Oin__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oin__idem) ).
fof(fact_refl__onD,axiom,
! [V_a_2,V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_refl__onD) ).
fof(fact_refl__onD1,axiom,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
file('theBenchmark.p',fact_refl__onD1) ).
fof(fact_refl__onD2,axiom,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ),
file('theBenchmark.p',fact_refl__onD2) ).
fof(fact_Inf__fin_Oinsert__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oinsert__idem) ).
fof(fact_Inf__fin_Osubset__idem,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Osubset__idem) ).
fof(fact_Inf__fin_Ounion__idem,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Ounion__idem) ).
fof(fact_Inf__le__Sup,axiom,
! [V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2))) ) ) ),
file('theBenchmark.p',fact_Inf__le__Sup) ).
fof(fact_Inf__fin_Oinsert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oinsert) ).
fof(fact_Inf__fin_Oinsert__remove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oinsert__remove) ).
fof(fact_Inf__fin_Ounion__disjoint,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Ounion__disjoint) ).
fof(fact_Inf__fin_Ounion__inter,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Ounion__inter) ).
fof(fact_Inf__fin_Oclosed,axiom,
! [V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oclosed) ).
fof(fact_card__quotient__disjoint,axiom,
! [V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2)
=> hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ),
file('theBenchmark.p',fact_card__quotient__disjoint) ).
fof(fact_Id__onE,axiom,
! [V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2)))
=> ~ ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ),
file('theBenchmark.p',fact_Id__onE) ).
fof(fact_inj__on__empty,axiom,
! [V_f_2,T_c,T_b] : c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
file('theBenchmark.p',fact_inj__on__empty) ).
fof(fact_inj__uminus,axiom,
! [V_A_2,T_b] :
( class_Groups_Oordered__ab__group__add(T_b)
=> c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ),
file('theBenchmark.p',fact_inj__uminus) ).
fof(fact_inj__on__Int,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
=> c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_inj__on__Int) ).
fof(fact_inj__on__contraD,axiom,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( V_x_2 != V_y_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
=> hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ),
file('theBenchmark.p',fact_inj__on__contraD) ).
fof(fact_inj__on__iff,axiom,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
=> ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ) ),
file('theBenchmark.p',fact_inj__on__iff) ).
fof(fact_inj__onD,axiom,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
=> V_x_2 = V_y_2 ) ) ) ),
file('theBenchmark.p',fact_inj__onD) ).
fof(fact_subset__inj__on,axiom,
! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
file('theBenchmark.p',fact_subset__inj__on) ).
fof(fact_strict__mono__imp__inj__on,axiom,
! [V_A_2,V_f_2,T_b,T_c] :
( ( class_Orderings_Olinorder(T_b)
& class_Orderings_Oorder(T_c) )
=> ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
=> c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
file('theBenchmark.p',fact_strict__mono__imp__inj__on) ).
fof(fact_inj__on__diff,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
file('theBenchmark.p',fact_inj__on__diff) ).
fof(fact_inj__on__id2,axiom,
! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2),
file('theBenchmark.p',fact_inj__on__id2) ).
fof(fact_inj__on__def,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
=> ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
=> B_x = B_xa ) ) ) ),
file('theBenchmark.p',fact_inj__on__def) ).
fof(fact_finite__imageD,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
=> ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ),
file('theBenchmark.p',fact_finite__imageD) ).
fof(fact_inj__on__Un__image__eq__iff,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
<=> V_A_2 = V_B_2 ) ),
file('theBenchmark.p',fact_inj__on__Un__image__eq__iff) ).
fof(fact_card__image,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ),
file('theBenchmark.p',fact_card__image) ).
fof(fact_inj__on__strict__subset,axiom,
! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ),
file('theBenchmark.p',fact_inj__on__strict__subset) ).
fof(fact_finite__surj__inj,axiom,
! [V_f_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)))
=> c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ),
file('theBenchmark.p',fact_finite__surj__inj) ).
fof(fact_endo__inj__surj,axiom,
! [V_f_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)),V_A_2))
=> ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
=> hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ),
file('theBenchmark.p',fact_endo__inj__surj) ).
fof(fact_inj__on__image__Int,axiom,
! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
=> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_inj__on__image__Int) ).
fof(fact_eq__card__imp__inj__on,axiom,
! [V_f_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
=> c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
file('theBenchmark.p',fact_eq__card__imp__inj__on) ).
fof(fact_inj__on__iff__eq__card,axiom,
! [V_f_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
<=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ),
file('theBenchmark.p',fact_inj__on__iff__eq__card) ).
fof(fact_inj__on__image__set__diff,axiom,
! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
=> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_inj__on__image__set__diff) ).
fof(fact_pigeonhole,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)))
=> ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ),
file('theBenchmark.p',fact_pigeonhole) ).
fof(fact_inj__on__fun__updI,axiom,
! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
=> c_Fun_Oinj__on(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_A_2) ) ),
file('theBenchmark.p',fact_inj__on__fun__updI) ).
fof(fact_card__bij__eq,axiom,
! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
=> ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ),
file('theBenchmark.p',fact_card__bij__eq) ).
fof(fact_inj__on__insert,axiom,
! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
<=> ( ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
& c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
file('theBenchmark.p',fact_inj__on__insert) ).
fof(fact_inj__on__Un,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
<=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
& c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
& c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
file('theBenchmark.p',fact_inj__on__Un) ).
fof(fact_inj__on__iff__card__le,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( ? [B_f] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_B_2))
& c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) )
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ),
file('theBenchmark.p',fact_inj__on__iff__card__le) ).
fof(fact_card__inj__on__le,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ),
file('theBenchmark.p',fact_card__inj__on__le) ).
fof(fact_quotient__diff1,axiom,
! [V_a_2,V_A_2,V_r_2,T_b] :
( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)) ) ),
file('theBenchmark.p',fact_quotient__diff1) ).
fof(fact_inj__on__iff__surj,axiom,
! [V_A_H_2,T_c,T_b,V_A_2] :
( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ? [B_f] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_A_H_2))
& c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) )
<=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ),
file('theBenchmark.p',fact_inj__on__iff__surj) ).
fof(fact_image__INT,axiom,
! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) )
=> ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
=> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)) ) ) ),
file('theBenchmark.p',fact_image__INT) ).
fof(fact_the__inv__into__into,axiom,
! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ),
file('theBenchmark.p',fact_the__inv__into__into) ).
fof(fact_inj__Suc,axiom,
! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2),
file('theBenchmark.p',fact_inj__Suc) ).
fof(fact_inj__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_swap__inj__on,axiom,
! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(tc_prod(T_b,T_c),tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_c,T_b)),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))),V_A_2),
file('theBenchmark.p',fact_swap__inj__on) ).
fof(fact_the__inv__into__f__eq,axiom,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hAPP(V_f_2,V_x_2) = V_y_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ),
file('theBenchmark.p',fact_the__inv__into__f__eq) ).
fof(fact_the__inv__into__f__f,axiom,
! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ),
file('theBenchmark.p',fact_the__inv__into__f__f) ).
fof(fact_inj__on__the__inv__into,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> c_Fun_Oinj__on(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ),
file('theBenchmark.p',fact_inj__on__the__inv__into) ).
fof(fact_the__inv__into__onto,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> hAPP(c_Set_Oimage(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ),
file('theBenchmark.p',fact_the__inv__into__onto) ).
fof(fact_the__inv__into__def,axiom,
! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))),
file('theBenchmark.p',fact_the__inv__into__def) ).
fof(fact_f__the__inv__into__f,axiom,
! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
=> hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ),
file('theBenchmark.p',fact_f__the__inv__into__f) ).
fof(fact_fold__Un__disjoint,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_fold__Un__disjoint) ).
fof(fact_Inf__fin_Ohom__commute,axiom,
! [V_N_2,V_h_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Ohom__commute) ).
fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
( ( class_Groups_Ocomm__monoid__mult(T_b)
& class_Groups_Ocomm__monoid__add(T_b) )
=> ( V_A_2 = V_B_2
=> ( c_Nat__Transfer_Onat__set(V_B_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
=> hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ),
file('theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I2_J) ).
fof(fact_fold__image__empty,axiom,
! [V_z_2,V_g_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2,
file('theBenchmark.p',fact_fold__image__empty) ).
fof(fact_folding__image__simple_Oeq__fold__g,axiom,
! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ),
file('theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).
fof(fact_fold__image__distrib,axiom,
! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)) ) ),
file('theBenchmark.p',fact_fold__image__distrib) ).
fof(fact_fold__image__insert,axiom,
! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
( class_Groups_Oab__semigroup__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2)) ) ) ),
file('theBenchmark.p',fact_fold__image__insert) ).
fof(fact_setsum_Oeq__fold,axiom,
! [V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) ),
file('theBenchmark.p',fact_setsum_Oeq__fold) ).
fof(fact_setsum_OF__eq,axiom,
! [V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) ) ),
file('theBenchmark.p',fact_setsum_OF__eq) ).
fof(fact_setprod_OF__eq,axiom,
! [V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2) ) ) ),
file('theBenchmark.p',fact_setprod_OF__eq) ).
fof(fact_setprod_Oeq__fold,axiom,
! [V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2) ) ),
file('theBenchmark.p',fact_setprod_Oeq__fold) ).
fof(fact_fold__image__Un__Int,axiom,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
file('theBenchmark.p',fact_fold__image__Un__Int) ).
fof(fact_image__eq__fold__image,axiom,
! [V_f_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_c,tc_HOL_Obool),T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_A_2) ),
file('theBenchmark.p',fact_image__eq__fold__image) ).
fof(fact_card_Oeq__fold__g,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ),
file('theBenchmark.p',fact_card_Oeq__fold__g) ).
fof(fact_card__def,axiom,
! [V_A_2,T_b] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ),
file('theBenchmark.p',fact_card__def) ).
fof(fact_comm__monoid__big_OF__eq,axiom,
! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
=> ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_comm__monoid__big_OF__eq) ).
fof(fact_fold__image__Un__one,axiom,
! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
=> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_T_2)) ) ) ) ),
file('theBenchmark.p',fact_fold__image__Un__one) ).
fof(fact_fold__graph__permute__diff,axiom,
! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
( class_Groups_Oab__semigroup__mult(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_x_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2)) ) ) ) ),
file('theBenchmark.p',fact_fold__graph__permute__diff) ).
fof(fact_fold__graph__imp__finite,axiom,
! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('theBenchmark.p',fact_fold__graph__imp__finite) ).
fof(fact_fold__graph_Oequations_I1_J,axiom,
! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)),
file('theBenchmark.p',fact_fold__graph_Oequations_I1_J) ).
fof(fact_fold__graph_OemptyI,axiom,
! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)),
file('theBenchmark.p',fact_fold__graph_OemptyI) ).
fof(fact_empty__fold__graphE,axiom,
! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2))
=> V_x_2 = V_z_2 ),
file('theBenchmark.p',fact_empty__fold__graphE) ).
fof(fact_fold__graph_OinsertI,axiom,
! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ),
file('theBenchmark.p',fact_fold__graph_OinsertI) ).
fof(fact_fold__graph__insert__swap,axiom,
! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
( class_Groups_Oab__semigroup__mult(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_y_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2))) ) ) ),
file('theBenchmark.p',fact_fold__graph__insert__swap) ).
fof(fact_comm__monoid__big_Oinfinite,axiom,
! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
=> ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ),
file('theBenchmark.p',fact_comm__monoid__big_Oinfinite) ).
fof(fact_Diff1__fold__graph,axiom,
! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_y_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ),
file('theBenchmark.p',fact_Diff1__fold__graph) ).
fof(fact_fold1Set_Ointros,axiom,
! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_x_2)) ) ),
file('theBenchmark.p',fact_fold1Set_Ointros) ).
fof(fact_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_accp__acc__eq,axiom,
! [V_x_2,V_r_2,T_b] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
file('theBenchmark.p',fact_accp__acc__eq) ).
fof(fact_UNIV__I,axiom,
! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_UNIV__I) ).
fof(fact_Int__UNIV__right,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2,
file('theBenchmark.p',fact_Int__UNIV__right) ).
fof(fact_Int__UNIV__left,axiom,
! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2,
file('theBenchmark.p',fact_Int__UNIV__left) ).
fof(fact_inf__top__left,axiom,
! [V_x,T_a] :
( class_Lattices_Obounded__lattice__top(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ),
file('theBenchmark.p',fact_inf__top__left) ).
fof(fact_inf__top__right,axiom,
! [V_x,T_a] :
( class_Lattices_Obounded__lattice__top(T_a)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ),
file('theBenchmark.p',fact_inf__top__right) ).
fof(fact_inf__eq__top__iff,axiom,
! [V_y_2,V_x_2,T_b] :
( class_Lattices_Obounded__lattice__top(T_b)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
<=> ( V_y_2 = c_Orderings_Otop__class_Otop(T_b)
& V_x_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ),
file('theBenchmark.p',fact_inf__eq__top__iff) ).
fof(fact_UNIV__not__empty,axiom,
! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_UNIV__not__empty) ).
fof(fact_Un__UNIV__left,axiom,
! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Un__UNIV__left) ).
fof(fact_Un__UNIV__right,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Un__UNIV__right) ).
fof(fact_range__composition,axiom,
! [V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBB(T_d,T_b,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
file('theBenchmark.p',fact_range__composition) ).
fof(fact_INTER__UNIV__conv_I1_J,axiom,
! [V_B_2,V_A_2,T_c,T_b] :
( c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_INTER__UNIV__conv_I1_J) ).
fof(fact_INTER__UNIV__conv_I2_J,axiom,
! [V_B_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
=> hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_INTER__UNIV__conv_I2_J) ).
fof(fact_finite__Prod__UNIV,axiom,
! [T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_finite__Prod__UNIV) ).
fof(fact_finite__fun__UNIVD2,axiom,
! [T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_finite__fun__UNIVD2) ).
fof(fact_finite__Plus__UNIV__iff,axiom,
! [T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_finite__Plus__UNIV__iff) ).
fof(fact_finite__option__UNIV,axiom,
! [T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool))))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_finite__option__UNIV) ).
fof(fact_finite__UNIV,axiom,
! [T_b] :
( class_Finite__Set_Ofinite(T_b)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_finite__UNIV) ).
fof(fact_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_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_subset__UNIV,axiom,
! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_subset__UNIV) ).
fof(fact_UNIV__Plus__UNIV,axiom,
! [T_c,T_b] : c_Sum__Type_OPlus(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)),
file('theBenchmark.p',fact_UNIV__Plus__UNIV) ).
fof(fact_top__apply,axiom,
! [V_x_2,T_c,T_b] :
( class_Orderings_Otop(T_b)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ),
file('theBenchmark.p',fact_top__apply) ).
fof(fact_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_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_Pow__UNIV,axiom,
! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),
file('theBenchmark.p',fact_Pow__UNIV) ).
fof(fact_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_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_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__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_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_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_injD,axiom,
! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_injD) ).
fof(fact_inj__eq,axiom,
! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_inj__eq) ).
fof(fact_empty__fold1SetE,axiom,
! [V_x_2,V_f_2,T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)),
file('theBenchmark.p',fact_empty__fold1SetE) ).
fof(fact_fold1Set__nonempty,axiom,
! [V_x_2,V_A_2,V_f_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_fold1Set__nonempty) ).
fof(fact_range__eqI,axiom,
! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
( V_b_2 = hAPP(V_f_2,V_x_2)
=> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ),
file('theBenchmark.p',fact_range__eqI) ).
fof(fact_rangeI,axiom,
! [T_c,V_x_2,V_f_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))),
file('theBenchmark.p',fact_rangeI) ).
fof(fact_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_Diff__UNIV,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Diff__UNIV) ).
fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
=> ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
fof(fact_inj__image__eq__iff,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
<=> V_A_2 = V_B_2 ) ),
file('theBenchmark.p',fact_inj__image__eq__iff) ).
fof(fact_Compl__UNIV__eq,axiom,
! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Compl__UNIV__eq) ).
fof(fact_Compl__empty__eq,axiom,
! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Compl__empty__eq) ).
fof(fact_finite__compl,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_finite__compl) ).
fof(fact_Compl__partition2,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Compl__partition2) ).
fof(fact_Compl__partition,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Compl__partition) ).
fof(fact_Compl__eq__Diff__UNIV,axiom,
! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_A_2),
file('theBenchmark.p',fact_Compl__eq__Diff__UNIV) ).
fof(fact_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_SUP__UN__eq,axiom,
! [V_x_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ),
file('theBenchmark.p',fact_SUP__UN__eq) ).
fof(fact_finite__range__imageI,axiom,
! [V_f_2,T_d,V_g_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,hAPP(hAPP(c_COMBB(T_b,T_d,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ),
file('theBenchmark.p',fact_finite__range__imageI) ).
fof(fact_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_the__inv__f__f,axiom,
! [V_x_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(c_Fun_Othe__inv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ),
file('theBenchmark.p',fact_the__inv__f__f) ).
fof(fact_INF__INT__eq,axiom,
! [V_x_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ),
file('theBenchmark.p',fact_INF__INT__eq) ).
fof(fact_INT__empty,axiom,
! [V_B_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_INT__empty) ).
fof(fact_INT__constant,axiom,
! [V_c_2,T_c,T_b,V_A_2] :
( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_INT__constant) ).
fof(fact_finite__fun__UNIVD1,axiom,
! [T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))))
=> ( hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_finite__fun__UNIVD1) ).
fof(fact_inj__of__nat,axiom,
! [T_b] :
( class_Nat_Osemiring__char__0(T_b)
=> c_Fun_Oinj__on(tc_Nat_Onat,T_b,c_Nat_Osemiring__1__class_Oof__nat(T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_inj__of__nat) ).
fof(fact_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_acc__subset,axiom,
! [V_R2_2,V_R1_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R1_2),V_R2_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oacc(T_b,V_R2_2)),c_Wellfounded_Oacc(T_b,V_R1_2))) ),
file('theBenchmark.p',fact_acc__subset) ).
fof(fact_inj__fun,axiom,
! [T_d,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> c_Fun_Oinj__on(T_b,tc_fun(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_c),T_b),c_COMBK(T_c,T_d)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_inj__fun) ).
fof(fact_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_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_inj__image__mem__iff,axiom,
! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_inj__image__mem__iff) ).
fof(fact_range__ex1__eq,axiom,
! [V_b_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
<=> ? [B_x] :
( ! [B_y] :
( V_b_2 = hAPP(V_f_2,B_y)
=> B_y = B_x )
& V_b_2 = hAPP(V_f_2,B_x) ) ) ),
file('theBenchmark.p',fact_range__ex1__eq) ).
fof(fact_finite__UNIV__surj__inj,axiom,
! [V_f_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
=> ( hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
=> c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ),
file('theBenchmark.p',fact_finite__UNIV__surj__inj) ).
fof(fact_finite__UNIV__inj__surj,axiom,
! [V_f_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
=> ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_finite__UNIV__inj__surj) ).
fof(fact_inj__image__subset__iff,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_inj__image__subset__iff) ).
fof(fact_image__Int,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ),
file('theBenchmark.p',fact_image__Int) ).
fof(fact_image__set__diff,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ),
file('theBenchmark.p',fact_image__set__diff) ).
fof(fact_surj__Compl__image__subset,axiom,
! [V_A_2,V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))) ),
file('theBenchmark.p',fact_surj__Compl__image__subset) ).
fof(fact_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_INT__simps_I1_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_INT__simps_I1_J) ).
fof(fact_INT__simps_I2_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_INT__simps_I2_J) ).
fof(fact_INT__extend__simps_I3_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2) ) ),
file('theBenchmark.p',fact_INT__extend__simps_I3_J) ).
fof(fact_INT__simps_I3_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_INT__simps_I3_J) ).
fof(fact_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_fold1Set__sing,axiom,
! [V_b_2,V_a_2,V_f_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_b_2))
<=> V_a_2 = V_b_2 ),
file('theBenchmark.p',fact_fold1Set__sing) ).
fof(fact_acc__downward,axiom,
! [V_a_2,V_r_2,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_acc__downward) ).
fof(fact_acc_Osimps,axiom,
! [V_r_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_acc_Osimps) ).
fof(fact_UN__UN__finite__eq,axiom,
! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2),
file('theBenchmark.p',fact_UN__UN__finite__eq) ).
fof(fact_inj__singleton,axiom,
! [T_b] : c_Fun_Oinj__on(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),
file('theBenchmark.p',fact_inj__singleton) ).
fof(fact_INF__INT__eq2,axiom,
! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ),
file('theBenchmark.p',fact_INF__INT__eq2) ).
fof(fact_finite__UNIV__card__ge__0,axiom,
! [T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ),
file('theBenchmark.p',fact_finite__UNIV__card__ge__0) ).
fof(fact_card__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_inj__image__Compl__subset,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))) ),
file('theBenchmark.p',fact_inj__image__Compl__subset) ).
fof(fact_INT__simps_I4_J,axiom,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) )
& ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_INT__simps_I4_J) ).
fof(fact_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_SUP__UN__eq2,axiom,
! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ),
file('theBenchmark.p',fact_SUP__UN__eq2) ).
fof(fact_UN__finite2__subset,axiom,
! [V_B_2,V_k_2,V_A_2,T_b] :
( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))) ),
file('theBenchmark.p',fact_UN__finite2__subset) ).
fof(fact_UN__finite2__eq,axiom,
! [V_B_2,V_k_2,V_A_2,T_b] :
( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2) ),
file('theBenchmark.p',fact_UN__finite2__eq) ).
fof(fact_UN__finite__subset,axiom,
! [V_C_2,V_A_2,T_b] :
( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),V_C_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)) ),
file('theBenchmark.p',fact_UN__finite__subset) ).
fof(fact_top1I,axiom,
! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)),
file('theBenchmark.p',fact_top1I) ).
fof(fact_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_iso__tuple__UNIV__I,axiom,
! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_iso__tuple__UNIV__I) ).
fof(fact_equivp__equiv,axiom,
! [V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
<=> c_Equiv__Relations_Oequivp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_A_2)) ),
file('theBenchmark.p',fact_equivp__equiv) ).
fof(fact_identity__equivp,axiom,
! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal),
file('theBenchmark.p',fact_identity__equivp) ).
fof(fact_equivp__def,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
<=> ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
<=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ),
file('theBenchmark.p',fact_equivp__def) ).
fof(fact_equivp__reflp,axiom,
! [V_x_2,V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ),
file('theBenchmark.p',fact_equivp__reflp) ).
fof(fact_equivp__symp,axiom,
! [V_y_2,V_x_2,V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
=> ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_equivp__symp) ).
fof(fact_equivp__transp,axiom,
! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
=> ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ),
file('theBenchmark.p',fact_equivp__transp) ).
fof(fact_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_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_inj__vimage__singleton,axiom,
! [V_a_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ),
file('theBenchmark.p',fact_inj__vimage__singleton) ).
fof(fact_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_vimageI,axiom,
! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
( hAPP(V_f_2,V_a_2) = V_b_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ),
file('theBenchmark.p',fact_vimageI) ).
fof(fact_vimage__code,axiom,
! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
<=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ),
file('theBenchmark.p',fact_vimage__code) ).
fof(fact_vimage__Compl,axiom,
! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),
file('theBenchmark.p',fact_vimage__Compl) ).
fof(fact_vimage__ident,axiom,
! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2,
file('theBenchmark.p',fact_vimage__ident) ).
fof(fact_vimage__mono,axiom,
! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ),
file('theBenchmark.p',fact_vimage__mono) ).
fof(fact_vimageI2,axiom,
! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ),
file('theBenchmark.p',fact_vimageI2) ).
fof(fact_vimageD,axiom,
! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ),
file('theBenchmark.p',fact_vimageD) ).
fof(fact_vimage__eq,axiom,
! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
<=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ),
file('theBenchmark.p',fact_vimage__eq) ).
fof(fact_vimage__Un,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
file('theBenchmark.p',fact_vimage__Un) ).
fof(fact_vimage__empty,axiom,
! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_vimage__empty) ).
fof(fact_vimage__Int,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
file('theBenchmark.p',fact_vimage__Int) ).
fof(fact_vimage__Diff,axiom,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
file('theBenchmark.p',fact_vimage__Diff) ).
fof(fact_vimage__INT,axiom,
! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)),
file('theBenchmark.p',fact_vimage__INT) ).
fof(fact_vimage__UN,axiom,
! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)),
file('theBenchmark.p',fact_vimage__UN) ).
fof(fact_vimage__UNIV,axiom,
! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_vimage__UNIV) ).
fof(fact_image__vimage__subset,axiom,
! [V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))),V_A_2)),
file('theBenchmark.p',fact_image__vimage__subset) ).
fof(fact_surj__image__vimage__eq,axiom,
! [V_A_2,V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = V_A_2 ),
file('theBenchmark.p',fact_surj__image__vimage__eq) ).
fof(fact_vimage__singleton__eq,axiom,
! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
<=> hAPP(V_f_2,V_a_2) = V_b_2 ),
file('theBenchmark.p',fact_vimage__singleton__eq) ).
fof(fact_vimage__insert,axiom,
! [V_B_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
file('theBenchmark.p',fact_vimage__insert) ).
fof(fact_finite__vimageD,axiom,
! [V_F_2,V_h_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
=> ( hAPP(c_Set_Oimage(T_b,T_c,V_h_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ),
file('theBenchmark.p',fact_finite__vimageD) ).
fof(fact_vimage__subsetD,axiom,
! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ),
file('theBenchmark.p',fact_vimage__subsetD) ).
fof(fact_image__vimage__eq,axiom,
! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
file('theBenchmark.p',fact_image__vimage__eq) ).
fof(fact_finite__vimageI,axiom,
! [V_h_2,T_c,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ),
file('theBenchmark.p',fact_finite__vimageI) ).
fof(fact_inj__vimage__image__eq,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ),
file('theBenchmark.p',fact_inj__vimage__image__eq) ).
fof(fact_vimage__const,axiom,
! [T_c,V_A_2,V_c_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_vimage__const) ).
fof(fact_vimage__eq__UN,axiom,
! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Ovimage(T_b,T_c,V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),
file('theBenchmark.p',fact_vimage__eq__UN) ).
fof(fact_vimage__subsetI,axiom,
! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2)) ) ),
file('theBenchmark.p',fact_vimage__subsetI) ).
fof(fact_vimage__if,axiom,
! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
=> hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
=> hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) ) ) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
=> hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2 )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
=> hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ),
file('theBenchmark.p',fact_vimage__if) ).
fof(fact_type__definition_ORep__range,axiom,
! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> hAPP(c_Set_Oimage(T_b,T_c,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ),
file('theBenchmark.p',fact_type__definition_ORep__range) ).
fof(fact_type__definition_OAbs__image,axiom,
! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> hAPP(c_Set_Oimage(T_c,T_b,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
file('theBenchmark.p',fact_type__definition_OAbs__image) ).
fof(fact_type__definition_ORep,axiom,
! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ),
file('theBenchmark.p',fact_type__definition_ORep) ).
fof(fact_type__definition_ORep__inject,axiom,
! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_type__definition_ORep__inject) ).
fof(fact_type__definition_ORep__inverse,axiom,
! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ),
file('theBenchmark.p',fact_type__definition_ORep__inverse) ).
fof(fact_type__definition_OAbs__inject,axiom,
! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
=> ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ) ),
file('theBenchmark.p',fact_type__definition_OAbs__inject) ).
fof(fact_type__definition_OAbs__inverse,axiom,
! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
=> hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ),
file('theBenchmark.p',fact_type__definition_OAbs__inverse) ).
fof(fact_max__extp_Oequations,axiom,
! [V_a2_2,V_a1_2,V_R_2,T_b] :
( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
=> ? [B_xa] :
( hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) ) )
& V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) ) ),
file('theBenchmark.p',fact_max__extp_Oequations) ).
fof(fact_max__ext_Ointros,axiom,
! [V_R_2,V_Y_2,V_X_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
=> ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
=> ? [B_xa] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ) ) ),
file('theBenchmark.p',fact_max__ext_Ointros) ).
fof(fact_fold1Set_Oequations,axiom,
! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2)),V_a3_2))
<=> ? [B_a,B_A] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
& hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) ) ),
file('theBenchmark.p',fact_fold1Set_Oequations) ).
fof(fact_insert__fold1SetE,axiom,
! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2)),V_x_2))
=> ~ ! [B_a,B_A] :
( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ),
file('theBenchmark.p',fact_insert__fold1SetE) ).
fof(fact_image__split__eq__Sigma,axiom,
! [V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Set_Oimage(T_d,tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_Oimage(T_d,T_c,V_g_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_b),c_Set_Ovimage(T_d,T_b,V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_A_2))),
file('theBenchmark.p',fact_image__split__eq__Sigma) ).
fof(fact_fold1__Un,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Groups_Oab__semigroup__mult(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ),
file('theBenchmark.p',fact_fold1__Un) ).
fof(fact_SigmaI,axiom,
! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ),
file('theBenchmark.p',fact_SigmaI) ).
fof(fact_Times__eq__cancel2,axiom,
! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
=> ( hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))
<=> V_A_2 = V_B_2 ) ),
file('theBenchmark.p',fact_Times__eq__cancel2) ).
fof(fact_Sigma__empty1,axiom,
! [V_B_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
file('theBenchmark.p',fact_Sigma__empty1) ).
fof(fact_Sigma__Diff__distrib1,axiom,
! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
file('theBenchmark.p',fact_Sigma__Diff__distrib1) ).
fof(fact_Times__Diff__distrib1,axiom,
! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
file('theBenchmark.p',fact_Times__Diff__distrib1) ).
fof(fact_Sigma__Diff__distrib2,axiom,
! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
file('theBenchmark.p',fact_Sigma__Diff__distrib2) ).
fof(fact_card__cartesian__product,axiom,
! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)),
file('theBenchmark.p',fact_card__cartesian__product) ).
fof(fact_setsum__cartesian__product,axiom,
! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) ),
file('theBenchmark.p',fact_setsum__cartesian__product) ).
fof(fact_Times__empty,axiom,
! [V_B_2,V_A_2,T_c,T_b] :
( hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))
<=> ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_Times__empty) ).
fof(fact_Sigma__empty2,axiom,
! [V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
file('theBenchmark.p',fact_Sigma__empty2) ).
fof(fact_Compl__Times__UNIV1,axiom,
! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))),
file('theBenchmark.p',fact_Compl__Times__UNIV1) ).
fof(fact_Compl__Times__UNIV2,axiom,
! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
file('theBenchmark.p',fact_Compl__Times__UNIV2) ).
fof(fact_setprod__cartesian__product,axiom,
! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
( class_Groups_Ocomm__monoid__mult(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) ),
file('theBenchmark.p',fact_setprod__cartesian__product) ).
fof(fact_Sigma__Un__distrib1,axiom,
! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
file('theBenchmark.p',fact_Sigma__Un__distrib1) ).
fof(fact_Times__Un__distrib1,axiom,
! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
file('theBenchmark.p',fact_Times__Un__distrib1) ).
fof(fact_Sigma__Un__distrib2,axiom,
! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
file('theBenchmark.p',fact_Sigma__Un__distrib2) ).
fof(fact_swap__product,axiom,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_b,T_c)),hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2)),
file('theBenchmark.p',fact_swap__product) ).
fof(fact_finite__cartesian__product,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ) ),
file('theBenchmark.p',fact_finite__cartesian__product) ).
fof(fact_fold1__singleton__def,axiom,
! [V_a_2,V_f_2,T_b,V_g_2] :
( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
=> hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ),
file('theBenchmark.p',fact_fold1__singleton__def) ).
fof(fact_fold1__singleton,axiom,
! [V_a_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2,
file('theBenchmark.p',fact_fold1__singleton) ).
fof(fact_equiv__type,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ),
file('theBenchmark.p',fact_equiv__type) ).
fof(fact_Sigma__Int__distrib2,axiom,
! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
file('theBenchmark.p',fact_Sigma__Int__distrib2) ).
fof(fact_Times__Int__distrib1,axiom,
! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
file('theBenchmark.p',fact_Times__Int__distrib1) ).
fof(fact_Sigma__Int__distrib1,axiom,
! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
file('theBenchmark.p',fact_Sigma__Int__distrib1) ).
fof(fact_Id__on__subset__Times,axiom,
! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId__on(T_b,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))),
file('theBenchmark.p',fact_Id__on__subset__Times) ).
fof(fact_UNIV__Times__UNIV,axiom,
! [T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
file('theBenchmark.p',fact_UNIV__Times__UNIV) ).
fof(fact_SigmaE2,axiom,
! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ),
file('theBenchmark.p',fact_SigmaE2) ).
fof(fact_SigmaD2,axiom,
! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ),
file('theBenchmark.p',fact_SigmaD2) ).
fof(fact_SigmaD1,axiom,
! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
file('theBenchmark.p',fact_SigmaD1) ).
fof(fact_mem__Sigma__iff,axiom,
! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
& hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
file('theBenchmark.p',fact_mem__Sigma__iff) ).
fof(fact_folding__one_Oeq__fold,axiom,
! [V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ),
file('theBenchmark.p',fact_folding__one_Oeq__fold) ).
fof(fact_card__cartesian__product__singleton,axiom,
! [V_A_2,V_x_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2),
file('theBenchmark.p',fact_card__cartesian__product__singleton) ).
fof(fact_Times__subset__cancel2,axiom,
! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
file('theBenchmark.p',fact_Times__subset__cancel2) ).
fof(fact_Image__subset,axiom,
! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_C_2)),V_B_2)) ),
file('theBenchmark.p',fact_Image__subset) ).
fof(fact_finite__cartesian__productD1,axiom,
! [V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
file('theBenchmark.p',fact_finite__cartesian__productD1) ).
fof(fact_finite__cartesian__productD2,axiom,
! [V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ),
file('theBenchmark.p',fact_finite__cartesian__productD2) ).
fof(fact_fst__image__times,axiom,
! [V_A_2,T_c,T_b,V_B_2] :
( ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = V_A_2 )
& ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_fst__image__times) ).
fof(fact_snd__image__times,axiom,
! [V_B_2,T_c,T_b,V_A_2] :
( ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = V_B_2 )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_snd__image__times) ).
fof(fact_fold1__def,axiom,
! [V_A_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2)),
file('theBenchmark.p',fact_fold1__def) ).
fof(fact_Sup__fin_OF__eq,axiom,
! [V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_A_2) ) ),
file('theBenchmark.p',fact_Sup__fin_OF__eq) ).
fof(fact_Inf__fin_OF__eq,axiom,
! [V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2) ) ),
file('theBenchmark.p',fact_Inf__fin_OF__eq) ).
fof(fact_Min_OF__eq,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ),
file('theBenchmark.p',fact_Min_OF__eq) ).
fof(fact_Max_OF__eq,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ),
file('theBenchmark.p',fact_Max_OF__eq) ).
fof(fact_min__max_OInf__fin_OF__eq,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_OF__eq) ).
fof(fact_min__max_OSup__fin_OF__eq,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_OF__eq) ).
fof(fact_refl__on__def,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ),
file('theBenchmark.p',fact_refl__on__def) ).
fof(fact_insert__times__insert,axiom,
! [V_B_2,V_b_2,V_A_2,V_a_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))),
file('theBenchmark.p',fact_insert__times__insert) ).
fof(fact_finite__equiv__class,axiom,
! [V_X_2,V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ),
file('theBenchmark.p',fact_finite__equiv__class) ).
fof(fact_UN__Times__distrib,axiom,
! [V_F_2,V_E_2,V_B_2,V_A_2,T_c,T_b,T_e,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_d,T_e),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_d),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_d),c_Product__Type_OSigma(T_b,T_c)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_e),c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_F_2))),
file('theBenchmark.p',fact_UN__Times__distrib) ).
fof(fact_Sigma__def,axiom,
! [V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))),
file('theBenchmark.p',fact_Sigma__def) ).
fof(fact_fold1__belowI,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__inf(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)),V_a_2)) ) ) ),
file('theBenchmark.p',fact_fold1__belowI) ).
fof(fact_finite__quotient,axiom,
! [V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ),
file('theBenchmark.p',fact_finite__quotient) ).
fof(fact_below__fold1__iff,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__inf(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ),
file('theBenchmark.p',fact_below__fold1__iff) ).
fof(fact_min__max_Ofold1__belowI,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_a_2)) ) ) ),
file('theBenchmark.p',fact_min__max_Ofold1__belowI) ).
fof(fact_fold1__insert__idem,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Oab__semigroup__idem__mult(T_b)
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ),
file('theBenchmark.p',fact_fold1__insert__idem) ).
fof(fact_fold1__below__iff,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ) ) ),
file('theBenchmark.p',fact_fold1__below__iff) ).
fof(fact_min__max_Obelow__fold1__iff,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_Obelow__fold1__iff) ).
fof(fact_fold1__Un2,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Oab__semigroup__idem__mult(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ),
file('theBenchmark.p',fact_fold1__Un2) ).
fof(fact_strict__below__fold1__iff,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ),
file('theBenchmark.p',fact_strict__below__fold1__iff) ).
fof(fact_fold1__strict__below__iff,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ) ) ),
file('theBenchmark.p',fact_fold1__strict__below__iff) ).
fof(fact_fold1__insert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Groups_Oab__semigroup__mult(T_b)
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_fold1__insert) ).
fof(fact_fold1__antimono,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) ) ) ) ),
file('theBenchmark.p',fact_fold1__antimono) ).
fof(fact_semilattice__big_OF__eq,axiom,
! [V_A_2,V_F_2,V_f_2,T_b] :
( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ),
file('theBenchmark.p',fact_semilattice__big_OF__eq) ).
fof(fact_Ex__inj__on__UNION__Sigma,axiom,
! [V_A_2,V_I_2,T_c,T_b] :
? [B_f] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_prod(T_c,T_b),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_I_2),V_A_2)))
& c_Fun_Oinj__on(T_b,tc_prod(T_c,T_b),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) ),
file('theBenchmark.p',fact_Ex__inj__on__UNION__Sigma) ).
fof(fact_refl__onI,axiom,
! [V_A_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ),
file('theBenchmark.p',fact_refl__onI) ).
fof(fact_setprod__Sigma,axiom,
! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_setprod__Sigma) ).
fof(fact_setsum__Sigma,axiom,
! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_setsum__Sigma) ).
fof(fact_fold__image__Sigma,axiom,
! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBC(T_b,T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),T_b),c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d))),V_g_2)),c_Groups_Oone__class_Oone(T_d))),V_B_2)),c_Groups_Oone__class_Oone(T_d)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,tc_prod(T_b,T_c),c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_g_2)),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ),
file('theBenchmark.p',fact_fold__image__Sigma) ).
fof(fact_card__SigmaI,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
=> hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),V_B_2)),V_A_2) ) ),
file('theBenchmark.p',fact_card__SigmaI) ).
fof(fact_fold1__in,axiom,
! [V_A_2,T_b] :
( class_Groups_Oab__semigroup__mult(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_fold1__in) ).
fof(fact_finite__SigmaI,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_a] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ),
file('theBenchmark.p',fact_finite__SigmaI) ).
fof(fact_hom__fold1__commute,axiom,
! [V_N_2,V_h_2,T_b] :
( class_Lattices_Oab__semigroup__idem__mult(T_b)
=> ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
file('theBenchmark.p',fact_hom__fold1__commute) ).
fof(fact_SigmaE,axiom,
! [V_B_2,V_A_2,V_c_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
=> ~ ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
=> V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ),
file('theBenchmark.p',fact_SigmaE) ).
fof(fact_map__pair__surj,axiom,
! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
=> ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_map__pair__surj) ).
fof(fact_map__pair__imageI,axiom,
! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_R_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),tc_prod(T_d,T_e),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)),V_R_2))) ),
file('theBenchmark.p',fact_map__pair__imageI) ).
fof(fact_fst__map__pair,axiom,
! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2)),
file('theBenchmark.p',fact_fst__map__pair) ).
fof(fact_map__pair__ident,axiom,
! [V_z_2,T_c,T_b] : hAPP(c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)),V_z_2) = V_z_2,
file('theBenchmark.p',fact_map__pair__ident) ).
fof(fact_snd__prod__fun,axiom,
! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Omap__pair(T_d,T_c,T_e,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)),
file('theBenchmark.p',fact_snd__prod__fun) ).
fof(fact_map__pair__simp,axiom,
! [V_b_2,V_a_2,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)),
file('theBenchmark.p',fact_map__pair__simp) ).
fof(fact_map__pair__def,axiom,
! [V_g_2,V_f_2,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_d,T_e)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),T_b),c_COMBB(T_e,tc_prod(T_d,T_e),T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_e,tc_prod(T_d,T_e)),T_b),c_Product__Type_OPair(T_d,T_e)),V_f_2))),V_g_2)),
file('theBenchmark.p',fact_map__pair__def) ).
fof(fact_map__pair__surj__on,axiom,
! [V_B_H_2,V_B_2,V_g_2,T_d,T_e,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
=> ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
=> hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_H_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_H_2)) ) ),
file('theBenchmark.p',fact_map__pair__surj__on) ).
fof(fact_map__pair__inj__on,axiom,
! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
=> c_Fun_Oinj__on(tc_prod(T_b,T_d),tc_prod(T_c,T_e),c_Product__Type_Omap__pair(T_b,T_c,T_d,T_e,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_2))) ) ),
file('theBenchmark.p',fact_map__pair__inj__on) ).
fof(fact_prod__fun__imageE,axiom,
! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2)))
=> ~ ! [B_x,B_y] :
( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),B_x),B_y)),V_R_2)) ) ),
file('theBenchmark.p',fact_prod__fun__imageE) ).
fof(fact_folding__one__idem_Ohom__commute,axiom,
! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
=> ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(V_f_2,B_x),B_y)) = hAPP(hAPP(V_f_2,hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ),
file('theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).
fof(fact_setprod__pos__nat,axiom,
! [V_f_2,V_S_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2))) ) ),
file('theBenchmark.p',fact_setprod__pos__nat) ).
fof(fact_Rep__Integ__cases,axiom,
! [V_y_2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
=> ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ),
file('theBenchmark.p',fact_Rep__Integ__cases) ).
fof(fact_Rep__Integ__induct,axiom,
! [V_P_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_P_2,hAPP(c_Int_ORep__Integ,B_x)))
=> hBOOL(hAPP(V_P_2,V_y_2)) ) ),
file('theBenchmark.p',fact_Rep__Integ__induct) ).
fof(fact_fun__left__comm__idem__remove,axiom,
! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),
file('theBenchmark.p',fact_fun__left__comm__idem__remove) ).
fof(fact_fun__left__comm__idem__sup,axiom,
! [T_b] :
( class_Lattices_Osemilattice__sup(T_b)
=> c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ),
file('theBenchmark.p',fact_fun__left__comm__idem__sup) ).
fof(fact_fun__left__comm__idem__inf,axiom,
! [T_b] :
( class_Lattices_Osemilattice__inf(T_b)
=> c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ),
file('theBenchmark.p',fact_fun__left__comm__idem__inf) ).
fof(fact_fun__left__comm__idem,axiom,
! [T_b] :
( class_Lattices_Oab__semigroup__idem__mult(T_b)
=> c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ),
file('theBenchmark.p',fact_fun__left__comm__idem) ).
fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
! [V_g_2,T_d,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
=> c_Finite__Set_Ofun__left__comm__idem(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ),
file('theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__comm__idem__apply) ).
fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
=> hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) = hAPP(hAPP(V_f_2,V_x_2),V_z_2) ),
file('theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__idem) ).
fof(fact_fun__left__comm__idem__insert,axiom,
! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),
file('theBenchmark.p',fact_fun__left__comm__idem__insert) ).
fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
! [T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ),
file('theBenchmark.p',fact_min__max_Ofun__left__comm__idem__inf) ).
fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
! [T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ),
file('theBenchmark.p',fact_min__max_Ofun__left__comm__idem__sup) ).
fof(fact_inj__on__INTER,axiom,
! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
=> c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
=> c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) ) ),
file('theBenchmark.p',fact_inj__on__INTER) ).
fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
=> hAPP(V_g_2,B_x) = V_z_2 )
=> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_folding__image__simple_Ounion__inter__neutral) ).
fof(fact_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_b,V_a_2,V_P_2] :
( hBOOL(hAPP(V_P_2,V_a_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
file('theBenchmark.p',fact_CollectI) ).
fof(fact_finite__Collect__conjI,axiom,
! [V_Q_2,V_P_2,T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_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__def,axiom,
! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),V_P_2) = V_P_2,
file('theBenchmark.p',fact_Collect__def) ).
fof(fact_Collect__disj__eq,axiom,
! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)),
file('theBenchmark.p',fact_Collect__disj__eq) ).
fof(fact_empty__Collect__eq,axiom,
! [V_P_2,T_b] :
( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_P_2)
<=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ),
file('theBenchmark.p',fact_empty__Collect__eq) ).
fof(fact_Collect__empty__eq,axiom,
! [V_P_2,T_b] :
( hAPP(c_Set_OCollect(T_b),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ),
file('theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_empty__def,axiom,
! [T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse)),
file('theBenchmark.p',fact_empty__def) ).
fof(fact_insert__Collect,axiom,
! [V_P_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_P_2)),
file('theBenchmark.p',fact_insert__Collect) ).
fof(fact_Collect__conj__eq,axiom,
! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)),
file('theBenchmark.p',fact_Collect__conj__eq) ).
fof(fact_finite__Collect__disjI,axiom,
! [V_Q_2,V_P_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2))))
<=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ),
file('theBenchmark.p',fact_finite__Collect__disjI) ).
fof(fact_UNIV__def,axiom,
! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fTrue)),
file('theBenchmark.p',fact_UNIV__def) ).
fof(fact_Collect__mem__eq,axiom,
! [V_A_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)) = V_A_2,
file('theBenchmark.p',fact_Collect__mem__eq) ).
fof(fact_mem__Collect__eq,axiom,
! [V_P_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
<=> hBOOL(hAPP(V_P_2,V_a_2)) ),
file('theBenchmark.p',fact_mem__Collect__eq) ).
fof(fact_CollectD,axiom,
! [V_P_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
=> hBOOL(hAPP(V_P_2,V_a_2)) ),
file('theBenchmark.p',fact_CollectD) ).
fof(fact_CollectE,axiom,
! [V_P_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
=> hBOOL(hAPP(V_P_2,V_a_2)) ),
file('theBenchmark.p',fact_CollectE) ).
fof(fact_vimage__Collect__eq,axiom,
! [V_P_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_P_2),V_f_2)),
file('theBenchmark.p',fact_vimage__Collect__eq) ).
fof(fact_Collect__neg__eq,axiom,
! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),
file('theBenchmark.p',fact_Collect__neg__eq) ).
fof(fact_SetCompr__Sigma__eq,axiom,
! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Q_2)),
file('theBenchmark.p',fact_SetCompr__Sigma__eq) ).
fof(fact_Collect__split,axiom,
! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Q_2))),
file('theBenchmark.p',fact_Collect__split) ).
fof(fact_insert__compr,axiom,
! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
file('theBenchmark.p',fact_insert__compr) ).
fof(fact_insert__compr__raw,axiom,
! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
file('theBenchmark.p',fact_insert__compr__raw) ).
fof(fact_Un__def,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
file('theBenchmark.p',fact_Un__def) ).
fof(fact_Int__Collect,axiom,
! [V_P_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))))
<=> ( hBOOL(hAPP(V_P_2,V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
file('theBenchmark.p',fact_Int__Collect) ).
fof(fact_Int__def,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
file('theBenchmark.p',fact_Int__def) ).
fof(fact_Collect__conv__if,axiom,
! [T_b,V_a_2,V_P_2] :
( ( ~ hBOOL(hAPP(V_P_2,V_a_2))
=> hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hBOOL(hAPP(V_P_2,V_a_2))
=> hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ),
file('theBenchmark.p',fact_Collect__conv__if) ).
fof(fact_Collect__conv__if2,axiom,
! [T_b,V_a_2,V_P_2] :
( ( ~ hBOOL(hAPP(V_P_2,V_a_2))
=> hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hBOOL(hAPP(V_P_2,V_a_2))
=> hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ),
file('theBenchmark.p',fact_Collect__conv__if2) ).
fof(fact_singleton__conv,axiom,
! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
file('theBenchmark.p',fact_singleton__conv) ).
fof(fact_singleton__conv2,axiom,
! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
file('theBenchmark.p',fact_singleton__conv2) ).
fof(fact_set__diff__eq,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))),
file('theBenchmark.p',fact_set__diff__eq) ).
fof(fact_finite__Collect__not,axiom,
! [V_P_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
file('theBenchmark.p',fact_finite__Collect__not) ).
fof(fact_insert__def,axiom,
! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2),
file('theBenchmark.p',fact_insert__def) ).
fof(fact_Compl__eq,axiom,
! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),
file('theBenchmark.p',fact_Compl__eq) ).
fof(fact_vimage__def,axiom,
! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(T_c)),V_f_2)),V_B_2)),
file('theBenchmark.p',fact_vimage__def) ).
fof(fact_Collect__ball__eq,axiom,
! [V_P_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_P_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_P_2))),
file('theBenchmark.p',fact_Collect__ball__eq) ).
fof(fact_Collect__imp__eq,axiom,
! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(c_Set_OCollect(T_b),V_Q_2)),
file('theBenchmark.p',fact_Collect__imp__eq) ).
fof(fact_finite__M__bounded__by__nat,axiom,
! [V_i_2,V_P_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_P_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_c,V_S_2,T_b,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_d),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_d),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d)),hAPP(c_COMBC(T_b,T_c,T_d),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ),
file('theBenchmark.p',fact_setsum__setsum__restrict) ).
fof(fact_INTER__def,axiom,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_member(T_b))),V_B_2)))),
file('theBenchmark.p',fact_INTER__def) ).
fof(fact_if__image__distrib,axiom,
! [V_S_2,V_g_2,V_f_2,V_P_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),V_P_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_P_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_P_2))))),
file('theBenchmark.p',fact_if__image__distrib) ).
fof(fact_nat__seg__image__imp__finite,axiom,
! [V_na_2,V_f_2,T_b,V_A_2] :
( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,V_f_2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_na_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),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_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ),
file('theBenchmark.p',fact_setsum__restrict__set_H) ).
fof(fact_setsum__image__gen,axiom,
! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),T_c,T_d),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_b),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_S_2)) ) ),
file('theBenchmark.p',fact_setsum__image__gen) ).
fof(fact_Image__singleton,axiom,
! [V_a_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_b))),hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2))),V_r_2)),
file('theBenchmark.p',fact_Image__singleton) ).
fof(fact_setsum__cases,axiom,
! [V_g_2,V_f_2,V_P_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_P_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2))))) ) ),
file('theBenchmark.p',fact_setsum__cases) ).
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_setsum__multicount,axiom,
! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_c),V_T_2)) ) ) ),
file('theBenchmark.p',fact_setsum__multicount) ).
fof(fact_min__max_Osup__Inf1__distrib,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ),
file('theBenchmark.p',fact_min__max_Osup__Inf1__distrib) ).
fof(fact_min__max_Osup__Inf2__distrib,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omax(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_Osup__Inf2__distrib) ).
fof(fact_finite__Collect__subsets,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))) ),
file('theBenchmark.p',fact_finite__Collect__subsets) ).
fof(fact_Pow__Compl,axiom,
! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_b))))),
file('theBenchmark.p',fact_Pow__Compl) ).
fof(fact_Pow__def,axiom,
! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
file('theBenchmark.p',fact_Pow__def) ).
fof(fact_finite__image__set,axiom,
! [V_f_2,T_c,V_P_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal)),V_f_2)))),V_P_2))))) ),
file('theBenchmark.p',fact_finite__image__set) ).
fof(fact_finite__Collect__bounded__ex,axiom,
! [V_Q_2,T_c,V_P_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2)))))
<=> ! [B_y] :
( hBOOL(hAPP(V_P_2,B_y))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_y)))) ) ) ),
file('theBenchmark.p',fact_finite__Collect__bounded__ex) ).
fof(fact_inj__graph,axiom,
! [T_c,T_b] : c_Fun_Oinj__on(tc_fun(T_b,T_c),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Set_OCollect(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool)),hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))),
file('theBenchmark.p',fact_inj__graph) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
! [V_P_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_P_2))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) ).
fof(fact_finite__psubset__def,axiom,
! [T_b] : c_Wellfounded_Ofinite__psubset(T_b) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_b)))),
file('theBenchmark.p',fact_finite__psubset__def) ).
fof(fact_inv__image__def,axiom,
! [V_f_2,V_r_2,T_b,T_c] : hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_c,T_c)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_c),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),T_b),c_COMBB(T_c,tc_prod(T_c,T_c),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_prod(T_c,T_c)),T_b),c_Product__Type_OPair(T_c,T_c)),V_f_2))),V_f_2)))),V_r_2))),
file('theBenchmark.p',fact_inv__image__def) ).
fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
! [V_P_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_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_P_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_P_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_P_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_P_2),c_Int_Onat)))),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J) ).
fof(fact_add__Max__commute,axiom,
! [V_k_2,V_N_2,T_b] :
( class_Groups_Olinordered__ab__semigroup__add(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ),
file('theBenchmark.p',fact_add__Max__commute) ).
fof(fact_add__Min__commute,axiom,
! [V_k_2,V_N_2,T_b] :
( class_Groups_Olinordered__ab__semigroup__add(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
=> ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ),
file('theBenchmark.p',fact_add__Min__commute) ).
fof(fact_sup__Inf2__distrib,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Odistrib__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ),
file('theBenchmark.p',fact_sup__Inf2__distrib) ).
fof(fact_sup__Inf1__distrib,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Odistrib__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ),
file('theBenchmark.p',fact_sup__Inf1__distrib) ).
fof(fact_inf__Sup1__distrib,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Odistrib__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ),
file('theBenchmark.p',fact_inf__Sup1__distrib) ).
fof(fact_inf__Sup2__distrib,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Lattices_Odistrib__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ),
file('theBenchmark.p',fact_inf__Sup2__distrib) ).
fof(fact_min__max_Oinf__Sup2__distrib,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omin(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ),
file('theBenchmark.p',fact_min__max_Oinf__Sup2__distrib) ).
fof(fact_min__max_Oinf__Sup1__distrib,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ),
file('theBenchmark.p',fact_min__max_Oinf__Sup1__distrib) ).
fof(fact_Nitpick_Oprod__def,axiom,
! [V_B_2,V_A_2,T_c,T_b] : c_Nitpick_Oprod(T_b,T_c,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))),
file('theBenchmark.p',fact_Nitpick_Oprod__def) ).
fof(fact_int__ge__less__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_reflp__def,axiom,
! [V_r_2,T_b] :
( c_Predicate_Oreflp(T_b,V_r_2)
<=> c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
file('theBenchmark.p',fact_reflp__def) ).
fof(fact_setsum__mult__setsum__if__inj,axiom,
! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
( class_Rings_Osemiring__0(T_d)
=> ( c_Fun_Oinj__on(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_d),c_Fun_Oid(T_d)),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),T_d),c_COMBB(T_d,tc_HOL_Obool,T_c)),c_fequal))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))))) ) ),
file('theBenchmark.p',fact_setsum__mult__setsum__if__inj) ).
fof(fact_def__lfp__induct__set,axiom,
! [V_P_2,V_a_2,V_f_2,T_b,V_A_2] :
( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2)))))
=> hBOOL(hAPP(V_P_2,B_x)) )
=> hBOOL(hAPP(V_P_2,V_a_2)) ) ) ) ),
file('theBenchmark.p',fact_def__lfp__induct__set) ).
fof(fact_inj__on__id,axiom,
! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2),
file('theBenchmark.p',fact_inj__on__id) ).
fof(fact_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_vimage__id,axiom,
! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2,
file('theBenchmark.p',fact_vimage__id) ).
fof(fact_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_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_apfst__id,axiom,
! [T_c,T_b] : c_Product__Type_Oapfst(T_b,T_b,T_c,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_b,T_c)),
file('theBenchmark.p',fact_apfst__id) ).
fof(fact_apsnd__id,axiom,
! [T_b,T_c] : c_Product__Type_Oapsnd(T_c,T_c,T_b,c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
file('theBenchmark.p',fact_apsnd__id) ).
fof(fact_reflpE,axiom,
! [V_x_2,V_r_2,T_b] :
( c_Predicate_Oreflp(T_b,V_r_2)
=> hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ),
file('theBenchmark.p',fact_reflpE) ).
fof(fact_map__pair_Oidentity,axiom,
! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
file('theBenchmark.p',fact_map__pair_Oidentity) ).
fof(fact_map__pair_Oid,axiom,
! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_Fun_Oid(T_b),c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
file('theBenchmark.p',fact_map__pair_Oid) ).
fof(fact_image__id,axiom,
! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2,
file('theBenchmark.p',fact_image__id) ).
fof(fact_surj__id,axiom,
! [T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_surj__id) ).
fof(fact_apfst__def,axiom,
! [V_f_2,T_c,T_d,T_b] : c_Product__Type_Oapfst(T_b,T_d,T_c,V_f_2) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_c,V_f_2,c_Fun_Oid(T_c)),
file('theBenchmark.p',fact_apfst__def) ).
fof(fact_apsnd__def,axiom,
! [V_f_2,T_b,T_d,T_c] : c_Product__Type_Oapsnd(T_c,T_d,T_b,V_f_2) = c_Product__Type_Omap__pair(T_b,T_b,T_c,T_d,c_Fun_Oid(T_b),V_f_2),
file('theBenchmark.p',fact_apsnd__def) ).
fof(fact_split__Pair,axiom,
! [T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
file('theBenchmark.p',fact_split__Pair) ).
fof(fact_setsum__reindex__id,axiom,
! [V_B_2,V_f_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ),
file('theBenchmark.p',fact_setsum__reindex__id) ).
fof(fact_setprod__reindex__id,axiom,
! [V_B_2,V_f_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ),
file('theBenchmark.p',fact_setprod__reindex__id) ).
fof(fact_lfp__induct__set,axiom,
! [V_P_2,V_f_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))
=> ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)),hAPP(c_Set_OCollect(T_b),V_P_2)))))
=> hBOOL(hAPP(V_P_2,B_x)) )
=> hBOOL(hAPP(V_P_2,V_a_2)) ) ) ),
file('theBenchmark.p',fact_lfp__induct__set) ).
fof(fact_def__Collect__coinduct,axiom,
! [V_X_2,V_a_2,V_P_2,T_b,V_A_2] :
( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_OCollect(T_b)),V_P_2))
=> ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_OCollect(T_b)),V_P_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
=> ( ! [B_z] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_z),V_X_2))
=> hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_A_2)),B_z)) )
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ),
file('theBenchmark.p',fact_def__Collect__coinduct) ).
fof(fact_lfp__induct2,axiom,
! [V_P_2,V_f_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2)))
=> ( c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2)
=> ( ! [B_a,B_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2))))))
=> hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) )
=> hBOOL(hAPP(hAPP(V_P_2,V_a_2),V_b_2)) ) ) ),
file('theBenchmark.p',fact_lfp__induct2) ).
fof(fact_setsum__multicount__gen,axiom,
! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_s_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_k_2),V_t_2) ) ) ),
file('theBenchmark.p',fact_setsum__multicount__gen) ).
fof(fact_finite__conv__nat__seg__image,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
<=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n))) ),
file('theBenchmark.p',fact_finite__conv__nat__seg__image) ).
fof(fact_rel__comp__def,axiom,
! [V_s_2,V_r_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBC(T_d,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_d),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_b,T_d)))),c_Product__Type_OPair(T_b,T_d)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_d,T_c)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_d,T_c)))),hAPP(c_COMBC(T_d,T_c,tc_prod(T_d,T_c)),c_Product__Type_OPair(T_d,T_c))))),V_s_2))))),
file('theBenchmark.p',fact_rel__comp__def) ).
fof(fact_rel__compI,axiom,
! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_b_2),V_c_2)),V_s_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ),
file('theBenchmark.p',fact_rel__compI) ).
fof(fact_rel__comp__UNION__distrib,axiom,
! [V_r_2,V_I_2,T_e,V_s_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e),hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2)),V_r_2)),
file('theBenchmark.p',fact_rel__comp__UNION__distrib) ).
fof(fact_rel__comp__UNION__distrib2,axiom,
! [V_s_2,V_r_2,V_I_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_e),c_Relation_Orel__comp(T_b,T_d,T_c)),V_r_2)),V_s_2)),
file('theBenchmark.p',fact_rel__comp__UNION__distrib2) ).
fof(fact_rel__comp__distrib,axiom,
! [V_T_2,V_S_2,V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_T_2)),
file('theBenchmark.p',fact_rel__comp__distrib) ).
fof(fact_rel__comp__distrib2,axiom,
! [V_R_2,V_T_2,V_S_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_S_2),V_T_2)),V_R_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_T_2),V_R_2)),
file('theBenchmark.p',fact_rel__comp__distrib2) ).
fof(fact_rel__comp__empty2,axiom,
! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
file('theBenchmark.p',fact_rel__comp__empty2) ).
fof(fact_rel__comp__empty1,axiom,
! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
file('theBenchmark.p',fact_rel__comp__empty1) ).
fof(fact_O__assoc,axiom,
! [V_T_2,V_S_2,V_R_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_d),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_c),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_e,T_d,T_c),V_S_2),V_T_2)),
file('theBenchmark.p',fact_O__assoc) ).
fof(fact_rel__comp__mono,axiom,
! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_H_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ),
file('theBenchmark.p',fact_rel__comp__mono) ).
fof(fact_union__comp__emptyR,axiom,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
=> ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
=> hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_union__comp__emptyR) ).
fof(fact_union__comp__emptyL,axiom,
! [V_B_2,V_C_2,V_A_2,T_b] :
( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
=> ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
=> hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_union__comp__emptyL) ).
fof(fact_rel__comp__subset__Sigma,axiom,
! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_B_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_C_2)))) ) ),
file('theBenchmark.p',fact_rel__comp__subset__Sigma) ).
fof(fact_max__ext__compat,axiom,
! [V_S_2,V_R_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ),
file('theBenchmark.p',fact_max__ext__compat) ).
fof(fact_min__ext__compat,axiom,
! [V_S_2,V_R_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_b,V_R_2))) ),
file('theBenchmark.p',fact_min__ext__compat) ).
fof(fact_pred__comp__rel__comp__eq,axiom,
! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2)),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ),
file('theBenchmark.p',fact_pred__comp__rel__comp__eq) ).
fof(fact_reduction__pairI,axiom,
! [V_S_2,V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,V_R_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
=> c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ),
file('theBenchmark.p',fact_reduction__pairI) ).
fof(fact_Range__Collect__split,axiom,
! [V_P_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_P_2))),
file('theBenchmark.p',fact_Range__Collect__split) ).
fof(fact_wf__less__than,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('theBenchmark.p',fact_wf__less__than) ).
fof(fact_pred__comp_Ointros,axiom,
! [T_d,T_c,T_b,V_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_b,T_c,T_d,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_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),
file('theBenchmark.p',fact_wf__empty) ).
fof(fact_wf__inv__image,axiom,
! [V_f_2,T_c,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ),
file('theBenchmark.p',fact_wf__inv__image) ).
fof(fact_wf__lex__prod,axiom,
! [V_rb_2,T_c,V_ra_2,T_b] :
( c_Wellfounded_Owf(T_b,V_ra_2)
=> ( c_Wellfounded_Owf(T_c,V_rb_2)
=> c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ),
file('theBenchmark.p',fact_wf__lex__prod) ).
fof(fact_wf__measure,axiom,
! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)),
file('theBenchmark.p',fact_wf__measure) ).
fof(fact_RangeI,axiom,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_RangeI) ).
fof(fact_wf__comp__self,axiom,
! [V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,V_R_2)
<=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ),
file('theBenchmark.p',fact_wf__comp__self) ).
fof(fact_Range__Id__on,axiom,
! [V_A_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2,
file('theBenchmark.p',fact_Range__Id__on) ).
fof(fact_wf__finite__psubset,axiom,
! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)),
file('theBenchmark.p',fact_wf__finite__psubset) ).
fof(fact_wf__mlex,axiom,
! [V_f_2,V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,V_R_2)
=> c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ),
file('theBenchmark.p',fact_wf__mlex) ).
fof(fact_min__ext__wf,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ),
file('theBenchmark.p',fact_min__ext__wf) ).
fof(fact_pred__comp_Oequations,axiom,
! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a1_2),V_a3_2))
<=> ? [B_b] :
( hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2))
& hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) ) ),
file('theBenchmark.p',fact_pred__comp_Oequations) ).
fof(fact_wf__subset,axiom,
! [V_p_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_p_2),V_r_2))
=> c_Wellfounded_Owf(T_b,V_p_2) ) ),
file('theBenchmark.p',fact_wf__subset) ).
fof(fact_wf__pair__less,axiom,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('theBenchmark.p',fact_wf__pair__less) ).
fof(fact_max__ext__wf,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ),
file('theBenchmark.p',fact_max__ext__wf) ).
fof(fact_wf__Int1,axiom,
! [V_r_H_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2)) ),
file('theBenchmark.p',fact_wf__Int1) ).
fof(fact_wf__Int2,axiom,
! [V_r_H_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) ),
file('theBenchmark.p',fact_wf__Int2) ).
fof(fact_wf__not__refl,axiom,
! [V_a_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ),
file('theBenchmark.p',fact_wf__not__refl) ).
fof(fact_wf__not__sym,axiom,
! [V_x_2,V_a_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_wf__not__sym) ).
fof(fact_wf__asym,axiom,
! [V_x_2,V_a_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_wf__asym) ).
fof(fact_wf__irrefl,axiom,
! [V_a_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ),
file('theBenchmark.p',fact_wf__irrefl) ).
fof(fact_wf__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__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_acc__wfD,axiom,
! [V_x_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
file('theBenchmark.p',fact_acc__wfD) ).
fof(fact_wf__acc__iff,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
<=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ),
file('theBenchmark.p',fact_wf__acc__iff) ).
fof(fact_wf__no__loop,axiom,
! [V_R_2,T_b] :
( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
=> c_Wellfounded_Owf(T_b,V_R_2) ),
file('theBenchmark.p',fact_wf__no__loop) ).
fof(fact_wf__union__merge,axiom,
! [V_S_2,V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
<=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_S_2),V_R_2))),V_S_2)) ),
file('theBenchmark.p',fact_wf__union__merge) ).
fof(fact_Range__empty,axiom,
! [T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Range__empty) ).
fof(fact_Range__empty__iff,axiom,
! [V_r_2,T_b,T_c] :
( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ),
file('theBenchmark.p',fact_Range__empty__iff) ).
fof(fact_Range__Un__eq,axiom,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)),
file('theBenchmark.p',fact_Range__Un__eq) ).
fof(fact_finite__Range,axiom,
! [V_r_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_finite__Range) ).
fof(fact_snd__eq__Range,axiom,
! [V_R_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_b,c_Product__Type_Osnd(T_c,T_b)),V_R_2) = hAPP(c_Relation_ORange(T_c,T_b),V_R_2),
file('theBenchmark.p',fact_snd__eq__Range) ).
fof(fact_wf__iff__no__infinite__down__chain,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
<=> ~ ? [B_f] :
! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ),
file('theBenchmark.p',fact_wf__iff__no__infinite__down__chain) ).
fof(fact_wfE__pf,axiom,
! [V_A_2,V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,V_R_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),V_A_2)))
=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_wfE__pf) ).
fof(fact_wf__union__compatible,axiom,
! [V_S_2,V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,V_R_2)
=> ( c_Wellfounded_Owf(T_b,V_S_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ),
file('theBenchmark.p',fact_wf__union__compatible) ).
fof(fact_Range__iff,axiom,
! [V_r_2,T_c,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
<=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),V_a_2)),V_r_2)) ),
file('theBenchmark.p',fact_Range__iff) ).
fof(fact_wf,axiom,
! [T_b] :
( class_Orderings_Owellorder(T_b)
=> c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_b)))) ),
file('theBenchmark.p',fact_wf) ).
fof(fact_reduction__pair__def,axiom,
! [V_P_2,T_b] :
( c_FunDef_Oreduction__pair(T_b,V_P_2)
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
& c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)) ) ),
file('theBenchmark.p',fact_reduction__pair__def) ).
fof(fact_reduction__pair__lemma,axiom,
! [V_S_2,V_R_2,V_P_2,T_b] :
( c_FunDef_Oreduction__pair(T_b,V_P_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
=> ( c_Wellfounded_Owf(T_b,V_S_2)
=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ),
file('theBenchmark.p',fact_reduction__pair__lemma) ).
fof(fact_Range__insert,axiom,
! [V_r_2,V_b_2,V_a_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)),
file('theBenchmark.p',fact_Range__insert) ).
fof(fact_Range__Int__subset,axiom,
! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)))),
file('theBenchmark.p',fact_Range__Int__subset) ).
fof(fact_Range__Diff__subset,axiom,
! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2))),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))),
file('theBenchmark.p',fact_Range__Diff__subset) ).
fof(fact_wf__map__pair__image,axiom,
! [V_f_2,T_c,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> c_Wellfounded_Owf(T_c,hAPP(c_Set_Oimage(tc_prod(T_b,T_b),tc_prod(T_c,T_c),c_Product__Type_Omap__pair(T_b,T_c,T_b,T_c,V_f_2,V_f_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_wf__map__pair__image) ).
fof(fact_RangeP__Range__eq,axiom,
! [V_x_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_RangeP__Range__eq) ).
fof(fact_wf__lenlex,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ),
file('theBenchmark.p',fact_wf__lenlex) ).
fof(fact_RangeE,axiom,
! [V_r_2,T_c,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
=> ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ),
file('theBenchmark.p',fact_RangeE) ).
fof(fact_RangeP_Ointros,axiom,
! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
=> hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ),
file('theBenchmark.p',fact_RangeP_Ointros) ).
fof(fact_RangeP_Oequations,axiom,
! [V_a2_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
<=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ),
file('theBenchmark.p',fact_RangeP_Oequations) ).
fof(fact_pred__nat__def,axiom,
c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))),
file('theBenchmark.p',fact_pred__nat__def) ).
fof(fact_wf__lex,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ),
file('theBenchmark.p',fact_wf__lex) ).
fof(fact_wf__lexn,axiom,
! [V_na_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_na_2)) ),
file('theBenchmark.p',fact_wf__lexn) ).
fof(fact_lex__def,axiom,
! [V_r_2,T_b] : c_List_Olex(T_b,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_b,V_r_2)),
file('theBenchmark.p',fact_lex__def) ).
fof(fact_lexn_Osimps_I1_J,axiom,
! [V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),
file('theBenchmark.p',fact_lexn_Osimps_I1_J) ).
fof(fact_wf__pred__nat,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('theBenchmark.p',fact_wf__pred__nat) ).
fof(fact_wf__Un,axiom,
! [V_s_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ( c_Wellfounded_Owf(T_b,V_s_2)
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ),
file('theBenchmark.p',fact_wf__Un) ).
fof(fact_wf__same__fst,axiom,
! [T_b,V_R_2,T_c,V_P_2] :
( ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
=> c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
=> c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2)) ),
file('theBenchmark.p',fact_wf__same__fst) ).
fof(fact_wf__if__measure,axiom,
! [T_b,V_g_2,V_f_2,V_P_2] :
( ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,hAPP(V_g_2,B_x))),hAPP(V_f_2,B_x))) )
=> c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2))))) ),
file('theBenchmark.p',fact_wf__if__measure) ).
fof(fact_DomainI,axiom,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_DomainI) ).
fof(fact_Domain__Id__on,axiom,
! [V_A_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2,
file('theBenchmark.p',fact_Domain__Id__on) ).
fof(fact_Domain__empty__iff,axiom,
! [V_r_2,T_c,T_b] :
( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ),
file('theBenchmark.p',fact_Domain__empty__iff) ).
fof(fact_Domain__empty,axiom,
! [T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Domain__empty) ).
fof(fact_Domain__mono,axiom,
! [V_s_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_s_2))) ),
file('theBenchmark.p',fact_Domain__mono) ).
fof(fact_Domain__Un__eq,axiom,
! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)),
file('theBenchmark.p',fact_Domain__Un__eq) ).
fof(fact_finite__Domain,axiom,
! [V_r_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_finite__Domain) ).
fof(fact_fst__eq__Domain,axiom,
! [V_R_2,T_c,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),V_R_2) = hAPP(c_Relation_ODomain(T_b,T_c),V_R_2),
file('theBenchmark.p',fact_fst__eq__Domain) ).
fof(fact_Domain__iff,axiom,
! [V_r_2,T_c,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
<=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ),
file('theBenchmark.p',fact_Domain__iff) ).
fof(fact_Domain__insert,axiom,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),
file('theBenchmark.p',fact_Domain__insert) ).
fof(fact_Domain__Int__subset,axiom,
! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)))),
file('theBenchmark.p',fact_Domain__Int__subset) ).
fof(fact_Domain__Diff__subset,axiom,
! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2))),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)))),
file('theBenchmark.p',fact_Domain__Diff__subset) ).
fof(fact_Field__def,axiom,
! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_r_2)),
file('theBenchmark.p',fact_Field__def) ).
fof(fact_Domain__Collect__split,axiom,
! [V_P_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_P_2)),
file('theBenchmark.p',fact_Domain__Collect__split) ).
fof(fact_DomainP__Domain__eq,axiom,
! [V_x_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_DomainP__Domain__eq) ).
fof(fact_DomainE,axiom,
! [V_r_2,T_c,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
=> ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ),
file('theBenchmark.p',fact_DomainE) ).
fof(fact_wfP__def,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_OwfP(T_b,V_r_2)
<=> c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
file('theBenchmark.p',fact_wfP__def) ).
fof(fact_DomainP_Ointros,axiom,
! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
=> hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ),
file('theBenchmark.p',fact_DomainP_Ointros) ).
fof(fact_wfP__empty,axiom,
! [T_b] : c_Wellfounded_OwfP(T_b,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse))),
file('theBenchmark.p',fact_wfP__empty) ).
fof(fact_wfP__accp__iff,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_OwfP(T_b,V_r_2)
<=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ),
file('theBenchmark.p',fact_wfP__accp__iff) ).
fof(fact_accp__wfPD,axiom,
! [V_x_2,V_r_2,T_b] :
( c_Wellfounded_OwfP(T_b,V_r_2)
=> hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ),
file('theBenchmark.p',fact_accp__wfPD) ).
fof(fact_wfP__subset,axiom,
! [V_p_2,V_r_2,T_b] :
( c_Wellfounded_OwfP(T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_p_2),V_r_2))
=> c_Wellfounded_OwfP(T_b,V_p_2) ) ),
file('theBenchmark.p',fact_wfP__subset) ).
fof(fact_DomainP_Oequations,axiom,
! [V_a1_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
<=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ),
file('theBenchmark.p',fact_DomainP_Oequations) ).
fof(fact_wf__in__rel,axiom,
! [V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,V_R_2)
=> c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ),
file('theBenchmark.p',fact_wf__in__rel) ).
fof(fact_wfP__wf__eq,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2))
<=> c_Wellfounded_Owf(T_b,V_r_2) ),
file('theBenchmark.p',fact_wfP__wf__eq) ).
fof(fact_wfP__acyclicP,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_OwfP(T_b,V_r_2)
=> c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
file('theBenchmark.p',fact_wfP__acyclicP) ).
fof(fact_pigeonhole__infinite,axiom,
! [V_f_2,T_c,V_A_2,T_b] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
=> ? [B_x] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_f_2,B_x))))))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ),
file('theBenchmark.p',fact_pigeonhole__infinite) ).
fof(fact_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_acyclic__subset,axiom,
! [V_r_2,V_s_2,T_b] :
( c_Wellfounded_Oacyclic(T_b,V_s_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
file('theBenchmark.p',fact_acyclic__subset) ).
fof(fact_wf__acyclic,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Oacyclic(T_b,V_r_2) ),
file('theBenchmark.p',fact_wf__acyclic) ).
fof(fact_finite__acyclic__wf,axiom,
! [V_r_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
=> c_Wellfounded_Owf(T_b,V_r_2) ) ),
file('theBenchmark.p',fact_finite__acyclic__wf) ).
fof(fact_wf__iff__acyclic__if__finite,axiom,
! [V_r_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
=> ( c_Wellfounded_Owf(T_b,V_r_2)
<=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
file('theBenchmark.p',fact_wf__iff__acyclic__if__finite) ).
fof(fact_Nitpick_Owf_H__def,axiom,
! [V_r_2,T_b] :
( c_Nitpick_Owf_H(T_b,V_r_2)
<=> ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) )
& c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
file('theBenchmark.p',fact_Nitpick_Owf_H__def) ).
fof(fact_Abs__Integ__induct,axiom,
! [V_x_2,V_P_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_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
=> hBOOL(hAPP(V_P_2,V_x_2)) ),
file('theBenchmark.p',fact_Abs__Integ__induct) ).
fof(fact_finite__UN__I,axiom,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_a] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
file('theBenchmark.p',fact_finite__UN__I) ).
fof(fact_inj__on__diff__nat,axiom,
! [V_k_2,V_N_2] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
=> c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_k_2),V_N_2) ),
file('theBenchmark.p',fact_inj__on__diff__nat) ).
fof(fact_wfP__SUP,axiom,
! [T_b,V_r_2,T_c] :
( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
=> ( ! [B_i,B_j] :
( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Predicate_ODomainP(T_c,T_c,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_c,T_c,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
=> c_Wellfounded_OwfP(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)) ) ),
file('theBenchmark.p',fact_wfP__SUP) ).
fof(fact_mem__splitI2,axiom,
! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] :
( ! [B_a,B_b] :
( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
=> hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) )
=> hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_c_2),V_p_2))) ),
file('theBenchmark.p',fact_mem__splitI2) ).
fof(fact_mem__splitE,axiom,
! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),V_p_2)))
=> ~ ! [B_x,B_y] :
( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ),
file('theBenchmark.p',fact_mem__splitE) ).
fof(fact_vimage__Times,axiom,
! [V_B_2,V_A_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,tc_prod(T_c,T_d),V_f_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,T_b,c_Product__Type_Ofst(T_c,T_d)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_d,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_d,T_b,c_Product__Type_Osnd(T_c,T_d)),V_f_2)),V_B_2)),
file('theBenchmark.p',fact_vimage__Times) ).
fof(fact_id__o,axiom,
! [V_g_2,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_g_2) = V_g_2,
file('theBenchmark.p',fact_id__o) ).
fof(fact_o__id,axiom,
! [V_f_2,T_c,T_b] : hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_f_2),c_Fun_Oid(T_b)) = V_f_2,
file('theBenchmark.p',fact_o__id) ).
fof(fact_o__eq__id__dest,axiom,
! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_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_c,T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
=> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ),
file('theBenchmark.p',fact_fun__left__comm__idem_Ofun__comp__idem) ).
fof(fact_vimage__compose,axiom,
! [V_x_2,V_f_2,V_g_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_b,T_d,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_g_2),V_x_2)),
file('theBenchmark.p',fact_vimage__compose) ).
fof(fact_o__def,axiom,
! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)),
file('theBenchmark.p',fact_o__def) ).
fof(fact_o__assoc,axiom,
! [V_h_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(c_Fun_Ocomp(T_e,T_d,T_b,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_h_2),
file('theBenchmark.p',fact_o__assoc) ).
fof(fact_o__apply,axiom,
! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)),
file('theBenchmark.p',fact_o__apply) ).
fof(fact_o__eq__dest,axiom,
! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_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_e,V_b_2,V_a_2,T_b,T_c,T_d] :
( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_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_apfst__compose,axiom,
! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_d,T_c,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_e,V_f_2),V_g_2)),V_x_2),
file('theBenchmark.p',fact_apfst__compose) ).
fof(fact_apsnd__compose,axiom,
! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_x_2),
file('theBenchmark.p',fact_apsnd__compose) ).
fof(fact_comp__cong,axiom,
! [T_f,T_e,T_d,T_b,T_c,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] :
( hAPP(V_f_2,hAPP(V_g_2,V_x_2)) = hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2))
=> hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_e,T_b,T_f,V_f_H_2),V_g_H_2),V_x_H_2) ),
file('theBenchmark.p',fact_comp__cong) ).
fof(fact_fun__upd__comp,axiom,
! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),c_Fun_Ofun__upd(T_b,T_d,V_g_2,V_x_2,V_y_2)) = c_Fun_Ofun__upd(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2),V_x_2,hAPP(V_f_2,V_y_2)),
file('theBenchmark.p',fact_fun__upd__comp) ).
fof(fact_K__record__comp,axiom,
! [V_x_2,V_f_2,V_c_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_f_2),V_x_2) = V_c_2,
file('theBenchmark.p',fact_K__record__comp) ).
fof(fact_o__eq__dest__lhs,axiom,
! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_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_map__pair_Ocompositionality,axiom,
! [V_prod_2,V_i_2,V_h_2,T_g,T_f,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_f,T_b,T_g,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_e,T_c,T_g,V_g_2),V_i_2)),V_prod_2),
file('theBenchmark.p',fact_map__pair_Ocompositionality) ).
fof(fact_map__pair__compose,axiom,
! [V_g2_2,V_g1_2,T_g,V_f2_2,V_f1_2,T_f,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_f2_2,V_g2_2)),
file('theBenchmark.p',fact_map__pair__compose) ).
fof(fact_map__pair_Ocomp,axiom,
! [V_i_2,V_h_2,V_g_2,V_f_2,T_c,T_b,T_e,T_d,T_g,T_f] : hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g_2),V_i_2)),
file('theBenchmark.p',fact_map__pair_Ocomp) ).
fof(fact_image__compose,axiom,
! [V_r_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_b,T_c,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),V_r_2)),
file('theBenchmark.p',fact_image__compose) ).
fof(fact_comp__surj,axiom,
! [V_g_2,T_d,V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
=> ( hAPP(c_Set_Oimage(T_b,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_comp__surj) ).
fof(fact_inj__on__imageI2,axiom,
! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_H_2),V_f_2),V_A_2)
=> c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ),
file('theBenchmark.p',fact_inj__on__imageI2) ).
fof(fact_inj__comp,axiom,
! [V_g_2,T_d,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
=> c_Fun_Oinj__on(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) ) ),
file('theBenchmark.p',fact_inj__comp) ).
fof(fact_inj__on__imageI,axiom,
! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2),V_A_2)
=> c_Fun_Oinj__on(T_d,T_c,V_g_2,hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_A_2)) ),
file('theBenchmark.p',fact_inj__on__imageI) ).
fof(fact_comp__inj__on,axiom,
! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( c_Fun_Oinj__on(T_c,T_d,V_g_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
=> c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2) ) ),
file('theBenchmark.p',fact_comp__inj__on) ).
fof(fact_comp__inj__on__iff,axiom,
! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( c_Fun_Oinj__on(T_c,T_d,V_f_H_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
<=> c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2) ) ),
file('theBenchmark.p',fact_comp__inj__on__iff) ).
fof(fact_setsum__reindex,axiom,
! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ),
file('theBenchmark.p',fact_setsum__reindex) ).
fof(fact_setprod__reindex__cong,axiom,
! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
=> ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ),
file('theBenchmark.p',fact_setprod__reindex__cong) ).
fof(fact_setprod__reindex,axiom,
! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ),
file('theBenchmark.p',fact_setprod__reindex) ).
fof(fact_setsum_Oreindex,axiom,
! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ),
file('theBenchmark.p',fact_setsum_Oreindex) ).
fof(fact_setprod_Oreindex,axiom,
! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ),
file('theBenchmark.p',fact_setprod_Oreindex) ).
fof(fact_the__inv__into__comp,axiom,
! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))
=> ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))))
=> hAPP(c_Fun_Othe__inv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Fun_Othe__inv__into(T_d,T_b,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ),
file('theBenchmark.p',fact_the__inv__into__comp) ).
fof(fact_fold__image__reindex,axiom,
! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
( class_Groups_Oab__semigroup__mult(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_fold__image__reindex) ).
fof(fact_Nitpick_Odenom__def,axiom,
! [T_b] : c_Nitpick_Odenom(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)),
file('theBenchmark.p',fact_Nitpick_Odenom__def) ).
fof(fact_Nitpick_Onum__def,axiom,
! [T_b] : c_Nitpick_Onum(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)),
file('theBenchmark.p',fact_Nitpick_Onum__def) ).
fof(fact_fst__comp__map__pair,axiom,
! [V_g_2,V_f_2,T_c,T_b,T_e,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_e),T_d,tc_prod(T_b,T_c),c_Product__Type_Ofst(T_d,T_e)),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,tc_prod(T_b,T_c),V_f_2),c_Product__Type_Ofst(T_b,T_c)),
file('theBenchmark.p',fact_fst__comp__map__pair) ).
fof(fact_snd__comp__map__pair,axiom,
! [V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_d),T_d,tc_prod(T_b,T_c),c_Product__Type_Osnd(T_e,T_d)),c_Product__Type_Omap__pair(T_b,T_e,T_c,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_d,tc_prod(T_b,T_c),V_g_2),c_Product__Type_Osnd(T_b,T_c)),
file('theBenchmark.p',fact_snd__comp__map__pair) ).
fof(fact_UN__o,axiom,
! [V_f_2,V_g_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_b,tc_HOL_Obool),T_c,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_g_2),
file('theBenchmark.p',fact_UN__o) ).
fof(fact_split__comp,axiom,
! [V_x_2,V_g_2,V_f_2,T_e,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),hAPP(c_Fun_Ocomp(T_e,tc_fun(T_d,T_b),T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)),
file('theBenchmark.p',fact_split__comp) ).
fof(fact_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_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_folding_Oremove,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ),
file('theBenchmark.p',fact_folding_Oremove) ).
fof(fact_folding__image_Oreindex,axiom,
! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
=> hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_c,T_b,T_c,V_g_2),V_h_2)),V_A_2) ) ) ),
file('theBenchmark.p',fact_folding__image_Oreindex) ).
fof(fact_folding_Ocommute__comps_I1_J,axiom,
! [V_h_2,V_g_2,T_g,V_f_2,T_d,T_e,T_f,V_F_2,V_fa_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
=> hAPP(c_Fun_Ocomp(T_f,T_e,T_d,V_f_2),hAPP(c_Fun_Ocomp(T_g,T_f,T_d,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_g,T_e,T_d,hAPP(c_Fun_Ocomp(T_f,T_e,T_g,V_f_2),V_g_2)),V_h_2) ),
file('theBenchmark.p',fact_folding_Ocommute__comps_I1_J) ).
fof(fact_folding_Ocommute__comp,axiom,
! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ),
file('theBenchmark.p',fact_folding_Ocommute__comp) ).
fof(fact_folding_Ocommute__left__comp,axiom,
! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),V_g_2)) ),
file('theBenchmark.p',fact_folding_Ocommute__left__comp) ).
fof(fact_folding__image_Odistrib,axiom,
! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(V_f_2,hAPP(hAPP(V_F_2,V_g_2),V_A_2)),hAPP(hAPP(V_F_2,V_h_2),V_A_2)) ) ),
file('theBenchmark.p',fact_folding__image_Odistrib) ).
fof(fact_folding_Ocommute__comp_H,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ),
file('theBenchmark.p',fact_folding_Ocommute__comp_H) ).
fof(fact_folding_Ocommute__left__comp_H,axiom,
! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) ) ),
file('theBenchmark.p',fact_folding_Ocommute__left__comp_H) ).
fof(fact_folding_Ocommute__comp_H_H,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
file('theBenchmark.p',fact_folding_Ocommute__comp_H_H) ).
fof(fact_folding_Ocommute__left__comp_H_H,axiom,
! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),V_g_2)) ) ) ),
file('theBenchmark.p',fact_folding_Ocommute__left__comp_H_H) ).
fof(fact_folding_Oempty,axiom,
! [V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ),
file('theBenchmark.p',fact_folding_Oempty) ).
fof(fact_folding__image_Oeq__fold,axiom,
! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ),
file('theBenchmark.p',fact_folding__image_Oeq__fold) ).
fof(fact_folding_Oinsert,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ),
file('theBenchmark.p',fact_folding_Oinsert) ).
fof(fact_folding_Ounion__inter,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
file('theBenchmark.p',fact_folding_Ounion__inter) ).
fof(fact_folding_Oinsert__remove,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ),
file('theBenchmark.p',fact_folding_Oinsert__remove) ).
fof(fact_folding_Ounion,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ),
file('theBenchmark.p',fact_folding_Ounion) ).
fof(fact_setsum__reindex__nonzero,axiom,
! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
=> ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
=> ( B_x != B_y
=> ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
=> hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_S_2) ) ) ),
file('theBenchmark.p',fact_setsum__reindex__nonzero) ).
fof(fact_Random__Sequence_Omap__def,axiom,
! [V_P_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_P_2) = c_Random__Sequence_Obind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)),
file('theBenchmark.p',fact_Random__Sequence_Omap__def) ).
fof(fact_folding__idem_Ounion__idem,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
file('theBenchmark.p',fact_folding__idem_Ounion__idem) ).
fof(fact_folding__idem_Osubset__comp__idem,axiom,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2) ) ) ),
file('theBenchmark.p',fact_folding__idem_Osubset__comp__idem) ).
fof(fact_folding__idem_Oidem__comp,axiom,
! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
=> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ),
file('theBenchmark.p',fact_folding__idem_Oidem__comp) ).
fof(fact_folding__idem_Oidem__left__comp,axiom,
! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
=> hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2) ),
file('theBenchmark.p',fact_folding__idem_Oidem__left__comp) ).
fof(fact_folding__idem_Oin__comp__idem,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2) ) ) ),
file('theBenchmark.p',fact_folding__idem_Oin__comp__idem) ).
fof(fact_folding__idem_Oinsert__idem,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ),
file('theBenchmark.p',fact_folding__idem_Oinsert__idem) ).
fof(fact_strong__setprod__reindex__cong,axiom,
! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
( class_Groups_Ocomm__monoid__mult(T_d)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2),B_x) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ),
file('theBenchmark.p',fact_strong__setprod__reindex__cong) ).
fof(fact_neg__map__def,axiom,
! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)),
file('theBenchmark.p',fact_neg__map__def) ).
fof(fact_neg__single__def,axiom,
! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_b,V_x_2),
file('theBenchmark.p',fact_neg__single__def) ).
fof(fact_pos__map__def,axiom,
! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)),
file('theBenchmark.p',fact_pos__map__def) ).
fof(fact_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__single__def,axiom,
! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_b,V_x_2),
file('theBenchmark.p',fact_pos__single__def) ).
fof(fact_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_Eps__split,axiom,
! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))),
file('theBenchmark.p',fact_Eps__split) ).
fof(fact_exE__some,axiom,
! [T_b,V_c_2,V_P_2] :
( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
=> ( V_c_2 = c_Hilbert__Choice_OEps(T_b,V_P_2)
=> hBOOL(hAPP(V_P_2,V_c_2)) ) ),
file('theBenchmark.p',fact_exE__some) ).
fof(fact_some__sym__eq__trivial,axiom,
! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2,
file('theBenchmark.p',fact_some__sym__eq__trivial) ).
fof(fact_some__eq__trivial,axiom,
! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2,
file('theBenchmark.p',fact_some__eq__trivial) ).
fof(fact_some__eq__ex,axiom,
! [T_b,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
<=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ),
file('theBenchmark.p',fact_some__eq__ex) ).
fof(fact_someI__ex,axiom,
! [T_b,V_P_2] :
( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
=> hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ),
file('theBenchmark.p',fact_someI__ex) ).
fof(fact_tfl__some,axiom,
! [T_b,B_P] :
( ? [B_x] : hBOOL(hAPP(B_P,B_x))
=> hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ),
file('theBenchmark.p',fact_tfl__some) ).
fof(fact_someI,axiom,
! [T_b,V_x_2,V_P_2] :
( hBOOL(hAPP(V_P_2,V_x_2))
=> hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ),
file('theBenchmark.p',fact_someI) ).
fof(fact_split__paired__Eps,axiom,
! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_P_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))),
file('theBenchmark.p',fact_split__paired__Eps) ).
fof(fact_Eps__split__eq,axiom,
! [V_y_2,V_x_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2),
file('theBenchmark.p',fact_Eps__split__eq) ).
fof(fact_wfI__pf,axiom,
! [V_R_2,T_b] :
( ! [B_A] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),B_A)))
=> B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
=> c_Wellfounded_Owf(T_b,V_R_2) ),
file('theBenchmark.p',fact_wfI__pf) ).
fof(fact_Sigma__mono,axiom,
! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_C_2),V_D_2))) ) ),
file('theBenchmark.p',fact_Sigma__mono) ).
fof(fact_not__acc__down,axiom,
! [V_R_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
=> ~ ! [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_x_2)),V_R_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ),
file('theBenchmark.p',fact_not__acc__down) ).
fof(fact_acc_OaccI,axiom,
! [V_r_2,V_x_2,T_b] :
( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_x_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
file('theBenchmark.p',fact_acc_OaccI) ).
fof(fact_fold__image__1,axiom,
! [V_f_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
=> hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ),
file('theBenchmark.p',fact_fold__image__1) ).
fof(fact_card_Oneutral,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_card_Oneutral) ).
fof(fact_max__ext_Osimps,axiom,
! [V_R_2,V_a2_2,V_a1_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
=> ? [B_xa] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) ) )
& V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) ) ),
file('theBenchmark.p',fact_max__ext_Osimps) ).
fof(fact_fold__image__cong,axiom,
! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
( class_Groups_Oab__semigroup__mult(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
=> hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),V_z_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_fold__image__cong) ).
fof(fact_setprod__dvd__setprod__subset2,axiom,
! [V_g_2,V_f_2,V_A_2,V_B_2,T_b,T_c] :
( class_Rings_Ocomm__semiring__1(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))) ) ) ) ),
file('theBenchmark.p',fact_setprod__dvd__setprod__subset2) ).
fof(fact_Max__eqI,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_Max__eqI) ).
fof(fact_Min__eqI,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ),
file('theBenchmark.p',fact_Min__eqI) ).
fof(fact_wf__no__infinite__down__chainE,axiom,
! [V_f_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> ~ ! [B_k] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2)) ),
file('theBenchmark.p',fact_wf__no__infinite__down__chainE) ).
fof(fact_setsum__reindex__cong,axiom,
! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
( class_Groups_Ocomm__monoid__add(T_d)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
=> ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
=> ( ! [B_a] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
=> hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_g_2),V_A_2) ) ) ) ),
file('theBenchmark.p',fact_setsum__reindex__cong) ).
fof(fact_less__eq,axiom,
! [V_na_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_na_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_na_2)) ),
file('theBenchmark.p',fact_less__eq) ).
fof(fact_wf__trancl,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
=> c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ),
file('theBenchmark.p',fact_wf__trancl) ).
fof(fact_less__than__def,axiom,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('theBenchmark.p',fact_less__than__def) ).
fof(fact_acyclic__def,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Oacyclic(T_b,V_r_2)
<=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_acyclic__def) ).
fof(fact_trancl_Or__into__trancl,axiom,
! [V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_trancl_Or__into__trancl) ).
fof(fact_trancl__subset__Field2,axiom,
! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_Relation_OField(T_b),V_r_2))))),
file('theBenchmark.p',fact_trancl__subset__Field2) ).
fof(fact_r__into__trancl_H,axiom,
! [V_r_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_r__into__trancl_H) ).
fof(fact_trancl__empty,axiom,
! [T_b] : c_Transitive__Closure_Otrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),
file('theBenchmark.p',fact_trancl__empty) ).
fof(fact_trancl__domain,axiom,
! [V_r_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_b),V_r_2),
file('theBenchmark.p',fact_trancl__domain) ).
fof(fact_trancl__range,axiom,
! [V_r_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ORange(T_b,T_b),V_r_2),
file('theBenchmark.p',fact_trancl__range) ).
fof(fact_finite__trancl,axiom,
! [V_r_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ),
file('theBenchmark.p',fact_finite__trancl) ).
fof(fact_r__r__into__trancl,axiom,
! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_R_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_R_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ),
file('theBenchmark.p',fact_r__r__into__trancl) ).
fof(fact_trancl__into__trancl2,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_trancl__into__trancl2) ).
fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).
fof(fact_trancl__trans,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_trancl__trans) ).
fof(fact_trancl__mono,axiom,
! [V_s_2,V_r_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ),
file('theBenchmark.p',fact_trancl__mono) ).
fof(fact_trancl__unfold,axiom,
! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_r_2)),
file('theBenchmark.p',fact_trancl__unfold) ).
fof(fact_trancl__subset__Sigma,axiom,
! [V_A_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ),
file('theBenchmark.p',fact_trancl__subset__Sigma) ).
fof(fact_trancl__Int__subset,axiom,
! [V_s_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)) ) ),
file('theBenchmark.p',fact_trancl__Int__subset) ).
fof(fact_trancl__insert,axiom,
! [V_r_2,V_x_2,V_y_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBC(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),V_y_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))))),
file('theBenchmark.p',fact_trancl__insert) ).
fof(fact_reflcl__set__eq,axiom,
! [V_y_2,V_x_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),c_fequal),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))) ),
file('theBenchmark.p',fact_reflcl__set__eq) ).
fof(fact_r__into__rtrancl,axiom,
! [V_r_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_r__into__rtrancl) ).
fof(fact_rtrancl_Ortrancl__refl,axiom,
! [V_r_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))),
file('theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
fof(fact_IdI,axiom,
! [V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Relation_OId(T_b))),
file('theBenchmark.p',fact_IdI) ).
fof(fact_trancl__into__rtrancl,axiom,
! [V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_trancl__into__rtrancl) ).
fof(fact_rtrancl__trancl__absorb,axiom,
! [V_R_2,T_b] : c_Transitive__Closure_Otrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
file('theBenchmark.p',fact_rtrancl__trancl__absorb) ).
fof(fact_trancl__rtrancl__absorb,axiom,
! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Otrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
file('theBenchmark.p',fact_trancl__rtrancl__absorb) ).
fof(fact_reflcl__trancl,axiom,
! [V_r_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
file('theBenchmark.p',fact_reflcl__trancl) ).
fof(fact_trancl__reflcl,axiom,
! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
file('theBenchmark.p',fact_trancl__reflcl) ).
fof(fact_trancl__unfold__left,axiom,
! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
file('theBenchmark.p',fact_trancl__unfold__left) ).
fof(fact_trancl__unfold__right,axiom,
! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2),
file('theBenchmark.p',fact_trancl__unfold__right) ).
fof(fact_rtrancl__Int__subset,axiom,
! [V_r_2,V_s_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),V_s_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)) ) ),
file('theBenchmark.p',fact_rtrancl__Int__subset) ).
fof(fact_rtrancl__unfold,axiom,
! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2)),
file('theBenchmark.p',fact_rtrancl__unfold) ).
fof(fact_rtrancl__idemp__self__comp,axiom,
! [V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
file('theBenchmark.p',fact_rtrancl__idemp__self__comp) ).
fof(fact_r__comp__rtrancl__eq,axiom,
! [V_r_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2),
file('theBenchmark.p',fact_r__comp__rtrancl__eq) ).
fof(fact_Image__closed__trancl,axiom,
! [V_X_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),V_X_2)),V_X_2))
=> hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ),
file('theBenchmark.p',fact_Image__closed__trancl) ).
fof(fact_rtrancl__mono,axiom,
! [V_s_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ),
file('theBenchmark.p',fact_rtrancl__mono) ).
fof(fact_rtrancl__subset,axiom,
! [V_S_2,V_R_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
=> c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ),
file('theBenchmark.p',fact_rtrancl__subset) ).
fof(fact_rtrancl__subset__rtrancl,axiom,
! [V_s_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_s_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ),
file('theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
fof(fact_rtrancl__Un__subset,axiom,
! [V_S_2,V_R_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))),
file('theBenchmark.p',fact_rtrancl__Un__subset) ).
fof(fact_rtrancl__reflcl,axiom,
! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
file('theBenchmark.p',fact_rtrancl__reflcl) ).
fof(fact_rtrancl__Un__rtrancl,axiom,
! [V_S_2,V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) = c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),
file('theBenchmark.p',fact_rtrancl__Un__rtrancl) ).
fof(fact_rtrancl__reflcl__absorb,axiom,
! [V_R_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
file('theBenchmark.p',fact_rtrancl__reflcl__absorb) ).
fof(fact_Range__rtrancl,axiom,
! [V_R_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Range__rtrancl) ).
fof(fact_in__rtrancl__UnI,axiom,
! [V_S_2,V_R_2,V_x_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))) ),
file('theBenchmark.p',fact_in__rtrancl__UnI) ).
fof(fact_rtrancl__r__diff__Id,axiom,
! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
file('theBenchmark.p',fact_rtrancl__r__diff__Id) ).
fof(fact_converse__rtrancl__into__rtrancl,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
fof(fact_rtrancl__trans,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl__trans) ).
fof(fact_refl__rtrancl,axiom,
! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
file('theBenchmark.p',fact_refl__rtrancl) ).
fof(fact_rtrancl__idemp,axiom,
! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
file('theBenchmark.p',fact_rtrancl__idemp) ).
fof(fact_Domain__rtrancl,axiom,
! [V_R_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Domain__rtrancl) ).
fof(fact_rtrancl__empty,axiom,
! [T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Relation_OId(T_b),
file('theBenchmark.p',fact_rtrancl__empty) ).
fof(fact_Image__Id,axiom,
! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2,
file('theBenchmark.p',fact_Image__Id) ).
fof(fact_R__O__Id,axiom,
! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_c),V_R_2),c_Relation_OId(T_c)) = V_R_2,
file('theBenchmark.p',fact_R__O__Id) ).
fof(fact_Id__O__R,axiom,
! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_c),c_Relation_OId(T_b)),V_R_2) = V_R_2,
file('theBenchmark.p',fact_Id__O__R) ).
fof(fact_pair__in__Id__conv,axiom,
! [V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b)))
<=> V_a_2 = V_b_2 ),
file('theBenchmark.p',fact_pair__in__Id__conv) ).
fof(fact_rtrancl__eq__or__trancl,axiom,
! [V_R_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
& V_x_2 != V_y_2 )
| V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_rtrancl__eq__or__trancl) ).
fof(fact_rtrancl__into__trancl2,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl__into__trancl2) ).
fof(fact_rtranclD,axiom,
! [V_R_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
& V_a_2 != V_b_2 )
| V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_rtranclD) ).
fof(fact_rtrancl__into__trancl1,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl__into__trancl1) ).
fof(fact_trancl__rtrancl__trancl,axiom,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_trancl__rtrancl__trancl) ).
fof(fact_rtrancl__trancl__trancl,axiom,
! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_rtrancl__trancl__trancl) ).
fof(fact_Domain__Id,axiom,
! [T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Domain__Id) ).
fof(fact_Range__Id,axiom,
! [T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Range__Id) ).
fof(fact_refl__Id,axiom,
! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Relation_OId(T_b)),
file('theBenchmark.p',fact_refl__Id) ).
fof(fact_pair__leq__def,axiom,
c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))),
file('theBenchmark.p',fact_pair__leq__def) ).
fof(fact_Not__Domain__rtrancl,axiom,
! [V_y_2,V_R_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_Not__Domain__rtrancl) ).
fof(fact_acc__downwards,axiom,
! [V_b_2,V_r_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_acc__downwards) ).
fof(fact_acc__downwards__aux,axiom,
! [V_r_2,V_a_2,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_acc__downwards__aux) ).
fof(fact_wf__insert,axiom,
! [V_r_2,V_x_2,V_y_2,T_b] :
( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
<=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
& c_Wellfounded_Owf(T_b,V_r_2) ) ),
file('theBenchmark.p',fact_wf__insert) ).
fof(fact_acyclic__insert,axiom,
! [V_r_2,V_x_2,V_y_2,T_b] :
( c_Wellfounded_Oacyclic(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
<=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
& c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
file('theBenchmark.p',fact_acyclic__insert) ).
fof(fact_refl__reflcl,axiom,
! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))),
file('theBenchmark.p',fact_refl__reflcl) ).
fof(fact_Id__def,axiom,
! [T_b] : c_Relation_OId(T_b) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_b),tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),tc_prod(T_b,T_b)),c_COMBB(tc_prod(T_b,T_b),tc_HOL_Obool,T_b)),c_fequal)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))))),
file('theBenchmark.p',fact_Id__def) ).
fof(fact_irrefl__diff__Id,axiom,
! [V_r_2,T_b] : c_Relation_Oirrefl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))),
file('theBenchmark.p',fact_irrefl__diff__Id) ).
fof(fact_pred__nat__trancl__eq__le,axiom,
! [V_na_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_na_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_na_2)) ),
file('theBenchmark.p',fact_pred__nat__trancl__eq__le) ).
fof(fact_trancl__subset__Sigma__aux,axiom,
! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_trancl__subset__Sigma__aux) ).
fof(fact_irrefl__tranclI,axiom,
! [V_x_2,V_r_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_irrefl__tranclI) ).
fof(fact_sequence__trans,axiom,
! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
( ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))),hAPP(V_f_2,V_i_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_sequence__trans) ).
fof(fact_rtrancl__converse,axiom,
! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
file('theBenchmark.p',fact_rtrancl__converse) ).
fof(fact_converse__Id,axiom,
! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b),
file('theBenchmark.p',fact_converse__Id) ).
fof(fact_converse__rel__comp,axiom,
! [V_s_2,V_r_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_b),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(c_Relation_Oconverse(T_d,T_b),V_s_2)),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2)),
file('theBenchmark.p',fact_converse__rel__comp) ).
fof(fact_converse__Un,axiom,
! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)),
file('theBenchmark.p',fact_converse__Un) ).
fof(fact_converseD,axiom,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ),
file('theBenchmark.p',fact_converseD) ).
fof(fact_converseI,axiom,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_converseI) ).
fof(fact_converse__iff,axiom,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ),
file('theBenchmark.p',fact_converse__iff) ).
fof(fact_converse__INTER,axiom,
! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)),
file('theBenchmark.p',fact_converse__INTER) ).
fof(fact_finite__converse,axiom,
! [V_r_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ),
file('theBenchmark.p',fact_finite__converse) ).
fof(fact_refl__on__converse,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
<=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
file('theBenchmark.p',fact_refl__on__converse) ).
fof(fact_converse__Int,axiom,
! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)),
file('theBenchmark.p',fact_converse__Int) ).
fof(fact_converse__inv__image,axiom,
! [V_f_2,V_R_2,T_c,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_c),V_R_2)),V_f_2),
file('theBenchmark.p',fact_converse__inv__image) ).
fof(fact_converse__converse,axiom,
! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = V_r_2,
file('theBenchmark.p',fact_converse__converse) ).
fof(fact_Field__converse,axiom,
! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_OField(T_b),V_r_2),
file('theBenchmark.p',fact_Field__converse) ).
fof(fact_converse__Id__on,axiom,
! [V_A_2,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = c_Relation_OId__on(T_b,V_A_2),
file('theBenchmark.p',fact_converse__Id__on) ).
fof(fact_converse__UNION,axiom,
! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)),
file('theBenchmark.p',fact_converse__UNION) ).
fof(fact_acyclic__converse,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
<=> c_Wellfounded_Oacyclic(T_b,V_r_2) ),
file('theBenchmark.p',fact_acyclic__converse) ).
fof(fact_trancl__converse,axiom,
! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),
file('theBenchmark.p',fact_trancl__converse) ).
fof(fact_wf__converse__trancl,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
=> c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_wf__converse__trancl) ).
fof(fact_equiv__comp__eq,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2 ),
file('theBenchmark.p',fact_equiv__comp__eq) ).
fof(fact_Range__def,axiom,
! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),
file('theBenchmark.p',fact_Range__def) ).
fof(fact_Domain__converse,axiom,
! [V_r_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) = hAPP(c_Relation_ORange(T_c,T_b),V_r_2),
file('theBenchmark.p',fact_Domain__converse) ).
fof(fact_Range__converse,axiom,
! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_c),V_r_2),
file('theBenchmark.p',fact_Range__converse) ).
fof(fact_rtrancl__converseD,axiom,
! [V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
file('theBenchmark.p',fact_rtrancl__converseD) ).
fof(fact_rtrancl__converseI,axiom,
! [V_r_2,V_x_2,V_y_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ),
file('theBenchmark.p',fact_rtrancl__converseI) ).
fof(fact_trancl__converseD,axiom,
! [V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) ),
file('theBenchmark.p',fact_trancl__converseD) ).
fof(fact_trancl__converseI,axiom,
! [V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ),
file('theBenchmark.p',fact_trancl__converseI) ).
fof(fact_Image__subset__eq,axiom,
! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)),V_B_2))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))))) ),
file('theBenchmark.p',fact_Image__subset__eq) ).
fof(fact_refl__on__comp__subset,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2))) ),
file('theBenchmark.p',fact_refl__on__comp__subset) ).
fof(fact_comp__equivI,axiom,
! [V_A_2,V_r_2,T_b] :
( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2
=> ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
=> c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ),
file('theBenchmark.p',fact_comp__equivI) ).
fof(fact_finite__acyclic__wf__converse,axiom,
! [V_r_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
=> c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ),
file('theBenchmark.p',fact_finite__acyclic__wf__converse) ).
fof(fact_converse__def,axiom,
! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_b)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_c,T_b)))),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))))),V_r_2))),
file('theBenchmark.p',fact_converse__def) ).
fof(fact_Image__INT__eq,axiom,
! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
=> hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ) ),
file('theBenchmark.p',fact_Image__INT__eq) ).
fof(fact_total__on__diff__Id,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Ototal__on(T_b,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
<=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ),
file('theBenchmark.p',fact_total__on__diff__Id) ).
fof(fact_single__valued__Id,axiom,
! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)),
file('theBenchmark.p',fact_single__valued__Id) ).
fof(fact_single__valued__Id__on,axiom,
! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),
file('theBenchmark.p',fact_single__valued__Id__on) ).
fof(fact_single__valued__subset,axiom,
! [V_s_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
=> ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
=> c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ),
file('theBenchmark.p',fact_single__valued__subset) ).
fof(fact_single__valued__rel__comp,axiom,
! [V_s_2,T_d,V_r_2,T_c,T_b] :
( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
=> ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
=> c_Relation_Osingle__valued(T_b,T_d,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)) ) ),
file('theBenchmark.p',fact_single__valued__rel__comp) ).
fof(fact_total__on__empty,axiom,
! [V_r_2,T_b] : c_Relation_Ototal__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_r_2),
file('theBenchmark.p',fact_total__on__empty) ).
fof(fact_total__on__converse,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
<=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ),
file('theBenchmark.p',fact_total__on__converse) ).
fof(fact_single__valuedD,axiom,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_z_2)),V_r_2))
=> V_y_2 = V_z_2 ) ) ),
file('theBenchmark.p',fact_single__valuedD) ).
fof(fact_single__valued__def,axiom,
! [V_r_2,T_c,T_b] :
( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
<=> ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)),V_r_2))
=> ! [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)),V_r_2))
=> B_y = B_z ) ) ),
file('theBenchmark.p',fact_single__valued__def) ).
fof(fact_total__on__def,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
=> ( B_x != B_xa
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_xa),B_x)),V_r_2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2)) ) ) ) ) ),
file('theBenchmark.p',fact_total__on__def) ).
fof(fact_single__valued__confluent,axiom,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ) ),
file('theBenchmark.p',fact_single__valued__confluent) ).
fof(fact_Image__Int__eq,axiom,
! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
=> hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ),
file('theBenchmark.p',fact_Image__Int__eq) ).
fof(fact_rtrancl__imp__UN__rel__pow,axiom,
! [V_R_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)))) ),
file('theBenchmark.p',fact_rtrancl__imp__UN__rel__pow) ).
fof(fact_acyclicI,axiom,
! [V_r_2,T_b] :
( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
=> c_Wellfounded_Oacyclic(T_b,V_r_2) ),
file('theBenchmark.p',fact_acyclicI) ).
fof(fact_single__valued__rel__pow,axiom,
! [V_na_2,V_R_2,T_b] :
( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
=> c_Relation_Osingle__valued(T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)) ),
file('theBenchmark.p',fact_single__valued__rel__pow) ).
fof(fact_funpow__mult,axiom,
! [V_f_2,V_m_2,V_na_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_na_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_na_2)),V_f_2),
file('theBenchmark.p',fact_funpow__mult) ).
fof(fact_funpow__swap1,axiom,
! [V_x_2,V_na_2,T_b,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_na_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_na_2),V_f_2),hAPP(V_f_2,V_x_2)),
file('theBenchmark.p',fact_funpow__swap1) ).
fof(fact_wf__exp,axiom,
! [V_R_2,V_na_2,T_b] :
( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2))
=> c_Wellfounded_Owf(T_b,V_R_2) ),
file('theBenchmark.p',fact_wf__exp) ).
fof(fact_comp__funpow,axiom,
! [V_f_2,V_na_2,T_c,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),V_na_2),c_Fun_Ocomp(T_c,T_c,T_b,V_f_2)) = c_Fun_Ocomp(T_c,T_c,T_b,hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_na_2),V_f_2)),
file('theBenchmark.p',fact_comp__funpow) ).
fof(fact_rel__pow__1,axiom,
! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2,
file('theBenchmark.p',fact_rel__pow__1) ).
fof(fact_rel__pow__commute,axiom,
! [V_na_2,V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)),V_R_2),
file('theBenchmark.p',fact_rel__pow__commute) ).
fof(fact_rtrancl__power,axiom,
! [V_R_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
<=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ),
file('theBenchmark.p',fact_rtrancl__power) ).
fof(fact_rel__pow__imp__rtrancl,axiom,
! [V_R_2,V_na_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ),
file('theBenchmark.p',fact_rel__pow__imp__rtrancl) ).
fof(fact_relpow_Osimps_I2_J,axiom,
! [V_R_2,V_na_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_na_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_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_na_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)),
file('theBenchmark.p',fact_rel__pow__add) ).
fof(fact_relpow_Osimps_I1_J,axiom,
! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_b),
file('theBenchmark.p',fact_relpow_Osimps_I1_J) ).
fof(fact_rel__pow__0__E,axiom,
! [V_R_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2)))
=> V_x_2 = V_y_2 ),
file('theBenchmark.p',fact_rel__pow__0__E) ).
fof(fact_rel__pow__0__I,axiom,
! [V_R_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))),
file('theBenchmark.p',fact_rel__pow__0__I) ).
fof(fact_rel__pow__Suc__I,axiom,
! [V_z_2,V_R_2,V_na_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_R_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_na_2)),V_R_2))) ) ),
file('theBenchmark.p',fact_rel__pow__Suc__I) ).
fof(fact_rel__pow__Suc__I2,axiom,
! [V_na_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_na_2)),V_R_2))) ) ),
file('theBenchmark.p',fact_rel__pow__Suc__I2) ).
fof(fact_funpow_Osimps_I2_J,axiom,
! [V_f_2,V_na_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(c_Nat_OSuc,V_na_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_na_2),V_f_2)),
file('theBenchmark.p',fact_funpow_Osimps_I2_J) ).
fof(fact_funpow__add,axiom,
! [V_f_2,V_na_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_na_2),V_f_2)),
file('theBenchmark.p',fact_funpow__add) ).
fof(fact_funpow_Osimps_I1_J,axiom,
! [V_f_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_b),
file('theBenchmark.p',fact_funpow_Osimps_I1_J) ).
fof(fact_trancl__power,axiom,
! [V_R_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
<=> ? [B_n] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) ) ),
file('theBenchmark.p',fact_trancl__power) ).
fof(fact_rtrancl__is__UN__rel__pow,axiom,
! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)),
file('theBenchmark.p',fact_rtrancl__is__UN__rel__pow) ).
fof(fact_funpow__code__def,axiom,
! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b),
file('theBenchmark.p',fact_funpow__code__def) ).
fof(fact_rel__pow__E,axiom,
! [V_R_2,V_na_2,V_z_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)))
=> ( ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> V_x_2 != V_z_2 )
=> ~ ! [B_y,B_m] :
( V_na_2 = hAPP(c_Nat_OSuc,B_m)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ) ),
file('theBenchmark.p',fact_rel__pow__E) ).
fof(fact_rel__pow__E2,axiom,
! [V_R_2,V_na_2,V_z_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)))
=> ( ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> V_x_2 != V_z_2 )
=> ~ ! [B_y,B_m] :
( V_na_2 = hAPP(c_Nat_OSuc,B_m)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ),
file('theBenchmark.p',fact_rel__pow__E2) ).
fof(fact_rtrancl__Un__separatorE,axiom,
! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2))))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
=> ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_Q_2))
=> B_x = B_y ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) ) ),
file('theBenchmark.p',fact_rtrancl__Un__separatorE) ).
fof(fact_rtrancl__Un__separator__converseE,axiom,
! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2))))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
=> ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_Q_2))
=> B_y = B_x ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) ) ),
file('theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).
fof(fact_rel__pow__Suc__E,axiom,
! [V_R_2,V_na_2,V_z_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_na_2)),V_R_2)))
=> ~ ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ),
file('theBenchmark.p',fact_rel__pow__Suc__E) ).
fof(fact_rel__pow__Suc__D2,axiom,
! [V_R_2,V_na_2,V_z_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_na_2)),V_R_2)))
=> ? [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) ) ),
file('theBenchmark.p',fact_rel__pow__Suc__D2) ).
fof(fact_rel__pow__Suc__E2,axiom,
! [V_R_2,V_na_2,V_z_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_na_2)),V_R_2)))
=> ~ ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2))) ) ),
file('theBenchmark.p',fact_rel__pow__Suc__E2) ).
fof(fact_tranclD,axiom,
! [V_R_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
=> ? [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),V_R_2)) ) ),
file('theBenchmark.p',fact_tranclD) ).
fof(fact_tranclD2,axiom,
! [V_R_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
=> ? [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),V_R_2))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ),
file('theBenchmark.p',fact_tranclD2) ).
fof(fact_IdE,axiom,
! [V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
=> ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ),
file('theBenchmark.p',fact_IdE) ).
fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold_H) ).
fof(fact_fold__image__def,axiom,
! [V_g_2,V_f_2,T_c,T_b] : hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_c,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),
file('theBenchmark.p',fact_fold__image__def) ).
fof(fact_fold__empty,axiom,
! [V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2,
file('theBenchmark.p',fact_fold__empty) ).
fof(fact_folding_Oeq__fold,axiom,
! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_s_2),V_A_2) ) ),
file('theBenchmark.p',fact_folding_Oeq__fold) ).
fof(fact_fold__def,axiom,
! [V_A_2,V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold__graph(T_c,T_b,V_f_2,V_z_2,V_A_2)),
file('theBenchmark.p',fact_fold__def) ).
fof(fact_union__fold__insert,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),V_B_2),V_A_2) ),
file('theBenchmark.p',fact_union__fold__insert) ).
fof(fact_fold__sup__insert,axiom,
! [V_a_2,V_b_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__sup(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2)) ) ),
file('theBenchmark.p',fact_fold__sup__insert) ).
fof(fact_fold__inf__insert,axiom,
! [V_a_2,V_b_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__inf(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)) ) ),
file('theBenchmark.p',fact_fold__inf__insert) ).
fof(fact_min__max_Ofold__inf__insert,axiom,
! [V_a_2,V_b_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)) ) ),
file('theBenchmark.p',fact_min__max_Ofold__inf__insert) ).
fof(fact_min__max_Ofold__sup__insert,axiom,
! [V_a_2,V_b_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2)) ) ),
file('theBenchmark.p',fact_min__max_Ofold__sup__insert) ).
fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ),
file('theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem2) ).
fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ),
file('theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem) ).
fof(fact_sup__SUPR__fold__sup,axiom,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),V_B_2),V_A_2) ) ),
file('theBenchmark.p',fact_sup__SUPR__fold__sup) ).
fof(fact_inf__INFI__fold__inf,axiom,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),V_B_2),V_A_2) ) ),
file('theBenchmark.p',fact_inf__INFI__fold__inf) ).
fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_a_2),V_A_2) ) ),
file('theBenchmark.p',fact_folding__one__idem_Oeq__fold__idem_H) ).
fof(fact_sup__le__fold__sup,axiom,
! [V_b_2,V_a_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__sup(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2))) ) ) ),
file('theBenchmark.p',fact_sup__le__fold__sup) ).
fof(fact_fold__inf__le__inf,axiom,
! [V_b_2,V_a_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__inf(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2))) ) ) ),
file('theBenchmark.p',fact_fold__inf__le__inf) ).
fof(fact_min__max_Ofold__inf__le__inf,axiom,
! [V_b_2,V_a_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),V_b_2))) ) ) ),
file('theBenchmark.p',fact_min__max_Ofold__inf__le__inf) ).
fof(fact_min__max_Osup__le__fold__sup,axiom,
! [V_b_2,V_a_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2))) ) ) ),
file('theBenchmark.p',fact_min__max_Osup__le__fold__sup) ).
fof(fact_fold1__eq__fold__idem,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Lattices_Oab__semigroup__idem__mult(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ),
file('theBenchmark.p',fact_fold1__eq__fold__idem) ).
fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_a_2),V_A_2) ) ),
file('theBenchmark.p',fact_Sup__fin_Oeq__fold__idem_H) ).
fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_a_2),V_A_2) ) ),
file('theBenchmark.p',fact_Inf__fin_Oeq__fold__idem_H) ).
fof(fact_Min_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ),
file('theBenchmark.p',fact_Min_Oeq__fold__idem_H) ).
fof(fact_Max_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ),
file('theBenchmark.p',fact_Max_Oeq__fold__idem_H) ).
fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold__idem_H) ).
fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ),
file('theBenchmark.p',fact_min__max_OSup__fin_Oeq__fold__idem_H) ).
fof(fact_minus__fold__remove,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2),V_A_2) ),
file('theBenchmark.p',fact_minus__fold__remove) ).
fof(fact_folding__one_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_x_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_folding__one_Oeq__fold_H) ).
fof(fact_SUPR__fold__sup,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(T_c)),V_A_2) ) ),
file('theBenchmark.p',fact_SUPR__fold__sup) ).
fof(fact_INFI__fold__inf,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Complete__Lattice_Ocomplete__lattice(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),c_Orderings_Otop__class_Otop(T_c)),V_A_2) ) ),
file('theBenchmark.p',fact_INFI__fold__inf) ).
fof(fact_fold1__eq__fold,axiom,
! [V_a_2,V_A_2,T_b] :
( class_Groups_Oab__semigroup__mult(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_fold1__eq__fold) ).
fof(fact_Sup__fin_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_x_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_Sup__fin_Oeq__fold_H) ).
fof(fact_Inf__fin_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Lattices_Olattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_x_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_Inf__fin_Oeq__fold_H) ).
fof(fact_Min_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_Min_Oeq__fold_H) ).
fof(fact_Max_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_Max_Oeq__fold_H) ).
fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ),
file('theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold_H) ).
fof(fact_fun__left__comm_Ofold__rec,axiom,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__rec) ).
fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__insert__remove) ).
fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ),
file('theBenchmark.p',fact_fun__left__comm_Ofun__comp__comm) ).
fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
=> V_y_2 = V_x_2 ) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__determ) ).
fof(fact_fun__left__comm,axiom,
! [T_b] :
( class_Groups_Oab__semigroup__mult(T_b)
=> c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ),
file('theBenchmark.p',fact_fun__left__comm) ).
fof(fact_fun__left__comm_Ofun__left__comm,axiom,
! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_y_2),V_z_2)) = hAPP(hAPP(V_f_2,V_y_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) ),
file('theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).
fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
! [V_g_2,T_d,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> c_Finite__Set_Ofun__left__comm(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ),
file('theBenchmark.p',fact_fun__left__comm_Ofun__left__comm__apply) ).
fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__fun__comm) ).
fof(fact_fun__left__comm_Ofold__equality,axiom,
! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__equality) ).
fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2))) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__fold) ).
fof(fact_fun__left__comm_Ofold__insert2,axiom,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__insert2) ).
fof(fact_fun__left__comm_Ofold__insert,axiom,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__insert) ).
fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
=> ? [B_y_H] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),B_y_H))
& V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) ) ) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE__aux) ).
fof(fact_Inf__fold__inf,axiom,
! [V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ),
file('theBenchmark.p',fact_Inf__fold__inf) ).
fof(fact_finite__Inter,axiom,
! [V_M_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x))
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2)) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ),
file('theBenchmark.p',fact_finite__Inter) ).
fof(fact_InterD,axiom,
! [V_X_2,V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ),
file('theBenchmark.p',fact_InterD) ).
fof(fact_InterE,axiom,
! [V_X_2,V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ),
file('theBenchmark.p',fact_InterE) ).
fof(fact_Inter__lower,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ),
file('theBenchmark.p',fact_Inter__lower) ).
fof(fact_le__Inf__iff,axiom,
! [V_A_2,V_b_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ),
file('theBenchmark.p',fact_le__Inf__iff) ).
fof(fact_Inf__less__iff,axiom,
! [V_a_2,V_S_2,T_b] :
( ( class_Orderings_Olinorder(T_b)
& class_Complete__Lattice_Ocomplete__lattice(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) ) ),
file('theBenchmark.p',fact_Inf__less__iff) ).
fof(fact_Un__Inter,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),
file('theBenchmark.p',fact_Un__Inter) ).
fof(fact_Inter__anti__mono,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ),
file('theBenchmark.p',fact_Inter__anti__mono) ).
fof(fact_Inter__empty,axiom,
! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Inter__empty) ).
fof(fact_Inter__eq,axiom,
! [V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))),
file('theBenchmark.p',fact_Inter__eq) ).
fof(fact_Inter__insert,axiom,
! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
file('theBenchmark.p',fact_Inter__insert) ).
fof(fact_Inter__UNIV,axiom,
! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Inter__UNIV) ).
fof(fact_Inf__lower,axiom,
! [V_A_2,V_x_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)),V_x_2)) ) ),
file('theBenchmark.p',fact_Inf__lower) ).
fof(fact_Inter__Un__distrib,axiom,
! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
file('theBenchmark.p',fact_Inter__Un__distrib) ).
fof(fact_Inf__singleton,axiom,
! [V_a_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ),
file('theBenchmark.p',fact_Inf__singleton) ).
fof(fact_Inf__empty,axiom,
! [T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ),
file('theBenchmark.p',fact_Inf__empty) ).
fof(fact_Inf__UNIV,axiom,
! [T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ),
file('theBenchmark.p',fact_Inf__UNIV) ).
fof(fact_Inf__insert,axiom,
! [V_A_2,V_a_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) ),
file('theBenchmark.p',fact_Inf__insert) ).
fof(fact_INTER__eq__Inter__image,axiom,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)),
file('theBenchmark.p',fact_INTER__eq__Inter__image) ).
fof(fact_Inter__image__eq,axiom,
! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
file('theBenchmark.p',fact_Inter__image__eq) ).
fof(fact_Int__eq__Inter,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))),
file('theBenchmark.p',fact_Int__eq__Inter) ).
fof(fact_Int__Inter__image,axiom,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))),
file('theBenchmark.p',fact_Int__Inter__image) ).
fof(fact_Inter__Un__subset,axiom,
! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))),
file('theBenchmark.p',fact_Inter__Un__subset) ).
fof(fact_Inf__binary,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2) ),
file('theBenchmark.p',fact_Inf__binary) ).
fof(fact_inf__Inf__fold__inf,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_B_2),V_A_2) ) ),
file('theBenchmark.p',fact_inf__Inf__fold__inf) ).
fof(fact_Inf__fin__Inf,axiom,
! [V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ),
file('theBenchmark.p',fact_Inf__fin__Inf) ).
fof(fact_Inf__Sup,axiom,
! [V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_b))))) ),
file('theBenchmark.p',fact_Inf__Sup) ).
fof(fact_Sup__Inf,axiom,
! [V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b)))))) ),
file('theBenchmark.p',fact_Sup__Inf) ).
fof(fact_UnionI,axiom,
! [V_A_2,V_C_2,V_X_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ),
file('theBenchmark.p',fact_UnionI) ).
fof(fact_Inter__def,axiom,
! [V_S_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))),
file('theBenchmark.p',fact_Inter__def) ).
fof(fact_image__Union,axiom,
! [V_S_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_c,T_b,V_f_2)),
file('theBenchmark.p',fact_image__Union) ).
fof(fact_Domain__Union,axiom,
! [V_S_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_b,T_c)),
file('theBenchmark.p',fact_Domain__Union) ).
fof(fact_UN__simps_I8_J,axiom,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
file('theBenchmark.p',fact_UN__simps_I8_J) ).
fof(fact_UN__extend__simps_I8_J,axiom,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2),
file('theBenchmark.p',fact_UN__extend__simps_I8_J) ).
fof(fact_Int__Union2,axiom,
! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
file('theBenchmark.p',fact_Int__Union2) ).
fof(fact_Int__Union,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),
file('theBenchmark.p',fact_Int__Union) ).
fof(fact_Sigma__Union,axiom,
! [V_B_2,V_X_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Product__Type_OSigma(T_b,T_c)),V_B_2)),
file('theBenchmark.p',fact_Sigma__Union) ).
fof(fact_Range__Union,axiom,
! [V_S_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_c,T_b)),
file('theBenchmark.p',fact_Range__Union) ).
fof(fact_vimage__Union,axiom,
! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_b,T_c,V_f_2)),
file('theBenchmark.p',fact_vimage__Union) ).
fof(fact_Union__empty,axiom,
! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Union__empty) ).
fof(fact_Union__mono,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ),
file('theBenchmark.p',fact_Union__mono) ).
fof(fact_Union__disjoint,axiom,
! [V_A_2,V_C_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_Union__disjoint) ).
fof(fact_Field__Union,axiom,
! [V_R_2,T_b] : hAPP(c_Relation_OField(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Relation_OField(T_b)),V_R_2)),
file('theBenchmark.p',fact_Field__Union) ).
fof(fact_Union__Pow__eq,axiom,
! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OPow(T_b),V_A_2)) = V_A_2,
file('theBenchmark.p',fact_Union__Pow__eq) ).
fof(fact_less__Sup__iff,axiom,
! [V_S_2,V_a_2,T_b] :
( ( class_Orderings_Olinorder(T_b)
& class_Complete__Lattice_Ocomplete__lattice(T_b) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
<=> ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) ) ),
file('theBenchmark.p',fact_less__Sup__iff) ).
fof(fact_INT__extend__simps_I8_J,axiom,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2),
file('theBenchmark.p',fact_INT__extend__simps_I8_J) ).
fof(fact_INT__simps_I8_J,axiom,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
file('theBenchmark.p',fact_INT__simps_I8_J) ).
fof(fact_Sup__le__iff,axiom,
! [V_b_2,V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_b_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ),
file('theBenchmark.p',fact_Sup__le__iff) ).
fof(fact_Union__upper,axiom,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ),
file('theBenchmark.p',fact_Union__upper) ).
fof(fact_Union__insert,axiom,
! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
file('theBenchmark.p',fact_Union__insert) ).
fof(fact_Union__quotient,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = V_A_2 ),
file('theBenchmark.p',fact_Union__quotient) ).
fof(fact_finite__UnionD,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ),
file('theBenchmark.p',fact_finite__UnionD) ).
fof(fact_subset__Pow__Union,axiom,
! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))),
file('theBenchmark.p',fact_subset__Pow__Union) ).
fof(fact_Union__UNIV,axiom,
! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_Union__UNIV) ).
fof(fact_Union__Un__distrib,axiom,
! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
file('theBenchmark.p',fact_Union__Un__distrib) ).
fof(fact_UNION__eq__Union__image,axiom,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)),
file('theBenchmark.p',fact_UNION__eq__Union__image) ).
fof(fact_Union__image__eq,axiom,
! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
file('theBenchmark.p',fact_Union__image__eq) ).
fof(fact_Sup__upper,axiom,
! [V_A_2,V_x_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2))) ) ),
file('theBenchmark.p',fact_Sup__upper) ).
fof(fact_Sup__empty,axiom,
! [T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ),
file('theBenchmark.p',fact_Sup__empty) ).
fof(fact_Sup__singleton,axiom,
! [V_a_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ),
file('theBenchmark.p',fact_Sup__singleton) ).
fof(fact_Sup__insert,axiom,
! [V_A_2,V_a_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) ),
file('theBenchmark.p',fact_Sup__insert) ).
fof(fact_Sup__UNIV,axiom,
! [T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ),
file('theBenchmark.p',fact_Sup__UNIV) ).
fof(fact_Un__eq__Union,axiom,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))),
file('theBenchmark.p',fact_Un__eq__Union) ).
fof(fact_Un__Union__image,axiom,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))),
file('theBenchmark.p',fact_Un__Union__image) ).
fof(fact_Union__Int__subset,axiom,
! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)))),
file('theBenchmark.p',fact_Union__Int__subset) ).
fof(fact_Sup__binary,axiom,
! [V_b_2,V_a_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2) ),
file('theBenchmark.p',fact_Sup__binary) ).
fof(fact_sup__Sup__fold__sup,axiom,
! [V_B_2,V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_B_2),V_A_2) ) ),
file('theBenchmark.p',fact_sup__Sup__fold__sup) ).
fof(fact_Sup__fin__Sup,axiom,
! [V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ),
file('theBenchmark.p',fact_Sup__fin__Sup) ).
fof(fact_Sup__fold__sup,axiom,
! [V_A_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ),
file('theBenchmark.p',fact_Sup__fold__sup) ).
fof(fact_inj__on__Inter,axiom,
! [V_f_2,T_c,T_b,V_S_2] :
( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
=> ( ! [B_A] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
=> c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2)) ) ),
file('theBenchmark.p',fact_inj__on__Inter) ).
fof(fact_Inter__subset,axiom,
! [V_B_2,V_A_2,T_b] :
( ! [B_X] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ) ),
file('theBenchmark.p',fact_Inter__subset) ).
fof(fact_Union__def,axiom,
! [V_S_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))),
file('theBenchmark.p',fact_Union__def) ).
fof(fact_finite__Union,axiom,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
=> ( ! [B_M] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ),
file('theBenchmark.p',fact_finite__Union) ).
fof(fact_insert__partition,axiom,
! [V_F_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)))
=> ( B_x != B_xa
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_insert__partition) ).
fof(fact_card__partition,axiom,
! [V_k_2,V_C_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
=> ( ! [B_c] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
=> hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
=> ( ! [B_c1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
=> ! [B_c2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
=> ( B_c1 != B_c2
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)) ) ) ) ),
file('theBenchmark.p',fact_card__partition) ).
fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_v_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> ~ ! [B_y] :
( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
=> ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE) ).
fof(fact_min__max_Ofold__sup__le__sup,axiom,
! [V_c_2,V_b_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),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_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_c_2),V_A_2))) ) ) ),
file('theBenchmark.p',fact_min__max_Oinf__le__fold__inf) ).
fof(fact_InterI,axiom,
! [V_A_2,V_C_2,T_b] :
( ! [B_X] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
=> hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ),
file('theBenchmark.p',fact_InterI) ).
fof(fact_inf__le__fold__inf,axiom,
! [V_c_2,V_b_2,V_A_2,T_b] :
( class_Lattices_Osemilattice__inf(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_c_2),V_A_2))) ) ) ),
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_b] :
( class_Lattices_Osemilattice__sup(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_c_2))) ) ) ),
file('theBenchmark.p',fact_fold__sup__le__sup) ).
fof(fact_wf__eq__minimal,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
<=> ! [B_Q] :
( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
=> ? [B_x] :
( ! [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) )
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) ) ) ),
file('theBenchmark.p',fact_wf__eq__minimal) ).
fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
=> hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
file('theBenchmark.p',fact_folding__image__simple__idem_Ounion__idem) ).
fof(fact_transfer__nat__int__set__cong,axiom,
! [V_P_H_2,V_P_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_P_2,B_x))
<=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
=> hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2)) ),
file('theBenchmark.p',fact_transfer__nat__int__set__cong) ).
fof(fact_folding__image__simple__idem_Oidem,axiom,
! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ),
file('theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
fof(fact_folding__image__simple__idem_Oin__idem,axiom,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
=> hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ),
file('theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).
fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) ) ),
file('theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).
fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
=> hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ),
file('theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).
fof(fact_Int__Collect__mono,axiom,
! [V_Q_2,V_P_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> ( hBOOL(hAPP(V_P_2,B_x))
=> hBOOL(hAPP(V_Q_2,B_x)) ) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Q_2)))) ) ),
file('theBenchmark.p',fact_Int__Collect__mono) ).
fof(fact_UnionE,axiom,
! [V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
=> ~ ! [B_X] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ),
file('theBenchmark.p',fact_UnionE) ).
fof(fact_rel__compE,axiom,
! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2)))
=> ~ ! [B_x,B_y,B_z] :
( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),B_x),B_y)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_y),B_z)),V_s_2)) ) ) ),
file('theBenchmark.p',fact_rel__compE) ).
fof(fact_converseE,axiom,
! [V_r_2,V_yx_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_yx_2),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
=> ~ ! [B_x,B_y] :
( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),B_y)),V_r_2)) ) ),
file('theBenchmark.p',fact_converseE) ).
fof(fact_setprod__pos,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Rings_Olinordered__semidom(T_c)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ),
file('theBenchmark.p',fact_setprod__pos) ).
fof(fact_setprod__nonneg,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Rings_Olinordered__semidom(T_c)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ),
file('theBenchmark.p',fact_setprod__nonneg) ).
fof(fact_finite__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_finite__induct,axiom,
! [V_P_2,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
=> ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
=> ( ! [B_x,B_F] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
=> ( hBOOL(hAPP(V_P_2,B_F))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) )
=> hBOOL(hAPP(V_P_2,V_F_2)) ) ) ),
file('theBenchmark.p',fact_finite__induct) ).
fof(fact_lenlex__def,axiom,
! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_b),c_Wellfounded_Oless__than,c_List_Olex(T_b,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_b))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_COMBI(tc_List_Olist(T_b)))),
file('theBenchmark.p',fact_lenlex__def) ).
fof(fact_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_measure__snd,axiom,
! [T_c,V_f_2,T_b] :
( c_FunDef_Ois__measure(T_b,V_f_2)
=> c_FunDef_Ois__measure(tc_prod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_c,T_b)),V_f_2),c_Product__Type_Osnd(T_c,T_b))) ),
file('theBenchmark.p',fact_measure__snd) ).
fof(fact_measure__fst,axiom,
! [T_c,V_f_2,T_b] :
( c_FunDef_Ois__measure(T_b,V_f_2)
=> c_FunDef_Ois__measure(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_b,T_c)),V_f_2),c_Product__Type_Ofst(T_b,T_c))) ),
file('theBenchmark.p',fact_measure__fst) ).
fof(fact_is__measure_Osimps,axiom,
! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2),
file('theBenchmark.p',fact_is__measure_Osimps) ).
fof(fact_is__measure_Oequations,axiom,
! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2),
file('theBenchmark.p',fact_is__measure_Oequations) ).
fof(fact_is__measure_Ointros,axiom,
! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2),
file('theBenchmark.p',fact_is__measure_Ointros) ).
fof(fact_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_na_2,V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_b,V_r_2),V_na_2)))
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_na_2
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_na_2 ) ),
file('theBenchmark.p',fact_lexn__length) ).
fof(fact_measure__size,axiom,
! [T_b] :
( class_Nat_Osize(T_b)
=> c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ),
file('theBenchmark.p',fact_measure__size) ).
fof(fact_lenlex__conv,axiom,
! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_List_Olex(T_b,V_r_2)))))),
file('theBenchmark.p',fact_lenlex__conv) ).
fof(fact_length__sublist,axiom,
! [V_I_2,V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2)))),
file('theBenchmark.p',fact_length__sublist) ).
fof(fact_lexn_Osimps_I2_J,axiom,
! [V_na_2,V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),hAPP(c_Nat_OSuc,V_na_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_b,tc_List_Olist(T_b)),tc_prod(T_b,tc_List_Olist(T_b))),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_Product__Type_Omap__pair(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),c_Wellfounded_Olex__prod(T_b,tc_List_Olist(T_b),V_r_2,hAPP(c_List_Olexn(T_b,V_r_2),V_na_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_na_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_na_2)))))),
file('theBenchmark.p',fact_lexn_Osimps_I2_J) ).
fof(fact_impossible__Cons,axiom,
! [V_x,V_ys,V_xs,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)))
=> V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ),
file('theBenchmark.p',fact_impossible__Cons) ).
fof(fact_not__Cons__self,axiom,
! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),
file('theBenchmark.p',fact_not__Cons__self) ).
fof(fact_not__Cons__self2,axiom,
! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs,
file('theBenchmark.p',fact_not__Cons__self2) ).
fof(fact_list_Oinject,axiom,
! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
( hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_H_2),V_list_H_2)
<=> ( V_list_2 = V_list_H_2
& V_a_2 = V_a_H_2 ) ),
file('theBenchmark.p',fact_list_Oinject) ).
fof(fact_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_Osize_I4_J,axiom,
! [V_list,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),V_list)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_list)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_list_Osize_I4_J) ).
fof(fact_Cons__in__lex,axiom,
! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olex(T_b,V_r_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olex(T_b,V_r_2)))
& V_x_2 = V_y_2 )
| ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ),
file('theBenchmark.p',fact_Cons__in__lex) ).
fof(fact_set__Cons__def,axiom,
! [V_XS_2,V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBS(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_HOL_Obool,tc_List_Olist(T_b))),c_fequal))),c_List_Olist_OCons(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),V_XS_2)))))),
file('theBenchmark.p',fact_set__Cons__def) ).
fof(fact_pick_Osimps,axiom,
! [V_xs,V_x,T_a,V_i] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
=> hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Random_Opick(T_a,V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
=> hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a),V_x) ) ),
file('theBenchmark.p',fact_pick_Osimps) ).
fof(fact_select__weight__cons__zero,axiom,
! [V_xs_2,V_x_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2),
file('theBenchmark.p',fact_select__weight__cons__zero) ).
fof(fact_lexord__cons__cons,axiom,
! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2))),c_List_Olexord(T_b,V_r_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
& V_a_2 = V_b_2 )
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_lexord__cons__cons) ).
fof(fact_lexord__lex,axiom,
! [V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olex(T_b,V_r_2)))
<=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_lexord__lex) ).
fof(fact_rtrancl__listrel1__ConsI2,axiom,
! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ),
file('theBenchmark.p',fact_rtrancl__listrel1__ConsI2) ).
fof(fact_list_Osize_I2_J,axiom,
! [V_list_2,V_a_2,V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),c_List_Olist_Olist__size(T_b,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_list_Osize_I2_J) ).
fof(fact_Cons__acc__listrel1I,axiom,
! [V_xs_2,V_r_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ),
file('theBenchmark.p',fact_Cons__acc__listrel1I) ).
fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))),
file('theBenchmark.p',fact_listrel1__rtrancl__subset__rtrancl__listrel1) ).
fof(fact_listrel1__converse,axiom,
! [V_r_2,T_b] : c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)),
file('theBenchmark.p',fact_listrel1__converse) ).
fof(fact_listrel1__mono,axiom,
! [V_s_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel1(T_b,V_s_2))) ),
file('theBenchmark.p',fact_listrel1__mono) ).
fof(fact_listrel1I2,axiom,
! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) ),
file('theBenchmark.p',fact_listrel1I2) ).
fof(fact_rtrancl__listrel1__ConsI1,axiom,
! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
file('theBenchmark.p',fact_rtrancl__listrel1__ConsI1) ).
fof(fact_listrel1__eq__len,axiom,
! [V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
file('theBenchmark.p',fact_listrel1__eq__len) ).
fof(fact_rtrancl__listrel1__eq__len,axiom,
! [V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ),
file('theBenchmark.p',fact_rtrancl__listrel1__eq__len) ).
fof(fact_in__listrel1__converse,axiom,
! [V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)))) ),
file('theBenchmark.p',fact_in__listrel1__converse) ).
fof(fact_listrel1I1,axiom,
! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_xs_2))),c_List_Olistrel1(T_b,V_r_2))) ),
file('theBenchmark.p',fact_listrel1I1) ).
fof(fact_Cons__listrel1__Cons,axiom,
! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
& V_x_2 = V_y_2 )
| ( V_xs_2 = V_ys_2
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ),
file('theBenchmark.p',fact_Cons__listrel1__Cons) ).
fof(fact_listrel__Cons,axiom,
! [V_xs_2,V_x_2,V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = c_List_Oset__Cons(T_b,hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))))),
file('theBenchmark.p',fact_listrel__Cons) ).
fof(fact_lexord__irreflexive,axiom,
! [V_y_2,V_r_2,T_b] :
( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ),
file('theBenchmark.p',fact_lexord__irreflexive) ).
fof(fact_listrel__rtrancl__refl,axiom,
! [V_r_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_xs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))),
file('theBenchmark.p',fact_listrel__rtrancl__refl) ).
fof(fact_listrel__mono,axiom,
! [V_s_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_List_Olistrel(T_b,V_s_2))) ),
file('theBenchmark.p',fact_listrel__mono) ).
fof(fact_listrel__subset__rtrancl__listrel1,axiom,
! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))),
file('theBenchmark.p',fact_listrel__subset__rtrancl__listrel1) ).
fof(fact_listrel__eq__len,axiom,
! [V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
file('theBenchmark.p',fact_listrel__eq__len) ).
fof(fact_listrel__rtrancl__trans,axiom,
! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ),
file('theBenchmark.p',fact_listrel__rtrancl__trans) ).
fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
! [V_r_2,T_b] : c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)),
file('theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).
fof(fact_listrel__reflcl__if__listrel1,axiom,
! [V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ),
file('theBenchmark.p',fact_listrel__reflcl__if__listrel1) ).
fof(fact_listrel1__subset__listrel,axiom,
! [V_r_H_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2))
=> ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel(T_b,V_r_H_2))) ) ),
file('theBenchmark.p',fact_listrel1__subset__listrel) ).
fof(fact_rtrancl__listrel1__if__listrel,axiom,
! [V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
file('theBenchmark.p',fact_rtrancl__listrel1__if__listrel) ).
fof(fact_listrel_OCons,axiom,
! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_listrel_OCons) ).
fof(fact_listrelp__listrel__eq,axiom,
! [V_xa_2,V_x_2,V_r_2,T_b] :
( c_List_Olistrelp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2),V_x_2,V_xa_2)
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_xa_2)),c_List_Olistrel(T_b,V_r_2))) ),
file('theBenchmark.p',fact_listrelp__listrel__eq) ).
fof(fact_listrel__Cons2,axiom,
! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2)))
=> ~ ! [B_x,B_xs] :
( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_y_2)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),B_xs),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ) ) ),
file('theBenchmark.p',fact_listrel__Cons2) ).
fof(fact_listrelp_OCons,axiom,
! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
=> ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
=> c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ),
file('theBenchmark.p',fact_listrelp_OCons) ).
fof(fact_listrelp_Oequations_I2_J,axiom,
! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
( c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a4_2))
<=> ( c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2)
& hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ),
file('theBenchmark.p',fact_listrelp_Oequations_I2_J) ).
fof(fact_listrel__Cons1,axiom,
! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
=> ~ ! [B_y,B_ys] :
( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),B_y)),V_r_2))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),B_ys)),c_List_Olistrel(T_b,V_r_2))) ) ) ),
file('theBenchmark.p',fact_listrel__Cons1) ).
fof(fact_listrel__subset,axiom,
! [V_A_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2))))) ),
file('theBenchmark.p',fact_listrel__subset) ).
fof(fact_lists__UNIV,axiom,
! [T_b] : c_List_Olists(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),
file('theBenchmark.p',fact_lists__UNIV) ).
fof(fact_lists__mono,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olists(T_b,V_A_2)),c_List_Olists(T_b,V_B_2))) ),
file('theBenchmark.p',fact_lists__mono) ).
fof(fact_equiv__listrel,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> c_Equiv__Relations_Oequiv(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ),
file('theBenchmark.p',fact_equiv__listrel) ).
fof(fact_listrel__refl__on,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> c_Relation_Orefl__on(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ),
file('theBenchmark.p',fact_listrel__refl__on) ).
fof(fact_Cons__in__lists__iff,axiom,
! [V_A_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_List_Olists(T_b,V_A_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
file('theBenchmark.p',fact_Cons__in__lists__iff) ).
fof(fact_lists__accD,axiom,
! [V_r_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
file('theBenchmark.p',fact_lists__accD) ).
fof(fact_lists__accI,axiom,
! [V_r_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))) ),
file('theBenchmark.p',fact_lists__accI) ).
fof(fact_listrel__iff__nth,axiom,
! [V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
<=> ( ! [B_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_n))),V_r_2)) )
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ),
file('theBenchmark.p',fact_listrel__iff__nth) ).
fof(fact_lexord__linear,axiom,
! [V_y_2,V_x_2,V_r_2,T_b] :
( ! [B_a,B_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_b),B_a)),V_r_2))
| B_a = B_b
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_b)),V_r_2)) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_x_2)),c_List_Olexord(T_b,V_r_2)))
| V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_lexord__linear) ).
fof(fact_infinite__UNIV__listI,axiom,
! [T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))),
file('theBenchmark.p',fact_infinite__UNIV__listI) ).
fof(fact_nth__Cons__Suc,axiom,
! [V_n,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n),
file('theBenchmark.p',fact_nth__Cons__Suc) ).
fof(fact_nth__Cons__0,axiom,
! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_x,
file('theBenchmark.p',fact_nth__Cons__0) ).
fof(fact_nth_Osimps,axiom,
! [V_na_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_na_2) = c_Nat_Onat_Onat__case(T_b,V_x_2,hAPP(c_List_Onth(T_b),V_xs_2),V_na_2),
file('theBenchmark.p',fact_nth_Osimps) ).
fof(fact_list__eq__iff__nth__eq,axiom,
! [T_b,V_ys_2,V_xs_2] :
( V_xs_2 = V_ys_2
<=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) )
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ),
file('theBenchmark.p',fact_list__eq__iff__nth__eq) ).
fof(fact_nth__Cons_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_select__def,axiom,
! [V_xs_2,T_b] : c_Random_Oselect(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_b),V_xs_2)),c_Code__Numeral_Onat__of))),
file('theBenchmark.p',fact_select__def) ).
fof(fact_lexord__take__index__conv,axiom,
! [V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
<=> ( ? [B_i] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_y_2),B_i))),V_r_2))
& hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)))) )
| ( hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),V_y_2) = V_x_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2))) ) ) ),
file('theBenchmark.p',fact_lexord__take__index__conv) ).
fof(fact_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_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_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__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_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_sublist__upt__eq__take,axiom,
! [V_na_2,V_l_2,T_b] : c_List_Osublist(T_b,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_2)) = hAPP(hAPP(c_List_Otake(T_b),V_na_2),V_l_2),
file('theBenchmark.p',fact_sublist__upt__eq__take) ).
fof(fact_pick__same,axiom,
! [V_xs_2,T_b,V_l_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hAPP(c_Random_Opick(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)),hAPP(c_Code__Numeral_Oof__nat,V_l_2)) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_l_2) ),
file('theBenchmark.p',fact_pick__same) ).
fof(fact_finite__lists__length__le,axiom,
! [V_na_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_na_2))))) ),
file('theBenchmark.p',fact_finite__lists__length__le) ).
fof(fact_finite__set,axiom,
! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),
file('theBenchmark.p',fact_finite__set) ).
fof(fact_inj__mapI,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ),
file('theBenchmark.p',fact_inj__mapI) ).
fof(fact_set__take__subset,axiom,
! [V_xs_2,V_na_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_na_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
file('theBenchmark.p',fact_set__take__subset) ).
fof(fact_in__set__takeD,axiom,
! [V_xs_2,V_na_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_na_2),V_xs_2))))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
file('theBenchmark.p',fact_in__set__takeD) ).
fof(fact_take__map,axiom,
! [V_xs_2,V_f_2,T_c,V_na_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_na_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Otake(T_c),V_na_2),V_xs_2)),
file('theBenchmark.p',fact_take__map) ).
fof(fact_List_Oset_Osimps_I2_J,axiom,
! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)),
file('theBenchmark.p',fact_List_Oset_Osimps_I2_J) ).
fof(fact_set__map,axiom,
! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)),
file('theBenchmark.p',fact_set__map) ).
fof(fact_inj__on__mapI,axiom,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),V_A_2)))
=> c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),V_A_2) ),
file('theBenchmark.p',fact_inj__on__mapI) ).
fof(fact_inj__on__map__eq__map,axiom,
! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
=> ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
<=> V_xs_2 = V_ys_2 ) ),
file('theBenchmark.p',fact_inj__on__map__eq__map) ).
fof(fact_map__inj__on,axiom,
! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
=> ( c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(c_List_Oset(T_c),V_ys_2)))
=> V_xs_2 = V_ys_2 ) ),
file('theBenchmark.p',fact_map__inj__on) ).
fof(fact_map__eq__conv,axiom,
! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
=> hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ),
file('theBenchmark.p',fact_map__eq__conv) ).
fof(fact_map__ident,axiom,
! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2,
file('theBenchmark.p',fact_map__ident) ).
fof(fact_List_Omap_Oid,axiom,
! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)),
file('theBenchmark.p',fact_List_Omap_Oid) ).
fof(fact_List_Omap_Oidentity,axiom,
! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)),
file('theBenchmark.p',fact_List_Omap_Oidentity) ).
fof(fact_map__map,axiom,
! [V_xs_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_xs_2),
file('theBenchmark.p',fact_map__map) ).
fof(fact_List_Omap_Ocompositionality,axiom,
! [V_list_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_list_2),
file('theBenchmark.p',fact_List_Omap_Ocompositionality) ).
fof(fact_map__comp__map,axiom,
! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)),
file('theBenchmark.p',fact_map__comp__map) ).
fof(fact_List_Omap_Ocomp,axiom,
! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)),
file('theBenchmark.p',fact_List_Omap_Ocomp) ).
fof(fact_map_Osimps_I2_J,axiom,
! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_map_Osimps_I2_J) ).
fof(fact_map__fun__upd,axiom,
! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hAPP(hAPP(c_List_Omap(T_b,T_c),c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_y_2,V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) ),
file('theBenchmark.p',fact_map__fun__upd) ).
fof(fact_notin__set__sublistI,axiom,
! [V_I_2,V_xs_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))) ),
file('theBenchmark.p',fact_notin__set__sublistI) ).
fof(fact_in__set__sublistD,axiom,
! [V_I_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
file('theBenchmark.p',fact_in__set__sublistD) ).
fof(fact_set__ConsD,axiom,
! [V_xs_2,V_x_2,V_y_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
| V_y_2 = V_x_2 ) ),
file('theBenchmark.p',fact_set__ConsD) ).
fof(fact_map__eq__imp__length__eq,axiom,
! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2)
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2) ),
file('theBenchmark.p',fact_map__eq__imp__length__eq) ).
fof(fact_length__map,axiom,
! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2),
file('theBenchmark.p',fact_length__map) ).
fof(fact_inj__map__eq__map,axiom,
! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
<=> V_xs_2 = V_ys_2 ) ),
file('theBenchmark.p',fact_inj__map__eq__map) ).
fof(fact_map__injective,axiom,
! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
=> ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
=> V_xs_2 = V_ys_2 ) ),
file('theBenchmark.p',fact_map__injective) ).
fof(fact_set__sublist__subset,axiom,
! [V_I_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
file('theBenchmark.p',fact_set__sublist__subset) ).
fof(fact_set__subset__Cons,axiom,
! [V_x_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))),
file('theBenchmark.p',fact_set__subset__Cons) ).
fof(fact_nth__map,axiom,
! [V_f_2,T_c,V_xs_2,T_b,V_na_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)),V_na_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_na_2)) ),
file('theBenchmark.p',fact_nth__map) ).
fof(fact_inj__mapD,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_inj__mapD) ).
fof(fact_inj__map,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
<=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_inj__map) ).
fof(fact_card__length,axiom,
! [V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
file('theBenchmark.p',fact_card__length) ).
fof(fact_all__set__conv__all__nth,axiom,
! [V_P_2,V_xs_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,B_x)) )
<=> ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ),
file('theBenchmark.p',fact_all__set__conv__all__nth) ).
fof(fact_set__take__subset__set__take,axiom,
! [V_xs_2,T_b,V_na_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_na_2),V_xs_2)))) ),
file('theBenchmark.p',fact_set__take__subset__set__take) ).
fof(fact_list__size__map,axiom,
! [V_xs_2,V_g_2,T_c,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_c,hAPP(c_Fun_Ocomp(T_b,tc_Nat_Onat,T_c,V_f_2),V_g_2),V_xs_2),
file('theBenchmark.p',fact_list__size__map) ).
fof(fact_list__size__estimation,axiom,
! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ),
file('theBenchmark.p',fact_list__size__estimation) ).
fof(fact_list__size__estimation_H,axiom,
! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ),
file('theBenchmark.p',fact_list__size__estimation_H) ).
fof(fact_in__lists__conv__set,axiom,
! [V_A_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
file('theBenchmark.p',fact_in__lists__conv__set) ).
fof(fact_length__pos__if__in__set,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
file('theBenchmark.p',fact_length__pos__if__in__set) ).
fof(fact_in__set__conv__nth,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
<=> ? [B_i] :
( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ),
file('theBenchmark.p',fact_in__set__conv__nth) ).
fof(fact_nth__mem,axiom,
! [V_xs_2,T_b,V_na_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_na_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ),
file('theBenchmark.p',fact_nth__mem) ).
fof(fact_lists__eq__set,axiom,
! [V_A_2,T_b] : c_List_Olists(T_b,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2)),
file('theBenchmark.p',fact_lists__eq__set) ).
fof(fact_set__conv__nth,axiom,
! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))),
file('theBenchmark.p',fact_set__conv__nth) ).
fof(fact_finite__lists__length__eq,axiom,
! [V_na_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_na_2))))) ),
file('theBenchmark.p',fact_finite__lists__length__eq) ).
fof(fact_set__sublist,axiom,
! [V_I_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),V_xs_2))))),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2))))),
file('theBenchmark.p',fact_set__sublist) ).
fof(fact_listrel__iff__zip,axiom,
! [V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),B_x)) )
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ),
file('theBenchmark.p',fact_listrel__iff__zip) ).
fof(fact_select__weigth__select,axiom,
! [T_b,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_b)
=> c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_b,V_xs_2) ),
file('theBenchmark.p',fact_select__weigth__select) ).
fof(fact_lists_ONil,axiom,
! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olists(T_b,V_A_2))),
file('theBenchmark.p',fact_lists_ONil) ).
fof(fact_listrel__Nil2,axiom,
! [V_r_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2)))
=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_listrel__Nil2) ).
fof(fact_listrel__Nil1,axiom,
! [V_r_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_listrel__Nil1) ).
fof(fact_set__empty,axiom,
! [V_xs_2,T_b] :
( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_set__empty) ).
fof(fact_set__empty2,axiom,
! [V_xs_2,T_b] :
( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_set__empty2) ).
fof(fact_List_Oset_Osimps_I1_J,axiom,
! [T_b] : hAPP(c_List_Oset(T_b),c_List_Olist_ONil(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
file('theBenchmark.p',fact_List_Oset_Osimps_I1_J) ).
fof(fact_map__is__Nil__conv,axiom,
! [V_xs_2,V_f_2,T_b,T_c] :
( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
<=> V_xs_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_map__is__Nil__conv) ).
fof(fact_map_Osimps_I1_J,axiom,
! [V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b),
file('theBenchmark.p',fact_map_Osimps_I1_J) ).
fof(fact_Nil__is__map__conv,axiom,
! [V_xs_2,V_f_2,T_c,T_b] :
( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
<=> V_xs_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_Nil__is__map__conv) ).
fof(fact_zip__map__fst__snd,axiom,
! [V_zs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2)) = V_zs_2,
file('theBenchmark.p',fact_zip__map__fst__snd) ).
fof(fact_map__snd__zip,axiom,
! [V_ys_2,T_c,V_xs_2,T_b] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
=> hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_ys_2 ),
file('theBenchmark.p',fact_map__snd__zip) ).
fof(fact_zip__eq__conv,axiom,
! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
=> ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
<=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2) = V_ys_2
& hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2) = V_xs_2 ) ) ),
file('theBenchmark.p',fact_zip__eq__conv) ).
fof(fact_map__fst__zip,axiom,
! [V_ys_2,T_c,V_xs_2,T_b] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
=> hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_xs_2 ),
file('theBenchmark.p',fact_map__fst__zip) ).
fof(fact_listrelp_ONil,axiom,
! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)),
file('theBenchmark.p',fact_listrelp_ONil) ).
fof(fact_listrelp_Oequations_I1_J,axiom,
! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)),
file('theBenchmark.p',fact_listrelp_Oequations_I1_J) ).
fof(fact_sublist__empty,axiom,
! [V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_b),
file('theBenchmark.p',fact_sublist__empty) ).
fof(fact_list_Osize_I1_J,axiom,
! [V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,c_List_Olist_ONil(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_list_Osize_I1_J) ).
fof(fact_list_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_length__0__conv,axiom,
! [V_xs_2,T_b] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_length__0__conv) ).
fof(fact_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_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_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_sublist__nil,axiom,
! [V_A_2,T_b] : c_List_Osublist(T_b,c_List_Olist_ONil(T_b),V_A_2) = c_List_Olist_ONil(T_b),
file('theBenchmark.p',fact_sublist__nil) ).
fof(fact_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_take__Nil,axiom,
! [V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_take__Nil) ).
fof(fact_take__eq__Nil,axiom,
! [V_xs_2,V_na_2,T_b] :
( hAPP(hAPP(c_List_Otake(T_b),V_na_2),V_xs_2) = c_List_Olist_ONil(T_b)
<=> ( V_xs_2 = c_List_Olist_ONil(T_b)
| V_na_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__Cons,axiom,
! [V_xs_2,V_x_2,V_na_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_na_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otake(T_b)),V_xs_2)),V_na_2),
file('theBenchmark.p',fact_take__Cons) ).
fof(fact_zip__same__conv__map,axiom,
! [V_xs_2,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))),V_xs_2),
file('theBenchmark.p',fact_zip__same__conv__map) ).
fof(fact_length__greater__0__conv,axiom,
! [V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
<=> V_xs_2 != c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_length__greater__0__conv) ).
fof(fact_take__1__Cons,axiom,
! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)),
file('theBenchmark.p',fact_take__1__Cons) ).
fof(fact_map__zip__map,axiom,
! [V_ys_2,V_xs_2,V_g_2,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_e,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_d,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_d),V_f_2)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_e),c_Product__Type_OPair(T_c,T_d)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_e,T_d),V_xs_2),V_ys_2)),
file('theBenchmark.p',fact_map__zip__map) ).
fof(fact_map__zip__map2,axiom,
! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_e),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_e,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_c,T_d)),tc_fun(T_e,T_b),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_e),V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(tc_fun(T_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),T_c),c_COMBB(T_d,tc_prod(T_c,T_d),T_e)),c_Product__Type_OPair(T_c,T_d))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_c,T_e),V_xs_2),V_ys_2)),
file('theBenchmark.p',fact_map__zip__map2) ).
fof(fact_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_not__listrel1__Nil,axiom,
! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel1(T_b,V_r_2))),
file('theBenchmark.p',fact_not__listrel1__Nil) ).
fof(fact_not__Nil__listrel1,axiom,
! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel1(T_b,V_r_2))),
file('theBenchmark.p',fact_not__Nil__listrel1) ).
fof(fact_zip__map__map,axiom,
! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_e),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),T_d),c_COMBB(T_c,tc_prod(T_b,T_c),T_e)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_d,T_e),V_xs_2),V_ys_2)),
file('theBenchmark.p',fact_zip__map__map) ).
fof(fact_zip__map1,axiom,
! [V_ys_2,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)),
file('theBenchmark.p',fact_zip__map1) ).
fof(fact_zip__map2,axiom,
! [V_ys_2,V_f_2,T_d,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_prod(T_b,T_c))),T_b),c_COMBB(T_c,tc_prod(T_b,T_c),T_d)),c_Product__Type_OPair(T_b,T_c))),V_f_2))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)),
file('theBenchmark.p',fact_zip__map2) ).
fof(fact_listrel_ONil,axiom,
! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))),
file('theBenchmark.p',fact_listrel_ONil) ).
fof(fact_lexord__Nil__right,axiom,
! [V_r_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olexord(T_b,V_r_2))),
file('theBenchmark.p',fact_lexord__Nil__right) ).
fof(fact_Nil2__notin__lex,axiom,
! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olex(T_b,V_r_2))),
file('theBenchmark.p',fact_Nil2__notin__lex) ).
fof(fact_Nil__notin__lex,axiom,
! [V_r_2,V_ys_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_ys_2)),c_List_Olex(T_b,V_r_2))),
file('theBenchmark.p',fact_Nil__notin__lex) ).
fof(fact_list__eq__iff__zip__eq,axiom,
! [T_b,V_ys_2,V_xs_2] :
( V_xs_2 = V_ys_2
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) )
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ),
file('theBenchmark.p',fact_list__eq__iff__zip__eq) ).
fof(fact_zip__same,axiom,
! [V_xs_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2))))
<=> ( V_a_2 = V_b_2
& hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_zip__same) ).
fof(fact_set__zip__leftD,axiom,
! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
file('theBenchmark.p',fact_set__zip__leftD) ).
fof(fact_set__zip__rightD,axiom,
! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ),
file('theBenchmark.p',fact_set__zip__rightD) ).
fof(fact_in__set__zipE,axiom,
! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
=> ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ),
file('theBenchmark.p',fact_in__set__zipE) ).
fof(fact_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_sublist__singleton,axiom,
! [V_x_2,T_b,V_A_2] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
=> c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = c_List_Olist_ONil(T_b) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
=> c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ),
file('theBenchmark.p',fact_sublist__singleton) ).
fof(fact_lists__empty,axiom,
! [T_b] : c_List_Olists(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
file('theBenchmark.p',fact_lists__empty) ).
fof(fact_take__Cons_H,axiom,
! [V_xs,V_x,T_a,V_n] :
( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) )
& ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) ),
file('theBenchmark.p',fact_take__Cons_H) ).
fof(fact_select,axiom,
! [V_s_2,T_b,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ),
file('theBenchmark.p',fact_select) ).
fof(fact_listrel__Nil,axiom,
! [V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
file('theBenchmark.p',fact_listrel__Nil) ).
fof(fact_set__Cons__sing__Nil,axiom,
! [V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_b,tc_List_Olist(T_b),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))),V_A_2),
file('theBenchmark.p',fact_set__Cons__sing__Nil) ).
fof(fact_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_set__zip,axiom,
! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_c)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(T_b,T_c)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),tc_Nat_Onat),c_Product__Type_OPair(T_b,T_c)),hAPP(c_List_Onth(T_b),V_xs_2))),hAPP(c_List_Onth(T_c),V_ys_2)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))))),
file('theBenchmark.p',fact_set__zip) ).
fof(fact_listset_Osimps_I1_J,axiom,
! [T_b] : c_List_Olistset(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
file('theBenchmark.p',fact_listset_Osimps_I1_J) ).
fof(fact_select__weight__member,axiom,
! [V_s_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ),
file('theBenchmark.p',fact_select__weight__member) ).
fof(fact_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_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_listsum__0,axiom,
! [V_xs_2,T_c,T_b] :
( class_Groups_Omonoid__add(T_b)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_b) ),
file('theBenchmark.p',fact_listsum__0) ).
fof(fact_listsum__addf,axiom,
! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ),
file('theBenchmark.p',fact_listsum__addf) ).
fof(fact_listsum__mult__const,axiom,
! [V_xs_2,V_c_2,V_f_2,T_c,T_b] :
( class_Rings_Osemiring__0(T_b)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_c_2) ),
file('theBenchmark.p',fact_listsum__mult__const) ).
fof(fact_listsum__const__mult,axiom,
! [V_xs_2,V_f_2,V_c_2,T_c,T_b] :
( class_Rings_Osemiring__0(T_b)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ),
file('theBenchmark.p',fact_listsum__const__mult) ).
fof(fact_listsum__subtractf,axiom,
! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
( class_Groups_Oab__group__add(T_b)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ),
file('theBenchmark.p',fact_listsum__subtractf) ).
fof(fact_listsum__abs,axiom,
! [V_xs_2,T_b] :
( class_Groups_Oordered__ab__group__add__abs(T_b)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_b,T_b),c_Groups_Oabs__class_Oabs(T_b)),V_xs_2)))) ),
file('theBenchmark.p',fact_listsum__abs) ).
fof(fact_uminus__listsum__map,axiom,
! [V_xs_2,V_f_2,T_c,T_b] :
( class_Groups_Oab__group__add(T_b)
=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_xs_2)) ),
file('theBenchmark.p',fact_uminus__listsum__map) ).
fof(fact_listsum__triv,axiom,
! [V_xs_2,V_r_2,T_c,T_b] :
( class_Rings_Osemiring__1(T_b)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),V_r_2) ),
file('theBenchmark.p',fact_listsum__triv) ).
fof(fact_listset_Osimps_I2_J,axiom,
! [V_As_2,V_A_2,T_b] : c_List_Olistset(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_b,V_A_2,c_List_Olistset(T_b,V_As_2)),
file('theBenchmark.p',fact_listset_Osimps_I2_J) ).
fof(fact_listsum__setsum__nth,axiom,
! [V_xs_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
file('theBenchmark.p',fact_listsum__setsum__nth) ).
fof(fact_pick__member,axiom,
! [V_xs_2,T_b,V_i_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i_2),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Random_Opick(T_b,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ),
file('theBenchmark.p',fact_pick__member) ).
fof(fact_select__weight__def,axiom,
! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_b,V_xs_2))),
file('theBenchmark.p',fact_select__weight__def) ).
fof(fact_zip__Cons,axiom,
! [V_ys_2,V_y_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_b,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_b),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),c_List_Ozip(T_b,T_c)),V_ys_2))),V_xs_2),
file('theBenchmark.p',fact_zip__Cons) ).
fof(fact_zip__Cons1,axiom,
! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_c,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),T_c),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_c),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)))),hAPP(c_List_Ozip(T_b,T_c),V_xs_2))),V_ys_2),
file('theBenchmark.p',fact_zip__Cons1) ).
fof(fact_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_list__size__conv__listsum,axiom,
! [V_xs_2,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(T_b,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),
file('theBenchmark.p',fact_list__size__conv__listsum) ).
fof(fact_list_Osimps_I5_J,axiom,
! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2),
file('theBenchmark.p',fact_list_Osimps_I5_J) ).
fof(fact_list_Osimps_I4_J,axiom,
! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),c_List_Olist_ONil(T_c)) = V_f1_2,
file('theBenchmark.p',fact_list_Osimps_I4_J) ).
fof(fact_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_anamorph_Osimps,axiom,
! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(tc_List_Olist(T_b),T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),c_COMBB(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),T_b),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),T_c))),c_List_Olist_OCons(T_b))))),hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(V_f_2,V_x_2)) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
=> hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2) ) ),
file('theBenchmark.p',fact_anamorph_Osimps) ).
fof(fact_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_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_setsum__set__upto__conv__listsum__int,axiom,
! [V_j_2,V_i_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ),
file('theBenchmark.p',fact_setsum__set__upto__conv__listsum__int) ).
fof(fact_interv__listsum__conv__setsum__set__int,axiom,
! [V_l_2,V_k_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_k_2,V_l_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ),
file('theBenchmark.p',fact_interv__listsum__conv__setsum__set__int) ).
fof(fact_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_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_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_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__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_sublist__Cons,axiom,
! [V_A_2,V_l_2,V_x_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_b)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olist_ONil(T_b))),c_List_Osublist(T_b,V_l_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_A_2)))),
file('theBenchmark.p',fact_sublist__Cons) ).
fof(fact_append__eq__Cons__conv,axiom,
! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
<=> ( ? [B_ys_H] :
( hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2
& V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) )
| ( V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
& V_ys_2 = c_List_Olist_ONil(T_b) ) ) ),
file('theBenchmark.p',fact_append__eq__Cons__conv) ).
fof(fact_Cons__eq__append__conv,axiom,
! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)
<=> ( ? [B_ys_H] :
( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2)
& hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2 )
| ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2
& V_ys_2 = c_List_Olist_ONil(T_b) ) ) ),
file('theBenchmark.p',fact_Cons__eq__append__conv) ).
fof(fact_append1__eq__conv,axiom,
! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b)))
<=> ( V_x_2 = V_y_2
& V_xs_2 = V_ys_2 ) ),
file('theBenchmark.p',fact_append1__eq__conv) ).
fof(fact_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_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_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_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_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__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_set__append,axiom,
! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)),
file('theBenchmark.p',fact_set__append) ).
fof(fact_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_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_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_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_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_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_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_list__update__code_I1_J,axiom,
! [V_y,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_y) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_list__update__code_I1_J) ).
fof(fact_list__update_Osimps_I1_J,axiom,
! [V_v,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_v) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_list__update_Osimps_I1_J) ).
fof(fact_list__update__nonempty,axiom,
! [V_x_2,V_k_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_list__update__nonempty) ).
fof(fact_append__self__conv2,axiom,
! [V_ys_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_append__self__conv2) ).
fof(fact_append__self__conv,axiom,
! [V_ys_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
<=> V_ys_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_append__self__conv) ).
fof(fact_append__is__Nil__conv,axiom,
! [V_ys_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
<=> ( V_ys_2 = c_List_Olist_ONil(T_b)
& V_xs_2 = c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_append__is__Nil__conv) ).
fof(fact_self__append__conv2,axiom,
! [V_xs_2,T_b,V_ys_2] :
( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_self__append__conv2) ).
fof(fact_self__append__conv,axiom,
! [V_ys_2,T_b,V_xs_2] :
( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
<=> V_ys_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_self__append__conv) ).
fof(fact_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_Nil__is__append__conv,axiom,
! [V_ys_2,V_xs_2,T_b] :
( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
<=> ( V_ys_2 = c_List_Olist_ONil(T_b)
& V_xs_2 = c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_Nil__is__append__conv) ).
fof(fact_append__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_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_map__append,axiom,
! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)),
file('theBenchmark.p',fact_map__append) ).
fof(fact_map__update,axiom,
! [V_y_2,V_k_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)),
file('theBenchmark.p',fact_map__update) ).
fof(fact_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_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_append__eq__append__conv2,axiom,
! [V_tsa_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_tsa_2)
<=> ? [B_us] :
( ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_tsa_2)
& hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2 )
| ( hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_tsa_2
& V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us) ) ) ),
file('theBenchmark.p',fact_append__eq__append__conv2) ).
fof(fact_same__append__eq,axiom,
! [V_zs_2,V_ys_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2)
<=> V_ys_2 = V_zs_2 ),
file('theBenchmark.p',fact_same__append__eq) ).
fof(fact_append__same__eq,axiom,
! [V_zs_2,V_xs_2,V_ys_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_xs_2)
<=> V_ys_2 = V_zs_2 ),
file('theBenchmark.p',fact_append__same__eq) ).
fof(fact_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_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__in__lists__conv,axiom,
! [V_A_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)),c_List_Olists(T_b,V_A_2)))
<=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2)))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ),
file('theBenchmark.p',fact_append__in__lists__conv) ).
fof(fact_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_append__listrel1I,axiom,
! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_us_2),V_vs_2)),c_List_Olistrel1(T_b,V_r_2)))
& V_xs_2 = V_ys_2 )
| ( V_us_2 = V_vs_2
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) )
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2))),c_List_Olistrel1(T_b,V_r_2))) ),
file('theBenchmark.p',fact_append__listrel1I) ).
fof(fact_set__update__subsetI,axiom,
! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_A_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ),
file('theBenchmark.p',fact_set__update__subsetI) ).
fof(fact_set__update__subset__insert,axiom,
! [V_x_2,V_i_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))),
file('theBenchmark.p',fact_set__update__subset__insert) ).
fof(fact_lexord__append__leftI,axiom,
! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2))) ),
file('theBenchmark.p',fact_lexord__append__leftI) ).
fof(fact_nth__list__update__eq,axiom,
! [V_x,V_xs,T_a,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i) = V_x ),
file('theBenchmark.p',fact_nth__list__update__eq) ).
fof(fact_list__update__same__conv,axiom,
! [V_x_2,V_xs_2,T_b,V_i_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
<=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ),
file('theBenchmark.p',fact_list__update__same__conv) ).
fof(fact_nth__list__update,axiom,
! [V_x,V_j,V_xs,T_a,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> ( ( V_i != V_j
=> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) )
& ( V_i = V_j
=> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = V_x ) ) ),
file('theBenchmark.p',fact_nth__list__update) ).
fof(fact_list__update_Osimps_I2_J,axiom,
! [V_v_2,V_i_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_List_Olist(T_b)),c_List_Olist__update(T_b,V_xs_2)),V_v_2)),V_i_2),
file('theBenchmark.p',fact_list__update_Osimps_I2_J) ).
fof(fact_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_set__update__memI,axiom,
! [V_x_2,V_xs_2,T_b,V_na_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_na_2),V_x_2)))) ),
file('theBenchmark.p',fact_set__update__memI) ).
fof(fact_sublist__append,axiom,
! [V_A_2,V_l_H_2,V_l_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Osublist(T_b,V_l_2,V_A_2)),c_List_Osublist(T_b,V_l_H_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_l_2)))),V_A_2)))),
file('theBenchmark.p',fact_sublist__append) ).
fof(fact_listrel1I,axiom,
! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_vs_2))
=> ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_vs_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ),
file('theBenchmark.p',fact_listrel1I) ).
fof(fact_lexord__append__left__rightI,axiom,
! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2)))),c_List_Olexord(T_b,V_r_2))) ),
file('theBenchmark.p',fact_lexord__append__left__rightI) ).
fof(fact_take__Suc__conv__app__nth,axiom,
! [V_xs,T_a,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),c_List_Olist_ONil(T_a))) ),
file('theBenchmark.p',fact_take__Suc__conv__app__nth) ).
fof(fact_snoc__listrel1__snoc__iff,axiom,
! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))))),c_List_Olistrel1(T_b,V_r_2)))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
& V_xs_2 = V_ys_2 )
| ( V_x_2 = V_y_2
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ),
file('theBenchmark.p',fact_snoc__listrel1__snoc__iff) ).
fof(fact_listrel1__iff__update,axiom,
! [V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
<=> ? [B_y,B_n] :
( V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),B_y)),V_r_2)) ) ),
file('theBenchmark.p',fact_listrel1__iff__update) ).
fof(fact_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_listrel1E,axiom,
! [V_r_2,V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
=> ~ ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
=> ! [B_us,B_vs] :
( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
=> V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ),
file('theBenchmark.p',fact_listrel1E) ).
fof(fact_lexord__append__leftD,axiom,
! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2)))
=> ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_a)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) ) ),
file('theBenchmark.p',fact_lexord__append__leftD) ).
fof(fact_rotate1__def,axiom,
! [V_xs_2,T_b] : hAPP(c_List_Orotate1(T_b),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)))),V_xs_2),
file('theBenchmark.p',fact_rotate1__def) ).
fof(fact_upd__conv__take__nth__drop,axiom,
! [V_a,V_xs,T_a,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_a) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ),
file('theBenchmark.p',fact_upd__conv__take__nth__drop) ).
fof(fact_set__rotate1,axiom,
! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
file('theBenchmark.p',fact_set__rotate1) ).
fof(fact_in__set__dropD,axiom,
! [V_xs_2,V_na_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_na_2),V_xs_2))))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
file('theBenchmark.p',fact_in__set__dropD) ).
fof(fact_set__drop__subset,axiom,
! [V_xs_2,V_na_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_na_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
file('theBenchmark.p',fact_set__drop__subset) ).
fof(fact_drop__map,axiom,
! [V_xs_2,V_f_2,T_c,V_na_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_na_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Odrop(T_c),V_na_2),V_xs_2)),
file('theBenchmark.p',fact_drop__map) ).
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_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_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__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_drop__Nil,axiom,
! [V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_drop__Nil) ).
fof(fact_rotate1__is__Nil__conv,axiom,
! [V_xs_2,T_b] :
( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_rotate1__is__Nil__conv) ).
fof(fact_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_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_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_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_set__drop__subset__set__drop,axiom,
! [V_xs_2,T_b,V_m_2,V_na_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_m_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_na_2),V_xs_2)))) ),
file('theBenchmark.p',fact_set__drop__subset__set__drop) ).
fof(fact_drop__eq__Nil,axiom,
! [V_xs_2,V_na_2,T_b] :
( hAPP(hAPP(c_List_Odrop(T_b),V_na_2),V_xs_2) = c_List_Olist_ONil(T_b)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_na_2)) ),
file('theBenchmark.p',fact_drop__eq__Nil) ).
fof(fact_drop__all,axiom,
! [V_n,V_xs,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n))
=> hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ),
file('theBenchmark.p',fact_drop__all) ).
fof(fact_drop__append,axiom,
! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)),
file('theBenchmark.p',fact_drop__append) ).
fof(fact_append__eq__conv__conj,axiom,
! [V_zs_2,V_ys_2,V_xs_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
<=> ( V_ys_2 = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2)
& V_xs_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) ) ),
file('theBenchmark.p',fact_append__eq__conv__conj) ).
fof(fact_drop__Cons,axiom,
! [V_xs_2,V_x_2,V_na_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_na_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Odrop(T_b)),V_xs_2),V_na_2),
file('theBenchmark.p',fact_drop__Cons) ).
fof(fact_drop__Cons_H,axiom,
! [V_xs,V_x,T_a,V_n] :
( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) )
& ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ) ),
file('theBenchmark.p',fact_drop__Cons_H) ).
fof(fact_nth__drop,axiom,
! [V_xs,T_a,V_i,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)) ),
file('theBenchmark.p',fact_nth__drop) ).
fof(fact_append__eq__append__conv__if,axiom,
! [V_ys_092_060_094isub_0622_2,V_ys_092_060_094isub_0621_2,V_xs_092_060_094isub_0622_2,V_xs_092_060_094isub_0621_2,T_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2)
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)))
=> ( hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2)),V_xs_092_060_094isub_0622_2) = V_ys_092_060_094isub_0622_2
& hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2 ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)))
=> ( V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2)
& V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2) ) ) ) ),
file('theBenchmark.p',fact_append__eq__append__conv__if) ).
fof(fact_nth__drop_H,axiom,
! [V_xs,T_a,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs) ),
file('theBenchmark.p',fact_nth__drop_H) ).
fof(fact_rotate__simps,axiom,
! [V_xs,V_x,T_b,T_a] :
( hAPP(c_List_Orotate1(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),c_List_Olist_ONil(T_b)))
& hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ),
file('theBenchmark.p',fact_rotate__simps) ).
fof(fact_drop__Cons__number__of,axiom,
! [V_xs,V_x,T_a,V_v] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ) ),
file('theBenchmark.p',fact_drop__Cons__number__of) ).
fof(fact_take__add,axiom,
! [V_xs,T_a,V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_j),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ),
file('theBenchmark.p',fact_take__add) ).
fof(fact_rotate1__length01,axiom,
! [V_xs,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
=> hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ),
file('theBenchmark.p',fact_rotate1__length01) ).
fof(fact_zip__append1,axiom,
! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),
file('theBenchmark.p',fact_zip__append1) ).
fof(fact_zip__append2,axiom,
! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Oappend(T_b),V_ys),V_zs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_ys)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_zs)),
file('theBenchmark.p',fact_zip__append2) ).
fof(fact_id__take__nth__drop,axiom,
! [V_xs,T_a,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> V_xs = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ),
file('theBenchmark.p',fact_id__take__nth__drop) ).
fof(fact_take__hd__drop,axiom,
! [V_xs,T_a,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) ),
file('theBenchmark.p',fact_take__hd__drop) ).
fof(fact_hd__drop__conv__nth,axiom,
! [V_n,T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ) ),
file('theBenchmark.p',fact_hd__drop__conv__nth) ).
fof(fact_hd_Osimps,axiom,
! [V_xs,V_x,T_a] : hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x,
file('theBenchmark.p',fact_hd_Osimps) ).
fof(fact_hd__map,axiom,
! [V_f_2,T_c,T_b,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_b)
=> hAPP(c_List_Ohd(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_hd__map) ).
fof(fact_hd__append2,axiom,
! [V_ys,T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) ),
file('theBenchmark.p',fact_hd__append2) ).
fof(fact_hd__append,axiom,
! [V_ys,T_a,V_xs] :
( ( V_xs != c_List_Olist_ONil(T_a)
=> hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) )
& ( V_xs = c_List_Olist_ONil(T_a)
=> hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_ys) ) ),
file('theBenchmark.p',fact_hd__append) ).
fof(fact_hd__in__set,axiom,
! [T_b,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ),
file('theBenchmark.p',fact_hd__in__set) ).
fof(fact_hd__conv__nth,axiom,
! [T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> hAPP(c_List_Ohd(T_a),V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('theBenchmark.p',fact_hd__conv__nth) ).
fof(fact_rotate1__hd__tl,axiom,
! [T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> hAPP(c_List_Orotate1(T_a),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),c_List_Olist_ONil(T_a))) ),
file('theBenchmark.p',fact_rotate1__hd__tl) ).
fof(fact_distinct__list__update,axiom,
! [V_i_2,V_a_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
=> hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ),
file('theBenchmark.p',fact_distinct__list__update) ).
fof(fact_distinct__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_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_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_map__tl,axiom,
! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Otl(T_c),V_xs_2)) = hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_map__tl) ).
fof(fact_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__sublistI,axiom,
! [V_I_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ),
file('theBenchmark.p',fact_distinct__sublistI) ).
fof(fact_distinct__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__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_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_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_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_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_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_distinct1__rotate,axiom,
! [V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
<=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_distinct1__rotate) ).
fof(fact_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_distinct_Osimps_I2_J,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
<=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_distinct_Osimps_I2_J) ).
fof(fact_distinct__card,axiom,
! [V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ),
file('theBenchmark.p',fact_distinct__card) ).
fof(fact_card__distinct,axiom,
! [V_xs_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_card__distinct) ).
fof(fact_nth__eq__iff__index__eq,axiom,
! [V_j_2,V_i_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2)
<=> V_i_2 = V_j_2 ) ) ) ),
file('theBenchmark.p',fact_nth__eq__iff__index__eq) ).
fof(fact_distinct__conv__nth,axiom,
! [V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
<=> ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> ! [B_j] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> ( B_i != B_j
=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ),
file('theBenchmark.p',fact_distinct__conv__nth) ).
fof(fact_distinct__map,axiom,
! [V_xs_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
<=> ( c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2))
& hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2)) ) ),
file('theBenchmark.p',fact_distinct__map) ).
fof(fact_distinct__listsum__conv__Setsum,axiom,
! [V_xs_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_COMBI(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) ) ),
file('theBenchmark.p',fact_distinct__listsum__conv__Setsum) ).
fof(fact_tl__append,axiom,
! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,hAPP(c_List_Otl(T_b),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b)),V_ys_2))),V_xs_2),
file('theBenchmark.p',fact_tl__append) ).
fof(fact_distinct__append,axiom,
! [V_ys_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
<=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
& hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ),
file('theBenchmark.p',fact_distinct__append) ).
fof(fact_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_listsum__distinct__conv__setsum__set,axiom,
! [V_f_2,V_xs_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ),
file('theBenchmark.p',fact_listsum__distinct__conv__setsum__set) ).
fof(fact_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_Nitpick_Osetsum_H__def,axiom,
! [V_f_2,V_A_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b))))) ) ) ),
file('theBenchmark.p',fact_Nitpick_Osetsum_H__def) ).
fof(fact_Nitpick_Ocard_H__def,axiom,
! [V_A_2,T_b] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_Nitpick_Ocard_H(T_b,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b)))) ) ),
file('theBenchmark.p',fact_Nitpick_Ocard_H__def) ).
fof(fact_fold1__set,axiom,
! [V_xs_2,T_b] :
( class_Lattices_Oab__semigroup__idem__mult(T_b)
=> ( V_xs_2 != c_List_Olist_ONil(T_b)
=> hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Otl(T_b),V_xs_2)) ) ),
file('theBenchmark.p',fact_fold1__set) ).
fof(fact_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_distinct__rotate,axiom,
! [V_xs_2,V_na_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_na_2),V_xs_2)))
<=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_distinct__rotate) ).
fof(fact_set__rotate,axiom,
! [V_xs_2,V_na_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate(T_b,V_na_2),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
file('theBenchmark.p',fact_set__rotate) ).
fof(fact_foldl__map,axiom,
! [V_xs_2,V_f_2,T_d,V_a_2,V_g_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,T_b)),T_b),c_COMBB(T_c,T_b,T_d)),V_g_2)),V_f_2),V_a_2),V_xs_2),
file('theBenchmark.p',fact_foldl__map) ).
fof(fact_rotate__map,axiom,
! [V_xs_2,V_f_2,T_c,V_na_2,T_b] : hAPP(c_List_Orotate(T_b,V_na_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orotate(T_c,V_na_2),V_xs_2)),
file('theBenchmark.p',fact_rotate__map) ).
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_foldl__assoc,axiom,
! [V_zs_2,V_y_2,V_x_2,T_b] :
( class_Groups_Osemigroup__add(T_b)
=> hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_y_2),V_zs_2)) ),
file('theBenchmark.p',fact_foldl__assoc) ).
fof(fact_foldl__absorb0,axiom,
! [V_zs_2,V_x_2,T_b] :
( class_Groups_Omonoid__add(T_b)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_zs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_zs_2) ),
file('theBenchmark.p',fact_foldl__absorb0) ).
fof(fact_start__le__sum,axiom,
! [V_ns_2,V_na_2,V_m_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_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_na_2),V_ns_2))) ),
file('theBenchmark.p',fact_start__le__sum) ).
fof(fact_rotate__is__Nil__conv,axiom,
! [V_xs_2,V_na_2,T_b] :
( hAPP(c_List_Orotate(T_b,V_na_2),V_xs_2) = c_List_Olist_ONil(T_b)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_rotate__is__Nil__conv) ).
fof(fact_foldl__Nil,axiom,
! [V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),c_List_Olist_ONil(T_c)) = V_a_2,
file('theBenchmark.p',fact_foldl__Nil) ).
fof(fact_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_foldl__Cons,axiom,
! [V_xs_2,V_x_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2),
file('theBenchmark.p',fact_foldl__Cons) ).
fof(fact_foldl__append,axiom,
! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2)),V_ys_2),
file('theBenchmark.p',fact_foldl__append) ).
fof(fact_rotate__def,axiom,
! [V_na_2,T_b] : c_List_Orotate(T_b,V_na_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_na_2),c_List_Orotate1(T_b)),
file('theBenchmark.p',fact_rotate__def) ).
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__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_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_listsum__foldl,axiom,
! [T_b] :
( class_Groups_Omonoid__add(T_b)
=> c_List_Omonoid__add__class_Olistsum(T_b) = c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)) ),
file('theBenchmark.p',fact_listsum__foldl) ).
fof(fact_sum__eq__0__conv,axiom,
! [V_ns_2,V_m_2] :
( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
=> B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_sum__eq__0__conv) ).
fof(fact_rotate0,axiom,
! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)),
file('theBenchmark.p',fact_rotate0) ).
fof(fact_rotate__add,axiom,
! [V_na_2,V_m_2,T_b] : c_List_Orotate(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orotate(T_b,V_m_2)),c_List_Orotate(T_b,V_na_2)),
file('theBenchmark.p',fact_rotate__add) ).
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_fun__left__comm__idem_Ofold__set,axiom,
! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
=> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),V_xs_2) ),
file('theBenchmark.p',fact_fun__left__comm__idem_Ofold__set) ).
fof(fact_Sup__set__fold,axiom,
! [V_xs_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ),
file('theBenchmark.p',fact_Sup__set__fold) ).
fof(fact_Inf__set__fold,axiom,
! [V_xs_2,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ),
file('theBenchmark.p',fact_Inf__set__fold) ).
fof(fact_Sup__fin__set__fold,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Lattices_Olattice(T_b)
=> c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_xs_2) ),
file('theBenchmark.p',fact_Sup__fin__set__fold) ).
fof(fact_Inf__fin__set__fold,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Lattices_Olattice(T_b)
=> c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_xs_2) ),
file('theBenchmark.p',fact_Inf__fin__set__fold) ).
fof(fact_Min__fin__set__fold,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ),
file('theBenchmark.p',fact_Min__fin__set__fold) ).
fof(fact_Max__fin__set__fold,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ),
file('theBenchmark.p',fact_Max__fin__set__fold) ).
fof(fact_min__max_OInf__fin__set__fold,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ),
file('theBenchmark.p',fact_min__max_OInf__fin__set__fold) ).
fof(fact_min__max_OSup__fin__set__fold,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ),
file('theBenchmark.p',fact_min__max_OSup__fin__set__fold) ).
fof(fact_SUPR__set__fold,axiom,
! [V_f_2,V_xs_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ),
file('theBenchmark.p',fact_SUPR__set__fold) ).
fof(fact_INFI__set__fold,axiom,
! [V_f_2,V_xs_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ),
file('theBenchmark.p',fact_INFI__set__fold) ).
fof(fact_elem__le__sum,axiom,
! [V_ns_2,V_na_2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_na_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_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_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_lexord__append__rightI,axiom,
! [V_r_2,V_x_2,T_b,V_y_2] :
( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) ),
file('theBenchmark.p',fact_lexord__append__rightI) ).
fof(fact_lexord__Nil__left,axiom,
! [V_r_2,V_y_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_y_2)),c_List_Olexord(T_b,V_r_2)))
<=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ),
file('theBenchmark.p',fact_lexord__Nil__left) ).
fof(fact_last__list__update,axiom,
! [V_x,V_k,T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> ( ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Olast(T_a,V_xs) )
& ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) ) ),
file('theBenchmark.p',fact_last__list__update) ).
fof(fact_listsum__mono,axiom,
! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
( ( class_Groups_Oordered__ab__semigroup__add(T_c)
& class_Groups_Omonoid__add(T_c) )
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_g_2),V_xs_2)))) ) ),
file('theBenchmark.p',fact_listsum__mono) ).
fof(fact_last__map,axiom,
! [V_f_2,T_c,T_b,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_b)
=> c_List_Olast(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_b,V_xs_2)) ),
file('theBenchmark.p',fact_last__map) ).
fof(fact_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__appendL,axiom,
! [V_xs,T_a,V_ys] :
( V_ys = c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ),
file('theBenchmark.p',fact_last__appendL) ).
fof(fact_last__appendR,axiom,
! [V_xs,T_a,V_ys] :
( V_ys != c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ),
file('theBenchmark.p',fact_last__appendR) ).
fof(fact_last__append,axiom,
! [V_xs,T_a,V_ys] :
( ( V_ys != c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) )
& ( V_ys = c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ),
file('theBenchmark.p',fact_last__append) ).
fof(fact_last__in__set,axiom,
! [T_b,V_as_2] :
( V_as_2 != c_List_Olist_ONil(T_b)
=> hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ),
file('theBenchmark.p',fact_last__in__set) ).
fof(fact_last__snoc,axiom,
! [V_x,V_xs,T_a] : c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_x,
file('theBenchmark.p',fact_last__snoc) ).
fof(fact_last__drop,axiom,
! [V_xs,T_a,V_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ),
file('theBenchmark.p',fact_last__drop) ).
fof(fact_last__conv__nth,axiom,
! [T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
file('theBenchmark.p',fact_last__conv__nth) ).
fof(fact_lists_Osimps,axiom,
! [V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
<=> ( ? [B_a,B_l] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
& V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l) )
| V_a_2 = c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_lists_Osimps) ).
fof(fact_list__size__pointwise,axiom,
! [V_g_2,V_f_2,V_xs_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_b,V_g_2,V_xs_2))) ),
file('theBenchmark.p',fact_list__size__pointwise) ).
fof(fact_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_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_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_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_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_in__set__butlastD,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
file('theBenchmark.p',fact_in__set__butlastD) ).
fof(fact_map__butlast,axiom,
! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Obutlast(T_c,V_xs_2)) = c_List_Obutlast(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_map__butlast) ).
fof(fact_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_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_in__set__butlast__appendI,axiom,
! [V_ys_2,V_xs_2,V_x_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2))))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) )
=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))))) ),
file('theBenchmark.p',fact_in__set__butlast__appendI) ).
fof(fact_butlast__snoc,axiom,
! [V_x,V_xs,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_xs,
file('theBenchmark.p',fact_butlast__snoc) ).
fof(fact_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_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_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_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_b] :
( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = V_ys_2
<=> ( c_List_Olast(T_b,V_ys_2) = V_x_2
& c_List_Obutlast(T_b,V_ys_2) = V_xs_2
& V_ys_2 != c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_snoc__eq__iff__butlast) ).
fof(fact_listsum__map__remove1,axiom,
! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)))) ) ),
file('theBenchmark.p',fact_listsum__map__remove1) ).
fof(fact_set__remove1__eq,axiom,
! [V_x_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_set__remove1__eq) ).
fof(fact_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_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_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_set__remove1__subset,axiom,
! [V_xs_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
file('theBenchmark.p',fact_set__remove1__subset) ).
fof(fact_remove1__idem,axiom,
! [V_xs_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ),
file('theBenchmark.p',fact_remove1__idem) ).
fof(fact_notin__set__remove1,axiom,
! [V_y_2,V_xs_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_y_2,V_xs_2)))) ),
file('theBenchmark.p',fact_notin__set__remove1) ).
fof(fact_in__set__remove1,axiom,
! [V_xs_2,T_b,V_b_2,V_a_2] :
( V_a_2 != V_b_2
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_b_2,V_xs_2))))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_in__set__remove1) ).
fof(fact_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_remove1__append,axiom,
! [V_ys_2,V_xs_2,V_x_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oremove1(T_b,V_x_2,V_ys_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)),V_ys_2) ) ),
file('theBenchmark.p',fact_remove1__append) ).
fof(fact_length__remove1,axiom,
! [V_xs_2,V_x_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
file('theBenchmark.p',fact_length__remove1) ).
fof(fact_sorted__list__of__set__remove,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = c_List_Oremove1(T_b,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) ) ),
file('theBenchmark.p',fact_sorted__list__of__set__remove) ).
fof(fact_partition__set,axiom,
! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
( c_List_Opartition(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_yes_2)),hAPP(c_List_Oset(T_b),V_no_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ),
file('theBenchmark.p',fact_partition__set) ).
fof(fact_sorted__list__of__set__empty,axiom,
! [T_b] :
( class_Orderings_Olinorder(T_b)
=> c_List_Olinorder__class_Osorted__list__of__set(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_sorted__list__of__set__empty) ).
fof(fact_partition__P,axiom,
! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
( c_List_Opartition(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
=> ~ hBOOL(hAPP(V_P_2,B_x)) )
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
=> hBOOL(hAPP(V_P_2,B_x)) ) ) ),
file('theBenchmark.p',fact_partition__P) ).
fof(fact_partition_Osimps_I1_J,axiom,
! [V_P_2,T_b] : c_List_Opartition(T_b,V_P_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b)),
file('theBenchmark.p',fact_partition_Osimps_I1_J) ).
fof(fact_partition_Osimps_I2_J,axiom,
! [V_xs_2,V_x_2,V_P_2,T_b] : c_List_Opartition(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_P_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_P_2,V_xs_2)),
file('theBenchmark.p',fact_partition_Osimps_I2_J) ).
fof(fact_sorted__list__of__set__insert,axiom,
! [V_x_2,V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
file('theBenchmark.p',fact_sorted__list__of__set__insert) ).
fof(fact_lists__IntI,axiom,
! [V_B_2,V_A_2,V_l_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2)))
=> hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_l_2)) ) ),
file('theBenchmark.p',fact_lists__IntI) ).
fof(fact_listsp_ONil,axiom,
! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))),
file('theBenchmark.p',fact_listsp_ONil) ).
fof(fact_append__in__listsp__conv,axiom,
! [V_ys_2,V_xs_2,V_A_2,T_b] :
( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
<=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2))
& hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2)) ) ),
file('theBenchmark.p',fact_append__in__listsp__conv) ).
fof(fact_insort__key_Osimps_I1_J,axiom,
! [V_x_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ),
file('theBenchmark.p',fact_insort__key_Osimps_I1_J) ).
fof(fact_listsp_Oequations_I2_J,axiom,
! [V_a2_2,V_a1_2,V_A_2,T_b] :
( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2)))
<=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2))
& hBOOL(hAPP(V_A_2,V_a1_2)) ) ),
file('theBenchmark.p',fact_listsp_Oequations_I2_J) ).
fof(fact_insort__key_Osimps_I2_J,axiom,
! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_ys_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) ) ) ),
file('theBenchmark.p',fact_insort__key_Osimps_I2_J) ).
fof(fact_length__insort,axiom,
! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ),
file('theBenchmark.p',fact_length__insort) ).
fof(fact_listsp_Oequations_I1_J,axiom,
! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))),
file('theBenchmark.p',fact_listsp_Oequations_I1_J) ).
fof(fact_insort__not__Nil,axiom,
! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_insort__not__Nil) ).
fof(fact_fun__left__comm__insort,axiom,
! [T_b] :
( class_Orderings_Olinorder(T_b)
=> c_Finite__Set_Ofun__left__comm(T_b,tc_List_Olist(T_b),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))) ),
file('theBenchmark.p',fact_fun__left__comm__insort) ).
fof(fact_listsp__conj__eq,axiom,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_A_2)),V_B_2)),V_x_2))
<=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2))
& hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2)) ) ),
file('theBenchmark.p',fact_listsp__conj__eq) ).
fof(fact_insort__left__comm,axiom,
! [V_xs_2,V_y_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) ),
file('theBenchmark.p',fact_insort__left__comm) ).
fof(fact_insort__key__left__comm,axiom,
! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),V_xs_2)) ) ),
file('theBenchmark.p',fact_insort__key__left__comm) ).
fof(fact_listsp__inf__eq,axiom,
! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2)),
file('theBenchmark.p',fact_listsp__inf__eq) ).
fof(fact_listsp__infI,axiom,
! [V_B_2,V_l_2,V_A_2,T_b] :
( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2))
=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2))
=> hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2)) ) ),
file('theBenchmark.p',fact_listsp__infI) ).
fof(fact_in__listsp__conv__set,axiom,
! [V_xs_2,V_A_2,T_b] :
( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_A_2,B_x)) ) ),
file('theBenchmark.p',fact_in__listsp__conv__set) ).
fof(fact_set__insort,axiom,
! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_set__insort) ).
fof(fact_remove1__insort,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) = V_xs_2 ),
file('theBenchmark.p',fact_remove1__insort) ).
fof(fact_distinct__insort,axiom,
! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)))
<=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ),
file('theBenchmark.p',fact_distinct__insort) ).
fof(fact_listsp__mono,axiom,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2))) ),
file('theBenchmark.p',fact_listsp__mono) ).
fof(fact_listsp__lists__eq,axiom,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ),
file('theBenchmark.p',fact_listsp__lists__eq) ).
fof(fact_lists__Int__eq,axiom,
! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_B_2))),
file('theBenchmark.p',fact_lists__Int__eq) ).
fof(fact_insort__insert__insort__key,axiom,
! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
=> c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2) ) ),
file('theBenchmark.p',fact_insort__insert__insort__key) ).
fof(fact_insort__insert__insort,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2) ) ),
file('theBenchmark.p',fact_insort__insert__insort) ).
fof(fact_distinct__insort__insert,axiom,
! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_c,V_f_2,V_x_2,V_xs_2))) ) ),
file('theBenchmark.p',fact_distinct__insort__insert) ).
fof(fact_insort__insert__triv,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ),
file('theBenchmark.p',fact_insort__insert__triv) ).
fof(fact_set__insort__insert,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_set__insort__insert) ).
fof(fact_insort__insert__key__triv,axiom,
! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
=> c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ),
file('theBenchmark.p',fact_insort__insert__key__triv) ).
fof(fact_product_Osimps_I2_J,axiom,
! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : c_Enum_Oproduct(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Omap(T_c,tc_prod(T_b,T_c)),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)),
file('theBenchmark.p',fact_product_Osimps_I2_J) ).
fof(fact_list__all2__def,axiom,
! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x)) )
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ) ),
file('theBenchmark.p',fact_list__all2__def) ).
fof(fact_list__all2__append,axiom,
! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
=> ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_vs_2))
<=> ( c_List_Olist__all2(T_b,T_c,V_P_2,V_us_2,V_vs_2)
& c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ) ) ),
file('theBenchmark.p',fact_list__all2__append) ).
fof(fact_list__all2__appendI,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2)
=> ( c_List_Olist__all2(T_b,T_c,V_P_2,V_c_2,V_d_2)
=> c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_a_2),V_c_2),hAPP(hAPP(c_List_Oappend(T_c),V_b_2),V_d_2)) ) ),
file('theBenchmark.p',fact_list__all2__appendI) ).
fof(fact_list__all2__Cons,axiom,
! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))
<=> ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
& hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) ) ),
file('theBenchmark.p',fact_list__all2__Cons) ).
fof(fact_list__all2__lengthD,axiom,
! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ),
file('theBenchmark.p',fact_list__all2__lengthD) ).
fof(fact_list__all2__Nil2,axiom,
! [V_xs_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,c_List_Olist_ONil(T_c))
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_list__all2__Nil2) ).
fof(fact_list__all2__Nil,axiom,
! [V_ys_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,c_List_Olist_ONil(T_b),V_ys_2)
<=> V_ys_2 = c_List_Olist_ONil(T_c) ),
file('theBenchmark.p',fact_list__all2__Nil) ).
fof(fact_list__all2__takeI,axiom,
! [V_na_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
=> c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Otake(T_b),V_na_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_c),V_na_2),V_ys_2)) ),
file('theBenchmark.p',fact_list__all2__takeI) ).
fof(fact_list__all2__eq,axiom,
! [T_b,V_ys_2,V_xs_2] :
( V_xs_2 = V_ys_2
<=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ),
file('theBenchmark.p',fact_list__all2__eq) ).
fof(fact_list__all2__map1,axiom,
! [V_bs_2,V_as_2,V_f_2,T_d,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_as_2),V_bs_2)
<=> c_List_Olist__all2(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),V_P_2),V_f_2),V_as_2,V_bs_2) ),
file('theBenchmark.p',fact_list__all2__map1) ).
fof(fact_list__all2__map2,axiom,
! [V_bs_2,V_f_2,T_d,V_as_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_as_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_bs_2))
<=> c_List_Olist__all2(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_d)),V_P_2)),V_f_2),V_as_2,V_bs_2) ),
file('theBenchmark.p',fact_list__all2__map2) ).
fof(fact_list__all2__dropI,axiom,
! [V_na_2,V_bs_2,V_as_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_as_2,V_bs_2)
=> c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Odrop(T_b),V_na_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_c),V_na_2),V_bs_2)) ),
file('theBenchmark.p',fact_list__all2__dropI) ).
fof(fact_product_Osimps_I1_J,axiom,
! [V_uu,T_b,T_a] : c_Enum_Oproduct(T_a,T_b,c_List_Olist_ONil(T_a),V_uu) = c_List_Olist_ONil(tc_prod(T_a,T_b)),
file('theBenchmark.p',fact_product_Osimps_I1_J) ).
fof(fact_list__all2__conv__all__nth,axiom,
! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
<=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),B_i))) )
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2) ) ),
file('theBenchmark.p',fact_list__all2__conv__all__nth) ).
fof(fact_list__all2__nthD,axiom,
! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ),
file('theBenchmark.p',fact_list__all2__nthD) ).
fof(fact_list__all2__nthD2,axiom,
! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
=> hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ),
file('theBenchmark.p',fact_list__all2__nthD2) ).
fof(fact_list__all2__update__cong,axiom,
! [V_y_2,V_x_2,V_ys_2,V_P_2,T_c,V_xs_2,T_b,V_i_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
=> c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_list__all2__update__cong) ).
fof(fact_list__all2__update__cong2,axiom,
! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
=> c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_list__all2__update__cong2) ).
fof(fact_distinct__product,axiom,
! [V_ys,T_b,V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
=> hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ),
file('theBenchmark.p',fact_distinct__product) ).
fof(fact_product__list__set,axiom,
! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_List_Oset(T_c),V_ys_2))),
file('theBenchmark.p',fact_product__list__set) ).
fof(fact_sublists__powset,axiom,
! [V_xs_2,T_b] : hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_Osublists(T_b,V_xs_2))) = hAPP(c_Set_OPow(T_b),hAPP(c_List_Oset(T_b),V_xs_2)),
file('theBenchmark.p',fact_sublists__powset) ).
fof(fact_length__sublists,axiom,
! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_Osublists(T_a,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),
file('theBenchmark.p',fact_length__sublists) ).
fof(fact_sublists_Osimps_I1_J,axiom,
! [T_a] : c_Enum_Osublists(T_a,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))),
file('theBenchmark.p',fact_sublists_Osimps_I1_J) ).
fof(fact_sublists_Osimps_I2_J,axiom,
! [V_xs_2,V_x_2,T_b] : c_Enum_Osublists(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_Enum_Osublists(T_b,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_b)),tc_fun(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(tc_List_Olist(T_b))),c_List_Oappend(tc_List_Olist(T_b))),hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_b))))),
file('theBenchmark.p',fact_sublists_Osimps_I2_J) ).
fof(fact_distinct__set__sublists,axiom,
! [V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),c_List_Oset(T_b)),c_Enum_Osublists(T_b,V_xs_2)))) ),
file('theBenchmark.p',fact_distinct__set__sublists) ).
fof(fact_set__n__lists,axiom,
! [V_xs_2,V_na_2,T_b] : hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_na_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_na_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),hAPP(c_List_Oset(T_b),V_xs_2)))),
file('theBenchmark.p',fact_set__n__lists) ).
fof(fact_enum__the__def,axiom,
! [V_P_2,T_b] : c_Enum_Oenum__the(T_b,V_P_2) = c_HOL_OThe(T_b,V_P_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_na_2,V_ys_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_na_2,V_xs_2))))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_na_2 ),
file('theBenchmark.p',fact_length__n__lists__elem) ).
fof(fact_list__all2I,axiom,
! [V_P_2,V_b_2,V_a_2,T_c,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_a_2),V_b_2))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x)) )
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2)
=> c_List_Olist__all2(T_b,T_c,V_P_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_P_2,V_xs_2,T_b] :
( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,V_x_2)) ) ),
file('theBenchmark.p',fact_all__nth__imp__all__set) ).
fof(fact_,axiom,
! [V_s2_2,V_s1_2,T_c,T_b] : c_Lazy__Sequence_Oproduct(T_b,T_c,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_b,tc_prod(T_b,T_c),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_b),c_Lazy__Sequence_Obind(T_c,tc_prod(T_b,T_c),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_c),c_Lazy__Sequence_Osingle(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),
file('theBenchmark.p',fact_) ).
fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
=> hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),c_List_Oremdups(T_b,V_xs_2)) ),
file('theBenchmark.p',fact_fun__left__comm_Ofold__set__remdups) ).
fof(fact_distinct__remdups,axiom,
! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))),
file('theBenchmark.p',fact_distinct__remdups) ).
fof(fact_length__remdups__leq,axiom,
! [V_xs,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),
file('theBenchmark.p',fact_length__remdups__leq) ).
fof(fact_remdups__id__iff__distinct,axiom,
! [V_xs_2,T_b] :
( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
<=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_remdups__id__iff__distinct) ).
fof(fact_distinct__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_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_set__remdups,axiom,
! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
file('theBenchmark.p',fact_set__remdups) ).
fof(fact_length__remdups__eq,axiom,
! [V_xs_2,T_b] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
<=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ),
file('theBenchmark.p',fact_length__remdups__eq) ).
fof(fact_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__map__remdups,axiom,
! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremdups(T_c,V_xs_2))) = c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_remdups__map__remdups) ).
fof(fact_remdups_Osimps_I1_J,axiom,
! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_remdups_Osimps_I1_J) ).
fof(fact_remdups__eq__nil__right__iff,axiom,
! [V_x_2,T_b] :
( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
<=> V_x_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_remdups__eq__nil__right__iff) ).
fof(fact_remdups__eq__nil__iff,axiom,
! [V_x_2,T_b] :
( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
<=> V_x_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_remdups__eq__nil__iff) ).
fof(fact_remdups_Osimps_I2_J,axiom,
! [V_xs_2,V_x_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oremdups(T_b,V_xs_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Oremdups(T_b,V_xs_2) ) ),
file('theBenchmark.p',fact_remdups_Osimps_I2_J) ).
fof(fact_length__remdups__card__conv,axiom,
! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)),
file('theBenchmark.p',fact_length__remdups__card__conv) ).
fof(fact_length__remdups__concat,axiom,
! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,c_List_Oconcat(T_b,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)),c_List_Oset(T_b))),
file('theBenchmark.p',fact_length__remdups__concat) ).
fof(fact_sorted__list__of__set__sort__remdups,axiom,
! [V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),c_List_Oremdups(T_b,V_xs_2)) ),
file('theBenchmark.p',fact_sorted__list__of__set__sort__remdups) ).
fof(fact_Nil__eq__concat__conv,axiom,
! [V_xss_2,T_b] :
( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
=> B_x = c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_Nil__eq__concat__conv) ).
fof(fact_concat__eq__Nil__conv,axiom,
! [V_xss_2,T_b] :
( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
=> B_x = c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_concat__eq__Nil__conv) ).
fof(fact_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_sort__key__simps_I1_J,axiom,
! [V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_sort__key__simps_I1_J) ).
fof(fact_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_map__concat,axiom,
! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)),
file('theBenchmark.p',fact_map__concat) ).
fof(fact_concat__conv__foldl,axiom,
! [V_xss_2,T_b] : c_List_Oconcat(T_b,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),c_List_Olist_ONil(T_b)),V_xss_2),
file('theBenchmark.p',fact_concat__conv__foldl) ).
fof(fact_foldl__conv__concat,axiom,
! [V_xss_2,V_xs_2,T_b] : hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oconcat(T_b,V_xss_2)),
file('theBenchmark.p',fact_foldl__conv__concat) ).
fof(fact_length__sort,axiom,
! [V_xs_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ),
file('theBenchmark.p',fact_length__sort) ).
fof(fact_set__sort,axiom,
! [V_xs_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ),
file('theBenchmark.p',fact_set__sort) ).
fof(fact_distinct__sort,axiom,
! [V_xs_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)))
<=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ),
file('theBenchmark.p',fact_distinct__sort) ).
fof(fact_length__concat,axiom,
! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oconcat(T_b,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2)),
file('theBenchmark.p',fact_length__concat) ).
fof(fact_set__concat,axiom,
! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oconcat(T_b,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)),c_List_Oset(T_b)),
file('theBenchmark.p',fact_set__concat) ).
fof(fact_sort__key__simps_I2_J,axiom,
! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) ),
file('theBenchmark.p',fact_sort__key__simps_I2_J) ).
fof(fact_concat__append,axiom,
! [V_ys,V_xs,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Oappend(tc_List_Olist(T_a)),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oconcat(T_a,V_xs)),c_List_Oconcat(T_a,V_ys)),
file('theBenchmark.p',fact_concat__append) ).
fof(fact_sort__foldl__insort,axiom,
! [V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))),c_List_Olist_ONil(T_b)),V_xs_2) ),
file('theBenchmark.p',fact_sort__foldl__insort) ).
fof(fact_concat__injective,axiom,
! [V_ys_2,V_xs_2,T_b] :
( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
=> V_xs_2 = V_ys_2 ) ) ),
file('theBenchmark.p',fact_concat__injective) ).
fof(fact_concat__eq__concat__iff,axiom,
! [V_ys_2,V_xs_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
=> ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
<=> V_xs_2 = V_ys_2 ) ) ),
file('theBenchmark.p',fact_concat__eq__concat__iff) ).
fof(fact_concat__map__singleton,axiom,
! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_c),c_List_Olist_OCons(T_b)),V_f_2)),c_List_Olist_ONil(T_b))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2),
file('theBenchmark.p',fact_concat__map__singleton) ).
fof(fact_n__lists_Osimps_I2_J,axiom,
! [V_xs_2,V_na_2,T_b] : c_Enum_On__lists(T_b,hAPP(c_Nat_OSuc,V_na_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_List_Omap(T_b,tc_List_Olist(T_b))),hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),V_xs_2)),c_Enum_On__lists(T_b,V_na_2,V_xs_2))),
file('theBenchmark.p',fact_n__lists_Osimps_I2_J) ).
fof(fact_transpose_Osimps_I3_J,axiom,
! [V_xss_2,V_xs_2,V_x_2,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))),
file('theBenchmark.p',fact_transpose_Osimps_I3_J) ).
fof(fact_transpose__aux__filter__head,axiom,
! [V_xss_2,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),c_List_Ohd(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)),
file('theBenchmark.p',fact_transpose__aux__filter__head) ).
fof(fact_filter__concat,axiom,
! [V_xs_2,V_p_2,T_b] : hAPP(c_List_Ofilter(T_b,V_p_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Ofilter(T_b,V_p_2)),V_xs_2)),
file('theBenchmark.p',fact_filter__concat) ).
fof(fact_filter__sort,axiom,
! [V_xs_2,V_f_2,V_P_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) ),
file('theBenchmark.p',fact_filter__sort) ).
fof(fact_distinct__filter,axiom,
! [V_P_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ),
file('theBenchmark.p',fact_distinct__filter) ).
fof(fact_filter__id__conv,axiom,
! [V_xs_2,V_P_2,T_b] :
( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = V_xs_2
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,B_x)) ) ),
file('theBenchmark.p',fact_filter__id__conv) ).
fof(fact_filter__is__subset,axiom,
! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
file('theBenchmark.p',fact_filter__is__subset) ).
fof(fact_sum__length__filter__compl,axiom,
! [V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2),
file('theBenchmark.p',fact_sum__length__filter__compl) ).
fof(fact_length__filter__le,axiom,
! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
file('theBenchmark.p',fact_length__filter__le) ).
fof(fact_partition__filter2,axiom,
! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_P_2)),V_xs_2),
file('theBenchmark.p',fact_partition__filter2) ).
fof(fact_partition__filter1,axiom,
! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2),
file('theBenchmark.p',fact_partition__filter1) ).
fof(fact_partition__filter__conv,axiom,
! [V_xs_2,V_f_2,T_b] : c_List_Opartition(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_f_2)),V_xs_2)),
file('theBenchmark.p',fact_partition__filter__conv) ).
fof(fact_filter__filter,axiom,
! [V_xs_2,V_Q_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_Q_2)),V_P_2)),V_xs_2),
file('theBenchmark.p',fact_filter__filter) ).
fof(fact_remove1__filter__not,axiom,
! [V_xs_2,T_b,V_x_2,V_P_2] :
( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ),
file('theBenchmark.p',fact_remove1__filter__not) ).
fof(fact_filter__remove1,axiom,
! [V_xs_2,V_x_2,V_Q_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Q_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)),
file('theBenchmark.p',fact_filter__remove1) ).
fof(fact_filter__insort__triv,axiom,
! [V_xs_2,V_f_2,T_b,V_x_2,V_P_2,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ),
file('theBenchmark.p',fact_filter__insort__triv) ).
fof(fact_filter__map,axiom,
! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2)),V_xs_2)),
file('theBenchmark.p',fact_filter__map) ).
fof(fact_transpose_Osimps_I1_J,axiom,
! [T_a] : c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)),
file('theBenchmark.p',fact_transpose_Osimps_I1_J) ).
fof(fact_filter_Osimps_I1_J,axiom,
! [V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
file('theBenchmark.p',fact_filter_Osimps_I1_J) ).
fof(fact_filter_Osimps_I2_J,axiom,
! [V_xs_2,T_b,V_x_2,V_P_2] :
( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) )
& ( hBOOL(hAPP(V_P_2,V_x_2))
=> hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) ) ),
file('theBenchmark.p',fact_filter_Osimps_I2_J) ).
fof(fact_filter__append,axiom,
! [V_ys_2,V_xs_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2)),
file('theBenchmark.p',fact_filter__append) ).
fof(fact_filter__empty__conv,axiom,
! [V_xs_2,V_P_2,T_b] :
( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = c_List_Olist_ONil(T_b)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ~ hBOOL(hAPP(V_P_2,B_x)) ) ),
file('theBenchmark.p',fact_filter__empty__conv) ).
fof(fact_length__filter__map,axiom,
! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2)),V_xs_2)),
file('theBenchmark.p',fact_length__filter__map) ).
fof(fact_remdups__filter,axiom,
! [V_xs_2,V_P_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oremdups(T_b,V_xs_2)),
file('theBenchmark.p',fact_remdups__filter) ).
fof(fact_transpose_Osimps_I2_J,axiom,
! [V_xss,T_a] : c_List_Otranspose(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),V_xss)) = c_List_Otranspose(T_a,V_xss),
file('theBenchmark.p',fact_transpose_Osimps_I2_J) ).
fof(fact_nth__transpose,axiom,
! [V_xs_2,T_b,V_i_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
=> hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2)) ),
file('theBenchmark.p',fact_nth__transpose) ).
fof(fact_transpose__map__map,axiom,
! [V_xs_2,V_f_2,T_c,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),c_List_Otranspose(T_c,V_xs_2)),
file('theBenchmark.p',fact_transpose__map__map) ).
fof(fact_set__filter,axiom,
! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_P_2)),
file('theBenchmark.p',fact_set__filter) ).
fof(fact_length__filter__less,axiom,
! [V_P_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ),
file('theBenchmark.p',fact_length__filter__less) ).
fof(fact_set__minus__filter__out,axiom,
! [V_y_2,V_xs_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)),
file('theBenchmark.p',fact_set__minus__filter__out) ).
fof(fact_filter__in__sublist,axiom,
! [V_s_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_b,V_xs_2,V_s_2) ),
file('theBenchmark.p',fact_filter__in__sublist) ).
fof(fact_transpose__empty,axiom,
! [V_xs_2,T_b] :
( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
=> B_x = c_List_Olist_ONil(T_b) ) ),
file('theBenchmark.p',fact_transpose__empty) ).
fof(fact_length__filter__conv__card,axiom,
! [V_xs_2,V_p_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_p_2),V_xs_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_b),V_xs_2))))),
file('theBenchmark.p',fact_length__filter__conv__card) ).
fof(fact_transpose__aux__filter__tail,axiom,
! [V_xss_2,T_b] : c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otl(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)),
file('theBenchmark.p',fact_transpose__aux__filter__tail) ).
fof(fact_transpose_Opsimps_I3_J,axiom,
! [V_xss_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)))
=> c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ),
file('theBenchmark.p',fact_transpose_Opsimps_I3_J) ).
fof(fact_transpose_Opsimps_I2_J,axiom,
! [V_xss_2,T_b] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)))
=> c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)) = c_List_Otranspose(T_b,V_xss_2) ),
file('theBenchmark.p',fact_transpose_Opsimps_I2_J) ).
fof(fact_sublist__shift__lemma__Suc,axiom,
! [V_is_2,V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_P_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_P_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))),
file('theBenchmark.p',fact_sublist__shift__lemma__Suc) ).
fof(fact_pick__drop__zero,axiom,
! [V_xs_2,T_b] : c_Random_Opick(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Opick(T_b,V_xs_2),
file('theBenchmark.p',fact_pick__drop__zero) ).
fof(fact_select__weigth__drop__zero,axiom,
! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2),
file('theBenchmark.p',fact_select__weigth__drop__zero) ).
fof(fact_transpose_Opsimps_I1_J,axiom,
! [T_b] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),c_List_Olist_ONil(tc_List_Olist(T_b))))
=> c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ),
file('theBenchmark.p',fact_transpose_Opsimps_I1_J) ).
fof(fact_transpose__max__length,axiom,
! [V_xs_2,T_b] : c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xs_2)),
file('theBenchmark.p',fact_transpose__max__length) ).
fof(fact_transpose__aux__max,axiom,
! [V_xss_2,T_c,V_xs_2,T_b] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_c)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
file('theBenchmark.p',fact_transpose__aux__max) ).
fof(fact_foldr_Osimps_I1_J,axiom,
! [V_a_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c),V_a_2) = V_a_2,
file('theBenchmark.p',fact_foldr_Osimps_I1_J) ).
fof(fact_foldr_Osimps_I2_J,axiom,
! [V_a_2,V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2)),
file('theBenchmark.p',fact_foldr_Osimps_I2_J) ).
fof(fact_foldr__append,axiom,
! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,c_List_Ofoldr(T_c,T_b,V_f_2,V_ys_2,V_a_2)),
file('theBenchmark.p',fact_foldr__append) ).
fof(fact_foldr__conv__foldl,axiom,
! [V_a_2,V_xs_2,T_b] :
( class_Groups_Oab__semigroup__add(T_b)
=> c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) ),
file('theBenchmark.p',fact_foldr__conv__foldl) ).
fof(fact_foldr__map,axiom,
! [V_a_2,V_xs_2,V_f_2,T_d,V_g_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_g_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_d,T_b,hAPP(c_Fun_Ocomp(T_c,tc_fun(T_b,T_b),T_d,V_g_2),V_f_2),V_xs_2,V_a_2),
file('theBenchmark.p',fact_foldr__map) ).
fof(fact_foldl__foldr1,axiom,
! [V_xs_2,T_b] :
( class_Groups_Omonoid__add(T_b)
=> hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_xs_2) = c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b)) ),
file('theBenchmark.p',fact_foldl__foldr1) ).
fof(fact_foldl__foldr1__lemma,axiom,
! [V_xs_2,V_a_2,T_b] :
( class_Groups_Omonoid__add(T_b)
=> hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b))) ),
file('theBenchmark.p',fact_foldl__foldr1__lemma) ).
fof(fact_length__transpose,axiom,
! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_List_Ofoldr(tc_List_Olist(T_b),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_b)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_length__transpose) ).
fof(fact_sublist__def,axiom,
! [V_A_2,V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))),
file('theBenchmark.p',fact_sublist__def) ).
fof(fact_sublist__shift__lemma,axiom,
! [V_i_2,V_xs_2,V_A_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(V_i_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(T_b,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))),
file('theBenchmark.p',fact_sublist__shift__lemma) ).
fof(fact_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_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_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_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__0,axiom,
! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
file('theBenchmark.p',fact_upt__0) ).
fof(fact_upt__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__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_drop__upt,axiom,
! [V_j,V_i,V_m] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_j)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m),V_j),
file('theBenchmark.p',fact_drop__upt) ).
fof(fact_hd__upt,axiom,
! [V_j,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
=> hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ),
file('theBenchmark.p',fact_hd__upt) ).
fof(fact_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_na_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_na_2)) = c_List_Oupt(V_m_2,V_na_2),
file('theBenchmark.p',fact_sorted__list__of__set__range) ).
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_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_na_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_na_2)) = c_List_Oupt(hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_na_2)),
file('theBenchmark.p',fact_map__Suc__upt) ).
fof(fact_atLeastAtMost__upt,axiom,
! [V_m_2,V_na_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_na_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_na_2,hAPP(c_Nat_OSuc,V_m_2))),
file('theBenchmark.p',fact_atLeastAtMost__upt) ).
fof(fact_atLeast__upt,axiom,
! [V_na_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_na_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_na_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_na_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_na_2),hAPP(c_Nat_OSuc,V_m_2))),
file('theBenchmark.p',fact_greaterThanAtMost__upt) ).
fof(fact_greaterThanLessThan__upt,axiom,
! [V_m_2,V_na_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_na_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_na_2),V_m_2)),
file('theBenchmark.p',fact_greaterThanLessThan__upt) ).
fof(fact_atMost__upto,axiom,
! [V_na_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_na_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2))),
file('theBenchmark.p',fact_atMost__upto) ).
fof(fact_map__nth,axiom,
! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) = V_xs_2,
file('theBenchmark.p',fact_map__nth) ).
fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
! [V_na_2,V_m_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_na_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_na_2))) ),
file('theBenchmark.p',fact_setsum__set__upt__conv__listsum__nat) ).
fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
! [V_na_2,V_m_2,V_f_2,T_b] :
( class_Groups_Ocomm__monoid__add(T_b)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_na_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_na_2))) ),
file('theBenchmark.p',fact_interv__listsum__conv__setsum__set__nat) ).
fof(fact_nth__map__upt,axiom,
! [V_f_2,T_b,V_m_2,V_na_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_na_2),V_m_2)))
=> hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_na_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_na_2,T_b,V_xs_2] :
( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> ( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),B_i)) = V_na_2 )
=> c_List_Otranspose(T_b,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_b)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_Nat_Onat,T_b),tc_Nat_Onat),c_List_Onth(T_b)),hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_na_2)) ) ),
file('theBenchmark.p',fact_transpose__rectangle) ).
fof(fact_insort__key__remove1,axiom,
! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
=> ( hAPP(c_List_Ohd(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ),
file('theBenchmark.p',fact_insort__key__remove1) ).
fof(fact_sorted_ONil,axiom,
! [T_a] :
( class_Orderings_Olinorder(T_a)
=> c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ),
file('theBenchmark.p',fact_sorted_ONil) ).
fof(fact_sorted__single,axiom,
! [V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ),
file('theBenchmark.p',fact_sorted__single) ).
fof(fact_sorted__upt,axiom,
! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)),
file('theBenchmark.p',fact_sorted__upt) ).
fof(fact_sorted__sort,axiom,
! [V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_sorted__sort) ).
fof(fact_sorted__insort__insert,axiom,
! [V_x_2,V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
=> c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) ) ),
file('theBenchmark.p',fact_sorted__insort__insert) ).
fof(fact_sorted__tl,axiom,
! [V_xs,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_List_Olinorder__class_Osorted(T_a,V_xs)
=> c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ),
file('theBenchmark.p',fact_sorted__tl) ).
fof(fact_sorted__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__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__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__insort,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2))
<=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ),
file('theBenchmark.p',fact_sorted__insort) ).
fof(fact_sorted_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_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)))
<=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
file('theBenchmark.p',fact_sorted__many__eq) ).
fof(fact_sorted__butlast,axiom,
! [V_xs,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( V_xs != c_List_Olist_ONil(T_a)
=> ( c_List_Olinorder__class_Osorted(T_a,V_xs)
=> c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ),
file('theBenchmark.p',fact_sorted__butlast) ).
fof(fact_sorted__remdups,axiom,
! [V_l,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_List_Olinorder__class_Osorted(T_a,V_l)
=> c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ),
file('theBenchmark.p',fact_sorted__remdups) ).
fof(fact_sorted__distinct__set__unique,axiom,
! [V_ys_2,V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
=> ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
=> V_xs_2 = V_ys_2 ) ) ) ) ) ),
file('theBenchmark.p',fact_sorted__distinct__set__unique) ).
fof(fact_sorted__sort__key,axiom,
! [V_xs_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Osort__key(T_c,T_b,V_f_2,V_xs_2))) ),
file('theBenchmark.p',fact_sorted__sort__key) ).
fof(fact_sorted__insort__key,axiom,
! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)))
<=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ),
file('theBenchmark.p',fact_sorted__insort__key) ).
fof(fact_sorted__map__remove1,axiom,
! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremove1(T_c,V_x_2,V_xs_2))) ) ),
file('theBenchmark.p',fact_sorted__map__remove1) ).
fof(fact_sorted__insort__insert__key,axiom,
! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2))) ) ),
file('theBenchmark.p',fact_sorted__insort__insert__key) ).
fof(fact_sorted__filter,axiom,
! [V_P_2,V_xs_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_P_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_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_c),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ),
file('theBenchmark.p',fact_sorted__map__same) ).
fof(fact_sorted__same,axiom,
! [V_xs_2,V_g_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ),
file('theBenchmark.p',fact_sorted__same) ).
fof(fact_sorted__Cons,axiom,
! [V_xs_2,V_x_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
& c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ),
file('theBenchmark.p',fact_sorted__Cons) ).
fof(fact_sorted__append,axiom,
! [V_ys_2,V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) )
& c_List_Olinorder__class_Osorted(T_b,V_ys_2)
& c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ),
file('theBenchmark.p',fact_sorted__append) ).
fof(fact_filter__insort,axiom,
! [V_x_2,V_P_2,V_xs_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
=> ( hBOOL(hAPP(V_P_2,V_x_2))
=> hAPP(c_List_Ofilter(T_c,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2)) ) ) ),
file('theBenchmark.p',fact_filter__insort) ).
fof(fact_sorted_Oequations_I2_J,axiom,
! [V_a1_2,V_a2_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
<=> ( c_List_Olinorder__class_Osorted(T_b,V_a1_2)
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) ) ) ) ),
file('theBenchmark.p',fact_sorted_Oequations_I2_J) ).
fof(fact_sorted__list__of__set,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)))
& c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
& hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2 ) ) ),
file('theBenchmark.p',fact_sorted__list__of__set) ).
fof(fact_insort__remove1,axiom,
! [V_xs_2,V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ),
file('theBenchmark.p',fact_insort__remove1) ).
fof(fact_sorted__equals__nth__mono,axiom,
! [V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
<=> ! [B_j] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j))) ) ) ) ),
file('theBenchmark.p',fact_sorted__equals__nth__mono) ).
fof(fact_sorted__nth__mono,axiom,
! [V_j,V_i,V_xs,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_List_Olinorder__class_Osorted(T_a,V_xs)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j))) ) ) ) ),
file('theBenchmark.p',fact_sorted__nth__mono) ).
fof(fact_map__sorted__distinct__set__unique,axiom,
! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
=> ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
=> ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
=> ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
=> ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
=> V_xs_2 = V_ys_2 ) ) ) ) ) ) ),
file('theBenchmark.p',fact_map__sorted__distinct__set__unique) ).
fof(fact_transpose__column,axiom,
! [V_i_2,V_xs_2,T_b] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
=> hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2) ) ),
file('theBenchmark.p',fact_transpose__column) ).
fof(fact_nth__nth__transpose__sorted,axiom,
! [V_j_2,V_i_2,V_xs_2,T_b] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2))))
=> hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_j_2)),V_i_2) ) ) ),
file('theBenchmark.p',fact_nth__nth__transpose__sorted) ).
fof(fact_inj__on__rev,axiom,
! [V_A_2,T_b] : c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orev(T_b),V_A_2),
file('theBenchmark.p',fact_inj__on__rev) ).
fof(fact_distinct__rev,axiom,
! [V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
<=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
file('theBenchmark.p',fact_distinct__rev) ).
fof(fact_rev_Osimps_I1_J,axiom,
! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_rev_Osimps_I1_J) ).
fof(fact_Nil__is__rev__conv,axiom,
! [V_xs_2,T_b] :
( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_Nil__is__rev__conv) ).
fof(fact_rev__is__Nil__conv,axiom,
! [V_xs_2,T_b] :
( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
<=> V_xs_2 = c_List_Olist_ONil(T_b) ),
file('theBenchmark.p',fact_rev__is__Nil__conv) ).
fof(fact_singleton__rev__conv,axiom,
! [V_xs_2,V_x_2,T_b] :
( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(c_List_Orev(T_b),V_xs_2)
<=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ),
file('theBenchmark.p',fact_singleton__rev__conv) ).
fof(fact_rev__singleton__conv,axiom,
! [V_x_2,V_xs_2,T_b] :
( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
<=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ),
file('theBenchmark.p',fact_rev__singleton__conv) ).
fof(fact_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_b] : hAPP(c_List_Orev(T_b),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Orev(T_b)),hAPP(c_List_Orev(tc_List_Olist(T_b)),V_xs_2))),
file('theBenchmark.p',fact_rev__concat) ).
fof(fact_rev__map,axiom,
! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2)),
file('theBenchmark.p',fact_rev__map) ).
fof(fact_rev__filter,axiom,
! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Orev(T_b),V_xs_2)),
file('theBenchmark.p',fact_rev__filter) ).
fof(fact_zip__rev,axiom,
! [V_ys,T_b,V_xs,T_a] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)
=> hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(c_List_Orev(T_a),V_xs)),hAPP(c_List_Orev(T_b),V_ys)) = hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ),
file('theBenchmark.p',fact_zip__rev) ).
fof(fact_set__rev,axiom,
! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
file('theBenchmark.p',fact_set__rev) ).
fof(fact_list__all2__rev1,axiom,
! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2)
<=> c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ),
file('theBenchmark.p',fact_list__all2__rev1) ).
fof(fact_list__all2__rev,axiom,
! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2),hAPP(c_List_Orev(T_c),V_ys_2))
<=> c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ),
file('theBenchmark.p',fact_list__all2__rev) ).
fof(fact_rev__is__rev__conv,axiom,
! [V_ys_2,V_xs_2,T_b] :
( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
<=> V_xs_2 = V_ys_2 ),
file('theBenchmark.p',fact_rev__is__rev__conv) ).
fof(fact_rev__swap,axiom,
! [V_ys_2,V_xs_2,T_b] :
( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
<=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ),
file('theBenchmark.p',fact_rev__swap) ).
fof(fact_rev__rev__ident,axiom,
! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs,
file('theBenchmark.p',fact_rev__rev__ident) ).
fof(fact_listsum__rev,axiom,
! [V_xs,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs) ),
file('theBenchmark.p',fact_listsum__rev) ).
fof(fact_length__rev,axiom,
! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
file('theBenchmark.p',fact_length__rev) ).
fof(fact_foldr__foldl,axiom,
! [V_a_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),V_f_2),V_a_2),hAPP(c_List_Orev(T_c),V_xs_2)),
file('theBenchmark.p',fact_foldr__foldl) ).
fof(fact_foldl__foldr,axiom,
! [V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2),V_a_2),
file('theBenchmark.p',fact_foldl__foldr) ).
fof(fact_rev__eq__Cons__iff,axiom,
! [V_ys_2,V_y_2,V_xs_2,T_b] :
( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
<=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Orev(T_b),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) ),
file('theBenchmark.p',fact_rev__eq__Cons__iff) ).
fof(fact_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_last__rev,axiom,
! [T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ),
file('theBenchmark.p',fact_last__rev) ).
fof(fact_hd__rev,axiom,
! [T_a,V_xs] :
( V_xs != c_List_Olist_ONil(T_a)
=> hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ),
file('theBenchmark.p',fact_hd__rev) ).
fof(fact_sorted__transpose,axiom,
! [V_xs_2,T_b] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))),
file('theBenchmark.p',fact_sorted__transpose) ).
fof(fact_rev__foldl__cons,axiom,
! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)),V_xs_2),
file('theBenchmark.p',fact_rev__foldl__cons) ).
fof(fact_rev__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_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
=> ( ( V_xs_2 != c_List_Olist_ONil(T_b)
=> c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) )
& ( V_xs_2 = c_List_Olist_ONil(T_b)
=> c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 ) ) ) ),
file('theBenchmark.p',fact_foldr__max__sorted) ).
fof(fact_length__transpose__sorted,axiom,
! [V_xs_2,T_b] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
=> ( ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('theBenchmark.p',fact_length__transpose__sorted) ).
fof(fact_transpose__column__length,axiom,
! [V_i_2,V_xs_2,T_b] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2)) ) ),
file('theBenchmark.p',fact_transpose__column__length) ).
fof(fact_transpose__transpose,axiom,
! [V_xs_2,T_b] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
=> c_List_Otranspose(T_b,c_List_Otranspose(T_b,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b))),V_xs_2) ),
file('theBenchmark.p',fact_transpose__transpose) ).
fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
file('theBenchmark.p',fact_transfer__nat__int__list__functions_I2_J) ).
fof(fact_sorted__takeWhile,axiom,
! [V_P_2,V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
=> c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) ) ),
file('theBenchmark.p',fact_sorted__takeWhile) ).
fof(fact_length__takeWhile__le,axiom,
! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
file('theBenchmark.p',fact_length__takeWhile__le) ).
fof(fact_set__takeWhileD,axiom,
! [V_xs_2,V_P_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))
=> ( hBOOL(hAPP(V_P_2,V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_set__takeWhileD) ).
fof(fact_takeWhile__eq__all__conv,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = V_xs_2
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,B_x)) ) ),
file('theBenchmark.p',fact_takeWhile__eq__all__conv) ).
fof(fact_zip__takeWhile__snd,axiom,
! [V_ys_2,V_P_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_P_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_P_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),
file('theBenchmark.p',fact_zip__takeWhile__snd) ).
fof(fact_zip__takeWhile__fst,axiom,
! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_P_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),
file('theBenchmark.p',fact_zip__takeWhile__fst) ).
fof(fact_takeWhile__map,axiom,
! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_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_b,V_x_2,V_P_2] :
( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2) ),
file('theBenchmark.p',fact_takeWhile__tail) ).
fof(fact_takeWhile_Osimps_I2_J,axiom,
! [V_xs_2,T_b,V_x_2,V_P_2] :
( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) )
& ( hBOOL(hAPP(V_P_2,V_x_2))
=> c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) ) ),
file('theBenchmark.p',fact_takeWhile_Osimps_I2_J) ).
fof(fact_takeWhile_Osimps_I1_J,axiom,
! [V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
file('theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).
fof(fact_takeWhile__eq__take,axiom,
! [V_xs_2,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),V_xs_2),
file('theBenchmark.p',fact_takeWhile__eq__take) ).
fof(fact_distinct__takeWhile,axiom,
! [V_P_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_P_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_P_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2) ) ),
file('theBenchmark.p',fact_takeWhile__append1) ).
fof(fact_takeWhile__nth,axiom,
! [V_xs_2,V_P_2,T_b,V_j_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))
=> hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ),
file('theBenchmark.p',fact_takeWhile__nth) ).
fof(fact_nth__length__takeWhile,axiom,
! [V_xs_2,V_P_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))) ),
file('theBenchmark.p',fact_nth__length__takeWhile) ).
fof(fact_takeWhile__not__last,axiom,
! [T_b,V_xs_2] :
( V_xs_2 != c_List_Olist_ONil(T_b)
=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),c_List_Olast(T_b,V_xs_2))),V_xs_2) = c_List_Obutlast(T_b,V_xs_2) ) ),
file('theBenchmark.p',fact_takeWhile__not__last) ).
fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
=> hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2),V_xs_2) ) ),
file('theBenchmark.p',fact_filter__equals__takeWhile__sorted__rev) ).
fof(fact_transfer__nat__int__list__return__embed,axiom,
! [V_l] :
( c_List_Onat__list(V_l)
=> c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ),
file('theBenchmark.p',fact_transfer__nat__int__list__return__embed) ).
fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
! [V_m,V_l] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),V_l),V_m) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(V_l)),c_List_Oembed__list(V_m))),
file('theBenchmark.p',fact_transfer__nat__int__list__functions_I1_J) ).
fof(fact_embed__list__def,axiom,
! [V_l_2] : c_List_Oembed__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_l_2),
file('theBenchmark.p',fact_embed__list__def) ).
fof(fact_takeWhile__neq__rev,axiom,
! [V_x_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Orev(T_b),hAPP(c_List_Otl(T_b),c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ),
file('theBenchmark.p',fact_takeWhile__neq__rev) ).
fof(fact_dropWhile__neq__rev,axiom,
! [V_x_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Orev(T_b),c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ),
file('theBenchmark.p',fact_dropWhile__neq__rev) ).
fof(fact_takeWhile__dropWhile__id,axiom,
! [V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),c_List_OdropWhile(T_b,V_P_2,V_xs_2)) = V_xs_2,
file('theBenchmark.p',fact_takeWhile__dropWhile__id) ).
fof(fact_dropWhile__map,axiom,
! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_dropWhile__map) ).
fof(fact_sorted__dropWhile,axiom,
! [V_P_2,V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
=> c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_P_2,V_xs_2)) ) ),
file('theBenchmark.p',fact_sorted__dropWhile) ).
fof(fact_length__dropWhile__le,axiom,
! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
file('theBenchmark.p',fact_length__dropWhile__le) ).
fof(fact_dropWhile__eq__Nil__conv,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_OdropWhile(T_b,V_P_2,V_xs_2) = c_List_Olist_ONil(T_b)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,B_x)) ) ),
file('theBenchmark.p',fact_dropWhile__eq__Nil__conv) ).
fof(fact_dropWhile_Osimps_I2_J,axiom,
! [V_xs_2,T_b,V_x_2,V_P_2] :
( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
& ( hBOOL(hAPP(V_P_2,V_x_2))
=> c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_P_2,V_xs_2) ) ),
file('theBenchmark.p',fact_dropWhile_Osimps_I2_J) ).
fof(fact_dropWhile_Osimps_I1_J,axiom,
! [V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
file('theBenchmark.p',fact_dropWhile_Osimps_I1_J) ).
fof(fact_distinct__dropWhile,axiom,
! [V_P_2,V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
=> hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2))) ),
file('theBenchmark.p',fact_distinct__dropWhile) ).
fof(fact_hd__dropWhile,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_OdropWhile(T_b,V_P_2,V_xs_2) != c_List_Olist_ONil(T_b)
=> ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)))) ),
file('theBenchmark.p',fact_hd__dropWhile) ).
fof(fact_dropWhile__append1,axiom,
! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_OdropWhile(T_b,V_P_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_P_2,T_b] :
( c_List_OdropWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
<=> ( ~ hBOOL(hAPP(V_P_2,V_y_2))
& V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ),
file('theBenchmark.p',fact_dropWhile__eq__Cons__conv) ).
fof(fact_dropWhile__eq__drop,axiom,
! [V_xs_2,V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),V_xs_2),
file('theBenchmark.p',fact_dropWhile__eq__drop) ).
fof(fact_dropWhile__nth,axiom,
! [V_xs_2,V_P_2,T_b,V_j_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_P_2,V_xs_2))))
=> hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)))) ),
file('theBenchmark.p',fact_dropWhile__nth) ).
fof(fact_listsum__map__filter,axiom,
! [V_f_2,V_P_2,V_xs_2,T_b,T_c] :
( class_Groups_Omonoid__add(T_c)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> ( ~ hBOOL(hAPP(V_P_2,B_x))
=> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) )
=> hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ),
file('theBenchmark.p',fact_listsum__map__filter) ).
fof(fact_sorted__nth__monoI,axiom,
! [V_xs,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ! [B_i,B_j] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_j))) ) )
=> c_List_Olinorder__class_Osorted(T_a,V_xs) ) ),
file('theBenchmark.p',fact_sorted__nth__monoI) ).
fof(fact_takeWhile__eq__filter,axiom,
! [V_xs_2,V_P_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2))))
=> ~ hBOOL(hAPP(V_P_2,B_x)) )
=> c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ),
file('theBenchmark.p',fact_takeWhile__eq__filter) ).
fof(fact_takeWhile__eq__take__P__nth,axiom,
! [V_P_2,V_xs_2,T_b,V_na_2] :
( ! [B_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_na_2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) )
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_na_2))) )
=> c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_na_2),V_xs_2) ) ),
file('theBenchmark.p',fact_takeWhile__eq__take__P__nth) ).
fof(fact_length__takeWhile__less__P__nth,axiom,
! [V_xs_2,T_b,V_P_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_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)))) ) ),
file('theBenchmark.p',fact_length__takeWhile__less__P__nth) ).
fof(fact_sorted_Osimps,axiom,
! [V_a_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( c_List_Olinorder__class_Osorted(T_b,V_a_2)
<=> ( ? [B_xs,B_x] :
( c_List_Olinorder__class_Osorted(T_b,B_xs)
& ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) )
& V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs) )
| V_a_2 = c_List_Olist_ONil(T_b) ) ) ),
file('theBenchmark.p',fact_sorted_Osimps) ).
fof(fact_map__removeAll__inj__on,axiom,
! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ),
file('theBenchmark.p',fact_map__removeAll__inj__on) ).
fof(fact_set__removeAll,axiom,
! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
file('theBenchmark.p',fact_set__removeAll) ).
fof(fact_removeAll__append,axiom,
! [V_ys,V_xs,V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs)),hAPP(c_List_OremoveAll(T_a,V_x),V_ys)),
file('theBenchmark.p',fact_removeAll__append) ).
fof(fact_removeAll__id,axiom,
! [V_xs_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ),
file('theBenchmark.p',fact_removeAll__id) ).
fof(fact_removeAll__filter__not,axiom,
! [V_xs_2,T_b,V_x_2,V_P_2] :
( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> hAPP(c_List_OremoveAll(T_b,V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ),
file('theBenchmark.p',fact_removeAll__filter__not) ).
fof(fact_removeAll__filter__not__eq,axiom,
! [V_x_2,T_b] : c_List_OremoveAll(T_b,V_x_2) = c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(c_fequal,V_x_2))),
file('theBenchmark.p',fact_removeAll__filter__not__eq) ).
fof(fact_removeAll_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_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_distinct__removeAll,axiom,
! [V_x,V_xs,T_a] :
( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
=> hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ),
file('theBenchmark.p',fact_distinct__removeAll) ).
fof(fact_distinct__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_map__removeAll__inj,axiom,
! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ),
file('theBenchmark.p',fact_map__removeAll__inj) ).
fof(fact_not__in__set__insert,axiom,
! [V_xs_2,V_x_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ),
file('theBenchmark.p',fact_not__in__set__insert) ).
fof(fact_List_Oinsert__def,axiom,
! [V_xs_2,V_x_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ),
file('theBenchmark.p',fact_List_Oinsert__def) ).
fof(fact_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_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_in__set__insert,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
=> c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ),
file('theBenchmark.p',fact_in__set__insert) ).
fof(fact_List_Oset__insert,axiom,
! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oinsert(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)),
file('theBenchmark.p',fact_List_Oset__insert) ).
fof(fact_insert__Nil,axiom,
! [V_x,T_a] : c_List_Oinsert(T_a,V_x,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)),
file('theBenchmark.p',fact_insert__Nil) ).
fof(fact_maps__def,axiom,
! [V_xs_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)),
file('theBenchmark.p',fact_maps__def) ).
fof(fact_concat__map__maps,axiom,
! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)) = c_List_Omaps(T_c,T_b,V_f_2,V_xs_2),
file('theBenchmark.p',fact_concat__map__maps) ).
fof(fact_maps__simps_I2_J,axiom,
! [V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b),
file('theBenchmark.p',fact_maps__simps_I2_J) ).
fof(fact_maps__simps_I1_J,axiom,
! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_c,T_b,V_f_2,V_xs_2)),
file('theBenchmark.p',fact_maps__simps_I1_J) ).
fof(fact_distinct__concat,axiom,
! [V_xs_2,T_b] :
( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2))
=> ( ! [B_ys] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) )
=> ( ! [B_ys] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
=> ! [B_zs] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
=> ( B_ys != B_zs
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),B_ys)),hAPP(c_List_Oset(T_b),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
=> hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ),
file('theBenchmark.p',fact_distinct__concat) ).
fof(fact_measures__lesseq,axiom,
! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ),
file('theBenchmark.p',fact_measures__lesseq) ).
fof(fact_wf__measures,axiom,
! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)),
file('theBenchmark.p',fact_wf__measures) ).
fof(fact_in__measures_I1_J,axiom,
! [V_y_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_Nat_Onat))))),
file('theBenchmark.p',fact_in__measures_I1_J) ).
fof(fact_measures__def,axiom,
! [V_fs_2,T_b] : c_List_Omeasures(T_b,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_b),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_b),c_List_Omap(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_b,tc_Nat_Onat),T_b,tc_Nat_Onat),c_COMBI(tc_fun(T_b,tc_Nat_Onat))))),V_fs_2)),
file('theBenchmark.p',fact_measures__def) ).
fof(fact_measures__less,axiom,
! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ),
file('theBenchmark.p',fact_measures__less) ).
fof(fact_in__measures_I2_J,axiom,
! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2))))
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2)))
& hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ),
file('theBenchmark.p',fact_in__measures_I2_J) ).
fof(fact_foldl__apply,axiom,
! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hAPP(c_Fun_Ocomp(T_d,T_d,T_c,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_c,T_d,T_c,V_h_2),hAPP(V_g_2,B_x)) )
=> hAPP(c_List_Ofoldl(T_d,T_b,hAPP(c_COMBC(T_b,T_d,T_d),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_g_2),V_s_2),V_xs_2)) ),
file('theBenchmark.p',fact_foldl__apply) ).
fof(fact_order__fun_I2_J,axiom,
! [V_g_2,V_f_2,T_b,T_c] :
( ( class_Enum_Oenum(T_b)
& class_Orderings_Oorder(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
<=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_g_2))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) ) ),
file('theBenchmark.p',fact_order__fun_I2_J) ).
fof(fact_enum__ex,axiom,
! [V_P_2,T_b] :
( class_Enum_Oenum(T_b)
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2))
<=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ),
file('theBenchmark.p',fact_enum__ex) ).
fof(fact_exists__code,axiom,
! [V_P_2,T_b] :
( class_Enum_Oenum(T_b)
=> ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2)) ) ),
file('theBenchmark.p',fact_exists__code) ).
fof(fact_enum__ex__prod__def,axiom,
! [V_P_2,T_b,T_c] :
( ( class_Enum_Oenum(T_b)
& class_Enum_Oenum(T_c) )
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_P_2))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__ex(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c))))) ) ),
file('theBenchmark.p',fact_enum__ex__prod__def) ).
fof(fact_zip__obtain__same__length,axiom,
! [V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_ys_2))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Otake(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_ys_2)))) )
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ),
file('theBenchmark.p',fact_zip__obtain__same__length) ).
fof(fact_small__lazy__list_Osimps,axiom,
! [V_d_2,T_b] :
( class_Lazy__Sequence_Osmall__lazy(T_b)
=> c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_b),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),c_Lazy__Sequence_Oproduct(T_b,tc_List_Olist(T_b),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)))),c_List_Olist_OCons(T_b))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_b)))) ),
file('theBenchmark.p',fact_small__lazy__list_Osimps) ).
fof(fact_small__lazy__prod__def,axiom,
! [V_d,T_b,T_a] :
( ( class_Lazy__Sequence_Osmall__lazy(T_b)
& class_Lazy__Sequence_Osmall__lazy(T_a) )
=> c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(T_a,T_b),V_d) = c_Lazy__Sequence_Oproduct(T_a,T_b,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,V_d),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,V_d)) ),
file('theBenchmark.p',fact_small__lazy__prod__def) ).
fof(fact_New__DSequence_Opos__union__def,axiom,
! [V_i_2,V_yq_2,V_xq_2,T_b] : hAPP(c_New__DSequence_Opos__union(T_b,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_b,hAPP(V_xq_2,V_i_2),hAPP(V_yq_2,V_i_2)),
file('theBenchmark.p',fact_New__DSequence_Opos__union__def) ).
fof(fact_dropWhile__append2,axiom,
! [V_ys_2,V_P_2,V_xs_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,B_x)) )
=> c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_b,V_P_2,V_ys_2) ),
file('theBenchmark.p',fact_dropWhile__append2) ).
fof(fact_pos__union__def,axiom,
! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_b] : c_New__Random__Sequence_Opos__union(T_b,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_b,hAPP(hAPP(hAPP(V_R1_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(hAPP(V_R2_2,V_nrandom_2),V_size_2),V_seed_2)),
file('theBenchmark.p',fact_pos__union__def) ).
fof(fact_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_list__all2__all__nthI,axiom,
! [V_P_2,V_b_2,T_c,V_a_2,T_b] :
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2)
=> ( ! [B_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2)))
=> hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_c),V_b_2),B_n))) )
=> c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2) ) ),
file('theBenchmark.p',fact_list__all2__all__nthI) ).
fof(fact_small__lazy_H_Opinduct,axiom,
! [V_P_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_P_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_P_2,B_d),B_i)) ) )
=> hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ),
file('theBenchmark.p',fact_small__lazy_H_Opinduct) ).
fof(fact_finite__sorted__distinct__unique,axiom,
! [V_A_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ? [B_x] :
( ! [B_y] :
( ( hBOOL(hAPP(c_List_Odistinct(T_b),B_y))
& c_List_Olinorder__class_Osorted(T_b,B_y)
& hAPP(c_List_Oset(T_b),B_y) = V_A_2 )
=> B_y = B_x )
& hBOOL(hAPP(c_List_Odistinct(T_b),B_x))
& c_List_Olinorder__class_Osorted(T_b,B_x)
& hAPP(c_List_Oset(T_b),B_x) = V_A_2 ) ) ),
file('theBenchmark.p',fact_finite__sorted__distinct__unique) ).
fof(fact_takeWhile__append2,axiom,
! [V_ys_2,V_P_2,V_xs_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,B_x)) )
=> c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_OtakeWhile(T_b,V_P_2,V_ys_2)) ),
file('theBenchmark.p',fact_takeWhile__append2) ).
fof(fact_insort__is__Cons,axiom,
! [V_a_2,V_f_2,V_xs_2,T_b,T_c] :
( class_Orderings_Olinorder(T_c)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
=> hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_xs_2) ) ),
file('theBenchmark.p',fact_insort__is__Cons) ).
fof(fact_Cons__eq__filter__iff,axiom,
! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2)
<=> ? [B_us,B_vs] :
( V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs)
& hBOOL(hAPP(V_P_2,V_x_2))
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
=> ~ hBOOL(hAPP(V_P_2,B_x)) )
& V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs)) ) ),
file('theBenchmark.p',fact_Cons__eq__filter__iff) ).
fof(fact_filter__eq__Cons__iff,axiom,
! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_b] :
( hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
<=> ? [B_us,B_vs] :
( V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs)
& hBOOL(hAPP(V_P_2,V_x_2))
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
=> ~ hBOOL(hAPP(V_P_2,B_x)) )
& V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs)) ) ),
file('theBenchmark.p',fact_filter__eq__Cons__iff) ).
fof(fact_order__fun_I1_J,axiom,
! [V_g_2,V_f_2,T_b,T_c] :
( ( class_Enum_Oenum(T_b)
& class_Orderings_Oorder(T_c) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Oord__class_Oless__eq(T_c)),V_f_2)),V_g_2))) ) ),
file('theBenchmark.p',fact_order__fun_I1_J) ).
fof(fact_list__ball__nth,axiom,
! [V_P_2,V_xs_2,T_b,V_na_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,B_x)) )
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_na_2))) ) ),
file('theBenchmark.p',fact_list__ball__nth) ).
fof(fact_enum__all,axiom,
! [V_P_2,T_b] :
( class_Enum_Oenum(T_b)
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2))
<=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ),
file('theBenchmark.p',fact_enum__all) ).
fof(fact_all__code,axiom,
! [V_P_2,T_b] :
( class_Enum_Oenum(T_b)
=> ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2)) ) ),
file('theBenchmark.p',fact_all__code) ).
fof(fact_enum__all__prod__def,axiom,
! [V_P_2,T_b,T_c] :
( ( class_Enum_Oenum(T_b)
& class_Enum_Oenum(T_c) )
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_P_2))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__all(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c))))) ) ),
file('theBenchmark.p',fact_enum__all__prod__def) ).
fof(fact_sorted_OCons,axiom,
! [V_x_2,V_xs_2,T_b] :
( class_Orderings_Olinorder(T_b)
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ),
file('theBenchmark.p',fact_sorted_OCons) ).
fof(fact_list__ex__length,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
<=> ? [B_n] :
( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ),
file('theBenchmark.p',fact_list__ex__length) ).
fof(fact_list__ex__simps_I2_J,axiom,
! [V_P_2,T_b] : ~ c_List_Olist__ex(T_b,V_P_2,c_List_Olist_ONil(T_b)),
file('theBenchmark.p',fact_list__ex__simps_I2_J) ).
fof(fact_list__ex__rev,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_Olist__ex(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
<=> c_List_Olist__ex(T_b,V_P_2,V_xs_2) ),
file('theBenchmark.p',fact_list__ex__rev) ).
fof(fact_list__ex__iff,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
<=> ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_list__ex__iff) ).
fof(fact_list__ex__append,axiom,
! [V_ys_2,V_xs_2,V_P_2,T_b] :
( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
<=> ( c_List_Olist__ex(T_b,V_P_2,V_ys_2)
| c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ),
file('theBenchmark.p',fact_list__ex__append) ).
fof(fact_list__ex__simps_I1_J,axiom,
! [V_xs_2,V_x_2,V_P_2,T_b] :
( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
<=> ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
| hBOOL(hAPP(V_P_2,V_x_2)) ) ),
file('theBenchmark.p',fact_list__ex__simps_I1_J) ).
fof(fact_in__set__conv__decomp__first,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
<=> ? [B_ys] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys)))
& ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ) ),
file('theBenchmark.p',fact_in__set__conv__decomp__first) ).
fof(fact_in__set__conv__decomp__last,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
<=> ? [B_ys,B_zs] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs)))
& V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ) ),
file('theBenchmark.p',fact_in__set__conv__decomp__last) ).
fof(fact_in__set__conv__decomp,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
<=> ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ),
file('theBenchmark.p',fact_in__set__conv__decomp) ).
fof(fact_list__all__length,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_Olist__all(T_b,V_P_2,V_xs_2)
<=> ! [B_n] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
=> hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ),
file('theBenchmark.p',fact_list__all__length) ).
fof(fact_list__all__simps_I2_J,axiom,
! [V_P_2,T_b] : c_List_Olist__all(T_b,V_P_2,c_List_Olist_ONil(T_b)),
file('theBenchmark.p',fact_list__all__simps_I2_J) ).
fof(fact_list__all__rev,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_Olist__all(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
<=> c_List_Olist__all(T_b,V_P_2,V_xs_2) ),
file('theBenchmark.p',fact_list__all__rev) ).
fof(fact_list__all__iff,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_Olist__all(T_b,V_P_2,V_xs_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,B_x)) ) ),
file('theBenchmark.p',fact_list__all__iff) ).
fof(fact_list__all__append,axiom,
! [V_ys_2,V_xs_2,V_P_2,T_b] :
( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
<=> ( c_List_Olist__all(T_b,V_P_2,V_ys_2)
& c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ),
file('theBenchmark.p',fact_list__all__append) ).
fof(fact_Ball__set__list__all,axiom,
! [V_P_2,V_xs_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_2,B_x)) )
<=> c_List_Olist__all(T_b,V_P_2,V_xs_2) ),
file('theBenchmark.p',fact_Ball__set__list__all) ).
fof(fact_list__all__simps_I1_J,axiom,
! [V_xs_2,V_x_2,V_P_2,T_b] :
( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
<=> ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
& hBOOL(hAPP(V_P_2,V_x_2)) ) ),
file('theBenchmark.p',fact_list__all__simps_I1_J) ).
fof(fact_list__all__iff__raw,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_Olist__all(T_b,V_P_2,V_xs_2)
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
=> hBOOL(hAPP(V_P_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_P_2,T_b] :
( c_List_Olist__ex1(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
<=> ( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> c_List_Olist__ex1(T_b,V_P_2,V_xs_2) )
& ( hBOOL(hAPP(V_P_2,V_x_2))
=> c_List_Olist__all(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))),hAPP(c_fequal,V_x_2)),V_xs_2) ) ) ),
file('theBenchmark.p',fact_list__ex1__simps_I2_J) ).
fof(fact_length__splice,axiom,
! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osplice(T_a,V_xs,V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)),
file('theBenchmark.p',fact_length__splice) ).
fof(fact_splice_Osimps_I3_J,axiom,
! [V_ys,V_y,V_xs,V_x,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Osplice(T_a,V_xs,V_ys))),
file('theBenchmark.p',fact_splice_Osimps_I3_J) ).
fof(fact_splice__Nil2,axiom,
! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs,
file('theBenchmark.p',fact_splice__Nil2) ).
fof(fact_list__ex1__simps_I1_J,axiom,
! [V_P_2,T_b] : ~ c_List_Olist__ex1(T_b,V_P_2,c_List_Olist_ONil(T_b)),
file('theBenchmark.p',fact_list__ex1__simps_I1_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_list__ex1__iff,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
<=> ? [B_x] :
( ! [B_y] :
( ( hBOOL(hAPP(V_P_2,B_y))
& hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) )
=> B_y = B_x )
& hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_list__ex1__iff) ).
fof(fact_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_acyclicP__converse,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Predicate_Oconversep(T_b,T_b,V_r_2))))
<=> c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
file('theBenchmark.p',fact_acyclicP__converse) ).
fof(fact_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_in__set__replicate,axiom,
! [V_y_2,V_na_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_na_2,V_y_2))))
<=> ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_in__set__replicate) ).
fof(fact_filter__replicate,axiom,
! [V_na_2,T_b,V_x_2,V_P_2] :
( ( ~ hBOOL(hAPP(V_P_2,V_x_2))
=> hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oreplicate(T_b,V_na_2,V_x_2)) = c_List_Olist_ONil(T_b) )
& ( hBOOL(hAPP(V_P_2,V_x_2))
=> hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oreplicate(T_b,V_na_2,V_x_2)) = c_List_Oreplicate(T_b,V_na_2,V_x_2) ) ),
file('theBenchmark.p',fact_filter__replicate) ).
fof(fact_concat__replicate__trivial,axiom,
! [V_i,T_a] : c_List_Oconcat(T_a,c_List_Oreplicate(tc_List_Olist(T_a),V_i,c_List_Olist_ONil(T_a))) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_concat__replicate__trivial) ).
fof(fact_replicate__empty,axiom,
! [V_x_2,V_na_2,T_b] :
( c_List_Oreplicate(T_b,V_na_2,V_x_2) = c_List_Olist_ONil(T_b)
<=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_replicate__empty) ).
fof(fact_empty__replicate,axiom,
! [V_x_2,V_na_2,T_b] :
( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_na_2,V_x_2)
<=> V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_empty__replicate) ).
fof(fact_replicate__0,axiom,
! [V_x,T_a] : c_List_Oreplicate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x) = c_List_Olist_ONil(T_a),
file('theBenchmark.p',fact_replicate__0) ).
fof(fact_map__replicate__const,axiom,
! [V_lst_2,V_k_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_k_2)),V_lst_2) = c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_lst_2),V_k_2),
file('theBenchmark.p',fact_map__replicate__const) ).
fof(fact_map__replicate,axiom,
! [V_x_2,V_na_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oreplicate(T_c,V_na_2,V_x_2)) = c_List_Oreplicate(T_b,V_na_2,hAPP(V_f_2,V_x_2)),
file('theBenchmark.p',fact_map__replicate) ).
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_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_take__replicate,axiom,
! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_k),V_x),
file('theBenchmark.p',fact_take__replicate) ).
fof(fact_hd__replicate,axiom,
! [V_x,T_a,V_n] :
( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ),
file('theBenchmark.p',fact_hd__replicate) ).
fof(fact_drop__replicate,axiom,
! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_k),V_i),V_x),
file('theBenchmark.p',fact_drop__replicate) ).
fof(fact_replicate__length__filter,axiom,
! [V_xs_2,V_x_2,T_b] : c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2)),V_x_2) = hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2),
file('theBenchmark.p',fact_replicate__length__filter) ).
fof(fact_zip__replicate,axiom,
! [V_y,V_j,V_x,V_i,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Oreplicate(T_a,V_i,V_x)),c_List_Oreplicate(T_b,V_j,V_y)) = c_List_Oreplicate(tc_prod(T_a,T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_j),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),
file('theBenchmark.p',fact_zip__replicate) ).
fof(fact_Ball__set__replicate,axiom,
! [V_P_2,V_a_2,V_na_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_na_2,V_a_2))))
=> hBOOL(hAPP(V_P_2,B_x)) )
<=> ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(V_P_2,V_a_2)) ) ),
file('theBenchmark.p',fact_Ball__set__replicate) ).
fof(fact_Bex__set__replicate,axiom,
! [V_P_2,V_a_2,V_na_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_na_2,V_a_2)))) )
<=> ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(V_P_2,V_a_2)) ) ),
file('theBenchmark.p',fact_Bex__set__replicate) ).
fof(fact_converse__join,axiom,
! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)),
file('theBenchmark.p',fact_converse__join) ).
fof(fact_conversepD,axiom,
! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ),
file('theBenchmark.p',fact_conversepD) ).
fof(fact_conversep_Ointros,axiom,
! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
=> hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ),
file('theBenchmark.p',fact_conversep_Ointros) ).
fof(fact_conversep_Oequations,axiom,
! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
<=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ),
file('theBenchmark.p',fact_conversep_Oequations) ).
fof(fact_conversep__iff,axiom,
! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
<=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ),
file('theBenchmark.p',fact_conversep__iff) ).
fof(fact_conversep__conversep,axiom,
! [V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Oconversep(T_b,T_c,V_r_2)) = V_r_2,
file('theBenchmark.p',fact_conversep__conversep) ).
fof(fact_conversep__eq,axiom,
! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal,
file('theBenchmark.p',fact_conversep__eq) ).
fof(fact_conversep__noteq,axiom,
! [V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot)),c_fequal)),V_x_2),V_y_2))
<=> V_x_2 != V_y_2 ),
file('theBenchmark.p',fact_conversep__noteq) ).
fof(fact_replicate__eq__replicate,axiom,
! [V_y_2,V_na_2,V_x_2,V_m_2,T_b] :
( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_na_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_na_2 ) ),
file('theBenchmark.p',fact_replicate__eq__replicate) ).
fof(fact_converse__pred__comp,axiom,
! [V_s_2,V_r_2,T_d,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Opred__comp(T_c,T_d,T_b,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_b,T_d,T_c,c_Predicate_Oconversep(T_d,T_b,V_s_2),c_Predicate_Oconversep(T_c,T_d,V_r_2)),
file('theBenchmark.p',fact_converse__pred__comp) ).
fof(fact_converse__meet,axiom,
! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)),
file('theBenchmark.p',fact_converse__meet) ).
fof(fact_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_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_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_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__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_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_conversep__converse__eq,axiom,
! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2),V_y_2))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ),
file('theBenchmark.p',fact_conversep__converse__eq) ).
fof(fact_map__replicate__trivial,axiom,
! [V_i_2,V_x_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_COMBK(T_b,tc_Nat_Onat),V_x_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2)) = c_List_Oreplicate(T_b,V_i_2,V_x_2),
file('theBenchmark.p',fact_map__replicate__trivial) ).
fof(fact_set__replicate__conv__if,axiom,
! [V_x_2,T_b,V_na_2] :
( ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_na_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
& ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_na_2,V_x_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('theBenchmark.p',fact_set__replicate__conv__if) ).
fof(fact_set__replicate,axiom,
! [V_x_2,T_b,V_na_2] :
( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_na_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ),
file('theBenchmark.p',fact_set__replicate) ).
fof(fact_set__replicate__Suc,axiom,
! [V_x_2,V_na_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,hAPP(c_Nat_OSuc,V_na_2),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
file('theBenchmark.p',fact_set__replicate__Suc) ).
fof(fact_eq__comp__r,axiom,
! [V_R_2,T_b] : c_Predicate_Opred__comp(T_b,T_b,T_b,c_fequal,c_Predicate_Opred__comp(T_b,T_b,T_b,V_R_2,c_fequal)) = V_R_2,
file('theBenchmark.p',fact_eq__comp__r) ).
fof(fact_lazy__sequence_Osize_I4_J,axiom,
! [V_lazy__sequence,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a,V_lazy__sequence)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_lazy__sequence)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_lazy__sequence_Osize_I4_J) ).
fof(fact__01,axiom,
! [V_yq,V_xq,V_x,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq),V_yq) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,c_Lazy__Sequence_Oappend(T_a,V_xq,V_yq)),
file('theBenchmark.p',fact__01) ).
fof(fact_lazy__sequence_Oinject,axiom,
! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] :
( c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_H_2,V_lazy__sequence_H_2)
<=> ( V_lazy__sequence_2 = V_lazy__sequence_H_2
& V_a_2 = V_a_H_2 ) ),
file('theBenchmark.p',fact_lazy__sequence_Oinject) ).
fof(fact_lazy__sequence_Osize_I2_J,axiom,
! [V_lazy__sequence_2,V_a_2,V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('theBenchmark.p',fact_lazy__sequence_Osize_I2_J) ).
fof(fact_size__code,axiom,
! [V_xq_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),T_b),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)),
file('theBenchmark.p',fact_size__code) ).
fof(fact_lazy__sequence__size__code,axiom,
! [V_xq_2,V_s_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_b,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_b),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)),
file('theBenchmark.p',fact_lazy__sequence__size__code) ).
fof(fact_seq__case,axiom,
! [V_xq_2,V_g_2,V_f_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f_2,V_g_2,V_xq_2) = c_Option_Ooption_Ooption__case(T_b,tc_prod(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c),T_b),V_g_2),hAPP(c_Lazy__Sequence_Oyield(T_c),V_xq_2)),
file('theBenchmark.p',fact_seq__case) ).
fof(fact_yieldn__def,axiom,
! [T_b] : c_Lazy__Sequence_Oyieldn(T_b) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_b),T_b,c_Lazy__Sequence_Oyield(T_b)),
file('theBenchmark.p',fact_yieldn__def) ).
fof(fact_lazy__sequence_Osimps_I5_J,axiom,
! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2),
file('theBenchmark.p',fact_lazy__sequence_Osimps_I5_J) ).
fof(fact_refl__on__INTER,axiom,
! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
=> c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
=> c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ),
file('theBenchmark.p',fact_refl__on__INTER) ).
fof(fact_in__set__member,axiom,
! [V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
<=> hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) ),
file('theBenchmark.p',fact_in__set__member) ).
fof(fact_member__rec_I2_J,axiom,
! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)),
file('theBenchmark.p',fact_member__rec_I2_J) ).
fof(fact_member__set,axiom,
! [T_b] : c_List_Omember(T_b) = c_List_Oset(T_b),
file('theBenchmark.p',fact_member__set) ).
fof(fact_member__rec_I1_J,axiom,
! [V_y_2,V_xs_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_List_Omember(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_y_2))
<=> ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2))
| V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_member__rec_I1_J) ).
fof(fact_List_Omember__def,axiom,
! [V_x_2,V_xs_2,T_b] :
( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2))
<=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
file('theBenchmark.p',fact_List_Omember__def) ).
fof(fact_list__ex1__iff__raw,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
<=> ? [B_x] :
( ! [B_y] :
( ( hBOOL(hAPP(V_P_2,B_y))
& hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2))) )
=> B_y = B_x )
& hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_list__ex1__iff__raw) ).
fof(fact_setsum__UNION__zero,axiom,
! [V_f_2,V_S_2,T_b,T_c] :
( class_Groups_Ocomm__monoid__add(T_c)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
=> ( ! [B_T1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2))
=> ! [B_T2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2))
=> ( B_T1 != B_T2
=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1))
=> ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2))
=> hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) )
=> hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2)),V_S_2) ) ) ) ),
file('theBenchmark.p',fact_setsum__UNION__zero) ).
fof(fact_THE__default__def,axiom,
! [V_d_2,T_b,V_P_2] :
( ( ~ ? [B_x] :
( ! [B_y] :
( hBOOL(hAPP(V_P_2,B_y))
=> B_y = B_x )
& hBOOL(hAPP(V_P_2,B_x)) )
=> c_FunDef_OTHE__default(T_b,V_d_2,V_P_2) = V_d_2 )
& ( ? [B_x] :
( ! [B_y] :
( hBOOL(hAPP(V_P_2,B_y))
=> B_y = B_x )
& hBOOL(hAPP(V_P_2,B_x)) )
=> c_FunDef_OTHE__default(T_b,V_d_2,V_P_2) = c_HOL_OThe(T_b,V_P_2) ) ),
file('theBenchmark.p',fact_THE__default__def) ).
fof(fact_INF2__I,axiom,
! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,T_b] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) )
=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_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_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
=> ~ ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ),
file('theBenchmark.p',fact_SUP2__E) ).
fof(fact_finite__maxlen,axiom,
! [V_M_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2))
=> ? [B_n] :
! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),B_x)),B_n)) ) ),
file('theBenchmark.p',fact_finite__maxlen) ).
fof(fact_lazy__sequence_Osize_I3_J,axiom,
! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_lazy__sequence_Osize_I3_J) ).
fof(fact_lazy__sequence_Osize_I1_J,axiom,
! [V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_lazy__sequence_Osize_I1_J) ).
fof(fact_lazy__sequence_Osimps_I4_J,axiom,
! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2,
file('theBenchmark.p',fact_lazy__sequence_Osimps_I4_J) ).
fof(fact_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_list__all__iff__all__interval__int,axiom,
! [V_j_2,V_i_2,V_P_2] :
( c_List_Olist__all(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2))
<=> c_List_Oall__interval__int(V_P_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_P_2] :
( c_List_Olist__ex(tc_Int_Oint,V_P_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_P_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_P_2] :
( c_List_Oall__interval__int(V_P_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_P_2,B_x)) ) ),
file('theBenchmark.p',fact_all__interval__int__def) ).
fof(fact_Image__Collect__split,axiom,
! [V_A_2,V_P_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2))),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_P_2)))),
file('theBenchmark.p',fact_Image__Collect__split) ).
fof(fact_lexord__trans,axiom,
! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_z_2)),c_List_Olexord(T_b,V_r_2)))
=> ( c_Relation_Otrans(T_b,V_r_2)
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_z_2)),c_List_Olexord(T_b,V_r_2))) ) ) ),
file('theBenchmark.p',fact_lexord__trans) ).
fof(fact_trans__less__than,axiom,
c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('theBenchmark.p',fact_trans__less__than) ).
fof(fact_trans__lex__prod,axiom,
! [V_R2_2,T_c,V_R1_2,T_b] :
( c_Relation_Otrans(T_b,V_R1_2)
=> ( c_Relation_Otrans(T_c,V_R2_2)
=> c_Relation_Otrans(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_R1_2,V_R2_2)) ) ),
file('theBenchmark.p',fact_trans__lex__prod) ).
fof(fact_Bex__set__list__ex,axiom,
! [V_P_2,V_xs_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
<=> c_List_Olist__ex(T_b,V_P_2,V_xs_2) ),
file('theBenchmark.p',fact_Bex__set__list__ex) ).
fof(fact_list__ex__iff__raw,axiom,
! [V_xs_2,V_P_2,T_b] :
( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
<=> ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
file('theBenchmark.p',fact_list__ex__iff__raw) ).
fof(fact_UN__eq,axiom,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))),
file('theBenchmark.p',fact_UN__eq) ).
fof(fact_trans__inv__image,axiom,
! [V_f_2,T_c,V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> c_Relation_Otrans(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ),
file('theBenchmark.p',fact_trans__inv__image) ).
fof(fact_trans__O__subset,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),V_r_2)),V_r_2)) ),
file('theBenchmark.p',fact_trans__O__subset) ).
fof(fact_bex__UNIV,axiom,
! [V_P_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
<=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ),
file('theBenchmark.p',fact_bex__UNIV) ).
fof(fact_finite__Collect__bex,axiom,
! [V_Q_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),V_Q_2)))))
<=> ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_x)))) ) ) ),
file('theBenchmark.p',fact_finite__Collect__bex) ).
fof(fact_listrel__trans,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ),
file('theBenchmark.p',fact_listrel__trans) ).
fof(fact_bex__empty,axiom,
! [V_P_2,T_b] :
~ ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ),
file('theBenchmark.p',fact_bex__empty) ).
fof(fact_trans__converse,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
<=> c_Relation_Otrans(T_b,V_r_2) ),
file('theBenchmark.p',fact_trans__converse) ).
fof(fact_lexord__transI,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olexord(T_b,V_r_2)) ),
file('theBenchmark.p',fact_lexord__transI) ).
fof(fact_trans__Id,axiom,
! [T_b] : c_Relation_Otrans(T_b,c_Relation_OId(T_b)),
file('theBenchmark.p',fact_trans__Id) ).
fof(fact_trans__trancl,axiom,
! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)),
file('theBenchmark.p',fact_trans__trancl) ).
fof(fact_trancl__id,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> c_Transitive__Closure_Otrancl(T_b,V_r_2) = V_r_2 ),
file('theBenchmark.p',fact_trancl__id) ).
fof(fact_trans__Id__on,axiom,
! [V_A_2,T_b] : c_Relation_Otrans(T_b,c_Relation_OId__on(T_b,V_A_2)),
file('theBenchmark.p',fact_trans__Id__on) ).
fof(fact_trans__finite__psubset,axiom,
! [T_b] : c_Relation_Otrans(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)),
file('theBenchmark.p',fact_trans__finite__psubset) ).
fof(fact_trans__rtrancl,axiom,
! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
file('theBenchmark.p',fact_trans__rtrancl) ).
fof(fact_transD,axiom,
! [V_c_2,V_b_2,V_a_2,V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),V_r_2)) ) ) ),
file('theBenchmark.p',fact_transD) ).
fof(fact_trans__def,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
<=> ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
=> ! [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_z)),V_r_2)) ) ) ),
file('theBenchmark.p',fact_trans__def) ).
fof(fact_trans__Int,axiom,
! [V_s_2,V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> ( c_Relation_Otrans(T_b,V_s_2)
=> c_Relation_Otrans(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
file('theBenchmark.p',fact_trans__Int) ).
fof(fact_SUPR__bool__eq,axiom,
! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_HOL_Obool) = c_Set_OBex(T_b),
file('theBenchmark.p',fact_SUPR__bool__eq) ).
fof(fact_trans__reflclI,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> c_Relation_Otrans(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ),
file('theBenchmark.p',fact_trans__reflclI) ).
fof(fact_Union__eq,axiom,
! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))),
file('theBenchmark.p',fact_Union__eq) ).
fof(fact_INT__eq,axiom,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))),
file('theBenchmark.p',fact_INT__eq) ).
fof(fact_Sup__apply,axiom,
! [V_x_2,V_A_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ),
file('theBenchmark.p',fact_Sup__apply) ).
fof(fact_Sup__fun__def,axiom,
! [V_x_2,V_A_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ),
file('theBenchmark.p',fact_Sup__fun__def) ).
fof(fact_Inf__apply,axiom,
! [V_x_2,V_A_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ),
file('theBenchmark.p',fact_Inf__apply) ).
fof(fact_Inf__fun__def,axiom,
! [V_x_2,V_A_2,T_c,T_b] :
( class_Complete__Lattice_Ocomplete__lattice(T_b)
=> hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ),
file('theBenchmark.p',fact_Inf__fun__def) ).
fof(fact_max__extp_Ointros,axiom,
! [V_R_2,V_Y_2,V_X_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
=> ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
=> ? [B_xa] :
( hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) ) )
=> c_Wellfounded_Omax__extp(T_b,V_R_2,V_X_2,V_Y_2) ) ) ) ),
file('theBenchmark.p',fact_max__extp_Ointros) ).
fof(fact_transp__def,axiom,
! [V_r_2,T_b] :
( c_Predicate_Otransp(T_b,V_r_2)
<=> c_Relation_Otrans(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
file('theBenchmark.p',fact_transp__def) ).
fof(fact_transpE,axiom,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
( c_Predicate_Otransp(T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2))
=> hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)) ) ) ),
file('theBenchmark.p',fact_transpE) ).
fof(fact_equivp__reflp__symp__transp,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
<=> ( c_Predicate_Otransp(T_b,V_R_2)
& c_Predicate_Osymp(T_b,V_R_2)
& c_Predicate_Oreflp(T_b,V_R_2) ) ),
file('theBenchmark.p',fact_equivp__reflp__symp__transp) ).
fof(fact_equivpI,axiom,
! [V_R_2,T_b] :
( c_Predicate_Oreflp(T_b,V_R_2)
=> ( c_Predicate_Osymp(T_b,V_R_2)
=> ( c_Predicate_Otransp(T_b,V_R_2)
=> c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ) ),
file('theBenchmark.p',fact_equivpI) ).
fof(fact_sympE,axiom,
! [V_y_2,V_x_2,V_r_2,T_b] :
( c_Predicate_Osymp(T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_sympE) ).
fof(fact_equivpE,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
=> ~ ( c_Predicate_Oreflp(T_b,V_R_2)
=> ( c_Predicate_Osymp(T_b,V_R_2)
=> ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ),
file('theBenchmark.p',fact_equivpE) ).
fof(fact_max__extp_Osimps,axiom,
! [V_a2_2,V_a1_2,V_R_2,T_b] :
( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
<=> ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
=> ? [B_xa] :
( hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) ) )
& V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) ) ),
file('theBenchmark.p',fact_max__extp_Osimps) ).
fof(fact_trans__diff__Id,axiom,
! [V_r_2,T_b] :
( c_Relation_Otrans(T_b,V_r_2)
=> ( c_Relation_Oantisym(T_b,V_r_2)
=> c_Relation_Otrans(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ) ),
file('theBenchmark.p',fact_trans__diff__Id) ).
fof(fact_antisym__subset,axiom,
! [V_s_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
=> ( c_Relation_Oantisym(T_b,V_s_2)
=> c_Relation_Oantisym(T_b,V_r_2) ) ),
file('theBenchmark.p',fact_antisym__subset) ).
fof(fact_antisym__Id__on,axiom,
! [V_A_2,T_b] : c_Relation_Oantisym(T_b,c_Relation_OId__on(T_b,V_A_2)),
file('theBenchmark.p',fact_antisym__Id__on) ).
fof(fact_antisym__Id,axiom,
! [T_b] : c_Relation_Oantisym(T_b,c_Relation_OId(T_b)),
file('theBenchmark.p',fact_antisym__Id) ).
fof(fact_antisym__converse,axiom,
! [V_r_2,T_b] :
( c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
<=> c_Relation_Oantisym(T_b,V_r_2) ),
file('theBenchmark.p',fact_antisym__converse) ).
fof(fact_antisym__empty,axiom,
! [T_b] : c_Relation_Oantisym(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),
file('theBenchmark.p',fact_antisym__empty) ).
fof(fact_antisymD,axiom,
! [V_b_2,V_a_2,V_r_2,T_b] :
( c_Relation_Oantisym(T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),V_r_2))
=> V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_antisymD) ).
fof(fact_antisym__def,axiom,
! [V_r_2,T_b] :
( c_Relation_Oantisym(T_b,V_r_2)
<=> ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
=> B_x = B_y ) ) ),
file('theBenchmark.p',fact_antisym__def) ).
fof(fact_antisym__reflcl,axiom,
! [V_r_2,T_b] :
( c_Relation_Oantisym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
<=> c_Relation_Oantisym(T_b,V_r_2) ),
file('theBenchmark.p',fact_antisym__reflcl) ).
fof(fact_acyclic__impl__antisym__rtrancl,axiom,
! [V_r_2,T_b] :
( c_Wellfounded_Oacyclic(T_b,V_r_2)
=> c_Relation_Oantisym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ),
file('theBenchmark.p',fact_acyclic__impl__antisym__rtrancl) ).
fof(fact_fun__lub__def,axiom,
! [V_x_2,V_A_2,V_L_2,T_d,T_b,T_c] : c_Partial__Function_Ofun__lub(T_c,T_b,T_d,V_L_2,V_A_2,V_x_2) = hAPP(V_L_2,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_fun(T_d,T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),T_c),hAPP(c_COMBS(tc_fun(T_d,T_c),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_d,T_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_d,T_c))),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,tc_fun(T_d,T_c))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),T_d,T_c),c_COMBI(tc_fun(T_d,T_c))),V_x_2)))))),
file('theBenchmark.p',fact_fun__lub__def) ).
fof(fact_sym__trans__comp__subset,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> ( c_Relation_Otrans(T_b,V_r_2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_sym__trans__comp__subset) ).
fof(fact_sym__inv__image,axiom,
! [V_f_2,T_c,V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> c_Relation_Osym(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ),
file('theBenchmark.p',fact_sym__inv__image) ).
fof(fact_sym__Int__converse,axiom,
! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))),
file('theBenchmark.p',fact_sym__Int__converse) ).
fof(fact_listrel__sym,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> c_Relation_Osym(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ),
file('theBenchmark.p',fact_listrel__sym) ).
fof(fact_sym__converse,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
<=> c_Relation_Osym(T_b,V_r_2) ),
file('theBenchmark.p',fact_sym__converse) ).
fof(fact_sym__conv__converse__eq,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
<=> hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) = V_r_2 ),
file('theBenchmark.p',fact_sym__conv__converse__eq) ).
fof(fact_sym__Id,axiom,
! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)),
file('theBenchmark.p',fact_sym__Id) ).
fof(fact_sym__Un,axiom,
! [V_s_2,V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> ( c_Relation_Osym(T_b,V_s_2)
=> c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
file('theBenchmark.p',fact_sym__Un) ).
fof(fact_sym__trancl,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> c_Relation_Osym(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ),
file('theBenchmark.p',fact_sym__trancl) ).
fof(fact_sym__Id__on,axiom,
! [V_A_2,T_b] : c_Relation_Osym(T_b,c_Relation_OId__on(T_b,V_A_2)),
file('theBenchmark.p',fact_sym__Id__on) ).
fof(fact_sym__rtrancl,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> c_Relation_Osym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ),
file('theBenchmark.p',fact_sym__rtrancl) ).
fof(fact_symD,axiom,
! [V_b_2,V_a_2,V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),V_r_2)) ) ),
file('theBenchmark.p',fact_symD) ).
fof(fact_sym__def,axiom,
! [V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
<=> ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) ) ),
file('theBenchmark.p',fact_sym__def) ).
fof(fact_sym__Un__converse,axiom,
! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))),
file('theBenchmark.p',fact_sym__Un__converse) ).
fof(fact_sym__Int,axiom,
! [V_s_2,V_r_2,T_b] :
( c_Relation_Osym(T_b,V_r_2)
=> ( c_Relation_Osym(T_b,V_s_2)
=> c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
file('theBenchmark.p',fact_sym__Int) ).
fof(fact_equivE,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
=> ~ ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> ( c_Relation_Osym(T_b,V_r_2)
=> ~ c_Relation_Otrans(T_b,V_r_2) ) ) ),
file('theBenchmark.p',fact_equivE) ).
fof(fact_equivI,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
=> ( c_Relation_Osym(T_b,V_r_2)
=> ( c_Relation_Otrans(T_b,V_r_2)
=> c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ),
file('theBenchmark.p',fact_equivI) ).
fof(fact_equiv__def,axiom,
! [V_r_2,V_A_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
<=> ( c_Relation_Otrans(T_b,V_r_2)
& c_Relation_Osym(T_b,V_r_2)
& c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ),
file('theBenchmark.p',fact_equiv__def) ).
fof(fact_symp__def,axiom,
! [V_r_2,T_b] :
( c_Predicate_Osymp(T_b,V_r_2)
<=> c_Relation_Osym(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ),
file('theBenchmark.p',fact_symp__def) ).
fof(fact_part__equivp__refl__symp__transp,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
<=> ( c_Predicate_Otransp(T_b,V_R_2)
& c_Predicate_Osymp(T_b,V_R_2)
& ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) ) ),
file('theBenchmark.p',fact_part__equivp__refl__symp__transp) ).
fof(fact_part__equivpI,axiom,
! [T_b,V_R_2] :
( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
=> ( c_Predicate_Osymp(T_b,V_R_2)
=> ( c_Predicate_Otransp(T_b,V_R_2)
=> c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ) ),
file('theBenchmark.p',fact_part__equivpI) ).
fof(fact_equivp__implies__part__equivp,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Oequivp(T_b,V_R_2)
=> c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ),
file('theBenchmark.p',fact_equivp__implies__part__equivp) ).
fof(fact_part__equivp__def,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
<=> ( ! [B_x,B_y] :
( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
<=> ( hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y)
& hBOOL(hAPP(hAPP(V_R_2,B_y),B_y))
& hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) ) )
& ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x)) ) ),
file('theBenchmark.p',fact_part__equivp__def) ).
fof(fact_part__equivp__symp,axiom,
! [V_y_2,V_x_2,V_R_2,T_b] :
( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
=> ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
=> hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ),
file('theBenchmark.p',fact_part__equivp__symp) ).
fof(fact_part__equivp__transp,axiom,
! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
=> ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
=> ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ),
file('theBenchmark.p',fact_part__equivp__transp) ).
fof(fact_part__equivpE,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
=> ~ ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
=> ( c_Predicate_Osymp(T_b,V_R_2)
=> ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ),
file('theBenchmark.p',fact_part__equivpE) ).
fof(fact_part__equivp__typedef,axiom,
! [V_R_2,T_b] :
( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
=> ? [B_d] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBS(T_b,T_b,tc_HOL_Obool),V_R_2),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_fequal)),V_R_2))))) ),
file('theBenchmark.p',fact_part__equivp__typedef) ).
fof(fact_inv__o__cancel,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ),
file('theBenchmark.p',fact_inv__o__cancel) ).
fof(fact_inj__iff,axiom,
! [V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
<=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ),
file('theBenchmark.p',fact_inj__iff) ).
fof(fact_image__inv__into__cancel,axiom,
! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2))
=> hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2)),V_B_H_2)) = V_B_H_2 ) ),
file('theBenchmark.p',fact_image__inv__into__cancel) ).
fof(fact_surj__iff__all,axiom,
! [V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
<=> ! [B_x] : hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),B_x)) = B_x ),
file('theBenchmark.p',fact_surj__iff__all) ).
fof(fact_surj__f__inv__f,axiom,
! [V_y_2,V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),V_y_2)) = V_y_2 ),
file('theBenchmark.p',fact_surj__f__inv__f) ).
fof(fact_image__surj__f__inv__f,axiom,
! [V_A_2,V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
=> hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),V_A_2)) = V_A_2 ),
file('theBenchmark.p',fact_image__surj__f__inv__f) ).
fof(fact_f__inv__into__f,axiom,
! [V_A_2,V_f_2,T_c,V_y_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
=> hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ),
file('theBenchmark.p',fact_f__inv__into__f) ).
fof(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_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_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_Q_2,V_P_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_P_2),V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)),
file('theBenchmark.p',help_c__COMBB__1) ).
fof(help_c__COMBC__1,axiom,
! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2),
file('theBenchmark.p',help_c__COMBC__1) ).
fof(help_c__COMBS__1,axiom,
! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_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_P_2] :
( ~ hBOOL(V_P_2)
| ~ hBOOL(hAPP(c_fNot,V_P_2)) ),
file('theBenchmark.p',help_c__fNot__1) ).
fof(help_c__fNot__2,axiom,
! [V_P_2] :
( hBOOL(hAPP(c_fNot,V_P_2))
| ~ ~ hBOOL(V_P_2) ),
file('theBenchmark.p',help_c__fNot__2) ).
fof(help_c__fconj__1,axiom,
! [V_Q_2,V_P_2] :
( hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
| ~ hBOOL(V_Q_2)
| ~ hBOOL(V_P_2) ),
file('theBenchmark.p',help_c__fconj__1) ).
fof(help_c__fconj__2,axiom,
! [V_Q_2,V_P_2] :
( hBOOL(V_P_2)
| ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ),
file('theBenchmark.p',help_c__fconj__2) ).
fof(help_c__fconj__3,axiom,
! [V_Q_2,V_P_2] :
( hBOOL(V_Q_2)
| ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ),
file('theBenchmark.p',help_c__fconj__3) ).
fof(help_c__fdisj__1,axiom,
! [V_Q_2,V_P_2] :
( hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
| ~ hBOOL(V_P_2) ),
file('theBenchmark.p',help_c__fdisj__1) ).
fof(help_c__fdisj__2,axiom,
! [V_P_2,V_Q_2] :
( hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
| ~ hBOOL(V_Q_2) ),
file('theBenchmark.p',help_c__fdisj__2) ).
fof(help_c__fdisj__3,axiom,
! [V_Q_2,V_P_2] :
( hBOOL(V_Q_2)
| hBOOL(V_P_2)
| ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ),
file('theBenchmark.p',help_c__fdisj__3) ).
fof(help_c__fimplies__1,axiom,
! [V_Q_2,V_P_2] :
( hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
| hBOOL(V_P_2) ),
file('theBenchmark.p',help_c__fimplies__1) ).
fof(help_c__fimplies__2,axiom,
! [V_P_2,V_Q_2] :
( hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
| ~ hBOOL(V_Q_2) ),
file('theBenchmark.p',help_c__fimplies__2) ).
fof(help_c__fimplies__3,axiom,
! [V_Q_2,V_P_2] :
( hBOOL(V_Q_2)
| ~ hBOOL(V_P_2)
| ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ),
file('theBenchmark.p',help_c__fimplies__3) ).
fof(conj_0,hypothesis,
! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),B_x) ),
file('theBenchmark.p',conj_0) ).
fof(conj_1,conjecture,
! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,B_x) ),
file('theBenchmark.p',conj_1) ).
fof(f_1_1,plain,
! [V_g_2,V_f_2] :
( V_f_2 = V_g_2
| ? [B_x] : hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x) ),
inference(fof_nnf,[status(thm)],[fact_ext]) ).
fof(f_1_2,plain,
! [U_2,U_1] :
( U_1 = U_2
| ? [U_0] : hAPP(U_1,U_0) != hAPP(U_2,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_2,U_1] :
( U_1 = U_2
| hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_2,U_1))],[f_1_2]) ).
cnf(f_1_4,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_3]) ).
fof(f_2_1,plain,
! [V_t,V_n,T_a] :
( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t)
| ~ c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t) ),
inference(fof_nnf,[status(thm)],[fact_triple__valid__Suc]) ).
fof(f_2_2,plain,
! [U_5,U_4,U_3] :
( c_Hoare__Mirabelle_Otriple__valid(U_3,U_4,U_5)
| ~ c_Hoare__Mirabelle_Otriple__valid(U_3,hAPP(c_Nat_OSuc,U_4),U_5) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( c_Hoare__Mirabelle_Otriple__valid(U_3,U_4,U_5)
| ~ c_Hoare__Mirabelle_Otriple__valid(U_3,hAPP(c_Nat_OSuc,U_4),U_5) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [V_tsa_2,V_G_2,T_b] :
( ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_G_2,V_tsa_2)
| ? [B_n] :
( ? [B_x] :
( ~ c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2)) )
& ! [B_x] :
( c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_G_2)) ) ) )
& ( ! [B_n] :
( ! [B_x] :
( c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2)) )
| ? [B_x] :
( ~ c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_G_2)) ) )
| ~ c_Hoare__Mirabelle_Ohoare__valids(T_b,V_G_2,V_tsa_2) ) ),
inference(fof_nnf,[status(thm)],[fact_hoare__valids__def]) ).
fof(f_3_2,plain,
! [U_14,U_13,U_12] :
( ( c_Hoare__Mirabelle_Ohoare__valids(U_12,U_13,U_14)
| ? [U_11] :
( ? [U_10] :
( ~ c_Hoare__Mirabelle_Otriple__valid(U_12,U_11,U_10)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_12)),U_10),U_14)) )
& ! [U_9] :
( c_Hoare__Mirabelle_Otriple__valid(U_12,U_11,U_9)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_12)),U_9),U_13)) ) ) )
& ( ! [U_8] :
( ! [U_7] :
( c_Hoare__Mirabelle_Otriple__valid(U_12,U_8,U_7)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_12)),U_7),U_14)) )
| ? [U_6] :
( ~ c_Hoare__Mirabelle_Otriple__valid(U_12,U_8,U_6)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_12)),U_6),U_13)) ) )
| ~ c_Hoare__Mirabelle_Ohoare__valids(U_12,U_13,U_14) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_20,U_18,U_16] :
( c_Hoare__Mirabelle_Ohoare__valids(U_16,U_18,U_20)
| ? [U_11] :
( ? [U_10] :
( ~ c_Hoare__Mirabelle_Otriple__valid(U_16,U_11,U_10)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_16)),U_10),U_20)) )
& ! [U_9] :
( c_Hoare__Mirabelle_Otriple__valid(U_16,U_11,U_9)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_16)),U_9),U_18)) ) ) )
& ! [U_19,U_17,U_15] :
( ! [U_8] :
( ! [U_7] :
( c_Hoare__Mirabelle_Otriple__valid(U_15,U_8,U_7)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15)),U_7),U_19)) )
| ? [U_6] :
( ~ c_Hoare__Mirabelle_Otriple__valid(U_15,U_8,U_6)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15)),U_6),U_17)) ) )
| ~ c_Hoare__Mirabelle_Ohoare__valids(U_15,U_17,U_19) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_20,U_18,U_16] :
( c_Hoare__Mirabelle_Ohoare__valids(U_16,U_18,U_20)
| ? [U_11] :
( ? [U_10] :
( ~ c_Hoare__Mirabelle_Otriple__valid(U_16,U_11,U_10)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_16)),U_10),U_20)) )
& ! [U_9] :
( c_Hoare__Mirabelle_Otriple__valid(U_16,U_11,U_9)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_16)),U_9),U_18)) ) ) )
& ! [U_19,U_17,U_15] :
( ! [U_8] :
( ! [U_7] :
( c_Hoare__Mirabelle_Otriple__valid(U_15,U_8,U_7)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15)),U_7),U_19)) )
| ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15,U_8,sK2(U_19,U_17,U_15,U_8))
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15)),sK2(U_19,U_17,U_15,U_8)),U_17)) ) )
| ~ c_Hoare__Mirabelle_Ohoare__valids(U_15,U_17,U_19) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_6,sK2(U_19,U_17,U_15,U_8))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_20,U_18,U_16] :
( c_Hoare__Mirabelle_Ohoare__valids(U_16,U_18,U_20)
| ( ? [U_10] :
( ~ c_Hoare__Mirabelle_Otriple__valid(U_16,sK3(U_20,U_18,U_16),U_10)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_16)),U_10),U_20)) )
& ! [U_9] :
( c_Hoare__Mirabelle_Otriple__valid(U_16,sK3(U_20,U_18,U_16),U_9)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_16)),U_9),U_18)) ) ) )
& ! [U_19,U_17,U_15] :
( ! [U_8] :
( ! [U_7] :
( c_Hoare__Mirabelle_Otriple__valid(U_15,U_8,U_7)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15)),U_7),U_19)) )
| ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15,U_8,sK2(U_19,U_17,U_15,U_8))
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15)),sK2(U_19,U_17,U_15,U_8)),U_17)) ) )
| ~ c_Hoare__Mirabelle_Ohoare__valids(U_15,U_17,U_19) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_11,sK3(U_20,U_18,U_16))],[f_3_4]) ).
fof(f_3_6,plain,
( ! [U_20,U_18,U_16] :
( c_Hoare__Mirabelle_Ohoare__valids(U_16,U_18,U_20)
| ( ~ c_Hoare__Mirabelle_Otriple__valid(U_16,sK3(U_20,U_18,U_16),sK4(U_20,U_18,U_16))
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_16)),sK4(U_20,U_18,U_16)),U_20))
& ! [U_9] :
( c_Hoare__Mirabelle_Otriple__valid(U_16,sK3(U_20,U_18,U_16),U_9)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_16)),U_9),U_18)) ) ) )
& ! [U_19,U_17,U_15] :
( ! [U_8] :
( ! [U_7] :
( c_Hoare__Mirabelle_Otriple__valid(U_15,U_8,U_7)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15)),U_7),U_19)) )
| ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15,U_8,sK2(U_19,U_17,U_15,U_8))
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15)),sK2(U_19,U_17,U_15,U_8)),U_17)) ) )
| ~ c_Hoare__Mirabelle_Ohoare__valids(U_15,U_17,U_19) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_10,sK4(U_20,U_18,U_16))],[f_3_5]) ).
cnf(f_3_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15)),sK2(U_19,U_17,U_15,U_8)),U_17))
| c_Hoare__Mirabelle_Otriple__valid(U_15,U_8,U_7)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15)),U_7),U_19))
| ~ c_Hoare__Mirabelle_Ohoare__valids(U_15,U_17,U_19) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_8,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(U_15,U_8,sK2(U_19,U_17,U_15,U_8))
| c_Hoare__Mirabelle_Otriple__valid(U_15,U_8,U_7)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15)),U_7),U_19))
| ~ c_Hoare__Mirabelle_Ohoare__valids(U_15,U_17,U_19) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_9,plain,
( c_Hoare__Mirabelle_Otriple__valid(U_16,sK3(U_20,U_18,U_16),U_9)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_16)),U_9),U_18))
| c_Hoare__Mirabelle_Ohoare__valids(U_16,U_18,U_20) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_16)),sK4(U_20,U_18,U_16)),U_20))
| c_Hoare__Mirabelle_Ohoare__valids(U_16,U_18,U_20) ),
inference(clausify,[status(thm)],[f_3_6]) ).
cnf(f_3_11,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(U_16,sK3(U_20,U_18,U_16),sK4(U_20,U_18,U_16))
| c_Hoare__Mirabelle_Ohoare__valids(U_16,U_18,U_20) ),
inference(clausify,[status(thm)],[f_3_6]) ).
fof(f_4_1,plain,
! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n),
inference(fof_nnf,[status(thm)],[fact_n__not__Suc__n]) ).
fof(f_4_2,plain,
! [U_21] : U_21 != hAPP(c_Nat_OSuc,U_21),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
U_21 != hAPP(c_Nat_OSuc,U_21),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n,
inference(fof_nnf,[status(thm)],[fact_Suc__n__not__n]) ).
fof(f_5_2,plain,
! [U_22] : hAPP(c_Nat_OSuc,U_22) != U_22,
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
hAPP(c_Nat_OSuc,U_22) != U_22,
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_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_6_2,plain,
! [U_24,U_23] :
( ( hAPP(c_Nat_OSuc,U_23) = hAPP(c_Nat_OSuc,U_24)
| U_23 != U_24 )
& ( U_23 = U_24
| hAPP(c_Nat_OSuc,U_23) != hAPP(c_Nat_OSuc,U_24) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_28,U_26] :
( hAPP(c_Nat_OSuc,U_26) = hAPP(c_Nat_OSuc,U_28)
| U_26 != U_28 )
& ! [U_27,U_25] :
( U_25 = U_27
| hAPP(c_Nat_OSuc,U_25) != hAPP(c_Nat_OSuc,U_27) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( U_25 = U_27
| hAPP(c_Nat_OSuc,U_25) != hAPP(c_Nat_OSuc,U_27) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( hAPP(c_Nat_OSuc,U_26) = hAPP(c_Nat_OSuc,U_28)
| U_26 != U_28 ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_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_7_2,plain,
! [U_30,U_29] :
( U_29 = U_30
| hAPP(c_Nat_OSuc,U_29) != hAPP(c_Nat_OSuc,U_30) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( U_29 = U_30
| hAPP(c_Nat_OSuc,U_29) != hAPP(c_Nat_OSuc,U_30) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [V_i_2,V_na_2,V_inc_2,T_b] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,hAPP(c_Nat_OSuc,V_na_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,V_na_2,hAPP(V_inc_2,V_i_2))
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I2_J]) ).
fof(f_8_2,plain,
! [U_34,U_33,U_32,U_31] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(U_31,U_32,hAPP(c_Nat_OSuc,U_33),U_34) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_31,U_32,U_33,hAPP(U_32,U_34))
| ~ class_Rings_Osemiring__1(U_31) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(U_31,U_32,hAPP(c_Nat_OSuc,U_33),U_34) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_31,U_32,U_33,hAPP(U_32,U_34))
| ~ class_Rings_Osemiring__1(U_31) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [V_na_2,V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),hAPP(c_Nat_OSuc,V_na_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),V_na_2)),
inference(fof_nnf,[status(thm)],[fact_power_Opower_Opower__Suc]) ).
fof(f_9_2,plain,
! [U_39,U_38,U_37,U_36,U_35] : hAPP(hAPP(c_Power_Opower_Opower(U_35,U_36,U_37),U_38),hAPP(c_Nat_OSuc,U_39)) = hAPP(hAPP(U_37,U_38),hAPP(hAPP(c_Power_Opower_Opower(U_35,U_36,U_37),U_38),U_39)),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
hAPP(hAPP(c_Power_Opower_Opower(U_35,U_36,U_37),U_38),hAPP(c_Nat_OSuc,U_39)) = hAPP(hAPP(U_37,U_38),hAPP(hAPP(c_Power_Opower_Opower(U_35,U_36,U_37),U_38),U_39)),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [V_nat_2,V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2),
inference(fof_nnf,[status(thm)],[fact_nat__case__Suc]) ).
fof(f_10_2,plain,
! [U_43,U_42,U_41,U_40] : c_Nat_Onat_Onat__case(U_40,U_41,U_42,hAPP(c_Nat_OSuc,U_43)) = hAPP(U_42,U_43),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
c_Nat_Onat_Onat__case(U_40,U_41,U_42,hAPP(c_Nat_OSuc,U_43)) = hAPP(U_42,U_43),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [V_nat_2,V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(hAPP(V_f2_2,V_nat_2),hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),V_nat_2)),
inference(fof_nnf,[status(thm)],[fact_nat__rec__Suc]) ).
fof(f_11_2,plain,
! [U_47,U_46,U_45,U_44] : hAPP(c_Nat_Onat_Onat__rec(U_44,U_45,U_46),hAPP(c_Nat_OSuc,U_47)) = hAPP(hAPP(U_46,U_47),hAPP(c_Nat_Onat_Onat__rec(U_44,U_45,U_46),U_47)),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
hAPP(c_Nat_Onat_Onat__rec(U_44,U_45,U_46),hAPP(c_Nat_OSuc,U_47)) = hAPP(hAPP(U_46,U_47),hAPP(c_Nat_Onat_Onat__rec(U_44,U_45,U_46),U_47)),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b),
inference(fof_nnf,[status(thm)],[fact_INFI__bool__eq]) ).
fof(f_12_2,plain,
! [U_48] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_48,tc_HOL_Obool) = c_Set_OBall(U_48),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_48,tc_HOL_Obool) = c_Set_OBall(U_48),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),
inference(fof_nnf,[status(thm)],[fact_mono__Suc]) ).
cnf(f_13_2,plain,
c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
! [V_f_2,T_b] :
( ( ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,T_b,V_f_2)
| ? [B_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n)))) )
& ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n))))
| ~ c_Orderings_Oorder__class_Omono(tc_Nat_Onat,T_b,V_f_2) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mono__iff__le__Suc]) ).
fof(f_14_2,plain,
! [U_52,U_51] :
( ( ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,U_51,U_52)
| ? [U_50] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_51),hAPP(U_52,U_50)),hAPP(U_52,hAPP(c_Nat_OSuc,U_50)))) )
& ( ! [U_49] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_51),hAPP(U_52,U_49)),hAPP(U_52,hAPP(c_Nat_OSuc,U_49))))
| ~ c_Orderings_Oorder__class_Omono(tc_Nat_Onat,U_51,U_52) ) )
| ~ class_Orderings_Oorder(U_51) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_52,U_51] :
( ( ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,U_51,U_52)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_51),hAPP(U_52,sK5(U_52,U_51))),hAPP(U_52,hAPP(c_Nat_OSuc,sK5(U_52,U_51))))) )
& ( ! [U_49] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_51),hAPP(U_52,U_49)),hAPP(U_52,hAPP(c_Nat_OSuc,U_49))))
| ~ c_Orderings_Oorder__class_Omono(tc_Nat_Onat,U_51,U_52) ) )
| ~ class_Orderings_Oorder(U_51) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_50,sK5(U_52,U_51))],[f_14_2]) ).
cnf(f_14_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_51),hAPP(U_52,U_49)),hAPP(U_52,hAPP(c_Nat_OSuc,U_49))))
| ~ c_Orderings_Oorder__class_Omono(tc_Nat_Onat,U_51,U_52)
| ~ class_Orderings_Oorder(U_51) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,U_51,U_52)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_51),hAPP(U_52,sK5(U_52,U_51))),hAPP(U_52,hAPP(c_Nat_OSuc,sK5(U_52,U_51)))))
| ~ class_Orderings_Oorder(U_51) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [V_na_2,V_h_2,V_c_2,T_b,V_f_2] :
( hAPP(V_f_2,hAPP(c_Nat_OSuc,V_na_2)) = hAPP(hAPP(V_h_2,V_na_2),hAPP(V_f_2,V_na_2))
| ? [B_n] : hAPP(V_f_2,B_n) != hAPP(c_Nat_Onat_Onat__rec(T_b,V_c_2,V_h_2),B_n) ),
inference(fof_nnf,[status(thm)],[fact_def__nat__rec__Suc]) ).
fof(f_15_2,plain,
! [U_58,U_57,U_56,U_55,U_54] :
( hAPP(U_54,hAPP(c_Nat_OSuc,U_58)) = hAPP(hAPP(U_57,U_58),hAPP(U_54,U_58))
| ? [U_53] : hAPP(U_54,U_53) != hAPP(c_Nat_Onat_Onat__rec(U_55,U_56,U_57),U_53) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_58,U_57,U_56,U_55,U_54] :
( hAPP(U_54,hAPP(c_Nat_OSuc,U_58)) = hAPP(hAPP(U_57,U_58),hAPP(U_54,U_58))
| hAPP(U_54,sK6(U_58,U_57,U_56,U_55,U_54)) != hAPP(c_Nat_Onat_Onat__rec(U_55,U_56,U_57),sK6(U_58,U_57,U_56,U_55,U_54)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_53,sK6(U_58,U_57,U_56,U_55,U_54))],[f_15_2]) ).
cnf(f_15_4,plain,
( hAPP(U_54,hAPP(c_Nat_OSuc,U_58)) = hAPP(hAPP(U_57,U_58),hAPP(U_54,U_58))
| hAPP(U_54,sK6(U_58,U_57,U_56,U_55,U_54)) != hAPP(c_Nat_Onat_Onat__rec(U_55,U_56,U_57),sK6(U_58,U_57,U_56,U_55,U_54)) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [V_i_2,V_inc_2,T_b] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I1_J]) ).
fof(f_16_2,plain,
! [U_61,U_60,U_59] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(U_59,U_60,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_61) = U_61
| ~ class_Rings_Osemiring__1(U_59) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( c_Nat_Osemiring__1__class_Oof__nat__aux(U_59,U_60,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_61) = U_61
| ~ class_Rings_Osemiring__1(U_59) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2,
inference(fof_nnf,[status(thm)],[fact_power_Opower_Opower__0]) ).
fof(f_17_2,plain,
! [U_65,U_64,U_63,U_62] : hAPP(hAPP(c_Power_Opower_Opower(U_62,U_63,U_64),U_65),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_63,
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
hAPP(hAPP(c_Power_Opower_Opower(U_62,U_63,U_64),U_65),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_63,
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2,
inference(fof_nnf,[status(thm)],[fact_nat__rec__0]) ).
fof(f_18_2,plain,
! [U_68,U_67,U_66] : hAPP(c_Nat_Onat_Onat__rec(U_66,U_67,U_68),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_67,
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
hAPP(c_Nat_Onat_Onat__rec(U_66,U_67,U_68),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_67,
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2,
inference(fof_nnf,[status(thm)],[fact_nat__case__0]) ).
fof(f_19_2,plain,
! [U_71,U_70,U_69] : c_Nat_Onat_Onat__case(U_69,U_70,U_71,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_70,
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
c_Nat_Onat_Onat__case(U_69,U_70,U_71,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_70,
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_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_20_2,plain,
! [U_73,U_72] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_72)),hAPP(c_Nat_OSuc,U_73)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_72),U_73)) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_72)),hAPP(c_Nat_OSuc,U_73)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_72),U_73)) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_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_21_2,plain,
! [U_74] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_74),hAPP(c_Nat_OSuc,U_74))),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_74),hAPP(c_Nat_OSuc,U_74))),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [V_f_2,T_b,T_c] :
( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
| ~ c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
| ~ class_Orderings_Oorder(T_b)
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_strict__mono__mono]) ).
fof(f_22_2,plain,
! [U_77,U_76,U_75] :
( c_Orderings_Oorder__class_Omono(U_76,U_75,U_77)
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_76,U_75,U_77)
| ~ class_Orderings_Oorder(U_76)
| ~ class_Orderings_Oorder(U_75) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( c_Orderings_Oorder__class_Omono(U_76,U_75,U_77)
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_76,U_75,U_77)
| ~ class_Orderings_Oorder(U_76)
| ~ class_Orderings_Oorder(U_75) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_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_23_2,plain,
! [U_78] : hAPP(c_Nat_OSuc,U_78) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
hAPP(c_Nat_OSuc,U_78) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_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_24_2,plain,
! [U_79] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_79),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_79),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_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_25_2,plain,
! [U_80] : hAPP(c_Nat_OSuc,U_80) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
hAPP(c_Nat_OSuc,U_80) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_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_26_2,plain,
! [U_82,U_81] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_81),U_82),U_82))
| ~ class_Orderings_Opreorder(U_81) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_81),U_82),U_82))
| ~ class_Orderings_Opreorder(U_81) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_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_27_2,plain,
! [U_83] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_83)),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_83)),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_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_28_2,plain,
! [U_84] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_84),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_84),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_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_29_2,plain,
! [U_85] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_85))),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,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_85))),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_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_30_2,plain,
! [U_86] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_86),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_86),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_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_31_2,plain,
! [U_87] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_87),U_87)),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_87),U_87)),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [V_na_2] :
( ( V_na_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_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2))
| V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_neq0__conv]) ).
fof(f_32_2,plain,
! [U_88] :
( ( U_88 != 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_88)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_88))
| U_88 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ! [U_90] :
( U_90 != 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_90)) )
& ! [U_89] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_89))
| U_89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
cnf(f_32_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_89))
| U_89 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_5,plain,
( U_90 != 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_90)) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
! [V_na_2,V_m_2] :
( ( V_m_2 != V_na_2
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
| V_m_2 = V_na_2 ) ),
inference(fof_nnf,[status(thm)],[fact_nat__neq__iff]) ).
fof(f_33_2,plain,
! [U_92,U_91] :
( ( U_91 != U_92
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_92),U_91))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_91),U_92)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_92),U_91))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_91),U_92))
| U_91 = U_92 ) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_96,U_94] :
( U_94 != U_96
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_96),U_94))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_94),U_96)) ) )
& ! [U_95,U_93] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_95),U_93))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_93),U_95))
| U_93 = U_95 ) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
cnf(f_33_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_95),U_93))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_93),U_95))
| U_93 = U_95 ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_94),U_96))
| U_94 != U_96 ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_96),U_94))
| U_94 != U_96 ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_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_34_2,plain,
! [U_97] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_97)),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_97)),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_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_35_2,plain,
! [U_98] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_98),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_98),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [V_na_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(fof_nnf,[status(thm)],[fact_le__0__eq]) ).
fof(f_36_2,plain,
! [U_99] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_99),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_99 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_99 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_99),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( ! [U_101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_101),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_101 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_100] :
( U_100 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_100),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( U_100 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_100),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_101),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_101 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [V_na_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
| V_m_2 = V_na_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) )
& ( ( V_m_2 != V_na_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__le]) ).
fof(f_37_2,plain,
! [U_103,U_102] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_102),U_103))
| U_102 = U_103
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_102),U_103)) )
& ( ( U_102 != U_103
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_102),U_103)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_102),U_103)) ) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ! [U_107,U_105] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_105),U_107))
| U_105 = U_107
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_105),U_107)) )
& ! [U_106,U_104] :
( ( U_104 != U_106
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_104),U_106)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_104),U_106)) ) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_104),U_106))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_104),U_106)) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_5,plain,
( U_104 != U_106
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_104),U_106)) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_105),U_107))
| U_105 = U_107
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_105),U_107)) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [V_na_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
| ( V_m_2 != V_na_2
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) )
& ( V_m_2 = V_na_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq]) ).
fof(f_38_2,plain,
! [U_109,U_108] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_108),U_109))
| ( U_108 != U_109
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_108),U_109)) ) )
& ( U_108 = U_109
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_108),U_109))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_108),U_109)) ) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( ! [U_113,U_111] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_111),U_113))
| ( U_111 != U_113
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_111),U_113)) ) )
& ! [U_112,U_110] :
( U_110 = U_112
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_110),U_112))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_110),U_112)) ) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
cnf(f_38_4,plain,
( U_110 = U_112
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_110),U_112))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_110),U_112)) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_111),U_113))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_111),U_113)) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_6,plain,
( U_111 != U_113
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_111),U_113)) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_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_39_2,plain,
! [U_115,U_114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_115),U_114))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_114),U_115))
| U_114 = U_115 ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_115),U_114))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_114),U_115))
| U_114 = U_115 ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_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_40_2,plain,
! [U_116] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_116),U_116)),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_116),U_116)),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_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_41_2,plain,
! [U_118,U_117] :
( U_118 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_117),U_118)) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_118] :
( ! [U_117] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_117),U_118))
| U_118 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_41_2]) ).
cnf(f_41_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_117),U_118))
| U_118 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_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_42_2,plain,
! [U_120,U_119] :
( U_120 != U_119
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_119),U_120)) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( U_120 != U_119
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_119),U_120)) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_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_43_2,plain,
! [U_122,U_121] :
( U_121 != U_122
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_121),U_122)) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
cnf(f_43_3,plain,
( U_121 != U_122
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_121),U_122)) ),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_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_44_2,plain,
! [U_124,U_123] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_123),U_124))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_123),U_124)) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_123),U_124))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_123),U_124)) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_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_45_2,plain,
! [U_126,U_125] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_125),U_126))
| U_125 = U_126
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_125),U_126)) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_125),U_126))
| U_125 = U_126
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_125),U_126)) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_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_46_2,plain,
! [U_128,U_127] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_127),U_128))
| ( U_127 != U_128
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_127),U_128)) ) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_127),U_128))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_127),U_128)) ),
inference(clausify,[status(thm)],[f_46_2]) ).
cnf(f_46_4,plain,
( U_127 != U_128
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_127),U_128)) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_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_47_2,plain,
! [U_129] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_129))
| U_129 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_129))
| U_129 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_1,plain,
! [V_P_2,V_na_2,V_m_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_na_2),V_m_2))
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_na_2),V_m_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) )
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_na_2),V_m_2))
& V_m_2 = V_na_2 )
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_na_2),V_m_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__cases]) ).
fof(f_48_2,plain,
! [U_132,U_131,U_130] :
( hBOOL(hAPP(hAPP(U_132,U_131),U_130))
| ( ~ hBOOL(hAPP(hAPP(U_132,U_131),U_130))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_131),U_130)) )
| ( ~ hBOOL(hAPP(hAPP(U_132,U_131),U_130))
& U_130 = U_131 )
| ( ~ hBOOL(hAPP(hAPP(U_132,U_131),U_130))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_130),U_131)) ) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_131),U_130))
| hBOOL(hAPP(hAPP(U_132,U_131),U_130))
| U_130 = U_131
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_130),U_131)) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_4,plain,
( ~ hBOOL(hAPP(hAPP(U_132,U_131),U_130))
| hBOOL(hAPP(hAPP(U_132,U_131),U_130))
| U_130 = U_131
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_130),U_131)) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_131),U_130))
| hBOOL(hAPP(hAPP(U_132,U_131),U_130))
| ~ hBOOL(hAPP(hAPP(U_132,U_131),U_130))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_130),U_131)) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_6,plain,
( ~ hBOOL(hAPP(hAPP(U_132,U_131),U_130))
| hBOOL(hAPP(hAPP(U_132,U_131),U_130))
| ~ hBOOL(hAPP(hAPP(U_132,U_131),U_130))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_130),U_131)) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_131),U_130))
| hBOOL(hAPP(hAPP(U_132,U_131),U_130))
| U_130 = U_131
| ~ hBOOL(hAPP(hAPP(U_132,U_131),U_130)) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_8,plain,
( ~ hBOOL(hAPP(hAPP(U_132,U_131),U_130))
| hBOOL(hAPP(hAPP(U_132,U_131),U_130))
| U_130 = U_131
| ~ hBOOL(hAPP(hAPP(U_132,U_131),U_130)) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_131),U_130))
| hBOOL(hAPP(hAPP(U_132,U_131),U_130))
| ~ hBOOL(hAPP(hAPP(U_132,U_131),U_130))
| ~ hBOOL(hAPP(hAPP(U_132,U_131),U_130)) ),
inference(clausify,[status(thm)],[f_48_2]) ).
cnf(f_48_10,plain,
( ~ hBOOL(hAPP(hAPP(U_132,U_131),U_130))
| hBOOL(hAPP(hAPP(U_132,U_131),U_130))
| ~ hBOOL(hAPP(hAPP(U_132,U_131),U_130))
| ~ hBOOL(hAPP(hAPP(U_132,U_131),U_130)) ),
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_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_49_2,plain,
! [U_135,U_134,U_133] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_133),U_135),U_134))
| U_134 = U_135
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_133),U_134),U_135))
| ~ class_Orderings_Olinorder(U_133) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
cnf(f_49_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_133),U_135),U_134))
| U_134 = U_135
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_133),U_134),U_135))
| ~ class_Orderings_Olinorder(U_133) ),
inference(clausify,[status(thm)],[f_49_2]) ).
fof(f_50_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_50_2,plain,
! [U_138,U_137,U_136] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_136),U_138),U_137))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_136),U_137),U_138))
| ~ class_Orderings_Olinorder(U_136) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_136),U_138),U_137))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_136),U_137),U_138))
| ~ class_Orderings_Olinorder(U_136) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,plain,
! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
| ~ class_Orderings_Oord(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__funE]) ).
fof(f_51_2,plain,
! [U_143,U_142,U_141,U_140,U_139] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_139),hAPP(U_141,U_143)),hAPP(U_142,U_143)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_140,U_139)),U_141),U_142))
| ~ class_Orderings_Oord(U_139) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
cnf(f_51_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_139),hAPP(U_141,U_143)),hAPP(U_142,U_143)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_140,U_139)),U_141),U_142))
| ~ class_Orderings_Oord(U_139) ),
inference(clausify,[status(thm)],[f_51_2]) ).
fof(f_52_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_52_2,plain,
! [U_146,U_145,U_144] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_144),U_146),U_145))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_144),U_145),U_146))
| ~ class_Orderings_Opreorder(U_144) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
cnf(f_52_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_144),U_146),U_145))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_144),U_145),U_146))
| ~ class_Orderings_Opreorder(U_144) ),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_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_53_2,plain,
! [U_150,U_149,U_148,U_147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_147),U_150),U_149))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_147),U_150),U_148))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_147),U_148),U_149))
| ~ class_Orderings_Oorder(U_147) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_147),U_150),U_149))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_147),U_150),U_148))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_147),U_148),U_149))
| ~ class_Orderings_Oorder(U_147) ),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_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_54_2,plain,
! [U_153,U_152,U_151] :
( U_153 = U_152
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_151),U_153),U_152))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_151),U_152),U_153))
| ~ class_Orderings_Oorder(U_151) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
cnf(f_54_3,plain,
( U_153 = U_152
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_151),U_153),U_152))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_151),U_152),U_153))
| ~ class_Orderings_Oorder(U_151) ),
inference(clausify,[status(thm)],[f_54_2]) ).
fof(f_55_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_55_2,plain,
! [U_157,U_156,U_155,U_154] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_154),U_157),U_156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_154),U_157),U_155))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_154),U_155),U_156))
| ~ class_Orderings_Oorder(U_154) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
cnf(f_55_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_154),U_157),U_156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_154),U_157),U_155))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_154),U_155),U_156))
| ~ class_Orderings_Oorder(U_154) ),
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_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_56_2,plain,
! [U_161,U_160,U_159,U_158] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_158),U_159),U_161))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_158),U_160),U_161))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_158),U_159),U_160))
| ~ class_Orderings_Opreorder(U_158) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
cnf(f_56_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_158),U_159),U_161))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_158),U_160),U_161))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_158),U_159),U_160))
| ~ class_Orderings_Opreorder(U_158) ),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_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_57_2,plain,
! [U_164,U_163,U_162] :
( U_163 = U_164
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_162),U_164),U_163))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_162),U_163),U_164))
| ~ class_Orderings_Oorder(U_162) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
cnf(f_57_3,plain,
( U_163 = U_164
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_162),U_164),U_163))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_162),U_163),U_164))
| ~ class_Orderings_Oorder(U_162) ),
inference(clausify,[status(thm)],[f_57_2]) ).
fof(f_58_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_58_2,plain,
! [U_168,U_167,U_166,U_165] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_165),U_166),U_168))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_165),U_167),U_168))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_165),U_166),U_167))
| ~ class_Orderings_Opreorder(U_165) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
cnf(f_58_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_165),U_166),U_168))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_165),U_167),U_168))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_165),U_166),U_167))
| ~ class_Orderings_Opreorder(U_165) ),
inference(clausify,[status(thm)],[f_58_2]) ).
fof(f_59_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_59_2,plain,
! [U_172,U_171,U_170,U_169] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_169),U_172),U_171))
| U_170 != U_172
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_169),U_170),U_171))
| ~ class_Orderings_Oorder(U_169) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
cnf(f_59_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_169),U_172),U_171))
| U_170 != U_172
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_169),U_170),U_171))
| ~ class_Orderings_Oorder(U_169) ),
inference(clausify,[status(thm)],[f_59_2]) ).
fof(f_60_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_60_2,plain,
! [U_176,U_175,U_174,U_173] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_173),U_174),U_176))
| U_175 != U_176
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_173),U_174),U_175))
| ~ class_Orderings_Oord(U_173) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
cnf(f_60_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_173),U_174),U_176))
| U_175 != U_176
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_173),U_174),U_175))
| ~ class_Orderings_Oord(U_173) ),
inference(clausify,[status(thm)],[f_60_2]) ).
fof(f_61_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_61_2,plain,
! [U_180,U_179,U_178,U_177] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_177),U_180),U_179))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_177),U_180),U_178))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_177),U_178),U_179))
| ~ class_Orderings_Oorder(U_177) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
cnf(f_61_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_177),U_180),U_179))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_177),U_180),U_178))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_177),U_178),U_179))
| ~ class_Orderings_Oorder(U_177) ),
inference(clausify,[status(thm)],[f_61_2]) ).
fof(f_62_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_62_2,plain,
! [U_184,U_183,U_182,U_181] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_181),U_184),U_183))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_181),U_184),U_182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_181),U_182),U_183))
| ~ class_Orderings_Oorder(U_181) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
cnf(f_62_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_181),U_184),U_183))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_181),U_184),U_182))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_181),U_182),U_183))
| ~ class_Orderings_Oorder(U_181) ),
inference(clausify,[status(thm)],[f_62_2]) ).
fof(f_63_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_63_2,plain,
! [U_188,U_187,U_186,U_185] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_185),U_186),U_188))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_185),U_187),U_188))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_185),U_186),U_187))
| ~ class_Orderings_Opreorder(U_185) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
cnf(f_63_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_185),U_186),U_188))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_185),U_187),U_188))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_185),U_186),U_187))
| ~ class_Orderings_Opreorder(U_185) ),
inference(clausify,[status(thm)],[f_63_2]) ).
fof(f_64_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_64_2,plain,
! [U_192,U_191,U_190,U_189] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_189),U_190),U_192))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_189),U_191),U_192))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_189),U_190),U_191))
| ~ class_Orderings_Opreorder(U_189) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
cnf(f_64_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_189),U_190),U_192))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_189),U_191),U_192))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_189),U_190),U_191))
| ~ class_Orderings_Opreorder(U_189) ),
inference(clausify,[status(thm)],[f_64_2]) ).
fof(f_65_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_65_2,plain,
! [U_196,U_195,U_194,U_193] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_193),U_196),U_195))
| U_194 != U_196
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_193),U_194),U_195))
| ~ class_Orderings_Oorder(U_193) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
cnf(f_65_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_193),U_196),U_195))
| U_194 != U_196
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_193),U_194),U_195))
| ~ class_Orderings_Oorder(U_193) ),
inference(clausify,[status(thm)],[f_65_2]) ).
fof(f_66_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_66_2,plain,
! [U_200,U_199,U_198,U_197] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_197),U_198),U_200))
| U_199 != U_200
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_197),U_198),U_199))
| ~ class_Orderings_Oord(U_197) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
cnf(f_66_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_197),U_198),U_200))
| U_199 != U_200
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_197),U_198),U_199))
| ~ class_Orderings_Oord(U_197) ),
inference(clausify,[status(thm)],[f_66_2]) ).
fof(f_67_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_67_2,plain,
! [U_204,U_203,U_202,U_201] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_201),U_204),U_202))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_201),U_204),U_203))
| U_202 != U_203
| ~ class_Orderings_Oorder(U_201) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
cnf(f_67_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_201),U_204),U_202))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_201),U_204),U_203))
| U_202 != U_203
| ~ class_Orderings_Oorder(U_201) ),
inference(clausify,[status(thm)],[f_67_2]) ).
fof(f_68_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_68_2,plain,
! [U_208,U_207,U_206,U_205] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_205),U_206),U_208))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_205),U_207),U_208))
| U_206 != U_207
| ~ class_Orderings_Oord(U_205) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
cnf(f_68_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_205),U_206),U_208))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_205),U_207),U_208))
| U_206 != U_207
| ~ class_Orderings_Oord(U_205) ),
inference(clausify,[status(thm)],[f_68_2]) ).
fof(f_69_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_69_2,plain,
! [U_212,U_211,U_210,U_209] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_209),U_212),U_210))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_209),U_212),U_211))
| U_210 != U_211
| ~ class_Orderings_Oorder(U_209) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
cnf(f_69_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_209),U_212),U_210))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_209),U_212),U_211))
| U_210 != U_211
| ~ class_Orderings_Oorder(U_209) ),
inference(clausify,[status(thm)],[f_69_2]) ).
fof(f_70_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_70_2,plain,
! [U_216,U_215,U_214,U_213] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_213),U_214),U_216))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_213),U_215),U_216))
| U_214 != U_215
| ~ class_Orderings_Oord(U_213) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
cnf(f_70_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_213),U_214),U_216))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_213),U_215),U_216))
| U_214 != U_215
| ~ class_Orderings_Oord(U_213) ),
inference(clausify,[status(thm)],[f_70_2]) ).
fof(f_71_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_71_2,plain,
! [U_219,U_218,U_217] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_217),U_219),U_218))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_217),U_218),U_219))
| ~ class_Orderings_Oorder(U_217) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
cnf(f_71_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_217),U_219),U_218))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_217),U_218),U_219))
| ~ class_Orderings_Oorder(U_217) ),
inference(clausify,[status(thm)],[f_71_2]) ).
fof(f_72_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_72_2,plain,
! [U_222,U_221,U_220] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_220),U_222),U_221))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_220),U_221),U_222))
| ~ class_Orderings_Opreorder(U_220) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
cnf(f_72_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_220),U_222),U_221))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_220),U_221),U_222))
| ~ class_Orderings_Opreorder(U_220) ),
inference(clausify,[status(thm)],[f_72_2]) ).
fof(f_73_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_73_2,plain,
! [U_225,U_224,U_223] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_223),U_224),U_225))
| U_225 = U_224
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_223),U_224),U_225))
| ~ class_Orderings_Oorder(U_223) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
cnf(f_73_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_223),U_224),U_225))
| U_225 = U_224
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_223),U_224),U_225))
| ~ class_Orderings_Oorder(U_223) ),
inference(clausify,[status(thm)],[f_73_2]) ).
fof(f_74_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_74_2,plain,
! [U_228,U_227,U_226] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_226),U_227),U_228))
| U_227 = U_228
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_226),U_227),U_228))
| ~ class_Orderings_Oorder(U_226) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_226),U_227),U_228))
| U_227 = U_228
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_226),U_227),U_228))
| ~ class_Orderings_Oorder(U_226) ),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_1,plain,
! [V_x_2,V_y_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_order__antisym__conv]) ).
fof(f_75_2,plain,
! [U_231,U_230,U_229] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_229),U_231),U_230))
| U_231 != U_230 )
& ( U_231 = U_230
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_229),U_231),U_230)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_229),U_230),U_231))
| ~ class_Orderings_Oorder(U_229) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
cnf(f_75_3,plain,
( U_231 = U_230
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_229),U_231),U_230))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_229),U_230),U_231))
| ~ class_Orderings_Oorder(U_229) ),
inference(clausify,[status(thm)],[f_75_2]) ).
cnf(f_75_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_229),U_231),U_230))
| U_231 != U_230
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_229),U_230),U_231))
| ~ class_Orderings_Oorder(U_229) ),
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_76_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_76_2,plain,
! [U_234,U_233,U_232] :
( U_233 = U_234
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_232),U_233),U_234))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_232),U_233),U_234))
| ~ class_Orderings_Oorder(U_232) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
cnf(f_76_3,plain,
( U_233 = U_234
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_232),U_233),U_234))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_232),U_233),U_234))
| ~ class_Orderings_Oorder(U_232) ),
inference(clausify,[status(thm)],[f_76_2]) ).
fof(f_77_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_77_2,plain,
! [U_237,U_236,U_235] :
( U_237 != U_236
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_235),U_236),U_237))
| ~ class_Orderings_Oorder(U_235) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
cnf(f_77_3,plain,
( U_237 != U_236
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_235),U_236),U_237))
| ~ class_Orderings_Oorder(U_235) ),
inference(clausify,[status(thm)],[f_77_2]) ).
fof(f_78_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_78_2,plain,
! [U_240,U_239,U_238] :
( U_239 != U_240
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_238),U_239),U_240))
| ~ class_Orderings_Oorder(U_238) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
cnf(f_78_3,plain,
( U_239 != U_240
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_238),U_239),U_240))
| ~ class_Orderings_Oorder(U_238) ),
inference(clausify,[status(thm)],[f_78_2]) ).
fof(f_79_1,plain,
! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
| ~ class_Orderings_Oord(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__funD]) ).
fof(f_79_2,plain,
! [U_245,U_244,U_243,U_242,U_241] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_241),hAPP(U_243,U_245)),hAPP(U_244,U_245)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_242,U_241)),U_243),U_244))
| ~ class_Orderings_Oord(U_241) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
cnf(f_79_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_241),hAPP(U_243,U_245)),hAPP(U_244,U_245)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_242,U_241)),U_243),U_244))
| ~ class_Orderings_Oord(U_241) ),
inference(clausify,[status(thm)],[f_79_2]) ).
fof(f_80_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(f_80_2,plain,
! [U_248,U_247,U_246] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_246),U_247),U_248))
| U_247 != U_248 )
& ( U_247 = U_248
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_246),U_247),U_248)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_246),U_247),U_248))
| ~ class_Orderings_Olinorder(U_246) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
cnf(f_80_3,plain,
( U_247 = U_248
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_246),U_247),U_248))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_246),U_247),U_248))
| ~ class_Orderings_Olinorder(U_246) ),
inference(clausify,[status(thm)],[f_80_2]) ).
cnf(f_80_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_246),U_247),U_248))
| U_247 != U_248
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_246),U_247),U_248))
| ~ class_Orderings_Olinorder(U_246) ),
inference(clausify,[status(thm)],[f_80_2]) ).
fof(f_81_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_81_2,plain,
! [U_251,U_250,U_249] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_249),U_251),U_250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_249),U_250),U_251))
| ~ class_Orderings_Opreorder(U_249) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
cnf(f_81_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_249),U_251),U_250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_249),U_250),U_251))
| ~ class_Orderings_Opreorder(U_249) ),
inference(clausify,[status(thm)],[f_81_2]) ).
fof(f_82_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_82_2,plain,
! [U_254,U_253,U_252] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_252),U_253),U_254))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_252),U_253),U_254))
| ~ class_Orderings_Opreorder(U_252) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
cnf(f_82_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_252),U_253),U_254))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_252),U_253),U_254))
| ~ class_Orderings_Opreorder(U_252) ),
inference(clausify,[status(thm)],[f_82_2]) ).
fof(f_83_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_83_2,plain,
! [U_257,U_256,U_255] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_255),U_256),U_257))
| U_256 != U_257
| ~ class_Orderings_Opreorder(U_255) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
cnf(f_83_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_255),U_256),U_257))
| U_256 != U_257
| ~ class_Orderings_Opreorder(U_255) ),
inference(clausify,[status(thm)],[f_83_2]) ).
fof(f_84_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_84_2,plain,
! [U_260,U_259,U_258] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_258),U_260),U_259))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_258),U_259),U_260))
| ~ class_Orderings_Olinorder(U_258) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
cnf(f_84_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_258),U_260),U_259))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_258),U_259),U_260))
| ~ class_Orderings_Olinorder(U_258) ),
inference(clausify,[status(thm)],[f_84_2]) ).
fof(f_85_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_85_2,plain,
! [U_263,U_262,U_261] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_261),U_263),U_262))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_261),U_262),U_263))
| ~ class_Orderings_Opreorder(U_261) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
cnf(f_85_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_261),U_263),U_262))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_261),U_262),U_263))
| ~ class_Orderings_Opreorder(U_261) ),
inference(clausify,[status(thm)],[f_85_2]) ).
fof(f_86_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_86_2,plain,
! [U_266,U_265,U_264] :
( U_265 != U_266
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_264),U_265),U_266))
| ~ class_Orderings_Oorder(U_264) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
cnf(f_86_3,plain,
( U_265 != U_266
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_264),U_265),U_266))
| ~ class_Orderings_Oorder(U_264) ),
inference(clausify,[status(thm)],[f_86_2]) ).
fof(f_87_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_87_2,plain,
! [U_269,U_268,U_267] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_267),U_269),U_268))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_267),U_268),U_269))
| U_268 = U_269
| ~ class_Orderings_Olinorder(U_267) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
cnf(f_87_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_267),U_269),U_268))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_267),U_268),U_269))
| U_268 = U_269
| ~ class_Orderings_Olinorder(U_267) ),
inference(clausify,[status(thm)],[f_87_2]) ).
fof(f_88_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_88_2,plain,
! [U_272,U_271,U_270] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_270),U_272),U_271))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_270),U_272),U_271))
| U_271 = U_272
| ~ class_Orderings_Oorder(U_270) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
cnf(f_88_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_270),U_272),U_271))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_270),U_272),U_271))
| U_271 = U_272
| ~ class_Orderings_Oorder(U_270) ),
inference(clausify,[status(thm)],[f_88_2]) ).
fof(f_89_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_89_2,plain,
! [U_275,U_274,U_273] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_273),U_274),U_275))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_273),U_274),U_275))
| U_274 = U_275
| ~ class_Orderings_Oorder(U_273) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
cnf(f_89_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_273),U_274),U_275))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_273),U_274),U_275))
| U_274 = U_275
| ~ class_Orderings_Oorder(U_273) ),
inference(clausify,[status(thm)],[f_89_2]) ).
fof(f_90_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(f_90_2,plain,
! [U_278,U_277,U_276] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_276),U_277),U_278))
| U_277 != U_278 )
& ( U_277 = U_278
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_276),U_277),U_278)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_276),U_277),U_278))
| ~ class_Orderings_Olinorder(U_276) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
cnf(f_90_3,plain,
( U_277 = U_278
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_276),U_277),U_278))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_276),U_277),U_278))
| ~ class_Orderings_Olinorder(U_276) ),
inference(clausify,[status(thm)],[f_90_2]) ).
cnf(f_90_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_276),U_277),U_278))
| U_277 != U_278
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_276),U_277),U_278))
| ~ class_Orderings_Olinorder(U_276) ),
inference(clausify,[status(thm)],[f_90_2]) ).
fof(f_91_1,plain,
! [V_x_2,V_y_2,T_b] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(f_91_2,plain,
! [U_281,U_280,U_279] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_279),U_281),U_280))
| U_281 != U_280 )
& ( U_281 = U_280
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_279),U_281),U_280)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_279),U_280),U_281))
| ~ class_Orderings_Olinorder(U_279) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
cnf(f_91_3,plain,
( U_281 = U_280
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_279),U_281),U_280))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_279),U_280),U_281))
| ~ class_Orderings_Olinorder(U_279) ),
inference(clausify,[status(thm)],[f_91_2]) ).
cnf(f_91_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_279),U_281),U_280))
| U_281 != U_280
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_279),U_280),U_281))
| ~ class_Orderings_Olinorder(U_279) ),
inference(clausify,[status(thm)],[f_91_2]) ).
fof(f_92_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_92_2,plain,
! [U_284,U_283,U_282] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_282),U_284),U_283))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_282),U_283),U_284))
| ~ class_Orderings_Olinorder(U_282) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
cnf(f_92_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_282),U_284),U_283))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_282),U_283),U_284))
| ~ class_Orderings_Olinorder(U_282) ),
inference(clausify,[status(thm)],[f_92_2]) ).
fof(f_93_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_93_2,plain,
! [U_287,U_286,U_285] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_285),U_287),U_286))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_285),U_286),U_287))
| ~ class_Orderings_Olinorder(U_285) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
cnf(f_93_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_285),U_287),U_286))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_285),U_286),U_287))
| ~ class_Orderings_Olinorder(U_285) ),
inference(clausify,[status(thm)],[f_93_2]) ).
fof(f_94_1,plain,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| ~ c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
| ~ class_Orderings_Oorder(T_b)
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_strict__monoD]) ).
fof(f_94_2,plain,
! [U_292,U_291,U_290,U_289,U_288] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_288),hAPP(U_290,U_291)),hAPP(U_290,U_292)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_289),U_291),U_292))
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_289,U_288,U_290)
| ~ class_Orderings_Oorder(U_289)
| ~ class_Orderings_Oorder(U_288) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
cnf(f_94_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_288),hAPP(U_290,U_291)),hAPP(U_290,U_292)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_289),U_291),U_292))
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_289,U_288,U_290)
| ~ class_Orderings_Oorder(U_289)
| ~ class_Orderings_Oorder(U_288) ),
inference(clausify,[status(thm)],[f_94_2]) ).
fof(f_95_1,plain,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_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))) ) )
| ~ c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_strict__mono__less__eq]) ).
fof(f_95_2,plain,
! [U_297,U_296,U_295,U_294,U_293] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_293),hAPP(U_295,U_296)),hAPP(U_295,U_297)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_294),U_296),U_297)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_294),U_296),U_297))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_293),hAPP(U_295,U_296)),hAPP(U_295,U_297))) ) )
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_294,U_293,U_295)
| ~ class_Orderings_Olinorder(U_294)
| ~ class_Orderings_Oorder(U_293) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
cnf(f_95_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_294),U_296),U_297))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_293),hAPP(U_295,U_296)),hAPP(U_295,U_297)))
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_294,U_293,U_295)
| ~ class_Orderings_Olinorder(U_294)
| ~ class_Orderings_Oorder(U_293) ),
inference(clausify,[status(thm)],[f_95_2]) ).
cnf(f_95_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_293),hAPP(U_295,U_296)),hAPP(U_295,U_297)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_294),U_296),U_297))
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_294,U_293,U_295)
| ~ class_Orderings_Olinorder(U_294)
| ~ class_Orderings_Oorder(U_293) ),
inference(clausify,[status(thm)],[f_95_2]) ).
fof(f_96_1,plain,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) )
| ~ c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_strict__mono__less]) ).
fof(f_96_2,plain,
! [U_302,U_301,U_300,U_299,U_298] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_298),hAPP(U_300,U_301)),hAPP(U_300,U_302)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_299),U_301),U_302)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_299),U_301),U_302))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_298),hAPP(U_300,U_301)),hAPP(U_300,U_302))) ) )
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_299,U_298,U_300)
| ~ class_Orderings_Olinorder(U_299)
| ~ class_Orderings_Oorder(U_298) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
cnf(f_96_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_299),U_301),U_302))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_298),hAPP(U_300,U_301)),hAPP(U_300,U_302)))
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_299,U_298,U_300)
| ~ class_Orderings_Olinorder(U_299)
| ~ class_Orderings_Oorder(U_298) ),
inference(clausify,[status(thm)],[f_96_2]) ).
cnf(f_96_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_298),hAPP(U_300,U_301)),hAPP(U_300,U_302)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_299),U_301),U_302))
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_299,U_298,U_300)
| ~ class_Orderings_Olinorder(U_299)
| ~ class_Orderings_Oorder(U_298) ),
inference(clausify,[status(thm)],[f_96_2]) ).
fof(f_97_1,plain,
! [V_y_2,V_x_2,V_f_2,T_b,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_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_strict__mono__eq]) ).
fof(f_97_2,plain,
! [U_307,U_306,U_305,U_304,U_303] :
( ( ( hAPP(U_305,U_306) = hAPP(U_305,U_307)
| U_306 != U_307 )
& ( U_306 = U_307
| hAPP(U_305,U_306) != hAPP(U_305,U_307) ) )
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_304,U_303,U_305)
| ~ class_Orderings_Olinorder(U_304)
| ~ class_Orderings_Oorder(U_303) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
cnf(f_97_3,plain,
( U_306 = U_307
| hAPP(U_305,U_306) != hAPP(U_305,U_307)
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_304,U_303,U_305)
| ~ class_Orderings_Olinorder(U_304)
| ~ class_Orderings_Oorder(U_303) ),
inference(clausify,[status(thm)],[f_97_2]) ).
cnf(f_97_4,plain,
( hAPP(U_305,U_306) = hAPP(U_305,U_307)
| U_306 != U_307
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_304,U_303,U_305)
| ~ class_Orderings_Olinorder(U_304)
| ~ class_Orderings_Oorder(U_303) ),
inference(clausify,[status(thm)],[f_97_2]) ).
fof(f_98_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_98_2,plain,
! [U_310,U_309,U_308] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_308),U_310),U_309))
| U_309 = U_310
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_308),U_309),U_310))
| ~ class_Orderings_Olinorder(U_308) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
cnf(f_98_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_308),U_310),U_309))
| U_309 = U_310
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_308),U_309),U_310))
| ~ class_Orderings_Olinorder(U_308) ),
inference(clausify,[status(thm)],[f_98_2]) ).
fof(f_99_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| ( V_x_2 != V_y_2
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
& ( V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_order__le__less]) ).
fof(f_99_2,plain,
! [U_313,U_312,U_311] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_311),U_312),U_313))
| ( U_312 != U_313
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_311),U_312),U_313)) ) )
& ( U_312 = U_313
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_311),U_312),U_313))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_311),U_312),U_313)) ) )
| ~ class_Orderings_Oorder(U_311) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
cnf(f_99_3,plain,
( U_312 = U_313
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_311),U_312),U_313))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_311),U_312),U_313))
| ~ class_Orderings_Oorder(U_311) ),
inference(clausify,[status(thm)],[f_99_2]) ).
cnf(f_99_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_311),U_312),U_313))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_311),U_312),U_313))
| ~ class_Orderings_Oorder(U_311) ),
inference(clausify,[status(thm)],[f_99_2]) ).
cnf(f_99_5,plain,
( U_312 != U_313
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_311),U_312),U_313))
| ~ class_Orderings_Oorder(U_311) ),
inference(clausify,[status(thm)],[f_99_2]) ).
fof(f_100_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
| V_x_2 != V_y_2 ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_order__eq__iff]) ).
fof(f_100_2,plain,
! [U_316,U_315,U_314] :
( ( ( U_315 = U_316
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_314),U_316),U_315))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_314),U_315),U_316)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_314),U_316),U_315))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_314),U_315),U_316)) )
| U_315 != U_316 ) )
| ~ class_Orderings_Oorder(U_314) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
cnf(f_100_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_314),U_315),U_316))
| U_315 != U_316
| ~ class_Orderings_Oorder(U_314) ),
inference(clausify,[status(thm)],[f_100_2]) ).
cnf(f_100_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_314),U_316),U_315))
| U_315 != U_316
| ~ class_Orderings_Oorder(U_314) ),
inference(clausify,[status(thm)],[f_100_2]) ).
cnf(f_100_5,plain,
( U_315 = U_316
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_314),U_316),U_315))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_314),U_315),U_316))
| ~ class_Orderings_Oorder(U_314) ),
inference(clausify,[status(thm)],[f_100_2]) ).
fof(f_101_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Opreorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__le__not__le]) ).
fof(f_101_2,plain,
! [U_319,U_318,U_317] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_317),U_318),U_319))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_317),U_319),U_318))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_317),U_318),U_319)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_317),U_319),U_318))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_317),U_318),U_319)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_317),U_318),U_319)) ) )
| ~ class_Orderings_Opreorder(U_317) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
cnf(f_101_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_317),U_318),U_319))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_317),U_318),U_319))
| ~ class_Orderings_Opreorder(U_317) ),
inference(clausify,[status(thm)],[f_101_2]) ).
cnf(f_101_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_317),U_319),U_318))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_317),U_318),U_319))
| ~ class_Orderings_Opreorder(U_317) ),
inference(clausify,[status(thm)],[f_101_2]) ).
cnf(f_101_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_317),U_318),U_319))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_317),U_319),U_318))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_317),U_318),U_319))
| ~ class_Orderings_Opreorder(U_317) ),
inference(clausify,[status(thm)],[f_101_2]) ).
fof(f_102_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
& ( ( V_x_2 != V_y_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_order__less__le]) ).
fof(f_102_2,plain,
! [U_322,U_321,U_320] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_320),U_321),U_322))
| U_321 = U_322
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_320),U_321),U_322)) )
& ( ( U_321 != U_322
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_320),U_321),U_322)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_320),U_321),U_322)) ) )
| ~ class_Orderings_Oorder(U_320) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
cnf(f_102_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_320),U_321),U_322))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_320),U_321),U_322))
| ~ class_Orderings_Oorder(U_320) ),
inference(clausify,[status(thm)],[f_102_2]) ).
cnf(f_102_4,plain,
( U_321 != U_322
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_320),U_321),U_322))
| ~ class_Orderings_Oorder(U_320) ),
inference(clausify,[status(thm)],[f_102_2]) ).
cnf(f_102_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_320),U_321),U_322))
| U_321 = U_322
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_320),U_321),U_322))
| ~ class_Orderings_Oorder(U_320) ),
inference(clausify,[status(thm)],[f_102_2]) ).
fof(f_103_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_103_2,plain,
! [U_325,U_324,U_323] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_323),U_325),U_324))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_323),U_324),U_325))
| ~ class_Orderings_Olinorder(U_323) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
cnf(f_103_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_323),U_325),U_324))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_323),U_324),U_325))
| ~ class_Orderings_Olinorder(U_323) ),
inference(clausify,[status(thm)],[f_103_2]) ).
fof(f_104_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_104_2,plain,
! [U_328,U_327,U_326] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_326),U_328),U_327))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_326),U_327),U_328))
| ~ class_Orderings_Olinorder(U_326) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
cnf(f_104_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_326),U_328),U_327))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_326),U_327),U_328))
| ~ class_Orderings_Olinorder(U_326) ),
inference(clausify,[status(thm)],[f_104_2]) ).
fof(f_105_1,plain,
! [V_g_2,V_f_2,T_b,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
| ? [B_x] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
& ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) )
| ~ class_Orderings_Oord(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__fun__def]) ).
fof(f_105_2,plain,
! [U_334,U_333,U_332,U_331] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_332,U_331)),U_333),U_334))
| ? [U_330] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_331),hAPP(U_333,U_330)),hAPP(U_334,U_330))) )
& ( ! [U_329] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_331),hAPP(U_333,U_329)),hAPP(U_334,U_329)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_332,U_331)),U_333),U_334)) ) )
| ~ class_Orderings_Oord(U_331) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
! [U_334,U_333,U_332,U_331] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_332,U_331)),U_333),U_334))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_331),hAPP(U_333,sK7(U_334,U_333,U_332,U_331))),hAPP(U_334,sK7(U_334,U_333,U_332,U_331)))) )
& ( ! [U_329] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_331),hAPP(U_333,U_329)),hAPP(U_334,U_329)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_332,U_331)),U_333),U_334)) ) )
| ~ class_Orderings_Oord(U_331) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_330,sK7(U_334,U_333,U_332,U_331))],[f_105_2]) ).
cnf(f_105_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_331),hAPP(U_333,U_329)),hAPP(U_334,U_329)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_332,U_331)),U_333),U_334))
| ~ class_Orderings_Oord(U_331) ),
inference(clausify,[status(thm)],[f_105_3]) ).
cnf(f_105_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_332,U_331)),U_333),U_334))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_331),hAPP(U_333,sK7(U_334,U_333,U_332,U_331))),hAPP(U_334,sK7(U_334,U_333,U_332,U_331))))
| ~ class_Orderings_Oord(U_331) ),
inference(clausify,[status(thm)],[f_105_3]) ).
fof(f_106_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| ( V_x_2 != V_y_2
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) )
& ( V_x_2 = V_y_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(f_106_2,plain,
! [U_337,U_336,U_335] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_335),U_336),U_337))
| ( U_336 != U_337
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_335),U_337),U_336)) ) )
& ( U_336 = U_337
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_335),U_337),U_336))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_335),U_336),U_337)) ) )
| ~ class_Orderings_Olinorder(U_335) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
cnf(f_106_3,plain,
( U_336 = U_337
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_335),U_337),U_336))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_335),U_336),U_337))
| ~ class_Orderings_Olinorder(U_335) ),
inference(clausify,[status(thm)],[f_106_2]) ).
cnf(f_106_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_335),U_337),U_336))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_335),U_336),U_337))
| ~ class_Orderings_Olinorder(U_335) ),
inference(clausify,[status(thm)],[f_106_2]) ).
cnf(f_106_5,plain,
( U_336 != U_337
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_335),U_336),U_337))
| ~ class_Orderings_Olinorder(U_335) ),
inference(clausify,[status(thm)],[f_106_2]) ).
fof(f_107_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( V_x_2 != V_y_2
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| V_x_2 = V_y_2 ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff]) ).
fof(f_107_2,plain,
! [U_340,U_339,U_338] :
( ( ( U_339 != U_340
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_338),U_340),U_339))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_338),U_339),U_340)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_338),U_340),U_339))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_338),U_339),U_340))
| U_339 = U_340 ) )
| ~ class_Orderings_Olinorder(U_338) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
cnf(f_107_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_338),U_340),U_339))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_338),U_339),U_340))
| U_339 = U_340
| ~ class_Orderings_Olinorder(U_338) ),
inference(clausify,[status(thm)],[f_107_2]) ).
cnf(f_107_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_338),U_339),U_340))
| U_339 != U_340
| ~ class_Orderings_Olinorder(U_338) ),
inference(clausify,[status(thm)],[f_107_2]) ).
cnf(f_107_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_338),U_340),U_339))
| U_339 != U_340
| ~ class_Orderings_Olinorder(U_338) ),
inference(clausify,[status(thm)],[f_107_2]) ).
fof(f_108_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_linorder__not__le]) ).
fof(f_108_2,plain,
! [U_343,U_342,U_341] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_341),U_342),U_343))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_341),U_343),U_342)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_341),U_343),U_342))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_341),U_342),U_343)) ) )
| ~ class_Orderings_Olinorder(U_341) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
cnf(f_108_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_341),U_343),U_342))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_341),U_342),U_343))
| ~ class_Orderings_Olinorder(U_341) ),
inference(clausify,[status(thm)],[f_108_2]) ).
cnf(f_108_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_341),U_342),U_343))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_341),U_343),U_342))
| ~ class_Orderings_Olinorder(U_341) ),
inference(clausify,[status(thm)],[f_108_2]) ).
fof(f_109_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_linorder__not__less]) ).
fof(f_109_2,plain,
! [U_346,U_345,U_344] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_344),U_345),U_346))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_344),U_346),U_345)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_344),U_346),U_345))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_344),U_345),U_346)) ) )
| ~ class_Orderings_Olinorder(U_344) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
cnf(f_109_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_344),U_346),U_345))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_344),U_345),U_346))
| ~ class_Orderings_Olinorder(U_344) ),
inference(clausify,[status(thm)],[f_109_2]) ).
cnf(f_109_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_344),U_345),U_346))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_344),U_346),U_345))
| ~ class_Orderings_Olinorder(U_344) ),
inference(clausify,[status(thm)],[f_109_2]) ).
fof(f_110_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_110_2,plain,
! [U_348,U_347] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_347),U_348),U_348))
| ~ class_Orderings_Opreorder(U_347) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
cnf(f_110_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_347),U_348),U_348))
| ~ class_Orderings_Opreorder(U_347) ),
inference(clausify,[status(thm)],[f_110_2]) ).
fof(f_111_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_111_2,plain,
! [U_350,U_349] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_349),U_350))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_349)),U_350)) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
cnf(f_111_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_349),U_350))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_349)),U_350)) ),
inference(clausify,[status(thm)],[f_111_2]) ).
fof(f_112_1,plain,
! [V_na_2,V_m_2] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2)))
| V_na_2 != V_m_2 )
& ( V_na_2 = V_m_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ),
inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq]) ).
fof(f_112_2,plain,
! [U_352,U_351] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_352),hAPP(c_Nat_OSuc,U_351)))
| U_352 != U_351 )
& ( U_352 = U_351
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_352),hAPP(c_Nat_OSuc,U_351))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_351),U_352)) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
cnf(f_112_3,plain,
( U_352 = U_351
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_352),hAPP(c_Nat_OSuc,U_351)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_351),U_352)) ),
inference(clausify,[status(thm)],[f_112_2]) ).
cnf(f_112_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_352),hAPP(c_Nat_OSuc,U_351)))
| U_352 != U_351
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_351),U_352)) ),
inference(clausify,[status(thm)],[f_112_2]) ).
fof(f_113_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_113_2,plain,
! [U_354,U_353] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_353)),U_354))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_353),U_354)) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
cnf(f_113_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_353)),U_354))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_353),U_354)) ),
inference(clausify,[status(thm)],[f_113_2]) ).
fof(f_114_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_114_2,plain,
! [U_356,U_355] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_355),hAPP(c_Nat_OSuc,U_356)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_355),U_356)) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
cnf(f_114_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_355),hAPP(c_Nat_OSuc,U_356)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_355),U_356)) ),
inference(clausify,[status(thm)],[f_114_2]) ).
fof(f_115_1,plain,
! [V_na_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_na_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_na_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__le__eq]) ).
fof(f_115_2,plain,
! [U_358,U_357] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_357)),U_358))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_357),U_358)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_357),U_358))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_357)),U_358)) ) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
fof(f_115_3,plain,
( ! [U_362,U_360] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_360)),U_362))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_360),U_362)) )
& ! [U_361,U_359] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_359),U_361))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_359)),U_361)) ) ),
inference(miniscope,[status(thm)],[f_115_2]) ).
cnf(f_115_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_359),U_361))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_359)),U_361)) ),
inference(clausify,[status(thm)],[f_115_3]) ).
cnf(f_115_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_360)),U_362))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_360),U_362)) ),
inference(clausify,[status(thm)],[f_115_3]) ).
fof(f_116_1,plain,
! [V_na_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le]) ).
fof(f_116_2,plain,
! [U_364,U_363] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_363),hAPP(c_Nat_OSuc,U_364)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_363),U_364)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_363),U_364))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_363),hAPP(c_Nat_OSuc,U_364))) ) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
( ! [U_368,U_366] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_366),hAPP(c_Nat_OSuc,U_368)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_366),U_368)) )
& ! [U_367,U_365] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_365),U_367))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_365),hAPP(c_Nat_OSuc,U_367))) ) ),
inference(miniscope,[status(thm)],[f_116_2]) ).
cnf(f_116_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_365),U_367))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_365),hAPP(c_Nat_OSuc,U_367))) ),
inference(clausify,[status(thm)],[f_116_3]) ).
cnf(f_116_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_366),hAPP(c_Nat_OSuc,U_368)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_366),U_368)) ),
inference(clausify,[status(thm)],[f_116_3]) ).
fof(f_117_1,plain,
! [V_m_2,V_na_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le]) ).
fof(f_117_2,plain,
! [U_370,U_369] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_369),U_370))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_369)),U_370)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_369)),U_370))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_369),U_370)) ) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
( ! [U_374,U_372] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_372),U_374))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_372)),U_374)) )
& ! [U_373,U_371] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_371)),U_373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_371),U_373)) ) ),
inference(miniscope,[status(thm)],[f_117_2]) ).
cnf(f_117_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_371)),U_373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_371),U_373)) ),
inference(clausify,[status(thm)],[f_117_3]) ).
cnf(f_117_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_372),U_374))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_372)),U_374)) ),
inference(clausify,[status(thm)],[f_117_3]) ).
fof(f_118_1,plain,
! [V_na_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
| ( ! [B_j] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_na_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_na_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_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__0__disj]) ).
fof(f_118_2,plain,
! [U_378,U_377] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_377),hAPP(c_Nat_OSuc,U_378)))
| ( ! [U_376] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_376),U_378))
| U_377 != hAPP(c_Nat_OSuc,U_376) )
& U_377 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ? [U_375] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_375),U_378))
& U_377 = hAPP(c_Nat_OSuc,U_375) )
| U_377 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_377),hAPP(c_Nat_OSuc,U_378))) ) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
( ! [U_382,U_380] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_380),hAPP(c_Nat_OSuc,U_382)))
| ( ! [U_376] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_376),U_382))
| U_380 != hAPP(c_Nat_OSuc,U_376) )
& U_380 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_381,U_379] :
( ? [U_375] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_375),U_381))
& U_379 = hAPP(c_Nat_OSuc,U_375) )
| U_379 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_379),hAPP(c_Nat_OSuc,U_381))) ) ),
inference(miniscope,[status(thm)],[f_118_2]) ).
fof(f_118_4,plain,
( ! [U_382,U_380] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_380),hAPP(c_Nat_OSuc,U_382)))
| ( ! [U_376] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_376),U_382))
| U_380 != hAPP(c_Nat_OSuc,U_376) )
& U_380 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_381,U_379] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK8(U_381,U_379)),U_381))
& U_379 = hAPP(c_Nat_OSuc,sK8(U_381,U_379)) )
| U_379 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_379),hAPP(c_Nat_OSuc,U_381))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_375,sK8(U_381,U_379))],[f_118_3]) ).
cnf(f_118_5,plain,
( U_379 = hAPP(c_Nat_OSuc,sK8(U_381,U_379))
| U_379 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_379),hAPP(c_Nat_OSuc,U_381))) ),
inference(clausify,[status(thm)],[f_118_4]) ).
cnf(f_118_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK8(U_381,U_379)),U_381))
| U_379 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_379),hAPP(c_Nat_OSuc,U_381))) ),
inference(clausify,[status(thm)],[f_118_4]) ).
cnf(f_118_7,plain,
( U_380 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_380),hAPP(c_Nat_OSuc,U_382))) ),
inference(clausify,[status(thm)],[f_118_4]) ).
cnf(f_118_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_376),U_382))
| U_380 != hAPP(c_Nat_OSuc,U_376)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_380),hAPP(c_Nat_OSuc,U_382))) ),
inference(clausify,[status(thm)],[f_118_4]) ).
fof(f_119_1,plain,
! [V_na_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc0]) ).
fof(f_119_2,plain,
! [U_383] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_383),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_383 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_383 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_383),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
fof(f_119_3,plain,
( ! [U_385] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_385),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_385 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_384] :
( U_384 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_384),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(miniscope,[status(thm)],[f_119_2]) ).
cnf(f_119_4,plain,
( U_384 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_384),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(clausify,[status(thm)],[f_119_3]) ).
cnf(f_119_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_385),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_385 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_119_3]) ).
fof(f_120_1,plain,
! [V_na_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2))
| ! [B_m] : V_na_2 != hAPP(c_Nat_OSuc,B_m) )
& ( ? [B_m] : V_na_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_na_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc]) ).
fof(f_120_2,plain,
! [U_388] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_388))
| ! [U_387] : U_388 != hAPP(c_Nat_OSuc,U_387) )
& ( ? [U_386] : U_388 = hAPP(c_Nat_OSuc,U_386)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_388)) ) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
( ! [U_390] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_390))
| ! [U_387] : U_390 != hAPP(c_Nat_OSuc,U_387) )
& ! [U_389] :
( ? [U_386] : U_389 = hAPP(c_Nat_OSuc,U_386)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_389)) ) ),
inference(miniscope,[status(thm)],[f_120_2]) ).
fof(f_120_4,plain,
( ! [U_390] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_390))
| ! [U_387] : U_390 != hAPP(c_Nat_OSuc,U_387) )
& ! [U_389] :
( U_389 = hAPP(c_Nat_OSuc,sK9(U_389))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_389)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_386,sK9(U_389))],[f_120_3]) ).
cnf(f_120_5,plain,
( U_389 = hAPP(c_Nat_OSuc,sK9(U_389))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_389)) ),
inference(clausify,[status(thm)],[f_120_4]) ).
cnf(f_120_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_390))
| U_390 != hAPP(c_Nat_OSuc,U_387) ),
inference(clausify,[status(thm)],[f_120_4]) ).
fof(f_121_1,plain,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_INF__subset]) ).
fof(f_121_2,plain,
! [U_395,U_394,U_393,U_392,U_391] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_391),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_392,U_391),U_394),U_395)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_392,U_391),U_393),U_395)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_392,tc_HOL_Obool)),U_393),U_394))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_391) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
cnf(f_121_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_391),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_392,U_391),U_394),U_395)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_392,U_391),U_393),U_395)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_392,tc_HOL_Obool)),U_393),U_394))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_391) ),
inference(clausify,[status(thm)],[f_121_2]) ).
fof(f_122_1,plain,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
| ~ class_Orderings_Oorder(T_b)
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_monoD]) ).
fof(f_122_2,plain,
! [U_400,U_399,U_398,U_397,U_396] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_396),hAPP(U_398,U_399)),hAPP(U_398,U_400)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_397),U_399),U_400))
| ~ c_Orderings_Oorder__class_Omono(U_397,U_396,U_398)
| ~ class_Orderings_Oorder(U_397)
| ~ class_Orderings_Oorder(U_396) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
cnf(f_122_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_396),hAPP(U_398,U_399)),hAPP(U_398,U_400)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_397),U_399),U_400))
| ~ c_Orderings_Oorder__class_Omono(U_397,U_396,U_398)
| ~ class_Orderings_Oorder(U_397)
| ~ class_Orderings_Oorder(U_396) ),
inference(clausify,[status(thm)],[f_122_2]) ).
fof(f_123_1,plain,
! [V_na_2,V_m_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_not__less__eq]) ).
fof(f_123_2,plain,
! [U_402,U_401] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_401),U_402))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_402),hAPP(c_Nat_OSuc,U_401))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_402),hAPP(c_Nat_OSuc,U_401)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_401),U_402)) ) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
( ! [U_406,U_404] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_404),U_406))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_406),hAPP(c_Nat_OSuc,U_404))) )
& ! [U_405,U_403] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_405),hAPP(c_Nat_OSuc,U_403)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_403),U_405)) ) ),
inference(miniscope,[status(thm)],[f_123_2]) ).
cnf(f_123_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_405),hAPP(c_Nat_OSuc,U_403)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_403),U_405)) ),
inference(clausify,[status(thm)],[f_123_3]) ).
cnf(f_123_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_404),U_406))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_406),hAPP(c_Nat_OSuc,U_404))) ),
inference(clausify,[status(thm)],[f_123_3]) ).
fof(f_124_1,plain,
! [V_na_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
| ( V_m_2 != V_na_2
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) ) )
& ( V_m_2 = V_na_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq]) ).
fof(f_124_2,plain,
! [U_408,U_407] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_407),hAPP(c_Nat_OSuc,U_408)))
| ( U_407 != U_408
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_407),U_408)) ) )
& ( U_407 = U_408
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_407),U_408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_407),hAPP(c_Nat_OSuc,U_408))) ) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
( ! [U_412,U_410] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_410),hAPP(c_Nat_OSuc,U_412)))
| ( U_410 != U_412
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_410),U_412)) ) )
& ! [U_411,U_409] :
( U_409 = U_411
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_409),U_411))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_409),hAPP(c_Nat_OSuc,U_411))) ) ),
inference(miniscope,[status(thm)],[f_124_2]) ).
cnf(f_124_4,plain,
( U_409 = U_411
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_409),U_411))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_409),hAPP(c_Nat_OSuc,U_411))) ),
inference(clausify,[status(thm)],[f_124_3]) ).
cnf(f_124_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_410),U_412))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_410),hAPP(c_Nat_OSuc,U_412))) ),
inference(clausify,[status(thm)],[f_124_3]) ).
cnf(f_124_6,plain,
( U_410 != U_412
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_410),hAPP(c_Nat_OSuc,U_412))) ),
inference(clausify,[status(thm)],[f_124_3]) ).
fof(f_125_1,plain,
! [V_na_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_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__less__eq]) ).
fof(f_125_2,plain,
! [U_414,U_413] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_413)),hAPP(c_Nat_OSuc,U_414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_413),U_414)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_413),U_414))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_413)),hAPP(c_Nat_OSuc,U_414))) ) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
( ! [U_418,U_416] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_416)),hAPP(c_Nat_OSuc,U_418)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_416),U_418)) )
& ! [U_417,U_415] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_415),U_417))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_415)),hAPP(c_Nat_OSuc,U_417))) ) ),
inference(miniscope,[status(thm)],[f_125_2]) ).
cnf(f_125_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_415),U_417))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_415)),hAPP(c_Nat_OSuc,U_417))) ),
inference(clausify,[status(thm)],[f_125_3]) ).
cnf(f_125_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_416)),hAPP(c_Nat_OSuc,U_418)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_416),U_418)) ),
inference(clausify,[status(thm)],[f_125_3]) ).
fof(f_126_1,plain,
! [V_m_2,V_na_2] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2)))
| V_na_2 != V_m_2 )
& ( V_na_2 = V_m_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),hAPP(c_Nat_OSuc,V_m_2))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) ),
inference(fof_nnf,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(f_126_2,plain,
! [U_420,U_419] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_419),hAPP(c_Nat_OSuc,U_420)))
| U_419 != U_420 )
& ( U_419 = U_420
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_419),hAPP(c_Nat_OSuc,U_420))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_419),U_420)) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
cnf(f_126_3,plain,
( U_419 = U_420
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_419),hAPP(c_Nat_OSuc,U_420)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_419),U_420)) ),
inference(clausify,[status(thm)],[f_126_2]) ).
cnf(f_126_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_419),hAPP(c_Nat_OSuc,U_420)))
| U_419 != U_420
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_419),U_420)) ),
inference(clausify,[status(thm)],[f_126_2]) ).
fof(f_127_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_127_2,plain,
! [U_422,U_421] :
( U_422 = U_421
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_421),hAPP(c_Nat_OSuc,U_422)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_421),U_422)) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
cnf(f_127_3,plain,
( U_422 = U_421
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_421),hAPP(c_Nat_OSuc,U_422)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_421),U_422)) ),
inference(clausify,[status(thm)],[f_127_2]) ).
fof(f_128_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_128_2,plain,
! [U_424,U_423] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_423),hAPP(c_Nat_OSuc,U_424)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_423),U_424)) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
cnf(f_128_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_423),hAPP(c_Nat_OSuc,U_424)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_423),U_424)) ),
inference(clausify,[status(thm)],[f_128_2]) ).
fof(f_129_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_129_2,plain,
! [U_426,U_425] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_425)),U_426))
| hAPP(c_Nat_OSuc,U_425) = U_426
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_425),U_426)) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
cnf(f_129_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_425)),U_426))
| hAPP(c_Nat_OSuc,U_425) = U_426
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_425),U_426)) ),
inference(clausify,[status(thm)],[f_129_2]) ).
fof(f_130_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_130_2,plain,
! [U_429,U_428,U_427] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_427)),U_429))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_428),U_429))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_427),U_428)) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
cnf(f_130_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_427)),U_429))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_428),U_429))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_427),U_428)) ),
inference(clausify,[status(thm)],[f_130_2]) ).
fof(f_131_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_131_2,plain,
! [U_431,U_430] :
( U_430 = U_431
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_430),U_431))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_430),hAPP(c_Nat_OSuc,U_431))) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
cnf(f_131_3,plain,
( U_430 = U_431
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_430),U_431))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_430),hAPP(c_Nat_OSuc,U_431))) ),
inference(clausify,[status(thm)],[f_131_2]) ).
fof(f_132_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_132_2,plain,
! [U_433,U_432] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_432),U_433))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_432)),U_433)) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
cnf(f_132_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_432),U_433))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_432)),U_433)) ),
inference(clausify,[status(thm)],[f_132_2]) ).
fof(f_133_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_133_2,plain,
! [U_435,U_434] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_434),U_435))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_434)),hAPP(c_Nat_OSuc,U_435))) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
cnf(f_133_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_434),U_435))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_434)),hAPP(c_Nat_OSuc,U_435))) ),
inference(clausify,[status(thm)],[f_133_2]) ).
fof(f_134_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_134_2,plain,
! [U_436] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_436)),U_436)),
inference(variable_rename,[status(thm)],[f_134_1]) ).
cnf(f_134_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_436)),U_436)),
inference(clausify,[status(thm)],[f_134_2]) ).
fof(f_135_1,plain,
! [V_na_2,V_m_2] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_not__less__eq__eq]) ).
fof(f_135_2,plain,
! [U_438,U_437] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_437),U_438))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_438)),U_437)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_438)),U_437))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_437),U_438)) ) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
fof(f_135_3,plain,
( ! [U_442,U_440] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_440),U_442))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_442)),U_440)) )
& ! [U_441,U_439] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_441)),U_439))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_439),U_441)) ) ),
inference(miniscope,[status(thm)],[f_135_2]) ).
cnf(f_135_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_441)),U_439))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_439),U_441)) ),
inference(clausify,[status(thm)],[f_135_3]) ).
cnf(f_135_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_440),U_442))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_442)),U_440)) ),
inference(clausify,[status(thm)],[f_135_3]) ).
fof(f_136_1,plain,
! [V_na_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)))
| ( V_m_2 != hAPP(c_Nat_OSuc,V_na_2)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) )
& ( V_m_2 = hAPP(c_Nat_OSuc,V_na_2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_le__Suc__eq]) ).
fof(f_136_2,plain,
! [U_444,U_443] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_443),hAPP(c_Nat_OSuc,U_444)))
| ( U_443 != hAPP(c_Nat_OSuc,U_444)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_443),U_444)) ) )
& ( U_443 = hAPP(c_Nat_OSuc,U_444)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_443),U_444))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_443),hAPP(c_Nat_OSuc,U_444))) ) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
fof(f_136_3,plain,
( ! [U_448,U_446] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_446),hAPP(c_Nat_OSuc,U_448)))
| ( U_446 != hAPP(c_Nat_OSuc,U_448)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_446),U_448)) ) )
& ! [U_447,U_445] :
( U_445 = hAPP(c_Nat_OSuc,U_447)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_445),U_447))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_445),hAPP(c_Nat_OSuc,U_447))) ) ),
inference(miniscope,[status(thm)],[f_136_2]) ).
cnf(f_136_4,plain,
( U_445 = hAPP(c_Nat_OSuc,U_447)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_445),U_447))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_445),hAPP(c_Nat_OSuc,U_447))) ),
inference(clausify,[status(thm)],[f_136_3]) ).
cnf(f_136_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_446),U_448))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_446),hAPP(c_Nat_OSuc,U_448))) ),
inference(clausify,[status(thm)],[f_136_3]) ).
cnf(f_136_6,plain,
( U_446 != hAPP(c_Nat_OSuc,U_448)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_446),hAPP(c_Nat_OSuc,U_448))) ),
inference(clausify,[status(thm)],[f_136_3]) ).
fof(f_137_1,plain,
! [V_m_2,V_na_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),hAPP(c_Nat_OSuc,V_m_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_m_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_m_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),hAPP(c_Nat_OSuc,V_m_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__le__mono]) ).
fof(f_137_2,plain,
! [U_450,U_449] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_449)),hAPP(c_Nat_OSuc,U_450)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_449),U_450)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_449),U_450))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_449)),hAPP(c_Nat_OSuc,U_450))) ) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
( ! [U_454,U_452] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_452)),hAPP(c_Nat_OSuc,U_454)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_452),U_454)) )
& ! [U_453,U_451] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_451),U_453))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_451)),hAPP(c_Nat_OSuc,U_453))) ) ),
inference(miniscope,[status(thm)],[f_137_2]) ).
cnf(f_137_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_451),U_453))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_451)),hAPP(c_Nat_OSuc,U_453))) ),
inference(clausify,[status(thm)],[f_137_3]) ).
cnf(f_137_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_452)),hAPP(c_Nat_OSuc,U_454)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_452),U_454)) ),
inference(clausify,[status(thm)],[f_137_3]) ).
fof(f_138_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_138_2,plain,
! [U_456,U_455] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_455),hAPP(c_Nat_OSuc,U_456)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_455),U_456)) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
cnf(f_138_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_455),hAPP(c_Nat_OSuc,U_456)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_455),U_456)) ),
inference(clausify,[status(thm)],[f_138_2]) ).
fof(f_139_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_139_2,plain,
! [U_458,U_457] :
( U_457 = hAPP(c_Nat_OSuc,U_458)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_457),U_458))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_457),hAPP(c_Nat_OSuc,U_458))) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
cnf(f_139_3,plain,
( U_457 = hAPP(c_Nat_OSuc,U_458)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_457),U_458))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_457),hAPP(c_Nat_OSuc,U_458))) ),
inference(clausify,[status(thm)],[f_139_2]) ).
fof(f_140_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_140_2,plain,
! [U_460,U_459] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_459),U_460))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_459)),U_460)) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
cnf(f_140_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_459),U_460))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_459)),U_460)) ),
inference(clausify,[status(thm)],[f_140_2]) ).
fof(f_141_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_141_2,plain,
! [U_461] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_461),
inference(variable_rename,[status(thm)],[f_141_1]) ).
cnf(f_141_3,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_461),
inference(clausify,[status(thm)],[f_141_2]) ).
fof(f_142_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_142_2,plain,
! [U_462] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_462),
inference(variable_rename,[status(thm)],[f_142_1]) ).
cnf(f_142_3,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_462),
inference(clausify,[status(thm)],[f_142_2]) ).
fof(f_143_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_143_2,plain,
! [U_463] : hAPP(c_Nat_OSuc,U_463) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_143_1]) ).
cnf(f_143_3,plain,
hAPP(c_Nat_OSuc,U_463) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_143_2]) ).
fof(f_144_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_144_2,plain,
! [U_467,U_466,U_465,U_464] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_464),hAPP(hAPP(c_Power_Opower__class_Opower(U_464),U_465),U_467)),hAPP(hAPP(c_Power_Opower__class_Opower(U_464),U_466),U_467)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_467))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_464),c_Groups_Ozero__class_Ozero(U_464)),U_465))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_464),U_465),U_466))
| ~ class_Rings_Olinordered__semidom(U_464) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
cnf(f_144_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_464),hAPP(hAPP(c_Power_Opower__class_Opower(U_464),U_465),U_467)),hAPP(hAPP(c_Power_Opower__class_Opower(U_464),U_466),U_467)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_467))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_464),c_Groups_Ozero__class_Ozero(U_464)),U_465))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_464),U_465),U_466))
| ~ class_Rings_Olinordered__semidom(U_464) ),
inference(clausify,[status(thm)],[f_144_2]) ).
fof(f_145_1,plain,
! [V_na_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2))) ) )
| ~ class_Rings_Olinordered__semidom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__0__less__iff]) ).
fof(f_145_2,plain,
! [U_469,U_468] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_468),c_Groups_Ozero__class_Ozero(U_468)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_468),U_469)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_469)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_469))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_468),c_Groups_Ozero__class_Ozero(U_468)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_468),U_469))) ) )
| ~ class_Rings_Olinordered__semidom(U_468) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
cnf(f_145_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_469))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_468),c_Groups_Ozero__class_Ozero(U_468)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_468),U_469)))
| ~ class_Rings_Olinordered__semidom(U_468) ),
inference(clausify,[status(thm)],[f_145_2]) ).
cnf(f_145_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_468),c_Groups_Ozero__class_Ozero(U_468)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_468),U_469)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_469))
| ~ class_Rings_Olinordered__semidom(U_468) ),
inference(clausify,[status(thm)],[f_145_2]) ).
fof(f_146_1,plain,
! [V_n] :
( ? [B_m] : V_n = 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)) ),
inference(fof_nnf,[status(thm)],[fact_gr0__implies__Suc]) ).
fof(f_146_2,plain,
! [U_471] :
( ? [U_470] : U_471 = hAPP(c_Nat_OSuc,U_470)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_471)) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
fof(f_146_3,plain,
! [U_471] :
( U_471 = hAPP(c_Nat_OSuc,sK10(U_471))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_471)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_470,sK10(U_471))],[f_146_2]) ).
cnf(f_146_4,plain,
( U_471 = hAPP(c_Nat_OSuc,sK10(U_471))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_471)) ),
inference(clausify,[status(thm)],[f_146_3]) ).
fof(f_147_1,plain,
! [V_m_2,V_na_2,V_f_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_na_2)),hAPP(V_f_2,V_m_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_na_2)),hAPP(V_f_2,V_m_2))) ) )
| ? [B_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n))))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lift__Suc__mono__less__iff]) ).
fof(f_147_2,plain,
! [U_476,U_475,U_474,U_473] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_473),hAPP(U_474,U_475)),hAPP(U_474,U_476)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_475),U_476)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_475),U_476))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_473),hAPP(U_474,U_475)),hAPP(U_474,U_476))) ) )
| ? [U_472] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_473),hAPP(U_474,U_472)),hAPP(U_474,hAPP(c_Nat_OSuc,U_472))))
| ~ class_Orderings_Oorder(U_473) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
! [U_476,U_475,U_474,U_473] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_473),hAPP(U_474,U_475)),hAPP(U_474,U_476)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_475),U_476)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_475),U_476))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_473),hAPP(U_474,U_475)),hAPP(U_474,U_476))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_473),hAPP(U_474,sK11(U_476,U_475,U_474,U_473))),hAPP(U_474,hAPP(c_Nat_OSuc,sK11(U_476,U_475,U_474,U_473)))))
| ~ class_Orderings_Oorder(U_473) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_472,sK11(U_476,U_475,U_474,U_473))],[f_147_2]) ).
cnf(f_147_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_475),U_476))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_473),hAPP(U_474,U_475)),hAPP(U_474,U_476)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_473),hAPP(U_474,sK11(U_476,U_475,U_474,U_473))),hAPP(U_474,hAPP(c_Nat_OSuc,sK11(U_476,U_475,U_474,U_473)))))
| ~ class_Orderings_Oorder(U_473) ),
inference(clausify,[status(thm)],[f_147_3]) ).
cnf(f_147_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_473),hAPP(U_474,U_475)),hAPP(U_474,U_476)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_475),U_476))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_473),hAPP(U_474,sK11(U_476,U_475,U_474,U_473))),hAPP(U_474,hAPP(c_Nat_OSuc,sK11(U_476,U_475,U_474,U_473)))))
| ~ class_Orderings_Oorder(U_473) ),
inference(clausify,[status(thm)],[f_147_3]) ).
fof(f_148_1,plain,
! [V_n_H_2,V_na_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_na_2)),hAPP(V_f_2,V_n_H_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_n_H_2))
| ? [B_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n))))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lift__Suc__mono__less]) ).
fof(f_148_2,plain,
! [U_481,U_480,U_479,U_478] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_478),hAPP(U_479,U_480)),hAPP(U_479,U_481)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_480),U_481))
| ? [U_477] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_478),hAPP(U_479,U_477)),hAPP(U_479,hAPP(c_Nat_OSuc,U_477))))
| ~ class_Orderings_Oorder(U_478) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
! [U_481,U_480,U_479,U_478] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_478),hAPP(U_479,U_480)),hAPP(U_479,U_481)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_480),U_481))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_478),hAPP(U_479,sK12(U_481,U_480,U_479,U_478))),hAPP(U_479,hAPP(c_Nat_OSuc,sK12(U_481,U_480,U_479,U_478)))))
| ~ class_Orderings_Oorder(U_478) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_477,sK12(U_481,U_480,U_479,U_478))],[f_148_2]) ).
cnf(f_148_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_478),hAPP(U_479,U_480)),hAPP(U_479,U_481)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_480),U_481))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_478),hAPP(U_479,sK12(U_481,U_480,U_479,U_478))),hAPP(U_479,hAPP(c_Nat_OSuc,sK12(U_481,U_480,U_479,U_478)))))
| ~ class_Orderings_Oorder(U_478) ),
inference(clausify,[status(thm)],[f_148_3]) ).
fof(f_149_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_149_2,plain,
! [U_485,U_484,U_483,U_482] :
( U_483 = U_485
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_484))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_482),c_Groups_Ozero__class_Ozero(U_482)),U_485))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_482),c_Groups_Ozero__class_Ozero(U_482)),U_483))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_482),U_483),U_484) != hAPP(hAPP(c_Power_Opower__class_Opower(U_482),U_485),U_484)
| ~ class_Rings_Olinordered__semidom(U_482) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
cnf(f_149_3,plain,
( U_483 = U_485
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_484))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_482),c_Groups_Ozero__class_Ozero(U_482)),U_485))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_482),c_Groups_Ozero__class_Ozero(U_482)),U_483))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_482),U_483),U_484) != hAPP(hAPP(c_Power_Opower__class_Opower(U_482),U_485),U_484)
| ~ class_Rings_Olinordered__semidom(U_482) ),
inference(clausify,[status(thm)],[f_149_2]) ).
fof(f_150_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_150_2,plain,
! [U_487,U_486] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_486),U_487))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_486),U_487)) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
cnf(f_150_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_486),U_487))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_486),U_487)) ),
inference(clausify,[status(thm)],[f_150_2]) ).
fof(f_151_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_151_2,plain,
! [U_490,U_489,U_488] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_488),U_490),U_489))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_488),U_489),U_490))
| U_489 = U_490
| ~ class_Rings_Olinordered__idom(U_488) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
cnf(f_151_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_488),U_490),U_489))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_488),U_489),U_490))
| U_489 = U_490
| ~ class_Rings_Olinordered__idom(U_488) ),
inference(clausify,[status(thm)],[f_151_2]) ).
fof(f_152_1,plain,
! [V_x_2,T_b] :
( ( ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
| V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
| c_Groups_Ozero__class_Ozero(T_b) != V_x_2 ) )
| ~ class_Groups_Ozero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_zero__reorient]) ).
fof(f_152_2,plain,
! [U_492,U_491] :
( ( ( c_Groups_Ozero__class_Ozero(U_491) = U_492
| U_492 != c_Groups_Ozero__class_Ozero(U_491) )
& ( U_492 = c_Groups_Ozero__class_Ozero(U_491)
| c_Groups_Ozero__class_Ozero(U_491) != U_492 ) )
| ~ class_Groups_Ozero(U_491) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
cnf(f_152_3,plain,
( U_492 = c_Groups_Ozero__class_Ozero(U_491)
| c_Groups_Ozero__class_Ozero(U_491) != U_492
| ~ class_Groups_Ozero(U_491) ),
inference(clausify,[status(thm)],[f_152_2]) ).
cnf(f_152_4,plain,
( c_Groups_Ozero__class_Ozero(U_491) = U_492
| U_492 != c_Groups_Ozero__class_Ozero(U_491)
| ~ class_Groups_Ozero(U_491) ),
inference(clausify,[status(thm)],[f_152_2]) ).
fof(f_153_1,plain,
! [V_f_2,T_b,T_c] :
( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
| ? [B_x,B_y] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),B_y)) )
| ~ class_Orderings_Oorder(T_b)
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_strict__monoI]) ).
fof(f_153_2,plain,
! [U_497,U_496,U_495] :
( c_Orderings_Oorder__class_Ostrict__mono(U_496,U_495,U_497)
| ? [U_494,U_493] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_495),hAPP(U_497,U_494)),hAPP(U_497,U_493)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_496),U_494),U_493)) )
| ~ class_Orderings_Oorder(U_496)
| ~ class_Orderings_Oorder(U_495) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
! [U_497,U_496,U_495] :
( c_Orderings_Oorder__class_Ostrict__mono(U_496,U_495,U_497)
| ? [U_493] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_495),hAPP(U_497,sK13(U_497,U_496,U_495))),hAPP(U_497,U_493)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_496),sK13(U_497,U_496,U_495)),U_493)) )
| ~ class_Orderings_Oorder(U_496)
| ~ class_Orderings_Oorder(U_495) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_494,sK13(U_497,U_496,U_495))],[f_153_2]) ).
fof(f_153_4,plain,
! [U_497,U_496,U_495] :
( c_Orderings_Oorder__class_Ostrict__mono(U_496,U_495,U_497)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_495),hAPP(U_497,sK13(U_497,U_496,U_495))),hAPP(U_497,sK14(U_497,U_496,U_495))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_496),sK13(U_497,U_496,U_495)),sK14(U_497,U_496,U_495))) )
| ~ class_Orderings_Oorder(U_496)
| ~ class_Orderings_Oorder(U_495) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_493,sK14(U_497,U_496,U_495))],[f_153_3]) ).
cnf(f_153_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_496),sK13(U_497,U_496,U_495)),sK14(U_497,U_496,U_495)))
| c_Orderings_Oorder__class_Ostrict__mono(U_496,U_495,U_497)
| ~ class_Orderings_Oorder(U_496)
| ~ class_Orderings_Oorder(U_495) ),
inference(clausify,[status(thm)],[f_153_4]) ).
cnf(f_153_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_495),hAPP(U_497,sK13(U_497,U_496,U_495))),hAPP(U_497,sK14(U_497,U_496,U_495))))
| c_Orderings_Oorder__class_Ostrict__mono(U_496,U_495,U_497)
| ~ class_Orderings_Oorder(U_496)
| ~ class_Orderings_Oorder(U_495) ),
inference(clausify,[status(thm)],[f_153_4]) ).
fof(f_154_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_154_2,plain,
! [U_499,U_498] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_498),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_499),U_498)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_499))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_498)) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
cnf(f_154_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_498),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_499),U_498)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_499))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_498)) ),
inference(clausify,[status(thm)],[f_154_2]) ).
fof(f_155_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_155_2,plain,
! [U_500] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_500),U_500)),
inference(variable_rename,[status(thm)],[f_155_1]) ).
cnf(f_155_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_500),U_500)),
inference(clausify,[status(thm)],[f_155_2]) ).
fof(f_156_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_156_2,plain,
! [U_501] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_501),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_501),U_501))),
inference(variable_rename,[status(thm)],[f_156_1]) ).
cnf(f_156_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_501),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_501),U_501))),
inference(clausify,[status(thm)],[f_156_2]) ).
fof(f_157_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_157_2,plain,
! [U_502] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_502),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_502),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_502),U_502)))),
inference(variable_rename,[status(thm)],[f_157_1]) ).
cnf(f_157_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_502),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_502),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_502),U_502)))),
inference(clausify,[status(thm)],[f_157_2]) ).
fof(f_158_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_158_2,plain,
! [U_504,U_503] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_504),U_503))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_503),U_504)) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
cnf(f_158_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_504),U_503))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_503),U_504)) ),
inference(clausify,[status(thm)],[f_158_2]) ).
fof(f_159_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_159_2,plain,
! [U_506,U_505] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_505),U_506))
| U_505 != U_506 ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
cnf(f_159_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_505),U_506))
| U_505 != U_506 ),
inference(clausify,[status(thm)],[f_159_2]) ).
fof(f_160_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_160_2,plain,
! [U_509,U_508,U_507] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_507),U_509)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_508),U_509)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_507),U_508)) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
cnf(f_160_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_507),U_509)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_508),U_509)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_507),U_508)) ),
inference(clausify,[status(thm)],[f_160_2]) ).
fof(f_161_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_161_2,plain,
! [U_512,U_511,U_510] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_512),U_510)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_512),U_511)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_510),U_511)) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
cnf(f_161_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_512),U_510)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_512),U_511)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_510),U_511)) ),
inference(clausify,[status(thm)],[f_161_2]) ).
fof(f_162_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_162_2,plain,
! [U_515,U_514,U_513] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_513),U_515))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_514),U_515))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_513),U_514)) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
cnf(f_162_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_513),U_515))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_514),U_515))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_513),U_514)) ),
inference(clausify,[status(thm)],[f_162_2]) ).
fof(f_163_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_163_2,plain,
! [U_517,U_516] :
( U_516 = U_517
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_517),U_516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_516),U_517)) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
cnf(f_163_3,plain,
( U_516 = U_517
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_517),U_516))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_516),U_517)) ),
inference(clausify,[status(thm)],[f_163_2]) ).
fof(f_164_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_164_2,plain,
! [U_521,U_520,U_519,U_518] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_518),U_520)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_519),U_521)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_520),U_521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_518),U_519)) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
cnf(f_164_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_518),U_520)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_519),U_521)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_520),U_521))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_518),U_519)) ),
inference(clausify,[status(thm)],[f_164_2]) ).
fof(f_165_1,plain,
! [V_g_2,V_f_2,T_b,T_c] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) )
| ~ class_Orderings_Oord(T_c) ),
inference(fof_nnf,[status(thm)],[fact_less__fun__def]) ).
fof(f_165_2,plain,
! [U_525,U_524,U_523,U_522] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_523,U_522)),U_524),U_525))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,U_522)),U_525),U_524))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,U_522)),U_524),U_525)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,U_522)),U_525),U_524))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,U_522)),U_524),U_525)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_523,U_522)),U_524),U_525)) ) )
| ~ class_Orderings_Oord(U_522) ),
inference(variable_rename,[status(thm)],[f_165_1]) ).
cnf(f_165_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,U_522)),U_524),U_525))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_523,U_522)),U_524),U_525))
| ~ class_Orderings_Oord(U_522) ),
inference(clausify,[status(thm)],[f_165_2]) ).
cnf(f_165_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,U_522)),U_525),U_524))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_523,U_522)),U_524),U_525))
| ~ class_Orderings_Oord(U_522) ),
inference(clausify,[status(thm)],[f_165_2]) ).
cnf(f_165_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_523,U_522)),U_524),U_525))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,U_522)),U_525),U_524))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_523,U_522)),U_524),U_525))
| ~ class_Orderings_Oord(U_522) ),
inference(clausify,[status(thm)],[f_165_2]) ).
fof(f_166_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_166_2,plain,
! [U_529,U_528,U_527,U_526] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_526),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_526),U_527),U_528)),U_529) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_526),U_527),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_526),U_528),U_529))
| ~ class_Groups_Oab__semigroup__mult(U_526) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
cnf(f_166_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_526),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_526),U_527),U_528)),U_529) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_526),U_527),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_526),U_528),U_529))
| ~ class_Groups_Oab__semigroup__mult(U_526) ),
inference(clausify,[status(thm)],[f_166_2]) ).
fof(f_167_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_167_2,plain,
! [U_533,U_532,U_531,U_530] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_530),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_530),U_531),U_532)),U_533) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_530),hAPP(hAPP(c_Power_Opower__class_Opower(U_530),U_531),U_533)),hAPP(hAPP(c_Power_Opower__class_Opower(U_530),U_532),U_533))
| ~ class_Groups_Ocomm__monoid__mult(U_530) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
cnf(f_167_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_530),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_530),U_531),U_532)),U_533) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_530),hAPP(hAPP(c_Power_Opower__class_Opower(U_530),U_531),U_533)),hAPP(hAPP(c_Power_Opower__class_Opower(U_530),U_532),U_533))
| ~ class_Groups_Ocomm__monoid__mult(U_530) ),
inference(clausify,[status(thm)],[f_167_2]) ).
fof(f_168_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_168_2,plain,
! [U_536,U_535,U_534] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_534),U_535)),U_536) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_534),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_535),U_536)),
inference(variable_rename,[status(thm)],[f_168_1]) ).
cnf(f_168_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_534),U_535)),U_536) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_534),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_535),U_536)),
inference(clausify,[status(thm)],[f_168_2]) ).
fof(f_169_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_169_2,plain,
! [U_539,U_538,U_537] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_537),hAPP(hAPP(c_Power_Opower__class_Opower(U_537),U_538),U_539)),U_538) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_537),U_538),hAPP(hAPP(c_Power_Opower__class_Opower(U_537),U_538),U_539))
| ~ class_Groups_Omonoid__mult(U_537) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
cnf(f_169_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_537),hAPP(hAPP(c_Power_Opower__class_Opower(U_537),U_538),U_539)),U_538) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_537),U_538),hAPP(hAPP(c_Power_Opower__class_Opower(U_537),U_538),U_539))
| ~ class_Groups_Omonoid__mult(U_537) ),
inference(clausify,[status(thm)],[f_169_2]) ).
fof(f_170_1,plain,
! [V_na_2,V_m_2,T_b] :
( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)
| V_m_2 != V_na_2 )
& ( V_m_2 = V_na_2
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2) ) )
| ~ class_Nat_Osemiring__char__0(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__eq__iff]) ).
fof(f_170_2,plain,
! [U_542,U_541,U_540] :
( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_540),U_541) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_540),U_542)
| U_541 != U_542 )
& ( U_541 = U_542
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_540),U_541) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_540),U_542) ) )
| ~ class_Nat_Osemiring__char__0(U_540) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
cnf(f_170_3,plain,
( U_541 = U_542
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_540),U_541) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_540),U_542)
| ~ class_Nat_Osemiring__char__0(U_540) ),
inference(clausify,[status(thm)],[f_170_2]) ).
cnf(f_170_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_540),U_541) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_540),U_542)
| U_541 != U_542
| ~ class_Nat_Osemiring__char__0(U_540) ),
inference(clausify,[status(thm)],[f_170_2]) ).
fof(f_171_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_171_2,plain,
! [U_546,U_545,U_544,U_543] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_543),U_544),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_545),U_546)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_543),hAPP(hAPP(c_Power_Opower__class_Opower(U_543),U_544),U_545)),U_546)
| ~ class_Groups_Omonoid__mult(U_543) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
cnf(f_171_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_543),U_544),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_545),U_546)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_543),hAPP(hAPP(c_Power_Opower__class_Opower(U_543),U_544),U_545)),U_546)
| ~ class_Groups_Omonoid__mult(U_543) ),
inference(clausify,[status(thm)],[f_171_2]) ).
fof(f_172_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_172_2,plain,
! [U_548,U_547] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_547),U_548) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_548),U_547),
inference(variable_rename,[status(thm)],[f_172_1]) ).
cnf(f_172_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_547),U_548) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_548),U_547),
inference(clausify,[status(thm)],[f_172_2]) ).
fof(f_173_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_173_2,plain,
! [U_551,U_550,U_549] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_549),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_550),U_551)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_549),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_549),U_550)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_549),U_551))
| ~ class_Rings_Osemiring__1(U_549) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
cnf(f_173_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_549),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_550),U_551)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_549),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_549),U_550)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_549),U_551))
| ~ class_Rings_Osemiring__1(U_549) ),
inference(clausify,[status(thm)],[f_173_2]) ).
fof(f_174_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_174_2,plain,
! [U_554,U_553,U_552] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_552),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_553),U_554)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_552),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_552),U_553)),U_554)
| ~ class_Rings_Osemiring__1(U_552) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
cnf(f_174_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_552),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_553),U_554)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_552),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_552),U_553)),U_554)
| ~ class_Rings_Osemiring__1(U_552) ),
inference(clausify,[status(thm)],[f_174_2]) ).
fof(f_175_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_175_2,plain,
! [U_557,U_556,U_555] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_555),U_556),hAPP(c_Nat_OSuc,U_557)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_555),U_556),hAPP(hAPP(c_Power_Opower__class_Opower(U_555),U_556),U_557))
| ~ class_Power_Opower(U_555) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
cnf(f_175_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_555),U_556),hAPP(c_Nat_OSuc,U_557)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_555),U_556),hAPP(hAPP(c_Power_Opower__class_Opower(U_555),U_556),U_557))
| ~ class_Power_Opower(U_555) ),
inference(clausify,[status(thm)],[f_175_2]) ).
fof(f_176_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_176_2,plain,
! [U_560,U_559,U_558] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_558),U_559),hAPP(c_Nat_OSuc,U_560)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_558),hAPP(hAPP(c_Power_Opower__class_Opower(U_558),U_559),U_560)),U_559)
| ~ class_Groups_Omonoid__mult(U_558) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
cnf(f_176_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_558),U_559),hAPP(c_Nat_OSuc,U_560)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_558),hAPP(hAPP(c_Power_Opower__class_Opower(U_558),U_559),U_560)),U_559)
| ~ class_Groups_Omonoid__mult(U_558) ),
inference(clausify,[status(thm)],[f_176_2]) ).
fof(f_177_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_177_2,plain,
! [U_562,U_561] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_561),c_Groups_Ozero__class_Ozero(U_561)),U_562) = c_Groups_Ozero__class_Ozero(U_561)
| ~ class_Rings_Omult__zero(U_561) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
cnf(f_177_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_561),c_Groups_Ozero__class_Ozero(U_561)),U_562) = c_Groups_Ozero__class_Ozero(U_561)
| ~ class_Rings_Omult__zero(U_561) ),
inference(clausify,[status(thm)],[f_177_2]) ).
fof(f_178_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_178_2,plain,
! [U_564,U_563] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_563),U_564),c_Groups_Ozero__class_Ozero(U_563)) = c_Groups_Ozero__class_Ozero(U_563)
| ~ class_Rings_Omult__zero(U_563) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
cnf(f_178_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_563),U_564),c_Groups_Ozero__class_Ozero(U_563)) = c_Groups_Ozero__class_Ozero(U_563)
| ~ class_Rings_Omult__zero(U_563) ),
inference(clausify,[status(thm)],[f_178_2]) ).
fof(f_179_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
| ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
& V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
& ( V_b_2 = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Rings_Oring__no__zero__divisors(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff]) ).
fof(f_179_2,plain,
! [U_567,U_566,U_565] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_565),U_566),U_567) = c_Groups_Ozero__class_Ozero(U_565)
| ( U_567 != c_Groups_Ozero__class_Ozero(U_565)
& U_566 != c_Groups_Ozero__class_Ozero(U_565) ) )
& ( U_567 = c_Groups_Ozero__class_Ozero(U_565)
| U_566 = c_Groups_Ozero__class_Ozero(U_565)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_565),U_566),U_567) != c_Groups_Ozero__class_Ozero(U_565) ) )
| ~ class_Rings_Oring__no__zero__divisors(U_565) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
cnf(f_179_3,plain,
( U_567 = c_Groups_Ozero__class_Ozero(U_565)
| U_566 = c_Groups_Ozero__class_Ozero(U_565)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_565),U_566),U_567) != c_Groups_Ozero__class_Ozero(U_565)
| ~ class_Rings_Oring__no__zero__divisors(U_565) ),
inference(clausify,[status(thm)],[f_179_2]) ).
cnf(f_179_4,plain,
( U_566 != c_Groups_Ozero__class_Ozero(U_565)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_565),U_566),U_567) = c_Groups_Ozero__class_Ozero(U_565)
| ~ class_Rings_Oring__no__zero__divisors(U_565) ),
inference(clausify,[status(thm)],[f_179_2]) ).
cnf(f_179_5,plain,
( U_567 != c_Groups_Ozero__class_Ozero(U_565)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_565),U_566),U_567) = c_Groups_Ozero__class_Ozero(U_565)
| ~ class_Rings_Oring__no__zero__divisors(U_565) ),
inference(clausify,[status(thm)],[f_179_2]) ).
fof(f_180_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_180_2,plain,
! [U_570,U_569,U_568] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_568),U_569),U_570) != c_Groups_Ozero__class_Ozero(U_568)
| U_570 = c_Groups_Ozero__class_Ozero(U_568)
| U_569 = c_Groups_Ozero__class_Ozero(U_568)
| ~ class_Rings_Ono__zero__divisors(U_568) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
cnf(f_180_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_568),U_569),U_570) != c_Groups_Ozero__class_Ozero(U_568)
| U_570 = c_Groups_Ozero__class_Ozero(U_568)
| U_569 = c_Groups_Ozero__class_Ozero(U_568)
| ~ class_Rings_Ono__zero__divisors(U_568) ),
inference(clausify,[status(thm)],[f_180_2]) ).
fof(f_181_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_181_2,plain,
! [U_573,U_572,U_571] :
( U_573 = c_Groups_Ozero__class_Ozero(U_571)
| U_572 = c_Groups_Ozero__class_Ozero(U_571)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_571),U_572),U_573) != c_Groups_Ozero__class_Ozero(U_571)
| ~ class_Rings_Ono__zero__divisors(U_571) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
cnf(f_181_3,plain,
( U_573 = c_Groups_Ozero__class_Ozero(U_571)
| U_572 = c_Groups_Ozero__class_Ozero(U_571)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_571),U_572),U_573) != c_Groups_Ozero__class_Ozero(U_571)
| ~ class_Rings_Ono__zero__divisors(U_571) ),
inference(clausify,[status(thm)],[f_181_2]) ).
fof(f_182_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_182_2,plain,
! [U_576,U_575,U_574] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_574),U_575),U_576) != c_Groups_Ozero__class_Ozero(U_574)
| U_575 = c_Groups_Ozero__class_Ozero(U_574)
| ~ class_Rings_Oring__1__no__zero__divisors(U_574) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
cnf(f_182_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_574),U_575),U_576) != c_Groups_Ozero__class_Ozero(U_574)
| U_575 = c_Groups_Ozero__class_Ozero(U_574)
| ~ class_Rings_Oring__1__no__zero__divisors(U_574) ),
inference(clausify,[status(thm)],[f_182_2]) ).
fof(f_183_1,plain,
! [V_na_2,V_m_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2))) ) )
| ~ class_Rings_Olinordered__semidom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__le__iff]) ).
fof(f_183_2,plain,
! [U_579,U_578,U_577] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_577),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_577),U_578)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_577),U_579)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_578),U_579)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_578),U_579))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_577),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_577),U_578)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_577),U_579))) ) )
| ~ class_Rings_Olinordered__semidom(U_577) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
cnf(f_183_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_578),U_579))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_577),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_577),U_578)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_577),U_579)))
| ~ class_Rings_Olinordered__semidom(U_577) ),
inference(clausify,[status(thm)],[f_183_2]) ).
cnf(f_183_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_577),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_577),U_578)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_577),U_579)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_578),U_579))
| ~ class_Rings_Olinordered__semidom(U_577) ),
inference(clausify,[status(thm)],[f_183_2]) ).
fof(f_184_1,plain,
! [V_na_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_na_2),V_k_2)
| ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 != V_na_2 ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_na_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_na_2),V_k_2) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__cancel2]) ).
fof(f_184_2,plain,
! [U_582,U_581,U_580] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_580),U_581) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_582),U_581)
| ( U_581 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_580 != U_582 ) )
& ( U_581 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_580 = U_582
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_580),U_581) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_582),U_581) ) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
fof(f_184_3,plain,
( ! [U_588,U_586,U_584] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_584),U_586) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_588),U_586)
| ( U_586 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_584 != U_588 ) )
& ! [U_587,U_585,U_583] :
( U_585 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_583 = U_587
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_583),U_585) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_587),U_585) ) ),
inference(miniscope,[status(thm)],[f_184_2]) ).
cnf(f_184_4,plain,
( U_585 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_583 = U_587
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_583),U_585) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_587),U_585) ),
inference(clausify,[status(thm)],[f_184_3]) ).
cnf(f_184_5,plain,
( U_584 != U_588
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_584),U_586) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_588),U_586) ),
inference(clausify,[status(thm)],[f_184_3]) ).
cnf(f_184_6,plain,
( U_586 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_584),U_586) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_588),U_586) ),
inference(clausify,[status(thm)],[f_184_3]) ).
fof(f_185_1,plain,
! [V_na_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_na_2)
| ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 != V_na_2 ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_na_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_na_2) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__cancel1]) ).
fof(f_185_2,plain,
! [U_591,U_590,U_589] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_589),U_590) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_589),U_591)
| ( U_589 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_590 != U_591 ) )
& ( U_589 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_590 = U_591
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_589),U_590) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_589),U_591) ) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
fof(f_185_3,plain,
( ! [U_597,U_595,U_593] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_593),U_595) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_593),U_597)
| ( U_593 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_595 != U_597 ) )
& ! [U_596,U_594,U_592] :
( U_592 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_594 = U_596
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_592),U_594) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_592),U_596) ) ),
inference(miniscope,[status(thm)],[f_185_2]) ).
cnf(f_185_4,plain,
( U_592 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_594 = U_596
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_592),U_594) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_592),U_596) ),
inference(clausify,[status(thm)],[f_185_3]) ).
cnf(f_185_5,plain,
( U_595 != U_597
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_593),U_595) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_593),U_597) ),
inference(clausify,[status(thm)],[f_185_3]) ).
cnf(f_185_6,plain,
( U_593 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_593),U_595) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_593),U_597) ),
inference(clausify,[status(thm)],[f_185_3]) ).
fof(f_186_1,plain,
! [V_na_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_na_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( V_na_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_na_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__is__0]) ).
fof(f_186_2,plain,
! [U_599,U_598] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_598),U_599) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( U_599 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_598 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_599 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_598 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_598),U_599) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
fof(f_186_3,plain,
( ! [U_603,U_601] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_601),U_603) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( U_603 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_601 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_602,U_600] :
( U_602 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_600 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_600),U_602) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_186_2]) ).
cnf(f_186_4,plain,
( U_602 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_600 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_600),U_602) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_186_3]) ).
cnf(f_186_5,plain,
( U_601 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_601),U_603) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_186_3]) ).
cnf(f_186_6,plain,
( U_603 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_601),U_603) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_186_3]) ).
fof(f_187_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_187_2,plain,
! [U_604] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_604),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_187_1]) ).
cnf(f_187_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_604),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_187_2]) ).
fof(f_188_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_188_2,plain,
! [U_605] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_605) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_188_1]) ).
cnf(f_188_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_605) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_188_2]) ).
fof(f_189_1,plain,
! [V_na_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_na_2)
| V_m_2 != V_na_2 )
& ( V_m_2 = V_na_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_na_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1]) ).
fof(f_189_2,plain,
! [U_608,U_607,U_606] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_606)),U_607) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_606)),U_608)
| U_607 != U_608 )
& ( U_607 = U_608
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_606)),U_607) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_606)),U_608) ) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
fof(f_189_3,plain,
( ! [U_614,U_612] :
( ! [U_610] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_610)),U_612) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_610)),U_614)
| U_612 != U_614 )
& ! [U_613,U_611] :
( ! [U_609] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_609)),U_611) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_609)),U_613)
| U_611 = U_613 ) ),
inference(miniscope,[status(thm)],[f_189_2]) ).
cnf(f_189_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_609)),U_611) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_609)),U_613)
| U_611 = U_613 ),
inference(clausify,[status(thm)],[f_189_3]) ).
cnf(f_189_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_610)),U_612) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_610)),U_614)
| U_612 != U_614 ),
inference(clausify,[status(thm)],[f_189_3]) ).
fof(f_190_1,plain,
! [V_na_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_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_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_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1]) ).
fof(f_190_2,plain,
! [U_617,U_616,U_615] :
( ( 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_615)),U_616)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_615)),U_617)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_616),U_617)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_616),U_617))
| ~ 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_615)),U_616)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_615)),U_617))) ) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
fof(f_190_3,plain,
( ! [U_623,U_621] :
( ! [U_619] : 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_619)),U_621)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_619)),U_623)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_621),U_623)) )
& ! [U_622,U_620] :
( ! [U_618] : ~ 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_618)),U_620)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_618)),U_622)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_620),U_622)) ) ),
inference(miniscope,[status(thm)],[f_190_2]) ).
cnf(f_190_4,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_618)),U_620)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_618)),U_622)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_620),U_622)) ),
inference(clausify,[status(thm)],[f_190_3]) ).
cnf(f_190_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_619)),U_621)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_619)),U_623)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_621),U_623)) ),
inference(clausify,[status(thm)],[f_190_3]) ).
fof(f_191_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_191_2,plain,
! [U_625,U_624] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_624),c_Groups_Ozero__class_Ozero(U_624)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_624),U_625),U_625)))
| ~ class_Rings_Olinordered__ring(U_624) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
cnf(f_191_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_624),c_Groups_Ozero__class_Ozero(U_624)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_624),U_625),U_625)))
| ~ class_Rings_Olinordered__ring(U_624) ),
inference(clausify,[status(thm)],[f_191_2]) ).
fof(f_192_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff]) ).
fof(f_192_2,plain,
! [U_628,U_627,U_626] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),c_Groups_Ozero__class_Ozero(U_626)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_626),U_627),U_628)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),U_628),c_Groups_Ozero__class_Ozero(U_626)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),U_627),c_Groups_Ozero__class_Ozero(U_626))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),c_Groups_Ozero__class_Ozero(U_626)),U_628))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),c_Groups_Ozero__class_Ozero(U_626)),U_627)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),U_628),c_Groups_Ozero__class_Ozero(U_626)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),U_627),c_Groups_Ozero__class_Ozero(U_626))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),c_Groups_Ozero__class_Ozero(U_626)),U_628))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),c_Groups_Ozero__class_Ozero(U_626)),U_627)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),c_Groups_Ozero__class_Ozero(U_626)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_626),U_627),U_628))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_626) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
cnf(f_192_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),U_627),c_Groups_Ozero__class_Ozero(U_626)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),c_Groups_Ozero__class_Ozero(U_626)),U_627))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),c_Groups_Ozero__class_Ozero(U_626)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_626),U_627),U_628)))
| ~ class_Rings_Olinordered__ring__strict(U_626) ),
inference(clausify,[status(thm)],[f_192_2]) ).
cnf(f_192_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),U_628),c_Groups_Ozero__class_Ozero(U_626)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),c_Groups_Ozero__class_Ozero(U_626)),U_627))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),c_Groups_Ozero__class_Ozero(U_626)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_626),U_627),U_628)))
| ~ class_Rings_Olinordered__ring__strict(U_626) ),
inference(clausify,[status(thm)],[f_192_2]) ).
cnf(f_192_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),U_627),c_Groups_Ozero__class_Ozero(U_626)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),c_Groups_Ozero__class_Ozero(U_626)),U_628))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),c_Groups_Ozero__class_Ozero(U_626)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_626),U_627),U_628)))
| ~ class_Rings_Olinordered__ring__strict(U_626) ),
inference(clausify,[status(thm)],[f_192_2]) ).
cnf(f_192_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),U_628),c_Groups_Ozero__class_Ozero(U_626)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),c_Groups_Ozero__class_Ozero(U_626)),U_628))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),c_Groups_Ozero__class_Ozero(U_626)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_626),U_627),U_628)))
| ~ class_Rings_Olinordered__ring__strict(U_626) ),
inference(clausify,[status(thm)],[f_192_2]) ).
cnf(f_192_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),c_Groups_Ozero__class_Ozero(U_626)),U_628))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),c_Groups_Ozero__class_Ozero(U_626)),U_627))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),c_Groups_Ozero__class_Ozero(U_626)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_626),U_627),U_628)))
| ~ class_Rings_Olinordered__ring__strict(U_626) ),
inference(clausify,[status(thm)],[f_192_2]) ).
cnf(f_192_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),U_628),c_Groups_Ozero__class_Ozero(U_626)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),U_627),c_Groups_Ozero__class_Ozero(U_626)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_626),c_Groups_Ozero__class_Ozero(U_626)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_626),U_627),U_628)))
| ~ class_Rings_Olinordered__ring__strict(U_626) ),
inference(clausify,[status(thm)],[f_192_2]) ).
fof(f_193_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff]) ).
fof(f_193_2,plain,
! [U_631,U_630,U_629] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_629),U_630),U_631)),c_Groups_Ozero__class_Ozero(U_629)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),c_Groups_Ozero__class_Ozero(U_629)),U_631))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),U_630),c_Groups_Ozero__class_Ozero(U_629))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),U_631),c_Groups_Ozero__class_Ozero(U_629)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),c_Groups_Ozero__class_Ozero(U_629)),U_630)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),c_Groups_Ozero__class_Ozero(U_629)),U_631))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),U_630),c_Groups_Ozero__class_Ozero(U_629))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),U_631),c_Groups_Ozero__class_Ozero(U_629)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),c_Groups_Ozero__class_Ozero(U_629)),U_630)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_629),U_630),U_631)),c_Groups_Ozero__class_Ozero(U_629))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_629) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
cnf(f_193_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),U_630),c_Groups_Ozero__class_Ozero(U_629)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),c_Groups_Ozero__class_Ozero(U_629)),U_630))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_629),U_630),U_631)),c_Groups_Ozero__class_Ozero(U_629)))
| ~ class_Rings_Olinordered__ring__strict(U_629) ),
inference(clausify,[status(thm)],[f_193_2]) ).
cnf(f_193_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),c_Groups_Ozero__class_Ozero(U_629)),U_631))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),c_Groups_Ozero__class_Ozero(U_629)),U_630))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_629),U_630),U_631)),c_Groups_Ozero__class_Ozero(U_629)))
| ~ class_Rings_Olinordered__ring__strict(U_629) ),
inference(clausify,[status(thm)],[f_193_2]) ).
cnf(f_193_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),U_630),c_Groups_Ozero__class_Ozero(U_629)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),U_631),c_Groups_Ozero__class_Ozero(U_629)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_629),U_630),U_631)),c_Groups_Ozero__class_Ozero(U_629)))
| ~ class_Rings_Olinordered__ring__strict(U_629) ),
inference(clausify,[status(thm)],[f_193_2]) ).
cnf(f_193_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),c_Groups_Ozero__class_Ozero(U_629)),U_631))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),U_631),c_Groups_Ozero__class_Ozero(U_629)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_629),U_630),U_631)),c_Groups_Ozero__class_Ozero(U_629)))
| ~ class_Rings_Olinordered__ring__strict(U_629) ),
inference(clausify,[status(thm)],[f_193_2]) ).
cnf(f_193_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),U_631),c_Groups_Ozero__class_Ozero(U_629)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),c_Groups_Ozero__class_Ozero(U_629)),U_630))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_629),U_630),U_631)),c_Groups_Ozero__class_Ozero(U_629)))
| ~ class_Rings_Olinordered__ring__strict(U_629) ),
inference(clausify,[status(thm)],[f_193_2]) ).
cnf(f_193_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),c_Groups_Ozero__class_Ozero(U_629)),U_631))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),U_630),c_Groups_Ozero__class_Ozero(U_629)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_629),U_630),U_631)),c_Groups_Ozero__class_Ozero(U_629)))
| ~ class_Rings_Olinordered__ring__strict(U_629) ),
inference(clausify,[status(thm)],[f_193_2]) ).
fof(f_194_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_194_2,plain,
! [U_634,U_633,U_632] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_632),c_Groups_Ozero__class_Ozero(U_632)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_632),U_633),U_634)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_632),c_Groups_Ozero__class_Ozero(U_632)),U_634))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_632),c_Groups_Ozero__class_Ozero(U_632)),U_633))
| ~ class_Rings_Oordered__cancel__semiring(U_632) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
cnf(f_194_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_632),c_Groups_Ozero__class_Ozero(U_632)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_632),U_633),U_634)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_632),c_Groups_Ozero__class_Ozero(U_632)),U_634))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_632),c_Groups_Ozero__class_Ozero(U_632)),U_633))
| ~ class_Rings_Oordered__cancel__semiring(U_632) ),
inference(clausify,[status(thm)],[f_194_2]) ).
fof(f_195_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_195_2,plain,
! [U_637,U_636,U_635] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_635),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_635),U_636),U_637)),c_Groups_Ozero__class_Ozero(U_635)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_635),U_637),c_Groups_Ozero__class_Ozero(U_635)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_635),c_Groups_Ozero__class_Ozero(U_635)),U_636))
| ~ class_Rings_Oordered__cancel__semiring(U_635) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
cnf(f_195_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_635),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_635),U_636),U_637)),c_Groups_Ozero__class_Ozero(U_635)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_635),U_637),c_Groups_Ozero__class_Ozero(U_635)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_635),c_Groups_Ozero__class_Ozero(U_635)),U_636))
| ~ class_Rings_Oordered__cancel__semiring(U_635) ),
inference(clausify,[status(thm)],[f_195_2]) ).
fof(f_196_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_196_2,plain,
! [U_640,U_639,U_638] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_638),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_638),U_640),U_639)),c_Groups_Ozero__class_Ozero(U_638)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_638),U_640),c_Groups_Ozero__class_Ozero(U_638)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_638),c_Groups_Ozero__class_Ozero(U_638)),U_639))
| ~ class_Rings_Oordered__cancel__semiring(U_638) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
cnf(f_196_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_638),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_638),U_640),U_639)),c_Groups_Ozero__class_Ozero(U_638)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_638),U_640),c_Groups_Ozero__class_Ozero(U_638)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_638),c_Groups_Ozero__class_Ozero(U_638)),U_639))
| ~ class_Rings_Oordered__cancel__semiring(U_638) ),
inference(clausify,[status(thm)],[f_196_2]) ).
fof(f_197_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_197_2,plain,
! [U_643,U_642,U_641] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_641),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_641),U_642),U_643)),c_Groups_Ozero__class_Ozero(U_641)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_641),c_Groups_Ozero__class_Ozero(U_641)),U_643))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_641),U_642),c_Groups_Ozero__class_Ozero(U_641)))
| ~ class_Rings_Oordered__cancel__semiring(U_641) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
cnf(f_197_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_641),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_641),U_642),U_643)),c_Groups_Ozero__class_Ozero(U_641)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_641),c_Groups_Ozero__class_Ozero(U_641)),U_643))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_641),U_642),c_Groups_Ozero__class_Ozero(U_641)))
| ~ class_Rings_Oordered__cancel__semiring(U_641) ),
inference(clausify,[status(thm)],[f_197_2]) ).
fof(f_198_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_198_2,plain,
! [U_646,U_645,U_644] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_644),c_Groups_Ozero__class_Ozero(U_644)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_644),U_645),U_646)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_644),U_646),c_Groups_Ozero__class_Ozero(U_644)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_644),U_645),c_Groups_Ozero__class_Ozero(U_644)))
| ~ class_Rings_Oordered__ring(U_644) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
cnf(f_198_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_644),c_Groups_Ozero__class_Ozero(U_644)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_644),U_645),U_646)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_644),U_646),c_Groups_Ozero__class_Ozero(U_644)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_644),U_645),c_Groups_Ozero__class_Ozero(U_644)))
| ~ class_Rings_Oordered__ring(U_644) ),
inference(clausify,[status(thm)],[f_198_2]) ).
fof(f_199_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_199_2,plain,
! [U_650,U_649,U_648,U_647] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_647),U_648),U_650)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_647),U_649),U_650)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_647),c_Groups_Ozero__class_Ozero(U_647)),U_650))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_647),U_648),U_649))
| ~ class_Rings_Oordered__semiring(U_647) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
cnf(f_199_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_647),U_648),U_650)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_647),U_649),U_650)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_647),c_Groups_Ozero__class_Ozero(U_647)),U_650))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_647),U_648),U_649))
| ~ class_Rings_Oordered__semiring(U_647) ),
inference(clausify,[status(thm)],[f_199_2]) ).
fof(f_200_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_200_2,plain,
! [U_654,U_653,U_652,U_651] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_651),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_651),U_654),U_652)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_651),U_654),U_653)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_651),c_Groups_Ozero__class_Ozero(U_651)),U_654))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_651),U_652),U_653))
| ~ class_Rings_Oordered__semiring(U_651) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
cnf(f_200_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_651),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_651),U_654),U_652)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_651),U_654),U_653)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_651),c_Groups_Ozero__class_Ozero(U_651)),U_654))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_651),U_652),U_653))
| ~ class_Rings_Oordered__semiring(U_651) ),
inference(clausify,[status(thm)],[f_200_2]) ).
fof(f_201_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_201_2,plain,
! [U_658,U_657,U_656,U_655] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_655),U_658),U_656)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_655),U_658),U_657)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_655),c_Groups_Ozero__class_Ozero(U_655)),U_658))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_655),U_656),U_657))
| ~ class_Rings_Oordered__comm__semiring(U_655) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
cnf(f_201_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_655),U_658),U_656)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_655),U_658),U_657)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_655),c_Groups_Ozero__class_Ozero(U_655)),U_658))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_655),U_656),U_657))
| ~ class_Rings_Oordered__comm__semiring(U_655) ),
inference(clausify,[status(thm)],[f_201_2]) ).
fof(f_202_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_202_2,plain,
! [U_662,U_661,U_660,U_659] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_659),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_659),U_661),U_662)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_659),U_660),U_662)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_659),U_662),c_Groups_Ozero__class_Ozero(U_659)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_659),U_660),U_661))
| ~ class_Rings_Oordered__ring(U_659) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
cnf(f_202_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_659),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_659),U_661),U_662)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_659),U_660),U_662)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_659),U_662),c_Groups_Ozero__class_Ozero(U_659)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_659),U_660),U_661))
| ~ class_Rings_Oordered__ring(U_659) ),
inference(clausify,[status(thm)],[f_202_2]) ).
fof(f_203_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_203_2,plain,
! [U_666,U_665,U_664,U_663] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_665)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_664)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_663),U_666),c_Groups_Ozero__class_Ozero(U_663)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_663),U_664),U_665))
| ~ class_Rings_Oordered__ring(U_663) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
cnf(f_203_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_665)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_664)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_663),U_666),c_Groups_Ozero__class_Ozero(U_663)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_663),U_664),U_665))
| ~ class_Rings_Oordered__ring(U_663) ),
inference(clausify,[status(thm)],[f_203_2]) ).
fof(f_204_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_204_2,plain,
! [U_671,U_670,U_669,U_668,U_667] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_667),U_668),U_670)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_667),U_669),U_671)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_667),c_Groups_Ozero__class_Ozero(U_667)),U_670))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_667),c_Groups_Ozero__class_Ozero(U_667)),U_668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_667),U_670),U_671))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_667),U_668),U_669))
| ~ class_Rings_Oordered__semiring(U_667) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
cnf(f_204_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_667),U_668),U_670)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_667),U_669),U_671)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_667),c_Groups_Ozero__class_Ozero(U_667)),U_670))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_667),c_Groups_Ozero__class_Ozero(U_667)),U_668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_667),U_670),U_671))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_667),U_668),U_669))
| ~ class_Rings_Oordered__semiring(U_667) ),
inference(clausify,[status(thm)],[f_204_2]) ).
fof(f_205_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_205_2,plain,
! [U_676,U_675,U_674,U_673,U_672] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_672),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_672),U_673),U_675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_672),U_674),U_676)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_672),c_Groups_Ozero__class_Ozero(U_672)),U_675))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_672),c_Groups_Ozero__class_Ozero(U_672)),U_674))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_672),U_675),U_676))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_672),U_673),U_674))
| ~ class_Rings_Oordered__semiring(U_672) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
cnf(f_205_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_672),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_672),U_673),U_675)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_672),U_674),U_676)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_672),c_Groups_Ozero__class_Ozero(U_672)),U_675))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_672),c_Groups_Ozero__class_Ozero(U_672)),U_674))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_672),U_675),U_676))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_672),U_673),U_674))
| ~ class_Rings_Oordered__semiring(U_672) ),
inference(clausify,[status(thm)],[f_205_2]) ).
fof(f_206_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_206_2,plain,
! [U_679,U_678,U_677] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_677),c_Groups_Ozero__class_Ozero(U_677)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_677),U_678),U_679)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_677),U_679),c_Groups_Ozero__class_Ozero(U_677)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_677),U_678),c_Groups_Ozero__class_Ozero(U_677))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_677),c_Groups_Ozero__class_Ozero(U_677)),U_679))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_677),c_Groups_Ozero__class_Ozero(U_677)),U_678)) ) )
| ~ class_Rings_Oordered__ring(U_677) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
cnf(f_206_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_677),c_Groups_Ozero__class_Ozero(U_677)),U_679))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_677),c_Groups_Ozero__class_Ozero(U_677)),U_678))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_677),c_Groups_Ozero__class_Ozero(U_677)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_677),U_678),U_679)))
| ~ class_Rings_Oordered__ring(U_677) ),
inference(clausify,[status(thm)],[f_206_2]) ).
cnf(f_206_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_677),U_679),c_Groups_Ozero__class_Ozero(U_677)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_677),U_678),c_Groups_Ozero__class_Ozero(U_677)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_677),c_Groups_Ozero__class_Ozero(U_677)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_677),U_678),U_679)))
| ~ class_Rings_Oordered__ring(U_677) ),
inference(clausify,[status(thm)],[f_206_2]) ).
fof(f_207_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_207_2,plain,
! [U_682,U_681,U_680] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_680),U_681),U_682)),c_Groups_Ozero__class_Ozero(U_680)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_680),c_Groups_Ozero__class_Ozero(U_680)),U_682))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_680),U_681),c_Groups_Ozero__class_Ozero(U_680))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_680),U_682),c_Groups_Ozero__class_Ozero(U_680)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_680),c_Groups_Ozero__class_Ozero(U_680)),U_681)) ) )
| ~ class_Rings_Oordered__cancel__semiring(U_680) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
cnf(f_207_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_680),U_682),c_Groups_Ozero__class_Ozero(U_680)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_680),c_Groups_Ozero__class_Ozero(U_680)),U_681))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_680),U_681),U_682)),c_Groups_Ozero__class_Ozero(U_680)))
| ~ class_Rings_Oordered__cancel__semiring(U_680) ),
inference(clausify,[status(thm)],[f_207_2]) ).
cnf(f_207_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_680),c_Groups_Ozero__class_Ozero(U_680)),U_682))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_680),U_681),c_Groups_Ozero__class_Ozero(U_680)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_680),U_681),U_682)),c_Groups_Ozero__class_Ozero(U_680)))
| ~ class_Rings_Oordered__cancel__semiring(U_680) ),
inference(clausify,[status(thm)],[f_207_2]) ).
fof(f_208_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_208_2,plain,
! [U_684,U_683] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_683),U_684),U_684)),c_Groups_Ozero__class_Ozero(U_683)))
| ~ class_Rings_Olinordered__ring(U_683) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
cnf(f_208_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_683),U_684),U_684)),c_Groups_Ozero__class_Ozero(U_683)))
| ~ class_Rings_Olinordered__ring(U_683) ),
inference(clausify,[status(thm)],[f_208_2]) ).
fof(f_209_1,plain,
! [V_b_2,V_c_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj]) ).
fof(f_209_2,plain,
! [U_688,U_687,U_686,U_685] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_685),U_686),U_687)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_685),U_688),U_687)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),U_688),U_686))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),U_687),c_Groups_Ozero__class_Ozero(U_685))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),U_686),U_688))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),c_Groups_Ozero__class_Ozero(U_685)),U_687)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),U_688),U_686))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),U_687),c_Groups_Ozero__class_Ozero(U_685))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),U_686),U_688))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),c_Groups_Ozero__class_Ozero(U_685)),U_687)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_685),U_686),U_687)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_685),U_688),U_687))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_685) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
cnf(f_209_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),U_687),c_Groups_Ozero__class_Ozero(U_685)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),c_Groups_Ozero__class_Ozero(U_685)),U_687))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_685),U_686),U_687)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_685),U_688),U_687)))
| ~ class_Rings_Olinordered__ring__strict(U_685) ),
inference(clausify,[status(thm)],[f_209_2]) ).
cnf(f_209_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),U_688),U_686))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),c_Groups_Ozero__class_Ozero(U_685)),U_687))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_685),U_686),U_687)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_685),U_688),U_687)))
| ~ class_Rings_Olinordered__ring__strict(U_685) ),
inference(clausify,[status(thm)],[f_209_2]) ).
cnf(f_209_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),U_687),c_Groups_Ozero__class_Ozero(U_685)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),U_686),U_688))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_685),U_686),U_687)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_685),U_688),U_687)))
| ~ class_Rings_Olinordered__ring__strict(U_685) ),
inference(clausify,[status(thm)],[f_209_2]) ).
cnf(f_209_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),U_688),U_686))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),U_686),U_688))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_685),U_686),U_687)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_685),U_688),U_687)))
| ~ class_Rings_Olinordered__ring__strict(U_685) ),
inference(clausify,[status(thm)],[f_209_2]) ).
cnf(f_209_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),U_686),U_688))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),c_Groups_Ozero__class_Ozero(U_685)),U_687))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_685),U_686),U_687)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_685),U_688),U_687)))
| ~ class_Rings_Olinordered__ring__strict(U_685) ),
inference(clausify,[status(thm)],[f_209_2]) ).
cnf(f_209_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),U_688),U_686))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),U_687),c_Groups_Ozero__class_Ozero(U_685)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_685),U_686),U_687)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_685),U_688),U_687)))
| ~ class_Rings_Olinordered__ring__strict(U_685) ),
inference(clausify,[status(thm)],[f_209_2]) ).
fof(f_210_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj]) ).
fof(f_210_2,plain,
! [U_692,U_691,U_690,U_689] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),U_691)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),U_692)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),U_692),U_691))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),U_690),c_Groups_Ozero__class_Ozero(U_689))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),U_691),U_692))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),c_Groups_Ozero__class_Ozero(U_689)),U_690)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),U_692),U_691))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),U_690),c_Groups_Ozero__class_Ozero(U_689))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),U_691),U_692))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),c_Groups_Ozero__class_Ozero(U_689)),U_690)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),U_691)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),U_692))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_689) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
cnf(f_210_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),U_690),c_Groups_Ozero__class_Ozero(U_689)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),c_Groups_Ozero__class_Ozero(U_689)),U_690))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),U_691)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),U_692)))
| ~ class_Rings_Olinordered__ring__strict(U_689) ),
inference(clausify,[status(thm)],[f_210_2]) ).
cnf(f_210_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),U_692),U_691))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),c_Groups_Ozero__class_Ozero(U_689)),U_690))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),U_691)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),U_692)))
| ~ class_Rings_Olinordered__ring__strict(U_689) ),
inference(clausify,[status(thm)],[f_210_2]) ).
cnf(f_210_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),U_690),c_Groups_Ozero__class_Ozero(U_689)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),U_691),U_692))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),U_691)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),U_692)))
| ~ class_Rings_Olinordered__ring__strict(U_689) ),
inference(clausify,[status(thm)],[f_210_2]) ).
cnf(f_210_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),U_692),U_691))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),U_691),U_692))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),U_691)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),U_692)))
| ~ class_Rings_Olinordered__ring__strict(U_689) ),
inference(clausify,[status(thm)],[f_210_2]) ).
cnf(f_210_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),U_691),U_692))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),c_Groups_Ozero__class_Ozero(U_689)),U_690))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),U_691)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),U_692)))
| ~ class_Rings_Olinordered__ring__strict(U_689) ),
inference(clausify,[status(thm)],[f_210_2]) ).
cnf(f_210_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),U_692),U_691))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),U_690),c_Groups_Ozero__class_Ozero(U_689)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_689),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),U_691)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_689),U_690),U_692)))
| ~ class_Rings_Olinordered__ring__strict(U_689) ),
inference(clausify,[status(thm)],[f_210_2]) ).
fof(f_211_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos]) ).
fof(f_211_2,plain,
! [U_696,U_695,U_694,U_693] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_693),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_694),U_695)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_694),U_696)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_693),U_695),U_696)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_693),U_695),U_696))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_693),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_694),U_695)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_694),U_696))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_693),c_Groups_Ozero__class_Ozero(U_693)),U_694))
| ~ class_Rings_Olinordered__ring__strict(U_693) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
cnf(f_211_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_693),U_695),U_696))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_693),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_694),U_695)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_694),U_696)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_693),c_Groups_Ozero__class_Ozero(U_693)),U_694))
| ~ class_Rings_Olinordered__ring__strict(U_693) ),
inference(clausify,[status(thm)],[f_211_2]) ).
cnf(f_211_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_693),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_694),U_695)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_694),U_696)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_693),U_695),U_696))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_693),c_Groups_Ozero__class_Ozero(U_693)),U_694))
| ~ class_Rings_Olinordered__ring__strict(U_693) ),
inference(clausify,[status(thm)],[f_211_2]) ).
fof(f_212_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_212_2,plain,
! [U_699,U_698,U_697] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_697),c_Groups_Ozero__class_Ozero(U_697)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_697),U_698),U_699)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_697),c_Groups_Ozero__class_Ozero(U_697)),U_699))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_697),c_Groups_Ozero__class_Ozero(U_697)),U_698))
| ~ class_Rings_Olinordered__semiring__strict(U_697) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
cnf(f_212_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_697),c_Groups_Ozero__class_Ozero(U_697)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_697),U_698),U_699)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_697),c_Groups_Ozero__class_Ozero(U_697)),U_699))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_697),c_Groups_Ozero__class_Ozero(U_697)),U_698))
| ~ class_Rings_Olinordered__semiring__strict(U_697) ),
inference(clausify,[status(thm)],[f_212_2]) ).
fof(f_213_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_213_2,plain,
! [U_702,U_701,U_700] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_700),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_700),U_701),U_702)),c_Groups_Ozero__class_Ozero(U_700)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_700),U_702),c_Groups_Ozero__class_Ozero(U_700)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_700),c_Groups_Ozero__class_Ozero(U_700)),U_701))
| ~ class_Rings_Olinordered__semiring__strict(U_700) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
cnf(f_213_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_700),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_700),U_701),U_702)),c_Groups_Ozero__class_Ozero(U_700)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_700),U_702),c_Groups_Ozero__class_Ozero(U_700)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_700),c_Groups_Ozero__class_Ozero(U_700)),U_701))
| ~ class_Rings_Olinordered__semiring__strict(U_700) ),
inference(clausify,[status(thm)],[f_213_2]) ).
fof(f_214_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_214_2,plain,
! [U_705,U_704,U_703] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_703),U_705),U_704)),c_Groups_Ozero__class_Ozero(U_703)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_703),U_705),c_Groups_Ozero__class_Ozero(U_703)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_703),c_Groups_Ozero__class_Ozero(U_703)),U_704))
| ~ class_Rings_Olinordered__semiring__strict(U_703) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
cnf(f_214_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_703),U_705),U_704)),c_Groups_Ozero__class_Ozero(U_703)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_703),U_705),c_Groups_Ozero__class_Ozero(U_703)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_703),c_Groups_Ozero__class_Ozero(U_703)),U_704))
| ~ class_Rings_Olinordered__semiring__strict(U_703) ),
inference(clausify,[status(thm)],[f_214_2]) ).
fof(f_215_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_215_2,plain,
! [U_708,U_707,U_706] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),c_Groups_Ozero__class_Ozero(U_706)),U_708))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),c_Groups_Ozero__class_Ozero(U_706)),U_707))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),c_Groups_Ozero__class_Ozero(U_706)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_706),U_707),U_708)))
| ~ class_Rings_Olinordered__semiring__strict(U_706) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
cnf(f_215_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),c_Groups_Ozero__class_Ozero(U_706)),U_708))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),c_Groups_Ozero__class_Ozero(U_706)),U_707))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),c_Groups_Ozero__class_Ozero(U_706)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_706),U_707),U_708)))
| ~ class_Rings_Olinordered__semiring__strict(U_706) ),
inference(clausify,[status(thm)],[f_215_2]) ).
fof(f_216_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_216_2,plain,
! [U_711,U_710,U_709] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_709),c_Groups_Ozero__class_Ozero(U_709)),U_710))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_709),c_Groups_Ozero__class_Ozero(U_709)),U_711))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_709),c_Groups_Ozero__class_Ozero(U_709)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_709),U_710),U_711)))
| ~ class_Rings_Olinordered__semiring__strict(U_709) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
cnf(f_216_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_709),c_Groups_Ozero__class_Ozero(U_709)),U_710))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_709),c_Groups_Ozero__class_Ozero(U_709)),U_711))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_709),c_Groups_Ozero__class_Ozero(U_709)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_709),U_710),U_711)))
| ~ class_Rings_Olinordered__semiring__strict(U_709) ),
inference(clausify,[status(thm)],[f_216_2]) ).
fof(f_217_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg]) ).
fof(f_217_2,plain,
! [U_715,U_714,U_713,U_712] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_712),U_713),U_714)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_712),U_713),U_715)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_712),U_715),U_714)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_712),U_715),U_714))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_712),U_713),U_714)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_712),U_713),U_715))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_712),U_713),c_Groups_Ozero__class_Ozero(U_712)))
| ~ class_Rings_Olinordered__ring__strict(U_712) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
cnf(f_217_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_712),U_715),U_714))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_712),U_713),U_714)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_712),U_713),U_715)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_712),U_713),c_Groups_Ozero__class_Ozero(U_712)))
| ~ class_Rings_Olinordered__ring__strict(U_712) ),
inference(clausify,[status(thm)],[f_217_2]) ).
cnf(f_217_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_712),U_713),U_714)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_712),U_713),U_715)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_712),U_715),U_714))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_712),U_713),c_Groups_Ozero__class_Ozero(U_712)))
| ~ class_Rings_Olinordered__ring__strict(U_712) ),
inference(clausify,[status(thm)],[f_217_2]) ).
fof(f_218_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_218_2,plain,
! [U_718,U_717,U_716] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_716),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_716),U_717),U_718)),c_Groups_Ozero__class_Ozero(U_716)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_716),c_Groups_Ozero__class_Ozero(U_716)),U_718))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_716),U_717),c_Groups_Ozero__class_Ozero(U_716)))
| ~ class_Rings_Olinordered__semiring__strict(U_716) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
cnf(f_218_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_716),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_716),U_717),U_718)),c_Groups_Ozero__class_Ozero(U_716)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_716),c_Groups_Ozero__class_Ozero(U_716)),U_718))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_716),U_717),c_Groups_Ozero__class_Ozero(U_716)))
| ~ class_Rings_Olinordered__semiring__strict(U_716) ),
inference(clausify,[status(thm)],[f_218_2]) ).
fof(f_219_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_219_2,plain,
! [U_721,U_720,U_719] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_719),c_Groups_Ozero__class_Ozero(U_719)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_719),U_720),U_721)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_719),U_721),c_Groups_Ozero__class_Ozero(U_719)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_719),U_720),c_Groups_Ozero__class_Ozero(U_719)))
| ~ class_Rings_Olinordered__ring__strict(U_719) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
cnf(f_219_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_719),c_Groups_Ozero__class_Ozero(U_719)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_719),U_720),U_721)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_719),U_721),c_Groups_Ozero__class_Ozero(U_719)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_719),U_720),c_Groups_Ozero__class_Ozero(U_719)))
| ~ class_Rings_Olinordered__ring__strict(U_719) ),
inference(clausify,[status(thm)],[f_219_2]) ).
fof(f_220_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_220_2,plain,
! [U_725,U_724,U_723,U_722] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_722),U_723),U_725)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_722),U_724),U_725)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_722),c_Groups_Ozero__class_Ozero(U_722)),U_725))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_722),U_723),U_724))
| ~ class_Rings_Olinordered__semiring__strict(U_722) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
cnf(f_220_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_722),U_723),U_725)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_722),U_724),U_725)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_722),c_Groups_Ozero__class_Ozero(U_722)),U_725))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_722),U_723),U_724))
| ~ class_Rings_Olinordered__semiring__strict(U_722) ),
inference(clausify,[status(thm)],[f_220_2]) ).
fof(f_221_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_221_2,plain,
! [U_729,U_728,U_727,U_726] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_726),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_726),U_729),U_727)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_726),U_729),U_728)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_726),c_Groups_Ozero__class_Ozero(U_726)),U_729))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_726),U_727),U_728))
| ~ class_Rings_Olinordered__semiring__strict(U_726) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
cnf(f_221_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_726),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_726),U_729),U_727)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_726),U_729),U_728)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_726),c_Groups_Ozero__class_Ozero(U_726)),U_729))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_726),U_727),U_728))
| ~ class_Rings_Olinordered__semiring__strict(U_726) ),
inference(clausify,[status(thm)],[f_221_2]) ).
fof(f_222_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_222_2,plain,
! [U_733,U_732,U_731,U_730] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_730),U_733),U_731)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_730),U_733),U_732)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_730),c_Groups_Ozero__class_Ozero(U_730)),U_733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_730),U_731),U_732))
| ~ class_Rings_Olinordered__comm__semiring__strict(U_730) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
cnf(f_222_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_730),U_733),U_731)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_730),U_733),U_732)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_730),c_Groups_Ozero__class_Ozero(U_730)),U_733))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_730),U_731),U_732))
| ~ class_Rings_Olinordered__comm__semiring__strict(U_730) ),
inference(clausify,[status(thm)],[f_222_2]) ).
fof(f_223_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_223_2,plain,
! [U_737,U_736,U_735,U_734] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_734),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_734),U_736),U_737)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_734),U_735),U_737)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_734),U_737),c_Groups_Ozero__class_Ozero(U_734)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_734),U_735),U_736))
| ~ class_Rings_Olinordered__ring__strict(U_734) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
cnf(f_223_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_734),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_734),U_736),U_737)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_734),U_735),U_737)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_734),U_737),c_Groups_Ozero__class_Ozero(U_734)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_734),U_735),U_736))
| ~ class_Rings_Olinordered__ring__strict(U_734) ),
inference(clausify,[status(thm)],[f_223_2]) ).
fof(f_224_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_224_2,plain,
! [U_741,U_740,U_739,U_738] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_738),U_741),U_740)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_738),U_741),U_739)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_738),U_741),c_Groups_Ozero__class_Ozero(U_738)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_738),U_739),U_740))
| ~ class_Rings_Olinordered__ring__strict(U_738) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
cnf(f_224_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_738),U_741),U_740)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_738),U_741),U_739)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_738),U_741),c_Groups_Ozero__class_Ozero(U_738)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_738),U_739),U_740))
| ~ class_Rings_Olinordered__ring__strict(U_738) ),
inference(clausify,[status(thm)],[f_224_2]) ).
fof(f_225_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_225_2,plain,
! [U_745,U_744,U_743,U_742] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_742),hAPP(hAPP(c_Power_Opower__class_Opower(U_742),U_743),U_745)),hAPP(hAPP(c_Power_Opower__class_Opower(U_742),U_744),U_745)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_742),c_Groups_Ozero__class_Ozero(U_742)),U_743))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_742),U_743),U_744))
| ~ class_Rings_Olinordered__semidom(U_742) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
cnf(f_225_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_742),hAPP(hAPP(c_Power_Opower__class_Opower(U_742),U_743),U_745)),hAPP(hAPP(c_Power_Opower__class_Opower(U_742),U_744),U_745)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_742),c_Groups_Ozero__class_Ozero(U_742)),U_743))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_742),U_743),U_744))
| ~ class_Rings_Olinordered__semidom(U_742) ),
inference(clausify,[status(thm)],[f_225_2]) ).
fof(f_226_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_226_2,plain,
! [U_748,U_747,U_746] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_746),c_Groups_Ozero__class_Ozero(U_746)),hAPP(hAPP(c_Power_Opower__class_Opower(U_746),U_747),U_748)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_746),c_Groups_Ozero__class_Ozero(U_746)),U_747))
| ~ class_Rings_Olinordered__semidom(U_746) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
cnf(f_226_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_746),c_Groups_Ozero__class_Ozero(U_746)),hAPP(hAPP(c_Power_Opower__class_Opower(U_746),U_747),U_748)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_746),c_Groups_Ozero__class_Ozero(U_746)),U_747))
| ~ class_Rings_Olinordered__semidom(U_746) ),
inference(clausify,[status(thm)],[f_226_2]) ).
fof(f_227_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_227_2,plain,
! [U_751,U_750,U_749] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_749),c_Groups_Ozero__class_Ozero(U_749)),hAPP(hAPP(c_Power_Opower__class_Opower(U_749),U_750),U_751)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_749),c_Groups_Ozero__class_Ozero(U_749)),U_750))
| ~ class_Rings_Olinordered__semidom(U_749) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
cnf(f_227_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_749),c_Groups_Ozero__class_Ozero(U_749)),hAPP(hAPP(c_Power_Opower__class_Opower(U_749),U_750),U_751)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_749),c_Groups_Ozero__class_Ozero(U_749)),U_750))
| ~ class_Rings_Olinordered__semidom(U_749) ),
inference(clausify,[status(thm)],[f_227_2]) ).
fof(f_228_1,plain,
! [V_na_2,V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_na_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
| hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_na_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Rings_Ozero__neq__one(T_b)
| ~ class_Rings_Ono__zero__divisors(T_b)
| ~ class_Rings_Omult__zero(T_b)
| ~ class_Power_Opower(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff]) ).
fof(f_228_2,plain,
! [U_754,U_753,U_752] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_752),U_753),U_754) = c_Groups_Ozero__class_Ozero(U_752)
| U_754 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_753 != c_Groups_Ozero__class_Ozero(U_752) )
& ( ( U_754 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_753 = c_Groups_Ozero__class_Ozero(U_752) )
| hAPP(hAPP(c_Power_Opower__class_Opower(U_752),U_753),U_754) != c_Groups_Ozero__class_Ozero(U_752) ) )
| ~ class_Rings_Ozero__neq__one(U_752)
| ~ class_Rings_Ono__zero__divisors(U_752)
| ~ class_Rings_Omult__zero(U_752)
| ~ class_Power_Opower(U_752) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
cnf(f_228_3,plain,
( U_753 = c_Groups_Ozero__class_Ozero(U_752)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_752),U_753),U_754) != c_Groups_Ozero__class_Ozero(U_752)
| ~ class_Rings_Ozero__neq__one(U_752)
| ~ class_Rings_Ono__zero__divisors(U_752)
| ~ class_Rings_Omult__zero(U_752)
| ~ class_Power_Opower(U_752) ),
inference(clausify,[status(thm)],[f_228_2]) ).
cnf(f_228_4,plain,
( U_754 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_752),U_753),U_754) != c_Groups_Ozero__class_Ozero(U_752)
| ~ class_Rings_Ozero__neq__one(U_752)
| ~ class_Rings_Ono__zero__divisors(U_752)
| ~ class_Rings_Omult__zero(U_752)
| ~ class_Power_Opower(U_752) ),
inference(clausify,[status(thm)],[f_228_2]) ).
cnf(f_228_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_752),U_753),U_754) = c_Groups_Ozero__class_Ozero(U_752)
| U_754 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_753 != c_Groups_Ozero__class_Ozero(U_752)
| ~ class_Rings_Ozero__neq__one(U_752)
| ~ class_Rings_Ono__zero__divisors(U_752)
| ~ class_Rings_Omult__zero(U_752)
| ~ class_Power_Opower(U_752) ),
inference(clausify,[status(thm)],[f_228_2]) ).
fof(f_229_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_229_2,plain,
! [U_756,U_755] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_755),c_Groups_Ozero__class_Ozero(U_755)),hAPP(c_Nat_OSuc,U_756)) = c_Groups_Ozero__class_Ozero(U_755)
| ~ class_Rings_Osemiring__0(U_755)
| ~ class_Power_Opower(U_755) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
cnf(f_229_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_755),c_Groups_Ozero__class_Ozero(U_755)),hAPP(c_Nat_OSuc,U_756)) = c_Groups_Ozero__class_Ozero(U_755)
| ~ class_Rings_Osemiring__0(U_755)
| ~ class_Power_Opower(U_755) ),
inference(clausify,[status(thm)],[f_229_2]) ).
fof(f_230_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos]) ).
fof(f_230_2,plain,
! [U_760,U_759,U_758,U_757] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_757),U_758),U_759)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_757),U_758),U_760)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_757),U_759),U_760)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_757),U_759),U_760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_757),U_758),U_759)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_757),U_758),U_760))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_757),c_Groups_Ozero__class_Ozero(U_757)),U_758))
| ~ class_Rings_Olinordered__ring__strict(U_757) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
cnf(f_230_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_757),U_759),U_760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_757),U_758),U_759)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_757),U_758),U_760)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_757),c_Groups_Ozero__class_Ozero(U_757)),U_758))
| ~ class_Rings_Olinordered__ring__strict(U_757) ),
inference(clausify,[status(thm)],[f_230_2]) ).
cnf(f_230_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_757),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_757),U_758),U_759)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_757),U_758),U_760)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_757),U_759),U_760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_757),c_Groups_Ozero__class_Ozero(U_757)),U_758))
| ~ class_Rings_Olinordered__ring__strict(U_757) ),
inference(clausify,[status(thm)],[f_230_2]) ).
fof(f_231_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg]) ).
fof(f_231_2,plain,
! [U_764,U_763,U_762,U_761] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_761),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_761),U_762),U_763)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_761),U_762),U_764)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_761),U_764),U_763)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_761),U_764),U_763))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_761),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_761),U_762),U_763)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_761),U_762),U_764))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_761),U_762),c_Groups_Ozero__class_Ozero(U_761)))
| ~ class_Rings_Olinordered__ring__strict(U_761) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
cnf(f_231_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_761),U_764),U_763))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_761),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_761),U_762),U_763)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_761),U_762),U_764)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_761),U_762),c_Groups_Ozero__class_Ozero(U_761)))
| ~ class_Rings_Olinordered__ring__strict(U_761) ),
inference(clausify,[status(thm)],[f_231_2]) ).
cnf(f_231_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_761),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_761),U_762),U_763)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_761),U_762),U_764)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_761),U_764),U_763))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_761),U_762),c_Groups_Ozero__class_Ozero(U_761)))
| ~ class_Rings_Olinordered__ring__strict(U_761) ),
inference(clausify,[status(thm)],[f_231_2]) ).
fof(f_232_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_232_2,plain,
! [U_769,U_768,U_767,U_766,U_765] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_765),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_765),U_766),U_768)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_765),U_767),U_769)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_765),c_Groups_Ozero__class_Ozero(U_765)),U_768))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_765),c_Groups_Ozero__class_Ozero(U_765)),U_767))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_765),U_768),U_769))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_765),U_766),U_767))
| ~ class_Rings_Olinordered__semiring__strict(U_765) ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
cnf(f_232_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_765),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_765),U_766),U_768)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_765),U_767),U_769)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_765),c_Groups_Ozero__class_Ozero(U_765)),U_768))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_765),c_Groups_Ozero__class_Ozero(U_765)),U_767))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_765),U_768),U_769))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_765),U_766),U_767))
| ~ class_Rings_Olinordered__semiring__strict(U_765) ),
inference(clausify,[status(thm)],[f_232_2]) ).
fof(f_233_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_233_2,plain,
! [U_774,U_773,U_772,U_771,U_770] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_770),U_771),U_773)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_770),U_772),U_774)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_770),c_Groups_Ozero__class_Ozero(U_770)),U_773))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_770),c_Groups_Ozero__class_Ozero(U_770)),U_771))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_770),U_773),U_774))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_770),U_771),U_772))
| ~ class_Rings_Olinordered__semiring__strict(U_770) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
cnf(f_233_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_770),U_771),U_773)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_770),U_772),U_774)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_770),c_Groups_Ozero__class_Ozero(U_770)),U_773))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_770),c_Groups_Ozero__class_Ozero(U_770)),U_771))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_770),U_773),U_774))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_770),U_771),U_772))
| ~ class_Rings_Olinordered__semiring__strict(U_770) ),
inference(clausify,[status(thm)],[f_233_2]) ).
fof(f_234_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_234_2,plain,
! [U_779,U_778,U_777,U_776,U_775] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_775),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_775),U_776),U_778)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_775),U_777),U_779)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_775),c_Groups_Ozero__class_Ozero(U_775)),U_778))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_775),c_Groups_Ozero__class_Ozero(U_775)),U_776))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_775),U_778),U_779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_775),U_776),U_777))
| ~ class_Rings_Olinordered__semiring__strict(U_775) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
cnf(f_234_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_775),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_775),U_776),U_778)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_775),U_777),U_779)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_775),c_Groups_Ozero__class_Ozero(U_775)),U_778))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_775),c_Groups_Ozero__class_Ozero(U_775)),U_776))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_775),U_778),U_779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_775),U_776),U_777))
| ~ class_Rings_Olinordered__semiring__strict(U_775) ),
inference(clausify,[status(thm)],[f_234_2]) ).
fof(f_235_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_235_2,plain,
! [U_784,U_783,U_782,U_781,U_780] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_780),U_781),U_783)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_780),U_782),U_784)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),c_Groups_Ozero__class_Ozero(U_780)),U_783))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_780),c_Groups_Ozero__class_Ozero(U_780)),U_781))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_780),U_783),U_784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),U_781),U_782))
| ~ class_Rings_Olinordered__semiring__strict(U_780) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
cnf(f_235_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_780),U_781),U_783)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_780),U_782),U_784)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),c_Groups_Ozero__class_Ozero(U_780)),U_783))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_780),c_Groups_Ozero__class_Ozero(U_780)),U_781))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_780),U_783),U_784))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_780),U_781),U_782))
| ~ class_Rings_Olinordered__semiring__strict(U_780) ),
inference(clausify,[status(thm)],[f_235_2]) ).
fof(f_236_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_236_2,plain,
! [U_788,U_787,U_786,U_785] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_785),U_786),U_788))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_785),c_Groups_Ozero__class_Ozero(U_785)),U_787))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_785),U_786),U_787)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_785),U_788),U_787)))
| ~ class_Rings_Olinordered__semiring(U_785) ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
cnf(f_236_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_785),U_786),U_788))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_785),c_Groups_Ozero__class_Ozero(U_785)),U_787))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_785),U_786),U_787)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_785),U_788),U_787)))
| ~ class_Rings_Olinordered__semiring(U_785) ),
inference(clausify,[status(thm)],[f_236_2]) ).
fof(f_237_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_237_2,plain,
! [U_792,U_791,U_790,U_789] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_789),U_790),U_792))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_789),c_Groups_Ozero__class_Ozero(U_789)),U_791))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_789),U_790),U_791)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_789),U_792),U_791)))
| ~ class_Rings_Olinordered__semiring__strict(U_789) ),
inference(variable_rename,[status(thm)],[f_237_1]) ).
cnf(f_237_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_789),U_790),U_792))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_789),c_Groups_Ozero__class_Ozero(U_789)),U_791))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_789),U_790),U_791)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_789),U_792),U_791)))
| ~ class_Rings_Olinordered__semiring__strict(U_789) ),
inference(clausify,[status(thm)],[f_237_2]) ).
fof(f_238_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_238_2,plain,
! [U_796,U_795,U_794,U_793] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_793),U_795),U_796))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_793),c_Groups_Ozero__class_Ozero(U_793)),U_794))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_793),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_793),U_794),U_795)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_793),U_794),U_796)))
| ~ class_Rings_Olinordered__semiring(U_793) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
cnf(f_238_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_793),U_795),U_796))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_793),c_Groups_Ozero__class_Ozero(U_793)),U_794))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_793),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_793),U_794),U_795)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_793),U_794),U_796)))
| ~ class_Rings_Olinordered__semiring(U_793) ),
inference(clausify,[status(thm)],[f_238_2]) ).
fof(f_239_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_239_2,plain,
! [U_800,U_799,U_798,U_797] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_797),U_799),U_800))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_797),c_Groups_Ozero__class_Ozero(U_797)),U_798))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_798),U_799)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_798),U_800)))
| ~ class_Rings_Olinordered__semiring__strict(U_797) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
cnf(f_239_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_797),U_799),U_800))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_797),c_Groups_Ozero__class_Ozero(U_797)),U_798))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_798),U_799)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_798),U_800)))
| ~ class_Rings_Olinordered__semiring__strict(U_797) ),
inference(clausify,[status(thm)],[f_239_2]) ).
fof(f_240_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_240_2,plain,
! [U_804,U_803,U_802,U_801] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_801),U_802),U_804))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_801),c_Groups_Ozero__class_Ozero(U_801)),U_803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_801),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_801),U_802),U_803)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_801),U_804),U_803)))
| ~ class_Rings_Olinordered__semiring__strict(U_801) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
cnf(f_240_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_801),U_802),U_804))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_801),c_Groups_Ozero__class_Ozero(U_801)),U_803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_801),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_801),U_802),U_803)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_801),U_804),U_803)))
| ~ class_Rings_Olinordered__semiring__strict(U_801) ),
inference(clausify,[status(thm)],[f_240_2]) ).
fof(f_241_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_241_2,plain,
! [U_808,U_807,U_806,U_805] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_805),U_807),U_808))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_805),c_Groups_Ozero__class_Ozero(U_805)),U_806))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_805),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_805),U_806),U_807)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_805),U_806),U_808)))
| ~ class_Rings_Olinordered__semiring__strict(U_805) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
cnf(f_241_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_805),U_807),U_808))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_805),c_Groups_Ozero__class_Ozero(U_805)),U_806))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_805),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_805),U_806),U_807)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_805),U_806),U_808)))
| ~ class_Rings_Olinordered__semiring__strict(U_805) ),
inference(clausify,[status(thm)],[f_241_2]) ).
fof(f_242_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_242_2,plain,
! [U_809] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_809) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_242_1]) ).
cnf(f_242_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_809) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_242_2]) ).
fof(f_243_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_243_2,plain,
! [U_811,U_810] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_810),U_811) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( U_810 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_811 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_810 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_811 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_810),U_811) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
fof(f_243_3,plain,
( ! [U_815,U_813] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_813),U_815) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( U_813 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_815 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_814,U_812] :
( U_812 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_814 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_812),U_814) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_243_2]) ).
cnf(f_243_4,plain,
( U_812 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_814 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_812),U_814) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_243_3]) ).
cnf(f_243_5,plain,
( U_815 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_813),U_815) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_243_3]) ).
cnf(f_243_6,plain,
( U_813 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_813),U_815) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_243_3]) ).
fof(f_244_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_244_2,plain,
! [U_817,U_816] :
( 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_816),U_817)))
| ~ 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_816)) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
cnf(f_244_3,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_816),U_817)))
| ~ 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_816)) ),
inference(clausify,[status(thm)],[f_244_2]) ).
fof(f_245_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_245_2,plain,
! [U_820,U_819,U_818] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_819),U_820))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_818),U_819)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_818),U_820)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_818)) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
cnf(f_245_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_819),U_820))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_818),U_819)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_818),U_820)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_818)) ),
inference(clausify,[status(thm)],[f_245_2]) ).
fof(f_246_1,plain,
! [V_na_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_na_2)))
| ( V_na_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_na_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_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff]) ).
fof(f_246_2,plain,
! [U_822,U_821] :
( ( 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_821),U_822)))
| ( U_822 != 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_821)) ) )
& ( U_822 = 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_821))
| ~ 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_821),U_822))) ) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
fof(f_246_3,plain,
( ! [U_826,U_824] :
( 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_824),U_826)))
| ( U_826 != 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_824)) ) )
& ! [U_825,U_823] :
( U_825 = 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_823))
| ~ 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_823),U_825))) ) ),
inference(miniscope,[status(thm)],[f_246_2]) ).
cnf(f_246_4,plain,
( U_825 = 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_823))
| ~ 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_823),U_825))) ),
inference(clausify,[status(thm)],[f_246_3]) ).
cnf(f_246_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_824))
| 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_824),U_826))) ),
inference(clausify,[status(thm)],[f_246_3]) ).
cnf(f_246_6,plain,
( U_826 != 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)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_824),U_826))) ),
inference(clausify,[status(thm)],[f_246_3]) ).
fof(f_247_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_247_2,plain,
! [U_828,U_827] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_827),c_Groups_Ozero__class_Ozero(U_827)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_827),U_828)))
| ~ class_Rings_Olinordered__semidom(U_827) ),
inference(variable_rename,[status(thm)],[f_247_1]) ).
cnf(f_247_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_827),c_Groups_Ozero__class_Ozero(U_827)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_827),U_828)))
| ~ class_Rings_Olinordered__semidom(U_827) ),
inference(clausify,[status(thm)],[f_247_2]) ).
fof(f_248_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_248_2,plain,
! [U_830,U_829] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_829),c_Groups_Ozero__class_Ozero(U_829)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_829),U_830)))
| ~ class_Rings_Olinordered__semidom(U_829) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
cnf(f_248_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_829),c_Groups_Ozero__class_Ozero(U_829)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_829),U_830)))
| ~ class_Rings_Olinordered__semidom(U_829) ),
inference(clausify,[status(thm)],[f_248_2]) ).
fof(f_249_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_249_2,plain,
! [U_832,U_831] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_831),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_831),U_832)),c_Groups_Ozero__class_Ozero(U_831)))
| ~ class_Rings_Olinordered__semidom(U_831) ),
inference(variable_rename,[status(thm)],[f_249_1]) ).
cnf(f_249_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_831),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_831),U_832)),c_Groups_Ozero__class_Ozero(U_831)))
| ~ class_Rings_Olinordered__semidom(U_831) ),
inference(clausify,[status(thm)],[f_249_2]) ).
fof(f_250_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_250_2,plain,
! [U_833] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_833),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_833)
| ~ class_Rings_Osemiring__1(U_833) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
cnf(f_250_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_833),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_833)
| ~ class_Rings_Osemiring__1(U_833) ),
inference(clausify,[status(thm)],[f_250_2]) ).
fof(f_251_1,plain,
! [V_na_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_na_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_na_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_na_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_na_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_251_2,plain,
! [U_835,U_834] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_834),U_835) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_835 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_834 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( ( U_835 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_834 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_834),U_835) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
fof(f_251_3,plain,
( ! [U_839,U_837] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_837),U_839) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_839 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_837 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ! [U_838,U_836] :
( ( U_838 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_836 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_836),U_838) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_251_2]) ).
cnf(f_251_4,plain,
( U_836 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_836),U_838) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_5,plain,
( U_838 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_836),U_838) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_837),U_839) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_839 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_837 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_251_3]) ).
fof(f_252_1,plain,
! [V_na_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_na_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_na_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_na_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_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff]) ).
fof(f_252_2,plain,
! [U_841,U_840] :
( ( 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_840),U_841)))
| ~ 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_841))
| ~ 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_840)) )
& ( ( 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_841))
& 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_840)) )
| ~ 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_840),U_841))) ) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
fof(f_252_3,plain,
( ! [U_845,U_843] :
( 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_843),U_845)))
| ~ 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_845))
| ~ 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_843)) )
& ! [U_844,U_842] :
( ( 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_844))
& 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_842)) )
| ~ 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_842),U_844))) ) ),
inference(miniscope,[status(thm)],[f_252_2]) ).
cnf(f_252_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))),U_842))
| ~ 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_842),U_844))) ),
inference(clausify,[status(thm)],[f_252_3]) ).
cnf(f_252_5,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_844))
| ~ 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_842),U_844))) ),
inference(clausify,[status(thm)],[f_252_3]) ).
cnf(f_252_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_843),U_845)))
| ~ 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_845))
| ~ 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_843)) ),
inference(clausify,[status(thm)],[f_252_3]) ).
fof(f_253_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_253_2,plain,
! [U_848,U_847,U_846] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_847),U_848))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_846),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_846),U_847)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_846),U_848)))
| ~ class_Rings_Olinordered__semidom(U_846) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
cnf(f_253_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_847),U_848))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_846),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_846),U_847)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_846),U_848)))
| ~ class_Rings_Olinordered__semidom(U_846) ),
inference(clausify,[status(thm)],[f_253_2]) ).
fof(f_254_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_254_2,plain,
! [U_851,U_850,U_849] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_849),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_849),U_850)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_849),U_851)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_850),U_851))
| ~ class_Rings_Olinordered__semidom(U_849) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
cnf(f_254_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_849),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_849),U_850)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_849),U_851)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_850),U_851))
| ~ class_Rings_Olinordered__semidom(U_849) ),
inference(clausify,[status(thm)],[f_254_2]) ).
fof(f_255_1,plain,
! [V_na_2,V_m_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2))) ) )
| ~ class_Rings_Olinordered__semidom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__less__iff]) ).
fof(f_255_2,plain,
! [U_854,U_853,U_852] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_852),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_852),U_853)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_852),U_854)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_853),U_854)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_853),U_854))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_852),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_852),U_853)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_852),U_854))) ) )
| ~ class_Rings_Olinordered__semidom(U_852) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
cnf(f_255_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_853),U_854))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_852),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_852),U_853)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_852),U_854)))
| ~ class_Rings_Olinordered__semidom(U_852) ),
inference(clausify,[status(thm)],[f_255_2]) ).
cnf(f_255_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_852),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_852),U_853)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_852),U_854)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_853),U_854))
| ~ class_Rings_Olinordered__semidom(U_852) ),
inference(clausify,[status(thm)],[f_255_2]) ).
fof(f_256_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_256_2,plain,
! [U_857,U_856,U_855] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_857),U_855)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_857),U_856)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_857))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_855),U_856)) ),
inference(variable_rename,[status(thm)],[f_256_1]) ).
cnf(f_256_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_857),U_855)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_857),U_856)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_857))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_855),U_856)) ),
inference(clausify,[status(thm)],[f_256_2]) ).
fof(f_257_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_257_2,plain,
! [U_860,U_859,U_858] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_858),U_860)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_859),U_860)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_860))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_858),U_859)) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
cnf(f_257_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_858),U_860)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_859),U_860)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_860))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_858),U_859)) ),
inference(clausify,[status(thm)],[f_257_2]) ).
fof(f_258_1,plain,
! [V_na_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_na_2),V_k_2)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_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_na_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_na_2),V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2]) ).
fof(f_258_2,plain,
! [U_863,U_862,U_861] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_861),U_862)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_863),U_862)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_861),U_863))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_862)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_861),U_863))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_862))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_861),U_862)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_863),U_862))) ) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
fof(f_258_3,plain,
( ! [U_869,U_867,U_865] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_865),U_867)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_869),U_867)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_865),U_869))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_867)) ) )
& ! [U_868,U_866,U_864] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_864),U_868))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_866))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_864),U_866)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_868),U_866))) ) ),
inference(miniscope,[status(thm)],[f_258_2]) ).
cnf(f_258_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_864),U_868))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_866))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_864),U_866)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_868),U_866))) ),
inference(clausify,[status(thm)],[f_258_3]) ).
cnf(f_258_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_867))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_865),U_867)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_869),U_867))) ),
inference(clausify,[status(thm)],[f_258_3]) ).
cnf(f_258_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_865),U_869))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_865),U_867)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_869),U_867))) ),
inference(clausify,[status(thm)],[f_258_3]) ).
fof(f_259_1,plain,
! [V_na_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_na_2)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_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_na_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_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1]) ).
fof(f_259_2,plain,
! [U_872,U_871,U_870] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_870),U_871)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_870),U_872)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_871),U_872))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_870)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_871),U_872))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_870))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_870),U_871)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_870),U_872))) ) ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
fof(f_259_3,plain,
( ! [U_878,U_876,U_874] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_874),U_876)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_874),U_878)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_876),U_878))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_874)) ) )
& ! [U_877,U_875,U_873] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_875),U_877))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_873))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_873),U_875)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_873),U_877))) ) ),
inference(miniscope,[status(thm)],[f_259_2]) ).
cnf(f_259_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_875),U_877))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_873))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_873),U_875)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_873),U_877))) ),
inference(clausify,[status(thm)],[f_259_3]) ).
cnf(f_259_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_874))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_874),U_876)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_874),U_878))) ),
inference(clausify,[status(thm)],[f_259_3]) ).
cnf(f_259_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_876),U_878))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_874),U_876)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_874),U_878))) ),
inference(clausify,[status(thm)],[f_259_3]) ).
fof(f_260_1,plain,
! [V_na_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_na_2),V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_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_na_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_na_2),V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2]) ).
fof(f_260_2,plain,
! [U_881,U_880,U_879] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_879),U_880)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_881),U_880)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_879),U_881))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_880)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_879),U_881))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_880)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_879),U_880)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_881),U_880))) ) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
fof(f_260_3,plain,
( ! [U_887,U_885,U_883] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_883),U_885)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_887),U_885)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_883),U_887))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_885)) )
& ! [U_886,U_884,U_882] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_882),U_886))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_884)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_882),U_884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_886),U_884))) ) ),
inference(miniscope,[status(thm)],[f_260_2]) ).
cnf(f_260_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_884))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_882),U_884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_886),U_884))) ),
inference(clausify,[status(thm)],[f_260_3]) ).
cnf(f_260_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_882),U_886))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_882),U_884)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_886),U_884))) ),
inference(clausify,[status(thm)],[f_260_3]) ).
cnf(f_260_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_883),U_885)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_887),U_885)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_883),U_887))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_885)) ),
inference(clausify,[status(thm)],[f_260_3]) ).
fof(f_261_1,plain,
! [V_na_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_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_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_na_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_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1]) ).
fof(f_261_2,plain,
! [U_890,U_889,U_888] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_888),U_889)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_888),U_890)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_889),U_890))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_888)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_889),U_890))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_888)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_888),U_889)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_888),U_890))) ) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
fof(f_261_3,plain,
( ! [U_896,U_894,U_892] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_892),U_894)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_892),U_896)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_894),U_896))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_892)) )
& ! [U_895,U_893,U_891] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_893),U_895))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_891)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_891),U_893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_891),U_895))) ) ),
inference(miniscope,[status(thm)],[f_261_2]) ).
cnf(f_261_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_891))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_891),U_893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_891),U_895))) ),
inference(clausify,[status(thm)],[f_261_3]) ).
cnf(f_261_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_893),U_895))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_891),U_893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_891),U_895))) ),
inference(clausify,[status(thm)],[f_261_3]) ).
cnf(f_261_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_892),U_894)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_892),U_896)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_894),U_896))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_892)) ),
inference(clausify,[status(thm)],[f_261_3]) ).
fof(f_262_1,plain,
! [V_na_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_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_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_na_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_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff]) ).
fof(f_262_2,plain,
! [U_898,U_897] :
( ( 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_897),U_898)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_898))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_897)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_898))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_897)) )
| ~ 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_897),U_898))) ) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
fof(f_262_3,plain,
( ! [U_902,U_900] :
( 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_900),U_902)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_900)) )
& ! [U_901,U_899] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_901))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_899)) )
| ~ 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_899),U_901))) ) ),
inference(miniscope,[status(thm)],[f_262_2]) ).
cnf(f_262_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_899))
| ~ 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_899),U_901))) ),
inference(clausify,[status(thm)],[f_262_3]) ).
cnf(f_262_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_901))
| ~ 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_899),U_901))) ),
inference(clausify,[status(thm)],[f_262_3]) ).
cnf(f_262_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_900),U_902)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_900)) ),
inference(clausify,[status(thm)],[f_262_3]) ).
fof(f_263_1,plain,
! [V_na_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_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_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_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1]) ).
fof(f_263_2,plain,
! [U_905,U_904,U_903] :
( ( 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_903)),U_904)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_903)),U_905)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_904),U_905)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_904),U_905))
| ~ 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_903)),U_904)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_903)),U_905))) ) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
fof(f_263_3,plain,
( ! [U_911,U_909] :
( ! [U_907] : 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_907)),U_909)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_907)),U_911)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_909),U_911)) )
& ! [U_910,U_908] :
( ! [U_906] : ~ 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_906)),U_908)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_906)),U_910)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_908),U_910)) ) ),
inference(miniscope,[status(thm)],[f_263_2]) ).
cnf(f_263_4,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_906)),U_908)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_906)),U_910)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_908),U_910)) ),
inference(clausify,[status(thm)],[f_263_3]) ).
cnf(f_263_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_907)),U_909)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_907)),U_911)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_909),U_911)) ),
inference(clausify,[status(thm)],[f_263_3]) ).
fof(f_264_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_264_2,plain,
! [U_915,U_914,U_913,U_912] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_912),U_913),U_915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_912),c_Groups_Ozero__class_Ozero(U_912)),U_915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_912),hAPP(hAPP(c_Power_Opower__class_Opower(U_912),U_913),U_914)),hAPP(hAPP(c_Power_Opower__class_Opower(U_912),U_915),U_914)))
| ~ class_Rings_Olinordered__semidom(U_912) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
cnf(f_264_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_912),U_913),U_915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_912),c_Groups_Ozero__class_Ozero(U_912)),U_915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_912),hAPP(hAPP(c_Power_Opower__class_Opower(U_912),U_913),U_914)),hAPP(hAPP(c_Power_Opower__class_Opower(U_912),U_915),U_914)))
| ~ class_Rings_Olinordered__semidom(U_912) ),
inference(clausify,[status(thm)],[f_264_2]) ).
fof(f_265_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_265_2,plain,
! [U_919,U_918,U_917,U_916] :
( U_917 = U_919
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_916),c_Groups_Ozero__class_Ozero(U_916)),U_919))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_916),c_Groups_Ozero__class_Ozero(U_916)),U_917))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_916),U_917),hAPP(c_Nat_OSuc,U_918)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_916),U_919),hAPP(c_Nat_OSuc,U_918))
| ~ class_Rings_Olinordered__semidom(U_916) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
cnf(f_265_3,plain,
( U_917 = U_919
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_916),c_Groups_Ozero__class_Ozero(U_916)),U_919))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_916),c_Groups_Ozero__class_Ozero(U_916)),U_917))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_916),U_917),hAPP(c_Nat_OSuc,U_918)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_916),U_919),hAPP(c_Nat_OSuc,U_918))
| ~ class_Rings_Olinordered__semidom(U_916) ),
inference(clausify,[status(thm)],[f_265_2]) ).
fof(f_266_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_266_2,plain,
! [U_923,U_922,U_921,U_920] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_920),U_921),U_923))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_920),c_Groups_Ozero__class_Ozero(U_920)),U_923))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_920),hAPP(hAPP(c_Power_Opower__class_Opower(U_920),U_921),hAPP(c_Nat_OSuc,U_922))),hAPP(hAPP(c_Power_Opower__class_Opower(U_920),U_923),hAPP(c_Nat_OSuc,U_922))))
| ~ class_Rings_Olinordered__semidom(U_920) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
cnf(f_266_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_920),U_921),U_923))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_920),c_Groups_Ozero__class_Ozero(U_920)),U_923))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_920),hAPP(hAPP(c_Power_Opower__class_Opower(U_920),U_921),hAPP(c_Nat_OSuc,U_922))),hAPP(hAPP(c_Power_Opower__class_Opower(U_920),U_923),hAPP(c_Nat_OSuc,U_922))))
| ~ class_Rings_Olinordered__semidom(U_920) ),
inference(clausify,[status(thm)],[f_266_2]) ).
fof(f_267_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_267_2,plain,
! [U_925,U_924] :
( 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_925),U_924)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_925))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_924)) ),
inference(variable_rename,[status(thm)],[f_267_1]) ).
cnf(f_267_3,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_925),U_924)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_925))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_924)) ),
inference(clausify,[status(thm)],[f_267_2]) ).
fof(f_268_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_268_2,plain,
! [U_927,U_926] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_926),U_927)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_927))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_926)) ),
inference(variable_rename,[status(thm)],[f_268_1]) ).
cnf(f_268_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_926),U_927)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_927))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_926)) ),
inference(clausify,[status(thm)],[f_268_2]) ).
fof(f_269_1,plain,
! [V_na_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_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_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_na_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_269_2,plain,
! [U_930,U_929,U_928] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_928),U_929)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_928),U_930)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_929),U_930)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_929),U_930))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_928),U_929)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_928),U_930))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_928)) ),
inference(variable_rename,[status(thm)],[f_269_1]) ).
cnf(f_269_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_929),U_930))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_928),U_929)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_928),U_930)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_928)) ),
inference(clausify,[status(thm)],[f_269_2]) ).
cnf(f_269_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_928),U_929)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_928),U_930)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_929),U_930))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_928)) ),
inference(clausify,[status(thm)],[f_269_2]) ).
fof(f_270_1,plain,
! [V_na_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_na_2)
| V_m_2 != V_na_2 )
& ( V_m_2 = V_na_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_na_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_270_2,plain,
! [U_933,U_932,U_931] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_931),U_932) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_931),U_933)
| U_932 != U_933 )
& ( U_932 = U_933
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_931),U_932) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_931),U_933) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_931)) ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
cnf(f_270_3,plain,
( U_932 = U_933
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_931),U_932) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_931),U_933)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_931)) ),
inference(clausify,[status(thm)],[f_270_2]) ).
cnf(f_270_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_931),U_932) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_931),U_933)
| U_932 != U_933
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_931)) ),
inference(clausify,[status(thm)],[f_270_2]) ).
fof(f_271_1,plain,
! [V_na_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_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_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_na_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_271_2,plain,
! [U_936,U_935,U_934] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_934),U_935)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_934),U_936)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_935),U_936)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_935),U_936))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_934),U_935)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_934),U_936))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_934)) ),
inference(variable_rename,[status(thm)],[f_271_1]) ).
cnf(f_271_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_935),U_936))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_934),U_935)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_934),U_936)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_934)) ),
inference(clausify,[status(thm)],[f_271_2]) ).
cnf(f_271_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_934),U_935)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_934),U_936)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_935),U_936))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_934)) ),
inference(clausify,[status(thm)],[f_271_2]) ).
fof(f_272_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_272_2,plain,
! [U_939,U_938,U_937] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_937),U_938),hAPP(c_Nat_OSuc,U_939)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_937),U_938),hAPP(hAPP(c_Power_Opower__class_Opower(U_937),U_938),U_939))
| ~ class_Rings_Ocomm__semiring__1(U_937) ),
inference(variable_rename,[status(thm)],[f_272_1]) ).
cnf(f_272_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_937),U_938),hAPP(c_Nat_OSuc,U_939)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_937),U_938),hAPP(hAPP(c_Power_Opower__class_Opower(U_937),U_938),U_939))
| ~ class_Rings_Ocomm__semiring__1(U_937) ),
inference(clausify,[status(thm)],[f_272_2]) ).
fof(f_273_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_273_2,plain,
! [U_942,U_941,U_940] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_940),U_941),hAPP(hAPP(c_Power_Opower__class_Opower(U_940),U_941),U_942)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_940),U_941),hAPP(c_Nat_OSuc,U_942))
| ~ class_Rings_Ocomm__semiring__1(U_940) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
cnf(f_273_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_940),U_941),hAPP(hAPP(c_Power_Opower__class_Opower(U_940),U_941),U_942)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_940),U_941),hAPP(c_Nat_OSuc,U_942))
| ~ class_Rings_Ocomm__semiring__1(U_940) ),
inference(clausify,[status(thm)],[f_273_2]) ).
fof(f_274_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_274_2,plain,
! [U_945,U_944,U_943] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_943),hAPP(hAPP(c_Power_Opower__class_Opower(U_943),U_944),U_945)),U_944) = hAPP(hAPP(c_Power_Opower__class_Opower(U_943),U_944),hAPP(c_Nat_OSuc,U_945))
| ~ class_Rings_Ocomm__semiring__1(U_943) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
cnf(f_274_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_943),hAPP(hAPP(c_Power_Opower__class_Opower(U_943),U_944),U_945)),U_944) = hAPP(hAPP(c_Power_Opower__class_Opower(U_943),U_944),hAPP(c_Nat_OSuc,U_945))
| ~ class_Rings_Ocomm__semiring__1(U_943) ),
inference(clausify,[status(thm)],[f_274_2]) ).
fof(f_275_1,plain,
! [V_B_2,V_A_2,T_b] :
( V_A_2 = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_equalityI]) ).
fof(f_275_2,plain,
! [U_948,U_947,U_946] :
( U_947 = U_948
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_946,tc_HOL_Obool)),U_948),U_947))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_946,tc_HOL_Obool)),U_947),U_948)) ),
inference(variable_rename,[status(thm)],[f_275_1]) ).
cnf(f_275_3,plain,
( U_947 = U_948
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_946,tc_HOL_Obool)),U_948),U_947))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_946,tc_HOL_Obool)),U_947),U_948)) ),
inference(clausify,[status(thm)],[f_275_2]) ).
fof(f_276_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_276_2,plain,
! [U_952,U_951,U_950,U_949] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_949),hAPP(hAPP(c_Power_Opower__class_Opower(U_949),U_950),U_951)),U_952) = hAPP(hAPP(c_Power_Opower__class_Opower(U_949),U_950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_951),U_952))
| ~ class_Rings_Ocomm__semiring__1(U_949) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
cnf(f_276_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_949),hAPP(hAPP(c_Power_Opower__class_Opower(U_949),U_950),U_951)),U_952) = hAPP(hAPP(c_Power_Opower__class_Opower(U_949),U_950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_951),U_952))
| ~ class_Rings_Ocomm__semiring__1(U_949) ),
inference(clausify,[status(thm)],[f_276_2]) ).
fof(f_277_1,plain,
! [V_na_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_na_2)
| ( V_m_2 != V_na_2
& V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( V_m_2 = V_na_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_na_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj]) ).
fof(f_277_2,plain,
! [U_955,U_954,U_953] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_953),U_954) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_953),U_955)
| ( U_954 != U_955
& U_953 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_954 = U_955
| U_953 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_953),U_954) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_953),U_955) ) ),
inference(variable_rename,[status(thm)],[f_277_1]) ).
fof(f_277_3,plain,
( ! [U_961,U_959,U_957] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_957),U_959) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_957),U_961)
| ( U_959 != U_961
& U_957 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_960,U_958,U_956] :
( U_958 = U_960
| U_956 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_956),U_958) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_956),U_960) ) ),
inference(miniscope,[status(thm)],[f_277_2]) ).
cnf(f_277_4,plain,
( U_958 = U_960
| U_956 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_956),U_958) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_956),U_960) ),
inference(clausify,[status(thm)],[f_277_3]) ).
cnf(f_277_5,plain,
( U_957 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_957),U_959) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_957),U_961) ),
inference(clausify,[status(thm)],[f_277_3]) ).
cnf(f_277_6,plain,
( U_959 != U_961
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_957),U_959) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_957),U_961) ),
inference(clausify,[status(thm)],[f_277_3]) ).
fof(f_278_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_278_2,plain,
! [U_965,U_964,U_963,U_962] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_962),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_962),U_963),U_964)),U_965) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_962),hAPP(hAPP(c_Power_Opower__class_Opower(U_962),U_963),U_965)),hAPP(hAPP(c_Power_Opower__class_Opower(U_962),U_964),U_965))
| ~ class_Rings_Ocomm__semiring__1(U_962) ),
inference(variable_rename,[status(thm)],[f_278_1]) ).
cnf(f_278_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_962),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_962),U_963),U_964)),U_965) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_962),hAPP(hAPP(c_Power_Opower__class_Opower(U_962),U_963),U_965)),hAPP(hAPP(c_Power_Opower__class_Opower(U_962),U_964),U_965))
| ~ class_Rings_Ocomm__semiring__1(U_962) ),
inference(clausify,[status(thm)],[f_278_2]) ).
fof(f_279_1,plain,
! [V_na_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_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_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_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__int__conv]) ).
fof(f_279_2,plain,
! [U_966] :
( ( 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_966)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_966)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_966))
| ~ 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_966))) ) ),
inference(variable_rename,[status(thm)],[f_279_1]) ).
fof(f_279_3,plain,
( ! [U_968] :
( 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_968)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_968)) )
& ! [U_967] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_967))
| ~ 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_967))) ) ),
inference(miniscope,[status(thm)],[f_279_2]) ).
cnf(f_279_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_967))
| ~ 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_967))) ),
inference(clausify,[status(thm)],[f_279_3]) ).
cnf(f_279_5,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_968)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_968)) ),
inference(clausify,[status(thm)],[f_279_3]) ).
fof(f_280_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_280_2,plain,
! [U_971,U_970,U_969] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_971),U_969)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_971),U_970)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_971))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_969),U_970)) ),
inference(variable_rename,[status(thm)],[f_280_1]) ).
cnf(f_280_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_971),U_969)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_971),U_970)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_971))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_969),U_970)) ),
inference(clausify,[status(thm)],[f_280_2]) ).
fof(f_281_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_281_2,plain,
! [U_973,U_972] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_973),U_972))
| U_972 = U_973
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_972),U_973)) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
cnf(f_281_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_973),U_972))
| U_972 = U_973
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_972),U_973)) ),
inference(clausify,[status(thm)],[f_281_2]) ).
fof(f_282_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_282_2,plain,
! [U_975,U_974] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_974),U_975))
| U_974 = U_975
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_974),U_975)) )
& ( ( U_974 != U_975
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_974),U_975)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_974),U_975)) ) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
fof(f_282_3,plain,
( ! [U_979,U_977] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_977),U_979))
| U_977 = U_979
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_977),U_979)) )
& ! [U_978,U_976] :
( ( U_976 != U_978
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_976),U_978)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_976),U_978)) ) ),
inference(miniscope,[status(thm)],[f_282_2]) ).
cnf(f_282_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_976),U_978))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_976),U_978)) ),
inference(clausify,[status(thm)],[f_282_3]) ).
cnf(f_282_5,plain,
( U_976 != U_978
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_976),U_978)) ),
inference(clausify,[status(thm)],[f_282_3]) ).
cnf(f_282_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_977),U_979))
| U_977 = U_979
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_977),U_979)) ),
inference(clausify,[status(thm)],[f_282_3]) ).
fof(f_283_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_283_2,plain,
! [U_980] : 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_980))),
inference(variable_rename,[status(thm)],[f_283_1]) ).
cnf(f_283_3,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_980))),
inference(clausify,[status(thm)],[f_283_2]) ).
fof(f_284_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_284_2,plain,
! [U_981] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_981)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_284_1]) ).
cnf(f_284_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_981)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_284_2]) ).
fof(f_285_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_285_2,plain,
! [U_983,U_982] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_982),U_983)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_982)),U_983),
inference(variable_rename,[status(thm)],[f_285_1]) ).
cnf(f_285_3,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_982),U_983)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_982)),U_983),
inference(clausify,[status(thm)],[f_285_2]) ).
fof(f_286_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_286_2,plain,
! [U_985,U_984] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_984)),U_985) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_984),U_985)),
inference(variable_rename,[status(thm)],[f_286_1]) ).
cnf(f_286_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_984)),U_985) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_984),U_985)),
inference(clausify,[status(thm)],[f_286_2]) ).
fof(f_287_1,plain,
! [V_na_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_na_2)
| V_m_2 != V_na_2 )
& ( V_m_2 = V_na_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_na_2) ) ),
inference(fof_nnf,[status(thm)],[fact_int__int__eq]) ).
fof(f_287_2,plain,
! [U_987,U_986] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_986) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_987)
| U_986 != U_987 )
& ( U_986 = U_987
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_986) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_987) ) ),
inference(variable_rename,[status(thm)],[f_287_1]) ).
fof(f_287_3,plain,
( ! [U_991,U_989] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_989) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_991)
| U_989 != U_991 )
& ! [U_990,U_988] :
( U_988 = U_990
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_988) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_990) ) ),
inference(miniscope,[status(thm)],[f_287_2]) ).
cnf(f_287_4,plain,
( U_988 = U_990
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_988) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_990) ),
inference(clausify,[status(thm)],[f_287_3]) ).
cnf(f_287_5,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_989) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_991)
| U_989 != U_991 ),
inference(clausify,[status(thm)],[f_287_3]) ).
fof(f_288_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_288_2,plain,
! [U_993,U_992] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_992)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_993)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_992),U_993)),
inference(variable_rename,[status(thm)],[f_288_1]) ).
cnf(f_288_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_992)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_993)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_992),U_993)),
inference(clausify,[status(thm)],[f_288_2]) ).
fof(f_289_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_289_2,plain,
! [U_995,U_994] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_994),U_995)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_994)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_995)),
inference(variable_rename,[status(thm)],[f_289_1]) ).
cnf(f_289_3,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_994),U_995)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_994)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_995)),
inference(clausify,[status(thm)],[f_289_2]) ).
fof(f_290_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_290_2,plain,
! [U_998,U_997,U_996] :
( 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_998)),U_996)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_998)),U_997)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_998))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_996),U_997)) ),
inference(variable_rename,[status(thm)],[f_290_1]) ).
cnf(f_290_3,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_998)),U_996)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_998)),U_997)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_998))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_996),U_997)) ),
inference(clausify,[status(thm)],[f_290_2]) ).
fof(f_291_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_291_2,plain,
! [U_1003,U_1002,U_1001,U_1000,U_999] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_999),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_999),U_1000),U_1001)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_999),U_1002),U_1003)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_999),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_999),U_1000),U_1002)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_999),U_1001),U_1003))
| ~ class_Rings_Ocomm__semiring__1(U_999) ),
inference(variable_rename,[status(thm)],[f_291_1]) ).
cnf(f_291_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_999),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_999),U_1000),U_1001)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_999),U_1002),U_1003)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_999),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_999),U_1000),U_1002)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_999),U_1001),U_1003))
| ~ class_Rings_Ocomm__semiring__1(U_999) ),
inference(clausify,[status(thm)],[f_291_2]) ).
fof(f_292_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_292_2,plain,
! [U_1008,U_1007,U_1006,U_1005,U_1004] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1004),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1004),U_1005),U_1006)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1004),U_1007),U_1008)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1004),U_1007),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1004),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1004),U_1005),U_1006)),U_1008))
| ~ class_Rings_Ocomm__semiring__1(U_1004) ),
inference(variable_rename,[status(thm)],[f_292_1]) ).
cnf(f_292_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1004),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1004),U_1005),U_1006)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1004),U_1007),U_1008)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1004),U_1007),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1004),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1004),U_1005),U_1006)),U_1008))
| ~ class_Rings_Ocomm__semiring__1(U_1004) ),
inference(clausify,[status(thm)],[f_292_2]) ).
fof(f_293_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_293_2,plain,
! [U_1013,U_1012,U_1011,U_1010,U_1009] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1009),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1009),U_1010),U_1011)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1009),U_1012),U_1013)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1009),U_1010),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1009),U_1011),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1009),U_1012),U_1013)))
| ~ class_Rings_Ocomm__semiring__1(U_1009) ),
inference(variable_rename,[status(thm)],[f_293_1]) ).
cnf(f_293_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1009),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1009),U_1010),U_1011)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1009),U_1012),U_1013)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1009),U_1010),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1009),U_1011),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1009),U_1012),U_1013)))
| ~ class_Rings_Ocomm__semiring__1(U_1009) ),
inference(clausify,[status(thm)],[f_293_2]) ).
fof(f_294_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_294_2,plain,
! [U_1017,U_1016,U_1015,U_1014] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1014),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1014),U_1015),U_1016)),U_1017) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1014),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1014),U_1015),U_1017)),U_1016)
| ~ class_Rings_Ocomm__semiring__1(U_1014) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
cnf(f_294_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1014),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1014),U_1015),U_1016)),U_1017) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1014),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1014),U_1015),U_1017)),U_1016)
| ~ class_Rings_Ocomm__semiring__1(U_1014) ),
inference(clausify,[status(thm)],[f_294_2]) ).
fof(f_295_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_295_2,plain,
! [U_1021,U_1020,U_1019,U_1018] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1018),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1018),U_1019),U_1020)),U_1021) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1018),U_1019),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1018),U_1020),U_1021))
| ~ class_Rings_Ocomm__semiring__1(U_1018) ),
inference(variable_rename,[status(thm)],[f_295_1]) ).
cnf(f_295_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1018),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1018),U_1019),U_1020)),U_1021) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1018),U_1019),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1018),U_1020),U_1021))
| ~ class_Rings_Ocomm__semiring__1(U_1018) ),
inference(clausify,[status(thm)],[f_295_2]) ).
fof(f_296_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_296_2,plain,
! [U_1025,U_1024,U_1023,U_1022] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1022),U_1023),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1022),U_1024),U_1025)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1022),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1022),U_1023),U_1024)),U_1025)
| ~ class_Rings_Ocomm__semiring__1(U_1022) ),
inference(variable_rename,[status(thm)],[f_296_1]) ).
cnf(f_296_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1022),U_1023),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1022),U_1024),U_1025)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1022),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1022),U_1023),U_1024)),U_1025)
| ~ class_Rings_Ocomm__semiring__1(U_1022) ),
inference(clausify,[status(thm)],[f_296_2]) ).
fof(f_297_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_297_2,plain,
! [U_1029,U_1028,U_1027,U_1026] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1026),U_1027),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1026),U_1028),U_1029)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1026),U_1028),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1026),U_1027),U_1029))
| ~ class_Rings_Ocomm__semiring__1(U_1026) ),
inference(variable_rename,[status(thm)],[f_297_1]) ).
cnf(f_297_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1026),U_1027),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1026),U_1028),U_1029)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1026),U_1028),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1026),U_1027),U_1029))
| ~ class_Rings_Ocomm__semiring__1(U_1026) ),
inference(clausify,[status(thm)],[f_297_2]) ).
fof(f_298_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_298_2,plain,
! [U_1032,U_1031,U_1030] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1030),U_1031),U_1032) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1030),U_1032),U_1031)
| ~ class_Rings_Ocomm__semiring__1(U_1030) ),
inference(variable_rename,[status(thm)],[f_298_1]) ).
cnf(f_298_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1030),U_1031),U_1032) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1030),U_1032),U_1031)
| ~ class_Rings_Ocomm__semiring__1(U_1030) ),
inference(clausify,[status(thm)],[f_298_2]) ).
fof(f_299_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]) ).
cnf(f_299_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(clausify,[status(thm)],[f_299_1]) ).
fof(f_300_1,plain,
! [V_na_2] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_na_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_na_2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_nnf,[status(thm)],[fact_int__eq__0__conv]) ).
fof(f_300_2,plain,
! [U_1033] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1033) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_1033 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1033 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1033) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
fof(f_300_3,plain,
( ! [U_1035] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1035) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_1035 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1034] :
( U_1034 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1034) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_300_2]) ).
cnf(f_300_4,plain,
( U_1034 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1034) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_300_3]) ).
cnf(f_300_5,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1035) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_1035 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_300_3]) ).
fof(f_301_1,plain,
! [V_na_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_na_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_na_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_na_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(fof_nnf,[status(thm)],[fact_int__le__0__conv]) ).
fof(f_301_2,plain,
! [U_1036] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1036)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_1036 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1036 = 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_1036)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_301_1]) ).
fof(f_301_3,plain,
( ! [U_1038] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1038)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_1038 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1037] :
( U_1037 = 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_1037)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_301_2]) ).
cnf(f_301_4,plain,
( U_1037 = 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_1037)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_301_3]) ).
cnf(f_301_5,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_1038)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_1038 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_301_3]) ).
fof(f_302_1,plain,
! [V_na_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_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_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_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_zless__int]) ).
fof(f_302_2,plain,
! [U_1040,U_1039] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1039)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1040)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1039),U_1040)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1039),U_1040))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1039)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1040))) ) ),
inference(variable_rename,[status(thm)],[f_302_1]) ).
fof(f_302_3,plain,
( ! [U_1044,U_1042] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1042)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1042),U_1044)) )
& ! [U_1043,U_1041] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1041),U_1043))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1041)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1043))) ) ),
inference(miniscope,[status(thm)],[f_302_2]) ).
cnf(f_302_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1041),U_1043))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1041)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1043))) ),
inference(clausify,[status(thm)],[f_302_3]) ).
cnf(f_302_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_1042)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1042),U_1044)) ),
inference(clausify,[status(thm)],[f_302_3]) ).
fof(f_303_1,plain,
! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_subset__refl]) ).
fof(f_303_2,plain,
! [U_1046,U_1045] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1045,tc_HOL_Obool)),U_1046),U_1046)),
inference(variable_rename,[status(thm)],[f_303_1]) ).
cnf(f_303_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1045,tc_HOL_Obool)),U_1046),U_1046)),
inference(clausify,[status(thm)],[f_303_2]) ).
fof(f_304_1,plain,
! [V_B_2,V_A_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| V_A_2 = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( ( V_A_2 != V_B_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_psubset__eq]) ).
fof(f_304_2,plain,
! [U_1049,U_1048,U_1047] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1047,tc_HOL_Obool)),U_1048),U_1049))
| U_1048 = U_1049
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1047,tc_HOL_Obool)),U_1048),U_1049)) )
& ( ( U_1048 != U_1049
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1047,tc_HOL_Obool)),U_1048),U_1049)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1047,tc_HOL_Obool)),U_1048),U_1049)) ) ),
inference(variable_rename,[status(thm)],[f_304_1]) ).
fof(f_304_3,plain,
( ! [U_1055,U_1053,U_1051] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1051,tc_HOL_Obool)),U_1053),U_1055))
| U_1053 = U_1055
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1051,tc_HOL_Obool)),U_1053),U_1055)) )
& ! [U_1054,U_1052,U_1050] :
( ( U_1052 != U_1054
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1050,tc_HOL_Obool)),U_1052),U_1054)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1050,tc_HOL_Obool)),U_1052),U_1054)) ) ),
inference(miniscope,[status(thm)],[f_304_2]) ).
cnf(f_304_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1050,tc_HOL_Obool)),U_1052),U_1054))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1050,tc_HOL_Obool)),U_1052),U_1054)) ),
inference(clausify,[status(thm)],[f_304_3]) ).
cnf(f_304_5,plain,
( U_1052 != U_1054
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1050,tc_HOL_Obool)),U_1052),U_1054)) ),
inference(clausify,[status(thm)],[f_304_3]) ).
cnf(f_304_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1051,tc_HOL_Obool)),U_1053),U_1055))
| U_1053 = U_1055
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1051,tc_HOL_Obool)),U_1053),U_1055)) ),
inference(clausify,[status(thm)],[f_304_3]) ).
fof(f_305_1,plain,
! [T_b,V_B_2,V_A_2] :
( ( V_A_2 = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
| V_A_2 != V_B_2 ) ),
inference(fof_nnf,[status(thm)],[fact_set__eq__subset]) ).
fof(f_305_2,plain,
! [U_1058,U_1057,U_1056] :
( ( U_1056 = U_1057
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1058,tc_HOL_Obool)),U_1057),U_1056))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1058,tc_HOL_Obool)),U_1056),U_1057)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1058,tc_HOL_Obool)),U_1057),U_1056))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1058,tc_HOL_Obool)),U_1056),U_1057)) )
| U_1056 != U_1057 ) ),
inference(variable_rename,[status(thm)],[f_305_1]) ).
fof(f_305_3,plain,
( ! [U_1064,U_1062,U_1060] :
( U_1060 = U_1062
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1064,tc_HOL_Obool)),U_1062),U_1060))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1064,tc_HOL_Obool)),U_1060),U_1062)) )
& ! [U_1063,U_1061,U_1059] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1063,tc_HOL_Obool)),U_1061),U_1059))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1063,tc_HOL_Obool)),U_1059),U_1061)) )
| U_1059 != U_1061 ) ),
inference(miniscope,[status(thm)],[f_305_2]) ).
cnf(f_305_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1063,tc_HOL_Obool)),U_1059),U_1061))
| U_1059 != U_1061 ),
inference(clausify,[status(thm)],[f_305_3]) ).
cnf(f_305_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1063,tc_HOL_Obool)),U_1061),U_1059))
| U_1059 != U_1061 ),
inference(clausify,[status(thm)],[f_305_3]) ).
cnf(f_305_6,plain,
( U_1060 = U_1062
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1064,tc_HOL_Obool)),U_1062),U_1060))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1064,tc_HOL_Obool)),U_1060),U_1062)) ),
inference(clausify,[status(thm)],[f_305_3]) ).
fof(f_306_1,plain,
! [V_B_2,V_A_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ( V_A_2 != V_B_2
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) )
& ( V_A_2 = V_B_2
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq]) ).
fof(f_306_2,plain,
! [U_1067,U_1066,U_1065] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1065,tc_HOL_Obool)),U_1066),U_1067))
| ( U_1066 != U_1067
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1065,tc_HOL_Obool)),U_1066),U_1067)) ) )
& ( U_1066 = U_1067
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1065,tc_HOL_Obool)),U_1066),U_1067))
| ~ 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_306_1]) ).
fof(f_306_3,plain,
( ! [U_1073,U_1071,U_1069] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1069,tc_HOL_Obool)),U_1071),U_1073))
| ( U_1071 != U_1073
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1069,tc_HOL_Obool)),U_1071),U_1073)) ) )
& ! [U_1072,U_1070,U_1068] :
( U_1070 = U_1072
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1068,tc_HOL_Obool)),U_1070),U_1072))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1068,tc_HOL_Obool)),U_1070),U_1072)) ) ),
inference(miniscope,[status(thm)],[f_306_2]) ).
cnf(f_306_4,plain,
( U_1070 = U_1072
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1068,tc_HOL_Obool)),U_1070),U_1072))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1068,tc_HOL_Obool)),U_1070),U_1072)) ),
inference(clausify,[status(thm)],[f_306_3]) ).
cnf(f_306_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1069,tc_HOL_Obool)),U_1071),U_1073))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1069,tc_HOL_Obool)),U_1071),U_1073)) ),
inference(clausify,[status(thm)],[f_306_3]) ).
cnf(f_306_6,plain,
( U_1071 != U_1073
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1069,tc_HOL_Obool)),U_1071),U_1073)) ),
inference(clausify,[status(thm)],[f_306_3]) ).
fof(f_307_1,plain,
! [T_b,V_B_2,V_A_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_equalityD1]) ).
fof(f_307_2,plain,
! [U_1076,U_1075,U_1074] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1076,tc_HOL_Obool)),U_1074),U_1075))
| U_1074 != U_1075 ),
inference(variable_rename,[status(thm)],[f_307_1]) ).
cnf(f_307_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1076,tc_HOL_Obool)),U_1074),U_1075))
| U_1074 != U_1075 ),
inference(clausify,[status(thm)],[f_307_2]) ).
fof(f_308_1,plain,
! [T_b,V_B_2,V_A_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_equalityD2]) ).
fof(f_308_2,plain,
! [U_1079,U_1078,U_1077] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1079,tc_HOL_Obool)),U_1078),U_1077))
| U_1077 != U_1078 ),
inference(variable_rename,[status(thm)],[f_308_1]) ).
cnf(f_308_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1079,tc_HOL_Obool)),U_1078),U_1077))
| U_1077 != U_1078 ),
inference(clausify,[status(thm)],[f_308_2]) ).
fof(f_309_1,plain,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset]) ).
fof(f_309_2,plain,
! [U_1082,U_1081,U_1080] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1080,tc_HOL_Obool)),U_1081),U_1082))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1080,tc_HOL_Obool)),U_1081),U_1082)) ),
inference(variable_rename,[status(thm)],[f_309_1]) ).
cnf(f_309_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1080,tc_HOL_Obool)),U_1081),U_1082))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1080,tc_HOL_Obool)),U_1081),U_1082)) ),
inference(clausify,[status(thm)],[f_309_2]) ).
fof(f_310_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans]) ).
fof(f_310_2,plain,
! [U_1086,U_1085,U_1084,U_1083] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1083,tc_HOL_Obool)),U_1084),U_1086))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1083,tc_HOL_Obool)),U_1085),U_1086))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1083,tc_HOL_Obool)),U_1084),U_1085)) ),
inference(variable_rename,[status(thm)],[f_310_1]) ).
cnf(f_310_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1083,tc_HOL_Obool)),U_1084),U_1086))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1083,tc_HOL_Obool)),U_1085),U_1086))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1083,tc_HOL_Obool)),U_1084),U_1085)) ),
inference(clausify,[status(thm)],[f_310_2]) ).
fof(f_311_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans]) ).
fof(f_311_2,plain,
! [U_1090,U_1089,U_1088,U_1087] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1087,tc_HOL_Obool)),U_1088),U_1090))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1087,tc_HOL_Obool)),U_1089),U_1090))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1087,tc_HOL_Obool)),U_1088),U_1089)) ),
inference(variable_rename,[status(thm)],[f_311_1]) ).
cnf(f_311_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1087,tc_HOL_Obool)),U_1088),U_1090))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1087,tc_HOL_Obool)),U_1089),U_1090))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1087,tc_HOL_Obool)),U_1088),U_1089)) ),
inference(clausify,[status(thm)],[f_311_2]) ).
fof(f_312_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_subset__trans]) ).
fof(f_312_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)),U_1092),U_1094))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1091,tc_HOL_Obool)),U_1093),U_1094))
| ~ 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_312_1]) ).
cnf(f_312_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1091,tc_HOL_Obool)),U_1092),U_1094))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1091,tc_HOL_Obool)),U_1093),U_1094))
| ~ 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_312_2]) ).
fof(f_313_1,plain,
! [T_b,V_B_2,V_A_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_equalityE]) ).
fof(f_313_2,plain,
! [U_1097,U_1096,U_1095] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1097,tc_HOL_Obool)),U_1096),U_1095))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1097,tc_HOL_Obool)),U_1095),U_1096)) )
| U_1095 != U_1096 ),
inference(variable_rename,[status(thm)],[f_313_1]) ).
cnf(f_313_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1097,tc_HOL_Obool)),U_1095),U_1096))
| U_1095 != U_1096 ),
inference(clausify,[status(thm)],[f_313_2]) ).
cnf(f_313_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1097,tc_HOL_Obool)),U_1096),U_1095))
| U_1095 != U_1096 ),
inference(clausify,[status(thm)],[f_313_2]) ).
fof(f_314_1,plain,
! [V_na_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_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_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_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_zle__int]) ).
fof(f_314_2,plain,
! [U_1099,U_1098] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1098)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1099)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1098),U_1099)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1098),U_1099))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1098)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1099))) ) ),
inference(variable_rename,[status(thm)],[f_314_1]) ).
fof(f_314_3,plain,
( ! [U_1103,U_1101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1101)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1103)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1101),U_1103)) )
& ! [U_1102,U_1100] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1100),U_1102))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1100)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1102))) ) ),
inference(miniscope,[status(thm)],[f_314_2]) ).
cnf(f_314_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1100),U_1102))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1100)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1102))) ),
inference(clausify,[status(thm)],[f_314_3]) ).
cnf(f_314_5,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_1101)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1103)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1101),U_1103)) ),
inference(clausify,[status(thm)],[f_314_3]) ).
fof(f_315_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_315_2,plain,
! [U_1106,U_1105,U_1104] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1104),U_1105)),U_1106) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1104),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1105),U_1106)),
inference(variable_rename,[status(thm)],[f_315_1]) ).
cnf(f_315_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1104),U_1105)),U_1106) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1104),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1105),U_1106)),
inference(clausify,[status(thm)],[f_315_2]) ).
fof(f_316_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_316_2,plain,
! [U_1108,U_1107] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1107),U_1108),c_Groups_Ozero__class_Ozero(U_1107)) = c_Groups_Ozero__class_Ozero(U_1107)
| ~ class_Rings_Ocomm__semiring__1(U_1107) ),
inference(variable_rename,[status(thm)],[f_316_1]) ).
cnf(f_316_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1107),U_1108),c_Groups_Ozero__class_Ozero(U_1107)) = c_Groups_Ozero__class_Ozero(U_1107)
| ~ class_Rings_Ocomm__semiring__1(U_1107) ),
inference(clausify,[status(thm)],[f_316_2]) ).
fof(f_317_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_317_2,plain,
! [U_1110,U_1109] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1109),c_Groups_Ozero__class_Ozero(U_1109)),U_1110) = c_Groups_Ozero__class_Ozero(U_1109)
| ~ class_Rings_Ocomm__semiring__1(U_1109) ),
inference(variable_rename,[status(thm)],[f_317_1]) ).
cnf(f_317_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1109),c_Groups_Ozero__class_Ozero(U_1109)),U_1110) = c_Groups_Ozero__class_Ozero(U_1109)
| ~ class_Rings_Ocomm__semiring__1(U_1109) ),
inference(clausify,[status(thm)],[f_317_2]) ).
fof(f_318_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_318_2,plain,
! [U_1112,U_1111] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1111)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1112)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1111),U_1112)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1111),U_1112))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1111)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1112))) ) ),
inference(variable_rename,[status(thm)],[f_318_1]) ).
fof(f_318_3,plain,
( ! [U_1116,U_1114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1114)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1116)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1114),U_1116)) )
& ! [U_1115,U_1113] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1113),U_1115))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1113)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1115))) ) ),
inference(miniscope,[status(thm)],[f_318_2]) ).
cnf(f_318_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1113),U_1115))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1113)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1115))) ),
inference(clausify,[status(thm)],[f_318_3]) ).
cnf(f_318_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_1114)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1116)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1114),U_1116)) ),
inference(clausify,[status(thm)],[f_318_3]) ).
fof(f_319_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]) ).
cnf(f_319_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(clausify,[status(thm)],[f_319_1]) ).
fof(f_320_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_320_2,plain,
! [U_1118,U_1117] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1117)),U_1118) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1117),U_1118)),
inference(variable_rename,[status(thm)],[f_320_1]) ).
cnf(f_320_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1117)),U_1118) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1117),U_1118)),
inference(clausify,[status(thm)],[f_320_2]) ).
fof(f_321_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_321_2,plain,
! [U_1120,U_1119] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1119)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1120)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1119),U_1120)),
inference(variable_rename,[status(thm)],[f_321_1]) ).
cnf(f_321_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1119)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1120)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1119),U_1120)),
inference(clausify,[status(thm)],[f_321_2]) ).
fof(f_322_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_322_2,plain,
! [U_1122,U_1121] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1121)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1122)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1121),U_1122)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1121),U_1122))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1121)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1122))) ) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
fof(f_322_3,plain,
( ! [U_1126,U_1124] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1124)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1126)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1124),U_1126)) )
& ! [U_1125,U_1123] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1123),U_1125))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1123)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1125))) ) ),
inference(miniscope,[status(thm)],[f_322_2]) ).
cnf(f_322_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1123),U_1125))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1123)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1125))) ),
inference(clausify,[status(thm)],[f_322_3]) ).
cnf(f_322_5,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_1124)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1126)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1124),U_1126)) ),
inference(clausify,[status(thm)],[f_322_3]) ).
fof(f_323_1,plain,
! [V_P_2] :
( ( ! [B_x] :
( hBOOL(hAPP(V_P_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_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) )
& ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x)))
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_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_323_2,plain,
! [U_1131] :
( ( ! [U_1130] :
( hBOOL(hAPP(U_1131,U_1130))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1130)) )
| ? [U_1129] : ~ hBOOL(hAPP(U_1131,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1129))) )
& ( ! [U_1128] : hBOOL(hAPP(U_1131,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1128)))
| ? [U_1127] :
( ~ hBOOL(hAPP(U_1131,U_1127))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1127)) ) ) ),
inference(variable_rename,[status(thm)],[f_323_1]) ).
fof(f_323_3,plain,
( ! [U_1133] :
( ! [U_1130] :
( hBOOL(hAPP(U_1133,U_1130))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1130)) )
| ? [U_1129] : ~ hBOOL(hAPP(U_1133,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1129))) )
& ! [U_1132] :
( ! [U_1128] : hBOOL(hAPP(U_1132,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1128)))
| ? [U_1127] :
( ~ hBOOL(hAPP(U_1132,U_1127))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1127)) ) ) ),
inference(miniscope,[status(thm)],[f_323_2]) ).
fof(f_323_4,plain,
( ! [U_1133] :
( ! [U_1130] :
( hBOOL(hAPP(U_1133,U_1130))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1130)) )
| ? [U_1129] : ~ hBOOL(hAPP(U_1133,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1129))) )
& ! [U_1132] :
( ! [U_1128] : hBOOL(hAPP(U_1132,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1128)))
| ( ~ hBOOL(hAPP(U_1132,sK15(U_1132)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK15(U_1132))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_1127,sK15(U_1132))],[f_323_3]) ).
fof(f_323_5,plain,
( ! [U_1133] :
( ! [U_1130] :
( hBOOL(hAPP(U_1133,U_1130))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1130)) )
| ~ hBOOL(hAPP(U_1133,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK16(U_1133)))) )
& ! [U_1132] :
( ! [U_1128] : hBOOL(hAPP(U_1132,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1128)))
| ( ~ hBOOL(hAPP(U_1132,sK15(U_1132)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK15(U_1132))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_1129,sK16(U_1133))],[f_323_4]) ).
cnf(f_323_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK15(U_1132)))
| hBOOL(hAPP(U_1132,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1128))) ),
inference(clausify,[status(thm)],[f_323_5]) ).
cnf(f_323_7,plain,
( ~ hBOOL(hAPP(U_1132,sK15(U_1132)))
| hBOOL(hAPP(U_1132,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1128))) ),
inference(clausify,[status(thm)],[f_323_5]) ).
cnf(f_323_8,plain,
( hBOOL(hAPP(U_1133,U_1130))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1130))
| ~ hBOOL(hAPP(U_1133,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK16(U_1133)))) ),
inference(clausify,[status(thm)],[f_323_5]) ).
fof(f_324_1,plain,
! [V_P_2] :
( ( ? [B_x] :
( hBOOL(hAPP(V_P_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_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) )
& ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x)))
| ! [B_x] :
( ~ hBOOL(hAPP(V_P_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_324_2,plain,
! [U_1138] :
( ( ? [U_1137] :
( hBOOL(hAPP(U_1138,U_1137))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1137)) )
| ! [U_1136] : ~ hBOOL(hAPP(U_1138,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1136))) )
& ( ? [U_1135] : hBOOL(hAPP(U_1138,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1135)))
| ! [U_1134] :
( ~ hBOOL(hAPP(U_1138,U_1134))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1134)) ) ) ),
inference(variable_rename,[status(thm)],[f_324_1]) ).
fof(f_324_3,plain,
( ! [U_1140] :
( ? [U_1137] :
( hBOOL(hAPP(U_1140,U_1137))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1137)) )
| ! [U_1136] : ~ hBOOL(hAPP(U_1140,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1136))) )
& ! [U_1139] :
( ? [U_1135] : hBOOL(hAPP(U_1139,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1135)))
| ! [U_1134] :
( ~ hBOOL(hAPP(U_1139,U_1134))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1134)) ) ) ),
inference(miniscope,[status(thm)],[f_324_2]) ).
fof(f_324_4,plain,
( ! [U_1140] :
( ? [U_1137] :
( hBOOL(hAPP(U_1140,U_1137))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1137)) )
| ! [U_1136] : ~ hBOOL(hAPP(U_1140,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1136))) )
& ! [U_1139] :
( hBOOL(hAPP(U_1139,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK17(U_1139))))
| ! [U_1134] :
( ~ hBOOL(hAPP(U_1139,U_1134))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1134)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_1135,sK17(U_1139))],[f_324_3]) ).
fof(f_324_5,plain,
( ! [U_1140] :
( ( hBOOL(hAPP(U_1140,sK18(U_1140)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK18(U_1140))) )
| ! [U_1136] : ~ hBOOL(hAPP(U_1140,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1136))) )
& ! [U_1139] :
( hBOOL(hAPP(U_1139,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK17(U_1139))))
| ! [U_1134] :
( ~ hBOOL(hAPP(U_1139,U_1134))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1134)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_1137,sK18(U_1140))],[f_324_4]) ).
cnf(f_324_6,plain,
( hBOOL(hAPP(U_1139,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK17(U_1139))))
| ~ hBOOL(hAPP(U_1139,U_1134))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1134)) ),
inference(clausify,[status(thm)],[f_324_5]) ).
cnf(f_324_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK18(U_1140)))
| ~ hBOOL(hAPP(U_1140,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1136))) ),
inference(clausify,[status(thm)],[f_324_5]) ).
cnf(f_324_8,plain,
( hBOOL(hAPP(U_1140,sK18(U_1140)))
| ~ hBOOL(hAPP(U_1140,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1136))) ),
inference(clausify,[status(thm)],[f_324_5]) ).
fof(f_325_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_325_2,plain,
! [U_1141] : 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_1141))),
inference(variable_rename,[status(thm)],[f_325_1]) ).
cnf(f_325_3,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_1141))),
inference(clausify,[status(thm)],[f_325_2]) ).
fof(f_326_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_326_2,plain,
! [U_1143] :
( ? [U_1142] :
( U_1143 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1142)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1142)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1143)) ),
inference(variable_rename,[status(thm)],[f_326_1]) ).
fof(f_326_3,plain,
! [U_1143] :
( ( U_1143 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK19(U_1143))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK19(U_1143))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1143)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_1142,sK19(U_1143))],[f_326_2]) ).
cnf(f_326_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK19(U_1143)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1143)) ),
inference(clausify,[status(thm)],[f_326_3]) ).
cnf(f_326_5,plain,
( U_1143 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK19(U_1143))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1143)) ),
inference(clausify,[status(thm)],[f_326_3]) ).
fof(f_327_1,plain,
! [V_z_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__less__0__iff]) ).
fof(f_327_2,plain,
! [U_1145,U_1144] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1144),hAPP(c_Int_Oring__1__class_Oof__int(U_1144),U_1145)),c_Groups_Ozero__class_Ozero(U_1144)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1145),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1145),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1144),hAPP(c_Int_Oring__1__class_Oof__int(U_1144),U_1145)),c_Groups_Ozero__class_Ozero(U_1144))) ) )
| ~ class_Rings_Olinordered__idom(U_1144) ),
inference(variable_rename,[status(thm)],[f_327_1]) ).
cnf(f_327_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1145),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1144),hAPP(c_Int_Oring__1__class_Oof__int(U_1144),U_1145)),c_Groups_Ozero__class_Ozero(U_1144)))
| ~ class_Rings_Olinordered__idom(U_1144) ),
inference(clausify,[status(thm)],[f_327_2]) ).
cnf(f_327_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1144),hAPP(c_Int_Oring__1__class_Oof__int(U_1144),U_1145)),c_Groups_Ozero__class_Ozero(U_1144)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1145),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Olinordered__idom(U_1144) ),
inference(clausify,[status(thm)],[f_327_2]) ).
fof(f_328_1,plain,
! [V_z_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__0__less__iff]) ).
fof(f_328_2,plain,
! [U_1147,U_1146] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1146),c_Groups_Ozero__class_Ozero(U_1146)),hAPP(c_Int_Oring__1__class_Oof__int(U_1146),U_1147)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1147)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1147))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1146),c_Groups_Ozero__class_Ozero(U_1146)),hAPP(c_Int_Oring__1__class_Oof__int(U_1146),U_1147))) ) )
| ~ class_Rings_Olinordered__idom(U_1146) ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
cnf(f_328_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1147))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1146),c_Groups_Ozero__class_Ozero(U_1146)),hAPP(c_Int_Oring__1__class_Oof__int(U_1146),U_1147)))
| ~ class_Rings_Olinordered__idom(U_1146) ),
inference(clausify,[status(thm)],[f_328_2]) ).
cnf(f_328_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1146),c_Groups_Ozero__class_Ozero(U_1146)),hAPP(c_Int_Oring__1__class_Oof__int(U_1146),U_1147)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1147))
| ~ class_Rings_Olinordered__idom(U_1146) ),
inference(clausify,[status(thm)],[f_328_2]) ).
fof(f_329_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_329_2,plain,
! [U_1149,U_1148] :
( U_1148 = U_1149
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1149),U_1148))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1148),U_1149)) ),
inference(variable_rename,[status(thm)],[f_329_1]) ).
cnf(f_329_3,plain,
( U_1148 = U_1149
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1149),U_1148))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1148),U_1149)) ),
inference(clausify,[status(thm)],[f_329_2]) ).
fof(f_330_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_330_2,plain,
! [U_1152,U_1151,U_1150] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1150),U_1152))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1151),U_1152))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1150),U_1151)) ),
inference(variable_rename,[status(thm)],[f_330_1]) ).
cnf(f_330_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1150),U_1152))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1151),U_1152))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1150),U_1151)) ),
inference(clausify,[status(thm)],[f_330_2]) ).
fof(f_331_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_psubset__trans]) ).
fof(f_331_2,plain,
! [U_1156,U_1155,U_1154,U_1153] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1153,tc_HOL_Obool)),U_1154),U_1156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1153,tc_HOL_Obool)),U_1155),U_1156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1153,tc_HOL_Obool)),U_1154),U_1155)) ),
inference(variable_rename,[status(thm)],[f_331_1]) ).
cnf(f_331_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1153,tc_HOL_Obool)),U_1154),U_1156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1153,tc_HOL_Obool)),U_1155),U_1156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1153,tc_HOL_Obool)),U_1154),U_1155)) ),
inference(clausify,[status(thm)],[f_331_2]) ).
fof(f_332_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_332_2,plain,
! [U_1158,U_1157] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1158),U_1157))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1157),U_1158)) ),
inference(variable_rename,[status(thm)],[f_332_1]) ).
cnf(f_332_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1158),U_1157))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1157),U_1158)) ),
inference(clausify,[status(thm)],[f_332_2]) ).
fof(f_333_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_333_2,plain,
! [U_1159] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1159),U_1159)),
inference(variable_rename,[status(thm)],[f_333_1]) ).
cnf(f_333_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1159),U_1159)),
inference(clausify,[status(thm)],[f_333_2]) ).
fof(f_334_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_334_2,plain,
! [U_1161,U_1160] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1160),U_1161) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1161),U_1160),
inference(variable_rename,[status(thm)],[f_334_1]) ).
cnf(f_334_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1160),U_1161) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1161),U_1160),
inference(clausify,[status(thm)],[f_334_2]) ).
fof(f_335_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_335_2,plain,
! [U_1164,U_1163,U_1162] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1162),U_1163)),U_1164) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1162),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1163),U_1164)),
inference(variable_rename,[status(thm)],[f_335_1]) ).
cnf(f_335_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1162),U_1163)),U_1164) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1162),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1163),U_1164)),
inference(clausify,[status(thm)],[f_335_2]) ).
fof(f_336_1,plain,
! [V_z_2,V_w_2,T_b] :
( ( ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
| V_w_2 != V_z_2 )
& ( V_w_2 = V_z_2
| hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2) != hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) ) )
| ~ class_Int_Oring__char__0(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__eq__iff]) ).
fof(f_336_2,plain,
! [U_1167,U_1166,U_1165] :
( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_1165),U_1166) = hAPP(c_Int_Oring__1__class_Oof__int(U_1165),U_1167)
| U_1166 != U_1167 )
& ( U_1166 = U_1167
| hAPP(c_Int_Oring__1__class_Oof__int(U_1165),U_1166) != hAPP(c_Int_Oring__1__class_Oof__int(U_1165),U_1167) ) )
| ~ class_Int_Oring__char__0(U_1165) ),
inference(variable_rename,[status(thm)],[f_336_1]) ).
cnf(f_336_3,plain,
( U_1166 = U_1167
| hAPP(c_Int_Oring__1__class_Oof__int(U_1165),U_1166) != hAPP(c_Int_Oring__1__class_Oof__int(U_1165),U_1167)
| ~ class_Int_Oring__char__0(U_1165) ),
inference(clausify,[status(thm)],[f_336_2]) ).
cnf(f_336_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_1165),U_1166) = hAPP(c_Int_Oring__1__class_Oof__int(U_1165),U_1167)
| U_1166 != U_1167
| ~ class_Int_Oring__char__0(U_1165) ),
inference(clausify,[status(thm)],[f_336_2]) ).
fof(f_337_1,plain,
! [V_z_2,V_w_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__le__iff]) ).
fof(f_337_2,plain,
! [U_1170,U_1169,U_1168] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1168),hAPP(c_Int_Oring__1__class_Oof__int(U_1168),U_1169)),hAPP(c_Int_Oring__1__class_Oof__int(U_1168),U_1170)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1169),U_1170)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1169),U_1170))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1168),hAPP(c_Int_Oring__1__class_Oof__int(U_1168),U_1169)),hAPP(c_Int_Oring__1__class_Oof__int(U_1168),U_1170))) ) )
| ~ class_Rings_Olinordered__idom(U_1168) ),
inference(variable_rename,[status(thm)],[f_337_1]) ).
cnf(f_337_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1169),U_1170))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1168),hAPP(c_Int_Oring__1__class_Oof__int(U_1168),U_1169)),hAPP(c_Int_Oring__1__class_Oof__int(U_1168),U_1170)))
| ~ class_Rings_Olinordered__idom(U_1168) ),
inference(clausify,[status(thm)],[f_337_2]) ).
cnf(f_337_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1168),hAPP(c_Int_Oring__1__class_Oof__int(U_1168),U_1169)),hAPP(c_Int_Oring__1__class_Oof__int(U_1168),U_1170)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1169),U_1170))
| ~ class_Rings_Olinordered__idom(U_1168) ),
inference(clausify,[status(thm)],[f_337_2]) ).
fof(f_338_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_338_2,plain,
! [U_1173,U_1172,U_1171] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_1171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1172),U_1173)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1171),hAPP(c_Int_Oring__1__class_Oof__int(U_1171),U_1172)),hAPP(c_Int_Oring__1__class_Oof__int(U_1171),U_1173))
| ~ class_Rings_Oring__1(U_1171) ),
inference(variable_rename,[status(thm)],[f_338_1]) ).
cnf(f_338_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_1171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1172),U_1173)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1171),hAPP(c_Int_Oring__1__class_Oof__int(U_1171),U_1172)),hAPP(c_Int_Oring__1__class_Oof__int(U_1171),U_1173))
| ~ class_Rings_Oring__1(U_1171) ),
inference(clausify,[status(thm)],[f_338_2]) ).
fof(f_339_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_339_2,plain,
! [U_1174] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1174)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1174),
inference(variable_rename,[status(thm)],[f_339_1]) ).
cnf(f_339_3,plain,
hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1174)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1174),
inference(clausify,[status(thm)],[f_339_2]) ).
fof(f_340_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_340_2,plain,
! [U_1177,U_1176,U_1175] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_1175),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1176),U_1177)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1175),hAPP(c_Int_Oring__1__class_Oof__int(U_1175),U_1176)),U_1177)
| ~ class_Rings_Oring__1(U_1175) ),
inference(variable_rename,[status(thm)],[f_340_1]) ).
cnf(f_340_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_1175),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1176),U_1177)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1175),hAPP(c_Int_Oring__1__class_Oof__int(U_1175),U_1176)),U_1177)
| ~ class_Rings_Oring__1(U_1175) ),
inference(clausify,[status(thm)],[f_340_2]) ).
fof(f_341_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_341_2,plain,
! [U_1178] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_1178),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_1178)
| ~ class_Rings_Oring__1(U_1178) ),
inference(variable_rename,[status(thm)],[f_341_1]) ).
cnf(f_341_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_1178),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_1178)
| ~ class_Rings_Oring__1(U_1178) ),
inference(clausify,[status(thm)],[f_341_2]) ).
fof(f_342_1,plain,
! [V_z_2,T_b] :
( ( ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
| V_z_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Groups_Ozero__class_Ozero(T_b) != hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) ) )
| ~ class_Int_Oring__char__0(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__0__eq__iff]) ).
fof(f_342_2,plain,
! [U_1180,U_1179] :
( ( ( c_Groups_Ozero__class_Ozero(U_1179) = hAPP(c_Int_Oring__1__class_Oof__int(U_1179),U_1180)
| U_1180 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( U_1180 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Groups_Ozero__class_Ozero(U_1179) != hAPP(c_Int_Oring__1__class_Oof__int(U_1179),U_1180) ) )
| ~ class_Int_Oring__char__0(U_1179) ),
inference(variable_rename,[status(thm)],[f_342_1]) ).
cnf(f_342_3,plain,
( U_1180 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Groups_Ozero__class_Ozero(U_1179) != hAPP(c_Int_Oring__1__class_Oof__int(U_1179),U_1180)
| ~ class_Int_Oring__char__0(U_1179) ),
inference(clausify,[status(thm)],[f_342_2]) ).
cnf(f_342_4,plain,
( c_Groups_Ozero__class_Ozero(U_1179) = hAPP(c_Int_Oring__1__class_Oof__int(U_1179),U_1180)
| U_1180 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Int_Oring__char__0(U_1179) ),
inference(clausify,[status(thm)],[f_342_2]) ).
fof(f_343_1,plain,
! [V_z_2,T_b] :
( ( ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_z_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Int_Oring__char__0(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__eq__0__iff]) ).
fof(f_343_2,plain,
! [U_1182,U_1181] :
( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_1181),U_1182) = c_Groups_Ozero__class_Ozero(U_1181)
| U_1182 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( U_1182 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(c_Int_Oring__1__class_Oof__int(U_1181),U_1182) != c_Groups_Ozero__class_Ozero(U_1181) ) )
| ~ class_Int_Oring__char__0(U_1181) ),
inference(variable_rename,[status(thm)],[f_343_1]) ).
cnf(f_343_3,plain,
( U_1182 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(c_Int_Oring__1__class_Oof__int(U_1181),U_1182) != c_Groups_Ozero__class_Ozero(U_1181)
| ~ class_Int_Oring__char__0(U_1181) ),
inference(clausify,[status(thm)],[f_343_2]) ).
cnf(f_343_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_1181),U_1182) = c_Groups_Ozero__class_Ozero(U_1181)
| U_1182 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Int_Oring__char__0(U_1181) ),
inference(clausify,[status(thm)],[f_343_2]) ).
fof(f_344_1,plain,
! [V_z_2,V_w_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__less__iff]) ).
fof(f_344_2,plain,
! [U_1185,U_1184,U_1183] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1183),hAPP(c_Int_Oring__1__class_Oof__int(U_1183),U_1184)),hAPP(c_Int_Oring__1__class_Oof__int(U_1183),U_1185)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1184),U_1185)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1184),U_1185))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1183),hAPP(c_Int_Oring__1__class_Oof__int(U_1183),U_1184)),hAPP(c_Int_Oring__1__class_Oof__int(U_1183),U_1185))) ) )
| ~ class_Rings_Olinordered__idom(U_1183) ),
inference(variable_rename,[status(thm)],[f_344_1]) ).
cnf(f_344_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1184),U_1185))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1183),hAPP(c_Int_Oring__1__class_Oof__int(U_1183),U_1184)),hAPP(c_Int_Oring__1__class_Oof__int(U_1183),U_1185)))
| ~ class_Rings_Olinordered__idom(U_1183) ),
inference(clausify,[status(thm)],[f_344_2]) ).
cnf(f_344_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1183),hAPP(c_Int_Oring__1__class_Oof__int(U_1183),U_1184)),hAPP(c_Int_Oring__1__class_Oof__int(U_1183),U_1185)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1184),U_1185))
| ~ class_Rings_Olinordered__idom(U_1183) ),
inference(clausify,[status(thm)],[f_344_2]) ).
fof(f_345_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_345_2,plain,
! [U_1187,U_1186] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_1186),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1187)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1186),U_1187)
| ~ class_Rings_Oring__1(U_1186) ),
inference(variable_rename,[status(thm)],[f_345_1]) ).
cnf(f_345_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_1186),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1187)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1186),U_1187)
| ~ class_Rings_Oring__1(U_1186) ),
inference(clausify,[status(thm)],[f_345_2]) ).
fof(f_346_1,plain,
! [V_z_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__0__le__iff]) ).
fof(f_346_2,plain,
! [U_1189,U_1188] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1188),c_Groups_Ozero__class_Ozero(U_1188)),hAPP(c_Int_Oring__1__class_Oof__int(U_1188),U_1189)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1189)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1189))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1188),c_Groups_Ozero__class_Ozero(U_1188)),hAPP(c_Int_Oring__1__class_Oof__int(U_1188),U_1189))) ) )
| ~ class_Rings_Olinordered__idom(U_1188) ),
inference(variable_rename,[status(thm)],[f_346_1]) ).
cnf(f_346_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1189))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1188),c_Groups_Ozero__class_Ozero(U_1188)),hAPP(c_Int_Oring__1__class_Oof__int(U_1188),U_1189)))
| ~ class_Rings_Olinordered__idom(U_1188) ),
inference(clausify,[status(thm)],[f_346_2]) ).
cnf(f_346_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1188),c_Groups_Ozero__class_Ozero(U_1188)),hAPP(c_Int_Oring__1__class_Oof__int(U_1188),U_1189)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1189))
| ~ class_Rings_Olinordered__idom(U_1188) ),
inference(clausify,[status(thm)],[f_346_2]) ).
fof(f_347_1,plain,
! [V_z_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__le__0__iff]) ).
fof(f_347_2,plain,
! [U_1191,U_1190] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1190),hAPP(c_Int_Oring__1__class_Oof__int(U_1190),U_1191)),c_Groups_Ozero__class_Ozero(U_1190)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1191),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1191),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1190),hAPP(c_Int_Oring__1__class_Oof__int(U_1190),U_1191)),c_Groups_Ozero__class_Ozero(U_1190))) ) )
| ~ class_Rings_Olinordered__idom(U_1190) ),
inference(variable_rename,[status(thm)],[f_347_1]) ).
cnf(f_347_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1191),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1190),hAPP(c_Int_Oring__1__class_Oof__int(U_1190),U_1191)),c_Groups_Ozero__class_Ozero(U_1190)))
| ~ class_Rings_Olinordered__idom(U_1190) ),
inference(clausify,[status(thm)],[f_347_2]) ).
cnf(f_347_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1190),hAPP(c_Int_Oring__1__class_Oof__int(U_1190),U_1191)),c_Groups_Ozero__class_Ozero(U_1190)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1191),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Olinordered__idom(U_1190) ),
inference(clausify,[status(thm)],[f_347_2]) ).
fof(f_348_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]) ).
cnf(f_348_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(clausify,[status(thm)],[f_348_1]) ).
fof(f_349_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_349_2,plain,
! [U_1193,U_1192] :
( 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_1192),U_1193)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1192)) ),
inference(variable_rename,[status(thm)],[f_349_1]) ).
cnf(f_349_3,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_1192),U_1193)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1192)) ),
inference(clausify,[status(thm)],[f_349_2]) ).
fof(f_350_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_350_2,plain,
! [U_1195,U_1194] :
( 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_1194),U_1195)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1195))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1194)) ),
inference(variable_rename,[status(thm)],[f_350_1]) ).
cnf(f_350_3,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_1194),U_1195)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1195))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1194)) ),
inference(clausify,[status(thm)],[f_350_2]) ).
fof(f_351_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_351_2,plain,
! [U_1197,U_1196] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1196) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1197)
| U_1196 != U_1197 )
& ( U_1196 = U_1197
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1196) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1197) ) ),
inference(variable_rename,[status(thm)],[f_351_1]) ).
fof(f_351_3,plain,
( ! [U_1201,U_1199] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1199) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1201)
| U_1199 != U_1201 )
& ! [U_1200,U_1198] :
( U_1198 = U_1200
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1198) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1200) ) ),
inference(miniscope,[status(thm)],[f_351_2]) ).
cnf(f_351_4,plain,
( U_1198 = U_1200
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1198) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1200) ),
inference(clausify,[status(thm)],[f_351_3]) ).
cnf(f_351_5,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1199) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1201)
| U_1199 != U_1201 ),
inference(clausify,[status(thm)],[f_351_3]) ).
fof(f_352_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_352_2,plain,
! [U_1203,U_1202] :
( 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_1202,U_1203)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1203))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1202)) ),
inference(variable_rename,[status(thm)],[f_352_1]) ).
cnf(f_352_3,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_1202,U_1203)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1203))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1202)) ),
inference(clausify,[status(thm)],[f_352_2]) ).
fof(f_353_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_353_2,plain,
! [U_1205,U_1204] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1204)),U_1205))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1204),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1205))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1204),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1205)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1204)),U_1205)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1204)) ),
inference(variable_rename,[status(thm)],[f_353_1]) ).
cnf(f_353_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1204),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1205)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1204)),U_1205))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1204)) ),
inference(clausify,[status(thm)],[f_353_2]) ).
cnf(f_353_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1204)),U_1205))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1204),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1205)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1204)) ),
inference(clausify,[status(thm)],[f_353_2]) ).
fof(f_354_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_354_2,plain,
! [U_1207,U_1206] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1206),U_1207)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_1206)),U_1207)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1206)) ),
inference(variable_rename,[status(thm)],[f_354_1]) ).
cnf(f_354_3,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1206),U_1207)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_1206)),U_1207)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1206)) ),
inference(clausify,[status(thm)],[f_354_2]) ).
fof(f_355_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_355_2,plain,
! [U_1209,U_1208] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_1208)),U_1209) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1208),U_1209))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1208)) ),
inference(variable_rename,[status(thm)],[f_355_1]) ).
cnf(f_355_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_1208)),U_1209) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1208),U_1209))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1208)) ),
inference(clausify,[status(thm)],[f_355_2]) ).
fof(f_356_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_356_2,plain,
! [U_1212,U_1211,U_1210] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1210),c_Groups_Oone__class_Oone(U_1210)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1210),U_1211),U_1212)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1212))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1210),c_Groups_Oone__class_Oone(U_1210)),U_1211))
| ~ class_Rings_Olinordered__semidom(U_1210) ),
inference(variable_rename,[status(thm)],[f_356_1]) ).
cnf(f_356_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1210),c_Groups_Oone__class_Oone(U_1210)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1210),U_1211),U_1212)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1212))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1210),c_Groups_Oone__class_Oone(U_1210)),U_1211))
| ~ class_Rings_Olinordered__semidom(U_1210) ),
inference(clausify,[status(thm)],[f_356_2]) ).
fof(f_357_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_357_2,plain,
! [U_1216,U_1215,U_1214,U_1213] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1215),U_1216))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1213),hAPP(hAPP(c_Power_Opower__class_Opower(U_1213),U_1214),U_1215)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1213),U_1214),U_1216)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1213),c_Groups_Oone__class_Oone(U_1213)),U_1214))
| ~ class_Rings_Olinordered__semidom(U_1213) ),
inference(variable_rename,[status(thm)],[f_357_1]) ).
cnf(f_357_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1215),U_1216))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1213),hAPP(hAPP(c_Power_Opower__class_Opower(U_1213),U_1214),U_1215)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1213),U_1214),U_1216)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1213),c_Groups_Oone__class_Oone(U_1213)),U_1214))
| ~ class_Rings_Olinordered__semidom(U_1213) ),
inference(clausify,[status(thm)],[f_357_2]) ).
fof(f_358_1,plain,
! [V_y_2,V_x_2,V_b_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
| ~ class_Rings_Olinordered__semidom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power__increasing__iff]) ).
fof(f_358_2,plain,
! [U_1220,U_1219,U_1218,U_1217] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1217),hAPP(hAPP(c_Power_Opower__class_Opower(U_1217),U_1218),U_1219)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1217),U_1218),U_1220)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1219),U_1220)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1219),U_1220))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1217),hAPP(hAPP(c_Power_Opower__class_Opower(U_1217),U_1218),U_1219)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1217),U_1218),U_1220))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1217),c_Groups_Oone__class_Oone(U_1217)),U_1218))
| ~ class_Rings_Olinordered__semidom(U_1217) ),
inference(variable_rename,[status(thm)],[f_358_1]) ).
cnf(f_358_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1219),U_1220))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1217),hAPP(hAPP(c_Power_Opower__class_Opower(U_1217),U_1218),U_1219)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1217),U_1218),U_1220)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1217),c_Groups_Oone__class_Oone(U_1217)),U_1218))
| ~ class_Rings_Olinordered__semidom(U_1217) ),
inference(clausify,[status(thm)],[f_358_2]) ).
cnf(f_358_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1217),hAPP(hAPP(c_Power_Opower__class_Opower(U_1217),U_1218),U_1219)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1217),U_1218),U_1220)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1219),U_1220))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1217),c_Groups_Oone__class_Oone(U_1217)),U_1218))
| ~ class_Rings_Olinordered__semidom(U_1217) ),
inference(clausify,[status(thm)],[f_358_2]) ).
fof(f_359_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_359_2,plain,
! [U_1224,U_1223,U_1222,U_1221] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1221),hAPP(hAPP(c_Power_Opower__class_Opower(U_1221),U_1224),U_1223)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1221),U_1224),U_1222)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1221),U_1224),c_Groups_Oone__class_Oone(U_1221)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1221),c_Groups_Ozero__class_Ozero(U_1221)),U_1224))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1222),U_1223))
| ~ class_Rings_Olinordered__semidom(U_1221) ),
inference(variable_rename,[status(thm)],[f_359_1]) ).
cnf(f_359_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1221),hAPP(hAPP(c_Power_Opower__class_Opower(U_1221),U_1224),U_1223)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1221),U_1224),U_1222)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1221),U_1224),c_Groups_Oone__class_Oone(U_1221)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1221),c_Groups_Ozero__class_Ozero(U_1221)),U_1224))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1222),U_1223))
| ~ class_Rings_Olinordered__semidom(U_1221) ),
inference(clausify,[status(thm)],[f_359_2]) ).
fof(f_360_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_360_2,plain,
! [U_1228,U_1227,U_1226,U_1225] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1225),hAPP(hAPP(c_Power_Opower__class_Opower(U_1225),U_1228),U_1227)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1225),U_1228),U_1226)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1225),U_1228),c_Groups_Oone__class_Oone(U_1225)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1225),c_Groups_Ozero__class_Ozero(U_1225)),U_1228))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1226),U_1227))
| ~ class_Rings_Olinordered__semidom(U_1225) ),
inference(variable_rename,[status(thm)],[f_360_1]) ).
cnf(f_360_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1225),hAPP(hAPP(c_Power_Opower__class_Opower(U_1225),U_1228),U_1227)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1225),U_1228),U_1226)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1225),U_1228),c_Groups_Oone__class_Oone(U_1225)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1225),c_Groups_Ozero__class_Ozero(U_1225)),U_1228))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1226),U_1227))
| ~ class_Rings_Olinordered__semidom(U_1225) ),
inference(clausify,[status(thm)],[f_360_2]) ).
fof(f_361_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_361_2,plain,
! [U_1231,U_1230,U_1229] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1229),hAPP(hAPP(c_Power_Opower__class_Opower(U_1229),U_1230),hAPP(c_Nat_OSuc,U_1231))),c_Groups_Oone__class_Oone(U_1229)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1229),U_1230),c_Groups_Oone__class_Oone(U_1229)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1229),c_Groups_Ozero__class_Ozero(U_1229)),U_1230))
| ~ class_Rings_Olinordered__semidom(U_1229) ),
inference(variable_rename,[status(thm)],[f_361_1]) ).
cnf(f_361_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1229),hAPP(hAPP(c_Power_Opower__class_Opower(U_1229),U_1230),hAPP(c_Nat_OSuc,U_1231))),c_Groups_Oone__class_Oone(U_1229)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1229),U_1230),c_Groups_Oone__class_Oone(U_1229)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1229),c_Groups_Ozero__class_Ozero(U_1229)),U_1230))
| ~ class_Rings_Olinordered__semidom(U_1229) ),
inference(clausify,[status(thm)],[f_361_2]) ).
fof(f_362_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]) ).
cnf(f_362_2,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_362_1]) ).
fof(f_363_1,plain,
! [V_x_2,T_b] :
( ( ( c_Groups_Oone__class_Oone(T_b) = V_x_2
| V_x_2 != c_Groups_Oone__class_Oone(T_b) )
& ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
| c_Groups_Oone__class_Oone(T_b) != V_x_2 ) )
| ~ class_Groups_Oone(T_b) ),
inference(fof_nnf,[status(thm)],[fact_one__reorient]) ).
fof(f_363_2,plain,
! [U_1233,U_1232] :
( ( ( c_Groups_Oone__class_Oone(U_1232) = U_1233
| U_1233 != c_Groups_Oone__class_Oone(U_1232) )
& ( U_1233 = c_Groups_Oone__class_Oone(U_1232)
| c_Groups_Oone__class_Oone(U_1232) != U_1233 ) )
| ~ class_Groups_Oone(U_1232) ),
inference(variable_rename,[status(thm)],[f_363_1]) ).
cnf(f_363_3,plain,
( U_1233 = c_Groups_Oone__class_Oone(U_1232)
| c_Groups_Oone__class_Oone(U_1232) != U_1233
| ~ class_Groups_Oone(U_1232) ),
inference(clausify,[status(thm)],[f_363_2]) ).
cnf(f_363_4,plain,
( c_Groups_Oone__class_Oone(U_1232) = U_1233
| U_1233 != c_Groups_Oone__class_Oone(U_1232)
| ~ class_Groups_Oone(U_1232) ),
inference(clausify,[status(thm)],[f_363_2]) ).
fof(f_364_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_364_2,plain,
! [U_1234] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1234),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1234)
| ~ class_Rings_Osemiring__1(U_1234) ),
inference(variable_rename,[status(thm)],[f_364_1]) ).
cnf(f_364_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1234),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1234)
| ~ class_Rings_Osemiring__1(U_1234) ),
inference(clausify,[status(thm)],[f_364_2]) ).
fof(f_365_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]) ).
cnf(f_365_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(clausify,[status(thm)],[f_365_1]) ).
fof(f_366_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]) ).
cnf(f_366_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(clausify,[status(thm)],[f_366_1]) ).
fof(f_367_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_367_2,plain,
! [U_1235] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_1235),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_1235)
| ~ class_Rings_Oring__1(U_1235) ),
inference(variable_rename,[status(thm)],[f_367_1]) ).
cnf(f_367_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_1235),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_1235)
| ~ class_Rings_Oring__1(U_1235) ),
inference(clausify,[status(thm)],[f_367_2]) ).
fof(f_368_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]) ).
cnf(f_368_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(clausify,[status(thm)],[f_368_1]) ).
fof(f_369_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_369_2,plain,
! [U_1236] :
( c_Groups_Ozero__class_Ozero(U_1236) != c_Groups_Oone__class_Oone(U_1236)
| ~ class_Rings_Ozero__neq__one(U_1236) ),
inference(variable_rename,[status(thm)],[f_369_1]) ).
cnf(f_369_3,plain,
( c_Groups_Ozero__class_Ozero(U_1236) != c_Groups_Oone__class_Oone(U_1236)
| ~ class_Rings_Ozero__neq__one(U_1236) ),
inference(clausify,[status(thm)],[f_369_2]) ).
fof(f_370_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_370_2,plain,
! [U_1237] :
( c_Groups_Oone__class_Oone(U_1237) != c_Groups_Ozero__class_Ozero(U_1237)
| ~ class_Rings_Ozero__neq__one(U_1237) ),
inference(variable_rename,[status(thm)],[f_370_1]) ).
cnf(f_370_3,plain,
( c_Groups_Oone__class_Oone(U_1237) != c_Groups_Ozero__class_Ozero(U_1237)
| ~ class_Rings_Ozero__neq__one(U_1237) ),
inference(clausify,[status(thm)],[f_370_2]) ).
fof(f_371_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_371_2,plain,
! [U_1238] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1238)) = U_1238,
inference(variable_rename,[status(thm)],[f_371_1]) ).
cnf(f_371_3,plain,
hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1238)) = U_1238,
inference(clausify,[status(thm)],[f_371_2]) ).
fof(f_372_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_372_2,plain,
! [U_1240,U_1239] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1239),U_1240),c_Groups_Oone__class_Oone(U_1239)) = U_1240
| ~ class_Rings_Ocomm__semiring__1(U_1239) ),
inference(variable_rename,[status(thm)],[f_372_1]) ).
cnf(f_372_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1239),U_1240),c_Groups_Oone__class_Oone(U_1239)) = U_1240
| ~ class_Rings_Ocomm__semiring__1(U_1239) ),
inference(clausify,[status(thm)],[f_372_2]) ).
fof(f_373_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_373_2,plain,
! [U_1242,U_1241] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1241),c_Groups_Oone__class_Oone(U_1241)),U_1242) = U_1242
| ~ class_Rings_Ocomm__semiring__1(U_1241) ),
inference(variable_rename,[status(thm)],[f_373_1]) ).
cnf(f_373_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1241),c_Groups_Oone__class_Oone(U_1241)),U_1242) = U_1242
| ~ class_Rings_Ocomm__semiring__1(U_1241) ),
inference(clausify,[status(thm)],[f_373_2]) ).
fof(f_374_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_374_2,plain,
! [U_1244,U_1243] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1243),U_1244),c_Groups_Oone__class_Oone(U_1243)) = U_1244
| ~ class_Groups_Ocomm__monoid__mult(U_1243) ),
inference(variable_rename,[status(thm)],[f_374_1]) ).
cnf(f_374_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1243),U_1244),c_Groups_Oone__class_Oone(U_1243)) = U_1244
| ~ class_Groups_Ocomm__monoid__mult(U_1243) ),
inference(clausify,[status(thm)],[f_374_2]) ).
fof(f_375_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_375_2,plain,
! [U_1246,U_1245] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1245),U_1246),c_Groups_Oone__class_Oone(U_1245)) = U_1246
| ~ class_Groups_Omonoid__mult(U_1245) ),
inference(variable_rename,[status(thm)],[f_375_1]) ).
cnf(f_375_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1245),U_1246),c_Groups_Oone__class_Oone(U_1245)) = U_1246
| ~ class_Groups_Omonoid__mult(U_1245) ),
inference(clausify,[status(thm)],[f_375_2]) ).
fof(f_376_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_376_2,plain,
! [U_1248,U_1247] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1247),c_Groups_Oone__class_Oone(U_1247)),U_1248) = U_1248
| ~ class_Groups_Ocomm__monoid__mult(U_1247) ),
inference(variable_rename,[status(thm)],[f_376_1]) ).
cnf(f_376_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1247),c_Groups_Oone__class_Oone(U_1247)),U_1248) = U_1248
| ~ class_Groups_Ocomm__monoid__mult(U_1247) ),
inference(clausify,[status(thm)],[f_376_2]) ).
fof(f_377_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_377_2,plain,
! [U_1250,U_1249] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1249),c_Groups_Oone__class_Oone(U_1249)),U_1250) = U_1250
| ~ class_Groups_Omonoid__mult(U_1249) ),
inference(variable_rename,[status(thm)],[f_377_1]) ).
cnf(f_377_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1249),c_Groups_Oone__class_Oone(U_1249)),U_1250) = U_1250
| ~ class_Groups_Omonoid__mult(U_1249) ),
inference(clausify,[status(thm)],[f_377_2]) ).
fof(f_378_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_378_2,plain,
! [U_1252,U_1251] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1251),c_Groups_Oone__class_Oone(U_1251)),U_1252) = c_Groups_Oone__class_Oone(U_1251)
| ~ class_Groups_Omonoid__mult(U_1251) ),
inference(variable_rename,[status(thm)],[f_378_1]) ).
cnf(f_378_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1251),c_Groups_Oone__class_Oone(U_1251)),U_1252) = c_Groups_Oone__class_Oone(U_1251)
| ~ class_Groups_Omonoid__mult(U_1251) ),
inference(clausify,[status(thm)],[f_378_2]) ).
fof(f_379_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]) ).
cnf(f_379_2,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(clausify,[status(thm)],[f_379_1]) ).
fof(f_380_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_380_2,plain,
! [U_1254,U_1253] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1253),U_1254),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1254
| ~ class_Rings_Ocomm__semiring__1(U_1253) ),
inference(variable_rename,[status(thm)],[f_380_1]) ).
cnf(f_380_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1253),U_1254),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1254
| ~ class_Rings_Ocomm__semiring__1(U_1253) ),
inference(clausify,[status(thm)],[f_380_2]) ).
fof(f_381_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_381_2,plain,
! [U_1256,U_1255] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1255),U_1256),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1256
| ~ class_Groups_Omonoid__mult(U_1255) ),
inference(variable_rename,[status(thm)],[f_381_1]) ).
cnf(f_381_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1255),U_1256),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1256
| ~ class_Groups_Omonoid__mult(U_1255) ),
inference(clausify,[status(thm)],[f_381_2]) ).
fof(f_382_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_382_2,plain,
! [U_1257] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1257) = U_1257,
inference(variable_rename,[status(thm)],[f_382_1]) ).
cnf(f_382_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1257) = U_1257,
inference(clausify,[status(thm)],[f_382_2]) ).
fof(f_383_1,plain,
! [V_na_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_na_2)
| V_na_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( V_na_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_na_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff]) ).
fof(f_383_2,plain,
! [U_1259,U_1258] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1258),U_1259)
| U_1259 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1258 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( U_1259 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1258 = 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_1258),U_1259) ) ),
inference(variable_rename,[status(thm)],[f_383_1]) ).
fof(f_383_3,plain,
( ! [U_1263,U_1261] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1261),U_1263)
| U_1263 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1261 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_1262,U_1260] :
( ( U_1262 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1260 = 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_1260),U_1262) ) ),
inference(miniscope,[status(thm)],[f_383_2]) ).
cnf(f_383_4,plain,
( U_1260 = 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_1260),U_1262) ),
inference(clausify,[status(thm)],[f_383_3]) ).
cnf(f_383_5,plain,
( U_1262 = 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_1260),U_1262) ),
inference(clausify,[status(thm)],[f_383_3]) ).
cnf(f_383_6,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1261),U_1263)
| U_1263 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1261 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_383_3]) ).
fof(f_384_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_384_2,plain,
! [U_1264] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1264),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1264,
inference(variable_rename,[status(thm)],[f_384_1]) ).
cnf(f_384_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1264),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1264,
inference(clausify,[status(thm)],[f_384_2]) ).
fof(f_385_1,plain,
! [V_na_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_na_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_na_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( V_na_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_na_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__1__iff]) ).
fof(f_385_2,plain,
! [U_1266,U_1265] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1265),U_1266) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1266 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1265 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( U_1266 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1265 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1265),U_1266) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_385_1]) ).
fof(f_385_3,plain,
( ! [U_1270,U_1268] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1268),U_1270) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1270 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1268 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_1269,U_1267] :
( ( U_1269 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1267 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1267),U_1269) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_385_2]) ).
cnf(f_385_4,plain,
( U_1267 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1267),U_1269) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_385_3]) ).
cnf(f_385_5,plain,
( U_1269 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1267),U_1269) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_385_3]) ).
cnf(f_385_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1268),U_1270) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1270 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1268 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_385_3]) ).
fof(f_386_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_386_2,plain,
! [U_1271] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1271),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_1271,
inference(variable_rename,[status(thm)],[f_386_1]) ).
cnf(f_386_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1271),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_1271,
inference(clausify,[status(thm)],[f_386_2]) ).
fof(f_387_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_387_2,plain,
! [U_1272] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1272) = U_1272,
inference(variable_rename,[status(thm)],[f_387_1]) ).
cnf(f_387_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1272) = U_1272,
inference(clausify,[status(thm)],[f_387_2]) ).
fof(f_388_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_388_2,plain,
! [U_1273] :
( ( 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_1273)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1273)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1273))
| ~ 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_1273))) ) ),
inference(variable_rename,[status(thm)],[f_388_1]) ).
fof(f_388_3,plain,
( ! [U_1275] :
( 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_1275)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1275)) )
& ! [U_1274] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1274))
| ~ 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_1274))) ) ),
inference(miniscope,[status(thm)],[f_388_2]) ).
cnf(f_388_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1274))
| ~ 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_1274))) ),
inference(clausify,[status(thm)],[f_388_3]) ).
cnf(f_388_5,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_1275)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1275)) ),
inference(clausify,[status(thm)],[f_388_3]) ).
fof(f_389_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]) ).
cnf(f_389_2,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_389_1]) ).
fof(f_390_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]) ).
cnf(f_390_2,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_390_1]) ).
fof(f_391_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_391_2,plain,
! [U_1277,U_1276] :
( ( ( hAPP(c_Int_Onat,U_1276) = hAPP(c_Int_Onat,U_1277)
| U_1276 != U_1277 )
& ( U_1276 = U_1277
| hAPP(c_Int_Onat,U_1276) != hAPP(c_Int_Onat,U_1277) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1277))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1276)) ),
inference(variable_rename,[status(thm)],[f_391_1]) ).
cnf(f_391_3,plain,
( U_1276 = U_1277
| hAPP(c_Int_Onat,U_1276) != hAPP(c_Int_Onat,U_1277)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1277))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1276)) ),
inference(clausify,[status(thm)],[f_391_2]) ).
cnf(f_391_4,plain,
( hAPP(c_Int_Onat,U_1276) = hAPP(c_Int_Onat,U_1277)
| U_1276 != U_1277
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1277))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1276)) ),
inference(clausify,[status(thm)],[f_391_2]) ).
fof(f_392_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_392_2,plain,
! [U_1279,U_1278] :
( ( ( hAPP(c_Int_Onat,U_1278) = hAPP(c_Int_Onat,U_1279)
| U_1278 != U_1279 )
& ( U_1278 = U_1279
| hAPP(c_Int_Onat,U_1278) != hAPP(c_Int_Onat,U_1279) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1279))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1278)) ),
inference(variable_rename,[status(thm)],[f_392_1]) ).
cnf(f_392_3,plain,
( U_1278 = U_1279
| hAPP(c_Int_Onat,U_1278) != hAPP(c_Int_Onat,U_1279)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1279))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1278)) ),
inference(clausify,[status(thm)],[f_392_2]) ).
cnf(f_392_4,plain,
( hAPP(c_Int_Onat,U_1278) = hAPP(c_Int_Onat,U_1279)
| U_1278 != U_1279
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1279))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1278)) ),
inference(clausify,[status(thm)],[f_392_2]) ).
fof(f_393_1,plain,
! [V_P_2] :
( ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_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_P_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_P_2,B_x1)) ) ),
inference(fof_nnf,[status(thm)],[fact_all__nat]) ).
fof(f_393_2,plain,
! [U_1284] :
( ( ! [U_1283] : hBOOL(hAPP(U_1284,U_1283))
| ? [U_1282] :
( ~ hBOOL(hAPP(U_1284,hAPP(c_Int_Onat,U_1282)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1282)) ) )
& ( ! [U_1281] :
( hBOOL(hAPP(U_1284,hAPP(c_Int_Onat,U_1281)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1281)) )
| ? [U_1280] : ~ hBOOL(hAPP(U_1284,U_1280)) ) ),
inference(variable_rename,[status(thm)],[f_393_1]) ).
fof(f_393_3,plain,
( ! [U_1286] :
( ! [U_1283] : hBOOL(hAPP(U_1286,U_1283))
| ? [U_1282] :
( ~ hBOOL(hAPP(U_1286,hAPP(c_Int_Onat,U_1282)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1282)) ) )
& ! [U_1285] :
( ! [U_1281] :
( hBOOL(hAPP(U_1285,hAPP(c_Int_Onat,U_1281)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1281)) )
| ? [U_1280] : ~ hBOOL(hAPP(U_1285,U_1280)) ) ),
inference(miniscope,[status(thm)],[f_393_2]) ).
fof(f_393_4,plain,
( ! [U_1286] :
( ! [U_1283] : hBOOL(hAPP(U_1286,U_1283))
| ? [U_1282] :
( ~ hBOOL(hAPP(U_1286,hAPP(c_Int_Onat,U_1282)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1282)) ) )
& ! [U_1285] :
( ! [U_1281] :
( hBOOL(hAPP(U_1285,hAPP(c_Int_Onat,U_1281)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1281)) )
| ~ hBOOL(hAPP(U_1285,sK20(U_1285))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_1280,sK20(U_1285))],[f_393_3]) ).
fof(f_393_5,plain,
( ! [U_1286] :
( ! [U_1283] : hBOOL(hAPP(U_1286,U_1283))
| ( ~ hBOOL(hAPP(U_1286,hAPP(c_Int_Onat,sK21(U_1286))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK21(U_1286))) ) )
& ! [U_1285] :
( ! [U_1281] :
( hBOOL(hAPP(U_1285,hAPP(c_Int_Onat,U_1281)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1281)) )
| ~ hBOOL(hAPP(U_1285,sK20(U_1285))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_1282,sK21(U_1286))],[f_393_4]) ).
cnf(f_393_6,plain,
( hBOOL(hAPP(U_1285,hAPP(c_Int_Onat,U_1281)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1281))
| ~ hBOOL(hAPP(U_1285,sK20(U_1285))) ),
inference(clausify,[status(thm)],[f_393_5]) ).
cnf(f_393_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK21(U_1286)))
| hBOOL(hAPP(U_1286,U_1283)) ),
inference(clausify,[status(thm)],[f_393_5]) ).
cnf(f_393_8,plain,
( ~ hBOOL(hAPP(U_1286,hAPP(c_Int_Onat,sK21(U_1286))))
| hBOOL(hAPP(U_1286,U_1283)) ),
inference(clausify,[status(thm)],[f_393_5]) ).
fof(f_394_1,plain,
! [V_P_2] :
( ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
| ! [B_x] :
( ~ hBOOL(hAPP(V_P_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_P_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_P_2,B_x1)) ) ),
inference(fof_nnf,[status(thm)],[fact_ex__nat]) ).
fof(f_394_2,plain,
! [U_1291] :
( ( ? [U_1290] : hBOOL(hAPP(U_1291,U_1290))
| ! [U_1289] :
( ~ hBOOL(hAPP(U_1291,hAPP(c_Int_Onat,U_1289)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1289)) ) )
& ( ? [U_1288] :
( hBOOL(hAPP(U_1291,hAPP(c_Int_Onat,U_1288)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1288)) )
| ! [U_1287] : ~ hBOOL(hAPP(U_1291,U_1287)) ) ),
inference(variable_rename,[status(thm)],[f_394_1]) ).
fof(f_394_3,plain,
( ! [U_1293] :
( ? [U_1290] : hBOOL(hAPP(U_1293,U_1290))
| ! [U_1289] :
( ~ hBOOL(hAPP(U_1293,hAPP(c_Int_Onat,U_1289)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1289)) ) )
& ! [U_1292] :
( ? [U_1288] :
( hBOOL(hAPP(U_1292,hAPP(c_Int_Onat,U_1288)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1288)) )
| ! [U_1287] : ~ hBOOL(hAPP(U_1292,U_1287)) ) ),
inference(miniscope,[status(thm)],[f_394_2]) ).
fof(f_394_4,plain,
( ! [U_1293] :
( ? [U_1290] : hBOOL(hAPP(U_1293,U_1290))
| ! [U_1289] :
( ~ hBOOL(hAPP(U_1293,hAPP(c_Int_Onat,U_1289)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1289)) ) )
& ! [U_1292] :
( ( hBOOL(hAPP(U_1292,hAPP(c_Int_Onat,sK22(U_1292))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK22(U_1292))) )
| ! [U_1287] : ~ hBOOL(hAPP(U_1292,U_1287)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_1288,sK22(U_1292))],[f_394_3]) ).
fof(f_394_5,plain,
( ! [U_1293] :
( hBOOL(hAPP(U_1293,sK23(U_1293)))
| ! [U_1289] :
( ~ hBOOL(hAPP(U_1293,hAPP(c_Int_Onat,U_1289)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1289)) ) )
& ! [U_1292] :
( ( hBOOL(hAPP(U_1292,hAPP(c_Int_Onat,sK22(U_1292))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK22(U_1292))) )
| ! [U_1287] : ~ hBOOL(hAPP(U_1292,U_1287)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_1290,sK23(U_1293))],[f_394_4]) ).
cnf(f_394_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK22(U_1292)))
| ~ hBOOL(hAPP(U_1292,U_1287)) ),
inference(clausify,[status(thm)],[f_394_5]) ).
cnf(f_394_7,plain,
( hBOOL(hAPP(U_1292,hAPP(c_Int_Onat,sK22(U_1292))))
| ~ hBOOL(hAPP(U_1292,U_1287)) ),
inference(clausify,[status(thm)],[f_394_5]) ).
cnf(f_394_8,plain,
( hBOOL(hAPP(U_1293,sK23(U_1293)))
| ~ hBOOL(hAPP(U_1293,hAPP(c_Int_Onat,U_1289)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1289)) ),
inference(clausify,[status(thm)],[f_394_5]) ).
fof(f_395_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_395_2,plain,
! [U_1294] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1294),c_Groups_Ozero__class_Ozero(U_1294)),c_Groups_Oone__class_Oone(U_1294)))
| ~ class_Rings_Olinordered__semidom(U_1294) ),
inference(variable_rename,[status(thm)],[f_395_1]) ).
cnf(f_395_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1294),c_Groups_Ozero__class_Ozero(U_1294)),c_Groups_Oone__class_Oone(U_1294)))
| ~ class_Rings_Olinordered__semidom(U_1294) ),
inference(clausify,[status(thm)],[f_395_2]) ).
fof(f_396_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_396_2,plain,
! [U_1295] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1295),c_Groups_Oone__class_Oone(U_1295)),c_Groups_Ozero__class_Ozero(U_1295)))
| ~ class_Rings_Olinordered__semidom(U_1295) ),
inference(variable_rename,[status(thm)],[f_396_1]) ).
cnf(f_396_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1295),c_Groups_Oone__class_Oone(U_1295)),c_Groups_Ozero__class_Ozero(U_1295)))
| ~ class_Rings_Olinordered__semidom(U_1295) ),
inference(clausify,[status(thm)],[f_396_2]) ).
fof(f_397_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_397_2,plain,
! [U_1296] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1296),c_Groups_Ozero__class_Ozero(U_1296)),c_Groups_Oone__class_Oone(U_1296)))
| ~ class_Rings_Olinordered__semidom(U_1296) ),
inference(variable_rename,[status(thm)],[f_397_1]) ).
cnf(f_397_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1296),c_Groups_Ozero__class_Ozero(U_1296)),c_Groups_Oone__class_Oone(U_1296)))
| ~ class_Rings_Olinordered__semidom(U_1296) ),
inference(clausify,[status(thm)],[f_397_2]) ).
fof(f_398_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_398_2,plain,
! [U_1297] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1297),c_Groups_Oone__class_Oone(U_1297)),c_Groups_Ozero__class_Ozero(U_1297)))
| ~ class_Rings_Olinordered__semidom(U_1297) ),
inference(variable_rename,[status(thm)],[f_398_1]) ).
cnf(f_398_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1297),c_Groups_Oone__class_Oone(U_1297)),c_Groups_Ozero__class_Ozero(U_1297)))
| ~ class_Rings_Olinordered__semidom(U_1297) ),
inference(clausify,[status(thm)],[f_398_2]) ).
fof(f_399_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_399_2,plain,
! [U_1300,U_1299,U_1298] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1298),c_Groups_Oone__class_Oone(U_1298)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1298),U_1299),U_1300)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1298),c_Groups_Oone__class_Oone(U_1298)),U_1300))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1298),c_Groups_Oone__class_Oone(U_1298)),U_1299))
| ~ class_Rings_Olinordered__semidom(U_1298) ),
inference(variable_rename,[status(thm)],[f_399_1]) ).
cnf(f_399_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1298),c_Groups_Oone__class_Oone(U_1298)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1298),U_1299),U_1300)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1298),c_Groups_Oone__class_Oone(U_1298)),U_1300))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1298),c_Groups_Oone__class_Oone(U_1298)),U_1299))
| ~ class_Rings_Olinordered__semidom(U_1298) ),
inference(clausify,[status(thm)],[f_399_2]) ).
fof(f_400_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_400_2,plain,
! [U_1303,U_1302,U_1301] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1301),c_Groups_Oone__class_Oone(U_1301)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1301),U_1302),U_1303)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1301),c_Groups_Oone__class_Oone(U_1301)),U_1302))
| ~ class_Rings_Olinordered__semidom(U_1301) ),
inference(variable_rename,[status(thm)],[f_400_1]) ).
cnf(f_400_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1301),c_Groups_Oone__class_Oone(U_1301)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1301),U_1302),U_1303)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1301),c_Groups_Oone__class_Oone(U_1301)),U_1302))
| ~ class_Rings_Olinordered__semidom(U_1301) ),
inference(clausify,[status(thm)],[f_400_2]) ).
fof(f_401_1,plain,
! [V_na_2,V_m_2,V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_na_2)
| V_m_2 != V_na_2 )
& ( V_m_2 = V_na_2
| hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) != hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_na_2) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
| ~ class_Rings_Olinordered__semidom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power__inject__exp]) ).
fof(f_401_2,plain,
! [U_1307,U_1306,U_1305,U_1304] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1304),U_1305),U_1306) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1304),U_1305),U_1307)
| U_1306 != U_1307 )
& ( U_1306 = U_1307
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1304),U_1305),U_1306) != hAPP(hAPP(c_Power_Opower__class_Opower(U_1304),U_1305),U_1307) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1304),c_Groups_Oone__class_Oone(U_1304)),U_1305))
| ~ class_Rings_Olinordered__semidom(U_1304) ),
inference(variable_rename,[status(thm)],[f_401_1]) ).
cnf(f_401_3,plain,
( U_1306 = U_1307
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1304),U_1305),U_1306) != hAPP(hAPP(c_Power_Opower__class_Opower(U_1304),U_1305),U_1307)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1304),c_Groups_Oone__class_Oone(U_1304)),U_1305))
| ~ class_Rings_Olinordered__semidom(U_1304) ),
inference(clausify,[status(thm)],[f_401_2]) ).
cnf(f_401_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1304),U_1305),U_1306) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1304),U_1305),U_1307)
| U_1306 != U_1307
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1304),c_Groups_Oone__class_Oone(U_1304)),U_1305))
| ~ class_Rings_Olinordered__semidom(U_1304) ),
inference(clausify,[status(thm)],[f_401_2]) ).
fof(f_402_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_402_2,plain,
! [U_1309,U_1308] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1308),U_1309),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1308)
| ~ class_Rings_Ocomm__semiring__1(U_1308) ),
inference(variable_rename,[status(thm)],[f_402_1]) ).
cnf(f_402_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1308),U_1309),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1308)
| ~ class_Rings_Ocomm__semiring__1(U_1308) ),
inference(clausify,[status(thm)],[f_402_2]) ).
fof(f_403_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_403_2,plain,
! [U_1311,U_1310] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1310),U_1311),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1310)
| ~ class_Power_Opower(U_1310) ),
inference(variable_rename,[status(thm)],[f_403_1]) ).
cnf(f_403_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1310),U_1311),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1310)
| ~ class_Power_Opower(U_1310) ),
inference(clausify,[status(thm)],[f_403_2]) ).
fof(f_404_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]) ).
cnf(f_404_2,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_404_1]) ).
fof(f_405_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_405_2,plain,
! [U_1313,U_1312] :
( U_1312 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1313 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1312 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1312),U_1313) ),
inference(variable_rename,[status(thm)],[f_405_1]) ).
cnf(f_405_3,plain,
( U_1312 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1313 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1312 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1312),U_1313) ),
inference(clausify,[status(thm)],[f_405_2]) ).
fof(f_406_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]) ).
cnf(f_406_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(clausify,[status(thm)],[f_406_1]) ).
fof(f_407_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]) ).
cnf(f_407_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(clausify,[status(thm)],[f_407_1]) ).
fof(f_408_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_408_2,plain,
! [U_1314] :
( ( hAPP(c_Int_Onat,U_1314) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1314),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1314),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,U_1314) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_408_1]) ).
fof(f_408_3,plain,
( ! [U_1316] :
( hAPP(c_Int_Onat,U_1316) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1316),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_1315] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1315),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,U_1315) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_408_2]) ).
cnf(f_408_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1315),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onat,U_1315) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_408_3]) ).
cnf(f_408_5,plain,
( hAPP(c_Int_Onat,U_1316) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1316),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_408_3]) ).
fof(f_409_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_409_2,plain,
! [U_1317] :
( hAPP(c_Int_Onat,U_1317) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1317),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_409_1]) ).
cnf(f_409_3,plain,
( hAPP(c_Int_Onat,U_1317) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1317),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_409_2]) ).
fof(f_410_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_410_2,plain,
! [U_1319,U_1318] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1318)),hAPP(c_Int_Onat,U_1319)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1318),U_1319))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1319)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1318),U_1319))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1319)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1318)),hAPP(c_Int_Onat,U_1319))) ) ),
inference(variable_rename,[status(thm)],[f_410_1]) ).
fof(f_410_3,plain,
( ! [U_1323,U_1321] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1321)),hAPP(c_Int_Onat,U_1323)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1321),U_1323))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1323)) )
& ! [U_1322,U_1320] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1320),U_1322))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1322)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1320)),hAPP(c_Int_Onat,U_1322))) ) ),
inference(miniscope,[status(thm)],[f_410_2]) ).
cnf(f_410_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1322))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1320)),hAPP(c_Int_Onat,U_1322))) ),
inference(clausify,[status(thm)],[f_410_3]) ).
cnf(f_410_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1320),U_1322))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1320)),hAPP(c_Int_Onat,U_1322))) ),
inference(clausify,[status(thm)],[f_410_3]) ).
cnf(f_410_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1321)),hAPP(c_Int_Onat,U_1323)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1321),U_1323))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1323)) ),
inference(clausify,[status(thm)],[f_410_3]) ).
fof(f_411_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_411_2,plain,
! [U_1325,U_1324] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1325)),hAPP(c_Int_Onat,U_1324)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1325),U_1324)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1325),U_1324))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1325)),hAPP(c_Int_Onat,U_1324))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1324)) ),
inference(variable_rename,[status(thm)],[f_411_1]) ).
cnf(f_411_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1325),U_1324))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1325)),hAPP(c_Int_Onat,U_1324)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1324)) ),
inference(clausify,[status(thm)],[f_411_2]) ).
cnf(f_411_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1325)),hAPP(c_Int_Onat,U_1324)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1325),U_1324))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1324)) ),
inference(clausify,[status(thm)],[f_411_2]) ).
fof(f_412_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_412_2,plain,
! [U_1327,U_1326] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_1326)),hAPP(c_Int_Onat,U_1327)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1326),U_1327)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1326),U_1327))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_1326)),hAPP(c_Int_Onat,U_1327))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1327))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1326)) ),
inference(variable_rename,[status(thm)],[f_412_1]) ).
cnf(f_412_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1326),U_1327))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_1326)),hAPP(c_Int_Onat,U_1327)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1327))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1326)) ),
inference(clausify,[status(thm)],[f_412_2]) ).
cnf(f_412_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_1326)),hAPP(c_Int_Onat,U_1327)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1326),U_1327))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1327))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1326)) ),
inference(clausify,[status(thm)],[f_412_2]) ).
fof(f_413_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_413_2,plain,
! [U_1328] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1328)) = U_1328
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1328)) ),
inference(variable_rename,[status(thm)],[f_413_1]) ).
cnf(f_413_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1328)) = U_1328
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1328)) ),
inference(clausify,[status(thm)],[f_413_2]) ).
fof(f_414_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_414_2,plain,
! [U_1330,U_1329] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1329) = U_1330
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1330))
| U_1329 != hAPP(c_Int_Onat,U_1330) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1330))
& U_1329 = hAPP(c_Int_Onat,U_1330) )
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1329) != U_1330 ) ),
inference(variable_rename,[status(thm)],[f_414_1]) ).
fof(f_414_3,plain,
( ! [U_1334,U_1332] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1332) = U_1334
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1334))
| U_1332 != hAPP(c_Int_Onat,U_1334) )
& ! [U_1333,U_1331] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1333))
& U_1331 = hAPP(c_Int_Onat,U_1333) )
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1331) != U_1333 ) ),
inference(miniscope,[status(thm)],[f_414_2]) ).
cnf(f_414_4,plain,
( U_1331 = hAPP(c_Int_Onat,U_1333)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1331) != U_1333 ),
inference(clausify,[status(thm)],[f_414_3]) ).
cnf(f_414_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1333))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1331) != U_1333 ),
inference(clausify,[status(thm)],[f_414_3]) ).
cnf(f_414_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1332) = U_1334
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1334))
| U_1332 != hAPP(c_Int_Onat,U_1334) ),
inference(clausify,[status(thm)],[f_414_3]) ).
fof(f_415_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_415_2,plain,
! [U_1335] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1335)) = 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_1335)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1335)) = U_1335
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1335)) ) ),
inference(variable_rename,[status(thm)],[f_415_1]) ).
fof(f_415_3,plain,
( ! [U_1337] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1337)) = 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_1337)) )
& ! [U_1336] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1336)) = U_1336
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1336)) ) ),
inference(miniscope,[status(thm)],[f_415_2]) ).
cnf(f_415_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1336)) = U_1336
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1336)) ),
inference(clausify,[status(thm)],[f_415_3]) ).
cnf(f_415_5,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1337)) = 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_1337)) ),
inference(clausify,[status(thm)],[f_415_3]) ).
fof(f_416_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_416_2,plain,
! [U_1339,U_1338] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1338),hAPP(c_Int_Onat,U_1339)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1338)),U_1339)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1338)),U_1339))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1338),hAPP(c_Int_Onat,U_1339))) ) ),
inference(variable_rename,[status(thm)],[f_416_1]) ).
fof(f_416_3,plain,
( ! [U_1343,U_1341] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1341),hAPP(c_Int_Onat,U_1343)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1341)),U_1343)) )
& ! [U_1342,U_1340] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1340)),U_1342))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1340),hAPP(c_Int_Onat,U_1342))) ) ),
inference(miniscope,[status(thm)],[f_416_2]) ).
cnf(f_416_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_1340)),U_1342))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1340),hAPP(c_Int_Onat,U_1342))) ),
inference(clausify,[status(thm)],[f_416_3]) ).
cnf(f_416_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1341),hAPP(c_Int_Onat,U_1343)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1341)),U_1343)) ),
inference(clausify,[status(thm)],[f_416_3]) ).
fof(f_417_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_417_2,plain,
! [U_1346,U_1345,U_1344] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1344),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1344),U_1346),U_1345)),U_1345))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1344),U_1346),c_Groups_Oone__class_Oone(U_1344)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1344),c_Groups_Ozero__class_Ozero(U_1344)),U_1346))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1344),c_Groups_Ozero__class_Ozero(U_1344)),U_1345))
| ~ class_Rings_Olinordered__idom(U_1344) ),
inference(variable_rename,[status(thm)],[f_417_1]) ).
cnf(f_417_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1344),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1344),U_1346),U_1345)),U_1345))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1344),U_1346),c_Groups_Oone__class_Oone(U_1344)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1344),c_Groups_Ozero__class_Ozero(U_1344)),U_1346))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1344),c_Groups_Ozero__class_Ozero(U_1344)),U_1345))
| ~ class_Rings_Olinordered__idom(U_1344) ),
inference(clausify,[status(thm)],[f_417_2]) ).
fof(f_418_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_418_2,plain,
! [U_1349,U_1348,U_1347] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1347),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1347),U_1348),U_1349)),U_1348))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1347),U_1349),c_Groups_Oone__class_Oone(U_1347)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1347),c_Groups_Ozero__class_Ozero(U_1347)),U_1349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1347),c_Groups_Ozero__class_Ozero(U_1347)),U_1348))
| ~ class_Rings_Olinordered__idom(U_1347) ),
inference(variable_rename,[status(thm)],[f_418_1]) ).
cnf(f_418_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1347),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1347),U_1348),U_1349)),U_1348))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1347),U_1349),c_Groups_Oone__class_Oone(U_1347)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1347),c_Groups_Ozero__class_Ozero(U_1347)),U_1349))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1347),c_Groups_Ozero__class_Ozero(U_1347)),U_1348))
| ~ class_Rings_Olinordered__idom(U_1347) ),
inference(clausify,[status(thm)],[f_418_2]) ).
fof(f_419_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_419_2,plain,
! [U_1352,U_1351,U_1350] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1350),hAPP(hAPP(c_Power_Opower__class_Opower(U_1350),U_1351),U_1352)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1350),U_1351),hAPP(hAPP(c_Power_Opower__class_Opower(U_1350),U_1351),U_1352))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1350),c_Groups_Oone__class_Oone(U_1350)),U_1351))
| ~ class_Rings_Olinordered__semidom(U_1350) ),
inference(variable_rename,[status(thm)],[f_419_1]) ).
cnf(f_419_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1350),hAPP(hAPP(c_Power_Opower__class_Opower(U_1350),U_1351),U_1352)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1350),U_1351),hAPP(hAPP(c_Power_Opower__class_Opower(U_1350),U_1351),U_1352))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1350),c_Groups_Oone__class_Oone(U_1350)),U_1351))
| ~ class_Rings_Olinordered__semidom(U_1350) ),
inference(clausify,[status(thm)],[f_419_2]) ).
fof(f_420_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_420_2,plain,
! [U_1355,U_1354,U_1353] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1353),c_Groups_Oone__class_Oone(U_1353)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1353),U_1354),hAPP(hAPP(c_Power_Opower__class_Opower(U_1353),U_1354),U_1355))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1353),c_Groups_Oone__class_Oone(U_1353)),U_1354))
| ~ class_Rings_Olinordered__semidom(U_1353) ),
inference(variable_rename,[status(thm)],[f_420_1]) ).
cnf(f_420_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1353),c_Groups_Oone__class_Oone(U_1353)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1353),U_1354),hAPP(hAPP(c_Power_Opower__class_Opower(U_1353),U_1354),U_1355))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1353),c_Groups_Oone__class_Oone(U_1353)),U_1354))
| ~ class_Rings_Olinordered__semidom(U_1353) ),
inference(clausify,[status(thm)],[f_420_2]) ).
fof(f_421_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_421_2,plain,
! [U_1357,U_1356] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1356),c_Groups_Ozero__class_Ozero(U_1356)),U_1357) = c_Groups_Ozero__class_Ozero(U_1356)
| U_1357 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1356),c_Groups_Ozero__class_Ozero(U_1356)),U_1357) = c_Groups_Oone__class_Oone(U_1356)
| U_1357 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Osemiring__0(U_1356)
| ~ class_Power_Opower(U_1356) ),
inference(variable_rename,[status(thm)],[f_421_1]) ).
cnf(f_421_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1356),c_Groups_Ozero__class_Ozero(U_1356)),U_1357) = c_Groups_Oone__class_Oone(U_1356)
| U_1357 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Osemiring__0(U_1356)
| ~ class_Power_Opower(U_1356) ),
inference(clausify,[status(thm)],[f_421_2]) ).
cnf(f_421_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1356),c_Groups_Ozero__class_Ozero(U_1356)),U_1357) = c_Groups_Ozero__class_Ozero(U_1356)
| U_1357 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Osemiring__0(U_1356)
| ~ class_Power_Opower(U_1356) ),
inference(clausify,[status(thm)],[f_421_2]) ).
fof(f_422_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_422_2,plain,
! [U_1360,U_1359,U_1358] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1358),c_Groups_Oone__class_Oone(U_1358)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1358),U_1359),hAPP(c_Nat_OSuc,U_1360))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1358),c_Groups_Oone__class_Oone(U_1358)),U_1359))
| ~ class_Rings_Olinordered__semidom(U_1358) ),
inference(variable_rename,[status(thm)],[f_422_1]) ).
cnf(f_422_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1358),c_Groups_Oone__class_Oone(U_1358)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1358),U_1359),hAPP(c_Nat_OSuc,U_1360))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1358),c_Groups_Oone__class_Oone(U_1358)),U_1359))
| ~ class_Rings_Olinordered__semidom(U_1358) ),
inference(clausify,[status(thm)],[f_422_2]) ).
fof(f_423_1,plain,
! [V_y_2,V_x_2,V_b_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
| ~ class_Rings_Olinordered__semidom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff]) ).
fof(f_423_2,plain,
! [U_1364,U_1363,U_1362,U_1361] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1361),hAPP(hAPP(c_Power_Opower__class_Opower(U_1361),U_1362),U_1363)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1361),U_1362),U_1364)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1363),U_1364)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1363),U_1364))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1361),hAPP(hAPP(c_Power_Opower__class_Opower(U_1361),U_1362),U_1363)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1361),U_1362),U_1364))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1361),c_Groups_Oone__class_Oone(U_1361)),U_1362))
| ~ class_Rings_Olinordered__semidom(U_1361) ),
inference(variable_rename,[status(thm)],[f_423_1]) ).
cnf(f_423_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1363),U_1364))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1361),hAPP(hAPP(c_Power_Opower__class_Opower(U_1361),U_1362),U_1363)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1361),U_1362),U_1364)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1361),c_Groups_Oone__class_Oone(U_1361)),U_1362))
| ~ class_Rings_Olinordered__semidom(U_1361) ),
inference(clausify,[status(thm)],[f_423_2]) ).
cnf(f_423_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1361),hAPP(hAPP(c_Power_Opower__class_Opower(U_1361),U_1362),U_1363)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1361),U_1362),U_1364)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1363),U_1364))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1361),c_Groups_Oone__class_Oone(U_1361)),U_1362))
| ~ class_Rings_Olinordered__semidom(U_1361) ),
inference(clausify,[status(thm)],[f_423_2]) ).
fof(f_424_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_424_2,plain,
! [U_1368,U_1367,U_1366,U_1365] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1367),U_1368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1365),hAPP(hAPP(c_Power_Opower__class_Opower(U_1365),U_1366),U_1367)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1365),U_1366),U_1368)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1365),c_Groups_Oone__class_Oone(U_1365)),U_1366))
| ~ class_Rings_Olinordered__semidom(U_1365) ),
inference(variable_rename,[status(thm)],[f_424_1]) ).
cnf(f_424_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1367),U_1368))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1365),hAPP(hAPP(c_Power_Opower__class_Opower(U_1365),U_1366),U_1367)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1365),U_1366),U_1368)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1365),c_Groups_Oone__class_Oone(U_1365)),U_1366))
| ~ class_Rings_Olinordered__semidom(U_1365) ),
inference(clausify,[status(thm)],[f_424_2]) ).
fof(f_425_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_425_2,plain,
! [U_1372,U_1371,U_1370,U_1369] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1369),hAPP(hAPP(c_Power_Opower__class_Opower(U_1369),U_1372),U_1370)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1369),U_1372),U_1371)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1369),c_Groups_Oone__class_Oone(U_1369)),U_1372))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1370),U_1371))
| ~ class_Rings_Olinordered__semidom(U_1369) ),
inference(variable_rename,[status(thm)],[f_425_1]) ).
cnf(f_425_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1369),hAPP(hAPP(c_Power_Opower__class_Opower(U_1369),U_1372),U_1370)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1369),U_1372),U_1371)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1369),c_Groups_Oone__class_Oone(U_1369)),U_1372))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1370),U_1371))
| ~ class_Rings_Olinordered__semidom(U_1369) ),
inference(clausify,[status(thm)],[f_425_2]) ).
fof(f_426_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_426_2,plain,
! [U_1376,U_1375,U_1374,U_1373] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1373),hAPP(hAPP(c_Power_Opower__class_Opower(U_1373),U_1376),U_1374)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1373),U_1376),U_1375)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1373),c_Groups_Oone__class_Oone(U_1373)),U_1376))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1374),U_1375))
| ~ class_Rings_Olinordered__semidom(U_1373) ),
inference(variable_rename,[status(thm)],[f_426_1]) ).
cnf(f_426_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1373),hAPP(hAPP(c_Power_Opower__class_Opower(U_1373),U_1376),U_1374)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1373),U_1376),U_1375)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1373),c_Groups_Oone__class_Oone(U_1373)),U_1376))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1374),U_1375))
| ~ class_Rings_Olinordered__semidom(U_1373) ),
inference(clausify,[status(thm)],[f_426_2]) ).
fof(f_427_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_427_2,plain,
! [U_1377] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1377))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1377)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1377))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1377)) ) ),
inference(variable_rename,[status(thm)],[f_427_1]) ).
fof(f_427_3,plain,
( ! [U_1379] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1379))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1379)) )
& ! [U_1378] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1378)) ) ),
inference(miniscope,[status(thm)],[f_427_2]) ).
cnf(f_427_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1378)) ),
inference(clausify,[status(thm)],[f_427_3]) ).
cnf(f_427_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1379))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1379)) ),
inference(clausify,[status(thm)],[f_427_3]) ).
fof(f_428_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]) ).
cnf(f_428_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(clausify,[status(thm)],[f_428_1]) ).
fof(f_429_1,plain,
! [V_na_2,V_m_2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_na_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_na_2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_m_2 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( ( V_na_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_na_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_429_2,plain,
! [U_1381,U_1380] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1380),U_1381) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_1381 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_1380 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( ( U_1381 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& U_1380 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1380),U_1381) != 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_1380)) ),
inference(variable_rename,[status(thm)],[f_429_1]) ).
cnf(f_429_3,plain,
( U_1380 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1380),U_1381) != 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_1380)) ),
inference(clausify,[status(thm)],[f_429_2]) ).
cnf(f_429_4,plain,
( U_1381 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1380),U_1381) != 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_1380)) ),
inference(clausify,[status(thm)],[f_429_2]) ).
cnf(f_429_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1380),U_1381) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_1381 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_1380 != 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_1380)) ),
inference(clausify,[status(thm)],[f_429_2]) ).
fof(f_430_1,plain,
! [T_b] :
( c_Power_Opower__class_Opower(T_b) = c_Power_Opower_Opower(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Otimes__class_Otimes(T_b))
| ~ class_Power_Opower(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power__power__power]) ).
fof(f_430_2,plain,
! [U_1382] :
( c_Power_Opower__class_Opower(U_1382) = c_Power_Opower_Opower(U_1382,c_Groups_Oone__class_Oone(U_1382),c_Groups_Otimes__class_Otimes(U_1382))
| ~ class_Power_Opower(U_1382) ),
inference(variable_rename,[status(thm)],[f_430_1]) ).
cnf(f_430_3,plain,
( c_Power_Opower__class_Opower(U_1382) = c_Power_Opower_Opower(U_1382,c_Groups_Oone__class_Oone(U_1382),c_Groups_Otimes__class_Otimes(U_1382))
| ~ class_Power_Opower(U_1382) ),
inference(clausify,[status(thm)],[f_430_2]) ).
fof(f_431_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_431_2,plain,
! [U_1383] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1383)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1383)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1383))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1383))) ) ),
inference(variable_rename,[status(thm)],[f_431_1]) ).
fof(f_431_3,plain,
( ! [U_1385] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1385)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1385)) )
& ! [U_1384] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1384))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1384))) ) ),
inference(miniscope,[status(thm)],[f_431_2]) ).
cnf(f_431_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1384))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1384))) ),
inference(clausify,[status(thm)],[f_431_3]) ).
cnf(f_431_5,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_1385)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1385)) ),
inference(clausify,[status(thm)],[f_431_3]) ).
fof(f_432_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_432_2,plain,
! [U_1387,U_1386] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1386)),hAPP(c_Int_Onat,U_1387)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1386),U_1387)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1386),U_1387))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1386)),hAPP(c_Int_Onat,U_1387))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1386)) ),
inference(variable_rename,[status(thm)],[f_432_1]) ).
cnf(f_432_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1386),U_1387))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1386)),hAPP(c_Int_Onat,U_1387)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1386)) ),
inference(clausify,[status(thm)],[f_432_2]) ).
cnf(f_432_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1386)),hAPP(c_Int_Onat,U_1387)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1386),U_1387))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1386)) ),
inference(clausify,[status(thm)],[f_432_2]) ).
fof(f_433_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_433_2,plain,
! [U_1389,U_1388] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1388)),hAPP(c_Int_Onat,U_1389)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1388),U_1389)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1388),U_1389))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1388)),hAPP(c_Int_Onat,U_1389))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1389))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1388)) ),
inference(variable_rename,[status(thm)],[f_433_1]) ).
cnf(f_433_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1388),U_1389))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1388)),hAPP(c_Int_Onat,U_1389)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1389))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1388)) ),
inference(clausify,[status(thm)],[f_433_2]) ).
cnf(f_433_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1388)),hAPP(c_Int_Onat,U_1389)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1388),U_1389))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1389))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1388)) ),
inference(clausify,[status(thm)],[f_433_2]) ).
fof(f_434_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_434_2,plain,
! [U_1391,U_1390] :
( ( U_1390 = hAPP(c_Int_Onat,U_1391)
| ( U_1390 != 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_1391)) )
| ( U_1391 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1390)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1391)) ) )
& ( ( ( U_1390 = 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_1391)) )
& ( U_1391 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1390)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1391)) ) )
| U_1390 != hAPP(c_Int_Onat,U_1391) ) ),
inference(variable_rename,[status(thm)],[f_434_1]) ).
fof(f_434_3,plain,
( ! [U_1395,U_1393] :
( U_1393 = hAPP(c_Int_Onat,U_1395)
| ( U_1393 != 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_1395)) )
| ( U_1395 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1393)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1395)) ) )
& ! [U_1394,U_1392] :
( ( ( U_1392 = 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_1394)) )
& ( U_1394 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1392)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1394)) ) )
| U_1392 != hAPP(c_Int_Onat,U_1394) ) ),
inference(miniscope,[status(thm)],[f_434_2]) ).
cnf(f_434_4,plain,
( U_1394 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1392)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1394))
| U_1392 != hAPP(c_Int_Onat,U_1394) ),
inference(clausify,[status(thm)],[f_434_3]) ).
cnf(f_434_5,plain,
( U_1392 = 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_1394))
| U_1392 != hAPP(c_Int_Onat,U_1394) ),
inference(clausify,[status(thm)],[f_434_3]) ).
cnf(f_434_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1395))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1395))
| U_1393 = hAPP(c_Int_Onat,U_1395) ),
inference(clausify,[status(thm)],[f_434_3]) ).
cnf(f_434_7,plain,
( U_1393 != 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_1395))
| U_1393 = hAPP(c_Int_Onat,U_1395) ),
inference(clausify,[status(thm)],[f_434_3]) ).
cnf(f_434_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1395))
| U_1395 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1393)
| U_1393 = hAPP(c_Int_Onat,U_1395) ),
inference(clausify,[status(thm)],[f_434_3]) ).
cnf(f_434_9,plain,
( U_1393 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1395 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1393)
| U_1393 = hAPP(c_Int_Onat,U_1395) ),
inference(clausify,[status(thm)],[f_434_3]) ).
fof(f_435_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_435_2,plain,
! [U_1397,U_1396] :
( ( hAPP(c_Int_Onat,U_1396) = U_1397
| ( U_1397 != 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_1396)) )
| ( U_1396 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1397)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1396)) ) )
& ( ( ( U_1397 = 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_1396)) )
& ( U_1396 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1397)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1396)) ) )
| hAPP(c_Int_Onat,U_1396) != U_1397 ) ),
inference(variable_rename,[status(thm)],[f_435_1]) ).
fof(f_435_3,plain,
( ! [U_1401,U_1399] :
( hAPP(c_Int_Onat,U_1399) = U_1401
| ( U_1401 != 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_1399)) )
| ( U_1399 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1401)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1399)) ) )
& ! [U_1400,U_1398] :
( ( ( U_1400 = 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_1398)) )
& ( U_1398 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1400)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1398)) ) )
| hAPP(c_Int_Onat,U_1398) != U_1400 ) ),
inference(miniscope,[status(thm)],[f_435_2]) ).
cnf(f_435_4,plain,
( U_1398 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1400)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1398))
| hAPP(c_Int_Onat,U_1398) != U_1400 ),
inference(clausify,[status(thm)],[f_435_3]) ).
cnf(f_435_5,plain,
( U_1400 = 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_1398))
| hAPP(c_Int_Onat,U_1398) != U_1400 ),
inference(clausify,[status(thm)],[f_435_3]) ).
cnf(f_435_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1399))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1399))
| hAPP(c_Int_Onat,U_1399) = U_1401 ),
inference(clausify,[status(thm)],[f_435_3]) ).
cnf(f_435_7,plain,
( U_1401 != 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_1399))
| hAPP(c_Int_Onat,U_1399) = U_1401 ),
inference(clausify,[status(thm)],[f_435_3]) ).
cnf(f_435_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1399))
| U_1399 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1401)
| hAPP(c_Int_Onat,U_1399) = U_1401 ),
inference(clausify,[status(thm)],[f_435_3]) ).
cnf(f_435_9,plain,
( U_1401 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1399 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1401)
| hAPP(c_Int_Onat,U_1399) = U_1401 ),
inference(clausify,[status(thm)],[f_435_3]) ).
fof(f_436_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_436_2,plain,
! [U_1403,U_1402] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_1402)),hAPP(c_Int_Onat,U_1403)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1402),U_1403)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1402),U_1403))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_1402)),hAPP(c_Int_Onat,U_1403))) ) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1403))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1402)) ) ),
inference(variable_rename,[status(thm)],[f_436_1]) ).
cnf(f_436_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1402),U_1403))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_1402)),hAPP(c_Int_Onat,U_1403)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1402)) ),
inference(clausify,[status(thm)],[f_436_2]) ).
cnf(f_436_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_1402)),hAPP(c_Int_Onat,U_1403)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1402),U_1403))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1402)) ),
inference(clausify,[status(thm)],[f_436_2]) ).
cnf(f_436_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1402),U_1403))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_1402)),hAPP(c_Int_Onat,U_1403)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1403)) ),
inference(clausify,[status(thm)],[f_436_2]) ).
cnf(f_436_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_1402)),hAPP(c_Int_Onat,U_1403)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1402),U_1403))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1403)) ),
inference(clausify,[status(thm)],[f_436_2]) ).
fof(f_437_1,plain,
! [V_i_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
| ( ~ hBOOL(hAPP(V_P_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_P_2,B_n))
& V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) )
& ( ( ( hBOOL(hAPP(V_P_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_P_2,B_n))
| V_i_2 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) )
| ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__nat]) ).
fof(f_437_2,plain,
! [U_1407,U_1406] :
( ( hBOOL(hAPP(U_1406,hAPP(c_Int_Onat,U_1407)))
| ( ~ hBOOL(hAPP(U_1406,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1407),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ? [U_1405] :
( ~ hBOOL(hAPP(U_1406,U_1405))
& U_1407 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1405) ) )
& ( ( ( hBOOL(hAPP(U_1406,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1407),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_1404] :
( hBOOL(hAPP(U_1406,U_1404))
| U_1407 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1404) ) )
| ~ hBOOL(hAPP(U_1406,hAPP(c_Int_Onat,U_1407))) ) ),
inference(variable_rename,[status(thm)],[f_437_1]) ).
fof(f_437_3,plain,
( ! [U_1411,U_1409] :
( hBOOL(hAPP(U_1409,hAPP(c_Int_Onat,U_1411)))
| ( ~ hBOOL(hAPP(U_1409,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1411),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ? [U_1405] :
( ~ hBOOL(hAPP(U_1409,U_1405))
& U_1411 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1405) ) )
& ! [U_1410,U_1408] :
( ( ( hBOOL(hAPP(U_1408,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1410),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_1404] :
( hBOOL(hAPP(U_1408,U_1404))
| U_1410 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1404) ) )
| ~ hBOOL(hAPP(U_1408,hAPP(c_Int_Onat,U_1410))) ) ),
inference(miniscope,[status(thm)],[f_437_2]) ).
fof(f_437_4,plain,
( ! [U_1411,U_1409] :
( hBOOL(hAPP(U_1409,hAPP(c_Int_Onat,U_1411)))
| ( ~ hBOOL(hAPP(U_1409,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1411),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_1409,sK24(U_1411,U_1409)))
& U_1411 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK24(U_1411,U_1409)) ) )
& ! [U_1410,U_1408] :
( ( ( hBOOL(hAPP(U_1408,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1410),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_1404] :
( hBOOL(hAPP(U_1408,U_1404))
| U_1410 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1404) ) )
| ~ hBOOL(hAPP(U_1408,hAPP(c_Int_Onat,U_1410))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_1405,sK24(U_1411,U_1409))],[f_437_3]) ).
cnf(f_437_5,plain,
( hBOOL(hAPP(U_1408,U_1404))
| U_1410 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1404)
| ~ hBOOL(hAPP(U_1408,hAPP(c_Int_Onat,U_1410))) ),
inference(clausify,[status(thm)],[f_437_4]) ).
cnf(f_437_6,plain,
( hBOOL(hAPP(U_1408,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1410),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_1408,hAPP(c_Int_Onat,U_1410))) ),
inference(clausify,[status(thm)],[f_437_4]) ).
cnf(f_437_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1411),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_1411 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK24(U_1411,U_1409))
| hBOOL(hAPP(U_1409,hAPP(c_Int_Onat,U_1411))) ),
inference(clausify,[status(thm)],[f_437_4]) ).
cnf(f_437_8,plain,
( ~ hBOOL(hAPP(U_1409,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_1411 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK24(U_1411,U_1409))
| hBOOL(hAPP(U_1409,hAPP(c_Int_Onat,U_1411))) ),
inference(clausify,[status(thm)],[f_437_4]) ).
cnf(f_437_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1411),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_1409,sK24(U_1411,U_1409)))
| hBOOL(hAPP(U_1409,hAPP(c_Int_Onat,U_1411))) ),
inference(clausify,[status(thm)],[f_437_4]) ).
cnf(f_437_10,plain,
( ~ hBOOL(hAPP(U_1409,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(U_1409,sK24(U_1411,U_1409)))
| hBOOL(hAPP(U_1409,hAPP(c_Int_Onat,U_1411))) ),
inference(clausify,[status(thm)],[f_437_4]) ).
fof(f_438_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_438_2,plain,
! [U_1413,U_1412] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1412),U_1413)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_1412)),hAPP(c_Int_Onat,U_1413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1412)) ),
inference(variable_rename,[status(thm)],[f_438_1]) ).
cnf(f_438_3,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1412),U_1413)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_1412)),hAPP(c_Int_Onat,U_1413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1412)) ),
inference(clausify,[status(thm)],[f_438_2]) ).
fof(f_439_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_439_2,plain,
! [U_1415,U_1414] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_1414)),hAPP(c_Int_Onat,U_1415)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1414),U_1415))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1415))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1414)) ),
inference(variable_rename,[status(thm)],[f_439_1]) ).
cnf(f_439_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_1414)),hAPP(c_Int_Onat,U_1415)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1414),U_1415))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1415))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1414)) ),
inference(clausify,[status(thm)],[f_439_2]) ).
fof(f_440_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_440_2,plain,
! [U_1417,U_1416] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1416),hAPP(c_Int_Onat,U_1417)) = hAPP(c_Int_Oring__1__class_Oof__int(U_1416),U_1417)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1417))
| ~ class_Rings_Oring__1(U_1416) ),
inference(variable_rename,[status(thm)],[f_440_1]) ).
cnf(f_440_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1416),hAPP(c_Int_Onat,U_1417)) = hAPP(c_Int_Oring__1__class_Oof__int(U_1416),U_1417)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1417))
| ~ class_Rings_Oring__1(U_1416) ),
inference(clausify,[status(thm)],[f_440_2]) ).
fof(f_441_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_441_2,plain,
! [U_1420,U_1419,U_1418] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1418),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1418),U_1419),hAPP(hAPP(c_Power_Opower__class_Opower(U_1418),U_1419),U_1420))),hAPP(hAPP(c_Power_Opower__class_Opower(U_1418),U_1419),U_1420)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1418),U_1419),c_Groups_Oone__class_Oone(U_1418)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1418),c_Groups_Ozero__class_Ozero(U_1418)),U_1419))
| ~ class_Rings_Olinordered__semidom(U_1418) ),
inference(variable_rename,[status(thm)],[f_441_1]) ).
cnf(f_441_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1418),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1418),U_1419),hAPP(hAPP(c_Power_Opower__class_Opower(U_1418),U_1419),U_1420))),hAPP(hAPP(c_Power_Opower__class_Opower(U_1418),U_1419),U_1420)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1418),U_1419),c_Groups_Oone__class_Oone(U_1418)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1418),c_Groups_Ozero__class_Ozero(U_1418)),U_1419))
| ~ class_Rings_Olinordered__semidom(U_1418) ),
inference(clausify,[status(thm)],[f_441_2]) ).
fof(f_442_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]) ).
cnf(f_442_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(clausify,[status(thm)],[f_442_1]) ).
fof(f_443_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_443_2,plain,
! [U_1422,U_1421] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1421),U_1422)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1421))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1422)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1421),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_443_1]) ).
cnf(f_443_3,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1421),U_1422)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1421))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1422)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1421),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_443_2]) ).
fof(f_444_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_444_2,plain,
! [U_1428,U_1427,U_1426,U_1425,U_1424,U_1423] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1423),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1423),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1423),U_1427),U_1424)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1423),U_1428),U_1426))),U_1425))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1423),U_1427),U_1428) != c_Groups_Oone__class_Oone(U_1423)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1423),c_Groups_Ozero__class_Ozero(U_1423)),U_1428))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1423),c_Groups_Ozero__class_Ozero(U_1423)),U_1427))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1423),U_1426),U_1425))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1423),U_1424),U_1425))
| ~ class_Rings_Olinordered__semiring__1__strict(U_1423) ),
inference(variable_rename,[status(thm)],[f_444_1]) ).
cnf(f_444_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1423),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1423),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1423),U_1427),U_1424)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1423),U_1428),U_1426))),U_1425))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1423),U_1427),U_1428) != c_Groups_Oone__class_Oone(U_1423)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1423),c_Groups_Ozero__class_Ozero(U_1423)),U_1428))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1423),c_Groups_Ozero__class_Ozero(U_1423)),U_1427))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1423),U_1426),U_1425))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1423),U_1424),U_1425))
| ~ class_Rings_Olinordered__semiring__1__strict(U_1423) ),
inference(clausify,[status(thm)],[f_444_2]) ).
fof(f_445_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_445_2,plain,
! [U_1430,U_1429] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_1429)),hAPP(c_Int_Onat,U_1430)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_1429,U_1430))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1430))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1429)) ),
inference(variable_rename,[status(thm)],[f_445_1]) ).
cnf(f_445_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_1429)),hAPP(c_Int_Onat,U_1430)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_1429,U_1430))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1430))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1429)) ),
inference(clausify,[status(thm)],[f_445_2]) ).
fof(f_446_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_446_2,plain,
! [U_1432,U_1431] :
( c_Groups_Osgn__class_Osgn(U_1431,U_1432) = c_Groups_Oone__class_Oone(U_1431)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1431),c_Groups_Ozero__class_Ozero(U_1431)),U_1432))
| ~ class_Rings_Olinordered__idom(U_1431) ),
inference(variable_rename,[status(thm)],[f_446_1]) ).
cnf(f_446_3,plain,
( c_Groups_Osgn__class_Osgn(U_1431,U_1432) = c_Groups_Oone__class_Oone(U_1431)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1431),c_Groups_Ozero__class_Ozero(U_1431)),U_1432))
| ~ class_Rings_Olinordered__idom(U_1431) ),
inference(clausify,[status(thm)],[f_446_2]) ).
fof(f_447_1,plain,
! [V_a_2,T_b] :
( ( ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| c_Groups_Osgn__class_Osgn(T_b,V_a_2) != c_Groups_Oone__class_Oone(T_b) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sgn__1__pos]) ).
fof(f_447_2,plain,
! [U_1434,U_1433] :
( ( ( c_Groups_Osgn__class_Osgn(U_1433,U_1434) = c_Groups_Oone__class_Oone(U_1433)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1433),c_Groups_Ozero__class_Ozero(U_1433)),U_1434)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1433),c_Groups_Ozero__class_Ozero(U_1433)),U_1434))
| c_Groups_Osgn__class_Osgn(U_1433,U_1434) != c_Groups_Oone__class_Oone(U_1433) ) )
| ~ class_Rings_Olinordered__idom(U_1433) ),
inference(variable_rename,[status(thm)],[f_447_1]) ).
cnf(f_447_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1433),c_Groups_Ozero__class_Ozero(U_1433)),U_1434))
| c_Groups_Osgn__class_Osgn(U_1433,U_1434) != c_Groups_Oone__class_Oone(U_1433)
| ~ class_Rings_Olinordered__idom(U_1433) ),
inference(clausify,[status(thm)],[f_447_2]) ).
cnf(f_447_4,plain,
( c_Groups_Osgn__class_Osgn(U_1433,U_1434) = c_Groups_Oone__class_Oone(U_1433)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1433),c_Groups_Ozero__class_Ozero(U_1433)),U_1434))
| ~ class_Rings_Olinordered__idom(U_1433) ),
inference(clausify,[status(thm)],[f_447_2]) ).
fof(f_448_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_448_2,plain,
! [U_1435] :
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_1435)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1435))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1435)) ),
inference(variable_rename,[status(thm)],[f_448_1]) ).
cnf(f_448_3,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_1435)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1435))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1435)) ),
inference(clausify,[status(thm)],[f_448_2]) ).
fof(f_449_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_449_2,plain,
! [U_1439,U_1438,U_1437] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1437),U_1438),U_1439))
| ? [U_1436] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1437),U_1436),U_1438)),U_1439))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1437),U_1436),c_Groups_Oone__class_Oone(U_1437)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1437),c_Groups_Ozero__class_Ozero(U_1437)),U_1436)) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_1437) ),
inference(variable_rename,[status(thm)],[f_449_1]) ).
fof(f_449_3,plain,
! [U_1439,U_1438,U_1437] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1437),U_1438),U_1439))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1437),sK25(U_1439,U_1438,U_1437)),U_1438)),U_1439))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1437),sK25(U_1439,U_1438,U_1437)),c_Groups_Oone__class_Oone(U_1437)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1437),c_Groups_Ozero__class_Ozero(U_1437)),sK25(U_1439,U_1438,U_1437))) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_1437) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_1436,sK25(U_1439,U_1438,U_1437))],[f_449_2]) ).
cnf(f_449_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1437),c_Groups_Ozero__class_Ozero(U_1437)),sK25(U_1439,U_1438,U_1437)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1437),U_1438),U_1439))
| ~ class_Fields_Olinordered__field__inverse__zero(U_1437) ),
inference(clausify,[status(thm)],[f_449_3]) ).
cnf(f_449_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1437),sK25(U_1439,U_1438,U_1437)),c_Groups_Oone__class_Oone(U_1437)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1437),U_1438),U_1439))
| ~ class_Fields_Olinordered__field__inverse__zero(U_1437) ),
inference(clausify,[status(thm)],[f_449_3]) ).
cnf(f_449_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1437),sK25(U_1439,U_1438,U_1437)),U_1438)),U_1439))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1437),U_1438),U_1439))
| ~ class_Fields_Olinordered__field__inverse__zero(U_1437) ),
inference(clausify,[status(thm)],[f_449_3]) ).
fof(f_450_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_450_2,plain,
! [U_1441,U_1440] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1440) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1441)
| ~ 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_1441)))
| U_1440 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1441)) )
& ( ( 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_1441)))
& U_1440 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1441)) )
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1440) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1441) ) ),
inference(variable_rename,[status(thm)],[f_450_1]) ).
fof(f_450_3,plain,
( ! [U_1445,U_1443] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1443) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1445)
| ~ 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_1445)))
| U_1443 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1445)) )
& ! [U_1444,U_1442] :
( ( 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_1444)))
& U_1442 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1444)) )
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1442) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1444) ) ),
inference(miniscope,[status(thm)],[f_450_2]) ).
cnf(f_450_4,plain,
( U_1442 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1444))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1442) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1444) ),
inference(clausify,[status(thm)],[f_450_3]) ).
cnf(f_450_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),U_1444)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1442) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1444) ),
inference(clausify,[status(thm)],[f_450_3]) ).
cnf(f_450_6,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1443) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1445)
| ~ 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_1445)))
| U_1443 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1445)) ),
inference(clausify,[status(thm)],[f_450_3]) ).
fof(f_451_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_451_2,plain,
! [U_1446] : 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_1446)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_451_1]) ).
cnf(f_451_3,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_1446)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_451_2]) ).
fof(f_452_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_452_2,plain,
! [U_1448,U_1447] : 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_1447))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1448))),
inference(variable_rename,[status(thm)],[f_452_1]) ).
cnf(f_452_3,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_1447))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1448))),
inference(clausify,[status(thm)],[f_452_2]) ).
fof(f_453_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_453_2,plain,
! [U_1450,U_1449] : 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_1449)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1450))),
inference(variable_rename,[status(thm)],[f_453_1]) ).
cnf(f_453_3,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_1449)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1450))),
inference(clausify,[status(thm)],[f_453_2]) ).
fof(f_454_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_454_2,plain,
! [U_1451] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1451)),U_1451) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_454_1]) ).
cnf(f_454_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1451)),U_1451) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_454_2]) ).
fof(f_455_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_455_2,plain,
! [U_1454,U_1453,U_1452] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1452),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1453),U_1454)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1452),U_1454)),U_1453)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1452),U_1454)),U_1453))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1452),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1453),U_1454))) ) ),
inference(variable_rename,[status(thm)],[f_455_1]) ).
fof(f_455_3,plain,
( ! [U_1460,U_1458,U_1456] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1456),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1458),U_1460)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1456),U_1460)),U_1458)) )
& ! [U_1459,U_1457,U_1455] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1455),U_1459)),U_1457))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1455),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1457),U_1459))) ) ),
inference(miniscope,[status(thm)],[f_455_2]) ).
cnf(f_455_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1455),U_1459)),U_1457))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1455),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1457),U_1459))) ),
inference(clausify,[status(thm)],[f_455_3]) ).
cnf(f_455_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1456),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1458),U_1460)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1456),U_1460)),U_1458)) ),
inference(clausify,[status(thm)],[f_455_3]) ).
fof(f_456_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_456_2,plain,
! [U_1462,U_1461] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1462),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1461),U_1462)) = U_1461
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1461),U_1462)) ),
inference(variable_rename,[status(thm)],[f_456_1]) ).
cnf(f_456_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1462),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1461),U_1462)) = U_1461
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1461),U_1462)) ),
inference(clausify,[status(thm)],[f_456_2]) ).
fof(f_457_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_457_2,plain,
! [U_1467,U_1466,U_1465,U_1464,U_1463] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1463),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1463),U_1464),U_1465)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1463),U_1466),U_1467)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1463),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1463),U_1464),U_1466)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1463),U_1465),U_1467))
| ~ class_Rings_Ocomm__semiring__1(U_1463) ),
inference(variable_rename,[status(thm)],[f_457_1]) ).
cnf(f_457_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1463),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1463),U_1464),U_1465)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1463),U_1466),U_1467)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1463),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1463),U_1464),U_1466)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1463),U_1465),U_1467))
| ~ class_Rings_Ocomm__semiring__1(U_1463) ),
inference(clausify,[status(thm)],[f_457_2]) ).
fof(f_458_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_458_2,plain,
! [U_1471,U_1470,U_1469,U_1468] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1468),U_1469),U_1470)),U_1471) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1468),U_1469),U_1471)),U_1470)
| ~ class_Rings_Ocomm__semiring__1(U_1468) ),
inference(variable_rename,[status(thm)],[f_458_1]) ).
cnf(f_458_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1468),U_1469),U_1470)),U_1471) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1468),U_1469),U_1471)),U_1470)
| ~ class_Rings_Ocomm__semiring__1(U_1468) ),
inference(clausify,[status(thm)],[f_458_2]) ).
fof(f_459_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_459_2,plain,
! [U_1474,U_1473,U_1472] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1472),U_1473)),U_1474) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1472),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1473),U_1474)),
inference(variable_rename,[status(thm)],[f_459_1]) ).
cnf(f_459_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1472),U_1473)),U_1474) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1472),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1473),U_1474)),
inference(clausify,[status(thm)],[f_459_2]) ).
fof(f_460_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_460_2,plain,
! [U_1478,U_1477,U_1476,U_1475] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1475),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1475),U_1476),U_1477)),U_1478) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1475),U_1476),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1475),U_1477),U_1478))
| ~ class_Rings_Ocomm__semiring__1(U_1475) ),
inference(variable_rename,[status(thm)],[f_460_1]) ).
cnf(f_460_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1475),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1475),U_1476),U_1477)),U_1478) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1475),U_1476),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1475),U_1477),U_1478))
| ~ class_Rings_Ocomm__semiring__1(U_1475) ),
inference(clausify,[status(thm)],[f_460_2]) ).
fof(f_461_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_461_2,plain,
! [U_1482,U_1481,U_1480,U_1479] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1479),hAPP(c_Int_Onumber__class_Onumber__of(U_1479),U_1480)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1479),hAPP(c_Int_Onumber__class_Onumber__of(U_1479),U_1481)),U_1482)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1479),hAPP(c_Int_Onumber__class_Onumber__of(U_1479),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1480),U_1481))),U_1482)
| ~ class_Int_Onumber__ring(U_1479) ),
inference(variable_rename,[status(thm)],[f_461_1]) ).
cnf(f_461_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1479),hAPP(c_Int_Onumber__class_Onumber__of(U_1479),U_1480)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1479),hAPP(c_Int_Onumber__class_Onumber__of(U_1479),U_1481)),U_1482)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1479),hAPP(c_Int_Onumber__class_Onumber__of(U_1479),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1480),U_1481))),U_1482)
| ~ class_Int_Onumber__ring(U_1479) ),
inference(clausify,[status(thm)],[f_461_2]) ).
fof(f_462_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_462_2,plain,
! [U_1486,U_1485,U_1484,U_1483] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1483),hAPP(c_Int_Onumber__class_Onumber__of(U_1483),U_1484)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1483),hAPP(c_Int_Onumber__class_Onumber__of(U_1483),U_1485)),U_1486)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1483),hAPP(c_Int_Onumber__class_Onumber__of(U_1483),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1484),U_1485))),U_1486)
| ~ class_Int_Onumber__ring(U_1483) ),
inference(variable_rename,[status(thm)],[f_462_1]) ).
cnf(f_462_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1483),hAPP(c_Int_Onumber__class_Onumber__of(U_1483),U_1484)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1483),hAPP(c_Int_Onumber__class_Onumber__of(U_1483),U_1485)),U_1486)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1483),hAPP(c_Int_Onumber__class_Onumber__of(U_1483),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1484),U_1485))),U_1486)
| ~ class_Int_Onumber__ring(U_1483) ),
inference(clausify,[status(thm)],[f_462_2]) ).
fof(f_463_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_463_2,plain,
! [U_1490,U_1489,U_1488,U_1487] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1487),hAPP(c_Int_Onumber__class_Onumber__of(U_1487),U_1488)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1487),U_1489),hAPP(c_Int_Onumber__class_Onumber__of(U_1487),U_1490))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1487),hAPP(c_Int_Onumber__class_Onumber__of(U_1487),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1488),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1490)))),U_1489)
| ~ class_Int_Onumber__ring(U_1487) ),
inference(variable_rename,[status(thm)],[f_463_1]) ).
cnf(f_463_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1487),hAPP(c_Int_Onumber__class_Onumber__of(U_1487),U_1488)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1487),U_1489),hAPP(c_Int_Onumber__class_Onumber__of(U_1487),U_1490))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1487),hAPP(c_Int_Onumber__class_Onumber__of(U_1487),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1488),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1490)))),U_1489)
| ~ class_Int_Onumber__ring(U_1487) ),
inference(clausify,[status(thm)],[f_463_2]) ).
fof(f_464_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) ) )
| ~ class_Int_Oring__char__0(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__number__of]) ).
fof(f_464_2,plain,
! [U_1493,U_1492,U_1491] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_1491),U_1492) = hAPP(c_Int_Onumber__class_Onumber__of(U_1491),U_1493)
| U_1492 != U_1493 )
& ( U_1492 = U_1493
| hAPP(c_Int_Onumber__class_Onumber__of(U_1491),U_1492) != hAPP(c_Int_Onumber__class_Onumber__of(U_1491),U_1493) ) )
| ~ class_Int_Oring__char__0(U_1491)
| ~ class_Int_Onumber__ring(U_1491) ),
inference(variable_rename,[status(thm)],[f_464_1]) ).
cnf(f_464_3,plain,
( U_1492 = U_1493
| hAPP(c_Int_Onumber__class_Onumber__of(U_1491),U_1492) != hAPP(c_Int_Onumber__class_Onumber__of(U_1491),U_1493)
| ~ class_Int_Oring__char__0(U_1491)
| ~ class_Int_Onumber__ring(U_1491) ),
inference(clausify,[status(thm)],[f_464_2]) ).
cnf(f_464_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_1491),U_1492) = hAPP(c_Int_Onumber__class_Onumber__of(U_1491),U_1493)
| U_1492 != U_1493
| ~ class_Int_Oring__char__0(U_1491)
| ~ class_Int_Onumber__ring(U_1491) ),
inference(clausify,[status(thm)],[f_464_2]) ).
fof(f_465_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_465_2,plain,
! [U_1496,U_1495,U_1494] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1494),hAPP(c_Int_Onumber__class_Onumber__of(U_1494),U_1495)),hAPP(c_Int_Onumber__class_Onumber__of(U_1494),U_1496)) = hAPP(c_Int_Onumber__class_Onumber__of(U_1494),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1495),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1496)))
| ~ class_Int_Onumber__ring(U_1494) ),
inference(variable_rename,[status(thm)],[f_465_1]) ).
cnf(f_465_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1494),hAPP(c_Int_Onumber__class_Onumber__of(U_1494),U_1495)),hAPP(c_Int_Onumber__class_Onumber__of(U_1494),U_1496)) = hAPP(c_Int_Onumber__class_Onumber__of(U_1494),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1495),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1496)))
| ~ class_Int_Onumber__ring(U_1494) ),
inference(clausify,[status(thm)],[f_465_2]) ).
fof(f_466_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_466_2,plain,
! [U_1498,U_1497] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1497)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1498)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1497),U_1498)),
inference(variable_rename,[status(thm)],[f_466_1]) ).
cnf(f_466_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1497)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1498)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1497),U_1498)),
inference(clausify,[status(thm)],[f_466_2]) ).
fof(f_467_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_467_2,plain,
! [U_1501,U_1500,U_1499] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1499),hAPP(c_Int_Onumber__class_Onumber__of(U_1499),U_1500)),hAPP(c_Int_Onumber__class_Onumber__of(U_1499),U_1501)) = hAPP(c_Int_Onumber__class_Onumber__of(U_1499),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1500),U_1501))
| ~ class_Int_Onumber__ring(U_1499) ),
inference(variable_rename,[status(thm)],[f_467_1]) ).
cnf(f_467_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1499),hAPP(c_Int_Onumber__class_Onumber__of(U_1499),U_1500)),hAPP(c_Int_Onumber__class_Onumber__of(U_1499),U_1501)) = hAPP(c_Int_Onumber__class_Onumber__of(U_1499),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1500),U_1501))
| ~ class_Int_Onumber__ring(U_1499) ),
inference(clausify,[status(thm)],[f_467_2]) ).
fof(f_468_1,plain,
! [V_x_2,V_w_2,T_b] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
| V_x_2 != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) )
& ( V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
| hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != V_x_2 ) )
| ~ class_Int_Onumber(T_b) ),
inference(fof_nnf,[status(thm)],[fact_number__of__reorient]) ).
fof(f_468_2,plain,
! [U_1504,U_1503,U_1502] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_1502),U_1503) = U_1504
| U_1504 != hAPP(c_Int_Onumber__class_Onumber__of(U_1502),U_1503) )
& ( U_1504 = hAPP(c_Int_Onumber__class_Onumber__of(U_1502),U_1503)
| hAPP(c_Int_Onumber__class_Onumber__of(U_1502),U_1503) != U_1504 ) )
| ~ class_Int_Onumber(U_1502) ),
inference(variable_rename,[status(thm)],[f_468_1]) ).
cnf(f_468_3,plain,
( U_1504 = hAPP(c_Int_Onumber__class_Onumber__of(U_1502),U_1503)
| hAPP(c_Int_Onumber__class_Onumber__of(U_1502),U_1503) != U_1504
| ~ class_Int_Onumber(U_1502) ),
inference(clausify,[status(thm)],[f_468_2]) ).
cnf(f_468_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_1502),U_1503) = U_1504
| U_1504 != hAPP(c_Int_Onumber__class_Onumber__of(U_1502),U_1503)
| ~ class_Int_Onumber(U_1502) ),
inference(clausify,[status(thm)],[f_468_2]) ).
fof(f_469_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_469_2,plain,
! [U_1508,U_1507,U_1506,U_1505] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1505),U_1506),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1505),U_1507),U_1508)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1505),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1505),U_1506),U_1507)),U_1508)
| ~ class_Rings_Ocomm__semiring__1(U_1505) ),
inference(variable_rename,[status(thm)],[f_469_1]) ).
cnf(f_469_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1505),U_1506),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1505),U_1507),U_1508)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1505),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1505),U_1506),U_1507)),U_1508)
| ~ class_Rings_Ocomm__semiring__1(U_1505) ),
inference(clausify,[status(thm)],[f_469_2]) ).
fof(f_470_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_470_2,plain,
! [U_1511,U_1510,U_1509] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1509),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1510),U_1511)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1510),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1509),U_1511)),
inference(variable_rename,[status(thm)],[f_470_1]) ).
cnf(f_470_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1509),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1510),U_1511)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1510),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1509),U_1511)),
inference(clausify,[status(thm)],[f_470_2]) ).
fof(f_471_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_471_2,plain,
! [U_1515,U_1514,U_1513,U_1512] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1512),U_1513),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1512),U_1514),U_1515)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1512),U_1514),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1512),U_1513),U_1515))
| ~ class_Rings_Ocomm__semiring__1(U_1512) ),
inference(variable_rename,[status(thm)],[f_471_1]) ).
cnf(f_471_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1512),U_1513),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1512),U_1514),U_1515)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1512),U_1514),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1512),U_1513),U_1515))
| ~ class_Rings_Ocomm__semiring__1(U_1512) ),
inference(clausify,[status(thm)],[f_471_2]) ).
fof(f_472_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_472_2,plain,
! [U_1518,U_1517,U_1516] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1516),U_1517),U_1518) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1516),U_1517),hAPP(c_Groups_Ouminus__class_Ouminus(U_1516),U_1518))
| ~ class_Rings_Ocomm__ring__1(U_1516) ),
inference(variable_rename,[status(thm)],[f_472_1]) ).
cnf(f_472_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1516),U_1517),U_1518) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1516),U_1517),hAPP(c_Groups_Ouminus__class_Ouminus(U_1516),U_1518))
| ~ class_Rings_Ocomm__ring__1(U_1516) ),
inference(clausify,[status(thm)],[f_472_2]) ).
fof(f_473_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_473_2,plain,
! [U_1520,U_1519] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1519),U_1520) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1520),U_1519),
inference(variable_rename,[status(thm)],[f_473_1]) ).
cnf(f_473_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1519),U_1520) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1520),U_1519),
inference(clausify,[status(thm)],[f_473_2]) ).
fof(f_474_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_474_2,plain,
! [U_1523,U_1522,U_1521] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1521),U_1522),U_1523) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1521),U_1523),U_1522)
| ~ class_Rings_Ocomm__semiring__1(U_1521) ),
inference(variable_rename,[status(thm)],[f_474_1]) ).
cnf(f_474_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1521),U_1522),U_1523) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1521),U_1523),U_1522)
| ~ class_Rings_Ocomm__semiring__1(U_1521) ),
inference(clausify,[status(thm)],[f_474_2]) ).
fof(f_475_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_475_2,plain,
! [U_1526,U_1525,U_1524] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_1524),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_1525),U_1526)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1524),hAPP(c_Int_Onumber__class_Onumber__of(U_1524),U_1525)),hAPP(c_Int_Onumber__class_Onumber__of(U_1524),U_1526))
| ~ class_Int_Onumber__ring(U_1524) ),
inference(variable_rename,[status(thm)],[f_475_1]) ).
cnf(f_475_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_1524),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_1525),U_1526)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1524),hAPP(c_Int_Onumber__class_Onumber__of(U_1524),U_1525)),hAPP(c_Int_Onumber__class_Onumber__of(U_1524),U_1526))
| ~ class_Int_Onumber__ring(U_1524) ),
inference(clausify,[status(thm)],[f_475_2]) ).
fof(f_476_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_476_2,plain,
! [U_1529,U_1528,U_1527] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_1527),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1528),U_1529)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1527),hAPP(c_Int_Onumber__class_Onumber__of(U_1527),U_1528)),hAPP(c_Int_Onumber__class_Onumber__of(U_1527),U_1529))
| ~ class_Int_Onumber__ring(U_1527) ),
inference(variable_rename,[status(thm)],[f_476_1]) ).
cnf(f_476_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_1527),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1528),U_1529)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1527),hAPP(c_Int_Onumber__class_Onumber__of(U_1527),U_1528)),hAPP(c_Int_Onumber__class_Onumber__of(U_1527),U_1529))
| ~ class_Int_Onumber__ring(U_1527) ),
inference(clausify,[status(thm)],[f_476_2]) ).
fof(f_477_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_477_2,plain,
! [U_1531,U_1530] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1530),U_1531)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1530)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1531)),
inference(variable_rename,[status(thm)],[f_477_1]) ).
cnf(f_477_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1530),U_1531)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1530)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1531)),
inference(clausify,[status(thm)],[f_477_2]) ).
fof(f_478_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_478_2,plain,
! [U_1533,U_1532] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_1532),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1533)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1532),hAPP(c_Int_Onumber__class_Onumber__of(U_1532),U_1533))
| ~ class_Int_Onumber__ring(U_1532) ),
inference(variable_rename,[status(thm)],[f_478_1]) ).
cnf(f_478_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_1532),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1533)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1532),hAPP(c_Int_Onumber__class_Onumber__of(U_1532),U_1533))
| ~ class_Int_Onumber__ring(U_1532) ),
inference(clausify,[status(thm)],[f_478_2]) ).
fof(f_479_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_479_2,plain,
! [U_1534] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1534)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1534)),
inference(variable_rename,[status(thm)],[f_479_1]) ).
cnf(f_479_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1534)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1534)),
inference(clausify,[status(thm)],[f_479_2]) ).
fof(f_480_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_480_2,plain,
! [U_1536,U_1535] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1535),hAPP(c_Int_Onumber__class_Onumber__of(U_1535),U_1536)) = hAPP(c_Int_Onumber__class_Onumber__of(U_1535),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1536))
| ~ class_Int_Onumber__ring(U_1535) ),
inference(variable_rename,[status(thm)],[f_480_1]) ).
cnf(f_480_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1535),hAPP(c_Int_Onumber__class_Onumber__of(U_1535),U_1536)) = hAPP(c_Int_Onumber__class_Onumber__of(U_1535),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1536))
| ~ class_Int_Onumber__ring(U_1535) ),
inference(clausify,[status(thm)],[f_480_2]) ).
fof(f_481_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_481_2,plain,
! [U_1537] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1537)) = U_1537,
inference(variable_rename,[status(thm)],[f_481_1]) ).
cnf(f_481_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1537)) = U_1537,
inference(clausify,[status(thm)],[f_481_2]) ).
fof(f_482_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_482_2,plain,
! [U_1538] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1538) = U_1538,
inference(variable_rename,[status(thm)],[f_482_1]) ).
cnf(f_482_3,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1538) = U_1538,
inference(clausify,[status(thm)],[f_482_2]) ).
fof(f_483_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_483_2,plain,
! [U_1540,U_1539] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1539),c_Groups_Ozero__class_Ozero(U_1539)),U_1540) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1539),U_1540)
| ~ class_Groups_Ogroup__add(U_1539) ),
inference(variable_rename,[status(thm)],[f_483_1]) ).
cnf(f_483_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1539),c_Groups_Ozero__class_Ozero(U_1539)),U_1540) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1539),U_1540)
| ~ class_Groups_Ogroup__add(U_1539) ),
inference(clausify,[status(thm)],[f_483_2]) ).
fof(f_484_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_484_2,plain,
! [U_1542,U_1541] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1541),U_1542),hAPP(c_Groups_Ouminus__class_Ouminus(U_1541),U_1542)) = c_Groups_Ozero__class_Ozero(U_1541)
| ~ class_Groups_Ogroup__add(U_1541) ),
inference(variable_rename,[status(thm)],[f_484_1]) ).
cnf(f_484_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1541),U_1542),hAPP(c_Groups_Ouminus__class_Ouminus(U_1541),U_1542)) = c_Groups_Ozero__class_Ozero(U_1541)
| ~ class_Groups_Ogroup__add(U_1541) ),
inference(clausify,[status(thm)],[f_484_2]) ).
fof(f_485_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_b) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0]) ).
fof(f_485_2,plain,
! [U_1545,U_1544,U_1543] :
( ( ( U_1544 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1543),U_1545)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1543),U_1544),U_1545) != c_Groups_Ozero__class_Ozero(U_1543) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1543),U_1544),U_1545) = c_Groups_Ozero__class_Ozero(U_1543)
| U_1544 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1543),U_1545) ) )
| ~ class_Groups_Ogroup__add(U_1543) ),
inference(variable_rename,[status(thm)],[f_485_1]) ).
cnf(f_485_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1543),U_1544),U_1545) = c_Groups_Ozero__class_Ozero(U_1543)
| U_1544 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1543),U_1545)
| ~ class_Groups_Ogroup__add(U_1543) ),
inference(clausify,[status(thm)],[f_485_2]) ).
cnf(f_485_4,plain,
( U_1544 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1543),U_1545)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1543),U_1544),U_1545) != c_Groups_Ozero__class_Ozero(U_1543)
| ~ class_Groups_Ogroup__add(U_1543) ),
inference(clausify,[status(thm)],[f_485_2]) ).
fof(f_486_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_486_2,plain,
! [U_1547,U_1546] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1546),hAPP(c_Groups_Ouminus__class_Ouminus(U_1546),U_1547)),U_1547) = c_Groups_Ozero__class_Ozero(U_1546)
| ~ class_Groups_Ogroup__add(U_1546) ),
inference(variable_rename,[status(thm)],[f_486_1]) ).
cnf(f_486_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1546),hAPP(c_Groups_Ouminus__class_Ouminus(U_1546),U_1547)),U_1547) = c_Groups_Ozero__class_Ozero(U_1546)
| ~ class_Groups_Ogroup__add(U_1546) ),
inference(clausify,[status(thm)],[f_486_2]) ).
fof(f_487_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_487_2,plain,
! [U_1549,U_1548] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1548),hAPP(c_Groups_Ouminus__class_Ouminus(U_1548),U_1549)),U_1549) = c_Groups_Ozero__class_Ozero(U_1548)
| ~ class_Groups_Oab__group__add(U_1548) ),
inference(variable_rename,[status(thm)],[f_487_1]) ).
cnf(f_487_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1548),hAPP(c_Groups_Ouminus__class_Ouminus(U_1548),U_1549)),U_1549) = c_Groups_Ozero__class_Ozero(U_1548)
| ~ class_Groups_Oab__group__add(U_1548) ),
inference(clausify,[status(thm)],[f_487_2]) ).
fof(f_488_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_488_2,plain,
! [U_1552,U_1551,U_1550] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1550),U_1551) = U_1552
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1550),U_1551),U_1552) != c_Groups_Ozero__class_Ozero(U_1550)
| ~ class_Groups_Ogroup__add(U_1550) ),
inference(variable_rename,[status(thm)],[f_488_1]) ).
cnf(f_488_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1550),U_1551) = U_1552
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1550),U_1551),U_1552) != c_Groups_Ozero__class_Ozero(U_1550)
| ~ class_Groups_Ogroup__add(U_1550) ),
inference(clausify,[status(thm)],[f_488_2]) ).
fof(f_489_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_489_2,plain,
! [U_1555,U_1554,U_1553] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1553),U_1554)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1555),U_1554)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1553),U_1555),
inference(variable_rename,[status(thm)],[f_489_1]) ).
cnf(f_489_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1553),U_1554)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1555),U_1554)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1553),U_1555),
inference(clausify,[status(thm)],[f_489_2]) ).
fof(f_490_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_490_2,plain,
! [U_1558,U_1557,U_1556] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1556),U_1557)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1556),U_1558)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1557),U_1558),
inference(variable_rename,[status(thm)],[f_490_1]) ).
cnf(f_490_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1556),U_1557)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1556),U_1558)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1557),U_1558),
inference(clausify,[status(thm)],[f_490_2]) ).
fof(f_491_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_491_2,plain,
! [U_1561,U_1560,U_1559] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1559),U_1560)),U_1561) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1559),U_1561)),U_1560),
inference(variable_rename,[status(thm)],[f_491_1]) ).
cnf(f_491_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1559),U_1560)),U_1561) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1559),U_1561)),U_1560),
inference(clausify,[status(thm)],[f_491_2]) ).
fof(f_492_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_492_2,plain,
! [U_1564,U_1563,U_1562] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1562),U_1563)),U_1564) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1562),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1563),U_1564)),
inference(variable_rename,[status(thm)],[f_492_1]) ).
cnf(f_492_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1562),U_1563)),U_1564) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1562),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1563),U_1564)),
inference(clausify,[status(thm)],[f_492_2]) ).
fof(f_493_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_493_2,plain,
! [U_1566,U_1565] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1565),U_1566)),U_1565) = U_1566,
inference(variable_rename,[status(thm)],[f_493_1]) ).
cnf(f_493_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1565),U_1566)),U_1565) = U_1566,
inference(clausify,[status(thm)],[f_493_2]) ).
fof(f_494_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_494_2,plain,
! [U_1568,U_1567] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1567),U_1568)),U_1568) = U_1567,
inference(variable_rename,[status(thm)],[f_494_1]) ).
cnf(f_494_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1567),U_1568)),U_1568) = U_1567,
inference(clausify,[status(thm)],[f_494_2]) ).
fof(f_495_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( ( ( 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_b),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
| ~ class_Groups_Oab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq]) ).
fof(f_495_2,plain,
! [U_1573,U_1572,U_1571,U_1570,U_1569] :
( ( ( U_1570 = U_1571
| U_1572 != U_1573 )
& ( U_1572 = U_1573
| U_1570 != U_1571 ) )
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1569),U_1570),U_1571) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1569),U_1572),U_1573)
| ~ class_Groups_Oab__group__add(U_1569) ),
inference(variable_rename,[status(thm)],[f_495_1]) ).
cnf(f_495_3,plain,
( U_1572 = U_1573
| U_1570 != U_1571
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1569),U_1570),U_1571) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1569),U_1572),U_1573)
| ~ class_Groups_Oab__group__add(U_1569) ),
inference(clausify,[status(thm)],[f_495_2]) ).
cnf(f_495_4,plain,
( U_1570 = U_1571
| U_1572 != U_1573
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1569),U_1570),U_1571) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1569),U_1572),U_1573)
| ~ class_Groups_Oab__group__add(U_1569) ),
inference(clausify,[status(thm)],[f_495_2]) ).
fof(f_496_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_496_2,plain,
! [U_1577,U_1576,U_1575,U_1574] :
( U_1575 = U_1577
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1574),U_1575),U_1576) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1574),U_1577),U_1576)
| ~ class_Groups_Ocancel__semigroup__add(U_1574) ),
inference(variable_rename,[status(thm)],[f_496_1]) ).
cnf(f_496_3,plain,
( U_1575 = U_1577
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1574),U_1575),U_1576) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1574),U_1577),U_1576)
| ~ class_Groups_Ocancel__semigroup__add(U_1574) ),
inference(clausify,[status(thm)],[f_496_2]) ).
fof(f_497_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_497_2,plain,
! [U_1581,U_1580,U_1579,U_1578] :
( U_1580 = U_1581
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1578),U_1579),U_1580) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1578),U_1579),U_1581)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_1578) ),
inference(variable_rename,[status(thm)],[f_497_1]) ).
cnf(f_497_3,plain,
( U_1580 = U_1581
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1578),U_1579),U_1580) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1578),U_1579),U_1581)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_1578) ),
inference(clausify,[status(thm)],[f_497_2]) ).
fof(f_498_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_498_2,plain,
! [U_1585,U_1584,U_1583,U_1582] :
( U_1584 = U_1585
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1582),U_1583),U_1584) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1582),U_1583),U_1585)
| ~ class_Groups_Ocancel__semigroup__add(U_1582) ),
inference(variable_rename,[status(thm)],[f_498_1]) ).
cnf(f_498_3,plain,
( U_1584 = U_1585
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1582),U_1583),U_1584) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1582),U_1583),U_1585)
| ~ class_Groups_Ocancel__semigroup__add(U_1582) ),
inference(clausify,[status(thm)],[f_498_2]) ).
fof(f_499_1,plain,
! [V_c_2,V_a_2,V_b_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_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_b),V_b_2),V_a_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2) ) )
| ~ class_Groups_Ocancel__semigroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__right__cancel]) ).
fof(f_499_2,plain,
! [U_1589,U_1588,U_1587,U_1586] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1586),U_1587),U_1588) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1586),U_1589),U_1588)
| U_1587 != U_1589 )
& ( U_1587 = U_1589
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1586),U_1587),U_1588) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1586),U_1589),U_1588) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_1586) ),
inference(variable_rename,[status(thm)],[f_499_1]) ).
cnf(f_499_3,plain,
( U_1587 = U_1589
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1586),U_1587),U_1588) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1586),U_1589),U_1588)
| ~ class_Groups_Ocancel__semigroup__add(U_1586) ),
inference(clausify,[status(thm)],[f_499_2]) ).
cnf(f_499_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1586),U_1587),U_1588) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1586),U_1589),U_1588)
| U_1587 != U_1589
| ~ class_Groups_Ocancel__semigroup__add(U_1586) ),
inference(clausify,[status(thm)],[f_499_2]) ).
fof(f_500_1,plain,
! [V_c_2,V_b_2,V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)
| V_b_2 != V_c_2 )
& ( V_b_2 = V_c_2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2) ) )
| ~ class_Groups_Ocancel__semigroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__left__cancel]) ).
fof(f_500_2,plain,
! [U_1593,U_1592,U_1591,U_1590] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1590),U_1591),U_1592) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1590),U_1591),U_1593)
| U_1592 != U_1593 )
& ( U_1592 = U_1593
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1590),U_1591),U_1592) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1590),U_1591),U_1593) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_1590) ),
inference(variable_rename,[status(thm)],[f_500_1]) ).
cnf(f_500_3,plain,
( U_1592 = U_1593
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1590),U_1591),U_1592) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1590),U_1591),U_1593)
| ~ class_Groups_Ocancel__semigroup__add(U_1590) ),
inference(clausify,[status(thm)],[f_500_2]) ).
cnf(f_500_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1590),U_1591),U_1592) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1590),U_1591),U_1593)
| U_1592 != U_1593
| ~ class_Groups_Ocancel__semigroup__add(U_1590) ),
inference(clausify,[status(thm)],[f_500_2]) ).
fof(f_501_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_501_2,plain,
! [U_1597,U_1596,U_1595,U_1594] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1594),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1594),U_1595),U_1596)),U_1597) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1594),U_1595),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1594),U_1596),U_1597))
| ~ class_Groups_Oab__semigroup__add(U_1594) ),
inference(variable_rename,[status(thm)],[f_501_1]) ).
cnf(f_501_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1594),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1594),U_1595),U_1596)),U_1597) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1594),U_1595),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1594),U_1596),U_1597))
| ~ class_Groups_Oab__semigroup__add(U_1594) ),
inference(clausify,[status(thm)],[f_501_2]) ).
fof(f_502_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_502_2,plain,
! [U_1600,U_1599,U_1598] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1598),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1598),U_1599),U_1600)),U_1600) = U_1599
| ~ class_Groups_Ogroup__add(U_1598) ),
inference(variable_rename,[status(thm)],[f_502_1]) ).
cnf(f_502_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1598),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1598),U_1599),U_1600)),U_1600) = U_1599
| ~ class_Groups_Ogroup__add(U_1598) ),
inference(clausify,[status(thm)],[f_502_2]) ).
fof(f_503_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_503_2,plain,
! [U_1603,U_1602,U_1601] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1601),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1601),U_1602),U_1603)),U_1603) = U_1602
| ~ class_Groups_Ogroup__add(U_1601) ),
inference(variable_rename,[status(thm)],[f_503_1]) ).
cnf(f_503_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1601),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1601),U_1602),U_1603)),U_1603) = U_1602
| ~ class_Groups_Ogroup__add(U_1601) ),
inference(clausify,[status(thm)],[f_503_2]) ).
fof(f_504_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_504_2,plain,
! [U_1606,U_1605,U_1604] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),hAPP(c_Groups_Ouminus__class_Ouminus(U_1604),U_1605)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),U_1605),U_1606)) = U_1606
| ~ class_Groups_Ogroup__add(U_1604) ),
inference(variable_rename,[status(thm)],[f_504_1]) ).
cnf(f_504_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),hAPP(c_Groups_Ouminus__class_Ouminus(U_1604),U_1605)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),U_1605),U_1606)) = U_1606
| ~ class_Groups_Ogroup__add(U_1604) ),
inference(clausify,[status(thm)],[f_504_2]) ).
fof(f_505_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal]) ).
fof(f_505_2,plain,
! [U_1609,U_1608,U_1607] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1607),U_1608) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1607),U_1609)
| U_1608 != U_1609 )
& ( U_1608 = U_1609
| hAPP(c_Groups_Ouminus__class_Ouminus(U_1607),U_1608) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1607),U_1609) ) )
| ~ class_Groups_Ogroup__add(U_1607) ),
inference(variable_rename,[status(thm)],[f_505_1]) ).
cnf(f_505_3,plain,
( U_1608 = U_1609
| hAPP(c_Groups_Ouminus__class_Ouminus(U_1607),U_1608) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1607),U_1609)
| ~ class_Groups_Ogroup__add(U_1607) ),
inference(clausify,[status(thm)],[f_505_2]) ).
cnf(f_505_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1607),U_1608) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1607),U_1609)
| U_1608 != U_1609
| ~ class_Groups_Ogroup__add(U_1607) ),
inference(clausify,[status(thm)],[f_505_2]) ).
fof(f_506_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
| hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) != V_a_2 )
& ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2
| hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) != V_b_2 ) )
| ~ class_Groups_Ogroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_minus__equation__iff]) ).
fof(f_506_2,plain,
! [U_1612,U_1611,U_1610] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1610),U_1611) = U_1612
| hAPP(c_Groups_Ouminus__class_Ouminus(U_1610),U_1612) != U_1611 )
& ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1610),U_1612) = U_1611
| hAPP(c_Groups_Ouminus__class_Ouminus(U_1610),U_1611) != U_1612 ) )
| ~ class_Groups_Ogroup__add(U_1610) ),
inference(variable_rename,[status(thm)],[f_506_1]) ).
cnf(f_506_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1610),U_1612) = U_1611
| hAPP(c_Groups_Ouminus__class_Ouminus(U_1610),U_1611) != U_1612
| ~ class_Groups_Ogroup__add(U_1610) ),
inference(clausify,[status(thm)],[f_506_2]) ).
cnf(f_506_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1610),U_1611) = U_1612
| hAPP(c_Groups_Ouminus__class_Ouminus(U_1610),U_1612) != U_1611
| ~ class_Groups_Ogroup__add(U_1610) ),
inference(clausify,[status(thm)],[f_506_2]) ).
fof(f_507_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_507_2,plain,
! [U_1615,U_1614,U_1613] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1613),U_1614),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1613),hAPP(c_Groups_Ouminus__class_Ouminus(U_1613),U_1614)),U_1615)) = U_1615
| ~ class_Groups_Ogroup__add(U_1613) ),
inference(variable_rename,[status(thm)],[f_507_1]) ).
cnf(f_507_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1613),U_1614),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1613),hAPP(c_Groups_Ouminus__class_Ouminus(U_1613),U_1614)),U_1615)) = U_1615
| ~ class_Groups_Ogroup__add(U_1613) ),
inference(clausify,[status(thm)],[f_507_2]) ).
fof(f_508_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
| V_b_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) )
& ( V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
| V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_equation__minus__iff]) ).
fof(f_508_2,plain,
! [U_1618,U_1617,U_1616] :
( ( ( U_1617 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1616),U_1618)
| U_1618 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1616),U_1617) )
& ( U_1618 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1616),U_1617)
| U_1617 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1616),U_1618) ) )
| ~ class_Groups_Ogroup__add(U_1616) ),
inference(variable_rename,[status(thm)],[f_508_1]) ).
cnf(f_508_3,plain,
( U_1618 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1616),U_1617)
| U_1617 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1616),U_1618)
| ~ class_Groups_Ogroup__add(U_1616) ),
inference(clausify,[status(thm)],[f_508_2]) ).
cnf(f_508_4,plain,
( U_1617 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1616),U_1618)
| U_1618 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1616),U_1617)
| ~ class_Groups_Ogroup__add(U_1616) ),
inference(clausify,[status(thm)],[f_508_2]) ).
fof(f_509_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_509_2,plain,
! [U_1621,U_1620,U_1619] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1619),U_1620),hAPP(c_Groups_Ouminus__class_Ouminus(U_1619),U_1621)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1619),U_1620),U_1621)
| ~ class_Groups_Ogroup__add(U_1619) ),
inference(variable_rename,[status(thm)],[f_509_1]) ).
cnf(f_509_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1619),U_1620),hAPP(c_Groups_Ouminus__class_Ouminus(U_1619),U_1621)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1619),U_1620),U_1621)
| ~ class_Groups_Ogroup__add(U_1619) ),
inference(clausify,[status(thm)],[f_509_2]) ).
fof(f_510_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_510_2,plain,
! [U_1624,U_1623,U_1622] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1622),U_1623),U_1624) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1622),U_1623),hAPP(c_Groups_Ouminus__class_Ouminus(U_1622),U_1624))
| ~ class_Groups_Oab__group__add(U_1622) ),
inference(variable_rename,[status(thm)],[f_510_1]) ).
cnf(f_510_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1622),U_1623),U_1624) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1622),U_1623),hAPP(c_Groups_Ouminus__class_Ouminus(U_1622),U_1624))
| ~ class_Groups_Oab__group__add(U_1622) ),
inference(clausify,[status(thm)],[f_510_2]) ).
fof(f_511_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_511_2,plain,
! [U_1627,U_1626,U_1625] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1625),U_1626),U_1627) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1625),U_1626),hAPP(c_Groups_Ouminus__class_Ouminus(U_1625),U_1627))
| ~ class_Groups_Ogroup__add(U_1625) ),
inference(variable_rename,[status(thm)],[f_511_1]) ).
cnf(f_511_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1625),U_1626),U_1627) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1625),U_1626),hAPP(c_Groups_Ouminus__class_Ouminus(U_1625),U_1627))
| ~ class_Groups_Ogroup__add(U_1625) ),
inference(clausify,[status(thm)],[f_511_2]) ).
fof(f_512_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_512_2,plain,
! [U_1630,U_1629,U_1628] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1628),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1628),U_1629),U_1630)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1628),hAPP(c_Groups_Ouminus__class_Ouminus(U_1628),U_1630)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1628),U_1629))
| ~ class_Groups_Ogroup__add(U_1628) ),
inference(variable_rename,[status(thm)],[f_512_1]) ).
cnf(f_512_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1628),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1628),U_1629),U_1630)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1628),hAPP(c_Groups_Ouminus__class_Ouminus(U_1628),U_1630)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1628),U_1629))
| ~ class_Groups_Ogroup__add(U_1628) ),
inference(clausify,[status(thm)],[f_512_2]) ).
fof(f_513_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_513_2,plain,
! [U_1633,U_1632,U_1631] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1631),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1631),U_1632),U_1633)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1631),hAPP(c_Groups_Ouminus__class_Ouminus(U_1631),U_1632)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1631),U_1633))
| ~ class_Groups_Oab__group__add(U_1631) ),
inference(variable_rename,[status(thm)],[f_513_1]) ).
cnf(f_513_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1631),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1631),U_1632),U_1633)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1631),hAPP(c_Groups_Ouminus__class_Ouminus(U_1631),U_1632)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1631),U_1633))
| ~ class_Groups_Oab__group__add(U_1631) ),
inference(clausify,[status(thm)],[f_513_2]) ).
fof(f_514_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_514_2,plain,
! [U_1636,U_1635,U_1634] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1634),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1634),U_1635),U_1636)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1634),U_1636),U_1635)
| ~ class_Groups_Oab__group__add(U_1634) ),
inference(variable_rename,[status(thm)],[f_514_1]) ).
cnf(f_514_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1634),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1634),U_1635),U_1636)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1634),U_1636),U_1635)
| ~ class_Groups_Oab__group__add(U_1634) ),
inference(clausify,[status(thm)],[f_514_2]) ).
fof(f_515_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_515_2,plain,
! [U_1638,U_1637] :
( c_Groups_Osgn__class_Osgn(U_1637,c_Groups_Osgn__class_Osgn(U_1637,U_1638)) = c_Groups_Osgn__class_Osgn(U_1637,U_1638)
| ~ class_Rings_Olinordered__idom(U_1637) ),
inference(variable_rename,[status(thm)],[f_515_1]) ).
cnf(f_515_3,plain,
( c_Groups_Osgn__class_Osgn(U_1637,c_Groups_Osgn__class_Osgn(U_1637,U_1638)) = c_Groups_Osgn__class_Osgn(U_1637,U_1638)
| ~ class_Rings_Olinordered__idom(U_1637) ),
inference(clausify,[status(thm)],[f_515_2]) ).
fof(f_516_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_516_2,plain,
! [U_1640,U_1639] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1639),hAPP(c_Groups_Ouminus__class_Ouminus(U_1639),U_1640)) = U_1640
| ~ class_Groups_Ogroup__add(U_1639) ),
inference(variable_rename,[status(thm)],[f_516_1]) ).
cnf(f_516_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1639),hAPP(c_Groups_Ouminus__class_Ouminus(U_1639),U_1640)) = U_1640
| ~ class_Groups_Ogroup__add(U_1639) ),
inference(clausify,[status(thm)],[f_516_2]) ).
fof(f_517_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_517_2,plain,
! [U_1642,U_1641] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1641),U_1642)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_517_1]) ).
cnf(f_517_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1641),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1641),U_1642)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_517_2]) ).
fof(f_518_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
| V_c_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2) )
& ( V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2) ) )
| ~ class_Rings_Oring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__add__iff2]) ).
fof(f_518_2,plain,
! [U_1648,U_1647,U_1646,U_1645,U_1644,U_1643] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1643),U_1644),U_1645)),U_1646) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1643),U_1647),U_1645)),U_1648)
| U_1646 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1643),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1643),U_1647),U_1644)),U_1645)),U_1648) )
& ( U_1646 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1643),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1643),U_1647),U_1644)),U_1645)),U_1648)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1643),U_1644),U_1645)),U_1646) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1643),U_1647),U_1645)),U_1648) ) )
| ~ class_Rings_Oring(U_1643) ),
inference(variable_rename,[status(thm)],[f_518_1]) ).
cnf(f_518_3,plain,
( U_1646 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1643),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1643),U_1647),U_1644)),U_1645)),U_1648)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1643),U_1644),U_1645)),U_1646) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1643),U_1647),U_1645)),U_1648)
| ~ class_Rings_Oring(U_1643) ),
inference(clausify,[status(thm)],[f_518_2]) ).
cnf(f_518_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1643),U_1644),U_1645)),U_1646) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1643),U_1647),U_1645)),U_1648)
| U_1646 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1643),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1643),U_1647),U_1644)),U_1645)),U_1648)
| ~ class_Rings_Oring(U_1643) ),
inference(clausify,[status(thm)],[f_518_2]) ).
fof(f_519_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2) != V_d_2 )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2) ) )
| ~ class_Rings_Oring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__add__iff1]) ).
fof(f_519_2,plain,
! [U_1654,U_1653,U_1652,U_1651,U_1650,U_1649] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),U_1650),U_1651)),U_1652) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),U_1653),U_1651)),U_1654)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1649),U_1650),U_1653)),U_1651)),U_1652) != U_1654 )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1649),U_1650),U_1653)),U_1651)),U_1652) = U_1654
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),U_1650),U_1651)),U_1652) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),U_1653),U_1651)),U_1654) ) )
| ~ class_Rings_Oring(U_1649) ),
inference(variable_rename,[status(thm)],[f_519_1]) ).
cnf(f_519_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1649),U_1650),U_1653)),U_1651)),U_1652) = U_1654
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),U_1650),U_1651)),U_1652) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),U_1653),U_1651)),U_1654)
| ~ class_Rings_Oring(U_1649) ),
inference(clausify,[status(thm)],[f_519_2]) ).
cnf(f_519_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),U_1650),U_1651)),U_1652) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),U_1653),U_1651)),U_1654)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1649),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1649),U_1650),U_1653)),U_1651)),U_1652) != U_1654
| ~ class_Rings_Oring(U_1649) ),
inference(clausify,[status(thm)],[f_519_2]) ).
fof(f_520_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_520_2,plain,
! [U_1658,U_1657,U_1656,U_1655] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1655),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1655),U_1656),U_1657)),hAPP(c_Int_Onumber__class_Onumber__of(U_1655),U_1658)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1655),U_1656),hAPP(c_Int_Onumber__class_Onumber__of(U_1655),U_1658))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1655),U_1657),hAPP(c_Int_Onumber__class_Onumber__of(U_1655),U_1658)))
| ~ class_Rings_Oring(U_1655)
| ~ class_Int_Onumber(U_1655) ),
inference(variable_rename,[status(thm)],[f_520_1]) ).
cnf(f_520_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1655),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1655),U_1656),U_1657)),hAPP(c_Int_Onumber__class_Onumber__of(U_1655),U_1658)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1655),U_1656),hAPP(c_Int_Onumber__class_Onumber__of(U_1655),U_1658))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1655),U_1657),hAPP(c_Int_Onumber__class_Onumber__of(U_1655),U_1658)))
| ~ class_Rings_Oring(U_1655)
| ~ class_Int_Onumber(U_1655) ),
inference(clausify,[status(thm)],[f_520_2]) ).
fof(f_521_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_521_2,plain,
! [U_1662,U_1661,U_1660,U_1659] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1659),U_1660),U_1661)),hAPP(c_Int_Onumber__class_Onumber__of(U_1659),U_1662)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1659),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1659),U_1660),hAPP(c_Int_Onumber__class_Onumber__of(U_1659),U_1662))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1659),U_1661),hAPP(c_Int_Onumber__class_Onumber__of(U_1659),U_1662)))
| ~ class_Rings_Osemiring(U_1659)
| ~ class_Int_Onumber(U_1659) ),
inference(variable_rename,[status(thm)],[f_521_1]) ).
cnf(f_521_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1659),U_1660),U_1661)),hAPP(c_Int_Onumber__class_Onumber__of(U_1659),U_1662)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1659),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1659),U_1660),hAPP(c_Int_Onumber__class_Onumber__of(U_1659),U_1662))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1659),U_1661),hAPP(c_Int_Onumber__class_Onumber__of(U_1659),U_1662)))
| ~ class_Rings_Osemiring(U_1659)
| ~ class_Int_Onumber(U_1659) ),
inference(clausify,[status(thm)],[f_521_2]) ).
fof(f_522_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_522_2,plain,
! [U_1665,U_1664,U_1663] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1663),hAPP(c_Groups_Ouminus__class_Ouminus(U_1663),hAPP(c_Int_Onumber__class_Onumber__of(U_1663),U_1664))),U_1665) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1663),hAPP(c_Int_Onumber__class_Onumber__of(U_1663),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1664))),U_1665)
| ~ class_Int_Onumber__ring(U_1663) ),
inference(variable_rename,[status(thm)],[f_522_1]) ).
cnf(f_522_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1663),hAPP(c_Groups_Ouminus__class_Ouminus(U_1663),hAPP(c_Int_Onumber__class_Onumber__of(U_1663),U_1664))),U_1665) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1663),hAPP(c_Int_Onumber__class_Onumber__of(U_1663),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1664))),U_1665)
| ~ class_Int_Onumber__ring(U_1663) ),
inference(clausify,[status(thm)],[f_522_2]) ).
fof(f_523_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_523_2,plain,
! [U_1669,U_1668,U_1667,U_1666] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1666),hAPP(c_Int_Onumber__class_Onumber__of(U_1666),U_1667)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1666),U_1668),U_1669)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1666),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1666),hAPP(c_Int_Onumber__class_Onumber__of(U_1666),U_1667)),U_1668)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1666),hAPP(c_Int_Onumber__class_Onumber__of(U_1666),U_1667)),U_1669))
| ~ class_Rings_Oring(U_1666)
| ~ class_Int_Onumber(U_1666) ),
inference(variable_rename,[status(thm)],[f_523_1]) ).
cnf(f_523_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1666),hAPP(c_Int_Onumber__class_Onumber__of(U_1666),U_1667)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1666),U_1668),U_1669)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1666),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1666),hAPP(c_Int_Onumber__class_Onumber__of(U_1666),U_1667)),U_1668)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1666),hAPP(c_Int_Onumber__class_Onumber__of(U_1666),U_1667)),U_1669))
| ~ class_Rings_Oring(U_1666)
| ~ class_Int_Onumber(U_1666) ),
inference(clausify,[status(thm)],[f_523_2]) ).
fof(f_524_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_524_2,plain,
! [U_1673,U_1672,U_1671,U_1670] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1670),hAPP(c_Int_Onumber__class_Onumber__of(U_1670),U_1671)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1670),U_1672),U_1673)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1670),hAPP(c_Int_Onumber__class_Onumber__of(U_1670),U_1671)),U_1672)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1670),hAPP(c_Int_Onumber__class_Onumber__of(U_1670),U_1671)),U_1673))
| ~ class_Rings_Osemiring(U_1670)
| ~ class_Int_Onumber(U_1670) ),
inference(variable_rename,[status(thm)],[f_524_1]) ).
cnf(f_524_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1670),hAPP(c_Int_Onumber__class_Onumber__of(U_1670),U_1671)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1670),U_1672),U_1673)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1670),hAPP(c_Int_Onumber__class_Onumber__of(U_1670),U_1671)),U_1672)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1670),hAPP(c_Int_Onumber__class_Onumber__of(U_1670),U_1671)),U_1673))
| ~ class_Rings_Osemiring(U_1670)
| ~ class_Int_Onumber(U_1670) ),
inference(clausify,[status(thm)],[f_524_2]) ).
fof(f_525_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_525_2,plain,
! [U_1676,U_1675,U_1674] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1676),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1675),U_1674)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1676),U_1674)),U_1675)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1674),U_1675)) ),
inference(variable_rename,[status(thm)],[f_525_1]) ).
cnf(f_525_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1676),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1675),U_1674)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1676),U_1674)),U_1675)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1674),U_1675)) ),
inference(clausify,[status(thm)],[f_525_2]) ).
fof(f_526_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_526_2,plain,
! [U_1679,U_1678,U_1677] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1677),U_1678)),U_1679))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1679),U_1678))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1679),U_1678)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1677),U_1678)),U_1679)) ) ),
inference(variable_rename,[status(thm)],[f_526_1]) ).
fof(f_526_3,plain,
( ! [U_1685,U_1683,U_1681] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1681),U_1683)),U_1685))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1685),U_1683))) )
& ! [U_1684,U_1682,U_1680] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1680),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1684),U_1682)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1680),U_1682)),U_1684)) ) ),
inference(miniscope,[status(thm)],[f_526_2]) ).
cnf(f_526_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1680),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1684),U_1682)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1680),U_1682)),U_1684)) ),
inference(clausify,[status(thm)],[f_526_3]) ).
cnf(f_526_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1681),U_1683)),U_1685))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1681),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1685),U_1683))) ),
inference(clausify,[status(thm)],[f_526_3]) ).
fof(f_527_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_527_2,plain,
! [U_1688,U_1687,U_1686] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1688),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1687),U_1688)),U_1686)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1686),U_1687)) ),
inference(variable_rename,[status(thm)],[f_527_1]) ).
cnf(f_527_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1688),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1687),U_1688)),U_1686)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1686),U_1687)) ),
inference(clausify,[status(thm)],[f_527_2]) ).
fof(f_528_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_528_2,plain,
! [U_1690,U_1689] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1689),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1690),U_1689)) = U_1690
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1689),U_1690)) ),
inference(variable_rename,[status(thm)],[f_528_1]) ).
cnf(f_528_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1689),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1690),U_1689)) = U_1690
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1689),U_1690)) ),
inference(clausify,[status(thm)],[f_528_2]) ).
fof(f_529_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_529_2,plain,
! [U_1693,U_1692,U_1691] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1693),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1692),U_1691)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1693),U_1692)),U_1691)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1691),U_1692)) ),
inference(variable_rename,[status(thm)],[f_529_1]) ).
cnf(f_529_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1693),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1692),U_1691)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1693),U_1692)),U_1691)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1691),U_1692)) ),
inference(clausify,[status(thm)],[f_529_2]) ).
fof(f_530_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_530_2,plain,
! [U_1696,U_1695,U_1694] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1696),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1695),U_1694)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1696),U_1694)),U_1695)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1696),U_1694)),U_1695))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1696),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1695),U_1694))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1694),U_1695)) ),
inference(variable_rename,[status(thm)],[f_530_1]) ).
cnf(f_530_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1696),U_1694)),U_1695))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1696),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1695),U_1694)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1694),U_1695)) ),
inference(clausify,[status(thm)],[f_530_2]) ).
cnf(f_530_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1696),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1695),U_1694)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1696),U_1694)),U_1695))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1694),U_1695)) ),
inference(clausify,[status(thm)],[f_530_2]) ).
fof(f_531_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_531_2,plain,
! [U_1698,U_1697] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1698),U_1697)),U_1697) = U_1698
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1697),U_1698)) ),
inference(variable_rename,[status(thm)],[f_531_1]) ).
cnf(f_531_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1698),U_1697)),U_1697) = U_1698
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1697),U_1698)) ),
inference(clausify,[status(thm)],[f_531_2]) ).
fof(f_532_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_532_2,plain,
! [U_1701,U_1700,U_1699] :
( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1700),U_1699) = U_1701
| U_1700 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1701),U_1699) )
& ( U_1700 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1701),U_1699)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1700),U_1699) != U_1701 ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1699),U_1700)) ),
inference(variable_rename,[status(thm)],[f_532_1]) ).
cnf(f_532_3,plain,
( U_1700 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1701),U_1699)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1700),U_1699) != U_1701
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1699),U_1700)) ),
inference(clausify,[status(thm)],[f_532_2]) ).
cnf(f_532_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1700),U_1699) = U_1701
| U_1700 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1701),U_1699)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1699),U_1700)) ),
inference(clausify,[status(thm)],[f_532_2]) ).
fof(f_533_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_533_2,plain,
! [U_1704,U_1703,U_1702] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1704),U_1703)),U_1702) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1704),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1703),U_1702))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1702),U_1703)) ),
inference(variable_rename,[status(thm)],[f_533_1]) ).
cnf(f_533_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1704),U_1703)),U_1702) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1704),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1703),U_1702))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1702),U_1703)) ),
inference(clausify,[status(thm)],[f_533_2]) ).
fof(f_534_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_534_2,plain,
! [U_1707,U_1706,U_1705] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1706),U_1705)),U_1707) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1706),U_1707)),U_1705)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1705),U_1706)) ),
inference(variable_rename,[status(thm)],[f_534_1]) ).
cnf(f_534_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1706),U_1705)),U_1707) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1706),U_1707)),U_1705)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1705),U_1706)) ),
inference(clausify,[status(thm)],[f_534_2]) ).
fof(f_535_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_535_2,plain,
! [U_1710,U_1709,U_1708] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1709),U_1710)),U_1708) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1709),U_1708)),U_1710)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1708),U_1709)) ),
inference(variable_rename,[status(thm)],[f_535_1]) ).
cnf(f_535_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1709),U_1710)),U_1708) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1709),U_1708)),U_1710)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1708),U_1709)) ),
inference(clausify,[status(thm)],[f_535_2]) ).
fof(f_536_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_536_2,plain,
! [U_1713,U_1712,U_1711] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1711),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1712),U_1713)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1711),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1711),U_1712)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1711),U_1713))
| ~ class_Rings_Osemiring__1(U_1711) ),
inference(variable_rename,[status(thm)],[f_536_1]) ).
cnf(f_536_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1711),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1712),U_1713)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1711),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1711),U_1712)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1711),U_1713))
| ~ class_Rings_Osemiring__1(U_1711) ),
inference(clausify,[status(thm)],[f_536_2]) ).
fof(f_537_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_537_2,plain,
! [U_1716,U_1715,U_1714] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_1714),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_1715),U_1716)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1714),hAPP(c_Int_Oring__1__class_Oof__int(U_1714),U_1715)),hAPP(c_Int_Oring__1__class_Oof__int(U_1714),U_1716))
| ~ class_Rings_Oring__1(U_1714) ),
inference(variable_rename,[status(thm)],[f_537_1]) ).
cnf(f_537_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_1714),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_1715),U_1716)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1714),hAPP(c_Int_Oring__1__class_Oof__int(U_1714),U_1715)),hAPP(c_Int_Oring__1__class_Oof__int(U_1714),U_1716))
| ~ class_Rings_Oring__1(U_1714) ),
inference(clausify,[status(thm)],[f_537_2]) ).
fof(f_538_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_538_2,plain,
! [U_1718,U_1717] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1717)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1718)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1717),U_1718)),
inference(variable_rename,[status(thm)],[f_538_1]) ).
cnf(f_538_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1717)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1718)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1717),U_1718)),
inference(clausify,[status(thm)],[f_538_2]) ).
fof(f_539_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_539_2,plain,
! [U_1721,U_1720,U_1719] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1719)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1720)),U_1721)) = 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_1719),U_1720))),U_1721),
inference(variable_rename,[status(thm)],[f_539_1]) ).
cnf(f_539_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1719)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1720)),U_1721)) = 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_1719),U_1720))),U_1721),
inference(clausify,[status(thm)],[f_539_2]) ).
fof(f_540_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_540_2,plain,
! [U_1723,U_1722] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1722)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1723)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1722),U_1723)),
inference(variable_rename,[status(thm)],[f_540_1]) ).
cnf(f_540_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1722)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1723)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1722),U_1723)),
inference(clausify,[status(thm)],[f_540_2]) ).
fof(f_541_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_541_2,plain,
! [U_1725,U_1724] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_1724),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1725)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1724),hAPP(c_Int_Oring__1__class_Oof__int(U_1724),U_1725))
| ~ class_Rings_Oring__1(U_1724) ),
inference(variable_rename,[status(thm)],[f_541_1]) ).
cnf(f_541_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_1724),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1725)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1724),hAPP(c_Int_Oring__1__class_Oof__int(U_1724),U_1725))
| ~ class_Rings_Oring__1(U_1724) ),
inference(clausify,[status(thm)],[f_541_2]) ).
fof(f_542_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_542_2,plain,
! [U_1727,U_1726] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_1726),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1727)) = hAPP(c_Int_Onumber__class_Onumber__of(U_1726),U_1727)
| ~ class_Int_Onumber__ring(U_1726) ),
inference(variable_rename,[status(thm)],[f_542_1]) ).
cnf(f_542_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_1726),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_1727)) = hAPP(c_Int_Onumber__class_Onumber__of(U_1726),U_1727)
| ~ class_Int_Onumber__ring(U_1726) ),
inference(clausify,[status(thm)],[f_542_2]) ).
fof(f_543_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_543_2,plain,
! [U_1730,U_1729,U_1728] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_1728),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1729),U_1730)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1728),hAPP(c_Int_Oring__1__class_Oof__int(U_1728),U_1729)),hAPP(c_Int_Oring__1__class_Oof__int(U_1728),U_1730))
| ~ class_Rings_Oring__1(U_1728) ),
inference(variable_rename,[status(thm)],[f_543_1]) ).
cnf(f_543_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_1728),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1729),U_1730)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1728),hAPP(c_Int_Oring__1__class_Oof__int(U_1728),U_1729)),hAPP(c_Int_Oring__1__class_Oof__int(U_1728),U_1730))
| ~ class_Rings_Oring__1(U_1728) ),
inference(clausify,[status(thm)],[f_543_2]) ).
fof(f_544_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) ) )
| ~ class_Rings_Oordered__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__add__iff1]) ).
fof(f_544_2,plain,
! [U_1736,U_1735,U_1734,U_1733,U_1732,U_1731] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1731),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1731),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1731),U_1732),U_1733)),U_1734)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1731),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1731),U_1735),U_1733)),U_1736)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1731),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1731),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1731),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1731),U_1732),U_1735)),U_1733)),U_1734)),U_1736)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1731),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1731),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1731),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1731),U_1732),U_1735)),U_1733)),U_1734)),U_1736))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1731),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1731),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1731),U_1732),U_1733)),U_1734)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1731),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1731),U_1735),U_1733)),U_1736))) ) )
| ~ class_Rings_Oordered__ring(U_1731) ),
inference(variable_rename,[status(thm)],[f_544_1]) ).
cnf(f_544_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1731),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1731),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1731),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1731),U_1732),U_1735)),U_1733)),U_1734)),U_1736))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1731),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1731),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1731),U_1732),U_1733)),U_1734)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1731),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1731),U_1735),U_1733)),U_1736)))
| ~ class_Rings_Oordered__ring(U_1731) ),
inference(clausify,[status(thm)],[f_544_2]) ).
cnf(f_544_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1731),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1731),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1731),U_1732),U_1733)),U_1734)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1731),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1731),U_1735),U_1733)),U_1736)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1731),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1731),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1731),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1731),U_1732),U_1735)),U_1733)),U_1734)),U_1736))
| ~ class_Rings_Oordered__ring(U_1731) ),
inference(clausify,[status(thm)],[f_544_2]) ).
fof(f_545_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) ) )
| ~ class_Rings_Oordered__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__add__iff2]) ).
fof(f_545_2,plain,
! [U_1742,U_1741,U_1740,U_1739,U_1738,U_1737] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1737),U_1738),U_1739)),U_1740)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1737),U_1741),U_1739)),U_1742)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1740),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1737),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1737),U_1741),U_1738)),U_1739)),U_1742))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1740),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1737),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1737),U_1741),U_1738)),U_1739)),U_1742)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1737),U_1738),U_1739)),U_1740)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1737),U_1741),U_1739)),U_1742))) ) )
| ~ class_Rings_Oordered__ring(U_1737) ),
inference(variable_rename,[status(thm)],[f_545_1]) ).
cnf(f_545_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1740),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1737),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1737),U_1741),U_1738)),U_1739)),U_1742)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1737),U_1738),U_1739)),U_1740)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1737),U_1741),U_1739)),U_1742)))
| ~ class_Rings_Oordered__ring(U_1737) ),
inference(clausify,[status(thm)],[f_545_2]) ).
cnf(f_545_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1737),U_1738),U_1739)),U_1740)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1737),U_1741),U_1739)),U_1742)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1737),U_1740),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1737),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1737),U_1741),U_1738)),U_1739)),U_1742)))
| ~ class_Rings_Oordered__ring(U_1737) ),
inference(clausify,[status(thm)],[f_545_2]) ).
fof(f_546_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) ) )
| ~ class_Rings_Oordered__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__add__iff1]) ).
fof(f_546_2,plain,
! [U_1748,U_1747,U_1746,U_1745,U_1744,U_1743] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1743),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1744),U_1745)),U_1746)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1747),U_1745)),U_1748)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1743),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1743),U_1744),U_1747)),U_1745)),U_1746)),U_1748)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1743),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1743),U_1744),U_1747)),U_1745)),U_1746)),U_1748))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1743),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1744),U_1745)),U_1746)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1747),U_1745)),U_1748))) ) )
| ~ class_Rings_Oordered__ring(U_1743) ),
inference(variable_rename,[status(thm)],[f_546_1]) ).
cnf(f_546_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1743),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1743),U_1744),U_1747)),U_1745)),U_1746)),U_1748))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1743),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1744),U_1745)),U_1746)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1747),U_1745)),U_1748)))
| ~ class_Rings_Oordered__ring(U_1743) ),
inference(clausify,[status(thm)],[f_546_2]) ).
cnf(f_546_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1743),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1744),U_1745)),U_1746)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),U_1747),U_1745)),U_1748)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1743),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1743),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1743),U_1744),U_1747)),U_1745)),U_1746)),U_1748))
| ~ class_Rings_Oordered__ring(U_1743) ),
inference(clausify,[status(thm)],[f_546_2]) ).
fof(f_547_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2))) ) )
| ~ class_Rings_Oordered__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__add__iff2]) ).
fof(f_547_2,plain,
! [U_1754,U_1753,U_1752,U_1751,U_1750,U_1749] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1749),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1749),U_1750),U_1751)),U_1752)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1749),U_1753),U_1751)),U_1754)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1749),U_1752),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1749),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1749),U_1753),U_1750)),U_1751)),U_1754))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1749),U_1752),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1749),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1749),U_1753),U_1750)),U_1751)),U_1754)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1749),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1749),U_1750),U_1751)),U_1752)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1749),U_1753),U_1751)),U_1754))) ) )
| ~ class_Rings_Oordered__ring(U_1749) ),
inference(variable_rename,[status(thm)],[f_547_1]) ).
cnf(f_547_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1749),U_1752),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1749),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1749),U_1753),U_1750)),U_1751)),U_1754)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1749),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1749),U_1750),U_1751)),U_1752)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1749),U_1753),U_1751)),U_1754)))
| ~ class_Rings_Oordered__ring(U_1749) ),
inference(clausify,[status(thm)],[f_547_2]) ).
cnf(f_547_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1749),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1749),U_1750),U_1751)),U_1752)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1749),U_1753),U_1751)),U_1754)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1749),U_1752),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1749),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1749),U_1753),U_1750)),U_1751)),U_1754)))
| ~ class_Rings_Oordered__ring(U_1749) ),
inference(clausify,[status(thm)],[f_547_2]) ).
fof(f_548_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_548_2,plain,
! [U_1757,U_1756,U_1755] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1755),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1757),U_1756)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1755),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1755),U_1757)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1755),U_1756))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1756),U_1757))
| ~ class_Rings_Oring__1(U_1755) ),
inference(variable_rename,[status(thm)],[f_548_1]) ).
cnf(f_548_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1755),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1757),U_1756)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1755),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1755),U_1757)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1755),U_1756))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1756),U_1757))
| ~ class_Rings_Oring__1(U_1755) ),
inference(clausify,[status(thm)],[f_548_2]) ).
fof(f_549_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_549_2,plain,
! [U_1759,U_1758] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1758),U_1759) = 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_1758),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_1759))
| U_1758 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1758),U_1759) = U_1759
| U_1758 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_549_1]) ).
fof(f_549_3,plain,
( ! [U_1763,U_1761] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1761),U_1763) = 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_1761),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_1763))
| U_1761 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1762,U_1760] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1760),U_1762) = U_1762
| U_1760 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_549_2]) ).
cnf(f_549_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1760),U_1762) = U_1762
| U_1760 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_549_3]) ).
cnf(f_549_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1761),U_1763) = 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_1761),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_1763))
| U_1761 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_549_3]) ).
fof(f_550_1,plain,
! [V_b_2,V_a_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
| ? [B_d] :
( ~ hBOOL(hAPP(V_P_2,B_d))
& V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
| ( ~ hBOOL(hAPP(V_P_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_P_2,B_d))
| V_a_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
& ( hBOOL(hAPP(V_P_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_P_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_550_2,plain,
! [U_1768,U_1767,U_1766] :
( ( hBOOL(hAPP(U_1766,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1767),U_1768)))
| ? [U_1765] :
( ~ hBOOL(hAPP(U_1766,U_1765))
& U_1767 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1768),U_1765) )
| ( ~ hBOOL(hAPP(U_1766,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1767),U_1768)) ) )
& ( ( ! [U_1764] :
( hBOOL(hAPP(U_1766,U_1764))
| U_1767 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1768),U_1764) )
& ( hBOOL(hAPP(U_1766,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1767),U_1768)) ) )
| ~ hBOOL(hAPP(U_1766,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1767),U_1768))) ) ),
inference(variable_rename,[status(thm)],[f_550_1]) ).
fof(f_550_3,plain,
( ! [U_1774,U_1772,U_1770] :
( hBOOL(hAPP(U_1770,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1772),U_1774)))
| ? [U_1765] :
( ~ hBOOL(hAPP(U_1770,U_1765))
& U_1772 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1774),U_1765) )
| ( ~ hBOOL(hAPP(U_1770,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1772),U_1774)) ) )
& ! [U_1773,U_1771,U_1769] :
( ( ! [U_1764] :
( hBOOL(hAPP(U_1769,U_1764))
| U_1771 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1773),U_1764) )
& ( hBOOL(hAPP(U_1769,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1771),U_1773)) ) )
| ~ hBOOL(hAPP(U_1769,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1771),U_1773))) ) ),
inference(miniscope,[status(thm)],[f_550_2]) ).
fof(f_550_4,plain,
( ! [U_1774,U_1772,U_1770] :
( hBOOL(hAPP(U_1770,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1772),U_1774)))
| ( ~ hBOOL(hAPP(U_1770,sK26(U_1774,U_1772,U_1770)))
& U_1772 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1774),sK26(U_1774,U_1772,U_1770)) )
| ( ~ hBOOL(hAPP(U_1770,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1772),U_1774)) ) )
& ! [U_1773,U_1771,U_1769] :
( ( ! [U_1764] :
( hBOOL(hAPP(U_1769,U_1764))
| U_1771 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1773),U_1764) )
& ( hBOOL(hAPP(U_1769,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1771),U_1773)) ) )
| ~ hBOOL(hAPP(U_1769,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1771),U_1773))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_1765,sK26(U_1774,U_1772,U_1770))],[f_550_3]) ).
cnf(f_550_5,plain,
( hBOOL(hAPP(U_1769,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1771),U_1773))
| ~ hBOOL(hAPP(U_1769,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1771),U_1773))) ),
inference(clausify,[status(thm)],[f_550_4]) ).
cnf(f_550_6,plain,
( hBOOL(hAPP(U_1769,U_1764))
| U_1771 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1773),U_1764)
| ~ hBOOL(hAPP(U_1769,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1771),U_1773))) ),
inference(clausify,[status(thm)],[f_550_4]) ).
cnf(f_550_7,plain,
( U_1772 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1774),sK26(U_1774,U_1772,U_1770))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1772),U_1774))
| hBOOL(hAPP(U_1770,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1772),U_1774))) ),
inference(clausify,[status(thm)],[f_550_4]) ).
cnf(f_550_8,plain,
( ~ hBOOL(hAPP(U_1770,sK26(U_1774,U_1772,U_1770)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1772),U_1774))
| hBOOL(hAPP(U_1770,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1772),U_1774))) ),
inference(clausify,[status(thm)],[f_550_4]) ).
cnf(f_550_9,plain,
( U_1772 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1774),sK26(U_1774,U_1772,U_1770))
| ~ hBOOL(hAPP(U_1770,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_1770,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1772),U_1774))) ),
inference(clausify,[status(thm)],[f_550_4]) ).
cnf(f_550_10,plain,
( ~ hBOOL(hAPP(U_1770,sK26(U_1774,U_1772,U_1770)))
| ~ hBOOL(hAPP(U_1770,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_1770,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1772),U_1774))) ),
inference(clausify,[status(thm)],[f_550_4]) ).
fof(f_551_1,plain,
! [V_b_2,V_a_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
| ? [B_d] :
( ~ hBOOL(hAPP(V_P_2,B_d))
& V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
| ( ~ hBOOL(hAPP(V_P_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_P_2,B_d))
| V_a_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
& ( hBOOL(hAPP(V_P_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_P_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_551_2,plain,
! [U_1779,U_1778,U_1777] :
( ( hBOOL(hAPP(U_1777,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1778),U_1779)))
| ? [U_1776] :
( ~ hBOOL(hAPP(U_1777,U_1776))
& U_1778 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1779),U_1776) )
| ( ~ hBOOL(hAPP(U_1777,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1778),U_1779)) ) )
& ( ( ! [U_1775] :
( hBOOL(hAPP(U_1777,U_1775))
| U_1778 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1779),U_1775) )
& ( hBOOL(hAPP(U_1777,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1778),U_1779)) ) )
| ~ hBOOL(hAPP(U_1777,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1778),U_1779))) ) ),
inference(variable_rename,[status(thm)],[f_551_1]) ).
fof(f_551_3,plain,
( ! [U_1785,U_1783,U_1781] :
( hBOOL(hAPP(U_1781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1783),U_1785)))
| ? [U_1776] :
( ~ hBOOL(hAPP(U_1781,U_1776))
& U_1783 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1785),U_1776) )
| ( ~ hBOOL(hAPP(U_1781,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1783),U_1785)) ) )
& ! [U_1784,U_1782,U_1780] :
( ( ! [U_1775] :
( hBOOL(hAPP(U_1780,U_1775))
| U_1782 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1784),U_1775) )
& ( hBOOL(hAPP(U_1780,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1782),U_1784)) ) )
| ~ hBOOL(hAPP(U_1780,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1782),U_1784))) ) ),
inference(miniscope,[status(thm)],[f_551_2]) ).
fof(f_551_4,plain,
( ! [U_1785,U_1783,U_1781] :
( hBOOL(hAPP(U_1781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1783),U_1785)))
| ( ~ hBOOL(hAPP(U_1781,sK27(U_1785,U_1783,U_1781)))
& U_1783 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1785),sK27(U_1785,U_1783,U_1781)) )
| ( ~ hBOOL(hAPP(U_1781,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1783),U_1785)) ) )
& ! [U_1784,U_1782,U_1780] :
( ( ! [U_1775] :
( hBOOL(hAPP(U_1780,U_1775))
| U_1782 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1784),U_1775) )
& ( hBOOL(hAPP(U_1780,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1782),U_1784)) ) )
| ~ hBOOL(hAPP(U_1780,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1782),U_1784))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_1776,sK27(U_1785,U_1783,U_1781))],[f_551_3]) ).
cnf(f_551_5,plain,
( hBOOL(hAPP(U_1780,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1782),U_1784))
| ~ hBOOL(hAPP(U_1780,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1782),U_1784))) ),
inference(clausify,[status(thm)],[f_551_4]) ).
cnf(f_551_6,plain,
( hBOOL(hAPP(U_1780,U_1775))
| U_1782 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1784),U_1775)
| ~ hBOOL(hAPP(U_1780,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1782),U_1784))) ),
inference(clausify,[status(thm)],[f_551_4]) ).
cnf(f_551_7,plain,
( U_1783 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1785),sK27(U_1785,U_1783,U_1781))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1783),U_1785))
| hBOOL(hAPP(U_1781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1783),U_1785))) ),
inference(clausify,[status(thm)],[f_551_4]) ).
cnf(f_551_8,plain,
( ~ hBOOL(hAPP(U_1781,sK27(U_1785,U_1783,U_1781)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1783),U_1785))
| hBOOL(hAPP(U_1781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1783),U_1785))) ),
inference(clausify,[status(thm)],[f_551_4]) ).
cnf(f_551_9,plain,
( U_1783 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1785),sK27(U_1785,U_1783,U_1781))
| ~ hBOOL(hAPP(U_1781,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_1781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1783),U_1785))) ),
inference(clausify,[status(thm)],[f_551_4]) ).
cnf(f_551_10,plain,
( ~ hBOOL(hAPP(U_1781,sK27(U_1785,U_1783,U_1781)))
| ~ hBOOL(hAPP(U_1781,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_1781,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1783),U_1785))) ),
inference(clausify,[status(thm)],[f_551_4]) ).
fof(f_552_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_552_2,plain,
! [U_1788,U_1787,U_1786] :
( 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_1787),U_1786))),U_1788) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1787)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1786),U_1788))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1786),U_1787)) ),
inference(variable_rename,[status(thm)],[f_552_1]) ).
cnf(f_552_3,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_1787),U_1786))),U_1788) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1787)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1786),U_1788))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1786),U_1787)) ),
inference(clausify,[status(thm)],[f_552_2]) ).
fof(f_553_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_553_2,plain,
! [U_1791,U_1790,U_1789] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1791),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1790),U_1789))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1791),U_1789)),hAPP(c_Nat_OSuc,U_1790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1789),U_1790)) ),
inference(variable_rename,[status(thm)],[f_553_1]) ).
cnf(f_553_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1791),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1790),U_1789))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1791),U_1789)),hAPP(c_Nat_OSuc,U_1790))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1789),U_1790)) ),
inference(clausify,[status(thm)],[f_553_2]) ).
fof(f_554_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_554_2,plain,
! [U_1793,U_1792] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1792),U_1793) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1793),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1792),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_1793))
| U_1792 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1792),U_1793) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1792 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_554_1]) ).
fof(f_554_3,plain,
( ! [U_1797,U_1795] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1795),U_1797) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1795),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_1797))
| U_1795 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1796,U_1794] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1794),U_1796) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1794 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_554_2]) ).
cnf(f_554_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1794),U_1796) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1794 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_554_3]) ).
cnf(f_554_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1795),U_1797) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1795),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_1797))
| U_1795 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_554_3]) ).
fof(f_555_1,plain,
! [V_na_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_na_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_na_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_na_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_na_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_555_2,plain,
! [U_1802,U_1801,U_1800,U_1799,U_1798] :
( ( ( 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_1799),U_1800)),U_1801)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1798),U_1800)),U_1802)))
| ~ 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_1799),U_1798)),U_1800)),U_1801)),U_1802)) )
& ( 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_1799),U_1798)),U_1800)),U_1801)),U_1802))
| ~ 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_1799),U_1800)),U_1801)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1798),U_1800)),U_1802))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1798),U_1799)) ),
inference(variable_rename,[status(thm)],[f_555_1]) ).
cnf(f_555_3,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_1799),U_1798)),U_1800)),U_1801)),U_1802))
| ~ 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_1799),U_1800)),U_1801)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1798),U_1800)),U_1802)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1798),U_1799)) ),
inference(clausify,[status(thm)],[f_555_2]) ).
cnf(f_555_4,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_1799),U_1800)),U_1801)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1798),U_1800)),U_1802)))
| ~ 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_1799),U_1798)),U_1800)),U_1801)),U_1802))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1798),U_1799)) ),
inference(clausify,[status(thm)],[f_555_2]) ).
fof(f_556_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_556_2,plain,
! [U_1807,U_1806,U_1805,U_1804,U_1803] :
( 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_1804),U_1805)),U_1806)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1803),U_1805)),U_1807)) = 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_1804),U_1803)),U_1805)),U_1806)),U_1807)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1803),U_1804)) ),
inference(variable_rename,[status(thm)],[f_556_1]) ).
cnf(f_556_3,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_1804),U_1805)),U_1806)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1803),U_1805)),U_1807)) = 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_1804),U_1803)),U_1805)),U_1806)),U_1807)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1803),U_1804)) ),
inference(clausify,[status(thm)],[f_556_2]) ).
fof(f_557_1,plain,
! [V_na_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_na_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_na_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_na_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_na_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_557_2,plain,
! [U_1812,U_1811,U_1810,U_1809,U_1808] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1809),U_1810)),U_1811) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1808),U_1810)),U_1812)
| 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_1809),U_1808)),U_1810)),U_1811) != U_1812 )
& ( 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_1809),U_1808)),U_1810)),U_1811) = U_1812
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1809),U_1810)),U_1811) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1808),U_1810)),U_1812) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1808),U_1809)) ),
inference(variable_rename,[status(thm)],[f_557_1]) ).
cnf(f_557_3,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_1809),U_1808)),U_1810)),U_1811) = U_1812
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1809),U_1810)),U_1811) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1808),U_1810)),U_1812)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1808),U_1809)) ),
inference(clausify,[status(thm)],[f_557_2]) ).
cnf(f_557_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1809),U_1810)),U_1811) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1808),U_1810)),U_1812)
| 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_1809),U_1808)),U_1810)),U_1811) != U_1812
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1808),U_1809)) ),
inference(clausify,[status(thm)],[f_557_2]) ).
fof(f_558_1,plain,
! [V_na_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_na_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_na_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_na_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_na_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_558_2,plain,
! [U_1817,U_1816,U_1815,U_1814,U_1813] :
( ( ( 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_1813),U_1815)),U_1816)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1814),U_1815)),U_1817)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1816),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_1814),U_1813)),U_1815)),U_1817))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1816),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_1814),U_1813)),U_1815)),U_1817)))
| ~ 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_1813),U_1815)),U_1816)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1814),U_1815)),U_1817))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1813),U_1814)) ),
inference(variable_rename,[status(thm)],[f_558_1]) ).
cnf(f_558_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1816),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_1814),U_1813)),U_1815)),U_1817)))
| ~ 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_1813),U_1815)),U_1816)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1814),U_1815)),U_1817)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1813),U_1814)) ),
inference(clausify,[status(thm)],[f_558_2]) ).
cnf(f_558_4,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_1813),U_1815)),U_1816)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1814),U_1815)),U_1817)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1816),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_1814),U_1813)),U_1815)),U_1817)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1813),U_1814)) ),
inference(clausify,[status(thm)],[f_558_2]) ).
fof(f_559_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_559_2,plain,
! [U_1822,U_1821,U_1820,U_1819,U_1818] :
( 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_1818),U_1820)),U_1821)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1819),U_1820)),U_1822)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1821),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_1819),U_1818)),U_1820)),U_1822))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1818),U_1819)) ),
inference(variable_rename,[status(thm)],[f_559_1]) ).
cnf(f_559_3,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_1818),U_1820)),U_1821)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1819),U_1820)),U_1822)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_1821),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_1819),U_1818)),U_1820)),U_1822))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1818),U_1819)) ),
inference(clausify,[status(thm)],[f_559_2]) ).
fof(f_560_1,plain,
! [V_na_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_na_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_na_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_na_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_na_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_560_2,plain,
! [U_1827,U_1826,U_1825,U_1824,U_1823] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1823),U_1825)),U_1826) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1824),U_1825)),U_1827)
| U_1826 != 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_1824),U_1823)),U_1825)),U_1827) )
& ( U_1826 = 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_1824),U_1823)),U_1825)),U_1827)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1823),U_1825)),U_1826) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1824),U_1825)),U_1827) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1823),U_1824)) ),
inference(variable_rename,[status(thm)],[f_560_1]) ).
cnf(f_560_3,plain,
( U_1826 = 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_1824),U_1823)),U_1825)),U_1827)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1823),U_1825)),U_1826) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1824),U_1825)),U_1827)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1823),U_1824)) ),
inference(clausify,[status(thm)],[f_560_2]) ).
cnf(f_560_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1823),U_1825)),U_1826) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1824),U_1825)),U_1827)
| U_1826 != 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_1824),U_1823)),U_1825)),U_1827)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1823),U_1824)) ),
inference(clausify,[status(thm)],[f_560_2]) ).
fof(f_561_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq]) ).
fof(f_561_2,plain,
! [U_1832,U_1831,U_1830,U_1829,U_1828] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1828),U_1829),U_1830))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1828),U_1831),U_1832)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1828),U_1831),U_1832))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1828),U_1829),U_1830)) ) )
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1828),U_1829),U_1830) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1828),U_1831),U_1832)
| ~ class_Groups_Oordered__ab__group__add(U_1828) ),
inference(variable_rename,[status(thm)],[f_561_1]) ).
cnf(f_561_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1828),U_1831),U_1832))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1828),U_1829),U_1830))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1828),U_1829),U_1830) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1828),U_1831),U_1832)
| ~ class_Groups_Oordered__ab__group__add(U_1828) ),
inference(clausify,[status(thm)],[f_561_2]) ).
cnf(f_561_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1828),U_1829),U_1830))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1828),U_1831),U_1832))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1828),U_1829),U_1830) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1828),U_1831),U_1832)
| ~ class_Groups_Oordered__ab__group__add(U_1828) ),
inference(clausify,[status(thm)],[f_561_2]) ).
fof(f_562_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_562_2,plain,
! [U_1834,U_1833] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1833),U_1834),c_Groups_Ozero__class_Ozero(U_1833)) = U_1834
| ~ class_Groups_Ogroup__add(U_1833) ),
inference(variable_rename,[status(thm)],[f_562_1]) ).
cnf(f_562_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1833),U_1834),c_Groups_Ozero__class_Ozero(U_1833)) = U_1834
| ~ class_Groups_Ogroup__add(U_1833) ),
inference(clausify,[status(thm)],[f_562_2]) ).
fof(f_563_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_563_2,plain,
! [U_1836,U_1835] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1835),U_1836),U_1836) = c_Groups_Ozero__class_Ozero(U_1835)
| ~ class_Groups_Ogroup__add(U_1835) ),
inference(variable_rename,[status(thm)],[f_563_1]) ).
cnf(f_563_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1835),U_1836),U_1836) = c_Groups_Ozero__class_Ozero(U_1835)
| ~ class_Groups_Ogroup__add(U_1835) ),
inference(clausify,[status(thm)],[f_563_2]) ).
fof(f_564_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( V_a_2 = V_b_2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_b) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 != V_b_2 ) )
| ~ class_Groups_Oab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0]) ).
fof(f_564_2,plain,
! [U_1839,U_1838,U_1837] :
( ( ( U_1838 = U_1839
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1837),U_1838),U_1839) != c_Groups_Ozero__class_Ozero(U_1837) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1837),U_1838),U_1839) = c_Groups_Ozero__class_Ozero(U_1837)
| U_1838 != U_1839 ) )
| ~ class_Groups_Oab__group__add(U_1837) ),
inference(variable_rename,[status(thm)],[f_564_1]) ).
cnf(f_564_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1837),U_1838),U_1839) = c_Groups_Ozero__class_Ozero(U_1837)
| U_1838 != U_1839
| ~ class_Groups_Oab__group__add(U_1837) ),
inference(clausify,[status(thm)],[f_564_2]) ).
cnf(f_564_4,plain,
( U_1838 = U_1839
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1837),U_1838),U_1839) != c_Groups_Ozero__class_Ozero(U_1837)
| ~ class_Groups_Oab__group__add(U_1837) ),
inference(clausify,[status(thm)],[f_564_2]) ).
fof(f_565_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Groups_Ogroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_right__minus__eq]) ).
fof(f_565_2,plain,
! [U_1842,U_1841,U_1840] :
( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1840),U_1841),U_1842) = c_Groups_Ozero__class_Ozero(U_1840)
| U_1841 != U_1842 )
& ( U_1841 = U_1842
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1840),U_1841),U_1842) != c_Groups_Ozero__class_Ozero(U_1840) ) )
| ~ class_Groups_Ogroup__add(U_1840) ),
inference(variable_rename,[status(thm)],[f_565_1]) ).
cnf(f_565_3,plain,
( U_1841 = U_1842
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1840),U_1841),U_1842) != c_Groups_Ozero__class_Ozero(U_1840)
| ~ class_Groups_Ogroup__add(U_1840) ),
inference(clausify,[status(thm)],[f_565_2]) ).
cnf(f_565_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1840),U_1841),U_1842) = c_Groups_Ozero__class_Ozero(U_1840)
| U_1841 != U_1842
| ~ class_Groups_Ogroup__add(U_1840) ),
inference(clausify,[status(thm)],[f_565_2]) ).
fof(f_566_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) )
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less]) ).
fof(f_566_2,plain,
! [U_1847,U_1846,U_1845,U_1844,U_1843] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1843),U_1844),U_1845))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1843),U_1846),U_1847)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1843),U_1846),U_1847))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1843),U_1844),U_1845)) ) )
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1843),U_1844),U_1845) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1843),U_1846),U_1847)
| ~ class_Groups_Oordered__ab__group__add(U_1843) ),
inference(variable_rename,[status(thm)],[f_566_1]) ).
cnf(f_566_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1843),U_1846),U_1847))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1843),U_1844),U_1845))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1843),U_1844),U_1845) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1843),U_1846),U_1847)
| ~ class_Groups_Oordered__ab__group__add(U_1843) ),
inference(clausify,[status(thm)],[f_566_2]) ).
cnf(f_566_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1843),U_1844),U_1845))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1843),U_1846),U_1847))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1843),U_1844),U_1845) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_1843),U_1846),U_1847)
| ~ class_Groups_Oordered__ab__group__add(U_1843) ),
inference(clausify,[status(thm)],[f_566_2]) ).
fof(f_567_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__minus__iff]) ).
fof(f_567_2,plain,
! [U_1850,U_1849,U_1848] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1848),U_1849),hAPP(c_Groups_Ouminus__class_Ouminus(U_1848),U_1850)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1848),U_1850),hAPP(c_Groups_Ouminus__class_Ouminus(U_1848),U_1849))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1848),U_1850),hAPP(c_Groups_Ouminus__class_Ouminus(U_1848),U_1849)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1848),U_1849),hAPP(c_Groups_Ouminus__class_Ouminus(U_1848),U_1850))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1848) ),
inference(variable_rename,[status(thm)],[f_567_1]) ).
cnf(f_567_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1848),U_1850),hAPP(c_Groups_Ouminus__class_Ouminus(U_1848),U_1849)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1848),U_1849),hAPP(c_Groups_Ouminus__class_Ouminus(U_1848),U_1850)))
| ~ class_Groups_Oordered__ab__group__add(U_1848) ),
inference(clausify,[status(thm)],[f_567_2]) ).
cnf(f_567_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1848),U_1849),hAPP(c_Groups_Ouminus__class_Ouminus(U_1848),U_1850)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1848),U_1850),hAPP(c_Groups_Ouminus__class_Ouminus(U_1848),U_1849)))
| ~ class_Groups_Oordered__ab__group__add(U_1848) ),
inference(clausify,[status(thm)],[f_567_2]) ).
fof(f_568_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_minus__le__iff]) ).
fof(f_568_2,plain,
! [U_1853,U_1852,U_1851] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1851),hAPP(c_Groups_Ouminus__class_Ouminus(U_1851),U_1852)),U_1853))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1851),hAPP(c_Groups_Ouminus__class_Ouminus(U_1851),U_1853)),U_1852)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1851),hAPP(c_Groups_Ouminus__class_Ouminus(U_1851),U_1853)),U_1852))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1851),hAPP(c_Groups_Ouminus__class_Ouminus(U_1851),U_1852)),U_1853)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1851) ),
inference(variable_rename,[status(thm)],[f_568_1]) ).
cnf(f_568_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1851),hAPP(c_Groups_Ouminus__class_Ouminus(U_1851),U_1853)),U_1852))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1851),hAPP(c_Groups_Ouminus__class_Ouminus(U_1851),U_1852)),U_1853))
| ~ class_Groups_Oordered__ab__group__add(U_1851) ),
inference(clausify,[status(thm)],[f_568_2]) ).
cnf(f_568_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1851),hAPP(c_Groups_Ouminus__class_Ouminus(U_1851),U_1852)),U_1853))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1851),hAPP(c_Groups_Ouminus__class_Ouminus(U_1851),U_1853)),U_1852))
| ~ class_Groups_Oordered__ab__group__add(U_1851) ),
inference(clausify,[status(thm)],[f_568_2]) ).
fof(f_569_1,plain,
! [V_a_2,V_b_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le]) ).
fof(f_569_2,plain,
! [U_1856,U_1855,U_1854] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1854),hAPP(c_Groups_Ouminus__class_Ouminus(U_1854),U_1855)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1854),U_1856)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1854),U_1856),U_1855)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1854),U_1856),U_1855))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1854),hAPP(c_Groups_Ouminus__class_Ouminus(U_1854),U_1855)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1854),U_1856))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1854) ),
inference(variable_rename,[status(thm)],[f_569_1]) ).
cnf(f_569_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1854),U_1856),U_1855))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1854),hAPP(c_Groups_Ouminus__class_Ouminus(U_1854),U_1855)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1854),U_1856)))
| ~ class_Groups_Oordered__ab__group__add(U_1854) ),
inference(clausify,[status(thm)],[f_569_2]) ).
cnf(f_569_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1854),hAPP(c_Groups_Ouminus__class_Ouminus(U_1854),U_1855)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1854),U_1856)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1854),U_1856),U_1855))
| ~ class_Groups_Oordered__ab__group__add(U_1854) ),
inference(clausify,[status(thm)],[f_569_2]) ).
fof(f_570_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_570_2,plain,
! [U_1859,U_1858,U_1857] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1857),hAPP(c_Groups_Ouminus__class_Ouminus(U_1857),U_1859)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1857),U_1858)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1857),U_1858),U_1859))
| ~ class_Groups_Oordered__ab__group__add(U_1857) ),
inference(variable_rename,[status(thm)],[f_570_1]) ).
cnf(f_570_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1857),hAPP(c_Groups_Ouminus__class_Ouminus(U_1857),U_1859)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1857),U_1858)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1857),U_1858),U_1859))
| ~ class_Groups_Oordered__ab__group__add(U_1857) ),
inference(clausify,[status(thm)],[f_570_2]) ).
fof(f_571_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_571_2,plain,
! [U_1860] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1860),c_Groups_Ozero__class_Ozero(U_1860)) = c_Groups_Ozero__class_Ozero(U_1860)
| ~ class_Groups_Ogroup__add(U_1860) ),
inference(variable_rename,[status(thm)],[f_571_1]) ).
cnf(f_571_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1860),c_Groups_Ozero__class_Ozero(U_1860)) = c_Groups_Ozero__class_Ozero(U_1860)
| ~ class_Groups_Ogroup__add(U_1860) ),
inference(clausify,[status(thm)],[f_571_2]) ).
fof(f_572_1,plain,
! [V_a_2,T_b] :
( ( ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
| c_Groups_Ozero__class_Ozero(T_b) != V_a_2 )
& ( c_Groups_Ozero__class_Ozero(T_b) = V_a_2
| c_Groups_Ozero__class_Ozero(T_b) != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) )
| ~ class_Groups_Ogroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal]) ).
fof(f_572_2,plain,
! [U_1862,U_1861] :
( ( ( c_Groups_Ozero__class_Ozero(U_1861) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1861),U_1862)
| c_Groups_Ozero__class_Ozero(U_1861) != U_1862 )
& ( c_Groups_Ozero__class_Ozero(U_1861) = U_1862
| c_Groups_Ozero__class_Ozero(U_1861) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1861),U_1862) ) )
| ~ class_Groups_Ogroup__add(U_1861) ),
inference(variable_rename,[status(thm)],[f_572_1]) ).
cnf(f_572_3,plain,
( c_Groups_Ozero__class_Ozero(U_1861) = U_1862
| c_Groups_Ozero__class_Ozero(U_1861) != hAPP(c_Groups_Ouminus__class_Ouminus(U_1861),U_1862)
| ~ class_Groups_Ogroup__add(U_1861) ),
inference(clausify,[status(thm)],[f_572_2]) ).
cnf(f_572_4,plain,
( c_Groups_Ozero__class_Ozero(U_1861) = hAPP(c_Groups_Ouminus__class_Ouminus(U_1861),U_1862)
| c_Groups_Ozero__class_Ozero(U_1861) != U_1862
| ~ class_Groups_Ogroup__add(U_1861) ),
inference(clausify,[status(thm)],[f_572_2]) ).
fof(f_573_1,plain,
! [V_a_2,T_b] :
( ( ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_equal__neg__zero]) ).
fof(f_573_2,plain,
! [U_1864,U_1863] :
( ( ( U_1864 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1863),U_1864)
| U_1864 != c_Groups_Ozero__class_Ozero(U_1863) )
& ( U_1864 = c_Groups_Ozero__class_Ozero(U_1863)
| U_1864 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1863),U_1864) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1863) ),
inference(variable_rename,[status(thm)],[f_573_1]) ).
cnf(f_573_3,plain,
( U_1864 = c_Groups_Ozero__class_Ozero(U_1863)
| U_1864 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1863),U_1864)
| ~ class_Groups_Olinordered__ab__group__add(U_1863) ),
inference(clausify,[status(thm)],[f_573_2]) ).
cnf(f_573_4,plain,
( U_1864 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1863),U_1864)
| U_1864 != c_Groups_Ozero__class_Ozero(U_1863)
| ~ class_Groups_Olinordered__ab__group__add(U_1863) ),
inference(clausify,[status(thm)],[f_573_2]) ).
fof(f_574_1,plain,
! [V_a_2,T_b] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Groups_Ogroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal]) ).
fof(f_574_2,plain,
! [U_1866,U_1865] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1865),U_1866) = c_Groups_Ozero__class_Ozero(U_1865)
| U_1866 != c_Groups_Ozero__class_Ozero(U_1865) )
& ( U_1866 = c_Groups_Ozero__class_Ozero(U_1865)
| hAPP(c_Groups_Ouminus__class_Ouminus(U_1865),U_1866) != c_Groups_Ozero__class_Ozero(U_1865) ) )
| ~ class_Groups_Ogroup__add(U_1865) ),
inference(variable_rename,[status(thm)],[f_574_1]) ).
cnf(f_574_3,plain,
( U_1866 = c_Groups_Ozero__class_Ozero(U_1865)
| hAPP(c_Groups_Ouminus__class_Ouminus(U_1865),U_1866) != c_Groups_Ozero__class_Ozero(U_1865)
| ~ class_Groups_Ogroup__add(U_1865) ),
inference(clausify,[status(thm)],[f_574_2]) ).
cnf(f_574_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1865),U_1866) = c_Groups_Ozero__class_Ozero(U_1865)
| U_1866 != c_Groups_Ozero__class_Ozero(U_1865)
| ~ class_Groups_Ogroup__add(U_1865) ),
inference(clausify,[status(thm)],[f_574_2]) ).
fof(f_575_1,plain,
! [V_a_2,T_b] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) != V_a_2 ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__zero]) ).
fof(f_575_2,plain,
! [U_1868,U_1867] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1867),U_1868) = U_1868
| U_1868 != c_Groups_Ozero__class_Ozero(U_1867) )
& ( U_1868 = c_Groups_Ozero__class_Ozero(U_1867)
| hAPP(c_Groups_Ouminus__class_Ouminus(U_1867),U_1868) != U_1868 ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1867) ),
inference(variable_rename,[status(thm)],[f_575_1]) ).
cnf(f_575_3,plain,
( U_1868 = c_Groups_Ozero__class_Ozero(U_1867)
| hAPP(c_Groups_Ouminus__class_Ouminus(U_1867),U_1868) != U_1868
| ~ class_Groups_Olinordered__ab__group__add(U_1867) ),
inference(clausify,[status(thm)],[f_575_2]) ).
cnf(f_575_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1867),U_1868) = U_1868
| U_1868 != c_Groups_Ozero__class_Ozero(U_1867)
| ~ class_Groups_Olinordered__ab__group__add(U_1867) ),
inference(clausify,[status(thm)],[f_575_2]) ).
fof(f_576_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__minus__iff]) ).
fof(f_576_2,plain,
! [U_1871,U_1870,U_1869] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1869),U_1870),hAPP(c_Groups_Ouminus__class_Ouminus(U_1869),U_1871)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1869),U_1871),hAPP(c_Groups_Ouminus__class_Ouminus(U_1869),U_1870))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1869),U_1871),hAPP(c_Groups_Ouminus__class_Ouminus(U_1869),U_1870)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1869),U_1870),hAPP(c_Groups_Ouminus__class_Ouminus(U_1869),U_1871))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1869) ),
inference(variable_rename,[status(thm)],[f_576_1]) ).
cnf(f_576_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1869),U_1871),hAPP(c_Groups_Ouminus__class_Ouminus(U_1869),U_1870)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1869),U_1870),hAPP(c_Groups_Ouminus__class_Ouminus(U_1869),U_1871)))
| ~ class_Groups_Oordered__ab__group__add(U_1869) ),
inference(clausify,[status(thm)],[f_576_2]) ).
cnf(f_576_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1869),U_1870),hAPP(c_Groups_Ouminus__class_Ouminus(U_1869),U_1871)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1869),U_1871),hAPP(c_Groups_Ouminus__class_Ouminus(U_1869),U_1870)))
| ~ class_Groups_Oordered__ab__group__add(U_1869) ),
inference(clausify,[status(thm)],[f_576_2]) ).
fof(f_577_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_minus__less__iff]) ).
fof(f_577_2,plain,
! [U_1874,U_1873,U_1872] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1872),hAPP(c_Groups_Ouminus__class_Ouminus(U_1872),U_1873)),U_1874))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1872),hAPP(c_Groups_Ouminus__class_Ouminus(U_1872),U_1874)),U_1873)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1872),hAPP(c_Groups_Ouminus__class_Ouminus(U_1872),U_1874)),U_1873))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1872),hAPP(c_Groups_Ouminus__class_Ouminus(U_1872),U_1873)),U_1874)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1872) ),
inference(variable_rename,[status(thm)],[f_577_1]) ).
cnf(f_577_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1872),hAPP(c_Groups_Ouminus__class_Ouminus(U_1872),U_1874)),U_1873))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1872),hAPP(c_Groups_Ouminus__class_Ouminus(U_1872),U_1873)),U_1874))
| ~ class_Groups_Oordered__ab__group__add(U_1872) ),
inference(clausify,[status(thm)],[f_577_2]) ).
cnf(f_577_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1872),hAPP(c_Groups_Ouminus__class_Ouminus(U_1872),U_1873)),U_1874))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1872),hAPP(c_Groups_Ouminus__class_Ouminus(U_1872),U_1874)),U_1873))
| ~ class_Groups_Oordered__ab__group__add(U_1872) ),
inference(clausify,[status(thm)],[f_577_2]) ).
fof(f_578_1,plain,
! [V_a_2,V_b_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less]) ).
fof(f_578_2,plain,
! [U_1877,U_1876,U_1875] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),hAPP(c_Groups_Ouminus__class_Ouminus(U_1875),U_1876)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1875),U_1877)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),U_1877),U_1876)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),U_1877),U_1876))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),hAPP(c_Groups_Ouminus__class_Ouminus(U_1875),U_1876)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1875),U_1877))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1875) ),
inference(variable_rename,[status(thm)],[f_578_1]) ).
cnf(f_578_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),U_1877),U_1876))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),hAPP(c_Groups_Ouminus__class_Ouminus(U_1875),U_1876)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1875),U_1877)))
| ~ class_Groups_Oordered__ab__group__add(U_1875) ),
inference(clausify,[status(thm)],[f_578_2]) ).
cnf(f_578_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),hAPP(c_Groups_Ouminus__class_Ouminus(U_1875),U_1876)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1875),U_1877)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1875),U_1877),U_1876))
| ~ class_Groups_Oordered__ab__group__add(U_1875) ),
inference(clausify,[status(thm)],[f_578_2]) ).
fof(f_579_1,plain,
! [V_b,V_a,T_a] :
( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),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_579_2,plain,
! [U_1880,U_1879,U_1878] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1878),U_1879),U_1880)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1878),U_1879),hAPP(c_Groups_Ouminus__class_Ouminus(U_1878),U_1880))
| ~ class_Rings_Oring(U_1878) ),
inference(variable_rename,[status(thm)],[f_579_1]) ).
cnf(f_579_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1878),U_1879),U_1880)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1878),U_1879),hAPP(c_Groups_Ouminus__class_Ouminus(U_1878),U_1880))
| ~ class_Rings_Oring(U_1878) ),
inference(clausify,[status(thm)],[f_579_2]) ).
fof(f_580_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_580_2,plain,
! [U_1883,U_1882,U_1881] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),U_1882),U_1883)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),hAPP(c_Groups_Ouminus__class_Ouminus(U_1881),U_1882)),U_1883)
| ~ class_Rings_Oring(U_1881) ),
inference(variable_rename,[status(thm)],[f_580_1]) ).
cnf(f_580_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_1881),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),U_1882),U_1883)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1881),hAPP(c_Groups_Ouminus__class_Ouminus(U_1881),U_1882)),U_1883)
| ~ class_Rings_Oring(U_1881) ),
inference(clausify,[status(thm)],[f_580_2]) ).
fof(f_581_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),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_581_2,plain,
! [U_1886,U_1885,U_1884] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1884),hAPP(c_Groups_Ouminus__class_Ouminus(U_1884),U_1885)),U_1886) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1884),U_1885),hAPP(c_Groups_Ouminus__class_Ouminus(U_1884),U_1886))
| ~ class_Rings_Oring(U_1884) ),
inference(variable_rename,[status(thm)],[f_581_1]) ).
cnf(f_581_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1884),hAPP(c_Groups_Ouminus__class_Ouminus(U_1884),U_1885)),U_1886) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1884),U_1885),hAPP(c_Groups_Ouminus__class_Ouminus(U_1884),U_1886))
| ~ class_Rings_Oring(U_1884) ),
inference(clausify,[status(thm)],[f_581_2]) ).
fof(f_582_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_582_2,plain,
! [U_1889,U_1888,U_1887] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),hAPP(c_Groups_Ouminus__class_Ouminus(U_1887),U_1888)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1887),U_1889)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1888),U_1889)
| ~ class_Rings_Oring(U_1887) ),
inference(variable_rename,[status(thm)],[f_582_1]) ).
cnf(f_582_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),hAPP(c_Groups_Ouminus__class_Ouminus(U_1887),U_1888)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1887),U_1889)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1888),U_1889)
| ~ class_Rings_Oring(U_1887) ),
inference(clausify,[status(thm)],[f_582_2]) ).
fof(f_583_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2)
| ( V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
& V_a_2 != V_b_2 ) )
& ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
| V_a_2 = V_b_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2) ) )
| ~ class_Rings_Oidom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_square__eq__iff]) ).
fof(f_583_2,plain,
! [U_1892,U_1891,U_1890] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1890),U_1891),U_1891) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1890),U_1892),U_1892)
| ( U_1891 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1890),U_1892)
& U_1891 != U_1892 ) )
& ( U_1891 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1890),U_1892)
| U_1891 = U_1892
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1890),U_1891),U_1891) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1890),U_1892),U_1892) ) )
| ~ class_Rings_Oidom(U_1890) ),
inference(variable_rename,[status(thm)],[f_583_1]) ).
cnf(f_583_3,plain,
( U_1891 = hAPP(c_Groups_Ouminus__class_Ouminus(U_1890),U_1892)
| U_1891 = U_1892
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1890),U_1891),U_1891) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1890),U_1892),U_1892)
| ~ class_Rings_Oidom(U_1890) ),
inference(clausify,[status(thm)],[f_583_2]) ).
cnf(f_583_4,plain,
( U_1891 != U_1892
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1890),U_1891),U_1891) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1890),U_1892),U_1892)
| ~ class_Rings_Oidom(U_1890) ),
inference(clausify,[status(thm)],[f_583_2]) ).
cnf(f_583_5,plain,
( U_1891 != hAPP(c_Groups_Ouminus__class_Ouminus(U_1890),U_1892)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1890),U_1891),U_1891) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1890),U_1892),U_1892)
| ~ class_Rings_Oidom(U_1890) ),
inference(clausify,[status(thm)],[f_583_2]) ).
fof(f_584_1,plain,
! [V_b_2,V_c_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right]) ).
fof(f_584_2,plain,
! [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),U_1894),U_1895)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),U_1896),U_1895)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1893),U_1894),U_1896)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1893),U_1894),U_1896))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),U_1894),U_1895)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),U_1896),U_1895))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1893) ),
inference(variable_rename,[status(thm)],[f_584_1]) ).
cnf(f_584_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1893),U_1894),U_1896))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),U_1894),U_1895)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),U_1896),U_1895)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1893) ),
inference(clausify,[status(thm)],[f_584_2]) ).
cnf(f_584_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1893),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),U_1894),U_1895)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1893),U_1896),U_1895)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1893),U_1894),U_1896))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1893) ),
inference(clausify,[status(thm)],[f_584_2]) ).
fof(f_585_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left]) ).
fof(f_585_2,plain,
! [U_1900,U_1899,U_1898,U_1897] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1897),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1897),U_1898),U_1899)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1897),U_1898),U_1900)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1897),U_1899),U_1900)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1897),U_1899),U_1900))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1897),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1897),U_1898),U_1899)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1897),U_1898),U_1900))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1897) ),
inference(variable_rename,[status(thm)],[f_585_1]) ).
cnf(f_585_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1897),U_1899),U_1900))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1897),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1897),U_1898),U_1899)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1897),U_1898),U_1900)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1897) ),
inference(clausify,[status(thm)],[f_585_2]) ).
cnf(f_585_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1897),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1897),U_1898),U_1899)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1897),U_1898),U_1900)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1897),U_1899),U_1900))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1897) ),
inference(clausify,[status(thm)],[f_585_2]) ).
fof(f_586_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_586_2,plain,
! [U_1904,U_1903,U_1902,U_1901] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1901),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1901),U_1902),U_1904)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1901),U_1903),U_1904)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1901),U_1902),U_1903))
| ~ class_Groups_Oordered__ab__semigroup__add(U_1901) ),
inference(variable_rename,[status(thm)],[f_586_1]) ).
cnf(f_586_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1901),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1901),U_1902),U_1904)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1901),U_1903),U_1904)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1901),U_1902),U_1903))
| ~ class_Groups_Oordered__ab__semigroup__add(U_1901) ),
inference(clausify,[status(thm)],[f_586_2]) ).
fof(f_587_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_587_2,plain,
! [U_1908,U_1907,U_1906,U_1905] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1905),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),U_1908),U_1906)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),U_1908),U_1907)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1905),U_1906),U_1907))
| ~ class_Groups_Oordered__ab__semigroup__add(U_1905) ),
inference(variable_rename,[status(thm)],[f_587_1]) ).
cnf(f_587_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1905),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),U_1908),U_1906)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1905),U_1908),U_1907)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1905),U_1906),U_1907))
| ~ class_Groups_Oordered__ab__semigroup__add(U_1905) ),
inference(clausify,[status(thm)],[f_587_2]) ).
fof(f_588_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_588_2,plain,
! [U_1913,U_1912,U_1911,U_1910,U_1909] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1909),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1909),U_1910),U_1912)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1909),U_1911),U_1913)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1909),U_1912),U_1913))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1909),U_1910),U_1911))
| ~ class_Groups_Oordered__ab__semigroup__add(U_1909) ),
inference(variable_rename,[status(thm)],[f_588_1]) ).
cnf(f_588_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1909),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1909),U_1910),U_1912)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1909),U_1911),U_1913)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1909),U_1912),U_1913))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1909),U_1910),U_1911))
| ~ class_Groups_Oordered__ab__semigroup__add(U_1909) ),
inference(clausify,[status(thm)],[f_588_2]) ).
fof(f_589_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_589_2,plain,
! [U_1917,U_1916,U_1915,U_1914] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1914),U_1915),U_1917))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1914),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1914),U_1915),U_1916)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1914),U_1917),U_1916)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1914) ),
inference(variable_rename,[status(thm)],[f_589_1]) ).
cnf(f_589_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1914),U_1915),U_1917))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1914),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1914),U_1915),U_1916)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1914),U_1917),U_1916)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1914) ),
inference(clausify,[status(thm)],[f_589_2]) ).
fof(f_590_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_590_2,plain,
! [U_1921,U_1920,U_1919,U_1918] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1918),U_1920),U_1921))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1918),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1918),U_1919),U_1920)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1918),U_1919),U_1921)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1918) ),
inference(variable_rename,[status(thm)],[f_590_1]) ).
cnf(f_590_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1918),U_1920),U_1921))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1918),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1918),U_1919),U_1920)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1918),U_1919),U_1921)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1918) ),
inference(clausify,[status(thm)],[f_590_2]) ).
fof(f_591_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_591_2,plain,
! [U_1923,U_1922] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1922),c_Groups_Ozero__class_Ozero(U_1922)),U_1923) = U_1923
| ~ class_Groups_Omonoid__add(U_1922) ),
inference(variable_rename,[status(thm)],[f_591_1]) ).
cnf(f_591_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1922),c_Groups_Ozero__class_Ozero(U_1922)),U_1923) = U_1923
| ~ class_Groups_Omonoid__add(U_1922) ),
inference(clausify,[status(thm)],[f_591_2]) ).
fof(f_592_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_592_2,plain,
! [U_1925,U_1924] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1924),c_Groups_Ozero__class_Ozero(U_1924)),U_1925) = U_1925
| ~ class_Groups_Ocomm__monoid__add(U_1924) ),
inference(variable_rename,[status(thm)],[f_592_1]) ).
cnf(f_592_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1924),c_Groups_Ozero__class_Ozero(U_1924)),U_1925) = U_1925
| ~ class_Groups_Ocomm__monoid__add(U_1924) ),
inference(clausify,[status(thm)],[f_592_2]) ).
fof(f_593_1,plain,
! [V_a_2,T_b] :
( ( ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| c_Groups_Ozero__class_Ozero(T_b) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_double__zero__sym]) ).
fof(f_593_2,plain,
! [U_1927,U_1926] :
( ( ( c_Groups_Ozero__class_Ozero(U_1926) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1926),U_1927),U_1927)
| U_1927 != c_Groups_Ozero__class_Ozero(U_1926) )
& ( U_1927 = c_Groups_Ozero__class_Ozero(U_1926)
| c_Groups_Ozero__class_Ozero(U_1926) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1926),U_1927),U_1927) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1926) ),
inference(variable_rename,[status(thm)],[f_593_1]) ).
cnf(f_593_3,plain,
( U_1927 = c_Groups_Ozero__class_Ozero(U_1926)
| c_Groups_Ozero__class_Ozero(U_1926) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1926),U_1927),U_1927)
| ~ class_Groups_Olinordered__ab__group__add(U_1926) ),
inference(clausify,[status(thm)],[f_593_2]) ).
cnf(f_593_4,plain,
( c_Groups_Ozero__class_Ozero(U_1926) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1926),U_1927),U_1927)
| U_1927 != c_Groups_Ozero__class_Ozero(U_1926)
| ~ class_Groups_Olinordered__ab__group__add(U_1926) ),
inference(clausify,[status(thm)],[f_593_2]) ).
fof(f_594_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_594_2,plain,
! [U_1929,U_1928] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1928),U_1929),c_Groups_Ozero__class_Ozero(U_1928)) = U_1929
| ~ class_Groups_Omonoid__add(U_1928) ),
inference(variable_rename,[status(thm)],[f_594_1]) ).
cnf(f_594_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1928),U_1929),c_Groups_Ozero__class_Ozero(U_1928)) = U_1929
| ~ class_Groups_Omonoid__add(U_1928) ),
inference(clausify,[status(thm)],[f_594_2]) ).
fof(f_595_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_595_2,plain,
! [U_1931,U_1930] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1930),U_1931),c_Groups_Ozero__class_Ozero(U_1930)) = U_1931
| ~ class_Groups_Ocomm__monoid__add(U_1930) ),
inference(variable_rename,[status(thm)],[f_595_1]) ).
cnf(f_595_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1930),U_1931),c_Groups_Ozero__class_Ozero(U_1930)) = U_1931
| ~ class_Groups_Ocomm__monoid__add(U_1930) ),
inference(clausify,[status(thm)],[f_595_2]) ).
fof(f_596_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_596_2,plain,
! [U_1933,U_1932] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1932),c_Groups_Ozero__class_Ozero(U_1932)),U_1933) = U_1933
| ~ class_Rings_Ocomm__semiring__1(U_1932) ),
inference(variable_rename,[status(thm)],[f_596_1]) ).
cnf(f_596_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1932),c_Groups_Ozero__class_Ozero(U_1932)),U_1933) = U_1933
| ~ class_Rings_Ocomm__semiring__1(U_1932) ),
inference(clausify,[status(thm)],[f_596_2]) ).
fof(f_597_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_597_2,plain,
! [U_1935,U_1934] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1934),U_1935),c_Groups_Ozero__class_Ozero(U_1934)) = U_1935
| ~ class_Rings_Ocomm__semiring__1(U_1934) ),
inference(variable_rename,[status(thm)],[f_597_1]) ).
cnf(f_597_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1934),U_1935),c_Groups_Ozero__class_Ozero(U_1934)) = U_1935
| ~ class_Rings_Ocomm__semiring__1(U_1934) ),
inference(clausify,[status(thm)],[f_597_2]) ).
fof(f_598_1,plain,
! [V_a_2,V_b_2,T_b] :
( ( ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| V_b_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__0__iff]) ).
fof(f_598_2,plain,
! [U_1938,U_1937,U_1936] :
( ( ( U_1937 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1936),U_1937),U_1938)
| U_1938 != c_Groups_Ozero__class_Ozero(U_1936) )
& ( U_1938 = c_Groups_Ozero__class_Ozero(U_1936)
| U_1937 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1936),U_1937),U_1938) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1936) ),
inference(variable_rename,[status(thm)],[f_598_1]) ).
cnf(f_598_3,plain,
( U_1938 = c_Groups_Ozero__class_Ozero(U_1936)
| U_1937 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1936),U_1937),U_1938)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1936) ),
inference(clausify,[status(thm)],[f_598_2]) ).
cnf(f_598_4,plain,
( U_1937 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1936),U_1937),U_1938)
| U_1938 != c_Groups_Ozero__class_Ozero(U_1936)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1936) ),
inference(clausify,[status(thm)],[f_598_2]) ).
fof(f_599_1,plain,
! [V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff]) ).
fof(f_599_2,plain,
! [U_1940,U_1939] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1939),U_1940),U_1940) = c_Groups_Ozero__class_Ozero(U_1939)
| U_1940 != c_Groups_Ozero__class_Ozero(U_1939) )
& ( U_1940 = c_Groups_Ozero__class_Ozero(U_1939)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1939),U_1940),U_1940) != c_Groups_Ozero__class_Ozero(U_1939) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1939) ),
inference(variable_rename,[status(thm)],[f_599_1]) ).
cnf(f_599_3,plain,
( U_1940 = c_Groups_Ozero__class_Ozero(U_1939)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1939),U_1940),U_1940) != c_Groups_Ozero__class_Ozero(U_1939)
| ~ class_Groups_Olinordered__ab__group__add(U_1939) ),
inference(clausify,[status(thm)],[f_599_2]) ).
cnf(f_599_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1939),U_1940),U_1940) = c_Groups_Ozero__class_Ozero(U_1939)
| U_1940 != c_Groups_Ozero__class_Ozero(U_1939)
| ~ class_Groups_Olinordered__ab__group__add(U_1939) ),
inference(clausify,[status(thm)],[f_599_2]) ).
fof(f_600_1,plain,
! [V_b_2,V_c_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right]) ).
fof(f_600_2,plain,
! [U_1944,U_1943,U_1942,U_1941] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1941),U_1942),U_1943)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1941),U_1944),U_1943)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1941),U_1942),U_1944)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1941),U_1942),U_1944))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1941),U_1942),U_1943)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1941),U_1944),U_1943))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1941) ),
inference(variable_rename,[status(thm)],[f_600_1]) ).
cnf(f_600_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1941),U_1942),U_1944))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1941),U_1942),U_1943)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1941),U_1944),U_1943)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1941) ),
inference(clausify,[status(thm)],[f_600_2]) ).
cnf(f_600_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1941),U_1942),U_1943)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1941),U_1944),U_1943)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1941),U_1942),U_1944))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1941) ),
inference(clausify,[status(thm)],[f_600_2]) ).
fof(f_601_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left]) ).
fof(f_601_2,plain,
! [U_1948,U_1947,U_1946,U_1945] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1945),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1945),U_1946),U_1947)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1945),U_1946),U_1948)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1945),U_1947),U_1948)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1945),U_1947),U_1948))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1945),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1945),U_1946),U_1947)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1945),U_1946),U_1948))) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1945) ),
inference(variable_rename,[status(thm)],[f_601_1]) ).
cnf(f_601_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1945),U_1947),U_1948))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1945),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1945),U_1946),U_1947)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1945),U_1946),U_1948)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1945) ),
inference(clausify,[status(thm)],[f_601_2]) ).
cnf(f_601_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1945),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1945),U_1946),U_1947)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1945),U_1946),U_1948)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1945),U_1947),U_1948))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1945) ),
inference(clausify,[status(thm)],[f_601_2]) ).
fof(f_602_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_602_2,plain,
! [U_1952,U_1951,U_1950,U_1949] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1949),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1949),U_1950),U_1952)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1949),U_1951),U_1952)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1949),U_1950),U_1951))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1949) ),
inference(variable_rename,[status(thm)],[f_602_1]) ).
cnf(f_602_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1949),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1949),U_1950),U_1952)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1949),U_1951),U_1952)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1949),U_1950),U_1951))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1949) ),
inference(clausify,[status(thm)],[f_602_2]) ).
fof(f_603_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_603_2,plain,
! [U_1956,U_1955,U_1954,U_1953] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1953),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1953),U_1956),U_1954)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1953),U_1956),U_1955)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1953),U_1954),U_1955))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1953) ),
inference(variable_rename,[status(thm)],[f_603_1]) ).
cnf(f_603_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1953),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1953),U_1956),U_1954)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1953),U_1956),U_1955)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1953),U_1954),U_1955))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1953) ),
inference(clausify,[status(thm)],[f_603_2]) ).
fof(f_604_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_604_2,plain,
! [U_1961,U_1960,U_1959,U_1958,U_1957] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1957),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1957),U_1958),U_1960)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1957),U_1959),U_1961)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1957),U_1960),U_1961))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1957),U_1958),U_1959))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1957) ),
inference(variable_rename,[status(thm)],[f_604_1]) ).
cnf(f_604_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1957),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1957),U_1958),U_1960)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1957),U_1959),U_1961)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1957),U_1960),U_1961))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1957),U_1958),U_1959))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1957) ),
inference(clausify,[status(thm)],[f_604_2]) ).
fof(f_605_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_605_2,plain,
! [U_1965,U_1964,U_1963,U_1962] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1962),U_1963),U_1965))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1962),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1962),U_1963),U_1964)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1962),U_1965),U_1964)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1962) ),
inference(variable_rename,[status(thm)],[f_605_1]) ).
cnf(f_605_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1962),U_1963),U_1965))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1962),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1962),U_1963),U_1964)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1962),U_1965),U_1964)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1962) ),
inference(clausify,[status(thm)],[f_605_2]) ).
fof(f_606_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_606_2,plain,
! [U_1969,U_1968,U_1967,U_1966] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1966),U_1968),U_1969))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1966),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1966),U_1967),U_1968)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1966),U_1967),U_1969)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1966) ),
inference(variable_rename,[status(thm)],[f_606_1]) ).
cnf(f_606_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1966),U_1968),U_1969))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1966),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1966),U_1967),U_1968)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1966),U_1967),U_1969)))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1966) ),
inference(clausify,[status(thm)],[f_606_2]) ).
fof(f_607_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_607_2,plain,
! [U_1973,U_1972,U_1971,U_1970] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1970),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1970),U_1971),U_1972)),U_1973) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1970),U_1971),U_1973)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1970),U_1972),U_1973))
| ~ class_Rings_Ocomm__semiring(U_1970) ),
inference(variable_rename,[status(thm)],[f_607_1]) ).
cnf(f_607_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1970),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1970),U_1971),U_1972)),U_1973) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1970),U_1971),U_1973)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1970),U_1972),U_1973))
| ~ class_Rings_Ocomm__semiring(U_1970) ),
inference(clausify,[status(thm)],[f_607_2]) ).
fof(f_608_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_608_2,plain,
! [U_1978,U_1977,U_1976,U_1975,U_1974] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1974),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1975),U_1976)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1974),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1977),U_1976)),U_1978)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1974),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1974),U_1975),U_1977)),U_1976)),U_1978)
| ~ class_Rings_Osemiring(U_1974) ),
inference(variable_rename,[status(thm)],[f_608_1]) ).
cnf(f_608_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1974),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1975),U_1976)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1974),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1977),U_1976)),U_1978)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1974),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1974),U_1975),U_1977)),U_1976)),U_1978)
| ~ class_Rings_Osemiring(U_1974) ),
inference(clausify,[status(thm)],[f_608_2]) ).
fof(f_609_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_609_2,plain,
! [U_1982,U_1981,U_1980,U_1979] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1979),U_1980),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1979),U_1981),U_1982)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1979),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1979),U_1980),U_1981)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1979),U_1980),U_1982))
| ~ class_Rings_Ocomm__semiring__1(U_1979) ),
inference(variable_rename,[status(thm)],[f_609_1]) ).
cnf(f_609_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1979),U_1980),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1979),U_1981),U_1982)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1979),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1979),U_1980),U_1981)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1979),U_1980),U_1982))
| ~ class_Rings_Ocomm__semiring__1(U_1979) ),
inference(clausify,[status(thm)],[f_609_2]) ).
fof(f_610_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( ( ( ( V_c_2 != V_d_2
& V_a_2 != V_b_2 )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2))
| V_c_2 = V_d_2
| V_a_2 = V_b_2 ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) ),
inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq]) ).
fof(f_610_2,plain,
! [U_1987,U_1986,U_1985,U_1984,U_1983] :
( ( ( ( U_1986 != U_1987
& U_1984 != U_1985 )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1984),U_1986)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1985),U_1987)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1984),U_1987)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1985),U_1986)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1984),U_1986)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1985),U_1987)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1984),U_1987)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1985),U_1986))
| U_1986 = U_1987
| U_1984 = U_1985 ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1983) ),
inference(variable_rename,[status(thm)],[f_610_1]) ).
cnf(f_610_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1984),U_1986)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1985),U_1987)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1984),U_1987)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1985),U_1986))
| U_1986 = U_1987
| U_1984 = U_1985
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1983) ),
inference(clausify,[status(thm)],[f_610_2]) ).
cnf(f_610_4,plain,
( U_1984 != U_1985
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1984),U_1986)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1985),U_1987)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1984),U_1987)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1985),U_1986))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1983) ),
inference(clausify,[status(thm)],[f_610_2]) ).
cnf(f_610_5,plain,
( U_1986 != U_1987
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1984),U_1986)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1985),U_1987)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1984),U_1987)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1983),U_1985),U_1986))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1983) ),
inference(clausify,[status(thm)],[f_610_2]) ).
fof(f_611_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_611_2,plain,
! [U_1991,U_1990,U_1989,U_1988] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1988),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1988),U_1989),U_1990)),U_1991) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1988),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1988),U_1989),U_1991)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1988),U_1990),U_1991))
| ~ class_Rings_Ocomm__semiring__1(U_1988) ),
inference(variable_rename,[status(thm)],[f_611_1]) ).
cnf(f_611_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1988),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1988),U_1989),U_1990)),U_1991) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1988),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1988),U_1989),U_1991)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1988),U_1990),U_1991))
| ~ class_Rings_Ocomm__semiring__1(U_1988) ),
inference(clausify,[status(thm)],[f_611_2]) ).
fof(f_612_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_612_2,plain,
! [U_1995,U_1994,U_1993,U_1992] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1992),U_1993),U_1994)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1992),U_1995),U_1994)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1992),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1992),U_1993),U_1995)),U_1994)
| ~ class_Rings_Ocomm__semiring__1(U_1992) ),
inference(variable_rename,[status(thm)],[f_612_1]) ).
cnf(f_612_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1992),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1992),U_1993),U_1994)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1992),U_1995),U_1994)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1992),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1992),U_1993),U_1995)),U_1994)
| ~ class_Rings_Ocomm__semiring__1(U_1992) ),
inference(clausify,[status(thm)],[f_612_2]) ).
fof(f_613_1,plain,
! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2))
| ( V_y_2 != V_z_2
& V_w_2 != V_x_2 ) )
& ( V_y_2 = V_z_2
| V_w_2 = V_x_2
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2)) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) ),
inference(fof_nnf,[status(thm)],[fact_crossproduct__eq]) ).
fof(f_613_2,plain,
! [U_2000,U_1999,U_1998,U_1997,U_1996] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1996),U_1997),U_1998)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1996),U_1999),U_2000)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1996),U_1997),U_2000)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1996),U_1999),U_1998))
| ( U_1998 != U_2000
& U_1997 != U_1999 ) )
& ( U_1998 = U_2000
| U_1997 = U_1999
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1996),U_1997),U_1998)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1996),U_1999),U_2000)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1996),U_1997),U_2000)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1996),U_1999),U_1998)) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1996) ),
inference(variable_rename,[status(thm)],[f_613_1]) ).
cnf(f_613_3,plain,
( U_1998 = U_2000
| U_1997 = U_1999
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1996),U_1997),U_1998)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1996),U_1999),U_2000)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1996),U_1997),U_2000)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1996),U_1999),U_1998))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1996) ),
inference(clausify,[status(thm)],[f_613_2]) ).
cnf(f_613_4,plain,
( U_1997 != U_1999
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1996),U_1997),U_1998)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1996),U_1999),U_2000)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1996),U_1997),U_2000)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1996),U_1999),U_1998))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1996) ),
inference(clausify,[status(thm)],[f_613_2]) ).
cnf(f_613_5,plain,
( U_1998 != U_2000
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1996),U_1997),U_1998)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1996),U_1999),U_2000)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1996),U_1997),U_2000)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1996),U_1999),U_1998))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1996) ),
inference(clausify,[status(thm)],[f_613_2]) ).
fof(f_614_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_614_2,plain,
! [U_2002,U_2001] :
( U_2001 = U_2002
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2002),U_2001) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2001),U_2002) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_614_1]) ).
cnf(f_614_3,plain,
( U_2001 = U_2002
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2002),U_2001) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2001),U_2002) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_614_2]) ).
fof(f_615_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_615_2,plain,
! [U_2003] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2003),U_2003) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_615_1]) ).
cnf(f_615_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2003),U_2003) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_615_2]) ).
fof(f_616_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_616_2,plain,
! [U_2004] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2004),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2004,
inference(variable_rename,[status(thm)],[f_616_1]) ).
cnf(f_616_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2004),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2004,
inference(clausify,[status(thm)],[f_616_2]) ).
fof(f_617_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_617_2,plain,
! [U_2005] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2005) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_617_1]) ).
cnf(f_617_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2005) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_617_2]) ).
fof(f_618_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]) ).
cnf(f_618_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(clausify,[status(thm)],[f_618_1]) ).
fof(f_619_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_619_2,plain,
! [U_2008,U_2007,U_2006] : 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_2006)),U_2007)),hAPP(c_Nat_OSuc,U_2008)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2006),U_2007)),U_2008),
inference(variable_rename,[status(thm)],[f_619_1]) ).
cnf(f_619_3,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_2006)),U_2007)),hAPP(c_Nat_OSuc,U_2008)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2006),U_2007)),U_2008),
inference(clausify,[status(thm)],[f_619_2]) ).
fof(f_620_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_620_2,plain,
! [U_2010,U_2009] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2009)),hAPP(c_Nat_OSuc,U_2010)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2009),U_2010),
inference(variable_rename,[status(thm)],[f_620_1]) ).
cnf(f_620_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2009)),hAPP(c_Nat_OSuc,U_2010)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2009),U_2010),
inference(clausify,[status(thm)],[f_620_2]) ).
fof(f_621_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_621_2,plain,
! [U_2012,U_2011] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2011),hAPP(c_Nat_OSuc,U_2012)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2011),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_2012),
inference(variable_rename,[status(thm)],[f_621_1]) ).
cnf(f_621_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2011),hAPP(c_Nat_OSuc,U_2012)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2011),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_2012),
inference(clausify,[status(thm)],[f_621_2]) ).
fof(f_622_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_622_2,plain,
! [U_2013] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2013)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2013,
inference(variable_rename,[status(thm)],[f_622_1]) ).
cnf(f_622_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2013)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2013,
inference(clausify,[status(thm)],[f_622_2]) ).
fof(f_623_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_623_2,plain,
! [U_2016,U_2015,U_2014] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2016),U_2015)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2016),U_2014)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2014),U_2016))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2014),U_2015)) ),
inference(variable_rename,[status(thm)],[f_623_1]) ).
cnf(f_623_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2016),U_2015)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2016),U_2014)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2014),U_2016))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2014),U_2015)) ),
inference(clausify,[status(thm)],[f_623_2]) ).
fof(f_624_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_624_2,plain,
! [U_2019,U_2018,U_2017] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2017),U_2019)),U_2018))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2017),U_2018)) ),
inference(variable_rename,[status(thm)],[f_624_1]) ).
cnf(f_624_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2017),U_2019)),U_2018))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2017),U_2018)) ),
inference(clausify,[status(thm)],[f_624_2]) ).
fof(f_625_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_625_2,plain,
! [U_2020] :
( ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2020) = 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_2020)) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2020) = 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_2020)) ) )
| U_2020 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2020) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2020 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_625_1]) ).
fof(f_625_3,plain,
( ! [U_2022] :
( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2022) = 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_2022)) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2022) = 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_2022)) ) )
| U_2022 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_2021] :
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2021) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2021 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_625_2]) ).
cnf(f_625_4,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2021) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2021 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_625_3]) ).
cnf(f_625_5,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2022) = 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_2022))
| U_2022 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_625_3]) ).
cnf(f_625_6,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2022) = 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_2022))
| U_2022 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_625_3]) ).
fof(f_626_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_626_2,plain,
! [U_2024,U_2023] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2023),U_2024)),U_2023)),
inference(variable_rename,[status(thm)],[f_626_1]) ).
cnf(f_626_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2023),U_2024)),U_2023)),
inference(clausify,[status(thm)],[f_626_2]) ).
fof(f_627_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_627_2,plain,
! [U_2027,U_2026,U_2025] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2027),U_2026)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2027),U_2025)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2025),U_2026)) ),
inference(variable_rename,[status(thm)],[f_627_1]) ).
cnf(f_627_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2027),U_2026)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2027),U_2025)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2025),U_2026)) ),
inference(clausify,[status(thm)],[f_627_2]) ).
fof(f_628_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_628_2,plain,
! [U_2030,U_2029,U_2028] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2028),U_2030)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2029),U_2030)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2028),U_2029)) ),
inference(variable_rename,[status(thm)],[f_628_1]) ).
cnf(f_628_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2028),U_2030)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2029),U_2030)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2028),U_2029)) ),
inference(clausify,[status(thm)],[f_628_2]) ).
fof(f_629_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_629_2,plain,
! [U_2032,U_2031] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2032),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2032),U_2031)) = U_2031
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2031),U_2032)) ),
inference(variable_rename,[status(thm)],[f_629_1]) ).
cnf(f_629_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2032),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2032),U_2031)) = U_2031
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2031),U_2032)) ),
inference(clausify,[status(thm)],[f_629_2]) ).
fof(f_630_1,plain,
! [V_na_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_na_2),V_k_2)
| V_m_2 != V_na_2 )
& ( V_m_2 = V_na_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_na_2),V_k_2) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_na_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_630_2,plain,
! [U_2035,U_2034,U_2033] :
( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2034),U_2033) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2035),U_2033)
| U_2034 != U_2035 )
& ( U_2034 = U_2035
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2034),U_2033) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2035),U_2033) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2033),U_2035))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2033),U_2034)) ),
inference(variable_rename,[status(thm)],[f_630_1]) ).
cnf(f_630_3,plain,
( U_2034 = U_2035
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2034),U_2033) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2035),U_2033)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2033),U_2035))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2033),U_2034)) ),
inference(clausify,[status(thm)],[f_630_2]) ).
cnf(f_630_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2034),U_2033) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2035),U_2033)
| U_2034 != U_2035
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2033),U_2035))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2033),U_2034)) ),
inference(clausify,[status(thm)],[f_630_2]) ).
fof(f_631_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_631_2,plain,
! [U_2038,U_2037,U_2036] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2037),U_2036)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2038),U_2036)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2037),U_2038)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2036),U_2038))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2036),U_2037)) ),
inference(variable_rename,[status(thm)],[f_631_1]) ).
cnf(f_631_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2037),U_2036)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2038),U_2036)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2037),U_2038)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2036),U_2038))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2036),U_2037)) ),
inference(clausify,[status(thm)],[f_631_2]) ).
fof(f_632_1,plain,
! [V_na_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_na_2),V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_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_na_2),V_k_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_na_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_632_2,plain,
! [U_2041,U_2040,U_2039] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2040),U_2039)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2041),U_2039)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2040),U_2041)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2040),U_2041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2040),U_2039)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2041),U_2039))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2039),U_2041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2039),U_2040)) ),
inference(variable_rename,[status(thm)],[f_632_1]) ).
cnf(f_632_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2040),U_2041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2040),U_2039)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2041),U_2039)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2039),U_2041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2039),U_2040)) ),
inference(clausify,[status(thm)],[f_632_2]) ).
cnf(f_632_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_2040),U_2039)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2041),U_2039)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2040),U_2041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2039),U_2041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2039),U_2040)) ),
inference(clausify,[status(thm)],[f_632_2]) ).
fof(f_633_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_633_2,plain,
! [U_2043,U_2042] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2042)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2043)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2042),U_2043)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2042),U_2043))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2042)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2043))) ) ),
inference(variable_rename,[status(thm)],[f_633_1]) ).
fof(f_633_3,plain,
( ! [U_2047,U_2045] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2045)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2047)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2045),U_2047)) )
& ! [U_2046,U_2044] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2044),U_2046))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2044)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2046))) ) ),
inference(miniscope,[status(thm)],[f_633_2]) ).
cnf(f_633_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2044),U_2046))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2044)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2046))) ),
inference(clausify,[status(thm)],[f_633_3]) ).
cnf(f_633_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2045)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2047)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2045),U_2047)) ),
inference(clausify,[status(thm)],[f_633_3]) ).
fof(f_634_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_634_2,plain,
! [U_2048] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2048) = U_2048,
inference(variable_rename,[status(thm)],[f_634_1]) ).
cnf(f_634_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2048) = U_2048,
inference(clausify,[status(thm)],[f_634_2]) ).
fof(f_635_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_635_2,plain,
! [U_2049] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2049),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_2049,
inference(variable_rename,[status(thm)],[f_635_1]) ).
cnf(f_635_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2049),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_2049,
inference(clausify,[status(thm)],[f_635_2]) ).
fof(f_636_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_636_2,plain,
! [U_2050] : 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_2050)),U_2050) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_636_1]) ).
cnf(f_636_3,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_2050)),U_2050) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_636_2]) ).
fof(f_637_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_637_2,plain,
! [U_2052,U_2051] :
( U_2052 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2051),U_2052) != U_2051 ),
inference(variable_rename,[status(thm)],[f_637_1]) ).
fof(f_637_3,plain,
! [U_2052] :
( ! [U_2051] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2051),U_2052) != U_2051
| U_2052 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_637_2]) ).
cnf(f_637_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2051),U_2052) != U_2051
| U_2052 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_637_3]) ).
fof(f_638_1,plain,
! [V_na_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( V_na_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_na_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_add__is__0]) ).
fof(f_638_2,plain,
! [U_2054,U_2053] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2053),U_2054) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2054 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2053 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( U_2054 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2053 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2053),U_2054) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_638_1]) ).
fof(f_638_3,plain,
( ! [U_2058,U_2056] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2056),U_2058) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2058 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2056 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2057,U_2055] :
( ( U_2057 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2055 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2055),U_2057) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_638_2]) ).
cnf(f_638_4,plain,
( U_2055 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2055),U_2057) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_638_3]) ).
cnf(f_638_5,plain,
( U_2057 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2055),U_2057) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_638_3]) ).
cnf(f_638_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2056),U_2058) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2058 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2056 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_638_3]) ).
fof(f_639_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_639_2,plain,
! [U_2059] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2059),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2059,
inference(variable_rename,[status(thm)],[f_639_1]) ).
cnf(f_639_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2059),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2059,
inference(clausify,[status(thm)],[f_639_2]) ).
fof(f_640_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_640_2,plain,
! [U_2060] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2060) = U_2060,
inference(variable_rename,[status(thm)],[f_640_1]) ).
cnf(f_640_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2060) = U_2060,
inference(clausify,[status(thm)],[f_640_2]) ).
fof(f_641_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_641_2,plain,
! [U_2062,U_2061] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2061)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2062)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2061),U_2062)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2061),U_2062))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2061)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2062))) ) ),
inference(variable_rename,[status(thm)],[f_641_1]) ).
fof(f_641_3,plain,
( ! [U_2066,U_2064] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2064)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2066)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2064),U_2066)) )
& ! [U_2065,U_2063] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2063),U_2065))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2063)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2065))) ) ),
inference(miniscope,[status(thm)],[f_641_2]) ).
cnf(f_641_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2063),U_2065))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2063)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2065))) ),
inference(clausify,[status(thm)],[f_641_3]) ).
cnf(f_641_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2064)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2066)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2064),U_2066)) ),
inference(clausify,[status(thm)],[f_641_3]) ).
fof(f_642_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_642_2,plain,
! [U_2069,U_2068,U_2067] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2067),U_2068)),U_2069) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2067),U_2069)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2068),U_2069)),
inference(variable_rename,[status(thm)],[f_642_1]) ).
cnf(f_642_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2067),U_2068)),U_2069) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2067),U_2069)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2068),U_2069)),
inference(clausify,[status(thm)],[f_642_2]) ).
fof(f_643_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_643_2,plain,
! [U_2072,U_2071,U_2070] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2070),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2071),U_2072)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2070),U_2071)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2070),U_2072)),
inference(variable_rename,[status(thm)],[f_643_1]) ).
cnf(f_643_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2070),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2071),U_2072)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2070),U_2071)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2070),U_2072)),
inference(clausify,[status(thm)],[f_643_2]) ).
fof(f_644_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_644_2,plain,
! [U_2074,U_2073] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2073)),U_2074) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2073),hAPP(c_Nat_OSuc,U_2074)),
inference(variable_rename,[status(thm)],[f_644_1]) ).
cnf(f_644_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2073)),U_2074) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2073),hAPP(c_Nat_OSuc,U_2074)),
inference(clausify,[status(thm)],[f_644_2]) ).
fof(f_645_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_645_2,plain,
! [U_2076,U_2075] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2075)),U_2076) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2075),U_2076)),
inference(variable_rename,[status(thm)],[f_645_1]) ).
cnf(f_645_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2075)),U_2076) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2075),U_2076)),
inference(clausify,[status(thm)],[f_645_2]) ).
fof(f_646_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_646_2,plain,
! [U_2078,U_2077] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2077),hAPP(c_Nat_OSuc,U_2078)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2077),U_2078)),
inference(variable_rename,[status(thm)],[f_646_1]) ).
cnf(f_646_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2077),hAPP(c_Nat_OSuc,U_2078)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2077),U_2078)),
inference(clausify,[status(thm)],[f_646_2]) ).
fof(f_647_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_647_2,plain,
! [U_2079] : hAPP(c_Nat_OSuc,U_2079) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2079),
inference(variable_rename,[status(thm)],[f_647_1]) ).
cnf(f_647_3,plain,
hAPP(c_Nat_OSuc,U_2079) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2079),
inference(clausify,[status(thm)],[f_647_2]) ).
fof(f_648_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_648_2,plain,
! [U_2080] : hAPP(c_Nat_OSuc,U_2080) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2080),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_648_1]) ).
cnf(f_648_3,plain,
hAPP(c_Nat_OSuc,U_2080) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2080),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_648_2]) ).
fof(f_649_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_649_2,plain,
! [U_2082,U_2081] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2081)),U_2082) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2081),U_2082)),
inference(variable_rename,[status(thm)],[f_649_1]) ).
cnf(f_649_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2081)),U_2082) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2081),U_2082)),
inference(clausify,[status(thm)],[f_649_2]) ).
fof(f_650_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_650_2,plain,
! [U_2085,U_2084,U_2083] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2083),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2084),U_2085)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2083),U_2084)) ),
inference(variable_rename,[status(thm)],[f_650_1]) ).
cnf(f_650_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2083),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2084),U_2085)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2083),U_2084)) ),
inference(clausify,[status(thm)],[f_650_2]) ).
fof(f_651_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_651_2,plain,
! [U_2088,U_2087,U_2086] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2086),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2088),U_2087)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2086),U_2087)) ),
inference(variable_rename,[status(thm)],[f_651_1]) ).
cnf(f_651_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2086),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2088),U_2087)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2086),U_2087)) ),
inference(clausify,[status(thm)],[f_651_2]) ).
fof(f_652_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_652_2,plain,
! [U_2091,U_2090,U_2089] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2089),U_2091))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2089),U_2090)),U_2091)) ),
inference(variable_rename,[status(thm)],[f_652_1]) ).
cnf(f_652_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2089),U_2091))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2089),U_2090)),U_2091)) ),
inference(clausify,[status(thm)],[f_652_2]) ).
fof(f_653_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_653_2,plain,
! [U_2095,U_2094,U_2093,U_2092] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2094),U_2095))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2094),U_2093) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2092),U_2095)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2092),U_2093)) ),
inference(variable_rename,[status(thm)],[f_653_1]) ).
cnf(f_653_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2094),U_2095))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2094),U_2093) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2092),U_2095)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2092),U_2093)) ),
inference(clausify,[status(thm)],[f_653_2]) ).
fof(f_654_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_654_2,plain,
! [U_2099,U_2098,U_2097,U_2096] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2096),U_2098)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2097),U_2099)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2098),U_2099))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2096),U_2097)) ),
inference(variable_rename,[status(thm)],[f_654_1]) ).
cnf(f_654_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2096),U_2098)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2097),U_2099)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2098),U_2099))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2096),U_2097)) ),
inference(clausify,[status(thm)],[f_654_2]) ).
fof(f_655_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_655_2,plain,
! [U_2102,U_2101,U_2100] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2100),U_2102)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2101),U_2102)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2100),U_2101)) ),
inference(variable_rename,[status(thm)],[f_655_1]) ).
cnf(f_655_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2100),U_2102)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2101),U_2102)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2100),U_2101)) ),
inference(clausify,[status(thm)],[f_655_2]) ).
fof(f_656_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_656_2,plain,
! [U_2105,U_2104,U_2103] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2103),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2105),U_2104)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2103),U_2104)) ),
inference(variable_rename,[status(thm)],[f_656_1]) ).
cnf(f_656_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2103),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2105),U_2104)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2103),U_2104)) ),
inference(clausify,[status(thm)],[f_656_2]) ).
fof(f_657_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_657_2,plain,
! [U_2108,U_2107,U_2106] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2106),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2107),U_2108)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2106),U_2107)) ),
inference(variable_rename,[status(thm)],[f_657_1]) ).
cnf(f_657_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2106),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2107),U_2108)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2106),U_2107)) ),
inference(clausify,[status(thm)],[f_657_2]) ).
fof(f_658_1,plain,
! [V_na_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_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_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_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less]) ).
fof(f_658_2,plain,
! [U_2111,U_2110,U_2109] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2109),U_2110)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2109),U_2111)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2110),U_2111)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2110),U_2111))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2109),U_2110)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2109),U_2111))) ) ),
inference(variable_rename,[status(thm)],[f_658_1]) ).
fof(f_658_3,plain,
( ! [U_2117,U_2115] :
( ! [U_2113] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2113),U_2115)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2113),U_2117)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2115),U_2117)) )
& ! [U_2116,U_2114] :
( ! [U_2112] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2112),U_2114)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2112),U_2116)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2114),U_2116)) ) ),
inference(miniscope,[status(thm)],[f_658_2]) ).
cnf(f_658_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2112),U_2114)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2112),U_2116)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2114),U_2116)) ),
inference(clausify,[status(thm)],[f_658_3]) ).
cnf(f_658_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2113),U_2115)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2113),U_2117)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2115),U_2117)) ),
inference(clausify,[status(thm)],[f_658_3]) ).
fof(f_659_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_659_2,plain,
! [U_2119,U_2118] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2118),U_2119)),U_2119)),
inference(variable_rename,[status(thm)],[f_659_1]) ).
cnf(f_659_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2118),U_2119)),U_2119)),
inference(clausify,[status(thm)],[f_659_2]) ).
fof(f_660_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_660_2,plain,
! [U_2121,U_2120] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2120),U_2121)),U_2120)),
inference(variable_rename,[status(thm)],[f_660_1]) ).
cnf(f_660_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2120),U_2121)),U_2120)),
inference(clausify,[status(thm)],[f_660_2]) ).
fof(f_661_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_661_2,plain,
! [U_2124,U_2123,U_2122] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2124),U_2122)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2124),U_2123)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2122),U_2123)) ),
inference(variable_rename,[status(thm)],[f_661_1]) ).
cnf(f_661_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2124),U_2122)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2124),U_2123)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2122),U_2123)) ),
inference(clausify,[status(thm)],[f_661_2]) ).
fof(f_662_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_662_2,plain,
! [U_2127,U_2126,U_2125] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2125),U_2127)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2126),U_2127)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2125),U_2126)) ),
inference(variable_rename,[status(thm)],[f_662_1]) ).
cnf(f_662_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2125),U_2127)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2126),U_2127)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2125),U_2126)) ),
inference(clausify,[status(thm)],[f_662_2]) ).
fof(f_663_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_663_2,plain,
! [U_2129,U_2128] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2128),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2129),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ( U_2128 != U_2129
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2128),U_2129)) ) )
& ( U_2128 = U_2129
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2128),U_2129))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2128),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2129),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(variable_rename,[status(thm)],[f_663_1]) ).
fof(f_663_3,plain,
( ! [U_2133,U_2131] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2131),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2133),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ( U_2131 != U_2133
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2131),U_2133)) ) )
& ! [U_2132,U_2130] :
( U_2130 = U_2132
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2130),U_2132))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2130),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2132),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(miniscope,[status(thm)],[f_663_2]) ).
cnf(f_663_4,plain,
( U_2130 = U_2132
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2130),U_2132))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2130),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2132),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_663_3]) ).
cnf(f_663_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2131),U_2133))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2131),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2133),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_663_3]) ).
cnf(f_663_6,plain,
( U_2131 != U_2133
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2131),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2133),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_663_3]) ).
fof(f_664_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_664_2,plain,
! [U_2135,U_2134] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2134),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2135),U_2134))),
inference(variable_rename,[status(thm)],[f_664_1]) ).
cnf(f_664_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2134),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2135),U_2134))),
inference(clausify,[status(thm)],[f_664_2]) ).
fof(f_665_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_665_2,plain,
! [U_2137,U_2136] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2136),U_2137))),
inference(variable_rename,[status(thm)],[f_665_1]) ).
cnf(f_665_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2136),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2136),U_2137))),
inference(clausify,[status(thm)],[f_665_2]) ).
fof(f_666_1,plain,
! [V_na_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
| ! [B_k] : V_na_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) )
& ( ? [B_k] : V_na_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_na_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__add]) ).
fof(f_666_2,plain,
! [U_2141,U_2140] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2140),U_2141))
| ! [U_2139] : U_2141 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2140),U_2139) )
& ( ? [U_2138] : U_2141 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2140),U_2138)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2140),U_2141)) ) ),
inference(variable_rename,[status(thm)],[f_666_1]) ).
fof(f_666_3,plain,
( ! [U_2145,U_2143] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2143),U_2145))
| ! [U_2139] : U_2145 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2143),U_2139) )
& ! [U_2144,U_2142] :
( ? [U_2138] : U_2144 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2142),U_2138)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2142),U_2144)) ) ),
inference(miniscope,[status(thm)],[f_666_2]) ).
fof(f_666_4,plain,
( ! [U_2145,U_2143] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2143),U_2145))
| ! [U_2139] : U_2145 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2143),U_2139) )
& ! [U_2144,U_2142] :
( U_2144 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2142),sK28(U_2144,U_2142))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2142),U_2144)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_2138,sK28(U_2144,U_2142))],[f_666_3]) ).
cnf(f_666_5,plain,
( U_2144 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2142),sK28(U_2144,U_2142))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2142),U_2144)) ),
inference(clausify,[status(thm)],[f_666_4]) ).
cnf(f_666_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2143),U_2145))
| U_2145 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2143),U_2139) ),
inference(clausify,[status(thm)],[f_666_4]) ).
fof(f_667_1,plain,
! [V_na_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_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_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_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le]) ).
fof(f_667_2,plain,
! [U_2148,U_2147,U_2146] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2146),U_2147)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2146),U_2148)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2147),U_2148)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2147),U_2148))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2146),U_2147)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2146),U_2148))) ) ),
inference(variable_rename,[status(thm)],[f_667_1]) ).
fof(f_667_3,plain,
( ! [U_2154,U_2152] :
( ! [U_2150] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2150),U_2152)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2150),U_2154)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2152),U_2154)) )
& ! [U_2153,U_2151] :
( ! [U_2149] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2149),U_2151)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2149),U_2153)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2151),U_2153)) ) ),
inference(miniscope,[status(thm)],[f_667_2]) ).
cnf(f_667_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_2149),U_2151)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2149),U_2153)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2151),U_2153)) ),
inference(clausify,[status(thm)],[f_667_3]) ).
cnf(f_667_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_2150),U_2152)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2150),U_2154)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2152),U_2154)) ),
inference(clausify,[status(thm)],[f_667_3]) ).
fof(f_668_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_668_2,plain,
! [U_2157,U_2156,U_2155] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2155),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2156),U_2157)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2155),U_2156)) ),
inference(variable_rename,[status(thm)],[f_668_1]) ).
cnf(f_668_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2155),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2156),U_2157)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2155),U_2156)) ),
inference(clausify,[status(thm)],[f_668_2]) ).
fof(f_669_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_669_2,plain,
! [U_2160,U_2159,U_2158] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2158),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2160),U_2159)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2158),U_2159)) ),
inference(variable_rename,[status(thm)],[f_669_1]) ).
cnf(f_669_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2158),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2160),U_2159)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2158),U_2159)) ),
inference(clausify,[status(thm)],[f_669_2]) ).
fof(f_670_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_670_2,plain,
! [U_2163,U_2162,U_2161] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2161),U_2163)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2162),U_2163)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2161),U_2162)) ),
inference(variable_rename,[status(thm)],[f_670_1]) ).
cnf(f_670_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2161),U_2163)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2162),U_2163)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2161),U_2162)) ),
inference(clausify,[status(thm)],[f_670_2]) ).
fof(f_671_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_671_2,plain,
! [U_2167,U_2166,U_2165,U_2164] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2164),U_2166)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2165),U_2167)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2166),U_2167))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2164),U_2165)) ),
inference(variable_rename,[status(thm)],[f_671_1]) ).
cnf(f_671_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2164),U_2166)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2165),U_2167)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2166),U_2167))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2164),U_2165)) ),
inference(clausify,[status(thm)],[f_671_2]) ).
fof(f_672_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_672_2,plain,
! [U_2170,U_2169,U_2168] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2169),U_2170))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2168),U_2169)),U_2170)) ),
inference(variable_rename,[status(thm)],[f_672_1]) ).
fof(f_672_3,plain,
! [U_2170,U_2169] :
( ! [U_2168] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2168),U_2169)),U_2170))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2169),U_2170)) ),
inference(miniscope,[status(thm)],[f_672_2]) ).
cnf(f_672_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_2168),U_2169)),U_2170))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2169),U_2170)) ),
inference(clausify,[status(thm)],[f_672_3]) ).
fof(f_673_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_673_2,plain,
! [U_2173,U_2172,U_2171] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2171),U_2173))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2171),U_2172)),U_2173)) ),
inference(variable_rename,[status(thm)],[f_673_1]) ).
cnf(f_673_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2171),U_2173))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2171),U_2172)),U_2173)) ),
inference(clausify,[status(thm)],[f_673_2]) ).
fof(f_674_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_674_2,plain,
! [U_2176,U_2175,U_2174] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2175),U_2176))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2174),U_2176)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2174),U_2175)),U_2176)) ),
inference(variable_rename,[status(thm)],[f_674_1]) ).
cnf(f_674_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2174),U_2176))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2174),U_2175)),U_2176)) ),
inference(clausify,[status(thm)],[f_674_2]) ).
cnf(f_674_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2175),U_2176))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2174),U_2175)),U_2176)) ),
inference(clausify,[status(thm)],[f_674_2]) ).
fof(f_675_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_675_2,plain,
! [U_2179,U_2178,U_2177] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2177),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2179),U_2178)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2177),U_2178)) ),
inference(variable_rename,[status(thm)],[f_675_1]) ).
cnf(f_675_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2177),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2179),U_2178)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2177),U_2178)) ),
inference(clausify,[status(thm)],[f_675_2]) ).
fof(f_676_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_676_2,plain,
! [U_2182,U_2181,U_2180] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2180),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2181),U_2182)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2180),U_2181)) ),
inference(variable_rename,[status(thm)],[f_676_1]) ).
cnf(f_676_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2180),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2181),U_2182)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2180),U_2181)) ),
inference(clausify,[status(thm)],[f_676_2]) ).
fof(f_677_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_677_2,plain,
! [U_2184,U_2183] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2183)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2184)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2183),U_2184)),
inference(variable_rename,[status(thm)],[f_677_1]) ).
cnf(f_677_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2183)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2184)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2183),U_2184)),
inference(clausify,[status(thm)],[f_677_2]) ).
fof(f_678_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_678_2,plain,
! [U_2187,U_2186,U_2185] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2185),U_2186)),U_2187) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2185),U_2187)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2186),U_2187)),
inference(variable_rename,[status(thm)],[f_678_1]) ).
cnf(f_678_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2185),U_2186)),U_2187) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2185),U_2187)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2186),U_2187)),
inference(clausify,[status(thm)],[f_678_2]) ).
fof(f_679_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_679_2,plain,
! [U_2190,U_2189,U_2188] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2189),U_2190)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2188),U_2189)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2188),U_2190)),
inference(variable_rename,[status(thm)],[f_679_1]) ).
cnf(f_679_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2188),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2189),U_2190)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2188),U_2189)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2188),U_2190)),
inference(clausify,[status(thm)],[f_679_2]) ).
fof(f_680_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_680_2,plain,
! [U_2194,U_2193,U_2192,U_2191] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2191),U_2192)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2193),U_2192)),U_2194)) = 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_2191),U_2193)),U_2192)),U_2194),
inference(variable_rename,[status(thm)],[f_680_1]) ).
cnf(f_680_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2191),U_2192)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2193),U_2192)),U_2194)) = 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_2191),U_2193)),U_2192)),U_2194),
inference(clausify,[status(thm)],[f_680_2]) ).
fof(f_681_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_681_2,plain,
! [U_2196,U_2195] :
( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2195),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2196)) = c_Groups_Ozero__class_Ozero(U_2195)
| 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_2196))) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2195),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2196)) = hAPP(c_Int_Onumber__class_Onumber__of(U_2195),U_2196)
| ~ 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_2196))) ) )
| ~ class_Int_Onumber__ring(U_2195) ),
inference(variable_rename,[status(thm)],[f_681_1]) ).
cnf(f_681_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2195),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2196)) = hAPP(c_Int_Onumber__class_Onumber__of(U_2195),U_2196)
| ~ 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_2196)))
| ~ class_Int_Onumber__ring(U_2195) ),
inference(clausify,[status(thm)],[f_681_2]) ).
cnf(f_681_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2195),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2196)) = c_Groups_Ozero__class_Ozero(U_2195)
| 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_2196)))
| ~ class_Int_Onumber__ring(U_2195) ),
inference(clausify,[status(thm)],[f_681_2]) ).
fof(f_682_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_682_2,plain,
! [U_2199,U_2198,U_2197] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2197),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2198),U_2199)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2197),U_2198)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2197),U_2199)),
inference(variable_rename,[status(thm)],[f_682_1]) ).
cnf(f_682_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2197),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2198),U_2199)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2197),U_2198)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2197),U_2199)),
inference(clausify,[status(thm)],[f_682_2]) ).
fof(f_683_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_683_2,plain,
! [U_2202,U_2201,U_2200] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2200),U_2201)),U_2202) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2200),U_2202)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2201),U_2202)),
inference(variable_rename,[status(thm)],[f_683_1]) ).
cnf(f_683_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2200),U_2201)),U_2202) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2200),U_2202)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2201),U_2202)),
inference(clausify,[status(thm)],[f_683_2]) ).
fof(f_684_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_684_2,plain,
! [U_2204,U_2203] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_2203),U_2204) = hAPP(c_Int_Oring__1__class_Oof__int(U_2203),U_2204)
| ~ class_Int_Onumber__ring(U_2203) ),
inference(variable_rename,[status(thm)],[f_684_1]) ).
cnf(f_684_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_2203),U_2204) = hAPP(c_Int_Oring__1__class_Oof__int(U_2203),U_2204)
| ~ class_Int_Onumber__ring(U_2203) ),
inference(clausify,[status(thm)],[f_684_2]) ).
fof(f_685_1,plain,
! [V_na_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_na_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_na_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_na_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_na_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_685_2,plain,
! [U_2209,U_2208,U_2207,U_2206,U_2205] :
( ( ( 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_2206),U_2207)),U_2208)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2205),U_2207)),U_2209)))
| ~ 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_2206),U_2205)),U_2207)),U_2208)),U_2209)) )
& ( 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_2206),U_2205)),U_2207)),U_2208)),U_2209))
| ~ 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_2206),U_2207)),U_2208)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2205),U_2207)),U_2209))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2205),U_2206)) ),
inference(variable_rename,[status(thm)],[f_685_1]) ).
cnf(f_685_3,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_2206),U_2205)),U_2207)),U_2208)),U_2209))
| ~ 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_2206),U_2207)),U_2208)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2205),U_2207)),U_2209)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2205),U_2206)) ),
inference(clausify,[status(thm)],[f_685_2]) ).
cnf(f_685_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_2206),U_2207)),U_2208)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2205),U_2207)),U_2209)))
| ~ 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_2206),U_2205)),U_2207)),U_2208)),U_2209))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2205),U_2206)) ),
inference(clausify,[status(thm)],[f_685_2]) ).
fof(f_686_1,plain,
! [V_na_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_na_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_na_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_na_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_na_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_686_2,plain,
! [U_2214,U_2213,U_2212,U_2211,U_2210] :
( ( ( 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_2210),U_2212)),U_2213)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2211),U_2212)),U_2214)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2213),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_2211),U_2210)),U_2212)),U_2214))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2213),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_2211),U_2210)),U_2212)),U_2214)))
| ~ 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_2210),U_2212)),U_2213)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2211),U_2212)),U_2214))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2210),U_2211)) ),
inference(variable_rename,[status(thm)],[f_686_1]) ).
cnf(f_686_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2213),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_2211),U_2210)),U_2212)),U_2214)))
| ~ 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_2210),U_2212)),U_2213)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2211),U_2212)),U_2214)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2210),U_2211)) ),
inference(clausify,[status(thm)],[f_686_2]) ).
cnf(f_686_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_2210),U_2212)),U_2213)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2211),U_2212)),U_2214)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2213),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_2211),U_2210)),U_2212)),U_2214)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2210),U_2211)) ),
inference(clausify,[status(thm)],[f_686_2]) ).
fof(f_687_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_687_2,plain,
! [U_2216,U_2215] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2215)),hAPP(c_Int_Onat,U_2216)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2215),U_2216))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2216))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2215)) ),
inference(variable_rename,[status(thm)],[f_687_1]) ).
cnf(f_687_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2215)),hAPP(c_Int_Onat,U_2216)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2215),U_2216))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2216))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2215)) ),
inference(clausify,[status(thm)],[f_687_2]) ).
fof(f_688_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_688_2,plain,
! [U_2218,U_2217] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2217),U_2218)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2217)),hAPP(c_Int_Onat,U_2218))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2218))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2217)) ),
inference(variable_rename,[status(thm)],[f_688_1]) ).
cnf(f_688_3,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2217),U_2218)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2217)),hAPP(c_Int_Onat,U_2218))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2218))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2217)) ),
inference(clausify,[status(thm)],[f_688_2]) ).
fof(f_689_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_689_2,plain,
! [U_2220,U_2219] :
( ( ( ( ( c_Groups_Osgn__class_Osgn(U_2219,U_2220) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2219),c_Groups_Oone__class_Oone(U_2219))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2219),c_Groups_Ozero__class_Ozero(U_2219)),U_2220)) )
& ( c_Groups_Osgn__class_Osgn(U_2219,U_2220) = c_Groups_Oone__class_Oone(U_2219)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2219),c_Groups_Ozero__class_Ozero(U_2219)),U_2220)) ) )
| U_2220 = c_Groups_Ozero__class_Ozero(U_2219) )
& ( c_Groups_Osgn__class_Osgn(U_2219,U_2220) = c_Groups_Ozero__class_Ozero(U_2219)
| U_2220 != c_Groups_Ozero__class_Ozero(U_2219) ) )
| ~ class_Groups_Osgn__if(U_2219) ),
inference(variable_rename,[status(thm)],[f_689_1]) ).
cnf(f_689_3,plain,
( c_Groups_Osgn__class_Osgn(U_2219,U_2220) = c_Groups_Ozero__class_Ozero(U_2219)
| U_2220 != c_Groups_Ozero__class_Ozero(U_2219)
| ~ class_Groups_Osgn__if(U_2219) ),
inference(clausify,[status(thm)],[f_689_2]) ).
cnf(f_689_4,plain,
( c_Groups_Osgn__class_Osgn(U_2219,U_2220) = c_Groups_Oone__class_Oone(U_2219)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2219),c_Groups_Ozero__class_Ozero(U_2219)),U_2220))
| U_2220 = c_Groups_Ozero__class_Ozero(U_2219)
| ~ class_Groups_Osgn__if(U_2219) ),
inference(clausify,[status(thm)],[f_689_2]) ).
cnf(f_689_5,plain,
( c_Groups_Osgn__class_Osgn(U_2219,U_2220) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2219),c_Groups_Oone__class_Oone(U_2219))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2219),c_Groups_Ozero__class_Ozero(U_2219)),U_2220))
| U_2220 = c_Groups_Ozero__class_Ozero(U_2219)
| ~ class_Groups_Osgn__if(U_2219) ),
inference(clausify,[status(thm)],[f_689_2]) ).
fof(f_690_1,plain,
! [V_a_2,T_b] :
( ( ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| c_Groups_Osgn__class_Osgn(T_b,V_a_2) != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sgn__1__neg]) ).
fof(f_690_2,plain,
! [U_2222,U_2221] :
( ( ( c_Groups_Osgn__class_Osgn(U_2221,U_2222) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2221),c_Groups_Oone__class_Oone(U_2221))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2221),U_2222),c_Groups_Ozero__class_Ozero(U_2221))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2221),U_2222),c_Groups_Ozero__class_Ozero(U_2221)))
| c_Groups_Osgn__class_Osgn(U_2221,U_2222) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2221),c_Groups_Oone__class_Oone(U_2221)) ) )
| ~ class_Rings_Olinordered__idom(U_2221) ),
inference(variable_rename,[status(thm)],[f_690_1]) ).
cnf(f_690_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2221),U_2222),c_Groups_Ozero__class_Ozero(U_2221)))
| c_Groups_Osgn__class_Osgn(U_2221,U_2222) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2221),c_Groups_Oone__class_Oone(U_2221))
| ~ class_Rings_Olinordered__idom(U_2221) ),
inference(clausify,[status(thm)],[f_690_2]) ).
cnf(f_690_4,plain,
( c_Groups_Osgn__class_Osgn(U_2221,U_2222) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2221),c_Groups_Oone__class_Oone(U_2221))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2221),U_2222),c_Groups_Ozero__class_Ozero(U_2221)))
| ~ class_Rings_Olinordered__idom(U_2221) ),
inference(clausify,[status(thm)],[f_690_2]) ).
fof(f_691_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_691_2,plain,
! [U_2224,U_2223] :
( c_Groups_Osgn__class_Osgn(U_2223,U_2224) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2223),c_Groups_Oone__class_Oone(U_2223))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2223),U_2224),c_Groups_Ozero__class_Ozero(U_2223)))
| ~ class_Rings_Olinordered__idom(U_2223) ),
inference(variable_rename,[status(thm)],[f_691_1]) ).
cnf(f_691_3,plain,
( c_Groups_Osgn__class_Osgn(U_2223,U_2224) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2223),c_Groups_Oone__class_Oone(U_2223))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2223),U_2224),c_Groups_Ozero__class_Ozero(U_2223)))
| ~ class_Rings_Olinordered__idom(U_2223) ),
inference(clausify,[status(thm)],[f_691_2]) ).
fof(f_692_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_692_2,plain,
! [U_2225] :
( c_Groups_Osgn__class_Osgn(U_2225,c_Groups_Ozero__class_Ozero(U_2225)) = c_Groups_Ozero__class_Ozero(U_2225)
| ~ class_Groups_Osgn__if(U_2225) ),
inference(variable_rename,[status(thm)],[f_692_1]) ).
cnf(f_692_3,plain,
( c_Groups_Osgn__class_Osgn(U_2225,c_Groups_Ozero__class_Ozero(U_2225)) = c_Groups_Ozero__class_Ozero(U_2225)
| ~ class_Groups_Osgn__if(U_2225) ),
inference(clausify,[status(thm)],[f_692_2]) ).
fof(f_693_1,plain,
! [V_a_2,T_b] :
( ( ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| c_Groups_Osgn__class_Osgn(T_b,V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sgn__0__0]) ).
fof(f_693_2,plain,
! [U_2227,U_2226] :
( ( ( c_Groups_Osgn__class_Osgn(U_2226,U_2227) = c_Groups_Ozero__class_Ozero(U_2226)
| U_2227 != c_Groups_Ozero__class_Ozero(U_2226) )
& ( U_2227 = c_Groups_Ozero__class_Ozero(U_2226)
| c_Groups_Osgn__class_Osgn(U_2226,U_2227) != c_Groups_Ozero__class_Ozero(U_2226) ) )
| ~ class_Rings_Olinordered__idom(U_2226) ),
inference(variable_rename,[status(thm)],[f_693_1]) ).
cnf(f_693_3,plain,
( U_2227 = c_Groups_Ozero__class_Ozero(U_2226)
| c_Groups_Osgn__class_Osgn(U_2226,U_2227) != c_Groups_Ozero__class_Ozero(U_2226)
| ~ class_Rings_Olinordered__idom(U_2226) ),
inference(clausify,[status(thm)],[f_693_2]) ).
cnf(f_693_4,plain,
( c_Groups_Osgn__class_Osgn(U_2226,U_2227) = c_Groups_Ozero__class_Ozero(U_2226)
| U_2227 != c_Groups_Ozero__class_Ozero(U_2226)
| ~ class_Rings_Olinordered__idom(U_2226) ),
inference(clausify,[status(thm)],[f_693_2]) ).
fof(f_694_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_694_2,plain,
! [U_2230,U_2229,U_2228] :
( c_Groups_Osgn__class_Osgn(U_2228,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2228),U_2229),U_2230)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2228),c_Groups_Osgn__class_Osgn(U_2228,U_2229)),c_Groups_Osgn__class_Osgn(U_2228,U_2230))
| ~ class_Rings_Olinordered__idom(U_2228) ),
inference(variable_rename,[status(thm)],[f_694_1]) ).
cnf(f_694_3,plain,
( c_Groups_Osgn__class_Osgn(U_2228,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2228),U_2229),U_2230)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2228),c_Groups_Osgn__class_Osgn(U_2228,U_2229)),c_Groups_Osgn__class_Osgn(U_2228,U_2230))
| ~ class_Rings_Olinordered__idom(U_2228) ),
inference(clausify,[status(thm)],[f_694_2]) ).
fof(f_695_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0]) ).
fof(f_695_2,plain,
! [U_2233,U_2232,U_2231] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2231),U_2232),U_2233))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2231),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2231),U_2232),U_2233)),c_Groups_Ozero__class_Ozero(U_2231))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2231),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2231),U_2232),U_2233)),c_Groups_Ozero__class_Ozero(U_2231)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2231),U_2232),U_2233)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2231) ),
inference(variable_rename,[status(thm)],[f_695_1]) ).
cnf(f_695_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2231),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2231),U_2232),U_2233)),c_Groups_Ozero__class_Ozero(U_2231)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2231),U_2232),U_2233))
| ~ class_Groups_Oordered__ab__group__add(U_2231) ),
inference(clausify,[status(thm)],[f_695_2]) ).
cnf(f_695_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2231),U_2232),U_2233))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2231),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2231),U_2232),U_2233)),c_Groups_Ozero__class_Ozero(U_2231)))
| ~ class_Groups_Oordered__ab__group__add(U_2231) ),
inference(clausify,[status(thm)],[f_695_2]) ).
fof(f_696_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0]) ).
fof(f_696_2,plain,
! [U_2236,U_2235,U_2234] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2234),U_2235),U_2236))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2234),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2234),U_2235),U_2236)),c_Groups_Ozero__class_Ozero(U_2234))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2234),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2234),U_2235),U_2236)),c_Groups_Ozero__class_Ozero(U_2234)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2234),U_2235),U_2236)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2234) ),
inference(variable_rename,[status(thm)],[f_696_1]) ).
cnf(f_696_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2234),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2234),U_2235),U_2236)),c_Groups_Ozero__class_Ozero(U_2234)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2234),U_2235),U_2236))
| ~ class_Groups_Oordered__ab__group__add(U_2234) ),
inference(clausify,[status(thm)],[f_696_2]) ).
cnf(f_696_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2234),U_2235),U_2236))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2234),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2234),U_2235),U_2236)),c_Groups_Ozero__class_Ozero(U_2234)))
| ~ class_Groups_Oordered__ab__group__add(U_2234) ),
inference(clausify,[status(thm)],[f_696_2]) ).
fof(f_697_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le]) ).
fof(f_697_2,plain,
! [U_2238,U_2237] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2237),c_Groups_Ozero__class_Ozero(U_2237)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2237),U_2238)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2237),U_2238),c_Groups_Ozero__class_Ozero(U_2237))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2237),U_2238),c_Groups_Ozero__class_Ozero(U_2237)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2237),c_Groups_Ozero__class_Ozero(U_2237)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2237),U_2238))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2237) ),
inference(variable_rename,[status(thm)],[f_697_1]) ).
cnf(f_697_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2237),U_2238),c_Groups_Ozero__class_Ozero(U_2237)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2237),c_Groups_Ozero__class_Ozero(U_2237)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2237),U_2238)))
| ~ class_Groups_Oordered__ab__group__add(U_2237) ),
inference(clausify,[status(thm)],[f_697_2]) ).
cnf(f_697_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2237),c_Groups_Ozero__class_Ozero(U_2237)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2237),U_2238)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2237),U_2238),c_Groups_Ozero__class_Ozero(U_2237)))
| ~ class_Groups_Oordered__ab__group__add(U_2237) ),
inference(clausify,[status(thm)],[f_697_2]) ).
fof(f_698_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff]) ).
fof(f_698_2,plain,
! [U_2240,U_2239] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2239),U_2240),hAPP(c_Groups_Ouminus__class_Ouminus(U_2239),U_2240)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2239),U_2240),c_Groups_Ozero__class_Ozero(U_2239))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2239),U_2240),c_Groups_Ozero__class_Ozero(U_2239)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2239),U_2240),hAPP(c_Groups_Ouminus__class_Ouminus(U_2239),U_2240))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_2239) ),
inference(variable_rename,[status(thm)],[f_698_1]) ).
cnf(f_698_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2239),U_2240),c_Groups_Ozero__class_Ozero(U_2239)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2239),U_2240),hAPP(c_Groups_Ouminus__class_Ouminus(U_2239),U_2240)))
| ~ class_Groups_Olinordered__ab__group__add(U_2239) ),
inference(clausify,[status(thm)],[f_698_2]) ).
cnf(f_698_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2239),U_2240),hAPP(c_Groups_Ouminus__class_Ouminus(U_2239),U_2240)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2239),U_2240),c_Groups_Ozero__class_Ozero(U_2239)))
| ~ class_Groups_Olinordered__ab__group__add(U_2239) ),
inference(clausify,[status(thm)],[f_698_2]) ).
fof(f_699_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le]) ).
fof(f_699_2,plain,
! [U_2242,U_2241] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2241),hAPP(c_Groups_Ouminus__class_Ouminus(U_2241),U_2242)),c_Groups_Ozero__class_Ozero(U_2241)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2241),c_Groups_Ozero__class_Ozero(U_2241)),U_2242)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2241),c_Groups_Ozero__class_Ozero(U_2241)),U_2242))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2241),hAPP(c_Groups_Ouminus__class_Ouminus(U_2241),U_2242)),c_Groups_Ozero__class_Ozero(U_2241))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2241) ),
inference(variable_rename,[status(thm)],[f_699_1]) ).
cnf(f_699_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2241),c_Groups_Ozero__class_Ozero(U_2241)),U_2242))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2241),hAPP(c_Groups_Ouminus__class_Ouminus(U_2241),U_2242)),c_Groups_Ozero__class_Ozero(U_2241)))
| ~ class_Groups_Oordered__ab__group__add(U_2241) ),
inference(clausify,[status(thm)],[f_699_2]) ).
cnf(f_699_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2241),hAPP(c_Groups_Ouminus__class_Ouminus(U_2241),U_2242)),c_Groups_Ozero__class_Ozero(U_2241)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2241),c_Groups_Ozero__class_Ozero(U_2241)),U_2242))
| ~ class_Groups_Oordered__ab__group__add(U_2241) ),
inference(clausify,[status(thm)],[f_699_2]) ).
fof(f_700_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2)) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff]) ).
fof(f_700_2,plain,
! [U_2244,U_2243] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2243),hAPP(c_Groups_Ouminus__class_Ouminus(U_2243),U_2244)),U_2244))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2243),c_Groups_Ozero__class_Ozero(U_2243)),U_2244)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2243),c_Groups_Ozero__class_Ozero(U_2243)),U_2244))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2243),hAPP(c_Groups_Ouminus__class_Ouminus(U_2243),U_2244)),U_2244)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_2243) ),
inference(variable_rename,[status(thm)],[f_700_1]) ).
cnf(f_700_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2243),c_Groups_Ozero__class_Ozero(U_2243)),U_2244))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2243),hAPP(c_Groups_Ouminus__class_Ouminus(U_2243),U_2244)),U_2244))
| ~ class_Groups_Olinordered__ab__group__add(U_2243) ),
inference(clausify,[status(thm)],[f_700_2]) ).
cnf(f_700_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2243),hAPP(c_Groups_Ouminus__class_Ouminus(U_2243),U_2244)),U_2244))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2243),c_Groups_Ozero__class_Ozero(U_2243)),U_2244))
| ~ class_Groups_Olinordered__ab__group__add(U_2243) ),
inference(clausify,[status(thm)],[f_700_2]) ).
fof(f_701_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less]) ).
fof(f_701_2,plain,
! [U_2246,U_2245] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2245),c_Groups_Ozero__class_Ozero(U_2245)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2245),U_2246)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2245),U_2246),c_Groups_Ozero__class_Ozero(U_2245))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2245),U_2246),c_Groups_Ozero__class_Ozero(U_2245)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2245),c_Groups_Ozero__class_Ozero(U_2245)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2245),U_2246))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2245) ),
inference(variable_rename,[status(thm)],[f_701_1]) ).
cnf(f_701_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2245),U_2246),c_Groups_Ozero__class_Ozero(U_2245)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2245),c_Groups_Ozero__class_Ozero(U_2245)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2245),U_2246)))
| ~ class_Groups_Oordered__ab__group__add(U_2245) ),
inference(clausify,[status(thm)],[f_701_2]) ).
cnf(f_701_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2245),c_Groups_Ozero__class_Ozero(U_2245)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2245),U_2246)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2245),U_2246),c_Groups_Ozero__class_Ozero(U_2245)))
| ~ class_Groups_Oordered__ab__group__add(U_2245) ),
inference(clausify,[status(thm)],[f_701_2]) ).
fof(f_702_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff]) ).
fof(f_702_2,plain,
! [U_2248,U_2247] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2247),U_2248),hAPP(c_Groups_Ouminus__class_Ouminus(U_2247),U_2248)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2247),U_2248),c_Groups_Ozero__class_Ozero(U_2247))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2247),U_2248),c_Groups_Ozero__class_Ozero(U_2247)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2247),U_2248),hAPP(c_Groups_Ouminus__class_Ouminus(U_2247),U_2248))) ) )
| ~ class_Rings_Olinordered__idom(U_2247) ),
inference(variable_rename,[status(thm)],[f_702_1]) ).
cnf(f_702_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2247),U_2248),c_Groups_Ozero__class_Ozero(U_2247)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2247),U_2248),hAPP(c_Groups_Ouminus__class_Ouminus(U_2247),U_2248)))
| ~ class_Rings_Olinordered__idom(U_2247) ),
inference(clausify,[status(thm)],[f_702_2]) ).
cnf(f_702_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2247),U_2248),hAPP(c_Groups_Ouminus__class_Ouminus(U_2247),U_2248)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2247),U_2248),c_Groups_Ozero__class_Ozero(U_2247)))
| ~ class_Rings_Olinordered__idom(U_2247) ),
inference(clausify,[status(thm)],[f_702_2]) ).
fof(f_703_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less]) ).
fof(f_703_2,plain,
! [U_2250,U_2249] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2249),hAPP(c_Groups_Ouminus__class_Ouminus(U_2249),U_2250)),c_Groups_Ozero__class_Ozero(U_2249)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2249),c_Groups_Ozero__class_Ozero(U_2249)),U_2250)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2249),c_Groups_Ozero__class_Ozero(U_2249)),U_2250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2249),hAPP(c_Groups_Ouminus__class_Ouminus(U_2249),U_2250)),c_Groups_Ozero__class_Ozero(U_2249))) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2249) ),
inference(variable_rename,[status(thm)],[f_703_1]) ).
cnf(f_703_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2249),c_Groups_Ozero__class_Ozero(U_2249)),U_2250))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2249),hAPP(c_Groups_Ouminus__class_Ouminus(U_2249),U_2250)),c_Groups_Ozero__class_Ozero(U_2249)))
| ~ class_Groups_Oordered__ab__group__add(U_2249) ),
inference(clausify,[status(thm)],[f_703_2]) ).
cnf(f_703_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2249),hAPP(c_Groups_Ouminus__class_Ouminus(U_2249),U_2250)),c_Groups_Ozero__class_Ozero(U_2249)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2249),c_Groups_Ozero__class_Ozero(U_2249)),U_2250))
| ~ class_Groups_Oordered__ab__group__add(U_2249) ),
inference(clausify,[status(thm)],[f_703_2]) ).
fof(f_704_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2)) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg]) ).
fof(f_704_2,plain,
! [U_2252,U_2251] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2251),hAPP(c_Groups_Ouminus__class_Ouminus(U_2251),U_2252)),U_2252))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2251),c_Groups_Ozero__class_Ozero(U_2251)),U_2252)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2251),c_Groups_Ozero__class_Ozero(U_2251)),U_2252))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2251),hAPP(c_Groups_Ouminus__class_Ouminus(U_2251),U_2252)),U_2252)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_2251) ),
inference(variable_rename,[status(thm)],[f_704_1]) ).
cnf(f_704_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2251),c_Groups_Ozero__class_Ozero(U_2251)),U_2252))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2251),hAPP(c_Groups_Ouminus__class_Ouminus(U_2251),U_2252)),U_2252))
| ~ class_Groups_Olinordered__ab__group__add(U_2251) ),
inference(clausify,[status(thm)],[f_704_2]) ).
cnf(f_704_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2251),hAPP(c_Groups_Ouminus__class_Ouminus(U_2251),U_2252)),U_2252))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2251),c_Groups_Ozero__class_Ozero(U_2251)),U_2252))
| ~ class_Groups_Olinordered__ab__group__add(U_2251) ),
inference(clausify,[status(thm)],[f_704_2]) ).
fof(f_705_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_705_2,plain,
! [U_2253] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2253) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_2253),
inference(variable_rename,[status(thm)],[f_705_1]) ).
cnf(f_705_3,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2253) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_2253),
inference(clausify,[status(thm)],[f_705_2]) ).
fof(f_706_1,plain,
! [V_w_2,V_v_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Int_Onumber(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__number__of__eq__not__less]) ).
fof(f_706_2,plain,
! [U_2256,U_2255,U_2254] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2254),hAPP(c_Int_Onumber__class_Onumber__of(U_2254),U_2255)),hAPP(c_Int_Onumber__class_Onumber__of(U_2254),U_2256)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2254),hAPP(c_Int_Onumber__class_Onumber__of(U_2254),U_2256)),hAPP(c_Int_Onumber__class_Onumber__of(U_2254),U_2255))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2254),hAPP(c_Int_Onumber__class_Onumber__of(U_2254),U_2256)),hAPP(c_Int_Onumber__class_Onumber__of(U_2254),U_2255)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2254),hAPP(c_Int_Onumber__class_Onumber__of(U_2254),U_2255)),hAPP(c_Int_Onumber__class_Onumber__of(U_2254),U_2256))) ) )
| ~ class_Orderings_Olinorder(U_2254)
| ~ class_Int_Onumber(U_2254) ),
inference(variable_rename,[status(thm)],[f_706_1]) ).
cnf(f_706_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2254),hAPP(c_Int_Onumber__class_Onumber__of(U_2254),U_2256)),hAPP(c_Int_Onumber__class_Onumber__of(U_2254),U_2255)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2254),hAPP(c_Int_Onumber__class_Onumber__of(U_2254),U_2255)),hAPP(c_Int_Onumber__class_Onumber__of(U_2254),U_2256)))
| ~ class_Orderings_Olinorder(U_2254)
| ~ class_Int_Onumber(U_2254) ),
inference(clausify,[status(thm)],[f_706_2]) ).
cnf(f_706_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2254),hAPP(c_Int_Onumber__class_Onumber__of(U_2254),U_2255)),hAPP(c_Int_Onumber__class_Onumber__of(U_2254),U_2256)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2254),hAPP(c_Int_Onumber__class_Onumber__of(U_2254),U_2256)),hAPP(c_Int_Onumber__class_Onumber__of(U_2254),U_2255)))
| ~ class_Orderings_Olinorder(U_2254)
| ~ class_Int_Onumber(U_2254) ),
inference(clausify,[status(thm)],[f_706_2]) ).
fof(f_707_1,plain,
! [V_x_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
| ( V_x_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
& V_x_2 != c_Groups_Oone__class_Oone(T_b) ) )
& ( V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
| V_x_2 = c_Groups_Oone__class_Oone(T_b)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) != c_Groups_Oone__class_Oone(T_b) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_b) ),
inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff]) ).
fof(f_707_2,plain,
! [U_2258,U_2257] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2257),U_2258),U_2258) = c_Groups_Oone__class_Oone(U_2257)
| ( U_2258 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2257),c_Groups_Oone__class_Oone(U_2257))
& U_2258 != c_Groups_Oone__class_Oone(U_2257) ) )
& ( U_2258 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2257),c_Groups_Oone__class_Oone(U_2257))
| U_2258 = c_Groups_Oone__class_Oone(U_2257)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2257),U_2258),U_2258) != c_Groups_Oone__class_Oone(U_2257) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_2257) ),
inference(variable_rename,[status(thm)],[f_707_1]) ).
cnf(f_707_3,plain,
( U_2258 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2257),c_Groups_Oone__class_Oone(U_2257))
| U_2258 = c_Groups_Oone__class_Oone(U_2257)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2257),U_2258),U_2258) != c_Groups_Oone__class_Oone(U_2257)
| ~ class_Rings_Oring__1__no__zero__divisors(U_2257) ),
inference(clausify,[status(thm)],[f_707_2]) ).
cnf(f_707_4,plain,
( U_2258 != c_Groups_Oone__class_Oone(U_2257)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2257),U_2258),U_2258) = c_Groups_Oone__class_Oone(U_2257)
| ~ class_Rings_Oring__1__no__zero__divisors(U_2257) ),
inference(clausify,[status(thm)],[f_707_2]) ).
cnf(f_707_5,plain,
( U_2258 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2257),c_Groups_Oone__class_Oone(U_2257))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2257),U_2258),U_2258) = c_Groups_Oone__class_Oone(U_2257)
| ~ class_Rings_Oring__1__no__zero__divisors(U_2257) ),
inference(clausify,[status(thm)],[f_707_2]) ).
fof(f_708_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_708_2,plain,
! [U_2260,U_2259] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2259),U_2260) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2259),hAPP(c_Groups_Ouminus__class_Ouminus(U_2259),c_Groups_Oone__class_Oone(U_2259))),U_2260)
| ~ class_Rings_Ocomm__ring__1(U_2259) ),
inference(variable_rename,[status(thm)],[f_708_1]) ).
cnf(f_708_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2259),U_2260) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2259),hAPP(c_Groups_Ouminus__class_Ouminus(U_2259),c_Groups_Oone__class_Oone(U_2259))),U_2260)
| ~ class_Rings_Ocomm__ring__1(U_2259) ),
inference(clausify,[status(thm)],[f_708_2]) ).
fof(f_709_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2))) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__double__add__iff__zero__le__single__add]) ).
fof(f_709_2,plain,
! [U_2262,U_2261] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2261),c_Groups_Ozero__class_Ozero(U_2261)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2261),U_2262),U_2262)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2261),c_Groups_Ozero__class_Ozero(U_2261)),U_2262)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2261),c_Groups_Ozero__class_Ozero(U_2261)),U_2262))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2261),c_Groups_Ozero__class_Ozero(U_2261)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2261),U_2262),U_2262))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_2261) ),
inference(variable_rename,[status(thm)],[f_709_1]) ).
cnf(f_709_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2261),c_Groups_Ozero__class_Ozero(U_2261)),U_2262))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2261),c_Groups_Ozero__class_Ozero(U_2261)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2261),U_2262),U_2262)))
| ~ class_Groups_Olinordered__ab__group__add(U_2261) ),
inference(clausify,[status(thm)],[f_709_2]) ).
cnf(f_709_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2261),c_Groups_Ozero__class_Ozero(U_2261)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2261),U_2262),U_2262)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2261),c_Groups_Ozero__class_Ozero(U_2261)),U_2262))
| ~ class_Groups_Olinordered__ab__group__add(U_2261) ),
inference(clausify,[status(thm)],[f_709_2]) ).
fof(f_710_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero]) ).
fof(f_710_2,plain,
! [U_2264,U_2263] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2263),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2263),U_2264),U_2264)),c_Groups_Ozero__class_Ozero(U_2263)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2263),U_2264),c_Groups_Ozero__class_Ozero(U_2263))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2263),U_2264),c_Groups_Ozero__class_Ozero(U_2263)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2263),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2263),U_2264),U_2264)),c_Groups_Ozero__class_Ozero(U_2263))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_2263) ),
inference(variable_rename,[status(thm)],[f_710_1]) ).
cnf(f_710_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2263),U_2264),c_Groups_Ozero__class_Ozero(U_2263)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2263),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2263),U_2264),U_2264)),c_Groups_Ozero__class_Ozero(U_2263)))
| ~ class_Groups_Olinordered__ab__group__add(U_2263) ),
inference(clausify,[status(thm)],[f_710_2]) ).
cnf(f_710_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2263),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2263),U_2264),U_2264)),c_Groups_Ozero__class_Ozero(U_2263)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2263),U_2264),c_Groups_Ozero__class_Ozero(U_2263)))
| ~ class_Groups_Olinordered__ab__group__add(U_2263) ),
inference(clausify,[status(thm)],[f_710_2]) ).
fof(f_711_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_711_2,plain,
! [U_2267,U_2266,U_2265] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2265),c_Groups_Ozero__class_Ozero(U_2265)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2265),U_2266),U_2267)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2265),c_Groups_Ozero__class_Ozero(U_2265)),U_2267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2265),c_Groups_Ozero__class_Ozero(U_2265)),U_2266))
| ~ class_Groups_Oordered__comm__monoid__add(U_2265) ),
inference(variable_rename,[status(thm)],[f_711_1]) ).
cnf(f_711_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2265),c_Groups_Ozero__class_Ozero(U_2265)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2265),U_2266),U_2267)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2265),c_Groups_Ozero__class_Ozero(U_2265)),U_2267))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2265),c_Groups_Ozero__class_Ozero(U_2265)),U_2266))
| ~ class_Groups_Oordered__comm__monoid__add(U_2265) ),
inference(clausify,[status(thm)],[f_711_2]) ).
fof(f_712_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
| ~ class_Groups_Oordered__comm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff]) ).
fof(f_712_2,plain,
! [U_2270,U_2269,U_2268] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2268),U_2269),U_2270) = c_Groups_Ozero__class_Ozero(U_2268)
| U_2270 != c_Groups_Ozero__class_Ozero(U_2268)
| U_2269 != c_Groups_Ozero__class_Ozero(U_2268) )
& ( ( U_2270 = c_Groups_Ozero__class_Ozero(U_2268)
& U_2269 = c_Groups_Ozero__class_Ozero(U_2268) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2268),U_2269),U_2270) != c_Groups_Ozero__class_Ozero(U_2268) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),c_Groups_Ozero__class_Ozero(U_2268)),U_2270))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),c_Groups_Ozero__class_Ozero(U_2268)),U_2269))
| ~ class_Groups_Oordered__comm__monoid__add(U_2268) ),
inference(variable_rename,[status(thm)],[f_712_1]) ).
cnf(f_712_3,plain,
( U_2269 = c_Groups_Ozero__class_Ozero(U_2268)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2268),U_2269),U_2270) != c_Groups_Ozero__class_Ozero(U_2268)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),c_Groups_Ozero__class_Ozero(U_2268)),U_2270))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),c_Groups_Ozero__class_Ozero(U_2268)),U_2269))
| ~ class_Groups_Oordered__comm__monoid__add(U_2268) ),
inference(clausify,[status(thm)],[f_712_2]) ).
cnf(f_712_4,plain,
( U_2270 = c_Groups_Ozero__class_Ozero(U_2268)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2268),U_2269),U_2270) != c_Groups_Ozero__class_Ozero(U_2268)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),c_Groups_Ozero__class_Ozero(U_2268)),U_2270))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),c_Groups_Ozero__class_Ozero(U_2268)),U_2269))
| ~ class_Groups_Oordered__comm__monoid__add(U_2268) ),
inference(clausify,[status(thm)],[f_712_2]) ).
cnf(f_712_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2268),U_2269),U_2270) = c_Groups_Ozero__class_Ozero(U_2268)
| U_2270 != c_Groups_Ozero__class_Ozero(U_2268)
| U_2269 != c_Groups_Ozero__class_Ozero(U_2268)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),c_Groups_Ozero__class_Ozero(U_2268)),U_2270))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2268),c_Groups_Ozero__class_Ozero(U_2268)),U_2269))
| ~ class_Groups_Oordered__comm__monoid__add(U_2268) ),
inference(clausify,[status(thm)],[f_712_2]) ).
fof(f_713_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_713_2,plain,
! [U_2274,U_2273,U_2272,U_2271] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2271),U_2273),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2271),U_2272),U_2274)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2271),U_2273),U_2274))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2271),c_Groups_Ozero__class_Ozero(U_2271)),U_2272))
| ~ class_Groups_Oordered__comm__monoid__add(U_2271) ),
inference(variable_rename,[status(thm)],[f_713_1]) ).
cnf(f_713_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2271),U_2273),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2271),U_2272),U_2274)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2271),U_2273),U_2274))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2271),c_Groups_Ozero__class_Ozero(U_2271)),U_2272))
| ~ class_Groups_Oordered__comm__monoid__add(U_2271) ),
inference(clausify,[status(thm)],[f_713_2]) ).
fof(f_714_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_714_2,plain,
! [U_2278,U_2277,U_2276,U_2275] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2275),U_2277),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2275),U_2278),U_2276)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2275),U_2277),U_2278))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2275),c_Groups_Ozero__class_Ozero(U_2275)),U_2276))
| ~ class_Groups_Oordered__comm__monoid__add(U_2275) ),
inference(variable_rename,[status(thm)],[f_714_1]) ).
cnf(f_714_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2275),U_2277),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2275),U_2278),U_2276)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2275),U_2277),U_2278))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2275),c_Groups_Ozero__class_Ozero(U_2275)),U_2276))
| ~ class_Groups_Oordered__comm__monoid__add(U_2275) ),
inference(clausify,[status(thm)],[f_714_2]) ).
fof(f_715_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_715_2,plain,
! [U_2281,U_2280,U_2279] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2279),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2279),U_2280),U_2281)),c_Groups_Ozero__class_Ozero(U_2279)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2279),U_2281),c_Groups_Ozero__class_Ozero(U_2279)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2279),U_2280),c_Groups_Ozero__class_Ozero(U_2279)))
| ~ class_Groups_Oordered__comm__monoid__add(U_2279) ),
inference(variable_rename,[status(thm)],[f_715_1]) ).
cnf(f_715_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2279),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2279),U_2280),U_2281)),c_Groups_Ozero__class_Ozero(U_2279)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2279),U_2281),c_Groups_Ozero__class_Ozero(U_2279)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2279),U_2280),c_Groups_Ozero__class_Ozero(U_2279)))
| ~ class_Groups_Oordered__comm__monoid__add(U_2279) ),
inference(clausify,[status(thm)],[f_715_2]) ).
fof(f_716_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
| ~ class_Rings_Olinordered__idom(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__number__of]) ).
fof(f_716_2,plain,
! [U_2284,U_2283,U_2282] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2282),hAPP(c_Int_Onumber__class_Onumber__of(U_2282),U_2283)),hAPP(c_Int_Onumber__class_Onumber__of(U_2282),U_2284)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2283),U_2284)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2283),U_2284))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2282),hAPP(c_Int_Onumber__class_Onumber__of(U_2282),U_2283)),hAPP(c_Int_Onumber__class_Onumber__of(U_2282),U_2284))) ) )
| ~ class_Rings_Olinordered__idom(U_2282)
| ~ class_Int_Onumber__ring(U_2282) ),
inference(variable_rename,[status(thm)],[f_716_1]) ).
cnf(f_716_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2283),U_2284))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2282),hAPP(c_Int_Onumber__class_Onumber__of(U_2282),U_2283)),hAPP(c_Int_Onumber__class_Onumber__of(U_2282),U_2284)))
| ~ class_Rings_Olinordered__idom(U_2282)
| ~ class_Int_Onumber__ring(U_2282) ),
inference(clausify,[status(thm)],[f_716_2]) ).
cnf(f_716_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2282),hAPP(c_Int_Onumber__class_Onumber__of(U_2282),U_2283)),hAPP(c_Int_Onumber__class_Onumber__of(U_2282),U_2284)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2283),U_2284))
| ~ class_Rings_Olinordered__idom(U_2282)
| ~ class_Int_Onumber__ring(U_2282) ),
inference(clausify,[status(thm)],[f_716_2]) ).
fof(f_717_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_717_2,plain,
! [U_2289,U_2288,U_2287,U_2286,U_2285] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2285),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2285),U_2286),U_2288)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2285),U_2287),U_2289)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2285),U_2288),U_2289))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2285),U_2286),U_2287))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2285) ),
inference(variable_rename,[status(thm)],[f_717_1]) ).
cnf(f_717_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2285),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2285),U_2286),U_2288)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2285),U_2287),U_2289)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2285),U_2288),U_2289))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2285),U_2286),U_2287))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2285) ),
inference(clausify,[status(thm)],[f_717_2]) ).
fof(f_718_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_718_2,plain,
! [U_2294,U_2293,U_2292,U_2291,U_2290] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2290),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2290),U_2291),U_2293)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2290),U_2292),U_2294)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2290),U_2293),U_2294))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2290),U_2291),U_2292))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2290) ),
inference(variable_rename,[status(thm)],[f_718_1]) ).
cnf(f_718_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2290),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2290),U_2291),U_2293)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2290),U_2292),U_2294)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2290),U_2293),U_2294))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2290),U_2291),U_2292))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2290) ),
inference(clausify,[status(thm)],[f_718_2]) ).
fof(f_719_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2))) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__double__add__iff__zero__less__single__add]) ).
fof(f_719_2,plain,
! [U_2296,U_2295] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2295),c_Groups_Ozero__class_Ozero(U_2295)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2295),U_2296),U_2296)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2295),c_Groups_Ozero__class_Ozero(U_2295)),U_2296)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2295),c_Groups_Ozero__class_Ozero(U_2295)),U_2296))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2295),c_Groups_Ozero__class_Ozero(U_2295)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2295),U_2296),U_2296))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_2295) ),
inference(variable_rename,[status(thm)],[f_719_1]) ).
cnf(f_719_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2295),c_Groups_Ozero__class_Ozero(U_2295)),U_2296))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2295),c_Groups_Ozero__class_Ozero(U_2295)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2295),U_2296),U_2296)))
| ~ class_Groups_Olinordered__ab__group__add(U_2295) ),
inference(clausify,[status(thm)],[f_719_2]) ).
cnf(f_719_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2295),c_Groups_Ozero__class_Ozero(U_2295)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2295),U_2296),U_2296)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2295),c_Groups_Ozero__class_Ozero(U_2295)),U_2296))
| ~ class_Groups_Olinordered__ab__group__add(U_2295) ),
inference(clausify,[status(thm)],[f_719_2]) ).
fof(f_720_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_double__add__less__zero__iff__single__add__less__zero]) ).
fof(f_720_2,plain,
! [U_2298,U_2297] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2297),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2297),U_2298),U_2298)),c_Groups_Ozero__class_Ozero(U_2297)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2297),U_2298),c_Groups_Ozero__class_Ozero(U_2297))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2297),U_2298),c_Groups_Ozero__class_Ozero(U_2297)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2297),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2297),U_2298),U_2298)),c_Groups_Ozero__class_Ozero(U_2297))) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_2297) ),
inference(variable_rename,[status(thm)],[f_720_1]) ).
cnf(f_720_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2297),U_2298),c_Groups_Ozero__class_Ozero(U_2297)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2297),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2297),U_2298),U_2298)),c_Groups_Ozero__class_Ozero(U_2297)))
| ~ class_Groups_Olinordered__ab__group__add(U_2297) ),
inference(clausify,[status(thm)],[f_720_2]) ).
cnf(f_720_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2297),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2297),U_2298),U_2298)),c_Groups_Ozero__class_Ozero(U_2297)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2297),U_2298),c_Groups_Ozero__class_Ozero(U_2297)))
| ~ class_Groups_Olinordered__ab__group__add(U_2297) ),
inference(clausify,[status(thm)],[f_720_2]) ).
fof(f_721_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_721_2,plain,
! [U_2301,U_2300,U_2299] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2299),c_Groups_Ozero__class_Ozero(U_2299)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2299),U_2300),U_2301)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2299),c_Groups_Ozero__class_Ozero(U_2299)),U_2301))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2299),c_Groups_Ozero__class_Ozero(U_2299)),U_2300))
| ~ class_Groups_Oordered__comm__monoid__add(U_2299) ),
inference(variable_rename,[status(thm)],[f_721_1]) ).
cnf(f_721_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2299),c_Groups_Ozero__class_Ozero(U_2299)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2299),U_2300),U_2301)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2299),c_Groups_Ozero__class_Ozero(U_2299)),U_2301))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2299),c_Groups_Ozero__class_Ozero(U_2299)),U_2300))
| ~ class_Groups_Oordered__comm__monoid__add(U_2299) ),
inference(clausify,[status(thm)],[f_721_2]) ).
fof(f_722_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_722_2,plain,
! [U_2305,U_2304,U_2303,U_2302] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2302),U_2304),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2302),U_2303),U_2305)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2302),U_2304),U_2305))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2302),c_Groups_Ozero__class_Ozero(U_2302)),U_2303))
| ~ class_Rings_Olinordered__semidom(U_2302) ),
inference(variable_rename,[status(thm)],[f_722_1]) ).
cnf(f_722_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2302),U_2304),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2302),U_2303),U_2305)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2302),U_2304),U_2305))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2302),c_Groups_Ozero__class_Ozero(U_2302)),U_2303))
| ~ class_Rings_Olinordered__semidom(U_2302) ),
inference(clausify,[status(thm)],[f_722_2]) ).
fof(f_723_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_723_2,plain,
! [U_2308,U_2307,U_2306] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2306),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2306),U_2307),U_2308)),c_Groups_Ozero__class_Ozero(U_2306)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2306),U_2308),c_Groups_Ozero__class_Ozero(U_2306)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2306),U_2307),c_Groups_Ozero__class_Ozero(U_2306)))
| ~ class_Groups_Oordered__comm__monoid__add(U_2306) ),
inference(variable_rename,[status(thm)],[f_723_1]) ).
cnf(f_723_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2306),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2306),U_2307),U_2308)),c_Groups_Ozero__class_Ozero(U_2306)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2306),U_2308),c_Groups_Ozero__class_Ozero(U_2306)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2306),U_2307),c_Groups_Ozero__class_Ozero(U_2306)))
| ~ class_Groups_Oordered__comm__monoid__add(U_2306) ),
inference(clausify,[status(thm)],[f_723_2]) ).
fof(f_724_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_even__less__0__iff]) ).
fof(f_724_2,plain,
! [U_2310,U_2309] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2309),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2309),U_2310),U_2310)),c_Groups_Ozero__class_Ozero(U_2309)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2309),U_2310),c_Groups_Ozero__class_Ozero(U_2309))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2309),U_2310),c_Groups_Ozero__class_Ozero(U_2309)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2309),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2309),U_2310),U_2310)),c_Groups_Ozero__class_Ozero(U_2309))) ) )
| ~ class_Rings_Olinordered__idom(U_2309) ),
inference(variable_rename,[status(thm)],[f_724_1]) ).
cnf(f_724_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2309),U_2310),c_Groups_Ozero__class_Ozero(U_2309)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2309),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2309),U_2310),U_2310)),c_Groups_Ozero__class_Ozero(U_2309)))
| ~ class_Rings_Olinordered__idom(U_2309) ),
inference(clausify,[status(thm)],[f_724_2]) ).
cnf(f_724_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2309),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2309),U_2310),U_2310)),c_Groups_Ozero__class_Ozero(U_2309)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2309),U_2310),c_Groups_Ozero__class_Ozero(U_2309)))
| ~ class_Rings_Olinordered__idom(U_2309) ),
inference(clausify,[status(thm)],[f_724_2]) ).
fof(f_725_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
| ~ class_Rings_Olinordered__idom(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__number__of]) ).
fof(f_725_2,plain,
! [U_2313,U_2312,U_2311] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2311),hAPP(c_Int_Onumber__class_Onumber__of(U_2311),U_2312)),hAPP(c_Int_Onumber__class_Onumber__of(U_2311),U_2313)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2312),U_2313)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2312),U_2313))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2311),hAPP(c_Int_Onumber__class_Onumber__of(U_2311),U_2312)),hAPP(c_Int_Onumber__class_Onumber__of(U_2311),U_2313))) ) )
| ~ class_Rings_Olinordered__idom(U_2311)
| ~ class_Int_Onumber__ring(U_2311) ),
inference(variable_rename,[status(thm)],[f_725_1]) ).
cnf(f_725_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2312),U_2313))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2311),hAPP(c_Int_Onumber__class_Onumber__of(U_2311),U_2312)),hAPP(c_Int_Onumber__class_Onumber__of(U_2311),U_2313)))
| ~ class_Rings_Olinordered__idom(U_2311)
| ~ class_Int_Onumber__ring(U_2311) ),
inference(clausify,[status(thm)],[f_725_2]) ).
cnf(f_725_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2311),hAPP(c_Int_Onumber__class_Onumber__of(U_2311),U_2312)),hAPP(c_Int_Onumber__class_Onumber__of(U_2311),U_2313)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2312),U_2313))
| ~ class_Rings_Olinordered__idom(U_2311)
| ~ class_Int_Onumber__ring(U_2311) ),
inference(clausify,[status(thm)],[f_725_2]) ).
fof(f_726_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_b)
| V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff]) ).
fof(f_726_2,plain,
! [U_2316,U_2315,U_2314] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2314),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2314),U_2315),U_2315)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2314),U_2316),U_2316)) = c_Groups_Ozero__class_Ozero(U_2314)
| U_2316 != c_Groups_Ozero__class_Ozero(U_2314)
| U_2315 != c_Groups_Ozero__class_Ozero(U_2314) )
& ( ( U_2316 = c_Groups_Ozero__class_Ozero(U_2314)
& U_2315 = c_Groups_Ozero__class_Ozero(U_2314) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2314),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2314),U_2315),U_2315)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2314),U_2316),U_2316)) != c_Groups_Ozero__class_Ozero(U_2314) ) )
| ~ class_Rings_Olinordered__ring__strict(U_2314) ),
inference(variable_rename,[status(thm)],[f_726_1]) ).
cnf(f_726_3,plain,
( U_2315 = c_Groups_Ozero__class_Ozero(U_2314)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2314),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2314),U_2315),U_2315)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2314),U_2316),U_2316)) != c_Groups_Ozero__class_Ozero(U_2314)
| ~ class_Rings_Olinordered__ring__strict(U_2314) ),
inference(clausify,[status(thm)],[f_726_2]) ).
cnf(f_726_4,plain,
( U_2316 = c_Groups_Ozero__class_Ozero(U_2314)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2314),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2314),U_2315),U_2315)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2314),U_2316),U_2316)) != c_Groups_Ozero__class_Ozero(U_2314)
| ~ class_Rings_Olinordered__ring__strict(U_2314) ),
inference(clausify,[status(thm)],[f_726_2]) ).
cnf(f_726_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2314),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2314),U_2315),U_2315)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2314),U_2316),U_2316)) = c_Groups_Ozero__class_Ozero(U_2314)
| U_2316 != c_Groups_Ozero__class_Ozero(U_2314)
| U_2315 != c_Groups_Ozero__class_Ozero(U_2314)
| ~ class_Rings_Olinordered__ring__strict(U_2314) ),
inference(clausify,[status(thm)],[f_726_2]) ).
fof(f_727_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_727_2,plain,
! [U_2322,U_2321,U_2320,U_2319,U_2318,U_2317] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2317),U_2319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2317),U_2318),U_2321)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2317),U_2320),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2317),U_2318),U_2322))
| U_2321 = U_2322
| U_2319 != U_2320
| U_2318 = c_Groups_Ozero__class_Ozero(U_2317)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2317) ),
inference(variable_rename,[status(thm)],[f_727_1]) ).
cnf(f_727_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2317),U_2319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2317),U_2318),U_2321)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2317),U_2320),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2317),U_2318),U_2322))
| U_2321 = U_2322
| U_2319 != U_2320
| U_2318 = c_Groups_Ozero__class_Ozero(U_2317)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_2317) ),
inference(clausify,[status(thm)],[f_727_2]) ).
fof(f_728_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_728_2,plain,
! [U_2324,U_2323] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2323),U_2324),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2323),U_2324),c_Groups_Oone__class_Oone(U_2323))))
| ~ class_Rings_Olinordered__semidom(U_2323) ),
inference(variable_rename,[status(thm)],[f_728_1]) ).
cnf(f_728_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2323),U_2324),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2323),U_2324),c_Groups_Oone__class_Oone(U_2323))))
| ~ class_Rings_Olinordered__semidom(U_2323) ),
inference(clausify,[status(thm)],[f_728_2]) ).
fof(f_729_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_729_2,plain,
! [U_2327,U_2326,U_2325] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_2325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2326),U_2327)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2325),hAPP(c_Int_Onumber__class_Onumber__of(U_2325),U_2326)),hAPP(c_Int_Onumber__class_Onumber__of(U_2325),U_2327))
| ~ class_Int_Onumber__ring(U_2325) ),
inference(variable_rename,[status(thm)],[f_729_1]) ).
cnf(f_729_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_2325),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2326),U_2327)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2325),hAPP(c_Int_Onumber__class_Onumber__of(U_2325),U_2326)),hAPP(c_Int_Onumber__class_Onumber__of(U_2325),U_2327))
| ~ class_Int_Onumber__ring(U_2325) ),
inference(clausify,[status(thm)],[f_729_2]) ).
fof(f_730_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_730_2,plain,
! [U_2330,U_2329,U_2328] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2328),hAPP(c_Int_Onumber__class_Onumber__of(U_2328),U_2329)),hAPP(c_Int_Onumber__class_Onumber__of(U_2328),U_2330)) = hAPP(c_Int_Onumber__class_Onumber__of(U_2328),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2329),U_2330))
| ~ class_Int_Onumber__ring(U_2328) ),
inference(variable_rename,[status(thm)],[f_730_1]) ).
cnf(f_730_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2328),hAPP(c_Int_Onumber__class_Onumber__of(U_2328),U_2329)),hAPP(c_Int_Onumber__class_Onumber__of(U_2328),U_2330)) = hAPP(c_Int_Onumber__class_Onumber__of(U_2328),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2329),U_2330))
| ~ class_Int_Onumber__ring(U_2328) ),
inference(clausify,[status(thm)],[f_730_2]) ).
fof(f_731_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_731_2,plain,
! [U_2334,U_2333,U_2332,U_2331] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2331),hAPP(c_Int_Onumber__class_Onumber__of(U_2331),U_2332)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2331),hAPP(c_Int_Onumber__class_Onumber__of(U_2331),U_2333)),U_2334)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2331),hAPP(c_Int_Onumber__class_Onumber__of(U_2331),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2332),U_2333))),U_2334)
| ~ class_Int_Onumber__ring(U_2331) ),
inference(variable_rename,[status(thm)],[f_731_1]) ).
cnf(f_731_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2331),hAPP(c_Int_Onumber__class_Onumber__of(U_2331),U_2332)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2331),hAPP(c_Int_Onumber__class_Onumber__of(U_2331),U_2333)),U_2334)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2331),hAPP(c_Int_Onumber__class_Onumber__of(U_2331),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2332),U_2333))),U_2334)
| ~ class_Int_Onumber__ring(U_2331) ),
inference(clausify,[status(thm)],[f_731_2]) ).
fof(f_732_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_732_2,plain,
! [U_2336,U_2335] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2335),U_2336),U_2336) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2335),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2335),c_Groups_Oone__class_Oone(U_2335)),c_Groups_Oone__class_Oone(U_2335))),U_2336)
| ~ class_Rings_Ocomm__semiring__1(U_2335) ),
inference(variable_rename,[status(thm)],[f_732_1]) ).
cnf(f_732_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2335),U_2336),U_2336) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2335),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2335),c_Groups_Oone__class_Oone(U_2335)),c_Groups_Oone__class_Oone(U_2335))),U_2336)
| ~ class_Rings_Ocomm__semiring__1(U_2335) ),
inference(clausify,[status(thm)],[f_732_2]) ).
fof(f_733_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_733_2,plain,
! [U_2339,U_2338,U_2337] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2337),U_2338),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2337),U_2339),U_2338)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2337),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2337),U_2339),c_Groups_Oone__class_Oone(U_2337))),U_2338)
| ~ class_Rings_Ocomm__semiring__1(U_2337) ),
inference(variable_rename,[status(thm)],[f_733_1]) ).
cnf(f_733_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2337),U_2338),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2337),U_2339),U_2338)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2337),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2337),U_2339),c_Groups_Oone__class_Oone(U_2337))),U_2338)
| ~ class_Rings_Ocomm__semiring__1(U_2337) ),
inference(clausify,[status(thm)],[f_733_2]) ).
fof(f_734_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_734_2,plain,
! [U_2342,U_2341,U_2340] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2340),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2340),U_2341),U_2342)),U_2342) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2340),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2340),U_2341),c_Groups_Oone__class_Oone(U_2340))),U_2342)
| ~ class_Rings_Ocomm__semiring__1(U_2340) ),
inference(variable_rename,[status(thm)],[f_734_1]) ).
cnf(f_734_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2340),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2340),U_2341),U_2342)),U_2342) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2340),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2340),U_2341),c_Groups_Oone__class_Oone(U_2340))),U_2342)
| ~ class_Rings_Ocomm__semiring__1(U_2340) ),
inference(clausify,[status(thm)],[f_734_2]) ).
fof(f_735_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_735_2,plain,
! [U_2344,U_2343] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2344),U_2343)),U_2344))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2344))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2343)) ),
inference(variable_rename,[status(thm)],[f_735_1]) ).
cnf(f_735_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2344),U_2343)),U_2344))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2344))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2343)) ),
inference(clausify,[status(thm)],[f_735_2]) ).
fof(f_736_1,plain,
! [V_m_2,V_na_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_na_2),V_m_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_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_na_2),V_m_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__diff]) ).
fof(f_736_2,plain,
! [U_2346,U_2345] :
( ( 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_2345),U_2346)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2346),U_2345)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2346),U_2345))
| ~ 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_2345),U_2346))) ) ),
inference(variable_rename,[status(thm)],[f_736_1]) ).
fof(f_736_3,plain,
( ! [U_2350,U_2348] :
( 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_2348),U_2350)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2350),U_2348)) )
& ! [U_2349,U_2347] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2349),U_2347))
| ~ 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_2347),U_2349))) ) ),
inference(miniscope,[status(thm)],[f_736_2]) ).
cnf(f_736_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2349),U_2347))
| ~ 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_2347),U_2349))) ),
inference(clausify,[status(thm)],[f_736_3]) ).
cnf(f_736_5,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_2348),U_2350)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2350),U_2348)) ),
inference(clausify,[status(thm)],[f_736_3]) ).
fof(f_737_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_737_2,plain,
! [U_2352,U_2351] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2351),U_2352)),hAPP(c_Nat_OSuc,U_2351))),
inference(variable_rename,[status(thm)],[f_737_1]) ).
cnf(f_737_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2351),U_2352)),hAPP(c_Nat_OSuc,U_2351))),
inference(clausify,[status(thm)],[f_737_2]) ).
fof(f_738_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_738_2,plain,
! [U_2354,U_2353] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2353),U_2354) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2353),U_2354)) ),
inference(variable_rename,[status(thm)],[f_738_1]) ).
cnf(f_738_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2353),U_2354) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2353),U_2354)) ),
inference(clausify,[status(thm)],[f_738_2]) ).
fof(f_739_1,plain,
! [V_na_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_na_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_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_na_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq]) ).
fof(f_739_2,plain,
! [U_2356,U_2355] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2355),U_2356) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2355),U_2356)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2355),U_2356))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2355),U_2356) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_739_1]) ).
fof(f_739_3,plain,
( ! [U_2360,U_2358] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2358),U_2360) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2358),U_2360)) )
& ! [U_2359,U_2357] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2357),U_2359))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2357),U_2359) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_739_2]) ).
cnf(f_739_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2357),U_2359))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2357),U_2359) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_739_3]) ).
cnf(f_739_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2358),U_2360) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2358),U_2360)) ),
inference(clausify,[status(thm)],[f_739_3]) ).
fof(f_740_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_740_2,plain,
! [U_2362,U_2361] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2362)),U_2361) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2362),U_2361))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2361),U_2362)) ),
inference(variable_rename,[status(thm)],[f_740_1]) ).
cnf(f_740_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2362)),U_2361) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2362),U_2361))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2361),U_2362)) ),
inference(clausify,[status(thm)],[f_740_2]) ).
fof(f_741_1,plain,
! [V_na_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_na_2),V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_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_na_2),V_k_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_na_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_741_2,plain,
! [U_2365,U_2364,U_2363] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2364),U_2363)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2365),U_2363)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2364),U_2365)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2364),U_2365))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2364),U_2363)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2365),U_2363))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2363),U_2365))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2363),U_2364)) ),
inference(variable_rename,[status(thm)],[f_741_1]) ).
cnf(f_741_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2364),U_2365))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2364),U_2363)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2365),U_2363)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2363),U_2365))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2363),U_2364)) ),
inference(clausify,[status(thm)],[f_741_2]) ).
cnf(f_741_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2364),U_2363)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2365),U_2363)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2364),U_2365))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2363),U_2365))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2363),U_2364)) ),
inference(clausify,[status(thm)],[f_741_2]) ).
fof(f_742_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_742_2,plain,
! [U_2368,U_2367,U_2366] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2366),U_2368)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2367),U_2368)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2368),U_2366))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2366),U_2367)) ),
inference(variable_rename,[status(thm)],[f_742_1]) ).
cnf(f_742_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2366),U_2368)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2367),U_2368)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2368),U_2366))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2366),U_2367)) ),
inference(clausify,[status(thm)],[f_742_2]) ).
fof(f_743_1,plain,
! [V_m_2,V_na_2] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_na_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_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_na_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_na_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_743_2,plain,
! [U_2370,U_2369] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2369)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2370)
| U_2370 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2369 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( U_2370 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2369 = 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_2369)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2370) ) ),
inference(variable_rename,[status(thm)],[f_743_1]) ).
fof(f_743_3,plain,
( ! [U_2374,U_2372] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2372)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2374)
| U_2374 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2372 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2373,U_2371] :
( ( U_2373 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2371 = 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_2371)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2373) ) ),
inference(miniscope,[status(thm)],[f_743_2]) ).
cnf(f_743_4,plain,
( U_2371 = 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_2371)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2373) ),
inference(clausify,[status(thm)],[f_743_3]) ).
cnf(f_743_5,plain,
( U_2373 = 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_2371)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2373) ),
inference(clausify,[status(thm)],[f_743_3]) ).
cnf(f_743_6,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2372)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2374)
| U_2374 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2372 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_743_3]) ).
fof(f_744_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_744_2,plain,
! [U_2376,U_2375] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2375)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2376)))),
inference(variable_rename,[status(thm)],[f_744_1]) ).
cnf(f_744_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2375)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2376)))),
inference(clausify,[status(thm)],[f_744_2]) ).
fof(f_745_1,plain,
! [V_na_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_na_2)
| ( ( V_na_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_na_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_na_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_na_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_na_2) ) ),
inference(fof_nnf,[status(thm)],[fact_one__is__add]) ).
fof(f_745_2,plain,
! [U_2378,U_2377] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2377),U_2378)
| ( ( U_2378 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2377 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2378 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2377 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( U_2378 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2377 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_2378 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2377 = 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_2377),U_2378) ) ),
inference(variable_rename,[status(thm)],[f_745_1]) ).
fof(f_745_3,plain,
( ! [U_2382,U_2380] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2380),U_2382)
| ( ( U_2382 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2380 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2382 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2380 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ! [U_2381,U_2379] :
( ( U_2381 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2379 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_2381 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2379 = 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_2379),U_2381) ) ),
inference(miniscope,[status(thm)],[f_745_2]) ).
cnf(f_745_4,plain,
( U_2379 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2379 = 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_2379),U_2381) ),
inference(clausify,[status(thm)],[f_745_3]) ).
cnf(f_745_5,plain,
( U_2381 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2379 = 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_2379),U_2381) ),
inference(clausify,[status(thm)],[f_745_3]) ).
cnf(f_745_6,plain,
( U_2379 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2381 = 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_2379),U_2381) ),
inference(clausify,[status(thm)],[f_745_3]) ).
cnf(f_745_7,plain,
( U_2381 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2381 = 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_2379),U_2381) ),
inference(clausify,[status(thm)],[f_745_3]) ).
cnf(f_745_8,plain,
( U_2382 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2380 != 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_2380),U_2382) ),
inference(clausify,[status(thm)],[f_745_3]) ).
cnf(f_745_9,plain,
( U_2382 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2380 != 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_2380),U_2382) ),
inference(clausify,[status(thm)],[f_745_3]) ).
fof(f_746_1,plain,
! [V_na_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( V_na_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_na_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_na_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_na_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_na_2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[fact_add__is__1]) ).
fof(f_746_2,plain,
! [U_2384,U_2383] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2383),U_2384) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( U_2384 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2383 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2384 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2383 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( U_2384 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2383 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_2384 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2383 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2383),U_2384) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_746_1]) ).
fof(f_746_3,plain,
( ! [U_2388,U_2386] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2386),U_2388) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( U_2388 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2386 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2388 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2386 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ! [U_2387,U_2385] :
( ( U_2387 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2385 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_2387 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2385 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2385),U_2387) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_746_2]) ).
cnf(f_746_4,plain,
( U_2385 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2385 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2385),U_2387) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_746_3]) ).
cnf(f_746_5,plain,
( U_2387 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2385 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2385),U_2387) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_746_3]) ).
cnf(f_746_6,plain,
( U_2385 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2387 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2385),U_2387) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_746_3]) ).
cnf(f_746_7,plain,
( U_2387 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2387 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2385),U_2387) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_746_3]) ).
cnf(f_746_8,plain,
( U_2388 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2386 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2386),U_2388) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_746_3]) ).
cnf(f_746_9,plain,
( U_2388 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2386 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2386),U_2388) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_746_3]) ).
fof(f_747_1,plain,
! [V_na_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_na_2)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_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_na_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_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_add__gr__0]) ).
fof(f_747_2,plain,
! [U_2390,U_2389] :
( ( 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_2389),U_2390)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2390))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2389)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2390))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2389))
| ~ 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_2389),U_2390))) ) ),
inference(variable_rename,[status(thm)],[f_747_1]) ).
fof(f_747_3,plain,
( ! [U_2394,U_2392] :
( 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_2392),U_2394)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2394))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2392)) ) )
& ! [U_2393,U_2391] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2393))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2391))
| ~ 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_2391),U_2393))) ) ),
inference(miniscope,[status(thm)],[f_747_2]) ).
cnf(f_747_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2393))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2391))
| ~ 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_2391),U_2393))) ),
inference(clausify,[status(thm)],[f_747_3]) ).
cnf(f_747_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2392))
| 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_2392),U_2394))) ),
inference(clausify,[status(thm)],[f_747_3]) ).
cnf(f_747_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2394))
| 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_2392),U_2394))) ),
inference(clausify,[status(thm)],[f_747_3]) ).
fof(f_748_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_748_2,plain,
! [U_2396,U_2395] :
( 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_2395),U_2396)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2396))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2395)) ),
inference(variable_rename,[status(thm)],[f_748_1]) ).
cnf(f_748_3,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_2395),U_2396)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2396))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2395)) ),
inference(clausify,[status(thm)],[f_748_2]) ).
fof(f_749_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_749_2,plain,
! [U_2398,U_2397] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2397),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2397),U_2398)))),
inference(variable_rename,[status(thm)],[f_749_1]) ).
cnf(f_749_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2397),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2397),U_2398)))),
inference(clausify,[status(thm)],[f_749_2]) ).
fof(f_750_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_750_2,plain,
! [U_2400,U_2399] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2399),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2400),U_2399)))),
inference(variable_rename,[status(thm)],[f_750_1]) ).
cnf(f_750_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2399),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2400),U_2399)))),
inference(clausify,[status(thm)],[f_750_2]) ).
fof(f_751_1,plain,
! [V_na_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
| ! [B_k] : V_na_2 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) )
& ( ? [B_k] : V_na_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_na_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__iff__Suc__add]) ).
fof(f_751_2,plain,
! [U_2404,U_2403] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2403),U_2404))
| ! [U_2402] : U_2404 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2403),U_2402)) )
& ( ? [U_2401] : U_2404 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2403),U_2401))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2403),U_2404)) ) ),
inference(variable_rename,[status(thm)],[f_751_1]) ).
fof(f_751_3,plain,
( ! [U_2408,U_2406] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2406),U_2408))
| ! [U_2402] : U_2408 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2406),U_2402)) )
& ! [U_2407,U_2405] :
( ? [U_2401] : U_2407 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2405),U_2401))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2405),U_2407)) ) ),
inference(miniscope,[status(thm)],[f_751_2]) ).
fof(f_751_4,plain,
( ! [U_2408,U_2406] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2406),U_2408))
| ! [U_2402] : U_2408 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2406),U_2402)) )
& ! [U_2407,U_2405] :
( U_2407 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2405),sK29(U_2407,U_2405)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2405),U_2407)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_2401,sK29(U_2407,U_2405))],[f_751_3]) ).
cnf(f_751_5,plain,
( U_2407 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2405),sK29(U_2407,U_2405)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2405),U_2407)) ),
inference(clausify,[status(thm)],[f_751_4]) ).
cnf(f_751_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2406),U_2408))
| U_2408 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2406),U_2402)) ),
inference(clausify,[status(thm)],[f_751_4]) ).
fof(f_752_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_752_2,plain,
! [U_2409] :
( ( 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_2409)),U_2409)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2409),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2409),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_2409)),U_2409)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_752_1]) ).
fof(f_752_3,plain,
( ! [U_2411] :
( 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_2411)),U_2411)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2411),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_2410] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2410),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_2410)),U_2410)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_752_2]) ).
cnf(f_752_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2410),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_2410)),U_2410)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_752_3]) ).
cnf(f_752_5,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_2411)),U_2411)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2411),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_752_3]) ).
fof(f_753_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_753_2,plain,
! [U_2415,U_2414,U_2413,U_2412] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2412),U_2413),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2414),U_2415)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2412),hAPP(hAPP(c_Power_Opower__class_Opower(U_2412),U_2413),U_2414)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2412),U_2413),U_2415))
| ~ class_Groups_Omonoid__mult(U_2412) ),
inference(variable_rename,[status(thm)],[f_753_1]) ).
cnf(f_753_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2412),U_2413),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2414),U_2415)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2412),hAPP(hAPP(c_Power_Opower__class_Opower(U_2412),U_2413),U_2414)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2412),U_2413),U_2415))
| ~ class_Groups_Omonoid__mult(U_2412) ),
inference(clausify,[status(thm)],[f_753_2]) ).
fof(f_754_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_754_2,plain,
! [U_2419,U_2418,U_2417,U_2416] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2416),hAPP(hAPP(c_Power_Opower__class_Opower(U_2416),U_2417),U_2418)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2416),U_2417),U_2419)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2416),U_2417),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2418),U_2419))
| ~ class_Rings_Ocomm__semiring__1(U_2416) ),
inference(variable_rename,[status(thm)],[f_754_1]) ).
cnf(f_754_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2416),hAPP(hAPP(c_Power_Opower__class_Opower(U_2416),U_2417),U_2418)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2416),U_2417),U_2419)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2416),U_2417),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2418),U_2419))
| ~ class_Rings_Ocomm__semiring__1(U_2416) ),
inference(clausify,[status(thm)],[f_754_2]) ).
fof(f_755_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_755_2,plain,
! [U_2423,U_2422,U_2421,U_2420] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2420),U_2422)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2421),U_2423)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2422),U_2423))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2420),U_2421)) ),
inference(variable_rename,[status(thm)],[f_755_1]) ).
cnf(f_755_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2420),U_2422)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2421),U_2423)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2422),U_2423))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2420),U_2421)) ),
inference(clausify,[status(thm)],[f_755_2]) ).
fof(f_756_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_756_2,plain,
! [U_2425,U_2424] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2424),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2425),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2424),U_2425)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2424),U_2425))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2424),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2425),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(variable_rename,[status(thm)],[f_756_1]) ).
fof(f_756_3,plain,
( ! [U_2429,U_2427] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2427),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2429),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2427),U_2429)) )
& ! [U_2428,U_2426] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2426),U_2428))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2426),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2428),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(miniscope,[status(thm)],[f_756_2]) ).
cnf(f_756_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2426),U_2428))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2426),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2428),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_756_3]) ).
cnf(f_756_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2427),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2429),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2427),U_2429)) ),
inference(clausify,[status(thm)],[f_756_3]) ).
fof(f_757_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_757_2,plain,
! [U_2431,U_2430] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2430),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2431))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2430),U_2431)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2430),U_2431))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2430),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2431)) ) ),
inference(variable_rename,[status(thm)],[f_757_1]) ).
fof(f_757_3,plain,
( ! [U_2435,U_2433] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2433),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2435))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2433),U_2435)) )
& ! [U_2434,U_2432] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2432),U_2434))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2432),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2434)) ) ),
inference(miniscope,[status(thm)],[f_757_2]) ).
cnf(f_757_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2432),U_2434))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2432),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2434)) ),
inference(clausify,[status(thm)],[f_757_3]) ).
cnf(f_757_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2433),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2435))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2433),U_2435)) ),
inference(clausify,[status(thm)],[f_757_3]) ).
fof(f_758_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_758_2,plain,
! [U_2437,U_2436] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2436),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2437))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2436),U_2437)) ),
inference(variable_rename,[status(thm)],[f_758_1]) ).
cnf(f_758_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2436),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2437))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2436),U_2437)) ),
inference(clausify,[status(thm)],[f_758_2]) ).
fof(f_759_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_759_2,plain,
! [U_2438] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2438)) = 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_2438)),
inference(variable_rename,[status(thm)],[f_759_1]) ).
cnf(f_759_3,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2438)) = 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_2438)),
inference(clausify,[status(thm)],[f_759_2]) ).
fof(f_760_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_760_2,plain,
! [U_2440,U_2439] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2439),hAPP(c_Nat_OSuc,U_2440)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2439),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2439),U_2440)),
inference(variable_rename,[status(thm)],[f_760_1]) ).
cnf(f_760_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2439),hAPP(c_Nat_OSuc,U_2440)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2439),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2439),U_2440)),
inference(clausify,[status(thm)],[f_760_2]) ).
fof(f_761_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_761_2,plain,
! [U_2442,U_2441] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2441)),U_2442) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2442),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2441),U_2442)),
inference(variable_rename,[status(thm)],[f_761_1]) ).
cnf(f_761_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2441)),U_2442) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2442),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2441),U_2442)),
inference(clausify,[status(thm)],[f_761_2]) ).
fof(f_762_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_762_2,plain,
! [U_2446,U_2445] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2445),U_2446))
| ! [U_2444] : U_2446 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2445),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2444)) )
& ( ? [U_2443] : U_2446 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2445),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2443))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2445),U_2446)) ) ),
inference(variable_rename,[status(thm)],[f_762_1]) ).
fof(f_762_3,plain,
( ! [U_2450,U_2448] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2448),U_2450))
| ! [U_2444] : U_2450 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2448),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2444)) )
& ! [U_2449,U_2447] :
( ? [U_2443] : U_2449 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2447),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2443))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2447),U_2449)) ) ),
inference(miniscope,[status(thm)],[f_762_2]) ).
fof(f_762_4,plain,
( ! [U_2450,U_2448] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2448),U_2450))
| ! [U_2444] : U_2450 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2448),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2444)) )
& ! [U_2449,U_2447] :
( U_2449 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2447),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK30(U_2449,U_2447)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2447),U_2449)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_2443,sK30(U_2449,U_2447))],[f_762_3]) ).
cnf(f_762_5,plain,
( U_2449 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2447),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK30(U_2449,U_2447)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2447),U_2449)) ),
inference(clausify,[status(thm)],[f_762_4]) ).
cnf(f_762_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2448),U_2450))
| U_2450 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2448),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2444)) ),
inference(clausify,[status(thm)],[f_762_4]) ).
fof(f_763_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_763_2,plain,
! [U_2453,U_2452,U_2451] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2451),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2452),U_2453)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2451),U_2452)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2451),U_2453)),
inference(variable_rename,[status(thm)],[f_763_1]) ).
cnf(f_763_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2451),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2452),U_2453)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2451),U_2452)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2451),U_2453)),
inference(clausify,[status(thm)],[f_763_2]) ).
fof(f_764_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_764_2,plain,
! [U_2455,U_2454] :
( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_2454),U_2455) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2454),hAPP(c_Int_Onat,U_2455))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2455),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hAPP(c_Int_Oring__1__class_Oof__int(U_2454),U_2455) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2454),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2454),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2455))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2455),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| ~ class_Rings_Oring__1(U_2454) ),
inference(variable_rename,[status(thm)],[f_764_1]) ).
cnf(f_764_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_2454),U_2455) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2454),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2454),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2455))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2455),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Oring__1(U_2454) ),
inference(clausify,[status(thm)],[f_764_2]) ).
cnf(f_764_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_2454),U_2455) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2454),hAPP(c_Int_Onat,U_2455))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2455),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ class_Rings_Oring__1(U_2454) ),
inference(clausify,[status(thm)],[f_764_2]) ).
fof(f_765_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_765_2,plain,
! [U_2457,U_2456] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2456),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2457)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2456),U_2457)),
inference(variable_rename,[status(thm)],[f_765_1]) ).
cnf(f_765_3,plain,
c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2456),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2457)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2456),U_2457)),
inference(clausify,[status(thm)],[f_765_2]) ).
fof(f_766_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_766_2,plain,
! [U_2460,U_2459,U_2458] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2458),c_Groups_Ozero__class_Ozero(U_2458)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2458),U_2459),U_2460)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2458),c_Groups_Ozero__class_Ozero(U_2458)),U_2460))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2458),c_Groups_Ozero__class_Ozero(U_2458)),U_2459))
| ~ class_Groups_Oordered__comm__monoid__add(U_2458) ),
inference(variable_rename,[status(thm)],[f_766_1]) ).
cnf(f_766_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2458),c_Groups_Ozero__class_Ozero(U_2458)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2458),U_2459),U_2460)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2458),c_Groups_Ozero__class_Ozero(U_2458)),U_2460))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2458),c_Groups_Ozero__class_Ozero(U_2458)),U_2459))
| ~ class_Groups_Oordered__comm__monoid__add(U_2458) ),
inference(clausify,[status(thm)],[f_766_2]) ).
fof(f_767_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_767_2,plain,
! [U_2463,U_2462,U_2461] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2461),c_Groups_Ozero__class_Ozero(U_2461)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2461),U_2462),U_2463)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2461),c_Groups_Ozero__class_Ozero(U_2461)),U_2463))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2461),c_Groups_Ozero__class_Ozero(U_2461)),U_2462))
| ~ class_Groups_Oordered__comm__monoid__add(U_2461) ),
inference(variable_rename,[status(thm)],[f_767_1]) ).
cnf(f_767_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2461),c_Groups_Ozero__class_Ozero(U_2461)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2461),U_2462),U_2463)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2461),c_Groups_Ozero__class_Ozero(U_2461)),U_2463))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2461),c_Groups_Ozero__class_Ozero(U_2461)),U_2462))
| ~ class_Groups_Oordered__comm__monoid__add(U_2461) ),
inference(clausify,[status(thm)],[f_767_2]) ).
fof(f_768_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_768_2,plain,
! [U_2467,U_2466,U_2465,U_2464] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2464),U_2466),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2464),U_2465),U_2467)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2464),U_2466),U_2467))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2464),c_Groups_Ozero__class_Ozero(U_2464)),U_2465))
| ~ class_Groups_Oordered__comm__monoid__add(U_2464) ),
inference(variable_rename,[status(thm)],[f_768_1]) ).
cnf(f_768_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2464),U_2466),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2464),U_2465),U_2467)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2464),U_2466),U_2467))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2464),c_Groups_Ozero__class_Ozero(U_2464)),U_2465))
| ~ class_Groups_Oordered__comm__monoid__add(U_2464) ),
inference(clausify,[status(thm)],[f_768_2]) ).
fof(f_769_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_769_2,plain,
! [U_2471,U_2470,U_2469,U_2468] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2468),U_2470),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2468),U_2469),U_2471)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2468),U_2470),U_2471))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2468),c_Groups_Ozero__class_Ozero(U_2468)),U_2469))
| ~ class_Groups_Oordered__comm__monoid__add(U_2468) ),
inference(variable_rename,[status(thm)],[f_769_1]) ).
cnf(f_769_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2468),U_2470),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2468),U_2469),U_2471)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2468),U_2470),U_2471))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2468),c_Groups_Ozero__class_Ozero(U_2468)),U_2469))
| ~ class_Groups_Oordered__comm__monoid__add(U_2468) ),
inference(clausify,[status(thm)],[f_769_2]) ).
fof(f_770_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_770_2,plain,
! [U_2474,U_2473,U_2472] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2472),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2472),U_2473),U_2474)),c_Groups_Ozero__class_Ozero(U_2472)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2472),U_2474),c_Groups_Ozero__class_Ozero(U_2472)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2472),U_2473),c_Groups_Ozero__class_Ozero(U_2472)))
| ~ class_Groups_Oordered__comm__monoid__add(U_2472) ),
inference(variable_rename,[status(thm)],[f_770_1]) ).
cnf(f_770_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2472),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2472),U_2473),U_2474)),c_Groups_Ozero__class_Ozero(U_2472)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2472),U_2474),c_Groups_Ozero__class_Ozero(U_2472)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2472),U_2473),c_Groups_Ozero__class_Ozero(U_2472)))
| ~ class_Groups_Oordered__comm__monoid__add(U_2472) ),
inference(clausify,[status(thm)],[f_770_2]) ).
fof(f_771_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_771_2,plain,
! [U_2477,U_2476,U_2475] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2475),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2475),U_2476),U_2477)),c_Groups_Ozero__class_Ozero(U_2475)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2475),U_2477),c_Groups_Ozero__class_Ozero(U_2475)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2475),U_2476),c_Groups_Ozero__class_Ozero(U_2475)))
| ~ class_Groups_Oordered__comm__monoid__add(U_2475) ),
inference(variable_rename,[status(thm)],[f_771_1]) ).
cnf(f_771_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2475),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2475),U_2476),U_2477)),c_Groups_Ozero__class_Ozero(U_2475)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2475),U_2477),c_Groups_Ozero__class_Ozero(U_2475)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2475),U_2476),c_Groups_Ozero__class_Ozero(U_2475)))
| ~ class_Groups_Oordered__comm__monoid__add(U_2475) ),
inference(clausify,[status(thm)],[f_771_2]) ).
fof(f_772_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_b)))
| V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_b))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff]) ).
fof(f_772_2,plain,
! [U_2480,U_2479,U_2478] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2478),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2478),U_2479),U_2479)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2478),U_2480),U_2480))),c_Groups_Ozero__class_Ozero(U_2478)))
| U_2480 != c_Groups_Ozero__class_Ozero(U_2478)
| U_2479 != c_Groups_Ozero__class_Ozero(U_2478) )
& ( ( U_2480 = c_Groups_Ozero__class_Ozero(U_2478)
& U_2479 = c_Groups_Ozero__class_Ozero(U_2478) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2478),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2478),U_2479),U_2479)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2478),U_2480),U_2480))),c_Groups_Ozero__class_Ozero(U_2478))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_2478) ),
inference(variable_rename,[status(thm)],[f_772_1]) ).
cnf(f_772_3,plain,
( U_2479 = c_Groups_Ozero__class_Ozero(U_2478)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2478),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2478),U_2479),U_2479)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2478),U_2480),U_2480))),c_Groups_Ozero__class_Ozero(U_2478)))
| ~ class_Rings_Olinordered__ring__strict(U_2478) ),
inference(clausify,[status(thm)],[f_772_2]) ).
cnf(f_772_4,plain,
( U_2480 = c_Groups_Ozero__class_Ozero(U_2478)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2478),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2478),U_2479),U_2479)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2478),U_2480),U_2480))),c_Groups_Ozero__class_Ozero(U_2478)))
| ~ class_Rings_Olinordered__ring__strict(U_2478) ),
inference(clausify,[status(thm)],[f_772_2]) ).
cnf(f_772_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2478),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2478),U_2479),U_2479)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2478),U_2480),U_2480))),c_Groups_Ozero__class_Ozero(U_2478)))
| U_2480 != c_Groups_Ozero__class_Ozero(U_2478)
| U_2479 != c_Groups_Ozero__class_Ozero(U_2478)
| ~ class_Rings_Olinordered__ring__strict(U_2478) ),
inference(clausify,[status(thm)],[f_772_2]) ).
fof(f_773_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_773_2,plain,
! [U_2483,U_2482,U_2481] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2481),c_Groups_Ozero__class_Ozero(U_2481)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2481),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2481),U_2482),U_2482)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2481),U_2483),U_2483))))
| ~ class_Rings_Olinordered__ring(U_2481) ),
inference(variable_rename,[status(thm)],[f_773_1]) ).
cnf(f_773_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2481),c_Groups_Ozero__class_Ozero(U_2481)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2481),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2481),U_2482),U_2482)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2481),U_2483),U_2483))))
| ~ class_Rings_Olinordered__ring(U_2481) ),
inference(clausify,[status(thm)],[f_773_2]) ).
fof(f_774_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))))
| ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
& ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff]) ).
fof(f_774_2,plain,
! [U_2486,U_2485,U_2484] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2484),c_Groups_Ozero__class_Ozero(U_2484)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2484),U_2485),U_2485)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2484),U_2486),U_2486))))
| ( U_2486 = c_Groups_Ozero__class_Ozero(U_2484)
& U_2485 = c_Groups_Ozero__class_Ozero(U_2484) ) )
& ( U_2486 != c_Groups_Ozero__class_Ozero(U_2484)
| U_2485 != c_Groups_Ozero__class_Ozero(U_2484)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2484),c_Groups_Ozero__class_Ozero(U_2484)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2484),U_2485),U_2485)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2484),U_2486),U_2486)))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_2484) ),
inference(variable_rename,[status(thm)],[f_774_1]) ).
cnf(f_774_3,plain,
( U_2486 != c_Groups_Ozero__class_Ozero(U_2484)
| U_2485 != c_Groups_Ozero__class_Ozero(U_2484)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2484),c_Groups_Ozero__class_Ozero(U_2484)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2484),U_2485),U_2485)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2484),U_2486),U_2486))))
| ~ class_Rings_Olinordered__ring__strict(U_2484) ),
inference(clausify,[status(thm)],[f_774_2]) ).
cnf(f_774_4,plain,
( U_2485 = c_Groups_Ozero__class_Ozero(U_2484)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2484),c_Groups_Ozero__class_Ozero(U_2484)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2484),U_2485),U_2485)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2484),U_2486),U_2486))))
| ~ class_Rings_Olinordered__ring__strict(U_2484) ),
inference(clausify,[status(thm)],[f_774_2]) ).
cnf(f_774_5,plain,
( U_2486 = c_Groups_Ozero__class_Ozero(U_2484)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2484),c_Groups_Ozero__class_Ozero(U_2484)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2484),U_2485),U_2485)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2484),U_2486),U_2486))))
| ~ class_Rings_Olinordered__ring__strict(U_2484) ),
inference(clausify,[status(thm)],[f_774_2]) ).
fof(f_775_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_775_2,plain,
! [U_2489,U_2488,U_2487] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2487),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2487),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),U_2488),U_2488)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),U_2489),U_2489))),c_Groups_Ozero__class_Ozero(U_2487)))
| ~ class_Rings_Olinordered__ring(U_2487) ),
inference(variable_rename,[status(thm)],[f_775_1]) ).
cnf(f_775_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2487),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2487),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),U_2488),U_2488)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2487),U_2489),U_2489))),c_Groups_Ozero__class_Ozero(U_2487)))
| ~ class_Rings_Olinordered__ring(U_2487) ),
inference(clausify,[status(thm)],[f_775_2]) ).
fof(f_776_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_776_2,plain,
! [U_2492,U_2491,U_2490] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2490),hAPP(c_Groups_Ouminus__class_Ouminus(U_2490),U_2491)),U_2492) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2490),hAPP(hAPP(c_Power_Opower__class_Opower(U_2490),hAPP(c_Groups_Ouminus__class_Ouminus(U_2490),c_Groups_Oone__class_Oone(U_2490))),U_2492)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2490),U_2491),U_2492))
| ~ class_Rings_Oring__1(U_2490) ),
inference(variable_rename,[status(thm)],[f_776_1]) ).
cnf(f_776_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2490),hAPP(c_Groups_Ouminus__class_Ouminus(U_2490),U_2491)),U_2492) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2490),hAPP(hAPP(c_Power_Opower__class_Opower(U_2490),hAPP(c_Groups_Ouminus__class_Ouminus(U_2490),c_Groups_Oone__class_Oone(U_2490))),U_2492)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2490),U_2491),U_2492))
| ~ class_Rings_Oring__1(U_2490) ),
inference(clausify,[status(thm)],[f_776_2]) ).
fof(f_777_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_777_2,plain,
! [U_2493] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2493),c_Groups_Ozero__class_Ozero(U_2493)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2493),c_Groups_Oone__class_Oone(U_2493)),c_Groups_Oone__class_Oone(U_2493))))
| ~ class_Rings_Olinordered__semidom(U_2493) ),
inference(variable_rename,[status(thm)],[f_777_1]) ).
cnf(f_777_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2493),c_Groups_Ozero__class_Ozero(U_2493)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2493),c_Groups_Oone__class_Oone(U_2493)),c_Groups_Oone__class_Oone(U_2493))))
| ~ class_Rings_Olinordered__semidom(U_2493) ),
inference(clausify,[status(thm)],[f_777_2]) ).
fof(f_778_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_778_2,plain,
! [U_2495,U_2494] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2494),hAPP(c_Nat_OSuc,U_2495))),U_2494))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2494)) ),
inference(variable_rename,[status(thm)],[f_778_1]) ).
cnf(f_778_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2494),hAPP(c_Nat_OSuc,U_2495))),U_2494))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2494)) ),
inference(clausify,[status(thm)],[f_778_2]) ).
fof(f_779_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_779_2,plain,
! [U_2496] :
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2496),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_2496
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2496)) ),
inference(variable_rename,[status(thm)],[f_779_1]) ).
cnf(f_779_3,plain,
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2496),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_2496
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2496)) ),
inference(clausify,[status(thm)],[f_779_2]) ).
fof(f_780_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_780_2,plain,
! [U_2497] :
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2497),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_2497
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2497)) ),
inference(variable_rename,[status(thm)],[f_780_1]) ).
cnf(f_780_3,plain,
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2497),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_2497
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2497)) ),
inference(clausify,[status(thm)],[f_780_2]) ).
fof(f_781_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_781_2,plain,
! [U_2498] :
( U_2498 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2498),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_2498)) ),
inference(variable_rename,[status(thm)],[f_781_1]) ).
cnf(f_781_3,plain,
( U_2498 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2498),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_2498)) ),
inference(clausify,[status(thm)],[f_781_2]) ).
fof(f_782_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_782_2,plain,
! [U_2500,U_2499] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2499),hAPP(c_Nat_OSuc,U_2500)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2499),c_Groups_Oone__class_Oone(U_2499)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2499),U_2500))
| ~ class_Rings_Osemiring__1(U_2499) ),
inference(variable_rename,[status(thm)],[f_782_1]) ).
cnf(f_782_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2499),hAPP(c_Nat_OSuc,U_2500)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2499),c_Groups_Oone__class_Oone(U_2499)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2499),U_2500))
| ~ class_Rings_Osemiring__1(U_2499) ),
inference(clausify,[status(thm)],[f_782_2]) ).
fof(f_783_1,plain,
! [V_m_2,V_na_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_na_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_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_na_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_na_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_783_2,plain,
! [U_2502,U_2501] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2501)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2502))))
| U_2502 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2501 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( U_2502 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2501 = 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_2501)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2502)))) ) ),
inference(variable_rename,[status(thm)],[f_783_1]) ).
fof(f_783_3,plain,
( ! [U_2506,U_2504] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2504)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2506))))
| U_2506 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2504 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2505,U_2503] :
( ( U_2505 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2503 = 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_2503)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2505)))) ) ),
inference(miniscope,[status(thm)],[f_783_2]) ).
cnf(f_783_4,plain,
( U_2503 = 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_2503)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2505)))) ),
inference(clausify,[status(thm)],[f_783_3]) ).
cnf(f_783_5,plain,
( U_2505 = 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_2503)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2505)))) ),
inference(clausify,[status(thm)],[f_783_3]) ).
cnf(f_783_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_2504)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2506))))
| U_2506 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2504 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_783_3]) ).
fof(f_784_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_784_2,plain,
! [U_2507] : 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_2507))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_784_1]) ).
cnf(f_784_3,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_2507))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_784_2]) ).
fof(f_785_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sgn__greater]) ).
fof(f_785_2,plain,
! [U_2509,U_2508] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2508),c_Groups_Ozero__class_Ozero(U_2508)),c_Groups_Osgn__class_Osgn(U_2508,U_2509)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2508),c_Groups_Ozero__class_Ozero(U_2508)),U_2509)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2508),c_Groups_Ozero__class_Ozero(U_2508)),U_2509))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2508),c_Groups_Ozero__class_Ozero(U_2508)),c_Groups_Osgn__class_Osgn(U_2508,U_2509))) ) )
| ~ class_Rings_Olinordered__idom(U_2508) ),
inference(variable_rename,[status(thm)],[f_785_1]) ).
cnf(f_785_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2508),c_Groups_Ozero__class_Ozero(U_2508)),U_2509))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2508),c_Groups_Ozero__class_Ozero(U_2508)),c_Groups_Osgn__class_Osgn(U_2508,U_2509)))
| ~ class_Rings_Olinordered__idom(U_2508) ),
inference(clausify,[status(thm)],[f_785_2]) ).
cnf(f_785_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2508),c_Groups_Ozero__class_Ozero(U_2508)),c_Groups_Osgn__class_Osgn(U_2508,U_2509)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2508),c_Groups_Ozero__class_Ozero(U_2508)),U_2509))
| ~ class_Rings_Olinordered__idom(U_2508) ),
inference(clausify,[status(thm)],[f_785_2]) ).
fof(f_786_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sgn__less]) ).
fof(f_786_2,plain,
! [U_2511,U_2510] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2510),c_Groups_Osgn__class_Osgn(U_2510,U_2511)),c_Groups_Ozero__class_Ozero(U_2510)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2510),U_2511),c_Groups_Ozero__class_Ozero(U_2510))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2510),U_2511),c_Groups_Ozero__class_Ozero(U_2510)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2510),c_Groups_Osgn__class_Osgn(U_2510,U_2511)),c_Groups_Ozero__class_Ozero(U_2510))) ) )
| ~ class_Rings_Olinordered__idom(U_2510) ),
inference(variable_rename,[status(thm)],[f_786_1]) ).
cnf(f_786_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2510),U_2511),c_Groups_Ozero__class_Ozero(U_2510)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2510),c_Groups_Osgn__class_Osgn(U_2510,U_2511)),c_Groups_Ozero__class_Ozero(U_2510)))
| ~ class_Rings_Olinordered__idom(U_2510) ),
inference(clausify,[status(thm)],[f_786_2]) ).
cnf(f_786_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2510),c_Groups_Osgn__class_Osgn(U_2510,U_2511)),c_Groups_Ozero__class_Ozero(U_2510)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2510),U_2511),c_Groups_Ozero__class_Ozero(U_2510)))
| ~ class_Rings_Olinordered__idom(U_2510) ),
inference(clausify,[status(thm)],[f_786_2]) ).
fof(f_787_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_787_2,plain,
! [U_2512] : 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_2512))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_787_1]) ).
cnf(f_787_3,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_2512))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_787_2]) ).
fof(f_788_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_788_2,plain,
! [U_2513] :
( 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_2513)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2513)) ),
inference(variable_rename,[status(thm)],[f_788_1]) ).
cnf(f_788_3,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_2513)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2513)) ),
inference(clausify,[status(thm)],[f_788_2]) ).
fof(f_789_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_789_2,plain,
! [U_2517,U_2516] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2516),U_2517))
| ! [U_2515] : U_2517 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2516),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2515))) )
& ( ? [U_2514] : U_2517 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2516),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2514)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2516),U_2517)) ) ),
inference(variable_rename,[status(thm)],[f_789_1]) ).
fof(f_789_3,plain,
( ! [U_2521,U_2519] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2519),U_2521))
| ! [U_2515] : U_2521 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2519),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2515))) )
& ! [U_2520,U_2518] :
( ? [U_2514] : U_2520 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2518),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2514)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2518),U_2520)) ) ),
inference(miniscope,[status(thm)],[f_789_2]) ).
fof(f_789_4,plain,
( ! [U_2521,U_2519] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2519),U_2521))
| ! [U_2515] : U_2521 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2519),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2515))) )
& ! [U_2520,U_2518] :
( U_2520 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2518),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK31(U_2520,U_2518))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2518),U_2520)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_2514,sK31(U_2520,U_2518))],[f_789_3]) ).
cnf(f_789_5,plain,
( U_2520 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2518),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK31(U_2520,U_2518))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2518),U_2520)) ),
inference(clausify,[status(thm)],[f_789_4]) ).
cnf(f_789_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2519),U_2521))
| U_2521 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2519),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2515))) ),
inference(clausify,[status(thm)],[f_789_4]) ).
fof(f_790_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_790_2,plain,
! [U_2523,U_2522] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2523),U_2522) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2523),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2523),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2522),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_2522 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2523),U_2522) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2522 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_790_1]) ).
fof(f_790_3,plain,
( ! [U_2527,U_2525] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2527),U_2525) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2527),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2527),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2525),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_2525 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2526,U_2524] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2526),U_2524) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2524 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_790_2]) ).
cnf(f_790_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2526),U_2524) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_2524 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_790_3]) ).
cnf(f_790_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2527),U_2525) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2527),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2527),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2525),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_2525 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_790_3]) ).
fof(f_791_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_791_2,plain,
! [U_2533,U_2532,U_2531,U_2530,U_2529,U_2528] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2528),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2528),U_2532),U_2529)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2528),U_2533),U_2531))),U_2530))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2528),U_2532),U_2533) != c_Groups_Oone__class_Oone(U_2528)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),c_Groups_Ozero__class_Ozero(U_2528)),U_2533))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),c_Groups_Ozero__class_Ozero(U_2528)),U_2532))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),U_2531),U_2530))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),U_2529),U_2530))
| ~ class_Rings_Olinordered__semiring__1(U_2528) ),
inference(variable_rename,[status(thm)],[f_791_1]) ).
cnf(f_791_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2528),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2528),U_2532),U_2529)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2528),U_2533),U_2531))),U_2530))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2528),U_2532),U_2533) != c_Groups_Oone__class_Oone(U_2528)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),c_Groups_Ozero__class_Ozero(U_2528)),U_2533))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),c_Groups_Ozero__class_Ozero(U_2528)),U_2532))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),U_2531),U_2530))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2528),U_2529),U_2530))
| ~ class_Rings_Olinordered__semiring__1(U_2528) ),
inference(clausify,[status(thm)],[f_791_2]) ).
fof(f_792_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_792_2,plain,
! [U_2534] : ~ 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_2534))))),
inference(variable_rename,[status(thm)],[f_792_1]) ).
cnf(f_792_3,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_2534))))),
inference(clausify,[status(thm)],[f_792_2]) ).
fof(f_793_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_793_2,plain,
! [U_2537,U_2536,U_2535] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2537),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_2536))
| U_2535 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2536),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2535),U_2537))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2535)) ),
inference(variable_rename,[status(thm)],[f_793_1]) ).
cnf(f_793_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2537),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_2536))
| U_2535 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2536),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2535),U_2537))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2535)) ),
inference(clausify,[status(thm)],[f_793_2]) ).
fof(f_794_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_794_2,plain,
! [U_2540,U_2539,U_2538] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2540))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2539),U_2538))
| U_2538 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2539),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2538),U_2540))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2538)) ),
inference(variable_rename,[status(thm)],[f_794_1]) ).
cnf(f_794_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2540))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2539),U_2538))
| U_2538 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2539),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2538),U_2540))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2538)) ),
inference(clausify,[status(thm)],[f_794_2]) ).
fof(f_795_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_795_2,plain,
! [U_2543,U_2542,U_2541] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2542))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2541))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2543),U_2541))
| ~ 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_2541),U_2542)),U_2543))) ),
inference(variable_rename,[status(thm)],[f_795_1]) ).
cnf(f_795_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2542))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2541))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2543),U_2541))
| ~ 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_2541),U_2542)),U_2543))) ),
inference(clausify,[status(thm)],[f_795_2]) ).
fof(f_796_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_796_2,plain,
! [U_2546,U_2545,U_2544] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2545),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_2544))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2546))
| ~ 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_2544),U_2545)),U_2546)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_796_1]) ).
cnf(f_796_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2545),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_2544))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2546))
| ~ 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_2544),U_2545)),U_2546)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_796_2]) ).
fof(f_797_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_797_2,plain,
! [U_2551,U_2550,U_2549,U_2548,U_2547] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2548),U_2550))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2551),U_2547))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2549),U_2547))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2549))
| ~ 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_2547),U_2548)),U_2549)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2547),U_2550)),U_2551))) ),
inference(variable_rename,[status(thm)],[f_797_1]) ).
cnf(f_797_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2548),U_2550))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2551),U_2547))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2549),U_2547))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2549))
| ~ 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_2547),U_2548)),U_2549)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2547),U_2550)),U_2551))) ),
inference(clausify,[status(thm)],[f_797_2]) ).
fof(f_798_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_798_2,plain,
! [U_2557,U_2556,U_2555,U_2554,U_2553,U_2552] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2553),U_2556))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2555),U_2552))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2555))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2554))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2557),U_2555))
| ~ 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_2555),U_2556)),U_2557)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2552),U_2553)),U_2554) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2555),U_2556)),U_2557) ),
inference(variable_rename,[status(thm)],[f_798_1]) ).
cnf(f_798_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2553),U_2556))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2555),U_2552))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2555))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2554))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2557),U_2555))
| ~ 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_2555),U_2556)),U_2557)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2552),U_2553)),U_2554) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2555),U_2556)),U_2557) ),
inference(clausify,[status(thm)],[f_798_2]) ).
fof(f_799_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_799_2,plain,
! [U_2562,U_2561,U_2560,U_2559,U_2558] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2561),U_2559))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2558),U_2560))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2558),U_2562))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2562),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_2558),U_2559)),U_2560)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2558),U_2561)),U_2562))) ),
inference(variable_rename,[status(thm)],[f_799_1]) ).
cnf(f_799_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2561),U_2559))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2558),U_2560))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2558),U_2562))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2562),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_2558),U_2559)),U_2560)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2558),U_2561)),U_2562))) ),
inference(clausify,[status(thm)],[f_799_2]) ).
fof(f_800_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_800_2,plain,
! [U_2568,U_2567,U_2566,U_2565,U_2564,U_2563] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2567),U_2564))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2566),U_2563))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2566))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2568))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2565),U_2563))
| ~ 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_2566),U_2567)),U_2568)),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_2563),U_2564)),U_2565) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2566),U_2567)),U_2568) ),
inference(variable_rename,[status(thm)],[f_800_1]) ).
cnf(f_800_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2567),U_2564))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2566),U_2563))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2566))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2568))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2565),U_2563))
| ~ 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_2566),U_2567)),U_2568)),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_2563),U_2564)),U_2565) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2566),U_2567)),U_2568) ),
inference(clausify,[status(thm)],[f_800_2]) ).
fof(f_801_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_801_2,plain,
! [U_2570,U_2569] : c_Int_Onat__aux(U_2569,U_2570) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2569)),U_2570),
inference(variable_rename,[status(thm)],[f_801_1]) ).
cnf(f_801_3,plain,
c_Int_Onat__aux(U_2569,U_2570) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2569)),U_2570),
inference(clausify,[status(thm)],[f_801_2]) ).
fof(f_802_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2))) ) )
| ~ class_Lattices_Oboolean__algebra(T_b) ),
inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff]) ).
fof(f_802_2,plain,
! [U_2573,U_2572,U_2571] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2571),hAPP(c_Groups_Ouminus__class_Ouminus(U_2571),U_2572)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2571),U_2573)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2571),U_2573),U_2572)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2571),U_2573),U_2572))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2571),hAPP(c_Groups_Ouminus__class_Ouminus(U_2571),U_2572)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2571),U_2573))) ) )
| ~ class_Lattices_Oboolean__algebra(U_2571) ),
inference(variable_rename,[status(thm)],[f_802_1]) ).
cnf(f_802_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2571),U_2573),U_2572))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2571),hAPP(c_Groups_Ouminus__class_Ouminus(U_2571),U_2572)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2571),U_2573)))
| ~ class_Lattices_Oboolean__algebra(U_2571) ),
inference(clausify,[status(thm)],[f_802_2]) ).
cnf(f_802_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2571),hAPP(c_Groups_Ouminus__class_Ouminus(U_2571),U_2572)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2571),U_2573)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2571),U_2573),U_2572))
| ~ class_Lattices_Oboolean__algebra(U_2571) ),
inference(clausify,[status(thm)],[f_802_2]) ).
fof(f_803_1,plain,
! [V_na_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_na_2),V_k_2)
| V_m_2 != V_na_2 )
& ( V_m_2 = V_na_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_na_2),V_k_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel]) ).
fof(f_803_2,plain,
! [U_2576,U_2575,U_2574] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2574),U_2575) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2576),U_2575)
| U_2574 != U_2576 )
& ( U_2574 = U_2576
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2574),U_2575) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2576),U_2575) ) ),
inference(variable_rename,[status(thm)],[f_803_1]) ).
fof(f_803_3,plain,
( ! [U_2582,U_2580,U_2578] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2578),U_2580) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2582),U_2580)
| U_2578 != U_2582 )
& ! [U_2581,U_2579,U_2577] :
( U_2577 = U_2581
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2577),U_2579) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2581),U_2579) ) ),
inference(miniscope,[status(thm)],[f_803_2]) ).
cnf(f_803_4,plain,
( U_2577 = U_2581
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2577),U_2579) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2581),U_2579) ),
inference(clausify,[status(thm)],[f_803_3]) ).
cnf(f_803_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2578),U_2580) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2582),U_2580)
| U_2578 != U_2582 ),
inference(clausify,[status(thm)],[f_803_3]) ).
fof(f_804_1,plain,
! [V_na_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_na_2)
| V_m_2 != V_na_2 )
& ( V_m_2 = V_na_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_na_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel]) ).
fof(f_804_2,plain,
! [U_2585,U_2584,U_2583] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2583),U_2584) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2583),U_2585)
| U_2584 != U_2585 )
& ( U_2584 = U_2585
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2583),U_2584) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2583),U_2585) ) ),
inference(variable_rename,[status(thm)],[f_804_1]) ).
fof(f_804_3,plain,
( ! [U_2591,U_2589] :
( ! [U_2587] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2587),U_2589) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2587),U_2591)
| U_2589 != U_2591 )
& ! [U_2590,U_2588] :
( ! [U_2586] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2586),U_2588) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2586),U_2590)
| U_2588 = U_2590 ) ),
inference(miniscope,[status(thm)],[f_804_2]) ).
cnf(f_804_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2586),U_2588) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2586),U_2590)
| U_2588 = U_2590 ),
inference(clausify,[status(thm)],[f_804_3]) ).
cnf(f_804_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2587),U_2589) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2587),U_2591)
| U_2589 != U_2591 ),
inference(clausify,[status(thm)],[f_804_3]) ).
fof(f_805_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_805_2,plain,
! [U_2594,U_2593,U_2592] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2592),U_2593)),U_2594) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2592),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2593),U_2594)),
inference(variable_rename,[status(thm)],[f_805_1]) ).
cnf(f_805_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2592),U_2593)),U_2594) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2592),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2593),U_2594)),
inference(clausify,[status(thm)],[f_805_2]) ).
fof(f_806_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_806_2,plain,
! [U_2597,U_2596,U_2595] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2595),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2596),U_2597)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2596),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2595),U_2597)),
inference(variable_rename,[status(thm)],[f_806_1]) ).
cnf(f_806_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2595),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2596),U_2597)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2596),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2595),U_2597)),
inference(clausify,[status(thm)],[f_806_2]) ).
fof(f_807_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_807_2,plain,
! [U_2599,U_2598] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2598),U_2599) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2599),U_2598),
inference(variable_rename,[status(thm)],[f_807_1]) ).
cnf(f_807_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2598),U_2599) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2599),U_2598),
inference(clausify,[status(thm)],[f_807_2]) ).
fof(f_808_1,plain,
! [V_B_2,V_A_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Compl__subset__Compl__iff]) ).
fof(f_808_2,plain,
! [U_2602,U_2601,U_2600] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2600,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2600,tc_HOL_Obool)),U_2601)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2600,tc_HOL_Obool)),U_2602)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2600,tc_HOL_Obool)),U_2602),U_2601)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2600,tc_HOL_Obool)),U_2602),U_2601))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2600,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2600,tc_HOL_Obool)),U_2601)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2600,tc_HOL_Obool)),U_2602))) ) ),
inference(variable_rename,[status(thm)],[f_808_1]) ).
fof(f_808_3,plain,
( ! [U_2608,U_2606,U_2604] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2604,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2604,tc_HOL_Obool)),U_2606)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2604,tc_HOL_Obool)),U_2608)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2604,tc_HOL_Obool)),U_2608),U_2606)) )
& ! [U_2607,U_2605,U_2603] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2603,tc_HOL_Obool)),U_2607),U_2605))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2603,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2603,tc_HOL_Obool)),U_2605)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2603,tc_HOL_Obool)),U_2607))) ) ),
inference(miniscope,[status(thm)],[f_808_2]) ).
cnf(f_808_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2603,tc_HOL_Obool)),U_2607),U_2605))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2603,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2603,tc_HOL_Obool)),U_2605)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2603,tc_HOL_Obool)),U_2607))) ),
inference(clausify,[status(thm)],[f_808_3]) ).
cnf(f_808_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2604,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2604,tc_HOL_Obool)),U_2606)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2604,tc_HOL_Obool)),U_2608)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2604,tc_HOL_Obool)),U_2608),U_2606)) ),
inference(clausify,[status(thm)],[f_808_3]) ).
fof(f_809_1,plain,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Compl__anti__mono]) ).
fof(f_809_2,plain,
! [U_2611,U_2610,U_2609] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2609,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2609,tc_HOL_Obool)),U_2611)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2609,tc_HOL_Obool)),U_2610)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2609,tc_HOL_Obool)),U_2610),U_2611)) ),
inference(variable_rename,[status(thm)],[f_809_1]) ).
cnf(f_809_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2609,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2609,tc_HOL_Obool)),U_2611)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2609,tc_HOL_Obool)),U_2610)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2609,tc_HOL_Obool)),U_2610),U_2611)) ),
inference(clausify,[status(thm)],[f_809_2]) ).
fof(f_810_1,plain,
! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Diff__subset]) ).
fof(f_810_2,plain,
! [U_2614,U_2613,U_2612] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2612,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2612,tc_HOL_Obool)),U_2613),U_2614)),U_2613)),
inference(variable_rename,[status(thm)],[f_810_1]) ).
cnf(f_810_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2612,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2612,tc_HOL_Obool)),U_2613),U_2614)),U_2613)),
inference(clausify,[status(thm)],[f_810_2]) ).
fof(f_811_1,plain,
! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Diff__mono]) ).
fof(f_811_2,plain,
! [U_2619,U_2618,U_2617,U_2616,U_2615] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2615,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2615,tc_HOL_Obool)),U_2616),U_2619)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2615,tc_HOL_Obool)),U_2617),U_2618)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2615,tc_HOL_Obool)),U_2618),U_2619))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2615,tc_HOL_Obool)),U_2616),U_2617)) ),
inference(variable_rename,[status(thm)],[f_811_1]) ).
cnf(f_811_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2615,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2615,tc_HOL_Obool)),U_2616),U_2619)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2615,tc_HOL_Obool)),U_2617),U_2618)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2615,tc_HOL_Obool)),U_2618),U_2619))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2615,tc_HOL_Obool)),U_2616),U_2617)) ),
inference(clausify,[status(thm)],[f_811_2]) ).
fof(f_812_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_double__diff]) ).
fof(f_812_2,plain,
! [U_2623,U_2622,U_2621,U_2620] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2620,tc_HOL_Obool)),U_2622),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2620,tc_HOL_Obool)),U_2623),U_2621)) = U_2621
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2620,tc_HOL_Obool)),U_2622),U_2623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2620,tc_HOL_Obool)),U_2621),U_2622)) ),
inference(variable_rename,[status(thm)],[f_812_1]) ).
cnf(f_812_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2620,tc_HOL_Obool)),U_2622),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2620,tc_HOL_Obool)),U_2623),U_2621)) = U_2621
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2620,tc_HOL_Obool)),U_2622),U_2623))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2620,tc_HOL_Obool)),U_2621),U_2622)) ),
inference(clausify,[status(thm)],[f_812_2]) ).
fof(f_813_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_813_2,plain,
! [U_2626,U_2625,U_2624] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2624),U_2625)),U_2626) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2624),U_2626)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2625),U_2626)),
inference(variable_rename,[status(thm)],[f_813_1]) ).
cnf(f_813_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2624),U_2625)),U_2626) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2624),U_2626)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2625),U_2626)),
inference(clausify,[status(thm)],[f_813_2]) ).
fof(f_814_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_814_2,plain,
! [U_2629,U_2628,U_2627] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2627),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2628),U_2629)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2627),U_2628)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2627),U_2629)),
inference(variable_rename,[status(thm)],[f_814_1]) ).
cnf(f_814_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2627),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2628),U_2629)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2627),U_2628)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2627),U_2629)),
inference(clausify,[status(thm)],[f_814_2]) ).
fof(f_815_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_815_2,plain,
! [U_2631,U_2630] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2630),U_2631))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2630),U_2631)),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_2630),U_2631)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2630),U_2631)) ) ),
inference(variable_rename,[status(thm)],[f_815_1]) ).
fof(f_815_3,plain,
( ! [U_2635,U_2633] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2633),U_2635))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2633),U_2635)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_2634,U_2632] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2632),U_2634)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2632),U_2634)) ) ),
inference(miniscope,[status(thm)],[f_815_2]) ).
cnf(f_815_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2632),U_2634)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2632),U_2634)) ),
inference(clausify,[status(thm)],[f_815_3]) ).
cnf(f_815_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2633),U_2635))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2633),U_2635)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_815_3]) ).
fof(f_816_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_816_2,plain,
! [U_2637,U_2636] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2636),U_2637) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2636),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2637)),
inference(variable_rename,[status(thm)],[f_816_1]) ).
cnf(f_816_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2636),U_2637) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2636),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2637)),
inference(clausify,[status(thm)],[f_816_2]) ).
fof(f_817_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_817_2,plain,
! [U_2639,U_2638] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2638),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2639)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2638),U_2639),
inference(variable_rename,[status(thm)],[f_817_1]) ).
cnf(f_817_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2638),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2639)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2638),U_2639),
inference(clausify,[status(thm)],[f_817_2]) ).
fof(f_818_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_818_2,plain,
! [U_2640] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2640) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2640)),
inference(variable_rename,[status(thm)],[f_818_1]) ).
cnf(f_818_3,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2640) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2640)),
inference(clausify,[status(thm)],[f_818_2]) ).
fof(f_819_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_819_2,plain,
! [U_2641] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2641)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2641),
inference(variable_rename,[status(thm)],[f_819_1]) ).
cnf(f_819_3,plain,
hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2641)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2641),
inference(clausify,[status(thm)],[f_819_2]) ).
fof(f_820_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_820_2,plain,
! [U_2643,U_2642] :
( c_Nat__Transfer_Otsub(U_2643,U_2642) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2643),U_2642)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2642),U_2643)) ),
inference(variable_rename,[status(thm)],[f_820_1]) ).
cnf(f_820_3,plain,
( c_Nat__Transfer_Otsub(U_2643,U_2642) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2643),U_2642)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2642),U_2643)) ),
inference(clausify,[status(thm)],[f_820_2]) ).
fof(f_821_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_821_2,plain,
! [U_2645,U_2644] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2644),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2645),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2644),U_2645)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2644),U_2645))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2644),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2645),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(variable_rename,[status(thm)],[f_821_1]) ).
fof(f_821_3,plain,
( ! [U_2649,U_2647] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2647),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2649),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2647),U_2649)) )
& ! [U_2648,U_2646] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2646),U_2648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2646),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2648),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(miniscope,[status(thm)],[f_821_2]) ).
cnf(f_821_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2646),U_2648))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2646),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2648),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(clausify,[status(thm)],[f_821_3]) ).
cnf(f_821_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2647),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2649),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2647),U_2649)) ),
inference(clausify,[status(thm)],[f_821_3]) ).
fof(f_822_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_822_2,plain,
! [U_2651,U_2650] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2651)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2650)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2651),U_2650))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2650),U_2651)) ),
inference(variable_rename,[status(thm)],[f_822_1]) ).
cnf(f_822_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2651)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2650)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2651),U_2650))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2650),U_2651)) ),
inference(clausify,[status(thm)],[f_822_2]) ).
fof(f_823_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_823_2,plain,
! [U_2653,U_2652] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2652)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2653)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2652),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2653))),
inference(variable_rename,[status(thm)],[f_823_1]) ).
cnf(f_823_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2652)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2653)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2652),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2653))),
inference(clausify,[status(thm)],[f_823_2]) ).
fof(f_824_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_824_2,plain,
! [U_2656,U_2655,U_2654] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2654),U_2655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2654),U_2655),U_2656)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2654),U_2655),U_2656)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2654) ),
inference(variable_rename,[status(thm)],[f_824_1]) ).
cnf(f_824_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2654),U_2655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2654),U_2655),U_2656)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2654),U_2655),U_2656)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2654) ),
inference(clausify,[status(thm)],[f_824_2]) ).
fof(f_825_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_825_2,plain,
! [U_2658,U_2657] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2657),U_2658),U_2658) = U_2658
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2657) ),
inference(variable_rename,[status(thm)],[f_825_1]) ).
cnf(f_825_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2657),U_2658),U_2658) = U_2658
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2657) ),
inference(clausify,[status(thm)],[f_825_2]) ).
fof(f_826_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_826_2,plain,
! [U_2660,U_2659] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2659),U_2660),U_2660) = U_2660
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2659) ),
inference(variable_rename,[status(thm)],[f_826_1]) ).
cnf(f_826_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2659),U_2660),U_2660) = U_2660
| ~ class_Lattices_Oab__semigroup__idem__mult(U_2659) ),
inference(clausify,[status(thm)],[f_826_2]) ).
fof(f_827_1,plain,
! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2))
| ~ class_Groups_Ominus(T_b) ),
inference(fof_nnf,[status(thm)],[fact_minus__apply]) ).
fof(f_827_2,plain,
! [U_2665,U_2664,U_2663,U_2662,U_2661] :
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2662,U_2661)),U_2663),U_2664),U_2665) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2661),hAPP(U_2663,U_2665)),hAPP(U_2664,U_2665))
| ~ class_Groups_Ominus(U_2661) ),
inference(variable_rename,[status(thm)],[f_827_1]) ).
cnf(f_827_3,plain,
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2662,U_2661)),U_2663),U_2664),U_2665) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2661),hAPP(U_2663,U_2665)),hAPP(U_2664,U_2665))
| ~ class_Groups_Ominus(U_2661) ),
inference(clausify,[status(thm)],[f_827_2]) ).
fof(f_828_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2) ) )
| ~ class_Lattices_Oboolean__algebra(T_b) ),
inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff]) ).
fof(f_828_2,plain,
! [U_2668,U_2667,U_2666] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2666),U_2667) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2666),U_2668)
| U_2667 != U_2668 )
& ( U_2667 = U_2668
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2666),U_2667) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2666),U_2668) ) )
| ~ class_Lattices_Oboolean__algebra(U_2666) ),
inference(variable_rename,[status(thm)],[f_828_1]) ).
cnf(f_828_3,plain,
( U_2667 = U_2668
| hAPP(c_Groups_Ouminus__class_Ouminus(U_2666),U_2667) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2666),U_2668)
| ~ class_Lattices_Oboolean__algebra(U_2666) ),
inference(clausify,[status(thm)],[f_828_2]) ).
cnf(f_828_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2666),U_2667) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2666),U_2668)
| U_2667 != U_2668
| ~ class_Lattices_Oboolean__algebra(U_2666) ),
inference(clausify,[status(thm)],[f_828_2]) ).
fof(f_829_1,plain,
! [V_x_2,V_A_2,T_c,T_b] :
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2))
| ~ class_Groups_Ouminus(T_b) ),
inference(fof_nnf,[status(thm)],[fact_uminus__apply]) ).
fof(f_829_2,plain,
! [U_2672,U_2671,U_2670,U_2669] :
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2670,U_2669)),U_2671),U_2672) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2669),hAPP(U_2671,U_2672))
| ~ class_Groups_Ouminus(U_2669) ),
inference(variable_rename,[status(thm)],[f_829_1]) ).
cnf(f_829_3,plain,
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2670,U_2669)),U_2671),U_2672) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2669),hAPP(U_2671,U_2672))
| ~ class_Groups_Ouminus(U_2669) ),
inference(clausify,[status(thm)],[f_829_2]) ).
fof(f_830_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_830_2,plain,
! [U_2674,U_2673] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2673),hAPP(c_Groups_Ouminus__class_Ouminus(U_2673),U_2674)) = U_2674
| ~ class_Lattices_Oboolean__algebra(U_2673) ),
inference(variable_rename,[status(thm)],[f_830_1]) ).
cnf(f_830_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_2673),hAPP(c_Groups_Ouminus__class_Ouminus(U_2673),U_2674)) = U_2674
| ~ class_Lattices_Oboolean__algebra(U_2673) ),
inference(clausify,[status(thm)],[f_830_2]) ).
fof(f_831_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_831_2,plain,
! [U_2676,U_2675] :
( ( c_Nat__Transfer_Otsub(U_2676,U_2675) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2675),U_2676)) )
& ( c_Nat__Transfer_Otsub(U_2676,U_2675) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2676),U_2675)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2675),U_2676)) ) ),
inference(variable_rename,[status(thm)],[f_831_1]) ).
fof(f_831_3,plain,
( ! [U_2680,U_2678] :
( c_Nat__Transfer_Otsub(U_2680,U_2678) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2678),U_2680)) )
& ! [U_2679,U_2677] :
( c_Nat__Transfer_Otsub(U_2679,U_2677) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2679),U_2677)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2677),U_2679)) ) ),
inference(miniscope,[status(thm)],[f_831_2]) ).
cnf(f_831_4,plain,
( c_Nat__Transfer_Otsub(U_2679,U_2677) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2679),U_2677)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2677),U_2679)) ),
inference(clausify,[status(thm)],[f_831_3]) ).
cnf(f_831_5,plain,
( c_Nat__Transfer_Otsub(U_2680,U_2678) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2678),U_2680)) ),
inference(clausify,[status(thm)],[f_831_3]) ).
fof(f_832_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_832_2,plain,
! [U_2682,U_2681] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2682),U_2681)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2682)),hAPP(c_Int_Onat,U_2681))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2681),U_2682))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2681)) ),
inference(variable_rename,[status(thm)],[f_832_1]) ).
cnf(f_832_3,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2682),U_2681)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2682)),hAPP(c_Int_Onat,U_2681))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2681),U_2682))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2681)) ),
inference(clausify,[status(thm)],[f_832_2]) ).
fof(f_833_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_833_2,plain,
! [U_2683] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2683) = 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_2683)),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_2683))) ),
inference(variable_rename,[status(thm)],[f_833_1]) ).
cnf(f_833_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2683) = 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_2683)),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_2683))) ),
inference(clausify,[status(thm)],[f_833_2]) ).
fof(f_834_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_834_2,plain,
! [U_2686,U_2685,U_2684] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2684),hAPP(c_Groups_Ouminus__class_Ouminus(U_2684),U_2686)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2684),U_2685)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2684),U_2685),U_2686))
| ~ class_Lattices_Oboolean__algebra(U_2684) ),
inference(variable_rename,[status(thm)],[f_834_1]) ).
cnf(f_834_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2684),hAPP(c_Groups_Ouminus__class_Ouminus(U_2684),U_2686)),hAPP(c_Groups_Ouminus__class_Ouminus(U_2684),U_2685)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2684),U_2685),U_2686))
| ~ class_Lattices_Oboolean__algebra(U_2684) ),
inference(clausify,[status(thm)],[f_834_2]) ).
fof(f_835_1,plain,
! [V_y_2,V_x_2,V_P_2] :
( ( hBOOL(hAPP(V_P_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_P_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_P_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_P_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_P_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_P_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_835_2,plain,
! [U_2689,U_2688,U_2687] :
( ( hBOOL(hAPP(U_2687,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2688),U_2689))))
| ( ~ hBOOL(hAPP(U_2687,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2688),U_2689)) )
| ( ~ hBOOL(hAPP(U_2687,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2688)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2689))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2689),U_2688)) ) )
& ( ( ( hBOOL(hAPP(U_2687,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2688),U_2689)) )
& ( hBOOL(hAPP(U_2687,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2688)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2689))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2689),U_2688)) ) )
| ~ hBOOL(hAPP(U_2687,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2688),U_2689)))) ) ),
inference(variable_rename,[status(thm)],[f_835_1]) ).
fof(f_835_3,plain,
( ! [U_2695,U_2693,U_2691] :
( hBOOL(hAPP(U_2691,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2693),U_2695))))
| ( ~ hBOOL(hAPP(U_2691,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2693),U_2695)) )
| ( ~ hBOOL(hAPP(U_2691,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2693)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2695))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2695),U_2693)) ) )
& ! [U_2694,U_2692,U_2690] :
( ( ( hBOOL(hAPP(U_2690,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2692),U_2694)) )
& ( hBOOL(hAPP(U_2690,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2692)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2694))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2694),U_2692)) ) )
| ~ hBOOL(hAPP(U_2690,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2692),U_2694)))) ) ),
inference(miniscope,[status(thm)],[f_835_2]) ).
cnf(f_835_4,plain,
( hBOOL(hAPP(U_2690,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2692)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2694))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2694),U_2692))
| ~ hBOOL(hAPP(U_2690,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2692),U_2694)))) ),
inference(clausify,[status(thm)],[f_835_3]) ).
cnf(f_835_5,plain,
( hBOOL(hAPP(U_2690,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2692),U_2694))
| ~ hBOOL(hAPP(U_2690,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2692),U_2694)))) ),
inference(clausify,[status(thm)],[f_835_3]) ).
cnf(f_835_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2693),U_2695))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2695),U_2693))
| hBOOL(hAPP(U_2691,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2693),U_2695)))) ),
inference(clausify,[status(thm)],[f_835_3]) ).
cnf(f_835_7,plain,
( ~ hBOOL(hAPP(U_2691,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2695),U_2693))
| hBOOL(hAPP(U_2691,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2693),U_2695)))) ),
inference(clausify,[status(thm)],[f_835_3]) ).
cnf(f_835_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2693),U_2695))
| ~ hBOOL(hAPP(U_2691,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2693)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2695))))
| hBOOL(hAPP(U_2691,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2693),U_2695)))) ),
inference(clausify,[status(thm)],[f_835_3]) ).
cnf(f_835_9,plain,
( ~ hBOOL(hAPP(U_2691,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_2691,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2693)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2695))))
| hBOOL(hAPP(U_2691,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2693),U_2695)))) ),
inference(clausify,[status(thm)],[f_835_3]) ).
fof(f_836_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_836_2,plain,
! [U_2697,U_2696] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2696)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2697)) = 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_2696)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2697)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2696))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2696)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2697)) = 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_2697))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2696))) ) ),
inference(variable_rename,[status(thm)],[f_836_1]) ).
fof(f_836_3,plain,
( ! [U_2701,U_2699] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2699)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2701)) = 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_2699)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2701)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2699))) )
& ! [U_2700,U_2698] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2698)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2700)) = 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_2700))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2698))) ) ),
inference(miniscope,[status(thm)],[f_836_2]) ).
cnf(f_836_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2698)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2700)) = 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_2700))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2698))) ),
inference(clausify,[status(thm)],[f_836_3]) ).
cnf(f_836_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2699)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2701)) = 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_2699)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2701)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2699))) ),
inference(clausify,[status(thm)],[f_836_3]) ).
fof(f_837_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_837_2,plain,
! [U_2703,U_2702] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2702)),U_2703) = 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_2702)),U_2703))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2702))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2702)),U_2703) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2703)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2702))) ) ),
inference(variable_rename,[status(thm)],[f_837_1]) ).
fof(f_837_3,plain,
( ! [U_2707,U_2705] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2705)),U_2707) = 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_2705)),U_2707))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2705))) )
& ! [U_2706,U_2704] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2704)),U_2706) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2706)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2704))) ) ),
inference(miniscope,[status(thm)],[f_837_2]) ).
cnf(f_837_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2704)),U_2706) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2706)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2704))) ),
inference(clausify,[status(thm)],[f_837_3]) ).
cnf(f_837_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2705)),U_2707) = 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_2705)),U_2707))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2705))) ),
inference(clausify,[status(thm)],[f_837_3]) ).
fof(f_838_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_838_2,plain,
! [U_2709,U_2708] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2709),U_2708)),U_2709) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2709),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2708),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_2709))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2708)) ),
inference(variable_rename,[status(thm)],[f_838_1]) ).
cnf(f_838_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2709),U_2708)),U_2709) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2709),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_2708),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_2709))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2708)) ),
inference(clausify,[status(thm)],[f_838_2]) ).
fof(f_839_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_839_2,plain,
! [U_2711] :
( ? [U_2710] : U_2711 = 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_2710)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2711),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_839_1]) ).
fof(f_839_3,plain,
! [U_2711] :
( U_2711 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK32(U_2711))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2711),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_2710,sK32(U_2711))],[f_839_2]) ).
cnf(f_839_4,plain,
( U_2711 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK32(U_2711))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2711),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_839_3]) ).
fof(f_840_1,plain,
! [V_na_2,V_P_2] :
( ? [B_k] :
( hBOOL(hAPP(V_P_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_P_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_na_2)) )
| ~ hBOOL(hAPP(V_P_2,V_na_2))
| hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(fof_nnf,[status(thm)],[fact_ex__least__nat__less]) ).
fof(f_840_2,plain,
! [U_2715,U_2714] :
( ? [U_2713] :
( hBOOL(hAPP(U_2714,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2713),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [U_2712] :
( ~ hBOOL(hAPP(U_2714,U_2712))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2712),U_2713)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2713),U_2715)) )
| ~ hBOOL(hAPP(U_2714,U_2715))
| hBOOL(hAPP(U_2714,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[f_840_1]) ).
fof(f_840_3,plain,
! [U_2715,U_2714] :
( ( hBOOL(hAPP(U_2714,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK33(U_2715,U_2714)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [U_2712] :
( ~ hBOOL(hAPP(U_2714,U_2712))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2712),sK33(U_2715,U_2714))) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK33(U_2715,U_2714)),U_2715)) )
| ~ hBOOL(hAPP(U_2714,U_2715))
| hBOOL(hAPP(U_2714,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_2713,sK33(U_2715,U_2714))],[f_840_2]) ).
cnf(f_840_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK33(U_2715,U_2714)),U_2715))
| ~ hBOOL(hAPP(U_2714,U_2715))
| hBOOL(hAPP(U_2714,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_840_3]) ).
cnf(f_840_5,plain,
( ~ hBOOL(hAPP(U_2714,U_2712))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2712),sK33(U_2715,U_2714)))
| ~ hBOOL(hAPP(U_2714,U_2715))
| hBOOL(hAPP(U_2714,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_840_3]) ).
cnf(f_840_6,plain,
( hBOOL(hAPP(U_2714,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK33(U_2715,U_2714)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(U_2714,U_2715))
| hBOOL(hAPP(U_2714,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_840_3]) ).
fof(f_841_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_841_2,plain,
! [U_2717,U_2716] :
( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2716),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2717)) = hAPP(c_Int_Onumber__class_Onumber__of(U_2716),U_2717)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2717))) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2716),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2717)) = c_Groups_Ozero__class_Ozero(U_2716)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2717))) ) )
| ~ class_Int_Onumber__ring(U_2716) ),
inference(variable_rename,[status(thm)],[f_841_1]) ).
cnf(f_841_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2716),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2717)) = c_Groups_Ozero__class_Ozero(U_2716)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2717)))
| ~ class_Int_Onumber__ring(U_2716) ),
inference(clausify,[status(thm)],[f_841_2]) ).
cnf(f_841_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2716),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2717)) = hAPP(c_Int_Onumber__class_Onumber__of(U_2716),U_2717)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2717)))
| ~ class_Int_Onumber__ring(U_2716) ),
inference(clausify,[status(thm)],[f_841_2]) ).
fof(f_842_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
| ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) )
& ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2))))
| hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) ) )
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__number__of__eq]) ).
fof(f_842_2,plain,
! [U_2720,U_2719,U_2718] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_2718),U_2719) = hAPP(c_Int_Onumber__class_Onumber__of(U_2718),U_2720)
| ~ c_Int_Oiszero(U_2718,hAPP(c_Int_Onumber__class_Onumber__of(U_2718),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2719),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2720)))) )
& ( c_Int_Oiszero(U_2718,hAPP(c_Int_Onumber__class_Onumber__of(U_2718),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2719),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2720))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_2718),U_2719) != hAPP(c_Int_Onumber__class_Onumber__of(U_2718),U_2720) ) )
| ~ class_Int_Onumber__ring(U_2718) ),
inference(variable_rename,[status(thm)],[f_842_1]) ).
cnf(f_842_3,plain,
( c_Int_Oiszero(U_2718,hAPP(c_Int_Onumber__class_Onumber__of(U_2718),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2719),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2720))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_2718),U_2719) != hAPP(c_Int_Onumber__class_Onumber__of(U_2718),U_2720)
| ~ class_Int_Onumber__ring(U_2718) ),
inference(clausify,[status(thm)],[f_842_2]) ).
cnf(f_842_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_2718),U_2719) = hAPP(c_Int_Onumber__class_Onumber__of(U_2718),U_2720)
| ~ c_Int_Oiszero(U_2718,hAPP(c_Int_Onumber__class_Onumber__of(U_2718),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2719),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2720))))
| ~ class_Int_Onumber__ring(U_2718) ),
inference(clausify,[status(thm)],[f_842_2]) ).
fof(f_843_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
inference(fof_nnf,[status(thm)],[fact_Diff__idemp]) ).
fof(f_843_2,plain,
! [U_2723,U_2722,U_2721] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2721,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2721,tc_HOL_Obool)),U_2722),U_2723)),U_2723) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2721,tc_HOL_Obool)),U_2722),U_2723),
inference(variable_rename,[status(thm)],[f_843_1]) ).
cnf(f_843_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2721,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2721,tc_HOL_Obool)),U_2722),U_2723)),U_2723) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2721,tc_HOL_Obool)),U_2722),U_2723),
inference(clausify,[status(thm)],[f_843_2]) ).
fof(f_844_1,plain,
! [V_B_2,V_A_2,T_b] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)
| V_A_2 != V_B_2 )
& ( V_A_2 = V_B_2
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Compl__eq__Compl__iff]) ).
fof(f_844_2,plain,
! [U_2726,U_2725,U_2724] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2724,tc_HOL_Obool)),U_2725) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2724,tc_HOL_Obool)),U_2726)
| U_2725 != U_2726 )
& ( U_2725 = U_2726
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2724,tc_HOL_Obool)),U_2725) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2724,tc_HOL_Obool)),U_2726) ) ),
inference(variable_rename,[status(thm)],[f_844_1]) ).
fof(f_844_3,plain,
( ! [U_2732,U_2730] :
( ! [U_2728] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2728,tc_HOL_Obool)),U_2730) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2728,tc_HOL_Obool)),U_2732)
| U_2730 != U_2732 )
& ! [U_2731,U_2729] :
( ! [U_2727] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2727,tc_HOL_Obool)),U_2729) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2727,tc_HOL_Obool)),U_2731)
| U_2729 = U_2731 ) ),
inference(miniscope,[status(thm)],[f_844_2]) ).
cnf(f_844_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2727,tc_HOL_Obool)),U_2729) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2727,tc_HOL_Obool)),U_2731)
| U_2729 = U_2731 ),
inference(clausify,[status(thm)],[f_844_3]) ).
cnf(f_844_5,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2728,tc_HOL_Obool)),U_2730) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2728,tc_HOL_Obool)),U_2732)
| U_2730 != U_2732 ),
inference(clausify,[status(thm)],[f_844_3]) ).
fof(f_845_1,plain,
! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_double__complement]) ).
fof(f_845_2,plain,
! [U_2734,U_2733] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2733,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2733,tc_HOL_Obool)),U_2734)) = U_2734,
inference(variable_rename,[status(thm)],[f_845_1]) ).
cnf(f_845_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2733,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2733,tc_HOL_Obool)),U_2734)) = U_2734,
inference(clausify,[status(thm)],[f_845_2]) ).
fof(f_846_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_846_2,plain,
! [U_2735] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2735) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_846_1]) ).
cnf(f_846_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2735) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_846_2]) ).
fof(f_847_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_847_2,plain,
! [U_2737,U_2736] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2736),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2737)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2736)),U_2737),
inference(variable_rename,[status(thm)],[f_847_1]) ).
cnf(f_847_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2736),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2737)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2736)),U_2737),
inference(clausify,[status(thm)],[f_847_2]) ).
fof(f_848_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_848_2,plain,
! [U_2739,U_2738] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2738)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2739)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2738),U_2739),
inference(variable_rename,[status(thm)],[f_848_1]) ).
cnf(f_848_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2738)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2739)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2738),U_2739),
inference(clausify,[status(thm)],[f_848_2]) ).
fof(f_849_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_849_2,plain,
! [U_2741,U_2740] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2740),c_Groups_Ozero__class_Ozero(U_2740)),U_2741) = c_Groups_Ozero__class_Ozero(U_2740)
| ~ class_Divides_Osemiring__div(U_2740) ),
inference(variable_rename,[status(thm)],[f_849_1]) ).
cnf(f_849_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2740),c_Groups_Ozero__class_Ozero(U_2740)),U_2741) = c_Groups_Ozero__class_Ozero(U_2740)
| ~ class_Divides_Osemiring__div(U_2740) ),
inference(clausify,[status(thm)],[f_849_2]) ).
fof(f_850_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_850_2,plain,
! [U_2743,U_2742] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2742),U_2743),c_Groups_Ozero__class_Ozero(U_2742)) = c_Groups_Ozero__class_Ozero(U_2742)
| ~ class_Divides_Osemiring__div(U_2742) ),
inference(variable_rename,[status(thm)],[f_850_1]) ).
cnf(f_850_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2742),U_2743),c_Groups_Ozero__class_Ozero(U_2742)) = c_Groups_Ozero__class_Ozero(U_2742)
| ~ class_Divides_Osemiring__div(U_2742) ),
inference(clausify,[status(thm)],[f_850_2]) ).
fof(f_851_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_851_2,plain,
! [U_2745,U_2744] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2744),U_2745),c_Groups_Oone__class_Oone(U_2744)) = U_2745
| ~ class_Divides_Osemiring__div(U_2744) ),
inference(variable_rename,[status(thm)],[f_851_1]) ).
cnf(f_851_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2744),U_2745),c_Groups_Oone__class_Oone(U_2744)) = U_2745
| ~ class_Divides_Osemiring__div(U_2744) ),
inference(clausify,[status(thm)],[f_851_2]) ).
fof(f_852_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]) ).
cnf(f_852_2,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_852_1]) ).
fof(f_853_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_853_2,plain,
! [U_2746] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2746))),
inference(variable_rename,[status(thm)],[f_853_1]) ).
cnf(f_853_3,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2746))),
inference(clausify,[status(thm)],[f_853_2]) ).
fof(f_854_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]) ).
cnf(f_854_2,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_854_1]) ).
fof(f_855_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_855_2,plain,
! [U_2747] :
( c_Int_Oiszero(U_2747,c_Groups_Ozero__class_Ozero(U_2747))
| ~ class_Rings_Osemiring__1(U_2747) ),
inference(variable_rename,[status(thm)],[f_855_1]) ).
cnf(f_855_3,plain,
( c_Int_Oiszero(U_2747,c_Groups_Ozero__class_Ozero(U_2747))
| ~ class_Rings_Osemiring__1(U_2747) ),
inference(clausify,[status(thm)],[f_855_2]) ).
fof(f_856_1,plain,
! [V_z_2,T_b] :
( ( ( c_Int_Oiszero(T_b,V_z_2)
| V_z_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_z_2 = c_Groups_Ozero__class_Ozero(T_b)
| ~ c_Int_Oiszero(T_b,V_z_2) ) )
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_iszero__def]) ).
fof(f_856_2,plain,
! [U_2749,U_2748] :
( ( ( c_Int_Oiszero(U_2748,U_2749)
| U_2749 != c_Groups_Ozero__class_Ozero(U_2748) )
& ( U_2749 = c_Groups_Ozero__class_Ozero(U_2748)
| ~ c_Int_Oiszero(U_2748,U_2749) ) )
| ~ class_Rings_Osemiring__1(U_2748) ),
inference(variable_rename,[status(thm)],[f_856_1]) ).
cnf(f_856_3,plain,
( U_2749 = c_Groups_Ozero__class_Ozero(U_2748)
| ~ c_Int_Oiszero(U_2748,U_2749)
| ~ class_Rings_Osemiring__1(U_2748) ),
inference(clausify,[status(thm)],[f_856_2]) ).
cnf(f_856_4,plain,
( c_Int_Oiszero(U_2748,U_2749)
| U_2749 != c_Groups_Ozero__class_Ozero(U_2748)
| ~ class_Rings_Osemiring__1(U_2748) ),
inference(clausify,[status(thm)],[f_856_2]) ).
fof(f_857_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_857_2,plain,
! [U_2751,U_2750] :
( 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_2750),U_2751)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2751))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2750)) ),
inference(variable_rename,[status(thm)],[f_857_1]) ).
cnf(f_857_3,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_2750),U_2751)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2751))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2750)) ),
inference(clausify,[status(thm)],[f_857_2]) ).
fof(f_858_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_858_2,plain,
! [U_2752] :
( ~ c_Int_Oiszero(U_2752,c_Groups_Oone__class_Oone(U_2752))
| ~ class_Rings_Osemiring__1(U_2752) ),
inference(variable_rename,[status(thm)],[f_858_1]) ).
cnf(f_858_3,plain,
( ~ c_Int_Oiszero(U_2752,c_Groups_Oone__class_Oone(U_2752))
| ~ class_Rings_Osemiring__1(U_2752) ),
inference(clausify,[status(thm)],[f_858_2]) ).
fof(f_859_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_859_2,plain,
! [U_2754,U_2753] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2754),U_2753)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2754),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2754),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_2754),U_2753)),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_2753)) ),
inference(variable_rename,[status(thm)],[f_859_1]) ).
cnf(f_859_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2754),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_2754),U_2753)),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_2753)) ),
inference(clausify,[status(thm)],[f_859_2]) ).
cnf(f_859_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2754),U_2753)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2754),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_2753)) ),
inference(clausify,[status(thm)],[f_859_2]) ).
fof(f_860_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_860_2,plain,
! [U_2756,U_2755] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2756),U_2755)),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_2756)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2756))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2756),U_2755)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2755),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_860_1]) ).
cnf(f_860_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2756))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2756),U_2755)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2755),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_860_2]) ).
cnf(f_860_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2756),U_2755)),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_2756))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2755),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_860_2]) ).
fof(f_861_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_861_2,plain,
! [U_2758,U_2757] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2757),U_2758)),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_2758))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2757),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_861_1]) ).
cnf(f_861_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2757),U_2758)),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_2758))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2757),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_861_2]) ).
fof(f_862_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_862_2,plain,
! [U_2759] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2759),U_2759) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2759 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_862_1]) ).
cnf(f_862_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2759),U_2759) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2759 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_862_2]) ).
fof(f_863_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_863_2,plain,
! [U_2763,U_2762,U_2761,U_2760] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2760),U_2761),U_2762)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2760),U_2761),U_2763)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2760),U_2762),U_2763)
| U_2761 = c_Groups_Ozero__class_Ozero(U_2760)
| ~ class_Divides_Osemiring__div(U_2760) ),
inference(variable_rename,[status(thm)],[f_863_1]) ).
cnf(f_863_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2760),U_2761),U_2762)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2760),U_2761),U_2763)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2760),U_2762),U_2763)
| U_2761 = c_Groups_Ozero__class_Ozero(U_2760)
| ~ class_Divides_Osemiring__div(U_2760) ),
inference(clausify,[status(thm)],[f_863_2]) ).
fof(f_864_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_864_2,plain,
! [U_2767,U_2766,U_2765,U_2764] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2764),U_2766),U_2765)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2764),U_2767),U_2765)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2764),U_2766),U_2767)
| U_2765 = c_Groups_Ozero__class_Ozero(U_2764)
| ~ class_Divides_Osemiring__div(U_2764) ),
inference(variable_rename,[status(thm)],[f_864_1]) ).
cnf(f_864_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2764),U_2766),U_2765)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2764),U_2767),U_2765)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2764),U_2766),U_2767)
| U_2765 = c_Groups_Ozero__class_Ozero(U_2764)
| ~ class_Divides_Osemiring__div(U_2764) ),
inference(clausify,[status(thm)],[f_864_2]) ).
fof(f_865_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_865_2,plain,
! [U_2770,U_2769,U_2768] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2768),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2768),U_2769),U_2770)),U_2769) = U_2770
| U_2769 = c_Groups_Ozero__class_Ozero(U_2768)
| ~ class_Divides_Osemiring__div(U_2768) ),
inference(variable_rename,[status(thm)],[f_865_1]) ).
cnf(f_865_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2768),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2768),U_2769),U_2770)),U_2769) = U_2770
| U_2769 = c_Groups_Ozero__class_Ozero(U_2768)
| ~ class_Divides_Osemiring__div(U_2768) ),
inference(clausify,[status(thm)],[f_865_2]) ).
fof(f_866_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_866_2,plain,
! [U_2773,U_2772,U_2771] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2771),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2771),U_2773),U_2772)),U_2772) = U_2773
| U_2772 = c_Groups_Ozero__class_Ozero(U_2771)
| ~ class_Divides_Osemiring__div(U_2771) ),
inference(variable_rename,[status(thm)],[f_866_1]) ).
cnf(f_866_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2771),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2771),U_2773),U_2772)),U_2772) = U_2773
| U_2772 = c_Groups_Ozero__class_Ozero(U_2771)
| ~ class_Divides_Osemiring__div(U_2771) ),
inference(clausify,[status(thm)],[f_866_2]) ).
fof(f_867_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_867_2,plain,
! [U_2777,U_2776,U_2775,U_2774] :
( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2774),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2774),U_2775),U_2776)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2774),U_2775),U_2777)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2774),U_2776),U_2777)
| U_2775 = c_Groups_Ozero__class_Ozero(U_2774) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2774),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2774),U_2775),U_2776)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2774),U_2775),U_2777)) = c_Groups_Ozero__class_Ozero(U_2774)
| U_2775 != c_Groups_Ozero__class_Ozero(U_2774) ) )
| ~ class_Divides_Osemiring__div(U_2774) ),
inference(variable_rename,[status(thm)],[f_867_1]) ).
cnf(f_867_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2774),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2774),U_2775),U_2776)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2774),U_2775),U_2777)) = c_Groups_Ozero__class_Ozero(U_2774)
| U_2775 != c_Groups_Ozero__class_Ozero(U_2774)
| ~ class_Divides_Osemiring__div(U_2774) ),
inference(clausify,[status(thm)],[f_867_2]) ).
cnf(f_867_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2774),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2774),U_2775),U_2776)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2774),U_2775),U_2777)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2774),U_2776),U_2777)
| U_2775 = c_Groups_Ozero__class_Ozero(U_2774)
| ~ class_Divides_Osemiring__div(U_2774) ),
inference(clausify,[status(thm)],[f_867_2]) ).
fof(f_868_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_868_2,plain,
! [U_2779,U_2778] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2778),U_2779),U_2779) = c_Groups_Oone__class_Oone(U_2778)
| U_2779 = c_Groups_Ozero__class_Ozero(U_2778)
| ~ class_Divides_Osemiring__div(U_2778) ),
inference(variable_rename,[status(thm)],[f_868_1]) ).
cnf(f_868_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2778),U_2779),U_2779) = c_Groups_Oone__class_Oone(U_2778)
| U_2779 = c_Groups_Ozero__class_Ozero(U_2778)
| ~ class_Divides_Osemiring__div(U_2778) ),
inference(clausify,[status(thm)],[f_868_2]) ).
fof(f_869_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_869_2,plain,
! [U_2780] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_2780))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2780)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2780))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_2780)) ) ),
inference(variable_rename,[status(thm)],[f_869_1]) ).
fof(f_869_3,plain,
( ! [U_2782] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_2782))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2782)) )
& ! [U_2781] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2781))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_2781)) ) ),
inference(miniscope,[status(thm)],[f_869_2]) ).
cnf(f_869_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2781))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_2781)) ),
inference(clausify,[status(thm)],[f_869_3]) ).
cnf(f_869_5,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_2782))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2782)) ),
inference(clausify,[status(thm)],[f_869_3]) ).
fof(f_870_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_870_2,plain,
! [U_2783] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_2783))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2783),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2783),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_2783)) ) ),
inference(variable_rename,[status(thm)],[f_870_1]) ).
fof(f_870_3,plain,
( ! [U_2785] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_2785))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2785),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_2784] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2784),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_2784)) ) ),
inference(miniscope,[status(thm)],[f_870_2]) ).
cnf(f_870_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2784),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_2784)) ),
inference(clausify,[status(thm)],[f_870_3]) ).
cnf(f_870_5,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_2785))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2785),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_870_3]) ).
fof(f_871_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_871_2,plain,
! [U_2786] :
( hAPP(c_Int_Onat,U_2786) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_2786)) ),
inference(variable_rename,[status(thm)],[f_871_1]) ).
cnf(f_871_3,plain,
( hAPP(c_Int_Onat,U_2786) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_2786)) ),
inference(clausify,[status(thm)],[f_871_2]) ).
fof(f_872_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_872_2,plain,
! [U_2787] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2787)) = U_2787
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_2787)) ),
inference(variable_rename,[status(thm)],[f_872_1]) ).
cnf(f_872_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_2787)) = U_2787
| hBOOL(hAPP(c_Nat__Numeral_Oneg,U_2787)) ),
inference(clausify,[status(thm)],[f_872_2]) ).
fof(f_873_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_873_2,plain,
! [U_2789,U_2788] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2788),U_2789) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2789),U_2788))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2788),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2788),U_2789))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2788)) )
& U_2789 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2789),U_2788))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2788),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2788),U_2789))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2788)) )
| U_2789 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2788),U_2789) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_873_1]) ).
fof(f_873_3,plain,
( ! [U_2793,U_2791] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2791),U_2793) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2793),U_2791))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2791),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2791),U_2793))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2791)) )
& U_2793 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_2792,U_2790] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2792),U_2790))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2790),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2790),U_2792))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2790)) )
| U_2792 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2790),U_2792) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_873_2]) ).
cnf(f_873_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2790),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_2790))
| U_2792 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2790),U_2792) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_873_3]) ).
cnf(f_873_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2792),U_2790))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2790))
| U_2792 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2790),U_2792) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_873_3]) ).
cnf(f_873_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2790),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2790),U_2792))
| U_2792 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2790),U_2792) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_873_3]) ).
cnf(f_873_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2792),U_2790))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2790),U_2792))
| U_2792 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2790),U_2792) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_873_3]) ).
cnf(f_873_8,plain,
( U_2793 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2791),U_2793) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_873_3]) ).
cnf(f_873_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2791),U_2793))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2791))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2791),U_2793) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_873_3]) ).
cnf(f_873_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2793),U_2791))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2791),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2791),U_2793) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_873_3]) ).
fof(f_874_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_874_2,plain,
! [U_2795,U_2794] :
( ( ( 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_2795),U_2794)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2795)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2795))
| ~ 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_2795),U_2794))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2794)) ),
inference(variable_rename,[status(thm)],[f_874_1]) ).
cnf(f_874_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2795))
| ~ 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_2795),U_2794)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2794)) ),
inference(clausify,[status(thm)],[f_874_2]) ).
cnf(f_874_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_2795),U_2794)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2795))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2794)) ),
inference(clausify,[status(thm)],[f_874_2]) ).
fof(f_875_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_875_2,plain,
! [U_2797,U_2796] :
( ( ( 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_2797),U_2796)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2796),U_2797)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2796),U_2797))
| ~ 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_2797),U_2796))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2796)) ),
inference(variable_rename,[status(thm)],[f_875_1]) ).
cnf(f_875_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2796),U_2797))
| ~ 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_2797),U_2796)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2796)) ),
inference(clausify,[status(thm)],[f_875_2]) ).
cnf(f_875_4,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_2797),U_2796)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2796),U_2797))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2796)) ),
inference(clausify,[status(thm)],[f_875_2]) ).
fof(f_876_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_876_2,plain,
! [U_2799,U_2798] :
( ( ( 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_2798),U_2799)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2799))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2799),U_2798)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2799))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2799),U_2798)) )
| ~ 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_2798),U_2799))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2798)) ),
inference(variable_rename,[status(thm)],[f_876_1]) ).
cnf(f_876_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2799),U_2798))
| ~ 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_2798),U_2799)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2798)) ),
inference(clausify,[status(thm)],[f_876_2]) ).
cnf(f_876_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2799))
| ~ 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_2798),U_2799)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2798)) ),
inference(clausify,[status(thm)],[f_876_2]) ).
cnf(f_876_5,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_2798),U_2799)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2799))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2799),U_2798))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2798)) ),
inference(clausify,[status(thm)],[f_876_2]) ).
fof(f_877_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_877_2,plain,
! [U_2802,U_2801,U_2800] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2800),U_2802)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2800),U_2801)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2801),U_2802))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2801))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2800)) ),
inference(variable_rename,[status(thm)],[f_877_1]) ).
cnf(f_877_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2800),U_2802)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2800),U_2801)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2801),U_2802))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2801))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2800)) ),
inference(clausify,[status(thm)],[f_877_2]) ).
fof(f_878_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_878_2,plain,
! [U_2804,U_2803] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2803),U_2804)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2804),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_2803)) ),
inference(variable_rename,[status(thm)],[f_878_1]) ).
cnf(f_878_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2803),U_2804)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2804),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_2803)) ),
inference(clausify,[status(thm)],[f_878_2]) ).
fof(f_879_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_879_2,plain,
! [U_2806,U_2805] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2805),U_2806) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2805),U_2806))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2805)) ),
inference(variable_rename,[status(thm)],[f_879_1]) ).
cnf(f_879_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2805),U_2806) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2805),U_2806))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2805)) ),
inference(clausify,[status(thm)],[f_879_2]) ).
fof(f_880_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_880_2,plain,
! [U_2808,U_2807] :
( ( ( 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_2808),U_2807)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2808),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2808),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_2808),U_2807))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2807),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_880_1]) ).
cnf(f_880_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2808),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_2808),U_2807)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2807),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_880_2]) ).
cnf(f_880_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_2808),U_2807)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2808),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2807),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_880_2]) ).
fof(f_881_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_881_2,plain,
! [U_2810,U_2809] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2809),U_2810)),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_2810))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2809),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_881_1]) ).
cnf(f_881_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2809),U_2810)),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_2810))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2809),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_881_2]) ).
fof(f_882_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_882_2,plain,
! [U_2813,U_2812,U_2811] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2811),U_2812)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2811),U_2813)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2812),U_2813))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2812))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2811),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_882_1]) ).
cnf(f_882_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2811),U_2812)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2811),U_2813)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2812),U_2813))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2812))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2811),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_882_2]) ).
fof(f_883_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_883_2,plain,
! [U_2815,U_2814] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2814),U_2815) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2815),U_2814))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2814),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_883_1]) ).
cnf(f_883_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2814),U_2815) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2815),U_2814))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2814),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_883_2]) ).
fof(f_884_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_884_2,plain,
! [U_2818,U_2817,U_2816] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2816),U_2818)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2817),U_2818)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2818))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2816),U_2817)) ),
inference(variable_rename,[status(thm)],[f_884_1]) ).
cnf(f_884_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2816),U_2818)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2817),U_2818)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2818))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2816),U_2817)) ),
inference(clausify,[status(thm)],[f_884_2]) ).
fof(f_885_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_885_2,plain,
! [U_2821,U_2820,U_2819] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2820),U_2821)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2819),U_2821)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2821),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2819),U_2820)) ),
inference(variable_rename,[status(thm)],[f_885_1]) ).
cnf(f_885_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2820),U_2821)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2819),U_2821)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2821),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2819),U_2820)) ),
inference(clausify,[status(thm)],[f_885_2]) ).
fof(f_886_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_886_2,plain,
! [U_2823,U_2822] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2822),U_2823)),U_2822))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2823))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2822)) ),
inference(variable_rename,[status(thm)],[f_886_1]) ).
cnf(f_886_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2822),U_2823)),U_2822))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2823))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2822)) ),
inference(clausify,[status(thm)],[f_886_2]) ).
fof(f_887_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_887_2,plain,
! [U_2826,U_2825,U_2824] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2826),U_2824)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2825),U_2826)),U_2824)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2824)) ),
inference(variable_rename,[status(thm)],[f_887_1]) ).
cnf(f_887_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2826),U_2824)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2825),U_2826)),U_2824)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2824)) ),
inference(clausify,[status(thm)],[f_887_2]) ).
fof(f_888_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_888_2,plain,
! [U_2830,U_2829,U_2828,U_2827] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2827),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2827),U_2829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2827),U_2830),U_2828))),U_2828) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2827),U_2830),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2827),U_2829),U_2828))
| U_2828 = c_Groups_Ozero__class_Ozero(U_2827)
| ~ class_Divides_Osemiring__div(U_2827) ),
inference(variable_rename,[status(thm)],[f_888_1]) ).
cnf(f_888_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2827),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2827),U_2829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2827),U_2830),U_2828))),U_2828) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2827),U_2830),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2827),U_2829),U_2828))
| U_2828 = c_Groups_Ozero__class_Ozero(U_2827)
| ~ class_Divides_Osemiring__div(U_2827) ),
inference(clausify,[status(thm)],[f_888_2]) ).
fof(f_889_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_889_2,plain,
! [U_2834,U_2833,U_2832,U_2831] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2831),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2831),U_2833),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2831),U_2832),U_2834))),U_2832) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2831),U_2834),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2831),U_2833),U_2832))
| U_2832 = c_Groups_Ozero__class_Ozero(U_2831)
| ~ class_Divides_Osemiring__div(U_2831) ),
inference(variable_rename,[status(thm)],[f_889_1]) ).
cnf(f_889_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2831),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2831),U_2833),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2831),U_2832),U_2834))),U_2832) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2831),U_2834),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2831),U_2833),U_2832))
| U_2832 = c_Groups_Ozero__class_Ozero(U_2831)
| ~ class_Divides_Osemiring__div(U_2831) ),
inference(clausify,[status(thm)],[f_889_2]) ).
fof(f_890_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_890_2,plain,
! [U_2837,U_2836,U_2835] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2835),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2835),U_2836),U_2837)),U_2836) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2835),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2835),U_2837),U_2836)),c_Groups_Oone__class_Oone(U_2835))
| U_2836 = c_Groups_Ozero__class_Ozero(U_2835)
| ~ class_Divides_Osemiring__div(U_2835) ),
inference(variable_rename,[status(thm)],[f_890_1]) ).
cnf(f_890_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2835),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2835),U_2836),U_2837)),U_2836) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2835),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2835),U_2837),U_2836)),c_Groups_Oone__class_Oone(U_2835))
| U_2836 = c_Groups_Ozero__class_Ozero(U_2835)
| ~ class_Divides_Osemiring__div(U_2835) ),
inference(clausify,[status(thm)],[f_890_2]) ).
fof(f_891_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_891_2,plain,
! [U_2840,U_2839,U_2838] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2838),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2838),U_2840),U_2839)),U_2839) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2838),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2838),U_2840),U_2839)),c_Groups_Oone__class_Oone(U_2838))
| U_2839 = c_Groups_Ozero__class_Ozero(U_2838)
| ~ class_Divides_Osemiring__div(U_2838) ),
inference(variable_rename,[status(thm)],[f_891_1]) ).
cnf(f_891_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2838),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2838),U_2840),U_2839)),U_2839) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2838),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_2838),U_2840),U_2839)),c_Groups_Oone__class_Oone(U_2838))
| U_2839 = c_Groups_Ozero__class_Ozero(U_2838)
| ~ class_Divides_Osemiring__div(U_2838) ),
inference(clausify,[status(thm)],[f_891_2]) ).
fof(f_892_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_892_2,plain,
! [U_2841] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2841) = 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_2841))) ),
inference(variable_rename,[status(thm)],[f_892_1]) ).
cnf(f_892_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2841) = 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_2841))) ),
inference(clausify,[status(thm)],[f_892_2]) ).
fof(f_893_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_893_2,plain,
! [U_2842] : 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_2842))))),
inference(variable_rename,[status(thm)],[f_893_1]) ).
cnf(f_893_3,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_2842))))),
inference(clausify,[status(thm)],[f_893_2]) ).
fof(f_894_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_894_2,plain,
! [U_2844,U_2843] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2843) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2844)
| ( ( ( U_2843 != U_2844
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2844))) )
| ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2843) != 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_2844))) ) )
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2843))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2844)),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_2843))) ) )
& ( ( ( ( ( U_2843 = U_2844
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2844))) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2843) = 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_2844))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2843))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2844)),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_2843))) ) )
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2843) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2844) ) ),
inference(variable_rename,[status(thm)],[f_894_1]) ).
fof(f_894_3,plain,
( ! [U_2848,U_2846] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2846) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2848)
| ( ( ( U_2846 != U_2848
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2848))) )
| ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2846) != 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_2848))) ) )
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2846))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2848)),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_2846))) ) )
& ! [U_2847,U_2845] :
( ( ( ( ( U_2845 = U_2847
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2847))) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2845) = 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_2847))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2845))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2847)),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_2845))) ) )
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2845) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2847) ) ),
inference(miniscope,[status(thm)],[f_894_2]) ).
cnf(f_894_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2847)),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_2845)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2845) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2847) ),
inference(clausify,[status(thm)],[f_894_3]) ).
cnf(f_894_5,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2845) = 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_2847)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2845)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2845) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2847) ),
inference(clausify,[status(thm)],[f_894_3]) ).
cnf(f_894_6,plain,
( U_2845 = U_2847
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2847)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2845)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2845) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2847) ),
inference(clausify,[status(thm)],[f_894_3]) ).
cnf(f_894_7,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2846)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2846)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2846) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2848) ),
inference(clausify,[status(thm)],[f_894_3]) ).
cnf(f_894_8,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2848)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2848)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2846)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2846) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2848) ),
inference(clausify,[status(thm)],[f_894_3]) ).
cnf(f_894_9,plain,
( U_2846 != U_2848
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2848)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2846)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2846) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2848) ),
inference(clausify,[status(thm)],[f_894_3]) ).
cnf(f_894_10,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2848)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2846) != 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_2846)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2846) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2848) ),
inference(clausify,[status(thm)],[f_894_3]) ).
cnf(f_894_11,plain,
( U_2846 != U_2848
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2846) != 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_2846)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2846) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2848) ),
inference(clausify,[status(thm)],[f_894_3]) ).
cnf(f_894_12,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2846)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2848)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2846) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2848) ),
inference(clausify,[status(thm)],[f_894_3]) ).
cnf(f_894_13,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2848)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2848)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2848)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2846) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2848) ),
inference(clausify,[status(thm)],[f_894_3]) ).
cnf(f_894_14,plain,
( U_2846 != U_2848
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2848)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2848)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2846) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2848) ),
inference(clausify,[status(thm)],[f_894_3]) ).
cnf(f_894_15,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2848)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2846) != c_Groups_Ozero__class_Ozero(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),U_2848)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2846) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2848) ),
inference(clausify,[status(thm)],[f_894_3]) ).
cnf(f_894_16,plain,
( U_2846 != U_2848
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2846) != c_Groups_Ozero__class_Ozero(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),U_2848)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2846) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2848) ),
inference(clausify,[status(thm)],[f_894_3]) ).
fof(f_895_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_895_2,plain,
! [U_2851,U_2850,U_2849] :
( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2849)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2850)),U_2851)) = 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_2849),U_2850))),U_2851)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2850))) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2849)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2850)),U_2851)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2849)),U_2851)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2850))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2849))) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2849)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2850)),U_2851)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2850)),U_2851)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2849))) ) ),
inference(variable_rename,[status(thm)],[f_895_1]) ).
fof(f_895_3,plain,
( ! [U_2857,U_2855,U_2853] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2853)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2855)),U_2857)) = 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_2853),U_2855))),U_2857)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2855))) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2853)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2855)),U_2857)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2853)),U_2857)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2855))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2853))) )
& ! [U_2856,U_2854,U_2852] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2852)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2854)),U_2856)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2854)),U_2856)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2852))) ) ),
inference(miniscope,[status(thm)],[f_895_2]) ).
cnf(f_895_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2852)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2854)),U_2856)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2854)),U_2856)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2852))) ),
inference(clausify,[status(thm)],[f_895_3]) ).
cnf(f_895_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2853)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2855)),U_2857)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2853)),U_2857)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2855)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2853))) ),
inference(clausify,[status(thm)],[f_895_3]) ).
cnf(f_895_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2853)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2855)),U_2857)) = 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_2853),U_2855))),U_2857)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2855)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2853))) ),
inference(clausify,[status(thm)],[f_895_3]) ).
fof(f_896_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_896_2,plain,
! [U_2858] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2858)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2858)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2858))) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2858)) = 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_2858))) ) ),
inference(variable_rename,[status(thm)],[f_896_1]) ).
fof(f_896_3,plain,
( ! [U_2860] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2860)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2860)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2860))) )
& ! [U_2859] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2859)) = 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_2859))) ) ),
inference(miniscope,[status(thm)],[f_896_2]) ).
cnf(f_896_4,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2859)) = 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_2859))) ),
inference(clausify,[status(thm)],[f_896_3]) ).
cnf(f_896_5,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2860)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2860)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2860))) ),
inference(clausify,[status(thm)],[f_896_3]) ).
fof(f_897_1,plain,
! [V_k_2,V_na_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_na_2),V_k_2)))
| ( ? [B_i] :
( ~ hBOOL(hAPP(V_P_2,B_i))
& ? [B_j] :
( V_na_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_P_2,B_i))
& ? [B_j] :
( V_na_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_P_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_P_2,B_i))
| ! [B_j] :
( V_na_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_P_2,B_i))
| ! [B_j] :
( V_na_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_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_na_2),V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__zdiv]) ).
fof(f_897_2,plain,
! [U_2871,U_2870,U_2869] :
( ( hBOOL(hAPP(U_2869,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2870),U_2871)))
| ( ? [U_2868] :
( ~ hBOOL(hAPP(U_2869,U_2868))
& ? [U_2867] :
( U_2870 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2871),U_2868)),U_2867)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2867),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2871),U_2867)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2871),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_2866] :
( ~ hBOOL(hAPP(U_2869,U_2866))
& ? [U_2865] :
( U_2870 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2871),U_2866)),U_2865)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2865),U_2871))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2865)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2871)) )
| ( ~ hBOOL(hAPP(U_2869,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_2871 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( ( ! [U_2864] :
( hBOOL(hAPP(U_2869,U_2864))
| ! [U_2863] :
( U_2870 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2871),U_2864)),U_2863)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2863),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2871),U_2863)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2871),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_2862] :
( hBOOL(hAPP(U_2869,U_2862))
| ! [U_2861] :
( U_2870 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2871),U_2862)),U_2861)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2861),U_2871))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2861)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2871)) )
& ( hBOOL(hAPP(U_2869,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2871 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_2869,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2870),U_2871))) ) ),
inference(variable_rename,[status(thm)],[f_897_1]) ).
fof(f_897_3,plain,
( ! [U_2877,U_2875,U_2873] :
( hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877)))
| ( ? [U_2868] :
( ~ hBOOL(hAPP(U_2873,U_2868))
& ? [U_2867] :
( U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),U_2868)),U_2867)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2867),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),U_2867)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_2866] :
( ~ hBOOL(hAPP(U_2873,U_2866))
& ? [U_2865] :
( U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),U_2866)),U_2865)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2865),U_2877))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2865)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2877)) )
| ( ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_2876,U_2874,U_2872] :
( ( ( ! [U_2864] :
( hBOOL(hAPP(U_2872,U_2864))
| ! [U_2863] :
( U_2874 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2876),U_2864)),U_2863)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2863),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2876),U_2863)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2876),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_2862] :
( hBOOL(hAPP(U_2872,U_2862))
| ! [U_2861] :
( U_2874 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2876),U_2862)),U_2861)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2861),U_2876))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2861)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2876)) )
& ( hBOOL(hAPP(U_2872,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2876 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_2872,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2874),U_2876))) ) ),
inference(miniscope,[status(thm)],[f_897_2]) ).
fof(f_897_4,plain,
( ! [U_2877,U_2875,U_2873] :
( hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877)))
| ( ? [U_2868] :
( ~ hBOOL(hAPP(U_2873,U_2868))
& ? [U_2867] :
( U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),U_2868)),U_2867)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2867),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),U_2867)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_2873,sK34(U_2877,U_2875,U_2873)))
& ? [U_2865] :
( U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK34(U_2877,U_2875,U_2873))),U_2865)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2865),U_2877))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2865)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2877)) )
| ( ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_2876,U_2874,U_2872] :
( ( ( ! [U_2864] :
( hBOOL(hAPP(U_2872,U_2864))
| ! [U_2863] :
( U_2874 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2876),U_2864)),U_2863)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2863),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2876),U_2863)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2876),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_2862] :
( hBOOL(hAPP(U_2872,U_2862))
| ! [U_2861] :
( U_2874 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2876),U_2862)),U_2861)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2861),U_2876))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2861)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2876)) )
& ( hBOOL(hAPP(U_2872,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2876 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_2872,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2874),U_2876))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_2866,sK34(U_2877,U_2875,U_2873))],[f_897_3]) ).
fof(f_897_5,plain,
( ! [U_2877,U_2875,U_2873] :
( hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877)))
| ( ? [U_2868] :
( ~ hBOOL(hAPP(U_2873,U_2868))
& ? [U_2867] :
( U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),U_2868)),U_2867)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2867),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),U_2867)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_2873,sK34(U_2877,U_2875,U_2873)))
& U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK34(U_2877,U_2875,U_2873))),sK35(U_2877,U_2875,U_2873))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK35(U_2877,U_2875,U_2873)),U_2877))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK35(U_2877,U_2875,U_2873)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2877)) )
| ( ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_2876,U_2874,U_2872] :
( ( ( ! [U_2864] :
( hBOOL(hAPP(U_2872,U_2864))
| ! [U_2863] :
( U_2874 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2876),U_2864)),U_2863)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2863),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2876),U_2863)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2876),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_2862] :
( hBOOL(hAPP(U_2872,U_2862))
| ! [U_2861] :
( U_2874 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2876),U_2862)),U_2861)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2861),U_2876))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2861)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2876)) )
& ( hBOOL(hAPP(U_2872,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2876 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_2872,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2874),U_2876))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_2865,sK35(U_2877,U_2875,U_2873))],[f_897_4]) ).
fof(f_897_6,plain,
( ! [U_2877,U_2875,U_2873] :
( hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877)))
| ( ~ hBOOL(hAPP(U_2873,sK36(U_2877,U_2875,U_2873)))
& ? [U_2867] :
( U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK36(U_2877,U_2875,U_2873))),U_2867)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2867),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),U_2867)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_2873,sK34(U_2877,U_2875,U_2873)))
& U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK34(U_2877,U_2875,U_2873))),sK35(U_2877,U_2875,U_2873))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK35(U_2877,U_2875,U_2873)),U_2877))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK35(U_2877,U_2875,U_2873)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2877)) )
| ( ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_2876,U_2874,U_2872] :
( ( ( ! [U_2864] :
( hBOOL(hAPP(U_2872,U_2864))
| ! [U_2863] :
( U_2874 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2876),U_2864)),U_2863)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2863),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2876),U_2863)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2876),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_2862] :
( hBOOL(hAPP(U_2872,U_2862))
| ! [U_2861] :
( U_2874 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2876),U_2862)),U_2861)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2861),U_2876))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2861)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2876)) )
& ( hBOOL(hAPP(U_2872,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2876 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_2872,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2874),U_2876))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_2868,sK36(U_2877,U_2875,U_2873))],[f_897_5]) ).
fof(f_897_7,plain,
( ! [U_2877,U_2875,U_2873] :
( hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877)))
| ( ~ hBOOL(hAPP(U_2873,sK36(U_2877,U_2875,U_2873)))
& U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK36(U_2877,U_2875,U_2873))),sK37(U_2877,U_2875,U_2873))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK37(U_2877,U_2875,U_2873)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),sK37(U_2877,U_2875,U_2873)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_2873,sK34(U_2877,U_2875,U_2873)))
& U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK34(U_2877,U_2875,U_2873))),sK35(U_2877,U_2875,U_2873))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK35(U_2877,U_2875,U_2873)),U_2877))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK35(U_2877,U_2875,U_2873)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2877)) )
| ( ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_2876,U_2874,U_2872] :
( ( ( ! [U_2864] :
( hBOOL(hAPP(U_2872,U_2864))
| ! [U_2863] :
( U_2874 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2876),U_2864)),U_2863)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2863),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2876),U_2863)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2876),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_2862] :
( hBOOL(hAPP(U_2872,U_2862))
| ! [U_2861] :
( U_2874 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2876),U_2862)),U_2861)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2861),U_2876))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2861)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2876)) )
& ( hBOOL(hAPP(U_2872,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2876 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_2872,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2874),U_2876))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_2867,sK37(U_2877,U_2875,U_2873))],[f_897_6]) ).
cnf(f_897_8,plain,
( hBOOL(hAPP(U_2872,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2876 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_2872,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2874),U_2876))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_9,plain,
( hBOOL(hAPP(U_2872,U_2862))
| U_2874 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2876),U_2862)),U_2861)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2861),U_2876))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2861))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2876))
| ~ hBOOL(hAPP(U_2872,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2874),U_2876))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_10,plain,
( hBOOL(hAPP(U_2872,U_2864))
| U_2874 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2876),U_2864)),U_2863)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2863),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2876),U_2863))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2876),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_2872,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2874),U_2876))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2877))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_12,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK35(U_2877,U_2875,U_2873)))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_13,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK35(U_2877,U_2875,U_2873)),U_2877))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_14,plain,
( U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK34(U_2877,U_2875,U_2873))),sK35(U_2877,U_2875,U_2873))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_15,plain,
( ~ hBOOL(hAPP(U_2873,sK34(U_2877,U_2875,U_2873)))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_16,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2877))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_17,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK35(U_2877,U_2875,U_2873)))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_18,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK35(U_2877,U_2875,U_2873)),U_2877))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_19,plain,
( U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK34(U_2877,U_2875,U_2873))),sK35(U_2877,U_2875,U_2873))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_20,plain,
( ~ hBOOL(hAPP(U_2873,sK34(U_2877,U_2875,U_2873)))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_21,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2877))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),sK37(U_2877,U_2875,U_2873)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_22,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK35(U_2877,U_2875,U_2873)))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),sK37(U_2877,U_2875,U_2873)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_23,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK35(U_2877,U_2875,U_2873)),U_2877))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),sK37(U_2877,U_2875,U_2873)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_24,plain,
( U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK34(U_2877,U_2875,U_2873))),sK35(U_2877,U_2875,U_2873))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),sK37(U_2877,U_2875,U_2873)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_25,plain,
( ~ hBOOL(hAPP(U_2873,sK34(U_2877,U_2875,U_2873)))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),sK37(U_2877,U_2875,U_2873)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_26,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2877))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK37(U_2877,U_2875,U_2873)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_27,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK35(U_2877,U_2875,U_2873)))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK37(U_2877,U_2875,U_2873)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_28,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK35(U_2877,U_2875,U_2873)),U_2877))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK37(U_2877,U_2875,U_2873)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_29,plain,
( U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK34(U_2877,U_2875,U_2873))),sK35(U_2877,U_2875,U_2873))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK37(U_2877,U_2875,U_2873)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_30,plain,
( ~ hBOOL(hAPP(U_2873,sK34(U_2877,U_2875,U_2873)))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK37(U_2877,U_2875,U_2873)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_31,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2877))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK36(U_2877,U_2875,U_2873))),sK37(U_2877,U_2875,U_2873))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_32,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK35(U_2877,U_2875,U_2873)))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK36(U_2877,U_2875,U_2873))),sK37(U_2877,U_2875,U_2873))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_33,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK35(U_2877,U_2875,U_2873)),U_2877))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK36(U_2877,U_2875,U_2873))),sK37(U_2877,U_2875,U_2873))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_34,plain,
( U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK34(U_2877,U_2875,U_2873))),sK35(U_2877,U_2875,U_2873))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK36(U_2877,U_2875,U_2873))),sK37(U_2877,U_2875,U_2873))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_35,plain,
( ~ hBOOL(hAPP(U_2873,sK34(U_2877,U_2875,U_2873)))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK36(U_2877,U_2875,U_2873))),sK37(U_2877,U_2875,U_2873))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_36,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2877))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_2873,sK36(U_2877,U_2875,U_2873)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_37,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK35(U_2877,U_2875,U_2873)))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_2873,sK36(U_2877,U_2875,U_2873)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_38,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK35(U_2877,U_2875,U_2873)),U_2877))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_2873,sK36(U_2877,U_2875,U_2873)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_39,plain,
( U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK34(U_2877,U_2875,U_2873))),sK35(U_2877,U_2875,U_2873))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_2873,sK36(U_2877,U_2875,U_2873)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_40,plain,
( ~ hBOOL(hAPP(U_2873,sK34(U_2877,U_2875,U_2873)))
| U_2877 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_2873,sK36(U_2877,U_2875,U_2873)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_41,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2877))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),sK37(U_2877,U_2875,U_2873)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_42,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK35(U_2877,U_2875,U_2873)))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),sK37(U_2877,U_2875,U_2873)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_43,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK35(U_2877,U_2875,U_2873)),U_2877))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),sK37(U_2877,U_2875,U_2873)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_44,plain,
( U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK34(U_2877,U_2875,U_2873))),sK35(U_2877,U_2875,U_2873))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),sK37(U_2877,U_2875,U_2873)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_45,plain,
( ~ hBOOL(hAPP(U_2873,sK34(U_2877,U_2875,U_2873)))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2877),sK37(U_2877,U_2875,U_2873)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_46,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2877))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK37(U_2877,U_2875,U_2873)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_47,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK35(U_2877,U_2875,U_2873)))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK37(U_2877,U_2875,U_2873)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_48,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK35(U_2877,U_2875,U_2873)),U_2877))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK37(U_2877,U_2875,U_2873)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_49,plain,
( U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK34(U_2877,U_2875,U_2873))),sK35(U_2877,U_2875,U_2873))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK37(U_2877,U_2875,U_2873)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_50,plain,
( ~ hBOOL(hAPP(U_2873,sK34(U_2877,U_2875,U_2873)))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK37(U_2877,U_2875,U_2873)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_51,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2877))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK36(U_2877,U_2875,U_2873))),sK37(U_2877,U_2875,U_2873))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_52,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK35(U_2877,U_2875,U_2873)))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK36(U_2877,U_2875,U_2873))),sK37(U_2877,U_2875,U_2873))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_53,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK35(U_2877,U_2875,U_2873)),U_2877))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK36(U_2877,U_2875,U_2873))),sK37(U_2877,U_2875,U_2873))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_54,plain,
( U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK34(U_2877,U_2875,U_2873))),sK35(U_2877,U_2875,U_2873))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK36(U_2877,U_2875,U_2873))),sK37(U_2877,U_2875,U_2873))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_55,plain,
( ~ hBOOL(hAPP(U_2873,sK34(U_2877,U_2875,U_2873)))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK36(U_2877,U_2875,U_2873))),sK37(U_2877,U_2875,U_2873))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_56,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2877))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_2873,sK36(U_2877,U_2875,U_2873)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_57,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK35(U_2877,U_2875,U_2873)))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_2873,sK36(U_2877,U_2875,U_2873)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_58,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK35(U_2877,U_2875,U_2873)),U_2877))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_2873,sK36(U_2877,U_2875,U_2873)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_59,plain,
( U_2875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2877),sK34(U_2877,U_2875,U_2873))),sK35(U_2877,U_2875,U_2873))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_2873,sK36(U_2877,U_2875,U_2873)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
cnf(f_897_60,plain,
( ~ hBOOL(hAPP(U_2873,sK34(U_2877,U_2875,U_2873)))
| ~ hBOOL(hAPP(U_2873,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_2873,sK36(U_2877,U_2875,U_2873)))
| hBOOL(hAPP(U_2873,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2875),U_2877))) ),
inference(clausify,[status(thm)],[f_897_7]) ).
fof(f_898_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_898_2,plain,
! [U_2881,U_2880,U_2879,U_2878] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2878),U_2879) = U_2880
| U_2879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2881),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2879),U_2881)) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2879)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2881),U_2879))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2881)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2879)) )
| U_2878 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2879),U_2880)),U_2881) ),
inference(variable_rename,[status(thm)],[f_898_1]) ).
cnf(f_898_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2879))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2879))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2878),U_2879) = U_2880
| U_2879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2878 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2879),U_2880)),U_2881) ),
inference(clausify,[status(thm)],[f_898_2]) ).
cnf(f_898_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2881),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2879),U_2881))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2879))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2878),U_2879) = U_2880
| U_2879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2878 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2879),U_2880)),U_2881) ),
inference(clausify,[status(thm)],[f_898_2]) ).
cnf(f_898_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2879))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2881),U_2879))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2881))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2878),U_2879) = U_2880
| U_2879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2878 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2879),U_2880)),U_2881) ),
inference(clausify,[status(thm)],[f_898_2]) ).
cnf(f_898_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2881),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2879),U_2881))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2881),U_2879))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2881))
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2878),U_2879) = U_2880
| U_2879 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2878 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2879),U_2880)),U_2881) ),
inference(clausify,[status(thm)],[f_898_2]) ).
fof(f_899_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_899_2,plain,
! [U_2883,U_2882] :
( ( 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_2882)),U_2883)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_2882))),U_2883)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2882))) )
& ( 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_2882)),U_2883)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2883)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2882))) ) ),
inference(variable_rename,[status(thm)],[f_899_1]) ).
fof(f_899_3,plain,
( ! [U_2887,U_2885] :
( 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_2885)),U_2887)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_2885))),U_2887)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2885))) )
& ! [U_2886,U_2884] :
( 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_2884)),U_2886)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2886)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2884))) ) ),
inference(miniscope,[status(thm)],[f_899_2]) ).
cnf(f_899_4,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_2884)),U_2886)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2886)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2884))) ),
inference(clausify,[status(thm)],[f_899_3]) ).
cnf(f_899_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_2885)),U_2887)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_2885))),U_2887)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2885))) ),
inference(clausify,[status(thm)],[f_899_3]) ).
fof(f_900_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_900_2,plain,
! [U_2889,U_2888] :
( ( c_SMT_Oz3div(U_2889,U_2888) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2889),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2888)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2888)) )
& ( c_SMT_Oz3div(U_2889,U_2888) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2889),U_2888)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2888)) ) ),
inference(variable_rename,[status(thm)],[f_900_1]) ).
fof(f_900_3,plain,
( ! [U_2893,U_2891] :
( c_SMT_Oz3div(U_2893,U_2891) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2893),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2891)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2891)) )
& ! [U_2892,U_2890] :
( c_SMT_Oz3div(U_2892,U_2890) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2892),U_2890)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2890)) ) ),
inference(miniscope,[status(thm)],[f_900_2]) ).
cnf(f_900_4,plain,
( c_SMT_Oz3div(U_2892,U_2890) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2892),U_2890)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2890)) ),
inference(clausify,[status(thm)],[f_900_3]) ).
cnf(f_900_5,plain,
( c_SMT_Oz3div(U_2893,U_2891) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2893),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2891)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2891)) ),
inference(clausify,[status(thm)],[f_900_3]) ).
fof(f_901_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_901_2,plain,
! [U_2894] :
( ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2894)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_2894))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2894))) )
& ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2894)) = 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_2894))) ) ),
inference(variable_rename,[status(thm)],[f_901_1]) ).
fof(f_901_3,plain,
( ! [U_2896] :
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2896)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_2896))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2896))) )
& ! [U_2895] :
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2895)) = 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_2895))) ) ),
inference(miniscope,[status(thm)],[f_901_2]) ).
cnf(f_901_4,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2895)) = 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_2895))) ),
inference(clausify,[status(thm)],[f_901_3]) ).
cnf(f_901_5,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_2896)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_2896))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_2896))) ),
inference(clausify,[status(thm)],[f_901_3]) ).
fof(f_902_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_902_2,plain,
! [U_2897] : 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_2897)) = 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_2897))),
inference(variable_rename,[status(thm)],[f_902_1]) ).
cnf(f_902_3,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_2897)) = 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_2897))),
inference(clausify,[status(thm)],[f_902_2]) ).
fof(f_903_1,plain,
! [V_k_2,V_P_2,V_d_2] :
( ! [B_x] :
( hBOOL(hAPP(V_P_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_P_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_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2)))
& hBOOL(hAPP(V_P_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_903_2,plain,
! [U_2902,U_2901,U_2900] :
( ! [U_2899] :
( hBOOL(hAPP(U_2901,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2902),U_2900))))
| ~ hBOOL(hAPP(U_2901,U_2899)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2902))
| ? [U_2898] :
( ~ hBOOL(hAPP(U_2901,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2898),U_2900)))
& hBOOL(hAPP(U_2901,U_2898)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2900)) ),
inference(variable_rename,[status(thm)],[f_903_1]) ).
fof(f_903_3,plain,
! [U_2902,U_2901,U_2900] :
( ! [U_2899] :
( hBOOL(hAPP(U_2901,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2902),U_2900))))
| ~ hBOOL(hAPP(U_2901,U_2899)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2902))
| ( ~ hBOOL(hAPP(U_2901,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK38(U_2902,U_2901,U_2900)),U_2900)))
& hBOOL(hAPP(U_2901,sK38(U_2902,U_2901,U_2900))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2900)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_2898,sK38(U_2902,U_2901,U_2900))],[f_903_2]) ).
cnf(f_903_4,plain,
( hBOOL(hAPP(U_2901,sK38(U_2902,U_2901,U_2900)))
| hBOOL(hAPP(U_2901,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2902),U_2900))))
| ~ hBOOL(hAPP(U_2901,U_2899))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2900)) ),
inference(clausify,[status(thm)],[f_903_3]) ).
cnf(f_903_5,plain,
( ~ hBOOL(hAPP(U_2901,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK38(U_2902,U_2901,U_2900)),U_2900)))
| hBOOL(hAPP(U_2901,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2902),U_2900))))
| ~ hBOOL(hAPP(U_2901,U_2899))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2900)) ),
inference(clausify,[status(thm)],[f_903_3]) ).
fof(f_904_1,plain,
! [V_k_2,V_P_2,V_d_2] :
( ! [B_x] :
( hBOOL(hAPP(V_P_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_P_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_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2)))
& hBOOL(hAPP(V_P_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_904_2,plain,
! [U_2907,U_2906,U_2905] :
( ! [U_2904] :
( hBOOL(hAPP(U_2906,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2904),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2907),U_2905))))
| ~ hBOOL(hAPP(U_2906,U_2904)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2907))
| ? [U_2903] :
( ~ hBOOL(hAPP(U_2906,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2903),U_2905)))
& hBOOL(hAPP(U_2906,U_2903)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2905)) ),
inference(variable_rename,[status(thm)],[f_904_1]) ).
fof(f_904_3,plain,
! [U_2907,U_2906,U_2905] :
( ! [U_2904] :
( hBOOL(hAPP(U_2906,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2904),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2907),U_2905))))
| ~ hBOOL(hAPP(U_2906,U_2904)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2907))
| ( ~ hBOOL(hAPP(U_2906,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK39(U_2907,U_2906,U_2905)),U_2905)))
& hBOOL(hAPP(U_2906,sK39(U_2907,U_2906,U_2905))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2905)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_2903,sK39(U_2907,U_2906,U_2905))],[f_904_2]) ).
cnf(f_904_4,plain,
( hBOOL(hAPP(U_2906,sK39(U_2907,U_2906,U_2905)))
| hBOOL(hAPP(U_2906,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2904),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2907),U_2905))))
| ~ hBOOL(hAPP(U_2906,U_2904))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2907))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2905)) ),
inference(clausify,[status(thm)],[f_904_3]) ).
cnf(f_904_5,plain,
( ~ hBOOL(hAPP(U_2906,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK39(U_2907,U_2906,U_2905)),U_2905)))
| hBOOL(hAPP(U_2906,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2904),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2907),U_2905))))
| ~ hBOOL(hAPP(U_2906,U_2904))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2907))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2905)) ),
inference(clausify,[status(thm)],[f_904_3]) ).
fof(f_905_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_905_2,plain,
! [U_2909,U_2908] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2908),U_2909) = 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_2908),U_2909)),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_2908)) ),
inference(variable_rename,[status(thm)],[f_905_1]) ).
cnf(f_905_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2908),U_2909) = 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_2908),U_2909)),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_2908)) ),
inference(clausify,[status(thm)],[f_905_2]) ).
fof(f_906_1,plain,
! [V_na_2,V_P_2,V_k_2] :
( ( ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_na_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_na_2,V_k_2)))
| ? [B_i,B_j] :
( ~ hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
& V_na_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_P_2,B_i),B_j))
| V_na_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_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_na_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_na_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_906_2,plain,
! [U_2916,U_2915,U_2914] :
( ( ( hBOOL(hAPP(hAPP(U_2915,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2916),U_2914)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2916,U_2914)))
| ? [U_2913,U_2912] :
( ~ hBOOL(hAPP(hAPP(U_2915,U_2913),U_2912))
& U_2916 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2914),U_2913)),U_2912)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2912),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2914),U_2912)) ) )
& ( ! [U_2911,U_2910] :
( hBOOL(hAPP(hAPP(U_2915,U_2911),U_2910))
| U_2916 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2914),U_2911)),U_2910)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2910),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2914),U_2910)) )
| ~ hBOOL(hAPP(hAPP(U_2915,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2916),U_2914)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2916,U_2914))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2914),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_906_1]) ).
fof(f_906_3,plain,
! [U_2916,U_2915,U_2914] :
( ( ( hBOOL(hAPP(hAPP(U_2915,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2916),U_2914)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2916,U_2914)))
| ? [U_2912] :
( ~ hBOOL(hAPP(hAPP(U_2915,sK40(U_2916,U_2915,U_2914)),U_2912))
& U_2916 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2914),sK40(U_2916,U_2915,U_2914))),U_2912)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2912),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2914),U_2912)) ) )
& ( ! [U_2911,U_2910] :
( hBOOL(hAPP(hAPP(U_2915,U_2911),U_2910))
| U_2916 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2914),U_2911)),U_2910)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2910),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2914),U_2910)) )
| ~ hBOOL(hAPP(hAPP(U_2915,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2916),U_2914)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2916,U_2914))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2914),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_2913,sK40(U_2916,U_2915,U_2914))],[f_906_2]) ).
fof(f_906_4,plain,
! [U_2916,U_2915,U_2914] :
( ( ( hBOOL(hAPP(hAPP(U_2915,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2916),U_2914)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2916,U_2914)))
| ( ~ hBOOL(hAPP(hAPP(U_2915,sK40(U_2916,U_2915,U_2914)),sK41(U_2916,U_2915,U_2914)))
& U_2916 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2914),sK40(U_2916,U_2915,U_2914))),sK41(U_2916,U_2915,U_2914))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK41(U_2916,U_2915,U_2914)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2914),sK41(U_2916,U_2915,U_2914))) ) )
& ( ! [U_2911,U_2910] :
( hBOOL(hAPP(hAPP(U_2915,U_2911),U_2910))
| U_2916 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2914),U_2911)),U_2910)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2910),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2914),U_2910)) )
| ~ hBOOL(hAPP(hAPP(U_2915,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2916),U_2914)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2916,U_2914))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2914),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_2912,sK41(U_2916,U_2915,U_2914))],[f_906_3]) ).
cnf(f_906_5,plain,
( hBOOL(hAPP(hAPP(U_2915,U_2911),U_2910))
| U_2916 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2914),U_2911)),U_2910)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2910),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2914),U_2910))
| ~ hBOOL(hAPP(hAPP(U_2915,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2916),U_2914)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2916,U_2914)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2914),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_906_4]) ).
cnf(f_906_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2914),sK41(U_2916,U_2915,U_2914)))
| hBOOL(hAPP(hAPP(U_2915,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2916),U_2914)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2916,U_2914)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2914),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_906_4]) ).
cnf(f_906_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK41(U_2916,U_2915,U_2914)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(U_2915,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2916),U_2914)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2916,U_2914)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2914),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_906_4]) ).
cnf(f_906_8,plain,
( U_2916 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2914),sK40(U_2916,U_2915,U_2914))),sK41(U_2916,U_2915,U_2914))
| hBOOL(hAPP(hAPP(U_2915,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2916),U_2914)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2916,U_2914)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2914),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_906_4]) ).
cnf(f_906_9,plain,
( ~ hBOOL(hAPP(hAPP(U_2915,sK40(U_2916,U_2915,U_2914)),sK41(U_2916,U_2915,U_2914)))
| hBOOL(hAPP(hAPP(U_2915,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_2916),U_2914)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2916,U_2914)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2914),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_906_4]) ).
fof(f_907_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_907_2,plain,
! [U_2917] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2917),c_Int_OMin) = c_Int_Osucc(U_2917),
inference(variable_rename,[status(thm)],[f_907_1]) ).
cnf(f_907_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_2917),c_Int_OMin) = c_Int_Osucc(U_2917),
inference(clausify,[status(thm)],[f_907_2]) ).
fof(f_908_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_908_2,plain,
! [U_2920,U_2919,U_2918] :
( c_Divides_Odiv__class_Omod(U_2918,c_Divides_Odiv__class_Omod(U_2918,U_2919,U_2920),U_2920) = c_Divides_Odiv__class_Omod(U_2918,U_2919,U_2920)
| ~ class_Divides_Osemiring__div(U_2918) ),
inference(variable_rename,[status(thm)],[f_908_1]) ).
cnf(f_908_3,plain,
( c_Divides_Odiv__class_Omod(U_2918,c_Divides_Odiv__class_Omod(U_2918,U_2919,U_2920),U_2920) = c_Divides_Odiv__class_Omod(U_2918,U_2919,U_2920)
| ~ class_Divides_Osemiring__div(U_2918) ),
inference(clausify,[status(thm)],[f_908_2]) ).
fof(f_909_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_909_2,plain,
! [U_2921] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2921,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_909_1]) ).
cnf(f_909_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2921,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_909_2]) ).
fof(f_910_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_910_2,plain,
! [U_2923,U_2922] :
( c_Divides_Odiv__class_Omod(U_2922,c_Groups_Ozero__class_Ozero(U_2922),U_2923) = c_Groups_Ozero__class_Ozero(U_2922)
| ~ class_Divides_Osemiring__div(U_2922) ),
inference(variable_rename,[status(thm)],[f_910_1]) ).
cnf(f_910_3,plain,
( c_Divides_Odiv__class_Omod(U_2922,c_Groups_Ozero__class_Ozero(U_2922),U_2923) = c_Groups_Ozero__class_Ozero(U_2922)
| ~ class_Divides_Osemiring__div(U_2922) ),
inference(clausify,[status(thm)],[f_910_2]) ).
fof(f_911_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_911_2,plain,
! [U_2925,U_2924] :
( c_Divides_Odiv__class_Omod(U_2924,U_2925,c_Groups_Ozero__class_Ozero(U_2924)) = U_2925
| ~ class_Divides_Osemiring__div(U_2924) ),
inference(variable_rename,[status(thm)],[f_911_1]) ).
cnf(f_911_3,plain,
( c_Divides_Odiv__class_Omod(U_2924,U_2925,c_Groups_Ozero__class_Ozero(U_2924)) = U_2925
| ~ class_Divides_Osemiring__div(U_2924) ),
inference(clausify,[status(thm)],[f_911_2]) ).
fof(f_912_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_912_2,plain,
! [U_2927,U_2926] :
( c_Divides_Odiv__class_Omod(U_2926,U_2927,U_2927) = c_Groups_Ozero__class_Ozero(U_2926)
| ~ class_Divides_Osemiring__div(U_2926) ),
inference(variable_rename,[status(thm)],[f_912_1]) ).
cnf(f_912_3,plain,
( c_Divides_Odiv__class_Omod(U_2926,U_2927,U_2927) = c_Groups_Ozero__class_Ozero(U_2926)
| ~ class_Divides_Osemiring__div(U_2926) ),
inference(clausify,[status(thm)],[f_912_2]) ).
fof(f_913_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_913_2,plain,
! [U_2930,U_2929,U_2928] :
( c_Divides_Odiv__class_Omod(U_2928,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2928),U_2929),U_2930),U_2930) = c_Divides_Odiv__class_Omod(U_2928,U_2929,U_2930)
| ~ class_Divides_Osemiring__div(U_2928) ),
inference(variable_rename,[status(thm)],[f_913_1]) ).
cnf(f_913_3,plain,
( c_Divides_Odiv__class_Omod(U_2928,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2928),U_2929),U_2930),U_2930) = c_Divides_Odiv__class_Omod(U_2928,U_2929,U_2930)
| ~ class_Divides_Osemiring__div(U_2928) ),
inference(clausify,[status(thm)],[f_913_2]) ).
fof(f_914_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_914_2,plain,
! [U_2933,U_2932,U_2931] :
( c_Divides_Odiv__class_Omod(U_2931,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2931),U_2932),U_2933),U_2932) = c_Divides_Odiv__class_Omod(U_2931,U_2933,U_2932)
| ~ class_Divides_Osemiring__div(U_2931) ),
inference(variable_rename,[status(thm)],[f_914_1]) ).
cnf(f_914_3,plain,
( c_Divides_Odiv__class_Omod(U_2931,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2931),U_2932),U_2933),U_2932) = c_Divides_Odiv__class_Omod(U_2931,U_2933,U_2932)
| ~ class_Divides_Osemiring__div(U_2931) ),
inference(clausify,[status(thm)],[f_914_2]) ).
fof(f_915_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_915_2,plain,
! [U_2937,U_2936,U_2935,U_2934] :
( c_Divides_Odiv__class_Omod(U_2934,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2934),U_2935),U_2936),U_2937) = c_Divides_Odiv__class_Omod(U_2934,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2934),U_2935),c_Divides_Odiv__class_Omod(U_2934,U_2936,U_2937)),U_2937)
| ~ class_Divides_Osemiring__div(U_2934) ),
inference(variable_rename,[status(thm)],[f_915_1]) ).
cnf(f_915_3,plain,
( c_Divides_Odiv__class_Omod(U_2934,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2934),U_2935),U_2936),U_2937) = c_Divides_Odiv__class_Omod(U_2934,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2934),U_2935),c_Divides_Odiv__class_Omod(U_2934,U_2936,U_2937)),U_2937)
| ~ class_Divides_Osemiring__div(U_2934) ),
inference(clausify,[status(thm)],[f_915_2]) ).
fof(f_916_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_916_2,plain,
! [U_2941,U_2940,U_2939,U_2938] :
( c_Divides_Odiv__class_Omod(U_2938,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2938),U_2939),U_2940),U_2941) = c_Divides_Odiv__class_Omod(U_2938,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2938),c_Divides_Odiv__class_Omod(U_2938,U_2939,U_2941)),U_2940),U_2941)
| ~ class_Divides_Osemiring__div(U_2938) ),
inference(variable_rename,[status(thm)],[f_916_1]) ).
cnf(f_916_3,plain,
( c_Divides_Odiv__class_Omod(U_2938,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2938),U_2939),U_2940),U_2941) = c_Divides_Odiv__class_Omod(U_2938,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2938),c_Divides_Odiv__class_Omod(U_2938,U_2939,U_2941)),U_2940),U_2941)
| ~ class_Divides_Osemiring__div(U_2938) ),
inference(clausify,[status(thm)],[f_916_2]) ).
fof(f_917_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_917_2,plain,
! [U_2945,U_2944,U_2943,U_2942] :
( c_Divides_Odiv__class_Omod(U_2942,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2942),U_2943),U_2944),U_2945) = c_Divides_Odiv__class_Omod(U_2942,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2942),c_Divides_Odiv__class_Omod(U_2942,U_2943,U_2945)),c_Divides_Odiv__class_Omod(U_2942,U_2944,U_2945)),U_2945)
| ~ class_Divides_Osemiring__div(U_2942) ),
inference(variable_rename,[status(thm)],[f_917_1]) ).
cnf(f_917_3,plain,
( c_Divides_Odiv__class_Omod(U_2942,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2942),U_2943),U_2944),U_2945) = c_Divides_Odiv__class_Omod(U_2942,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2942),c_Divides_Odiv__class_Omod(U_2942,U_2943,U_2945)),c_Divides_Odiv__class_Omod(U_2942,U_2944,U_2945)),U_2945)
| ~ class_Divides_Osemiring__div(U_2942) ),
inference(clausify,[status(thm)],[f_917_2]) ).
fof(f_918_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_918_2,plain,
! [U_2949,U_2948,U_2947,U_2946] :
( c_Divides_Odiv__class_Omod(U_2946,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2946),U_2947),c_Divides_Odiv__class_Omod(U_2946,U_2948,U_2949)),U_2949) = c_Divides_Odiv__class_Omod(U_2946,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2946),U_2947),U_2948),U_2949)
| ~ class_Divides_Osemiring__div(U_2946) ),
inference(variable_rename,[status(thm)],[f_918_1]) ).
cnf(f_918_3,plain,
( c_Divides_Odiv__class_Omod(U_2946,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2946),U_2947),c_Divides_Odiv__class_Omod(U_2946,U_2948,U_2949)),U_2949) = c_Divides_Odiv__class_Omod(U_2946,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2946),U_2947),U_2948),U_2949)
| ~ class_Divides_Osemiring__div(U_2946) ),
inference(clausify,[status(thm)],[f_918_2]) ).
fof(f_919_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_919_2,plain,
! [U_2953,U_2952,U_2951,U_2950] :
( c_Divides_Odiv__class_Omod(U_2950,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2950),c_Divides_Odiv__class_Omod(U_2950,U_2951,U_2952)),U_2953),U_2952) = c_Divides_Odiv__class_Omod(U_2950,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2950),U_2951),U_2953),U_2952)
| ~ class_Divides_Osemiring__div(U_2950) ),
inference(variable_rename,[status(thm)],[f_919_1]) ).
cnf(f_919_3,plain,
( c_Divides_Odiv__class_Omod(U_2950,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2950),c_Divides_Odiv__class_Omod(U_2950,U_2951,U_2952)),U_2953),U_2952) = c_Divides_Odiv__class_Omod(U_2950,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2950),U_2951),U_2953),U_2952)
| ~ class_Divides_Osemiring__div(U_2950) ),
inference(clausify,[status(thm)],[f_919_2]) ).
fof(f_920_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_920_2,plain,
! [U_2959,U_2958,U_2957,U_2956,U_2955,U_2954] :
( c_Divides_Odiv__class_Omod(U_2954,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2954),U_2955),U_2958),U_2956) = c_Divides_Odiv__class_Omod(U_2954,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2954),U_2957),U_2959),U_2956)
| c_Divides_Odiv__class_Omod(U_2954,U_2958,U_2956) != c_Divides_Odiv__class_Omod(U_2954,U_2959,U_2956)
| c_Divides_Odiv__class_Omod(U_2954,U_2955,U_2956) != c_Divides_Odiv__class_Omod(U_2954,U_2957,U_2956)
| ~ class_Divides_Osemiring__div(U_2954) ),
inference(variable_rename,[status(thm)],[f_920_1]) ).
cnf(f_920_3,plain,
( c_Divides_Odiv__class_Omod(U_2954,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2954),U_2955),U_2958),U_2956) = c_Divides_Odiv__class_Omod(U_2954,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2954),U_2957),U_2959),U_2956)
| c_Divides_Odiv__class_Omod(U_2954,U_2958,U_2956) != c_Divides_Odiv__class_Omod(U_2954,U_2959,U_2956)
| c_Divides_Odiv__class_Omod(U_2954,U_2955,U_2956) != c_Divides_Odiv__class_Omod(U_2954,U_2957,U_2956)
| ~ class_Divides_Osemiring__div(U_2954) ),
inference(clausify,[status(thm)],[f_920_2]) ).
fof(f_921_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_921_2,plain,
! [U_2963,U_2962,U_2961,U_2960] :
( c_Divides_Odiv__class_Omod(U_2960,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2960),U_2961),U_2962),U_2963) = c_Divides_Odiv__class_Omod(U_2960,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2960),U_2961),c_Divides_Odiv__class_Omod(U_2960,U_2962,U_2963)),U_2963)
| ~ class_Divides_Osemiring__div(U_2960) ),
inference(variable_rename,[status(thm)],[f_921_1]) ).
cnf(f_921_3,plain,
( c_Divides_Odiv__class_Omod(U_2960,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2960),U_2961),U_2962),U_2963) = c_Divides_Odiv__class_Omod(U_2960,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2960),U_2961),c_Divides_Odiv__class_Omod(U_2960,U_2962,U_2963)),U_2963)
| ~ class_Divides_Osemiring__div(U_2960) ),
inference(clausify,[status(thm)],[f_921_2]) ).
fof(f_922_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_922_2,plain,
! [U_2967,U_2966,U_2965,U_2964] :
( c_Divides_Odiv__class_Omod(U_2964,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2964),U_2965),U_2966),U_2967) = c_Divides_Odiv__class_Omod(U_2964,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2964),c_Divides_Odiv__class_Omod(U_2964,U_2965,U_2967)),U_2966),U_2967)
| ~ class_Divides_Osemiring__div(U_2964) ),
inference(variable_rename,[status(thm)],[f_922_1]) ).
cnf(f_922_3,plain,
( c_Divides_Odiv__class_Omod(U_2964,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2964),U_2965),U_2966),U_2967) = c_Divides_Odiv__class_Omod(U_2964,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2964),c_Divides_Odiv__class_Omod(U_2964,U_2965,U_2967)),U_2966),U_2967)
| ~ class_Divides_Osemiring__div(U_2964) ),
inference(clausify,[status(thm)],[f_922_2]) ).
fof(f_923_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_923_2,plain,
! [U_2971,U_2970,U_2969,U_2968] :
( c_Divides_Odiv__class_Omod(U_2968,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2968),U_2969),U_2970),U_2971) = c_Divides_Odiv__class_Omod(U_2968,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2968),c_Divides_Odiv__class_Omod(U_2968,U_2969,U_2971)),c_Divides_Odiv__class_Omod(U_2968,U_2970,U_2971)),U_2971)
| ~ class_Divides_Osemiring__div(U_2968) ),
inference(variable_rename,[status(thm)],[f_923_1]) ).
cnf(f_923_3,plain,
( c_Divides_Odiv__class_Omod(U_2968,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2968),U_2969),U_2970),U_2971) = c_Divides_Odiv__class_Omod(U_2968,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2968),c_Divides_Odiv__class_Omod(U_2968,U_2969,U_2971)),c_Divides_Odiv__class_Omod(U_2968,U_2970,U_2971)),U_2971)
| ~ class_Divides_Osemiring__div(U_2968) ),
inference(clausify,[status(thm)],[f_923_2]) ).
fof(f_924_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_924_2,plain,
! [U_2975,U_2974,U_2973,U_2972] :
( c_Divides_Odiv__class_Omod(U_2972,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2972),U_2973),U_2974),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2972),U_2973),U_2975)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2972),U_2973),c_Divides_Odiv__class_Omod(U_2972,U_2974,U_2975))
| ~ class_Divides_Osemiring__div(U_2972) ),
inference(variable_rename,[status(thm)],[f_924_1]) ).
cnf(f_924_3,plain,
( c_Divides_Odiv__class_Omod(U_2972,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2972),U_2973),U_2974),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2972),U_2973),U_2975)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2972),U_2973),c_Divides_Odiv__class_Omod(U_2972,U_2974,U_2975))
| ~ class_Divides_Osemiring__div(U_2972) ),
inference(clausify,[status(thm)],[f_924_2]) ).
fof(f_925_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_925_2,plain,
! [U_2979,U_2978,U_2977,U_2976] :
( c_Divides_Odiv__class_Omod(U_2976,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2976),U_2977),U_2978),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2976),U_2979),U_2978)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2976),c_Divides_Odiv__class_Omod(U_2976,U_2977,U_2979)),U_2978)
| ~ class_Divides_Osemiring__div(U_2976) ),
inference(variable_rename,[status(thm)],[f_925_1]) ).
cnf(f_925_3,plain,
( c_Divides_Odiv__class_Omod(U_2976,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2976),U_2977),U_2978),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2976),U_2979),U_2978)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2976),c_Divides_Odiv__class_Omod(U_2976,U_2977,U_2979)),U_2978)
| ~ class_Divides_Osemiring__div(U_2976) ),
inference(clausify,[status(thm)],[f_925_2]) ).
fof(f_926_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_926_2,plain,
! [U_2983,U_2982,U_2981,U_2980] :
( c_Divides_Odiv__class_Omod(U_2980,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2980),c_Divides_Odiv__class_Omod(U_2980,U_2981,U_2982)),U_2983),U_2982) = c_Divides_Odiv__class_Omod(U_2980,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2980),U_2981),U_2983),U_2982)
| ~ class_Divides_Osemiring__div(U_2980) ),
inference(variable_rename,[status(thm)],[f_926_1]) ).
cnf(f_926_3,plain,
( c_Divides_Odiv__class_Omod(U_2980,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2980),c_Divides_Odiv__class_Omod(U_2980,U_2981,U_2982)),U_2983),U_2982) = c_Divides_Odiv__class_Omod(U_2980,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2980),U_2981),U_2983),U_2982)
| ~ class_Divides_Osemiring__div(U_2980) ),
inference(clausify,[status(thm)],[f_926_2]) ).
fof(f_927_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_927_2,plain,
! [U_2989,U_2988,U_2987,U_2986,U_2985,U_2984] :
( c_Divides_Odiv__class_Omod(U_2984,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2984),U_2985),U_2988),U_2986) = c_Divides_Odiv__class_Omod(U_2984,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2984),U_2987),U_2989),U_2986)
| c_Divides_Odiv__class_Omod(U_2984,U_2988,U_2986) != c_Divides_Odiv__class_Omod(U_2984,U_2989,U_2986)
| c_Divides_Odiv__class_Omod(U_2984,U_2985,U_2986) != c_Divides_Odiv__class_Omod(U_2984,U_2987,U_2986)
| ~ class_Divides_Osemiring__div(U_2984) ),
inference(variable_rename,[status(thm)],[f_927_1]) ).
cnf(f_927_3,plain,
( c_Divides_Odiv__class_Omod(U_2984,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2984),U_2985),U_2988),U_2986) = c_Divides_Odiv__class_Omod(U_2984,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2984),U_2987),U_2989),U_2986)
| c_Divides_Odiv__class_Omod(U_2984,U_2988,U_2986) != c_Divides_Odiv__class_Omod(U_2984,U_2989,U_2986)
| c_Divides_Odiv__class_Omod(U_2984,U_2985,U_2986) != c_Divides_Odiv__class_Omod(U_2984,U_2987,U_2986)
| ~ class_Divides_Osemiring__div(U_2984) ),
inference(clausify,[status(thm)],[f_927_2]) ).
fof(f_928_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_928_2,plain,
! [U_2995,U_2994,U_2993,U_2992,U_2991,U_2990] :
( c_Divides_Odiv__class_Omod(U_2990,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2990),U_2991),U_2994),U_2992) = c_Divides_Odiv__class_Omod(U_2990,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2990),U_2993),U_2995),U_2992)
| c_Divides_Odiv__class_Omod(U_2990,U_2994,U_2992) != c_Divides_Odiv__class_Omod(U_2990,U_2995,U_2992)
| c_Divides_Odiv__class_Omod(U_2990,U_2991,U_2992) != c_Divides_Odiv__class_Omod(U_2990,U_2993,U_2992)
| ~ class_Divides_Oring__div(U_2990) ),
inference(variable_rename,[status(thm)],[f_928_1]) ).
cnf(f_928_3,plain,
( c_Divides_Odiv__class_Omod(U_2990,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2990),U_2991),U_2994),U_2992) = c_Divides_Odiv__class_Omod(U_2990,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2990),U_2993),U_2995),U_2992)
| c_Divides_Odiv__class_Omod(U_2990,U_2994,U_2992) != c_Divides_Odiv__class_Omod(U_2990,U_2995,U_2992)
| c_Divides_Odiv__class_Omod(U_2990,U_2991,U_2992) != c_Divides_Odiv__class_Omod(U_2990,U_2993,U_2992)
| ~ class_Divides_Oring__div(U_2990) ),
inference(clausify,[status(thm)],[f_928_2]) ).
fof(f_929_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_929_2,plain,
! [U_2999,U_2998,U_2997,U_2996] :
( c_Divides_Odiv__class_Omod(U_2996,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2996),U_2997),U_2998),U_2999) = c_Divides_Odiv__class_Omod(U_2996,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2996),c_Divides_Odiv__class_Omod(U_2996,U_2997,U_2999)),c_Divides_Odiv__class_Omod(U_2996,U_2998,U_2999)),U_2999)
| ~ class_Divides_Oring__div(U_2996) ),
inference(variable_rename,[status(thm)],[f_929_1]) ).
cnf(f_929_3,plain,
( c_Divides_Odiv__class_Omod(U_2996,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2996),U_2997),U_2998),U_2999) = c_Divides_Odiv__class_Omod(U_2996,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_2996),c_Divides_Odiv__class_Omod(U_2996,U_2997,U_2999)),c_Divides_Odiv__class_Omod(U_2996,U_2998,U_2999)),U_2999)
| ~ class_Divides_Oring__div(U_2996) ),
inference(clausify,[status(thm)],[f_929_2]) ).
fof(f_930_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_930_2,plain,
! [U_3003,U_3002,U_3001,U_3000] :
( c_Divides_Odiv__class_Omod(U_3000,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3000),U_3001),U_3002),U_3003) = c_Divides_Odiv__class_Omod(U_3000,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3000),c_Divides_Odiv__class_Omod(U_3000,U_3001,U_3003)),U_3002),U_3003)
| ~ class_Divides_Oring__div(U_3000) ),
inference(variable_rename,[status(thm)],[f_930_1]) ).
cnf(f_930_3,plain,
( c_Divides_Odiv__class_Omod(U_3000,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3000),U_3001),U_3002),U_3003) = c_Divides_Odiv__class_Omod(U_3000,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3000),c_Divides_Odiv__class_Omod(U_3000,U_3001,U_3003)),U_3002),U_3003)
| ~ class_Divides_Oring__div(U_3000) ),
inference(clausify,[status(thm)],[f_930_2]) ).
fof(f_931_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_931_2,plain,
! [U_3007,U_3006,U_3005,U_3004] :
( c_Divides_Odiv__class_Omod(U_3004,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3004),U_3005),U_3006),U_3007) = c_Divides_Odiv__class_Omod(U_3004,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3004),U_3005),c_Divides_Odiv__class_Omod(U_3004,U_3006,U_3007)),U_3007)
| ~ class_Divides_Oring__div(U_3004) ),
inference(variable_rename,[status(thm)],[f_931_1]) ).
cnf(f_931_3,plain,
( c_Divides_Odiv__class_Omod(U_3004,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3004),U_3005),U_3006),U_3007) = c_Divides_Odiv__class_Omod(U_3004,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3004),U_3005),c_Divides_Odiv__class_Omod(U_3004,U_3006,U_3007)),U_3007)
| ~ class_Divides_Oring__div(U_3004) ),
inference(clausify,[status(thm)],[f_931_2]) ).
fof(f_932_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_932_2,plain,
! [U_3011,U_3010,U_3009,U_3008] :
( c_Divides_Odiv__class_Omod(U_3008,hAPP(c_Groups_Ouminus__class_Ouminus(U_3008),U_3009),U_3010) = c_Divides_Odiv__class_Omod(U_3008,hAPP(c_Groups_Ouminus__class_Ouminus(U_3008),U_3011),U_3010)
| c_Divides_Odiv__class_Omod(U_3008,U_3009,U_3010) != c_Divides_Odiv__class_Omod(U_3008,U_3011,U_3010)
| ~ class_Divides_Oring__div(U_3008) ),
inference(variable_rename,[status(thm)],[f_932_1]) ).
cnf(f_932_3,plain,
( c_Divides_Odiv__class_Omod(U_3008,hAPP(c_Groups_Ouminus__class_Ouminus(U_3008),U_3009),U_3010) = c_Divides_Odiv__class_Omod(U_3008,hAPP(c_Groups_Ouminus__class_Ouminus(U_3008),U_3011),U_3010)
| c_Divides_Odiv__class_Omod(U_3008,U_3009,U_3010) != c_Divides_Odiv__class_Omod(U_3008,U_3011,U_3010)
| ~ class_Divides_Oring__div(U_3008) ),
inference(clausify,[status(thm)],[f_932_2]) ).
fof(f_933_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_933_2,plain,
! [U_3014,U_3013,U_3012] :
( c_Divides_Odiv__class_Omod(U_3012,hAPP(c_Groups_Ouminus__class_Ouminus(U_3012),U_3013),U_3014) = c_Divides_Odiv__class_Omod(U_3012,hAPP(c_Groups_Ouminus__class_Ouminus(U_3012),c_Divides_Odiv__class_Omod(U_3012,U_3013,U_3014)),U_3014)
| ~ class_Divides_Oring__div(U_3012) ),
inference(variable_rename,[status(thm)],[f_933_1]) ).
cnf(f_933_3,plain,
( c_Divides_Odiv__class_Omod(U_3012,hAPP(c_Groups_Ouminus__class_Ouminus(U_3012),U_3013),U_3014) = c_Divides_Odiv__class_Omod(U_3012,hAPP(c_Groups_Ouminus__class_Ouminus(U_3012),c_Divides_Odiv__class_Omod(U_3012,U_3013,U_3014)),U_3014)
| ~ class_Divides_Oring__div(U_3012) ),
inference(clausify,[status(thm)],[f_933_2]) ).
fof(f_934_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_934_2,plain,
! [U_3016,U_3015] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3015),U_3016)),U_3015)),
inference(variable_rename,[status(thm)],[f_934_1]) ).
cnf(f_934_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3015),U_3016)),U_3015)),
inference(clausify,[status(thm)],[f_934_2]) ).
fof(f_935_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_935_2,plain,
! [U_3019,U_3018,U_3017] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3017),U_3019)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3018),U_3019)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3017),U_3018)) ),
inference(variable_rename,[status(thm)],[f_935_1]) ).
cnf(f_935_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3017),U_3019)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3018),U_3019)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3017),U_3018)) ),
inference(clausify,[status(thm)],[f_935_2]) ).
fof(f_936_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_936_2,plain,
! [U_3022,U_3021,U_3020] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3020),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3021),U_3022)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3020),U_3021)),U_3022),
inference(variable_rename,[status(thm)],[f_936_1]) ).
cnf(f_936_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3020),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3021),U_3022)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3020),U_3021)),U_3022),
inference(clausify,[status(thm)],[f_936_2]) ).
fof(f_937_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_937_2,plain,
! [U_3023] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3023,U_3023) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_937_1]) ).
cnf(f_937_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3023,U_3023) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_937_2]) ).
fof(f_938_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_938_2,plain,
! [U_3024] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3024) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_938_1]) ).
cnf(f_938_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3024) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_938_2]) ).
fof(f_939_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]) ).
cnf(f_939_2,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
inference(clausify,[status(thm)],[f_939_1]) ).
fof(f_940_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]) ).
cnf(f_940_2,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
inference(clausify,[status(thm)],[f_940_1]) ).
fof(f_941_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_941_2,plain,
! [U_3027,U_3026,U_3025] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3025),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3026,U_3027)),U_3027) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3025),U_3026),U_3027),
inference(variable_rename,[status(thm)],[f_941_1]) ).
cnf(f_941_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3025),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3026,U_3027)),U_3027) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3025),U_3026),U_3027),
inference(clausify,[status(thm)],[f_941_2]) ).
fof(f_942_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_942_2,plain,
! [U_3030,U_3029,U_3028] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3028),U_3029),U_3030) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3028),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3029,U_3030)),U_3030),
inference(variable_rename,[status(thm)],[f_942_1]) ).
cnf(f_942_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3028),U_3029),U_3030) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3028),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3029,U_3030)),U_3030),
inference(clausify,[status(thm)],[f_942_2]) ).
fof(f_943_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_943_2,plain,
! [U_3033,U_3032,U_3031] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3031),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3032,U_3033)),U_3033) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3031),U_3032),U_3033),
inference(variable_rename,[status(thm)],[f_943_1]) ).
cnf(f_943_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3031),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3032,U_3033)),U_3033) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3031),U_3032),U_3033),
inference(clausify,[status(thm)],[f_943_2]) ).
fof(f_944_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_944_2,plain,
! [U_3036,U_3035,U_3034] : 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_3034,U_3035)),U_3036),U_3035) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3034),U_3036),U_3035),
inference(variable_rename,[status(thm)],[f_944_1]) ).
cnf(f_944_3,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_3034,U_3035)),U_3036),U_3035) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3034),U_3036),U_3035),
inference(clausify,[status(thm)],[f_944_2]) ).
fof(f_945_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_945_2,plain,
! [U_3038,U_3037] : 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_3037,U_3038)),U_3038) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3037),U_3038),
inference(variable_rename,[status(thm)],[f_945_1]) ).
cnf(f_945_3,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_3037,U_3038)),U_3038) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3037),U_3038),
inference(clausify,[status(thm)],[f_945_2]) ).
fof(f_946_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_946_2,plain,
! [U_3040,U_3039] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3039),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3040)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3039,U_3040)),
inference(variable_rename,[status(thm)],[f_946_1]) ).
cnf(f_946_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3039),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3040)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3039,U_3040)),
inference(clausify,[status(thm)],[f_946_2]) ).
fof(f_947_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_947_2,plain,
! [U_3042,U_3041] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3041,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3042)) = 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_3041),U_3042)),
inference(variable_rename,[status(thm)],[f_947_1]) ).
cnf(f_947_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3041,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3042)) = 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_3041),U_3042)),
inference(clausify,[status(thm)],[f_947_2]) ).
fof(f_948_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_948_2,plain,
! [U_3045,U_3044,U_3043] : 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_3043,U_3044)),U_3045),U_3044) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3043),U_3045),U_3044),
inference(variable_rename,[status(thm)],[f_948_1]) ).
cnf(f_948_3,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_3043,U_3044)),U_3045),U_3044) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3043),U_3045),U_3044),
inference(clausify,[status(thm)],[f_948_2]) ).
fof(f_949_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_949_2,plain,
! [U_3048,U_3047,U_3046] :
( c_Divides_Odiv__class_Omod(U_3046,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3046),U_3047),U_3048),U_3048) = c_Groups_Ozero__class_Ozero(U_3046)
| ~ class_Divides_Osemiring__div(U_3046) ),
inference(variable_rename,[status(thm)],[f_949_1]) ).
cnf(f_949_3,plain,
( c_Divides_Odiv__class_Omod(U_3046,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3046),U_3047),U_3048),U_3048) = c_Groups_Ozero__class_Ozero(U_3046)
| ~ class_Divides_Osemiring__div(U_3046) ),
inference(clausify,[status(thm)],[f_949_2]) ).
fof(f_950_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_950_2,plain,
! [U_3051,U_3050,U_3049] :
( c_Divides_Odiv__class_Omod(U_3049,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3049),U_3050),U_3051),U_3050) = c_Groups_Ozero__class_Ozero(U_3049)
| ~ class_Divides_Osemiring__div(U_3049) ),
inference(variable_rename,[status(thm)],[f_950_1]) ).
cnf(f_950_3,plain,
( c_Divides_Odiv__class_Omod(U_3049,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3049),U_3050),U_3051),U_3050) = c_Groups_Ozero__class_Ozero(U_3049)
| ~ class_Divides_Osemiring__div(U_3049) ),
inference(clausify,[status(thm)],[f_950_2]) ).
fof(f_951_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_951_2,plain,
! [U_3055,U_3054,U_3053,U_3052] :
( c_Divides_Odiv__class_Omod(U_3052,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3052),U_3053),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3052),U_3054),U_3055)),U_3054) = c_Divides_Odiv__class_Omod(U_3052,U_3053,U_3054)
| ~ class_Divides_Osemiring__div(U_3052) ),
inference(variable_rename,[status(thm)],[f_951_1]) ).
cnf(f_951_3,plain,
( c_Divides_Odiv__class_Omod(U_3052,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3052),U_3053),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3052),U_3054),U_3055)),U_3054) = c_Divides_Odiv__class_Omod(U_3052,U_3053,U_3054)
| ~ class_Divides_Osemiring__div(U_3052) ),
inference(clausify,[status(thm)],[f_951_2]) ).
fof(f_952_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_952_2,plain,
! [U_3059,U_3058,U_3057,U_3056] :
( c_Divides_Odiv__class_Omod(U_3056,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3056),U_3057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3056),U_3058),U_3059)),U_3059) = c_Divides_Odiv__class_Omod(U_3056,U_3057,U_3059)
| ~ class_Divides_Osemiring__div(U_3056) ),
inference(variable_rename,[status(thm)],[f_952_1]) ).
cnf(f_952_3,plain,
( c_Divides_Odiv__class_Omod(U_3056,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3056),U_3057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3056),U_3058),U_3059)),U_3059) = c_Divides_Odiv__class_Omod(U_3056,U_3057,U_3059)
| ~ class_Divides_Osemiring__div(U_3056) ),
inference(clausify,[status(thm)],[f_952_2]) ).
fof(f_953_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_953_2,plain,
! [U_3061,U_3060] :
( c_Divides_Odiv__class_Omod(U_3060,U_3061,c_Groups_Oone__class_Oone(U_3060)) = c_Groups_Ozero__class_Ozero(U_3060)
| ~ class_Divides_Osemiring__div(U_3060) ),
inference(variable_rename,[status(thm)],[f_953_1]) ).
cnf(f_953_3,plain,
( c_Divides_Odiv__class_Omod(U_3060,U_3061,c_Groups_Oone__class_Oone(U_3060)) = c_Groups_Ozero__class_Ozero(U_3060)
| ~ class_Divides_Osemiring__div(U_3060) ),
inference(clausify,[status(thm)],[f_953_2]) ).
fof(f_954_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_954_2,plain,
! [U_3064,U_3063,U_3062] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3062),c_Divides_Odiv__class_Omod(U_3062,U_3063,U_3064)),U_3064) = c_Groups_Ozero__class_Ozero(U_3062)
| ~ class_Divides_Osemiring__div(U_3062) ),
inference(variable_rename,[status(thm)],[f_954_1]) ).
cnf(f_954_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3062),c_Divides_Odiv__class_Omod(U_3062,U_3063,U_3064)),U_3064) = c_Groups_Ozero__class_Ozero(U_3062)
| ~ class_Divides_Osemiring__div(U_3062) ),
inference(clausify,[status(thm)],[f_954_2]) ).
fof(f_955_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_955_2,plain,
! [U_3065] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3065),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_3065,
inference(variable_rename,[status(thm)],[f_955_1]) ).
cnf(f_955_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3065),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_3065,
inference(clausify,[status(thm)],[f_955_2]) ).
fof(f_956_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_956_2,plain,
! [U_3067,U_3066] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3066),U_3067) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3066),U_3067)) ),
inference(variable_rename,[status(thm)],[f_956_1]) ).
cnf(f_956_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3066),U_3067) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3066),U_3067)) ),
inference(clausify,[status(thm)],[f_956_2]) ).
fof(f_957_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_957_2,plain,
! [U_3070,U_3069,U_3068] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3068),U_3069)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3068),U_3070)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3069),U_3070)
| U_3068 = 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_3068),U_3069)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3068),U_3070)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3068 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_957_1]) ).
fof(f_957_3,plain,
( ! [U_3076,U_3074,U_3072] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3072),U_3074)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3072),U_3076)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3074),U_3076)
| U_3072 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_3075,U_3073,U_3071] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3071),U_3073)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3071),U_3075)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3071 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_957_2]) ).
cnf(f_957_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3071),U_3073)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3071),U_3075)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3071 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_957_3]) ).
cnf(f_957_5,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3072),U_3074)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3072),U_3076)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3074),U_3076)
| U_3072 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_957_3]) ).
fof(f_958_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_958_2,plain,
! [U_3078,U_3077] :
( 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_3077,U_3078)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3078))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3077)) ),
inference(variable_rename,[status(thm)],[f_958_1]) ).
cnf(f_958_3,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_3077,U_3078)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3078))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3077)) ),
inference(clausify,[status(thm)],[f_958_2]) ).
fof(f_959_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_959_2,plain,
! [U_3080,U_3079] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3079,U_3080)),U_3079))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3079)) ),
inference(variable_rename,[status(thm)],[f_959_1]) ).
cnf(f_959_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3079,U_3080)),U_3079))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3079)) ),
inference(clausify,[status(thm)],[f_959_2]) ).
fof(f_960_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_960_2,plain,
! [U_3082,U_3081] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3081),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3082,U_3081)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3081),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_960_1]) ).
cnf(f_960_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3081),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3082,U_3081)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3081),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_960_2]) ).
fof(f_961_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_961_2,plain,
! [U_3084,U_3083] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3084,U_3083)),U_3083))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3083)) ),
inference(variable_rename,[status(thm)],[f_961_1]) ).
cnf(f_961_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3084,U_3083)),U_3083))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3083)) ),
inference(clausify,[status(thm)],[f_961_2]) ).
fof(f_962_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_962_2,plain,
! [U_3086,U_3085] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3085),U_3086)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3085)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3086)),
inference(variable_rename,[status(thm)],[f_962_1]) ).
cnf(f_962_3,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3085),U_3086)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3085)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3086)),
inference(clausify,[status(thm)],[f_962_2]) ).
fof(f_963_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_963_2,plain,
! [U_3088,U_3087] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3087)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3088)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3087),U_3088)),
inference(variable_rename,[status(thm)],[f_963_1]) ).
cnf(f_963_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3087)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3088)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3087),U_3088)),
inference(clausify,[status(thm)],[f_963_2]) ).
fof(f_964_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_964_2,plain,
! [U_3092,U_3091] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3091,U_3092) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ! [U_3090] : U_3091 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3092),U_3090) )
& ( ? [U_3089] : U_3091 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3092),U_3089)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3091,U_3092) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_964_1]) ).
fof(f_964_3,plain,
( ! [U_3096,U_3094] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3094,U_3096) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ! [U_3090] : U_3094 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3096),U_3090) )
& ! [U_3095,U_3093] :
( ? [U_3089] : U_3093 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3095),U_3089)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3093,U_3095) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_964_2]) ).
fof(f_964_4,plain,
( ! [U_3096,U_3094] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3094,U_3096) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ! [U_3090] : U_3094 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3096),U_3090) )
& ! [U_3095,U_3093] :
( U_3093 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3095),sK42(U_3095,U_3093))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3093,U_3095) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_3089,sK42(U_3095,U_3093))],[f_964_3]) ).
cnf(f_964_5,plain,
( U_3093 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3095),sK42(U_3095,U_3093))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3093,U_3095) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_964_4]) ).
cnf(f_964_6,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3094,U_3096) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3094 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3096),U_3090) ),
inference(clausify,[status(thm)],[f_964_4]) ).
fof(f_965_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]) ).
cnf(f_965_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(clausify,[status(thm)],[f_965_1]) ).
fof(f_966_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_966_2,plain,
! [U_3098,U_3097] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3097,U_3098) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3097,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3098)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_966_1]) ).
cnf(f_966_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3097,U_3098) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3097,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3098)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_966_2]) ).
fof(f_967_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_967_2,plain,
! [U_3100,U_3099] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3099,U_3100) != 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_3099),U_3100) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_967_1]) ).
cnf(f_967_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3099,U_3100) != 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_3099),U_3100) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_967_2]) ).
fof(f_968_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_968_2,plain,
! [U_3102,U_3101] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3101,U_3102)),U_3102) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_968_1]) ).
cnf(f_968_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3101,U_3102)),U_3102) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_968_2]) ).
fof(f_969_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_969_2,plain,
! [U_3103] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3103,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_3103
& hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3103),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_969_1]) ).
fof(f_969_3,plain,
( ! [U_3105] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3105,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_3105
& ! [U_3104] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3104),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(miniscope,[status(thm)],[f_969_2]) ).
cnf(f_969_4,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3104),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_969_3]) ).
cnf(f_969_5,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3105,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_3105,
inference(clausify,[status(thm)],[f_969_3]) ).
fof(f_970_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_970_2,plain,
! [U_3108,U_3107,U_3106] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3106),U_3107)),U_3108) = 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_3106),U_3108)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3107),U_3108))),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_3106,U_3108)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3107,U_3108))),U_3108)),
inference(variable_rename,[status(thm)],[f_970_1]) ).
cnf(f_970_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3106),U_3107)),U_3108) = 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_3106),U_3108)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3107),U_3108))),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_3106,U_3108)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3107,U_3108))),U_3108)),
inference(clausify,[status(thm)],[f_970_2]) ).
fof(f_971_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]) ).
cnf(f_971_2,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_971_1]) ).
fof(f_972_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_972_2,plain,
! [U_3109] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_3109) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3109),
inference(variable_rename,[status(thm)],[f_972_1]) ).
cnf(f_972_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_3109) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3109),
inference(clausify,[status(thm)],[f_972_2]) ).
fof(f_973_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]) ).
cnf(f_973_2,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_973_1]) ).
fof(f_974_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_974_2,plain,
! [U_3110] :
( ~ c_Int_Oiszero(U_3110,hAPP(c_Int_Onumber__class_Onumber__of(U_3110),c_Int_OMin))
| ~ class_Int_Onumber__ring(U_3110) ),
inference(variable_rename,[status(thm)],[f_974_1]) ).
cnf(f_974_3,plain,
( ~ c_Int_Oiszero(U_3110,hAPP(c_Int_Onumber__class_Onumber__of(U_3110),c_Int_OMin))
| ~ class_Int_Onumber__ring(U_3110) ),
inference(clausify,[status(thm)],[f_974_2]) ).
fof(f_975_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_975_2,plain,
! [U_3111] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_3111) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3111),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_3111)) ),
inference(variable_rename,[status(thm)],[f_975_1]) ).
cnf(f_975_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_3111) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3111),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_3111)) ),
inference(clausify,[status(thm)],[f_975_2]) ).
fof(f_976_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_976_2,plain,
! [U_3114,U_3113,U_3112] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3112),c_Divides_Odiv__class_Omod(U_3112,U_3113,U_3114)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3112),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3112),U_3113),U_3114)),U_3114)) = U_3113
| ~ class_Divides_Osemiring__div(U_3112) ),
inference(variable_rename,[status(thm)],[f_976_1]) ).
cnf(f_976_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3112),c_Divides_Odiv__class_Omod(U_3112,U_3113,U_3114)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3112),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3112),U_3113),U_3114)),U_3114)) = U_3113
| ~ class_Divides_Osemiring__div(U_3112) ),
inference(clausify,[status(thm)],[f_976_2]) ).
fof(f_977_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_977_2,plain,
! [U_3117,U_3116,U_3115] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3115),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3115),U_3116),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3115),U_3117),U_3116))),c_Divides_Odiv__class_Omod(U_3115,U_3117,U_3116)) = U_3117
| ~ class_Divides_Osemiring__div(U_3115) ),
inference(variable_rename,[status(thm)],[f_977_1]) ).
cnf(f_977_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3115),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3115),U_3116),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3115),U_3117),U_3116))),c_Divides_Odiv__class_Omod(U_3115,U_3117,U_3116)) = U_3117
| ~ class_Divides_Osemiring__div(U_3115) ),
inference(clausify,[status(thm)],[f_977_2]) ).
fof(f_978_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_978_2,plain,
! [U_3120,U_3119,U_3118] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3118),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3118),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3118),U_3119),U_3120)),U_3120)),c_Divides_Odiv__class_Omod(U_3118,U_3119,U_3120)) = U_3119
| ~ class_Divides_Osemiring__div(U_3118) ),
inference(variable_rename,[status(thm)],[f_978_1]) ).
cnf(f_978_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3118),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3118),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3118),U_3119),U_3120)),U_3120)),c_Divides_Odiv__class_Omod(U_3118,U_3119,U_3120)) = U_3119
| ~ class_Divides_Osemiring__div(U_3118) ),
inference(clausify,[status(thm)],[f_978_2]) ).
fof(f_979_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_979_2,plain,
! [U_3124,U_3123,U_3122,U_3121] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3121),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3121),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3121),U_3122),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3121),U_3123),U_3122))),c_Divides_Odiv__class_Omod(U_3121,U_3123,U_3122))),U_3124) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3121),U_3123),U_3124)
| ~ class_Divides_Osemiring__div(U_3121) ),
inference(variable_rename,[status(thm)],[f_979_1]) ).
cnf(f_979_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3121),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3121),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3121),U_3122),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3121),U_3123),U_3122))),c_Divides_Odiv__class_Omod(U_3121,U_3123,U_3122))),U_3124) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3121),U_3123),U_3124)
| ~ class_Divides_Osemiring__div(U_3121) ),
inference(clausify,[status(thm)],[f_979_2]) ).
fof(f_980_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_980_2,plain,
! [U_3128,U_3127,U_3126,U_3125] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3125),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3125),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3125),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3125),U_3126),U_3127)),U_3127)),c_Divides_Odiv__class_Omod(U_3125,U_3126,U_3127))),U_3128) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3125),U_3126),U_3128)
| ~ class_Divides_Osemiring__div(U_3125) ),
inference(variable_rename,[status(thm)],[f_980_1]) ).
cnf(f_980_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3125),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3125),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3125),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3125),U_3126),U_3127)),U_3127)),c_Divides_Odiv__class_Omod(U_3125,U_3126,U_3127))),U_3128) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3125),U_3126),U_3128)
| ~ class_Divides_Osemiring__div(U_3125) ),
inference(clausify,[status(thm)],[f_980_2]) ).
fof(f_981_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_981_2,plain,
! [U_3131,U_3130,U_3129] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3131),U_3130)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3131),U_3129)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3129),U_3130))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3129)) ),
inference(variable_rename,[status(thm)],[f_981_1]) ).
cnf(f_981_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3131),U_3130)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3131),U_3129)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3129),U_3130))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3129)) ),
inference(clausify,[status(thm)],[f_981_2]) ).
fof(f_982_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_982_2,plain,
! [U_3133,U_3132] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3132),U_3133)),U_3132) = U_3133
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3132)) ),
inference(variable_rename,[status(thm)],[f_982_1]) ).
cnf(f_982_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3132),U_3133)),U_3132) = U_3133
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3132)) ),
inference(clausify,[status(thm)],[f_982_2]) ).
fof(f_983_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_983_2,plain,
! [U_3135,U_3134] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3135),U_3134)),U_3134) = U_3135
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3134)) ),
inference(variable_rename,[status(thm)],[f_983_1]) ).
cnf(f_983_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3135),U_3134)),U_3134) = U_3135
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3134)) ),
inference(clausify,[status(thm)],[f_983_2]) ).
fof(f_984_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_984_2,plain,
! [U_3138,U_3137,U_3136] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3136),U_3137)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3136),U_3138)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3137),U_3138)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3136)) ),
inference(variable_rename,[status(thm)],[f_984_1]) ).
cnf(f_984_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3136),U_3137)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3136),U_3138)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3137),U_3138)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3136)) ),
inference(clausify,[status(thm)],[f_984_2]) ).
fof(f_985_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_985_2,plain,
! [U_3140,U_3139] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3140),U_3139)),U_3140))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3140))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3139)) ),
inference(variable_rename,[status(thm)],[f_985_1]) ).
cnf(f_985_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3140),U_3139)),U_3140))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3140))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3139)) ),
inference(clausify,[status(thm)],[f_985_2]) ).
fof(f_986_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_986_2,plain,
! [U_3142,U_3141] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3141),U_3142),hAPP(c_Int_Onumber__class_Onumber__of(U_3141),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3141),U_3142)
| ~ class_Int_Onumber__ring(U_3141) ),
inference(variable_rename,[status(thm)],[f_986_1]) ).
cnf(f_986_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3141),U_3142),hAPP(c_Int_Onumber__class_Onumber__of(U_3141),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3141),U_3142)
| ~ class_Int_Onumber__ring(U_3141) ),
inference(clausify,[status(thm)],[f_986_2]) ).
fof(f_987_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_987_2,plain,
! [U_3144,U_3143] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3143),hAPP(c_Int_Onumber__class_Onumber__of(U_3143),c_Int_OMin)),U_3144) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3143),U_3144)
| ~ class_Int_Onumber__ring(U_3143) ),
inference(variable_rename,[status(thm)],[f_987_1]) ).
cnf(f_987_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3143),hAPP(c_Int_Onumber__class_Onumber__of(U_3143),c_Int_OMin)),U_3144) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3143),U_3144)
| ~ class_Int_Onumber__ring(U_3143) ),
inference(clausify,[status(thm)],[f_987_2]) ).
fof(f_988_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_988_2,plain,
! [U_3146,U_3145] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3145,U_3146) = U_3145
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3146),U_3145))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3145),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_988_1]) ).
cnf(f_988_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3145,U_3146) = U_3145
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3146),U_3145))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3145),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_988_2]) ).
fof(f_989_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_989_2,plain,
! [U_3148,U_3147] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3147),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3148,U_3147)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3148,U_3147)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3147),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_989_1]) ).
cnf(f_989_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3148,U_3147)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3147),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_989_2]) ).
cnf(f_989_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3147),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3148,U_3147)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3147),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_989_2]) ).
fof(f_990_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_990_2,plain,
! [U_3150,U_3149] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3150,U_3149)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3149),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_990_1]) ).
cnf(f_990_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3150,U_3149)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3149),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_990_2]) ).
fof(f_991_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_991_2,plain,
! [U_3152,U_3151] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3151,U_3152) = U_3151
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3151),U_3152))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3151)) ),
inference(variable_rename,[status(thm)],[f_991_1]) ).
cnf(f_991_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3151,U_3152) = U_3151
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3151),U_3152))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3151)) ),
inference(clausify,[status(thm)],[f_991_2]) ).
fof(f_992_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_992_2,plain,
! [U_3154,U_3153] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3154,U_3153)),U_3153))
& 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_3154,U_3153))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3153)) ),
inference(variable_rename,[status(thm)],[f_992_1]) ).
cnf(f_992_3,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_3154,U_3153)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3153)) ),
inference(clausify,[status(thm)],[f_992_2]) ).
cnf(f_992_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3154,U_3153)),U_3153))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3153)) ),
inference(clausify,[status(thm)],[f_992_2]) ).
fof(f_993_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_993_2,plain,
! [U_3156,U_3155] :
( 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_3156,U_3155)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3155)) ),
inference(variable_rename,[status(thm)],[f_993_1]) ).
cnf(f_993_3,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_3156,U_3155)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3155)) ),
inference(clausify,[status(thm)],[f_993_2]) ).
fof(f_994_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_994_2,plain,
! [U_3157] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_3157),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3157),c_Groups_Oone__class_Oone(U_3157))
| ~ class_Int_Onumber__ring(U_3157) ),
inference(variable_rename,[status(thm)],[f_994_1]) ).
cnf(f_994_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_3157),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3157),c_Groups_Oone__class_Oone(U_3157))
| ~ class_Int_Onumber__ring(U_3157) ),
inference(clausify,[status(thm)],[f_994_2]) ).
fof(f_995_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_995_2,plain,
! [U_3158] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3158),c_Groups_Oone__class_Oone(U_3158)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3158),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_3158) ),
inference(variable_rename,[status(thm)],[f_995_1]) ).
cnf(f_995_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_3158),c_Groups_Oone__class_Oone(U_3158)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3158),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_3158) ),
inference(clausify,[status(thm)],[f_995_2]) ).
fof(f_996_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_996_2,plain,
! [U_3160,U_3159] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3159,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3160)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3159,U_3160)),U_3160)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3159,U_3160) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3159,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3160)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3159,U_3160) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_996_1]) ).
fof(f_996_3,plain,
( ! [U_3164,U_3162] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3162,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3164)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3162,U_3164)),U_3164)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3162,U_3164) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_3163,U_3161] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3161,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3163)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3161,U_3163) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_996_2]) ).
cnf(f_996_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3161,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3163)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3161,U_3163) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_996_3]) ).
cnf(f_996_5,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3162,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3164)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3162,U_3164)),U_3164)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3162,U_3164) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_996_3]) ).
fof(f_997_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_997_2,plain,
! [U_3166,U_3165] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3165),U_3166) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3166),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3165,U_3166))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3165,U_3166) = 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_3165),U_3166) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3165,U_3166) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_997_1]) ).
fof(f_997_3,plain,
( ! [U_3170,U_3168] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3168),U_3170) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3170),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3168,U_3170))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3168,U_3170) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_3169,U_3167] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3167),U_3169) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3167,U_3169) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_997_2]) ).
cnf(f_997_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3167),U_3169) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3167,U_3169) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_997_3]) ).
cnf(f_997_5,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3168),U_3170) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3170),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3168,U_3170))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3168,U_3170) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_997_3]) ).
fof(f_998_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_998_2,plain,
! [U_3172,U_3171] : U_3171 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3172),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3171),U_3172))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3171,U_3172)),
inference(variable_rename,[status(thm)],[f_998_1]) ).
cnf(f_998_3,plain,
U_3171 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3172),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3171),U_3172))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3171,U_3172)),
inference(clausify,[status(thm)],[f_998_2]) ).
fof(f_999_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_999_2,plain,
! [U_3175,U_3174,U_3173] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3173),U_3174)),U_3175) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3173),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3174),U_3175))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3173),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3174,U_3175))),U_3175)),
inference(variable_rename,[status(thm)],[f_999_1]) ).
cnf(f_999_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3173),U_3174)),U_3175) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3173),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3174),U_3175))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3173),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3174,U_3175))),U_3175)),
inference(clausify,[status(thm)],[f_999_2]) ).
fof(f_1000_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_1000_2,plain,
! [U_3178,U_3177,U_3176] : 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_3176),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3177),U_3176))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3177,U_3176))),U_3178) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3177),U_3178),
inference(variable_rename,[status(thm)],[f_1000_1]) ).
cnf(f_1000_3,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_3176),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3177),U_3176))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3177,U_3176))),U_3178) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3177),U_3178),
inference(clausify,[status(thm)],[f_1000_2]) ).
fof(f_1001_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_1001_2,plain,
! [U_3181,U_3180,U_3179] : 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_3179),U_3180)),U_3180)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3179,U_3180))),U_3181) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3179),U_3181),
inference(variable_rename,[status(thm)],[f_1001_1]) ).
cnf(f_1001_3,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_3179),U_3180)),U_3180)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3179,U_3180))),U_3181) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3179),U_3181),
inference(clausify,[status(thm)],[f_1001_2]) ).
fof(f_1002_1,plain,
! [V_na_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_na_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ( ( V_na_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_na_2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_m_2 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
& ( ( V_na_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_na_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_na_2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(fof_nnf,[status(thm)],[fact_zmult__eq__1__iff]) ).
fof(f_1002_2,plain,
! [U_3183,U_3182] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3182),U_3183) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ( ( U_3183 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_3182 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
& ( U_3183 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_3182 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
& ( ( U_3183 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
& U_3182 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
| ( U_3183 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& U_3182 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3182),U_3183) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_1002_1]) ).
fof(f_1002_3,plain,
( ! [U_3187,U_3185] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3185),U_3187) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ( ( U_3187 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_3185 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
& ( U_3187 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_3185 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
& ! [U_3186,U_3184] :
( ( U_3186 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
& U_3184 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
| ( U_3186 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& U_3184 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3184),U_3186) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_1002_2]) ).
cnf(f_1002_4,plain,
( U_3184 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_3184 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3184),U_3186) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1002_3]) ).
cnf(f_1002_5,plain,
( U_3186 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_3184 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3184),U_3186) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1002_3]) ).
cnf(f_1002_6,plain,
( U_3184 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_3186 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3184),U_3186) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1002_3]) ).
cnf(f_1002_7,plain,
( U_3186 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_3186 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3184),U_3186) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1002_3]) ).
cnf(f_1002_8,plain,
( U_3187 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_3185 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3185),U_3187) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1002_3]) ).
cnf(f_1002_9,plain,
( U_3187 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_3185 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3185),U_3187) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1002_3]) ).
fof(f_1003_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_1003_2,plain,
! [U_3189,U_3188] :
( U_3188 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_3188 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3188),U_3189) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1003_1]) ).
cnf(f_1003_3,plain,
( U_3188 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| U_3188 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3188),U_3189) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1003_2]) ).
fof(f_1004_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_1004_2,plain,
! [U_3191,U_3190] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3190),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3191),U_3190)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3191),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3191,U_3190)),
inference(variable_rename,[status(thm)],[f_1004_1]) ).
cnf(f_1004_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3190),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3191),U_3190)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3191),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3191,U_3190)),
inference(clausify,[status(thm)],[f_1004_2]) ).
fof(f_1005_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_1005_2,plain,
! [U_3193,U_3192] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3192,U_3193) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3192),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3192),U_3193)),U_3193)),
inference(variable_rename,[status(thm)],[f_1005_1]) ).
cnf(f_1005_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3192,U_3193) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3192),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3192),U_3193)),U_3193)),
inference(clausify,[status(thm)],[f_1005_2]) ).
fof(f_1006_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_1006_2,plain,
! [U_3194] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_3194),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3194),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_3194) ),
inference(variable_rename,[status(thm)],[f_1006_1]) ).
cnf(f_1006_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_3194),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3194),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_3194) ),
inference(clausify,[status(thm)],[f_1006_2]) ).
fof(f_1007_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_1007_2,plain,
! [U_3195] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3195),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3195),
inference(variable_rename,[status(thm)],[f_1007_1]) ).
cnf(f_1007_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3195),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3195),
inference(clausify,[status(thm)],[f_1007_2]) ).
fof(f_1008_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_1008_2,plain,
! [U_3196] : c_Int_Osucc(U_3196) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3196),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[f_1008_1]) ).
cnf(f_1008_3,plain,
c_Int_Osucc(U_3196) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3196),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_1008_2]) ).
fof(f_1009_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_1009_2,plain,
! [U_3198,U_3197] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3198),U_3197) = 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_3198),U_3197)),U_3197))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3198),U_3197))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3197)) ),
inference(variable_rename,[status(thm)],[f_1009_1]) ).
cnf(f_1009_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3198),U_3197) = 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_3198),U_3197)),U_3197))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3198),U_3197))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3197)) ),
inference(clausify,[status(thm)],[f_1009_2]) ).
fof(f_1010_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_1010_2,plain,
! [U_3200,U_3199] :
( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3200),U_3199) = 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_3200),U_3199)),U_3199))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3200),U_3199)) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3200),U_3199) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3200),U_3199)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3199)) ),
inference(variable_rename,[status(thm)],[f_1010_1]) ).
cnf(f_1010_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3200),U_3199) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3200),U_3199))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3199)) ),
inference(clausify,[status(thm)],[f_1010_2]) ).
cnf(f_1010_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3200),U_3199) = 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_3200),U_3199)),U_3199))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3200),U_3199))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3199)) ),
inference(clausify,[status(thm)],[f_1010_2]) ).
fof(f_1011_1,plain,
! [V_k_2,V_na_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_na_2),V_k_2)))
| ( ? [B_i,B_j] :
( ~ hBOOL(hAPP(V_P_2,B_i))
& V_na_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_P_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_P_2,B_i))
| V_na_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_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_na_2),V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__div]) ).
fof(f_1011_2,plain,
! [U_3207,U_3206,U_3205] :
( ( hBOOL(hAPP(U_3205,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3206),U_3207)))
| ( ? [U_3204,U_3203] :
( ~ hBOOL(hAPP(U_3205,U_3204))
& U_3206 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3207),U_3204)),U_3203)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3203),U_3207)) )
& U_3207 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_3205,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_3207 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( ( ! [U_3202,U_3201] :
( hBOOL(hAPP(U_3205,U_3202))
| U_3206 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3207),U_3202)),U_3201)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3201),U_3207)) )
| U_3207 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_3205,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3207 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_3205,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3206),U_3207))) ) ),
inference(variable_rename,[status(thm)],[f_1011_1]) ).
fof(f_1011_3,plain,
( ! [U_3213,U_3211,U_3209] :
( hBOOL(hAPP(U_3209,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3211),U_3213)))
| ( ? [U_3204,U_3203] :
( ~ hBOOL(hAPP(U_3209,U_3204))
& U_3211 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3213),U_3204)),U_3203)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3203),U_3213)) )
& U_3213 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_3209,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_3213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_3212,U_3210,U_3208] :
( ( ( ! [U_3202,U_3201] :
( hBOOL(hAPP(U_3208,U_3202))
| U_3210 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3212),U_3202)),U_3201)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3201),U_3212)) )
| U_3212 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_3208,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3212 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_3208,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3210),U_3212))) ) ),
inference(miniscope,[status(thm)],[f_1011_2]) ).
fof(f_1011_4,plain,
( ! [U_3213,U_3211,U_3209] :
( hBOOL(hAPP(U_3209,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3211),U_3213)))
| ( ? [U_3203] :
( ~ hBOOL(hAPP(U_3209,sK43(U_3213,U_3211,U_3209)))
& U_3211 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3213),sK43(U_3213,U_3211,U_3209))),U_3203)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3203),U_3213)) )
& U_3213 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_3209,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_3213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_3212,U_3210,U_3208] :
( ( ( ! [U_3202,U_3201] :
( hBOOL(hAPP(U_3208,U_3202))
| U_3210 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3212),U_3202)),U_3201)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3201),U_3212)) )
| U_3212 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_3208,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3212 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_3208,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3210),U_3212))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_3204,sK43(U_3213,U_3211,U_3209))],[f_1011_3]) ).
fof(f_1011_5,plain,
( ! [U_3213,U_3211,U_3209] :
( hBOOL(hAPP(U_3209,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3211),U_3213)))
| ( ~ hBOOL(hAPP(U_3209,sK43(U_3213,U_3211,U_3209)))
& U_3211 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3213),sK43(U_3213,U_3211,U_3209))),sK44(U_3213,U_3211,U_3209))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK44(U_3213,U_3211,U_3209)),U_3213))
& U_3213 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_3209,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_3213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_3212,U_3210,U_3208] :
( ( ( ! [U_3202,U_3201] :
( hBOOL(hAPP(U_3208,U_3202))
| U_3210 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3212),U_3202)),U_3201)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3201),U_3212)) )
| U_3212 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_3208,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3212 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_3208,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3210),U_3212))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_3203,sK44(U_3213,U_3211,U_3209))],[f_1011_4]) ).
cnf(f_1011_6,plain,
( hBOOL(hAPP(U_3208,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3212 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_3208,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3210),U_3212))) ),
inference(clausify,[status(thm)],[f_1011_5]) ).
cnf(f_1011_7,plain,
( hBOOL(hAPP(U_3208,U_3202))
| U_3210 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3212),U_3202)),U_3201)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3201),U_3212))
| U_3212 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_3208,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3210),U_3212))) ),
inference(clausify,[status(thm)],[f_1011_5]) ).
cnf(f_1011_8,plain,
( U_3213 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_3209,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3211),U_3213))) ),
inference(clausify,[status(thm)],[f_1011_5]) ).
cnf(f_1011_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK44(U_3213,U_3211,U_3209)),U_3213))
| U_3213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_3209,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3211),U_3213))) ),
inference(clausify,[status(thm)],[f_1011_5]) ).
cnf(f_1011_10,plain,
( U_3211 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3213),sK43(U_3213,U_3211,U_3209))),sK44(U_3213,U_3211,U_3209))
| U_3213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_3209,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3211),U_3213))) ),
inference(clausify,[status(thm)],[f_1011_5]) ).
cnf(f_1011_11,plain,
( ~ hBOOL(hAPP(U_3209,sK43(U_3213,U_3211,U_3209)))
| U_3213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_3209,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3211),U_3213))) ),
inference(clausify,[status(thm)],[f_1011_5]) ).
cnf(f_1011_12,plain,
( U_3213 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_3209,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_3209,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3211),U_3213))) ),
inference(clausify,[status(thm)],[f_1011_5]) ).
cnf(f_1011_13,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK44(U_3213,U_3211,U_3209)),U_3213))
| ~ hBOOL(hAPP(U_3209,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_3209,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3211),U_3213))) ),
inference(clausify,[status(thm)],[f_1011_5]) ).
cnf(f_1011_14,plain,
( U_3211 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3213),sK43(U_3213,U_3211,U_3209))),sK44(U_3213,U_3211,U_3209))
| ~ hBOOL(hAPP(U_3209,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_3209,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3211),U_3213))) ),
inference(clausify,[status(thm)],[f_1011_5]) ).
cnf(f_1011_15,plain,
( ~ hBOOL(hAPP(U_3209,sK43(U_3213,U_3211,U_3209)))
| ~ hBOOL(hAPP(U_3209,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(U_3209,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3211),U_3213))) ),
inference(clausify,[status(thm)],[f_1011_5]) ).
fof(f_1012_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_1012_2,plain,
! [U_3215,U_3214] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3214)),hAPP(c_Int_Onat,U_3215)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3214),U_3215))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3215))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3214)) ),
inference(variable_rename,[status(thm)],[f_1012_1]) ).
cnf(f_1012_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3214)),hAPP(c_Int_Onat,U_3215)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3214),U_3215))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3215))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3214)) ),
inference(clausify,[status(thm)],[f_1012_2]) ).
fof(f_1013_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_1013_2,plain,
! [U_3217,U_3216] :
( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3216),U_3217)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3216)),hAPP(c_Int_Onat,U_3217))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3216)) ),
inference(variable_rename,[status(thm)],[f_1013_1]) ).
cnf(f_1013_3,plain,
( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3216),U_3217)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3216)),hAPP(c_Int_Onat,U_3217))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3216)) ),
inference(clausify,[status(thm)],[f_1013_2]) ).
fof(f_1014_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_1014_2,plain,
! [U_3219,U_3218] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3218,U_3219) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3218),U_3219)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3218),U_3219)),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_3218)) ),
inference(variable_rename,[status(thm)],[f_1014_1]) ).
cnf(f_1014_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3218,U_3219) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3218),U_3219)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3218),U_3219)),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_3218)) ),
inference(clausify,[status(thm)],[f_1014_2]) ).
fof(f_1015_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_1015_2,plain,
! [U_3220] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),U_3220) = 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_3220)) ),
inference(variable_rename,[status(thm)],[f_1015_1]) ).
cnf(f_1015_3,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_3220) = 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_3220)) ),
inference(clausify,[status(thm)],[f_1015_2]) ).
fof(f_1016_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_1016_2,plain,
! [U_3222,U_3221] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3222),U_3221) = 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_3222),U_3221)),U_3221))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3221),U_3222))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3221)) ),
inference(variable_rename,[status(thm)],[f_1016_1]) ).
cnf(f_1016_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3222),U_3221) = 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_3222),U_3221)),U_3221))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3221),U_3222))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3221)) ),
inference(clausify,[status(thm)],[f_1016_2]) ).
fof(f_1017_1,plain,
! [V_m_2,V_q_2,V_na_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_na_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_na_2),V_q_2)),V_m_2)) )
| V_q_2 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_na_2) )
& ( V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_na_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_na_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_na_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_na_2)) ),
inference(fof_nnf,[status(thm)],[fact_split__div__lemma]) ).
fof(f_1017_2,plain,
! [U_3225,U_3224,U_3223] :
( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3225),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3223),hAPP(c_Nat_OSuc,U_3224))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3223),U_3224)),U_3225)) )
| U_3224 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3225),U_3223) )
& ( U_3224 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3225),U_3223)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3225),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3223),hAPP(c_Nat_OSuc,U_3224))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3223),U_3224)),U_3225)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3223)) ),
inference(variable_rename,[status(thm)],[f_1017_1]) ).
cnf(f_1017_3,plain,
( U_3224 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3225),U_3223)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3225),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3223),hAPP(c_Nat_OSuc,U_3224))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3223),U_3224)),U_3225))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3223)) ),
inference(clausify,[status(thm)],[f_1017_2]) ).
cnf(f_1017_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_3223),U_3224)),U_3225))
| U_3224 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3225),U_3223)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3223)) ),
inference(clausify,[status(thm)],[f_1017_2]) ).
cnf(f_1017_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3225),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3223),hAPP(c_Nat_OSuc,U_3224))))
| U_3224 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3225),U_3223)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3223)) ),
inference(clausify,[status(thm)],[f_1017_2]) ).
fof(f_1018_1,plain,
! [V_na_2,V_m_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_na_2)))
| ( ! [B_q] :
( ~ hBOOL(hAPP(V_P_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_na_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_na_2),B_q)),V_m_2)) )
& ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ( ? [B_q] :
( hBOOL(hAPP(V_P_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_na_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_na_2),B_q)),V_m_2)) )
| ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__div_H]) ).
fof(f_1018_2,plain,
! [U_3230,U_3229,U_3228] :
( ( hBOOL(hAPP(U_3228,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3229),U_3230)))
| ( ! [U_3227] :
( ~ hBOOL(hAPP(U_3228,U_3227))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3229),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3230),hAPP(c_Nat_OSuc,U_3227))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3230),U_3227)),U_3229)) )
& ( ~ hBOOL(hAPP(U_3228,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3230 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ( ? [U_3226] :
( hBOOL(hAPP(U_3228,U_3226))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3229),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3230),hAPP(c_Nat_OSuc,U_3226))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3230),U_3226)),U_3229)) )
| ( hBOOL(hAPP(U_3228,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_3230 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(U_3228,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3229),U_3230))) ) ),
inference(variable_rename,[status(thm)],[f_1018_1]) ).
fof(f_1018_3,plain,
( ! [U_3236,U_3234,U_3232] :
( hBOOL(hAPP(U_3232,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3234),U_3236)))
| ( ! [U_3227] :
( ~ hBOOL(hAPP(U_3232,U_3227))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3234),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3236),hAPP(c_Nat_OSuc,U_3227))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3236),U_3227)),U_3234)) )
& ( ~ hBOOL(hAPP(U_3232,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3236 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ! [U_3235,U_3233,U_3231] :
( ? [U_3226] :
( hBOOL(hAPP(U_3231,U_3226))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3233),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3235),hAPP(c_Nat_OSuc,U_3226))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3235),U_3226)),U_3233)) )
| ( hBOOL(hAPP(U_3231,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_3235 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(U_3231,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3233),U_3235))) ) ),
inference(miniscope,[status(thm)],[f_1018_2]) ).
fof(f_1018_4,plain,
( ! [U_3236,U_3234,U_3232] :
( hBOOL(hAPP(U_3232,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3234),U_3236)))
| ( ! [U_3227] :
( ~ hBOOL(hAPP(U_3232,U_3227))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3234),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3236),hAPP(c_Nat_OSuc,U_3227))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3236),U_3227)),U_3234)) )
& ( ~ hBOOL(hAPP(U_3232,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3236 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
& ! [U_3235,U_3233,U_3231] :
( ( hBOOL(hAPP(U_3231,sK45(U_3235,U_3233,U_3231)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3233),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3235),hAPP(c_Nat_OSuc,sK45(U_3235,U_3233,U_3231)))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3235),sK45(U_3235,U_3233,U_3231))),U_3233)) )
| ( hBOOL(hAPP(U_3231,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& U_3235 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(U_3231,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3233),U_3235))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_3226,sK45(U_3235,U_3233,U_3231))],[f_1018_3]) ).
cnf(f_1018_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3235),sK45(U_3235,U_3233,U_3231))),U_3233))
| U_3235 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_3231,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3233),U_3235))) ),
inference(clausify,[status(thm)],[f_1018_4]) ).
cnf(f_1018_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3233),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3235),hAPP(c_Nat_OSuc,sK45(U_3235,U_3233,U_3231)))))
| U_3235 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_3231,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3233),U_3235))) ),
inference(clausify,[status(thm)],[f_1018_4]) ).
cnf(f_1018_7,plain,
( hBOOL(hAPP(U_3231,sK45(U_3235,U_3233,U_3231)))
| U_3235 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_3231,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3233),U_3235))) ),
inference(clausify,[status(thm)],[f_1018_4]) ).
cnf(f_1018_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3235),sK45(U_3235,U_3233,U_3231))),U_3233))
| hBOOL(hAPP(U_3231,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(U_3231,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3233),U_3235))) ),
inference(clausify,[status(thm)],[f_1018_4]) ).
cnf(f_1018_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3233),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3235),hAPP(c_Nat_OSuc,sK45(U_3235,U_3233,U_3231)))))
| hBOOL(hAPP(U_3231,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(U_3231,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3233),U_3235))) ),
inference(clausify,[status(thm)],[f_1018_4]) ).
cnf(f_1018_10,plain,
( hBOOL(hAPP(U_3231,sK45(U_3235,U_3233,U_3231)))
| hBOOL(hAPP(U_3231,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(U_3231,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3233),U_3235))) ),
inference(clausify,[status(thm)],[f_1018_4]) ).
cnf(f_1018_11,plain,
( ~ hBOOL(hAPP(U_3232,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_3236 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_3232,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3234),U_3236))) ),
inference(clausify,[status(thm)],[f_1018_4]) ).
cnf(f_1018_12,plain,
( ~ hBOOL(hAPP(U_3232,U_3227))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3234),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3236),hAPP(c_Nat_OSuc,U_3227))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3236),U_3227)),U_3234))
| hBOOL(hAPP(U_3232,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3234),U_3236))) ),
inference(clausify,[status(thm)],[f_1018_4]) ).
fof(f_1019_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_1019_2,plain,
! [U_3238,U_3237] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_3237),c_Int_Osucc(U_3238)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3237),c_Groups_Oone__class_Oone(U_3237)),hAPP(c_Int_Onumber__class_Onumber__of(U_3237),U_3238))
| ~ class_Int_Onumber__ring(U_3237) ),
inference(variable_rename,[status(thm)],[f_1019_1]) ).
cnf(f_1019_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_3237),c_Int_Osucc(U_3238)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3237),c_Groups_Oone__class_Oone(U_3237)),hAPP(c_Int_Onumber__class_Onumber__of(U_3237),U_3238))
| ~ class_Int_Onumber__ring(U_3237) ),
inference(clausify,[status(thm)],[f_1019_2]) ).
fof(f_1020_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_1020_2,plain,
! [U_3242,U_3241,U_3240,U_3239] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3239,U_3240) = U_3242
| U_3240 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3242),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3240),U_3242)) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3240)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3242),U_3240))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3242)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3240)) )
| U_3239 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3240),U_3241)),U_3242) ),
inference(variable_rename,[status(thm)],[f_1020_1]) ).
cnf(f_1020_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3240))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3240))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3239,U_3240) = U_3242
| U_3240 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3239 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3240),U_3241)),U_3242) ),
inference(clausify,[status(thm)],[f_1020_2]) ).
cnf(f_1020_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3242),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3240),U_3242))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3240))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3239,U_3240) = U_3242
| U_3240 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3239 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3240),U_3241)),U_3242) ),
inference(clausify,[status(thm)],[f_1020_2]) ).
cnf(f_1020_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3240))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3242),U_3240))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3242))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3239,U_3240) = U_3242
| U_3240 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3239 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3240),U_3241)),U_3242) ),
inference(clausify,[status(thm)],[f_1020_2]) ).
cnf(f_1020_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3242),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3240),U_3242))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3242),U_3240))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3242))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3239,U_3240) = U_3242
| U_3240 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3239 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3240),U_3241)),U_3242) ),
inference(clausify,[status(thm)],[f_1020_2]) ).
fof(f_1021_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_1021_2,plain,
! [U_3246,U_3245,U_3244,U_3243] :
( 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_3244),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3246,U_3243))),U_3245)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3245),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3244),U_3245))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3243)) ),
inference(variable_rename,[status(thm)],[f_1021_1]) ).
cnf(f_1021_3,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_3244),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3246,U_3243))),U_3245)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3245),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3244),U_3245))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3243)) ),
inference(clausify,[status(thm)],[f_1021_2]) ).
fof(f_1022_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_1022_2,plain,
! [U_3250,U_3249,U_3248,U_3247] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3248),U_3247)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3248),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3250,U_3247))),U_3249)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3249),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3248),U_3249))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3247)) ),
inference(variable_rename,[status(thm)],[f_1022_1]) ).
cnf(f_1022_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3248),U_3247)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3248),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3250,U_3247))),U_3249)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3249),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3248),U_3249))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3247)) ),
inference(clausify,[status(thm)],[f_1022_2]) ).
fof(f_1023_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_1023_2,plain,
! [U_3254,U_3253,U_3252,U_3251] :
( 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_3253),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3254,U_3251))),U_3252)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3253),U_3251)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3252),U_3253))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3252))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3251)) ),
inference(variable_rename,[status(thm)],[f_1023_1]) ).
cnf(f_1023_3,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_3253),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3254,U_3251))),U_3252)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3253),U_3251)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3252),U_3253))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3252))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3251)) ),
inference(clausify,[status(thm)],[f_1023_2]) ).
fof(f_1024_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_1024_2,plain,
! [U_3258,U_3257,U_3256,U_3255] :
( 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_3257),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3258,U_3255))),U_3256)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3256),U_3257))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3256))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3255)) ),
inference(variable_rename,[status(thm)],[f_1024_1]) ).
cnf(f_1024_3,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_3257),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3258,U_3255))),U_3256)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3256),U_3257))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3256))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3255)) ),
inference(clausify,[status(thm)],[f_1024_2]) ).
fof(f_1025_1,plain,
! [V_k_2,V_na_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_na_2,V_k_2)))
| ( ? [B_i,B_j] :
( ~ hBOOL(hAPP(V_P_2,B_j))
& V_na_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_P_2,B_j))
& V_na_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_P_2,V_na_2))
& V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( ( ! [B_i,B_j] :
( hBOOL(hAPP(V_P_2,B_j))
| V_na_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_P_2,B_j))
| V_na_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_P_2,V_na_2))
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_na_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__zmod]) ).
fof(f_1025_2,plain,
! [U_3269,U_3268,U_3267] :
( ( hBOOL(hAPP(U_3267,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3268,U_3269)))
| ( ? [U_3266,U_3265] :
( ~ hBOOL(hAPP(U_3267,U_3265))
& U_3268 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3269),U_3266)),U_3265)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3265),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3269),U_3265)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3269),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_3264,U_3263] :
( ~ hBOOL(hAPP(U_3267,U_3263))
& U_3268 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3269),U_3264)),U_3263)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3263),U_3269))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3263)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3269)) )
| ( ~ hBOOL(hAPP(U_3267,U_3268))
& U_3269 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( ( ( ! [U_3262,U_3261] :
( hBOOL(hAPP(U_3267,U_3261))
| U_3268 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3269),U_3262)),U_3261)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3261),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3269),U_3261)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3269),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_3260,U_3259] :
( hBOOL(hAPP(U_3267,U_3259))
| U_3268 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3269),U_3260)),U_3259)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3259),U_3269))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3259)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3269)) )
& ( hBOOL(hAPP(U_3267,U_3268))
| U_3269 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_3267,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3268,U_3269))) ) ),
inference(variable_rename,[status(thm)],[f_1025_1]) ).
fof(f_1025_3,plain,
( ! [U_3275,U_3273,U_3271] :
( hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275)))
| ( ? [U_3266,U_3265] :
( ~ hBOOL(hAPP(U_3271,U_3265))
& U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),U_3266)),U_3265)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3265),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),U_3265)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_3264,U_3263] :
( ~ hBOOL(hAPP(U_3271,U_3263))
& U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),U_3264)),U_3263)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3263),U_3275))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3263)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3275)) )
| ( ~ hBOOL(hAPP(U_3271,U_3273))
& U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_3274,U_3272,U_3270] :
( ( ( ! [U_3262,U_3261] :
( hBOOL(hAPP(U_3270,U_3261))
| U_3272 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3274),U_3262)),U_3261)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3261),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3274),U_3261)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3274),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_3260,U_3259] :
( hBOOL(hAPP(U_3270,U_3259))
| U_3272 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3274),U_3260)),U_3259)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3259),U_3274))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3259)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3274)) )
& ( hBOOL(hAPP(U_3270,U_3272))
| U_3274 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_3270,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3272,U_3274))) ) ),
inference(miniscope,[status(thm)],[f_1025_2]) ).
fof(f_1025_4,plain,
( ! [U_3275,U_3273,U_3271] :
( hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275)))
| ( ? [U_3266,U_3265] :
( ~ hBOOL(hAPP(U_3271,U_3265))
& U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),U_3266)),U_3265)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3265),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),U_3265)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ? [U_3263] :
( ~ hBOOL(hAPP(U_3271,U_3263))
& U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK46(U_3275,U_3273,U_3271))),U_3263)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3263),U_3275))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3263)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3275)) )
| ( ~ hBOOL(hAPP(U_3271,U_3273))
& U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_3274,U_3272,U_3270] :
( ( ( ! [U_3262,U_3261] :
( hBOOL(hAPP(U_3270,U_3261))
| U_3272 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3274),U_3262)),U_3261)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3261),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3274),U_3261)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3274),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_3260,U_3259] :
( hBOOL(hAPP(U_3270,U_3259))
| U_3272 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3274),U_3260)),U_3259)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3259),U_3274))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3259)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3274)) )
& ( hBOOL(hAPP(U_3270,U_3272))
| U_3274 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_3270,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3272,U_3274))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_3264,sK46(U_3275,U_3273,U_3271))],[f_1025_3]) ).
fof(f_1025_5,plain,
( ! [U_3275,U_3273,U_3271] :
( hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275)))
| ( ? [U_3266,U_3265] :
( ~ hBOOL(hAPP(U_3271,U_3265))
& U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),U_3266)),U_3265)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3265),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),U_3265)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_3271,sK47(U_3275,U_3273,U_3271)))
& U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK46(U_3275,U_3273,U_3271))),sK47(U_3275,U_3273,U_3271))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK47(U_3275,U_3273,U_3271)),U_3275))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK47(U_3275,U_3273,U_3271)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3275)) )
| ( ~ hBOOL(hAPP(U_3271,U_3273))
& U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_3274,U_3272,U_3270] :
( ( ( ! [U_3262,U_3261] :
( hBOOL(hAPP(U_3270,U_3261))
| U_3272 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3274),U_3262)),U_3261)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3261),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3274),U_3261)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3274),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_3260,U_3259] :
( hBOOL(hAPP(U_3270,U_3259))
| U_3272 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3274),U_3260)),U_3259)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3259),U_3274))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3259)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3274)) )
& ( hBOOL(hAPP(U_3270,U_3272))
| U_3274 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_3270,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3272,U_3274))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_3263,sK47(U_3275,U_3273,U_3271))],[f_1025_4]) ).
fof(f_1025_6,plain,
( ! [U_3275,U_3273,U_3271] :
( hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275)))
| ( ? [U_3265] :
( ~ hBOOL(hAPP(U_3271,U_3265))
& U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK48(U_3275,U_3273,U_3271))),U_3265)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3265),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),U_3265)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_3271,sK47(U_3275,U_3273,U_3271)))
& U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK46(U_3275,U_3273,U_3271))),sK47(U_3275,U_3273,U_3271))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK47(U_3275,U_3273,U_3271)),U_3275))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK47(U_3275,U_3273,U_3271)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3275)) )
| ( ~ hBOOL(hAPP(U_3271,U_3273))
& U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_3274,U_3272,U_3270] :
( ( ( ! [U_3262,U_3261] :
( hBOOL(hAPP(U_3270,U_3261))
| U_3272 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3274),U_3262)),U_3261)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3261),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3274),U_3261)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3274),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_3260,U_3259] :
( hBOOL(hAPP(U_3270,U_3259))
| U_3272 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3274),U_3260)),U_3259)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3259),U_3274))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3259)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3274)) )
& ( hBOOL(hAPP(U_3270,U_3272))
| U_3274 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_3270,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3272,U_3274))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_3266,sK48(U_3275,U_3273,U_3271))],[f_1025_5]) ).
fof(f_1025_7,plain,
( ! [U_3275,U_3273,U_3271] :
( hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275)))
| ( ~ hBOOL(hAPP(U_3271,sK49(U_3275,U_3273,U_3271)))
& U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK48(U_3275,U_3273,U_3271))),sK49(U_3275,U_3273,U_3271))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK49(U_3275,U_3273,U_3271)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),sK49(U_3275,U_3273,U_3271)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(U_3271,sK47(U_3275,U_3273,U_3271)))
& U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK46(U_3275,U_3273,U_3271))),sK47(U_3275,U_3273,U_3271))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK47(U_3275,U_3273,U_3271)),U_3275))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK47(U_3275,U_3273,U_3271)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3275)) )
| ( ~ hBOOL(hAPP(U_3271,U_3273))
& U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_3274,U_3272,U_3270] :
( ( ( ! [U_3262,U_3261] :
( hBOOL(hAPP(U_3270,U_3261))
| U_3272 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3274),U_3262)),U_3261)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3261),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3274),U_3261)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3274),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [U_3260,U_3259] :
( hBOOL(hAPP(U_3270,U_3259))
| U_3272 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3274),U_3260)),U_3259)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3259),U_3274))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3259)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3274)) )
& ( hBOOL(hAPP(U_3270,U_3272))
| U_3274 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ hBOOL(hAPP(U_3270,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3272,U_3274))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_3265,sK49(U_3275,U_3273,U_3271))],[f_1025_6]) ).
cnf(f_1025_8,plain,
( hBOOL(hAPP(U_3270,U_3272))
| U_3274 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_3270,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3272,U_3274))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_9,plain,
( hBOOL(hAPP(U_3270,U_3259))
| U_3272 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3274),U_3260)),U_3259)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3259),U_3274))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3259))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3274))
| ~ hBOOL(hAPP(U_3270,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3272,U_3274))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_10,plain,
( hBOOL(hAPP(U_3270,U_3261))
| U_3272 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3274),U_3262)),U_3261)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3261),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3274),U_3261))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3274),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(U_3270,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3272,U_3274))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3275))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_12,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK47(U_3275,U_3273,U_3271)))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_13,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK47(U_3275,U_3273,U_3271)),U_3275))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_14,plain,
( U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK46(U_3275,U_3273,U_3271))),sK47(U_3275,U_3273,U_3271))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_15,plain,
( ~ hBOOL(hAPP(U_3271,sK47(U_3275,U_3273,U_3271)))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_16,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3275))
| ~ hBOOL(hAPP(U_3271,U_3273))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_17,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK47(U_3275,U_3273,U_3271)))
| ~ hBOOL(hAPP(U_3271,U_3273))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_18,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK47(U_3275,U_3273,U_3271)),U_3275))
| ~ hBOOL(hAPP(U_3271,U_3273))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_19,plain,
( U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK46(U_3275,U_3273,U_3271))),sK47(U_3275,U_3273,U_3271))
| ~ hBOOL(hAPP(U_3271,U_3273))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_20,plain,
( ~ hBOOL(hAPP(U_3271,sK47(U_3275,U_3273,U_3271)))
| ~ hBOOL(hAPP(U_3271,U_3273))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_21,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3275))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),sK49(U_3275,U_3273,U_3271)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_22,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK47(U_3275,U_3273,U_3271)))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),sK49(U_3275,U_3273,U_3271)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_23,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK47(U_3275,U_3273,U_3271)),U_3275))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),sK49(U_3275,U_3273,U_3271)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_24,plain,
( U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK46(U_3275,U_3273,U_3271))),sK47(U_3275,U_3273,U_3271))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),sK49(U_3275,U_3273,U_3271)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_25,plain,
( ~ hBOOL(hAPP(U_3271,sK47(U_3275,U_3273,U_3271)))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),sK49(U_3275,U_3273,U_3271)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_26,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3275))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK49(U_3275,U_3273,U_3271)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_27,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK47(U_3275,U_3273,U_3271)))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK49(U_3275,U_3273,U_3271)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_28,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK47(U_3275,U_3273,U_3271)),U_3275))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK49(U_3275,U_3273,U_3271)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_29,plain,
( U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK46(U_3275,U_3273,U_3271))),sK47(U_3275,U_3273,U_3271))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK49(U_3275,U_3273,U_3271)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_30,plain,
( ~ hBOOL(hAPP(U_3271,sK47(U_3275,U_3273,U_3271)))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK49(U_3275,U_3273,U_3271)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_31,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3275))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK48(U_3275,U_3273,U_3271))),sK49(U_3275,U_3273,U_3271))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_32,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK47(U_3275,U_3273,U_3271)))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK48(U_3275,U_3273,U_3271))),sK49(U_3275,U_3273,U_3271))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_33,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK47(U_3275,U_3273,U_3271)),U_3275))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK48(U_3275,U_3273,U_3271))),sK49(U_3275,U_3273,U_3271))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_34,plain,
( U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK46(U_3275,U_3273,U_3271))),sK47(U_3275,U_3273,U_3271))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK48(U_3275,U_3273,U_3271))),sK49(U_3275,U_3273,U_3271))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_35,plain,
( ~ hBOOL(hAPP(U_3271,sK47(U_3275,U_3273,U_3271)))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK48(U_3275,U_3273,U_3271))),sK49(U_3275,U_3273,U_3271))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_36,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3275))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_3271,sK49(U_3275,U_3273,U_3271)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_37,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK47(U_3275,U_3273,U_3271)))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_3271,sK49(U_3275,U_3273,U_3271)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_38,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK47(U_3275,U_3273,U_3271)),U_3275))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_3271,sK49(U_3275,U_3273,U_3271)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_39,plain,
( U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK46(U_3275,U_3273,U_3271))),sK47(U_3275,U_3273,U_3271))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_3271,sK49(U_3275,U_3273,U_3271)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_40,plain,
( ~ hBOOL(hAPP(U_3271,sK47(U_3275,U_3273,U_3271)))
| U_3275 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(U_3271,sK49(U_3275,U_3273,U_3271)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_41,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3275))
| ~ hBOOL(hAPP(U_3271,U_3273))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),sK49(U_3275,U_3273,U_3271)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_42,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK47(U_3275,U_3273,U_3271)))
| ~ hBOOL(hAPP(U_3271,U_3273))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),sK49(U_3275,U_3273,U_3271)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_43,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK47(U_3275,U_3273,U_3271)),U_3275))
| ~ hBOOL(hAPP(U_3271,U_3273))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),sK49(U_3275,U_3273,U_3271)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_44,plain,
( U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK46(U_3275,U_3273,U_3271))),sK47(U_3275,U_3273,U_3271))
| ~ hBOOL(hAPP(U_3271,U_3273))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),sK49(U_3275,U_3273,U_3271)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_45,plain,
( ~ hBOOL(hAPP(U_3271,sK47(U_3275,U_3273,U_3271)))
| ~ hBOOL(hAPP(U_3271,U_3273))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3275),sK49(U_3275,U_3273,U_3271)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_46,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3275))
| ~ hBOOL(hAPP(U_3271,U_3273))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK49(U_3275,U_3273,U_3271)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_47,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK47(U_3275,U_3273,U_3271)))
| ~ hBOOL(hAPP(U_3271,U_3273))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK49(U_3275,U_3273,U_3271)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_48,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK47(U_3275,U_3273,U_3271)),U_3275))
| ~ hBOOL(hAPP(U_3271,U_3273))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK49(U_3275,U_3273,U_3271)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_49,plain,
( U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK46(U_3275,U_3273,U_3271))),sK47(U_3275,U_3273,U_3271))
| ~ hBOOL(hAPP(U_3271,U_3273))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK49(U_3275,U_3273,U_3271)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_50,plain,
( ~ hBOOL(hAPP(U_3271,sK47(U_3275,U_3273,U_3271)))
| ~ hBOOL(hAPP(U_3271,U_3273))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK49(U_3275,U_3273,U_3271)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_51,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3275))
| ~ hBOOL(hAPP(U_3271,U_3273))
| U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK48(U_3275,U_3273,U_3271))),sK49(U_3275,U_3273,U_3271))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_52,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK47(U_3275,U_3273,U_3271)))
| ~ hBOOL(hAPP(U_3271,U_3273))
| U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK48(U_3275,U_3273,U_3271))),sK49(U_3275,U_3273,U_3271))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_53,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK47(U_3275,U_3273,U_3271)),U_3275))
| ~ hBOOL(hAPP(U_3271,U_3273))
| U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK48(U_3275,U_3273,U_3271))),sK49(U_3275,U_3273,U_3271))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_54,plain,
( U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK46(U_3275,U_3273,U_3271))),sK47(U_3275,U_3273,U_3271))
| ~ hBOOL(hAPP(U_3271,U_3273))
| U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK48(U_3275,U_3273,U_3271))),sK49(U_3275,U_3273,U_3271))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_55,plain,
( ~ hBOOL(hAPP(U_3271,sK47(U_3275,U_3273,U_3271)))
| ~ hBOOL(hAPP(U_3271,U_3273))
| U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK48(U_3275,U_3273,U_3271))),sK49(U_3275,U_3273,U_3271))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_56,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3275))
| ~ hBOOL(hAPP(U_3271,U_3273))
| ~ hBOOL(hAPP(U_3271,sK49(U_3275,U_3273,U_3271)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_57,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK47(U_3275,U_3273,U_3271)))
| ~ hBOOL(hAPP(U_3271,U_3273))
| ~ hBOOL(hAPP(U_3271,sK49(U_3275,U_3273,U_3271)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_58,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK47(U_3275,U_3273,U_3271)),U_3275))
| ~ hBOOL(hAPP(U_3271,U_3273))
| ~ hBOOL(hAPP(U_3271,sK49(U_3275,U_3273,U_3271)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_59,plain,
( U_3273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3275),sK46(U_3275,U_3273,U_3271))),sK47(U_3275,U_3273,U_3271))
| ~ hBOOL(hAPP(U_3271,U_3273))
| ~ hBOOL(hAPP(U_3271,sK49(U_3275,U_3273,U_3271)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
cnf(f_1025_60,plain,
( ~ hBOOL(hAPP(U_3271,sK47(U_3275,U_3273,U_3271)))
| ~ hBOOL(hAPP(U_3271,U_3273))
| ~ hBOOL(hAPP(U_3271,sK49(U_3275,U_3273,U_3271)))
| hBOOL(hAPP(U_3271,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3273,U_3275))) ),
inference(clausify,[status(thm)],[f_1025_7]) ).
fof(f_1026_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_1026_2,plain,
! [U_3278,U_3277,U_3276] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3277,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3278),U_3276)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3278),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3277),U_3278),U_3276))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3277,U_3278))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3276)) ),
inference(variable_rename,[status(thm)],[f_1026_1]) ).
cnf(f_1026_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3277,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3278),U_3276)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3278),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3277),U_3278),U_3276))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3277,U_3278))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3276)) ),
inference(clausify,[status(thm)],[f_1026_2]) ).
fof(f_1027_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_1027_2,plain,
! [U_3280,U_3279] :
( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3280)),U_3279) = 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_3280),U_3279))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3280,U_3279) = 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_3280)),U_3279) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3280),U_3279))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3280,U_3279) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_3279 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1027_1]) ).
cnf(f_1027_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3280)),U_3279) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3280),U_3279))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3280,U_3279) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3279 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1027_2]) ).
cnf(f_1027_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3280)),U_3279) = 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_3280),U_3279))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3280,U_3279) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3279 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1027_2]) ).
fof(f_1028_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_1028_2,plain,
! [U_3282,U_3281] :
( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3282),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3281)) = 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_3282),U_3281))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3282,U_3281) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3282),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3281)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3282),U_3281))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3282,U_3281) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_3281 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1028_1]) ).
cnf(f_1028_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3282),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3281)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3282),U_3281))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3282,U_3281) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3281 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1028_2]) ).
cnf(f_1028_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3282),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3281)) = 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_3282),U_3281))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3282,U_3281) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_3281 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1028_2]) ).
fof(f_1029_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_1029_2,plain,
! [U_3284,U_3283] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3283)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3284)) = 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_3283)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3284)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3283))) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3283)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3284)) = 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_3283))) ) ),
inference(variable_rename,[status(thm)],[f_1029_1]) ).
fof(f_1029_3,plain,
( ! [U_3288,U_3286] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3286)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3288)) = 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_3286)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3288)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3286))) )
& ! [U_3287,U_3285] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3285)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3287)) = 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_3285))) ) ),
inference(miniscope,[status(thm)],[f_1029_2]) ).
cnf(f_1029_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3285)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3287)) = 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_3285))) ),
inference(clausify,[status(thm)],[f_1029_3]) ).
cnf(f_1029_5,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3286)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3288)) = 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_3286)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3288)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3286))) ),
inference(clausify,[status(thm)],[f_1029_3]) ).
fof(f_1030_1,plain,
! [V_na_2,V_P_2,V_k_2] :
( ( ( hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_na_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_na_2,V_k_2)))
| ? [B_i,B_j] :
( ~ hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
& V_na_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_P_2,B_i),B_j))
| V_na_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_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_na_2),V_k_2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_na_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_1030_2,plain,
! [U_3295,U_3294,U_3293] :
( ( ( hBOOL(hAPP(hAPP(U_3294,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3295),U_3293)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3295,U_3293)))
| ? [U_3292,U_3291] :
( ~ hBOOL(hAPP(hAPP(U_3294,U_3292),U_3291))
& U_3295 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3293),U_3292)),U_3291)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3291),U_3293))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3291)) ) )
& ( ! [U_3290,U_3289] :
( hBOOL(hAPP(hAPP(U_3294,U_3290),U_3289))
| U_3295 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3293),U_3290)),U_3289)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3289),U_3293))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3289)) )
| ~ hBOOL(hAPP(hAPP(U_3294,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3295),U_3293)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3295,U_3293))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3293)) ),
inference(variable_rename,[status(thm)],[f_1030_1]) ).
fof(f_1030_3,plain,
! [U_3295,U_3294,U_3293] :
( ( ( hBOOL(hAPP(hAPP(U_3294,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3295),U_3293)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3295,U_3293)))
| ? [U_3291] :
( ~ hBOOL(hAPP(hAPP(U_3294,sK50(U_3295,U_3294,U_3293)),U_3291))
& U_3295 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3293),sK50(U_3295,U_3294,U_3293))),U_3291)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3291),U_3293))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3291)) ) )
& ( ! [U_3290,U_3289] :
( hBOOL(hAPP(hAPP(U_3294,U_3290),U_3289))
| U_3295 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3293),U_3290)),U_3289)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3289),U_3293))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3289)) )
| ~ hBOOL(hAPP(hAPP(U_3294,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3295),U_3293)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3295,U_3293))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3293)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_3292,sK50(U_3295,U_3294,U_3293))],[f_1030_2]) ).
fof(f_1030_4,plain,
! [U_3295,U_3294,U_3293] :
( ( ( hBOOL(hAPP(hAPP(U_3294,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3295),U_3293)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3295,U_3293)))
| ( ~ hBOOL(hAPP(hAPP(U_3294,sK50(U_3295,U_3294,U_3293)),sK51(U_3295,U_3294,U_3293)))
& U_3295 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3293),sK50(U_3295,U_3294,U_3293))),sK51(U_3295,U_3294,U_3293))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK51(U_3295,U_3294,U_3293)),U_3293))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK51(U_3295,U_3294,U_3293))) ) )
& ( ! [U_3290,U_3289] :
( hBOOL(hAPP(hAPP(U_3294,U_3290),U_3289))
| U_3295 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3293),U_3290)),U_3289)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3289),U_3293))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3289)) )
| ~ hBOOL(hAPP(hAPP(U_3294,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3295),U_3293)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3295,U_3293))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3293)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_3291,sK51(U_3295,U_3294,U_3293))],[f_1030_3]) ).
cnf(f_1030_5,plain,
( hBOOL(hAPP(hAPP(U_3294,U_3290),U_3289))
| U_3295 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3293),U_3290)),U_3289)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3289),U_3293))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3289))
| ~ hBOOL(hAPP(hAPP(U_3294,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3295),U_3293)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3295,U_3293)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3293)) ),
inference(clausify,[status(thm)],[f_1030_4]) ).
cnf(f_1030_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK51(U_3295,U_3294,U_3293)))
| hBOOL(hAPP(hAPP(U_3294,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3295),U_3293)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3295,U_3293)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3293)) ),
inference(clausify,[status(thm)],[f_1030_4]) ).
cnf(f_1030_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK51(U_3295,U_3294,U_3293)),U_3293))
| hBOOL(hAPP(hAPP(U_3294,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3295),U_3293)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3295,U_3293)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3293)) ),
inference(clausify,[status(thm)],[f_1030_4]) ).
cnf(f_1030_8,plain,
( U_3295 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3293),sK50(U_3295,U_3294,U_3293))),sK51(U_3295,U_3294,U_3293))
| hBOOL(hAPP(hAPP(U_3294,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3295),U_3293)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3295,U_3293)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3293)) ),
inference(clausify,[status(thm)],[f_1030_4]) ).
cnf(f_1030_9,plain,
( ~ hBOOL(hAPP(hAPP(U_3294,sK50(U_3295,U_3294,U_3293)),sK51(U_3295,U_3294,U_3293)))
| hBOOL(hAPP(hAPP(U_3294,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3295),U_3293)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3295,U_3293)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3293)) ),
inference(clausify,[status(thm)],[f_1030_4]) ).
fof(f_1031_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_1031_2,plain,
! [U_3297,U_3296] :
( ( c_SMT_Oz3mod(U_3297,U_3296) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3297,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3296))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3296)) )
& ( c_SMT_Oz3mod(U_3297,U_3296) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3297,U_3296)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3296)) ) ),
inference(variable_rename,[status(thm)],[f_1031_1]) ).
fof(f_1031_3,plain,
( ! [U_3301,U_3299] :
( c_SMT_Oz3mod(U_3301,U_3299) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3301,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3299))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3299)) )
& ! [U_3300,U_3298] :
( c_SMT_Oz3mod(U_3300,U_3298) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3300,U_3298)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3298)) ) ),
inference(miniscope,[status(thm)],[f_1031_2]) ).
cnf(f_1031_4,plain,
( c_SMT_Oz3mod(U_3300,U_3298) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3300,U_3298)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3298)) ),
inference(clausify,[status(thm)],[f_1031_3]) ).
cnf(f_1031_5,plain,
( c_SMT_Oz3mod(U_3301,U_3299) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3301,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3299))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3299)) ),
inference(clausify,[status(thm)],[f_1031_3]) ).
fof(f_1032_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_1032_2,plain,
! [U_3302] :
( ( 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_3302)) = 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_3302)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3302))) )
& ( 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_3302)) = 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_3302))) ) ),
inference(variable_rename,[status(thm)],[f_1032_1]) ).
fof(f_1032_3,plain,
( ! [U_3304] :
( 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_3304)) = 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_3304)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3304))) )
& ! [U_3303] :
( 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_3303)) = 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_3303))) ) ),
inference(miniscope,[status(thm)],[f_1032_2]) ).
cnf(f_1032_4,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_3303)) = 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_3303))) ),
inference(clausify,[status(thm)],[f_1032_3]) ).
cnf(f_1032_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_3304)) = 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_3304)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3304))) ),
inference(clausify,[status(thm)],[f_1032_3]) ).
fof(f_1033_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_1033_2,plain,
! [U_3306,U_3305] :
( ( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3305),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3306)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3305),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3306)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3306))) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3305),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3306)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3305)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3306))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3305))) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3305),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3306)) = 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_3305))) ) ),
inference(variable_rename,[status(thm)],[f_1033_1]) ).
fof(f_1033_3,plain,
( ! [U_3310,U_3308] :
( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3308),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3310)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3308),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3310)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3310))) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3308),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3310)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3308)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3310))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3308))) )
& ! [U_3309,U_3307] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3307),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3309)) = 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_3307))) ) ),
inference(miniscope,[status(thm)],[f_1033_2]) ).
cnf(f_1033_4,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3307),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3309)) = 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_3307))) ),
inference(clausify,[status(thm)],[f_1033_3]) ).
cnf(f_1033_5,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3308),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3310)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3308)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3310)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3308))) ),
inference(clausify,[status(thm)],[f_1033_3]) ).
cnf(f_1033_6,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3308),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3310)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3308),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3310)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3310)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3308))) ),
inference(clausify,[status(thm)],[f_1033_3]) ).
fof(f_1034_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_1034_2,plain,
! [U_3313,U_3312,U_3311] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3312),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3313),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_3313),U_3312))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_3311))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3311)) ),
inference(variable_rename,[status(thm)],[f_1034_1]) ).
cnf(f_1034_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3312),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3313),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_3313),U_3312))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_3311))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3311)) ),
inference(clausify,[status(thm)],[f_1034_2]) ).
fof(f_1035_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_1035_2,plain,
! [U_3316,U_3315,U_3314] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3315),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_3315),U_3316))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_3314))),U_3316))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3314)) ),
inference(variable_rename,[status(thm)],[f_1035_1]) ).
cnf(f_1035_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3315),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_3315),U_3316))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_3314))),U_3316))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3314)) ),
inference(clausify,[status(thm)],[f_1035_2]) ).
fof(f_1036_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_1036_2,plain,
! [U_3317] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3317)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_3317))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3317),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3317)),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_3317),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1036_1]) ).
fof(f_1036_3,plain,
( ! [U_3319] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3319)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_3319))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3319),c_Int_OPls)) )
& ! [U_3318] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3318)),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_3318),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1036_2]) ).
cnf(f_1036_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3318)),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_3318),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1036_3]) ).
cnf(f_1036_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3319)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_3319))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3319),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1036_3]) ).
fof(f_1037_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_1037_2,plain,
! [U_3320] :
( ( 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_3320)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_3320))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3320),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_3320)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3320),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1037_1]) ).
fof(f_1037_3,plain,
( ! [U_3322] :
( 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_3322)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_3322))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3322),c_Int_OPls)) )
& ! [U_3321] :
( 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_3321)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3321),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1037_2]) ).
cnf(f_1037_4,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_3321)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3321),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1037_3]) ).
cnf(f_1037_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_3322)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_3322))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3322),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1037_3]) ).
fof(f_1038_1,plain,
! [V_y_2,T_b] :
( ( ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
| ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) )
& ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2))))
| c_Groups_Ozero__class_Ozero(T_b) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) ) )
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__special_I1_J]) ).
fof(f_1038_2,plain,
! [U_3324,U_3323] :
( ( ( c_Groups_Ozero__class_Ozero(U_3323) = hAPP(c_Int_Onumber__class_Onumber__of(U_3323),U_3324)
| ~ c_Int_Oiszero(U_3323,hAPP(c_Int_Onumber__class_Onumber__of(U_3323),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3324)))) )
& ( c_Int_Oiszero(U_3323,hAPP(c_Int_Onumber__class_Onumber__of(U_3323),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3324))))
| c_Groups_Ozero__class_Ozero(U_3323) != hAPP(c_Int_Onumber__class_Onumber__of(U_3323),U_3324) ) )
| ~ class_Int_Onumber__ring(U_3323) ),
inference(variable_rename,[status(thm)],[f_1038_1]) ).
cnf(f_1038_3,plain,
( c_Int_Oiszero(U_3323,hAPP(c_Int_Onumber__class_Onumber__of(U_3323),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3324))))
| c_Groups_Ozero__class_Ozero(U_3323) != hAPP(c_Int_Onumber__class_Onumber__of(U_3323),U_3324)
| ~ class_Int_Onumber__ring(U_3323) ),
inference(clausify,[status(thm)],[f_1038_2]) ).
cnf(f_1038_4,plain,
( c_Groups_Ozero__class_Ozero(U_3323) = hAPP(c_Int_Onumber__class_Onumber__of(U_3323),U_3324)
| ~ c_Int_Oiszero(U_3323,hAPP(c_Int_Onumber__class_Onumber__of(U_3323),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3324))))
| ~ class_Int_Onumber__ring(U_3323) ),
inference(clausify,[status(thm)],[f_1038_2]) ).
fof(f_1039_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_1039_2,plain,
! [U_3326,U_3325] :
( hAPP(c_Groups_Oabs__class_Oabs(U_3325),hAPP(c_Groups_Oabs__class_Oabs(U_3325),U_3326)) = hAPP(c_Groups_Oabs__class_Oabs(U_3325),U_3326)
| ~ class_Groups_Oordered__ab__group__add__abs(U_3325) ),
inference(variable_rename,[status(thm)],[f_1039_1]) ).
cnf(f_1039_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3325),hAPP(c_Groups_Oabs__class_Oabs(U_3325),U_3326)) = hAPP(c_Groups_Oabs__class_Oabs(U_3325),U_3326)
| ~ class_Groups_Oordered__ab__group__add__abs(U_3325) ),
inference(clausify,[status(thm)],[f_1039_2]) ).
fof(f_1040_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_1040_2,plain,
! [U_3328,U_3327] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3327),U_3328),hAPP(c_Groups_Oabs__class_Oabs(U_3327),U_3328)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3327) ),
inference(variable_rename,[status(thm)],[f_1040_1]) ).
cnf(f_1040_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3327),U_3328),hAPP(c_Groups_Oabs__class_Oabs(U_3327),U_3328)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3327) ),
inference(clausify,[status(thm)],[f_1040_2]) ).
fof(f_1041_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_1041_2,plain,
! [U_3331,U_3330,U_3329] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3329),U_3330),U_3331))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3329),hAPP(c_Groups_Oabs__class_Oabs(U_3329),U_3330)),U_3331))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3329) ),
inference(variable_rename,[status(thm)],[f_1041_1]) ).
cnf(f_1041_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3329),U_3330),U_3331))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3329),hAPP(c_Groups_Oabs__class_Oabs(U_3329),U_3330)),U_3331))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3329) ),
inference(clausify,[status(thm)],[f_1041_2]) ).
fof(f_1042_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_1042_2,plain,
! [U_3332] :
( hAPP(c_Groups_Oabs__class_Oabs(U_3332),c_Groups_Ozero__class_Ozero(U_3332)) = c_Groups_Ozero__class_Ozero(U_3332)
| ~ class_Groups_Oordered__ab__group__add__abs(U_3332) ),
inference(variable_rename,[status(thm)],[f_1042_1]) ).
cnf(f_1042_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3332),c_Groups_Ozero__class_Ozero(U_3332)) = c_Groups_Ozero__class_Ozero(U_3332)
| ~ class_Groups_Oordered__ab__group__add__abs(U_3332) ),
inference(clausify,[status(thm)],[f_1042_2]) ).
fof(f_1043_1,plain,
! [V_a_2,T_b] :
( ( ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
inference(fof_nnf,[status(thm)],[fact_abs__eq__0]) ).
fof(f_1043_2,plain,
! [U_3334,U_3333] :
( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_3333),U_3334) = c_Groups_Ozero__class_Ozero(U_3333)
| U_3334 != c_Groups_Ozero__class_Ozero(U_3333) )
& ( U_3334 = c_Groups_Ozero__class_Ozero(U_3333)
| hAPP(c_Groups_Oabs__class_Oabs(U_3333),U_3334) != c_Groups_Ozero__class_Ozero(U_3333) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_3333) ),
inference(variable_rename,[status(thm)],[f_1043_1]) ).
cnf(f_1043_3,plain,
( U_3334 = c_Groups_Ozero__class_Ozero(U_3333)
| hAPP(c_Groups_Oabs__class_Oabs(U_3333),U_3334) != c_Groups_Ozero__class_Ozero(U_3333)
| ~ class_Groups_Oordered__ab__group__add__abs(U_3333) ),
inference(clausify,[status(thm)],[f_1043_2]) ).
cnf(f_1043_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3333),U_3334) = c_Groups_Ozero__class_Ozero(U_3333)
| U_3334 != c_Groups_Ozero__class_Ozero(U_3333)
| ~ class_Groups_Oordered__ab__group__add__abs(U_3333) ),
inference(clausify,[status(thm)],[f_1043_2]) ).
fof(f_1044_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_1044_2,plain,
! [U_3337,U_3336,U_3335] :
( hAPP(c_Groups_Oabs__class_Oabs(U_3335),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3335),hAPP(c_Groups_Oabs__class_Oabs(U_3335),U_3336)),hAPP(c_Groups_Oabs__class_Oabs(U_3335),U_3337))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3335),hAPP(c_Groups_Oabs__class_Oabs(U_3335),U_3336)),hAPP(c_Groups_Oabs__class_Oabs(U_3335),U_3337))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3335) ),
inference(variable_rename,[status(thm)],[f_1044_1]) ).
cnf(f_1044_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3335),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3335),hAPP(c_Groups_Oabs__class_Oabs(U_3335),U_3336)),hAPP(c_Groups_Oabs__class_Oabs(U_3335),U_3337))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3335),hAPP(c_Groups_Oabs__class_Oabs(U_3335),U_3336)),hAPP(c_Groups_Oabs__class_Oabs(U_3335),U_3337))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3335) ),
inference(clausify,[status(thm)],[f_1044_2]) ).
fof(f_1045_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_1045_2,plain,
! [U_3340,U_3339,U_3338] :
( hAPP(c_Groups_Oabs__class_Oabs(U_3338),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3338),U_3339),U_3340)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3338),hAPP(c_Groups_Oabs__class_Oabs(U_3338),U_3339)),hAPP(c_Groups_Oabs__class_Oabs(U_3338),U_3340))
| ~ class_Rings_Olinordered__idom(U_3338) ),
inference(variable_rename,[status(thm)],[f_1045_1]) ).
cnf(f_1045_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3338),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3338),U_3339),U_3340)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3338),hAPP(c_Groups_Oabs__class_Oabs(U_3338),U_3339)),hAPP(c_Groups_Oabs__class_Oabs(U_3338),U_3340))
| ~ class_Rings_Olinordered__idom(U_3338) ),
inference(clausify,[status(thm)],[f_1045_2]) ).
fof(f_1046_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_1046_2,plain,
! [U_3342,U_3341] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3341),hAPP(c_Groups_Oabs__class_Oabs(U_3341),U_3342)),hAPP(c_Groups_Oabs__class_Oabs(U_3341),U_3342)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3341),U_3342),U_3342)
| ~ class_Rings_Olinordered__idom(U_3341) ),
inference(variable_rename,[status(thm)],[f_1046_1]) ).
cnf(f_1046_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3341),hAPP(c_Groups_Oabs__class_Oabs(U_3341),U_3342)),hAPP(c_Groups_Oabs__class_Oabs(U_3341),U_3342)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3341),U_3342),U_3342)
| ~ class_Rings_Olinordered__idom(U_3341) ),
inference(clausify,[status(thm)],[f_1046_2]) ).
fof(f_1047_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_1047_2,plain,
! [U_3345,U_3344,U_3343] :
( hAPP(c_Groups_Oabs__class_Oabs(U_3343),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3343),U_3344),U_3345)) = hAPP(c_Groups_Oabs__class_Oabs(U_3343),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3343),U_3345),U_3344))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3343) ),
inference(variable_rename,[status(thm)],[f_1047_1]) ).
cnf(f_1047_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3343),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3343),U_3344),U_3345)) = hAPP(c_Groups_Oabs__class_Oabs(U_3343),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3343),U_3345),U_3344))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3343) ),
inference(clausify,[status(thm)],[f_1047_2]) ).
fof(f_1048_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_1048_2,plain,
! [U_3346] :
( hAPP(c_Groups_Oabs__class_Oabs(U_3346),c_Groups_Oone__class_Oone(U_3346)) = c_Groups_Oone__class_Oone(U_3346)
| ~ class_Rings_Olinordered__idom(U_3346) ),
inference(variable_rename,[status(thm)],[f_1048_1]) ).
cnf(f_1048_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3346),c_Groups_Oone__class_Oone(U_3346)) = c_Groups_Oone__class_Oone(U_3346)
| ~ class_Rings_Olinordered__idom(U_3346) ),
inference(clausify,[status(thm)],[f_1048_2]) ).
fof(f_1049_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_1049_2,plain,
! [U_3348,U_3347] :
( hAPP(c_Groups_Oabs__class_Oabs(U_3347),hAPP(c_Groups_Ouminus__class_Ouminus(U_3347),U_3348)) = hAPP(c_Groups_Oabs__class_Oabs(U_3347),U_3348)
| ~ class_Groups_Oordered__ab__group__add__abs(U_3347) ),
inference(variable_rename,[status(thm)],[f_1049_1]) ).
cnf(f_1049_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3347),hAPP(c_Groups_Ouminus__class_Ouminus(U_3347),U_3348)) = hAPP(c_Groups_Oabs__class_Oabs(U_3347),U_3348)
| ~ class_Groups_Oordered__ab__group__add__abs(U_3347) ),
inference(clausify,[status(thm)],[f_1049_2]) ).
fof(f_1050_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_1050_2,plain,
! [U_3351,U_3350,U_3349] :
( hAPP(c_Groups_Oabs__class_Oabs(U_3349),hAPP(hAPP(c_Power_Opower__class_Opower(U_3349),U_3350),U_3351)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3349),hAPP(c_Groups_Oabs__class_Oabs(U_3349),U_3350)),U_3351)
| ~ class_Rings_Olinordered__idom(U_3349) ),
inference(variable_rename,[status(thm)],[f_1050_1]) ).
cnf(f_1050_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3349),hAPP(hAPP(c_Power_Opower__class_Opower(U_3349),U_3350),U_3351)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3349),hAPP(c_Groups_Oabs__class_Oabs(U_3349),U_3350)),U_3351)
| ~ class_Rings_Olinordered__idom(U_3349) ),
inference(clausify,[status(thm)],[f_1050_2]) ).
fof(f_1051_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_1051_2,plain,
! [U_3353,U_3352] :
( hAPP(c_Groups_Oabs__class_Oabs(U_3352),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3352),U_3353)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3352),U_3353)
| ~ class_Rings_Olinordered__idom(U_3352) ),
inference(variable_rename,[status(thm)],[f_1051_1]) ).
cnf(f_1051_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3352),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3352),U_3353)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3352),U_3353)
| ~ class_Rings_Olinordered__idom(U_3352) ),
inference(clausify,[status(thm)],[f_1051_2]) ).
fof(f_1052_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_1052_2,plain,
! [U_3355,U_3354] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3354),U_3355) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3354,U_3355)),U_3355),
inference(variable_rename,[status(thm)],[f_1052_1]) ).
cnf(f_1052_3,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3354),U_3355) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3354,U_3355)),U_3355),
inference(clausify,[status(thm)],[f_1052_2]) ).
fof(f_1053_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_1053_2,plain,
! [U_3357,U_3356] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3356,U_3357) = U_3356
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3356),U_3357)) ),
inference(variable_rename,[status(thm)],[f_1053_1]) ).
cnf(f_1053_3,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3356,U_3357) = U_3356
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3356),U_3357)) ),
inference(clausify,[status(thm)],[f_1053_2]) ).
fof(f_1054_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_1054_2,plain,
! [U_3359,U_3358] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3358,U_3359)),U_3358)),
inference(variable_rename,[status(thm)],[f_1054_1]) ).
cnf(f_1054_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3358,U_3359)),U_3358)),
inference(clausify,[status(thm)],[f_1054_2]) ).
fof(f_1055_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_1055_2,plain,
! [U_3360] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3360)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3360),
inference(variable_rename,[status(thm)],[f_1055_1]) ).
cnf(f_1055_3,plain,
hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3360)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3360),
inference(clausify,[status(thm)],[f_1055_2]) ).
fof(f_1056_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_1056_2,plain,
! [U_3363,U_3362,U_3361] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3361),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3362,U_3363)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3361),U_3362),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3361),U_3363)),
inference(variable_rename,[status(thm)],[f_1056_1]) ).
cnf(f_1056_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3361),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3362,U_3363)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3361),U_3362),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3361),U_3363)),
inference(clausify,[status(thm)],[f_1056_2]) ).
fof(f_1057_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_1057_2,plain,
! [U_3366,U_3365,U_3364] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3364,U_3365)),U_3366) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3364),U_3366),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3365),U_3366)),
inference(variable_rename,[status(thm)],[f_1057_1]) ).
cnf(f_1057_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3364,U_3365)),U_3366) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3364),U_3366),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3365),U_3366)),
inference(clausify,[status(thm)],[f_1057_2]) ).
fof(f_1058_1,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_Pls__def]) ).
cnf(f_1058_2,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1058_1]) ).
fof(f_1059_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]) ).
cnf(f_1059_2,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(clausify,[status(thm)],[f_1059_1]) ).
fof(f_1060_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]) ).
cnf(f_1060_2,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(clausify,[status(thm)],[f_1060_1]) ).
fof(f_1061_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_1061_2,plain,
! [U_3367] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3367),c_Int_OPls) = U_3367,
inference(variable_rename,[status(thm)],[f_1061_1]) ).
cnf(f_1061_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3367),c_Int_OPls) = U_3367,
inference(clausify,[status(thm)],[f_1061_2]) ).
fof(f_1062_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_1062_2,plain,
! [U_3368] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_3368) = U_3368,
inference(variable_rename,[status(thm)],[f_1062_1]) ).
cnf(f_1062_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_3368) = U_3368,
inference(clausify,[status(thm)],[f_1062_2]) ).
fof(f_1063_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_1063_2,plain,
! [U_3369] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_3369) = c_Int_OPls,
inference(variable_rename,[status(thm)],[f_1063_1]) ).
cnf(f_1063_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_3369) = c_Int_OPls,
inference(clausify,[status(thm)],[f_1063_2]) ).
fof(f_1064_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_1064_2,plain,
! [U_3370] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3370),c_Int_OPls) = U_3370,
inference(variable_rename,[status(thm)],[f_1064_1]) ).
cnf(f_1064_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3370),c_Int_OPls) = U_3370,
inference(clausify,[status(thm)],[f_1064_2]) ).
fof(f_1065_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]) ).
cnf(f_1065_2,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
inference(clausify,[status(thm)],[f_1065_1]) ).
fof(f_1066_1,plain,
c_Int_OPls != c_Int_OMin,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I37_J]) ).
cnf(f_1066_2,plain,
c_Int_OPls != c_Int_OMin,
inference(clausify,[status(thm)],[f_1066_1]) ).
fof(f_1067_1,plain,
c_Int_OMin != c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I40_J]) ).
cnf(f_1067_2,plain,
c_Int_OMin != c_Int_OPls,
inference(clausify,[status(thm)],[f_1067_1]) ).
fof(f_1068_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_1068_2,plain,
! [U_3372,U_3371] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3371),c_Groups_Ozero__class_Ozero(U_3371)),hAPP(c_Groups_Oabs__class_Oabs(U_3371),U_3372)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3371) ),
inference(variable_rename,[status(thm)],[f_1068_1]) ).
cnf(f_1068_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3371),c_Groups_Ozero__class_Ozero(U_3371)),hAPP(c_Groups_Oabs__class_Oabs(U_3371),U_3372)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3371) ),
inference(clausify,[status(thm)],[f_1068_2]) ).
fof(f_1069_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff]) ).
fof(f_1069_2,plain,
! [U_3374,U_3373] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3373),hAPP(c_Groups_Oabs__class_Oabs(U_3373),U_3374)),c_Groups_Ozero__class_Ozero(U_3373)))
| U_3374 != c_Groups_Ozero__class_Ozero(U_3373) )
& ( U_3374 = c_Groups_Ozero__class_Ozero(U_3373)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3373),hAPP(c_Groups_Oabs__class_Oabs(U_3373),U_3374)),c_Groups_Ozero__class_Ozero(U_3373))) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_3373) ),
inference(variable_rename,[status(thm)],[f_1069_1]) ).
cnf(f_1069_3,plain,
( U_3374 = c_Groups_Ozero__class_Ozero(U_3373)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3373),hAPP(c_Groups_Oabs__class_Oabs(U_3373),U_3374)),c_Groups_Ozero__class_Ozero(U_3373)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3373) ),
inference(clausify,[status(thm)],[f_1069_2]) ).
cnf(f_1069_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3373),hAPP(c_Groups_Oabs__class_Oabs(U_3373),U_3374)),c_Groups_Ozero__class_Ozero(U_3373)))
| U_3374 != c_Groups_Ozero__class_Ozero(U_3373)
| ~ class_Groups_Oordered__ab__group__add__abs(U_3373) ),
inference(clausify,[status(thm)],[f_1069_2]) ).
fof(f_1070_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_1070_2,plain,
! [U_3376,U_3375] :
( hAPP(c_Groups_Oabs__class_Oabs(U_3375),U_3376) = U_3376
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3375),c_Groups_Ozero__class_Ozero(U_3375)),U_3376))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3375) ),
inference(variable_rename,[status(thm)],[f_1070_1]) ).
cnf(f_1070_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3375),U_3376) = U_3376
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3375),c_Groups_Ozero__class_Ozero(U_3375)),U_3376))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3375) ),
inference(clausify,[status(thm)],[f_1070_2]) ).
fof(f_1071_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_1071_2,plain,
! [U_3378,U_3377] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3377),hAPP(c_Groups_Oabs__class_Oabs(U_3377),U_3378)),c_Groups_Ozero__class_Ozero(U_3377)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3377) ),
inference(variable_rename,[status(thm)],[f_1071_1]) ).
cnf(f_1071_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3377),hAPP(c_Groups_Oabs__class_Oabs(U_3377),U_3378)),c_Groups_Ozero__class_Ozero(U_3377)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3377) ),
inference(clausify,[status(thm)],[f_1071_2]) ).
fof(f_1072_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)))
| V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2))) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff]) ).
fof(f_1072_2,plain,
! [U_3380,U_3379] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),c_Groups_Ozero__class_Ozero(U_3379)),hAPP(c_Groups_Oabs__class_Oabs(U_3379),U_3380)))
| U_3380 = c_Groups_Ozero__class_Ozero(U_3379) )
& ( U_3380 != c_Groups_Ozero__class_Ozero(U_3379)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),c_Groups_Ozero__class_Ozero(U_3379)),hAPP(c_Groups_Oabs__class_Oabs(U_3379),U_3380))) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_3379) ),
inference(variable_rename,[status(thm)],[f_1072_1]) ).
cnf(f_1072_3,plain,
( U_3380 != c_Groups_Ozero__class_Ozero(U_3379)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),c_Groups_Ozero__class_Ozero(U_3379)),hAPP(c_Groups_Oabs__class_Oabs(U_3379),U_3380)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3379) ),
inference(clausify,[status(thm)],[f_1072_2]) ).
cnf(f_1072_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3379),c_Groups_Ozero__class_Ozero(U_3379)),hAPP(c_Groups_Oabs__class_Oabs(U_3379),U_3380)))
| U_3380 = c_Groups_Ozero__class_Ozero(U_3379)
| ~ class_Groups_Oordered__ab__group__add__abs(U_3379) ),
inference(clausify,[status(thm)],[f_1072_2]) ).
fof(f_1073_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_1073_2,plain,
! [U_3382,U_3381] :
( hAPP(c_Groups_Oabs__class_Oabs(U_3381),U_3382) = U_3382
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3381),c_Groups_Ozero__class_Ozero(U_3381)),U_3382))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3381) ),
inference(variable_rename,[status(thm)],[f_1073_1]) ).
cnf(f_1073_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3381),U_3382) = U_3382
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3381),c_Groups_Ozero__class_Ozero(U_3381)),U_3382))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3381) ),
inference(clausify,[status(thm)],[f_1073_2]) ).
fof(f_1074_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_1074_2,plain,
! [U_3385,U_3384,U_3383] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3383),hAPP(c_Groups_Oabs__class_Oabs(U_3383),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3383),U_3384),U_3385))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3383),hAPP(c_Groups_Oabs__class_Oabs(U_3383),U_3384)),hAPP(c_Groups_Oabs__class_Oabs(U_3383),U_3385))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3383) ),
inference(variable_rename,[status(thm)],[f_1074_1]) ).
cnf(f_1074_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3383),hAPP(c_Groups_Oabs__class_Oabs(U_3383),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3383),U_3384),U_3385))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3383),hAPP(c_Groups_Oabs__class_Oabs(U_3383),U_3384)),hAPP(c_Groups_Oabs__class_Oabs(U_3383),U_3385))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3383) ),
inference(clausify,[status(thm)],[f_1074_2]) ).
fof(f_1075_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_1075_2,plain,
! [U_3390,U_3389,U_3388,U_3387,U_3386] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3386),hAPP(c_Groups_Oabs__class_Oabs(U_3386),U_3387)),hAPP(c_Groups_Oabs__class_Oabs(U_3386),U_3389))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3386),U_3388),U_3390)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3386),hAPP(c_Groups_Oabs__class_Oabs(U_3386),U_3389)),U_3390))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3386),hAPP(c_Groups_Oabs__class_Oabs(U_3386),U_3387)),U_3388))
| ~ class_Rings_Olinordered__idom(U_3386) ),
inference(variable_rename,[status(thm)],[f_1075_1]) ).
cnf(f_1075_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3386),hAPP(c_Groups_Oabs__class_Oabs(U_3386),U_3387)),hAPP(c_Groups_Oabs__class_Oabs(U_3386),U_3389))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3386),U_3388),U_3390)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3386),hAPP(c_Groups_Oabs__class_Oabs(U_3386),U_3389)),U_3390))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3386),hAPP(c_Groups_Oabs__class_Oabs(U_3386),U_3387)),U_3388))
| ~ class_Rings_Olinordered__idom(U_3386) ),
inference(clausify,[status(thm)],[f_1075_2]) ).
fof(f_1076_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_1076_2,plain,
! [U_3393,U_3392,U_3391] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3391),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3391),hAPP(c_Groups_Oabs__class_Oabs(U_3391),U_3392)),hAPP(c_Groups_Oabs__class_Oabs(U_3391),U_3393))),hAPP(c_Groups_Oabs__class_Oabs(U_3391),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3391),U_3393),U_3392))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3391) ),
inference(variable_rename,[status(thm)],[f_1076_1]) ).
cnf(f_1076_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3391),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3391),hAPP(c_Groups_Oabs__class_Oabs(U_3391),U_3392)),hAPP(c_Groups_Oabs__class_Oabs(U_3391),U_3393))),hAPP(c_Groups_Oabs__class_Oabs(U_3391),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3391),U_3393),U_3392))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3391) ),
inference(clausify,[status(thm)],[f_1076_2]) ).
fof(f_1077_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_1077_2,plain,
! [U_3396,U_3395,U_3394] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3394),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3394),hAPP(c_Groups_Oabs__class_Oabs(U_3394),U_3395)),hAPP(c_Groups_Oabs__class_Oabs(U_3394),U_3396))),hAPP(c_Groups_Oabs__class_Oabs(U_3394),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3394),U_3395),U_3396))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3394) ),
inference(variable_rename,[status(thm)],[f_1077_1]) ).
cnf(f_1077_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3394),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3394),hAPP(c_Groups_Oabs__class_Oabs(U_3394),U_3395)),hAPP(c_Groups_Oabs__class_Oabs(U_3394),U_3396))),hAPP(c_Groups_Oabs__class_Oabs(U_3394),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3394),U_3395),U_3396))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3394) ),
inference(clausify,[status(thm)],[f_1077_2]) ).
fof(f_1078_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_1078_2,plain,
! [U_3399,U_3398,U_3397] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3397),hAPP(c_Groups_Oabs__class_Oabs(U_3397),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3397),hAPP(c_Groups_Oabs__class_Oabs(U_3397),U_3398)),hAPP(c_Groups_Oabs__class_Oabs(U_3397),U_3399)))),hAPP(c_Groups_Oabs__class_Oabs(U_3397),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3397),U_3398),U_3399))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3397) ),
inference(variable_rename,[status(thm)],[f_1078_1]) ).
cnf(f_1078_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3397),hAPP(c_Groups_Oabs__class_Oabs(U_3397),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3397),hAPP(c_Groups_Oabs__class_Oabs(U_3397),U_3398)),hAPP(c_Groups_Oabs__class_Oabs(U_3397),U_3399)))),hAPP(c_Groups_Oabs__class_Oabs(U_3397),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3397),U_3398),U_3399))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3397) ),
inference(clausify,[status(thm)],[f_1078_2]) ).
fof(f_1079_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_1079_2,plain,
! [U_3402,U_3401,U_3400] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3400),hAPP(c_Groups_Ouminus__class_Ouminus(U_3400),U_3401)),U_3402))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3400),hAPP(c_Groups_Oabs__class_Oabs(U_3400),U_3401)),U_3402))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3400) ),
inference(variable_rename,[status(thm)],[f_1079_1]) ).
cnf(f_1079_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3400),hAPP(c_Groups_Ouminus__class_Ouminus(U_3400),U_3401)),U_3402))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3400),hAPP(c_Groups_Oabs__class_Oabs(U_3400),U_3401)),U_3402))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3400) ),
inference(clausify,[status(thm)],[f_1079_2]) ).
fof(f_1080_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_1080_2,plain,
! [U_3405,U_3404,U_3403] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3403),hAPP(c_Groups_Oabs__class_Oabs(U_3403),U_3404)),U_3405))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3403),hAPP(c_Groups_Ouminus__class_Ouminus(U_3403),U_3404)),U_3405))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3403),U_3404),U_3405))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3403) ),
inference(variable_rename,[status(thm)],[f_1080_1]) ).
cnf(f_1080_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3403),hAPP(c_Groups_Oabs__class_Oabs(U_3403),U_3404)),U_3405))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3403),hAPP(c_Groups_Ouminus__class_Ouminus(U_3403),U_3404)),U_3405))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3403),U_3404),U_3405))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3403) ),
inference(clausify,[status(thm)],[f_1080_2]) ).
fof(f_1081_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
inference(fof_nnf,[status(thm)],[fact_abs__le__iff]) ).
fof(f_1081_2,plain,
! [U_3408,U_3407,U_3406] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3406),hAPP(c_Groups_Oabs__class_Oabs(U_3406),U_3407)),U_3408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3406),hAPP(c_Groups_Ouminus__class_Ouminus(U_3406),U_3407)),U_3408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3406),U_3407),U_3408)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3406),hAPP(c_Groups_Ouminus__class_Ouminus(U_3406),U_3407)),U_3408))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3406),U_3407),U_3408)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3406),hAPP(c_Groups_Oabs__class_Oabs(U_3406),U_3407)),U_3408)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_3406) ),
inference(variable_rename,[status(thm)],[f_1081_1]) ).
cnf(f_1081_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3406),U_3407),U_3408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3406),hAPP(c_Groups_Oabs__class_Oabs(U_3406),U_3407)),U_3408))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3406) ),
inference(clausify,[status(thm)],[f_1081_2]) ).
cnf(f_1081_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3406),hAPP(c_Groups_Ouminus__class_Ouminus(U_3406),U_3407)),U_3408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3406),hAPP(c_Groups_Oabs__class_Oabs(U_3406),U_3407)),U_3408))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3406) ),
inference(clausify,[status(thm)],[f_1081_2]) ).
cnf(f_1081_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3406),hAPP(c_Groups_Oabs__class_Oabs(U_3406),U_3407)),U_3408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3406),hAPP(c_Groups_Ouminus__class_Ouminus(U_3406),U_3407)),U_3408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3406),U_3407),U_3408))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3406) ),
inference(clausify,[status(thm)],[f_1081_2]) ).
fof(f_1082_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_1082_2,plain,
! [U_3410,U_3409] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3409),hAPP(c_Groups_Ouminus__class_Ouminus(U_3409),U_3410)),hAPP(c_Groups_Oabs__class_Oabs(U_3409),U_3410)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3409) ),
inference(variable_rename,[status(thm)],[f_1082_1]) ).
cnf(f_1082_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3409),hAPP(c_Groups_Ouminus__class_Ouminus(U_3409),U_3410)),hAPP(c_Groups_Oabs__class_Oabs(U_3409),U_3410)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3409) ),
inference(clausify,[status(thm)],[f_1082_2]) ).
fof(f_1083_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2)) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_abs__less__iff]) ).
fof(f_1083_2,plain,
! [U_3413,U_3412,U_3411] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3411),hAPP(c_Groups_Oabs__class_Oabs(U_3411),U_3412)),U_3413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3411),hAPP(c_Groups_Ouminus__class_Ouminus(U_3411),U_3412)),U_3413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3411),U_3412),U_3413)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3411),hAPP(c_Groups_Ouminus__class_Ouminus(U_3411),U_3412)),U_3413))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3411),U_3412),U_3413)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3411),hAPP(c_Groups_Oabs__class_Oabs(U_3411),U_3412)),U_3413)) ) )
| ~ class_Rings_Olinordered__idom(U_3411) ),
inference(variable_rename,[status(thm)],[f_1083_1]) ).
cnf(f_1083_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3411),U_3412),U_3413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3411),hAPP(c_Groups_Oabs__class_Oabs(U_3411),U_3412)),U_3413))
| ~ class_Rings_Olinordered__idom(U_3411) ),
inference(clausify,[status(thm)],[f_1083_2]) ).
cnf(f_1083_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3411),hAPP(c_Groups_Ouminus__class_Ouminus(U_3411),U_3412)),U_3413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3411),hAPP(c_Groups_Oabs__class_Oabs(U_3411),U_3412)),U_3413))
| ~ class_Rings_Olinordered__idom(U_3411) ),
inference(clausify,[status(thm)],[f_1083_2]) ).
cnf(f_1083_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3411),hAPP(c_Groups_Oabs__class_Oabs(U_3411),U_3412)),U_3413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3411),hAPP(c_Groups_Ouminus__class_Ouminus(U_3411),U_3412)),U_3413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3411),U_3412),U_3413))
| ~ class_Rings_Olinordered__idom(U_3411) ),
inference(clausify,[status(thm)],[f_1083_2]) ).
fof(f_1084_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_1084_2,plain,
! [U_3416,U_3415,U_3414] :
( hAPP(c_Groups_Oabs__class_Oabs(U_3414),hAPP(hAPP(c_Power_Opower__class_Opower(U_3414),hAPP(c_Groups_Ouminus__class_Ouminus(U_3414),U_3415)),U_3416)) = hAPP(c_Groups_Oabs__class_Oabs(U_3414),hAPP(hAPP(c_Power_Opower__class_Opower(U_3414),U_3415),U_3416))
| ~ class_Rings_Olinordered__idom(U_3414) ),
inference(variable_rename,[status(thm)],[f_1084_1]) ).
cnf(f_1084_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3414),hAPP(hAPP(c_Power_Opower__class_Opower(U_3414),hAPP(c_Groups_Ouminus__class_Ouminus(U_3414),U_3415)),U_3416)) = hAPP(c_Groups_Oabs__class_Oabs(U_3414),hAPP(hAPP(c_Power_Opower__class_Opower(U_3414),U_3415),U_3416))
| ~ class_Rings_Olinordered__idom(U_3414) ),
inference(clausify,[status(thm)],[f_1084_2]) ).
fof(f_1085_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_1085_2,plain,
! [U_3417] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3417,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_1085_1]) ).
cnf(f_1085_3,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3417,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_1085_2]) ).
fof(f_1086_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_1086_2,plain,
! [U_3419,U_3418] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3418),U_3419) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3418,U_3419))
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3418,U_3419)) = U_3419 )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3418),U_3419) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3418,U_3419)) != U_3419 ) ),
inference(variable_rename,[status(thm)],[f_1086_1]) ).
fof(f_1086_3,plain,
( ! [U_3423,U_3421] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3421),U_3423) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3421,U_3423))
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3421,U_3423)) = U_3423 )
& ! [U_3422,U_3420] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3420),U_3422) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3420,U_3422)) != U_3422 ) ),
inference(miniscope,[status(thm)],[f_1086_2]) ).
cnf(f_1086_4,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3420),U_3422) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3420,U_3422)) != U_3422 ),
inference(clausify,[status(thm)],[f_1086_3]) ).
cnf(f_1086_5,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3421),U_3423) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3421,U_3423))
| hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3421,U_3423)) = U_3423 ),
inference(clausify,[status(thm)],[f_1086_3]) ).
fof(f_1087_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_1087_2,plain,
! [U_3425,U_3424] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3425,U_3424)),U_3424))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3424)) ),
inference(variable_rename,[status(thm)],[f_1087_1]) ).
cnf(f_1087_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3425,U_3424)),U_3424))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3424)) ),
inference(clausify,[status(thm)],[f_1087_2]) ).
fof(f_1088_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_1088_2,plain,
! [U_3429,U_3428] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3428,U_3429) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ! [U_3427] : U_3428 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3429),U_3427) )
& ( ? [U_3426] : U_3428 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3429),U_3426)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3428,U_3429) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1088_1]) ).
fof(f_1088_3,plain,
( ! [U_3433,U_3431] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3431,U_3433) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ! [U_3427] : U_3431 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3433),U_3427) )
& ! [U_3432,U_3430] :
( ? [U_3426] : U_3430 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3432),U_3426)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3430,U_3432) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1088_2]) ).
fof(f_1088_4,plain,
( ! [U_3433,U_3431] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3431,U_3433) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ! [U_3427] : U_3431 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3433),U_3427) )
& ! [U_3432,U_3430] :
( U_3430 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3432),sK52(U_3432,U_3430))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3430,U_3432) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_3426,sK52(U_3432,U_3430))],[f_1088_3]) ).
cnf(f_1088_5,plain,
( U_3430 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3432),sK52(U_3432,U_3430))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3430,U_3432) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1088_4]) ).
cnf(f_1088_6,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3431,U_3433) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3431 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3433),U_3427) ),
inference(clausify,[status(thm)],[f_1088_4]) ).
fof(f_1089_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_1089_2,plain,
! [U_3435,U_3434] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3434,U_3435) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3434),U_3435),U_3435)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3434),U_3435)) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3434,U_3435) = U_3434
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3434),U_3435)) ) ),
inference(variable_rename,[status(thm)],[f_1089_1]) ).
fof(f_1089_3,plain,
( ! [U_3439,U_3437] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3437,U_3439) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3437),U_3439),U_3439)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3437),U_3439)) )
& ! [U_3438,U_3436] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3436,U_3438) = U_3436
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3436),U_3438)) ) ),
inference(miniscope,[status(thm)],[f_1089_2]) ).
cnf(f_1089_4,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3436,U_3438) = U_3436
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3436),U_3438)) ),
inference(clausify,[status(thm)],[f_1089_3]) ).
cnf(f_1089_5,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3437,U_3439) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3437),U_3439),U_3439)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3437),U_3439)) ),
inference(clausify,[status(thm)],[f_1089_3]) ).
fof(f_1090_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_1090_2,plain,
! [U_3441,U_3440] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3440,U_3441) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3440),U_3441),U_3441)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3440),U_3441)) ),
inference(variable_rename,[status(thm)],[f_1090_1]) ).
cnf(f_1090_3,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3440,U_3441) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3440),U_3441),U_3441)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3440),U_3441)) ),
inference(clausify,[status(thm)],[f_1090_2]) ).
fof(f_1091_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_1091_2,plain,
! [U_3444,U_3443,U_3442] : 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_3442),U_3443)),U_3444),U_3443) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3444,U_3443),
inference(variable_rename,[status(thm)],[f_1091_1]) ).
cnf(f_1091_3,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_3442),U_3443)),U_3444),U_3443) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3444,U_3443),
inference(clausify,[status(thm)],[f_1091_2]) ).
fof(f_1092_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_1092_2,plain,
! [U_3446,U_3445] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3446,U_3445) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3446),U_3445),U_3445)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3445),U_3446)) ),
inference(variable_rename,[status(thm)],[f_1092_1]) ).
cnf(f_1092_3,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3446,U_3445) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3446),U_3445),U_3445)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3445),U_3446)) ),
inference(clausify,[status(thm)],[f_1092_2]) ).
fof(f_1093_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_1093_2,plain,
! [U_3448,U_3447] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3447) = 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_3447),U_3448)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1093_1]) ).
cnf(f_1093_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3447) = 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_3447),U_3448)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1093_2]) ).
fof(f_1094_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_1094_2,plain,
! [U_3449] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_3449),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_3449)
| ~ class_Int_Onumber__ring(U_3449) ),
inference(variable_rename,[status(thm)],[f_1094_1]) ).
cnf(f_1094_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_3449),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_3449)
| ~ class_Int_Onumber__ring(U_3449) ),
inference(clausify,[status(thm)],[f_1094_2]) ).
fof(f_1095_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_1095_2,plain,
! [U_3450] :
( c_Groups_Ozero__class_Ozero(U_3450) = hAPP(c_Int_Onumber__class_Onumber__of(U_3450),c_Int_OPls)
| ~ class_Int_Onumber__ring(U_3450) ),
inference(variable_rename,[status(thm)],[f_1095_1]) ).
cnf(f_1095_3,plain,
( c_Groups_Ozero__class_Ozero(U_3450) = hAPP(c_Int_Onumber__class_Onumber__of(U_3450),c_Int_OPls)
| ~ class_Int_Onumber__ring(U_3450) ),
inference(clausify,[status(thm)],[f_1095_2]) ).
fof(f_1096_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_1096_2,plain,
! [U_3452,U_3451] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3451),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3452)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3451,U_3452)),
inference(variable_rename,[status(thm)],[f_1096_1]) ).
cnf(f_1096_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3451),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3452)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3451,U_3452)),
inference(clausify,[status(thm)],[f_1096_2]) ).
fof(f_1097_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_1097_2,plain,
! [U_3454,U_3453] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3453,U_3454)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3453),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3454)),
inference(variable_rename,[status(thm)],[f_1097_1]) ).
cnf(f_1097_3,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3453,U_3454)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3453),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3454)),
inference(clausify,[status(thm)],[f_1097_2]) ).
fof(f_1098_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_1098_2,plain,
! [U_3456,U_3455] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3455),hAPP(c_Int_Onumber__class_Onumber__of(U_3455),c_Int_OPls)),U_3456) = U_3456
| ~ class_Int_Onumber__ring(U_3455) ),
inference(variable_rename,[status(thm)],[f_1098_1]) ).
cnf(f_1098_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3455),hAPP(c_Int_Onumber__class_Onumber__of(U_3455),c_Int_OPls)),U_3456) = U_3456
| ~ class_Int_Onumber__ring(U_3455) ),
inference(clausify,[status(thm)],[f_1098_2]) ).
fof(f_1099_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_1099_2,plain,
! [U_3458,U_3457] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3457),U_3458),hAPP(c_Int_Onumber__class_Onumber__of(U_3457),c_Int_OPls)) = U_3458
| ~ class_Int_Onumber__ring(U_3457) ),
inference(variable_rename,[status(thm)],[f_1099_1]) ).
cnf(f_1099_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3457),U_3458),hAPP(c_Int_Onumber__class_Onumber__of(U_3457),c_Int_OPls)) = U_3458
| ~ class_Int_Onumber__ring(U_3457) ),
inference(clausify,[status(thm)],[f_1099_2]) ).
fof(f_1100_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_1100_2,plain,
! [U_3460,U_3459] :
( hAPP(c_Groups_Oabs__class_Oabs(U_3459),U_3460) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3459),U_3460),c_Groups_Osgn__class_Osgn(U_3459,U_3460))
| ~ class_Rings_Olinordered__idom(U_3459) ),
inference(variable_rename,[status(thm)],[f_1100_1]) ).
cnf(f_1100_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3459),U_3460) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3459),U_3460),c_Groups_Osgn__class_Osgn(U_3459,U_3460))
| ~ class_Rings_Olinordered__idom(U_3459) ),
inference(clausify,[status(thm)],[f_1100_2]) ).
fof(f_1101_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_1101_2,plain,
! [U_3462,U_3461] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3461),c_Groups_Osgn__class_Osgn(U_3461,U_3462)),hAPP(c_Groups_Oabs__class_Oabs(U_3461),U_3462)) = U_3462
| ~ class_Rings_Olinordered__idom(U_3461) ),
inference(variable_rename,[status(thm)],[f_1101_1]) ).
cnf(f_1101_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3461),c_Groups_Osgn__class_Osgn(U_3461,U_3462)),hAPP(c_Groups_Oabs__class_Oabs(U_3461),U_3462)) = U_3462
| ~ class_Rings_Olinordered__idom(U_3461) ),
inference(clausify,[status(thm)],[f_1101_2]) ).
fof(f_1102_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_1102_2,plain,
! [U_3465,U_3464,U_3463] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3463),U_3464)),U_3465) = 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_3463),U_3465)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3464),U_3465))),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_3463,U_3465)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3464,U_3465))),U_3465)),
inference(variable_rename,[status(thm)],[f_1102_1]) ).
cnf(f_1102_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3463),U_3464)),U_3465) = 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_3463),U_3465)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3464),U_3465))),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_3463,U_3465)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3464,U_3465))),U_3465)),
inference(clausify,[status(thm)],[f_1102_2]) ).
fof(f_1103_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]) ).
cnf(f_1103_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(clausify,[status(thm)],[f_1103_1]) ).
fof(f_1104_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]) ).
cnf(f_1104_2,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_1104_1]) ).
fof(f_1105_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]) ).
cnf(f_1105_2,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_1105_1]) ).
fof(f_1106_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]) ).
cnf(f_1106_2,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_1106_1]) ).
fof(f_1107_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]) ).
cnf(f_1107_2,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(clausify,[status(thm)],[f_1107_1]) ).
fof(f_1108_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]) ).
cnf(f_1108_2,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(clausify,[status(thm)],[f_1108_1]) ).
fof(f_1109_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]) ).
cnf(f_1109_2,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(clausify,[status(thm)],[f_1109_1]) ).
fof(f_1110_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]) ).
cnf(f_1110_2,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(clausify,[status(thm)],[f_1110_1]) ).
fof(f_1111_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]) ).
cnf(f_1111_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(clausify,[status(thm)],[f_1111_1]) ).
fof(f_1112_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]) ).
cnf(f_1112_2,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_1112_1]) ).
fof(f_1113_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_1113_2,plain,
! [U_3466] :
( c_Int_Oiszero(U_3466,hAPP(c_Int_Onumber__class_Onumber__of(U_3466),c_Int_OPls))
| ~ class_Int_Onumber__ring(U_3466) ),
inference(variable_rename,[status(thm)],[f_1113_1]) ).
cnf(f_1113_3,plain,
( c_Int_Oiszero(U_3466,hAPP(c_Int_Onumber__class_Onumber__of(U_3466),c_Int_OPls))
| ~ class_Int_Onumber__ring(U_3466) ),
inference(clausify,[status(thm)],[f_1113_2]) ).
fof(f_1114_1,plain,
c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_succ__Min]) ).
cnf(f_1114_2,plain,
c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
inference(clausify,[status(thm)],[f_1114_1]) ).
fof(f_1115_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_1115_2,plain,
! [U_3469,U_3468,U_3467] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3467),hAPP(c_Groups_Oabs__class_Oabs(U_3467),U_3469)),U_3468) = hAPP(c_Groups_Oabs__class_Oabs(U_3467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3467),U_3469),U_3468))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3467),c_Groups_Ozero__class_Ozero(U_3467)),U_3468))
| ~ class_Rings_Olinordered__idom(U_3467) ),
inference(variable_rename,[status(thm)],[f_1115_1]) ).
cnf(f_1115_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3467),hAPP(c_Groups_Oabs__class_Oabs(U_3467),U_3469)),U_3468) = hAPP(c_Groups_Oabs__class_Oabs(U_3467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3467),U_3469),U_3468))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3467),c_Groups_Ozero__class_Ozero(U_3467)),U_3468))
| ~ class_Rings_Olinordered__idom(U_3467) ),
inference(clausify,[status(thm)],[f_1115_2]) ).
fof(f_1116_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_1116_2,plain,
! [U_3472,U_3471,U_3470] :
( hAPP(c_Groups_Oabs__class_Oabs(U_3470),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3470),U_3471),U_3472)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3470),hAPP(c_Groups_Oabs__class_Oabs(U_3470),U_3471)),hAPP(c_Groups_Oabs__class_Oabs(U_3470),U_3472))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3470),U_3472),c_Groups_Ozero__class_Ozero(U_3470)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3470),c_Groups_Ozero__class_Ozero(U_3470)),U_3472)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3470),U_3471),c_Groups_Ozero__class_Ozero(U_3470)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3470),c_Groups_Ozero__class_Ozero(U_3470)),U_3471)) )
| ~ class_Rings_Oordered__ring__abs(U_3470) ),
inference(variable_rename,[status(thm)],[f_1116_1]) ).
cnf(f_1116_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3470),c_Groups_Ozero__class_Ozero(U_3470)),U_3472))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3470),c_Groups_Ozero__class_Ozero(U_3470)),U_3471))
| hAPP(c_Groups_Oabs__class_Oabs(U_3470),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3470),U_3471),U_3472)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3470),hAPP(c_Groups_Oabs__class_Oabs(U_3470),U_3471)),hAPP(c_Groups_Oabs__class_Oabs(U_3470),U_3472))
| ~ class_Rings_Oordered__ring__abs(U_3470) ),
inference(clausify,[status(thm)],[f_1116_2]) ).
cnf(f_1116_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3470),U_3472),c_Groups_Ozero__class_Ozero(U_3470)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3470),c_Groups_Ozero__class_Ozero(U_3470)),U_3471))
| hAPP(c_Groups_Oabs__class_Oabs(U_3470),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3470),U_3471),U_3472)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3470),hAPP(c_Groups_Oabs__class_Oabs(U_3470),U_3471)),hAPP(c_Groups_Oabs__class_Oabs(U_3470),U_3472))
| ~ class_Rings_Oordered__ring__abs(U_3470) ),
inference(clausify,[status(thm)],[f_1116_2]) ).
cnf(f_1116_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3470),c_Groups_Ozero__class_Ozero(U_3470)),U_3472))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3470),U_3471),c_Groups_Ozero__class_Ozero(U_3470)))
| hAPP(c_Groups_Oabs__class_Oabs(U_3470),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3470),U_3471),U_3472)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3470),hAPP(c_Groups_Oabs__class_Oabs(U_3470),U_3471)),hAPP(c_Groups_Oabs__class_Oabs(U_3470),U_3472))
| ~ class_Rings_Oordered__ring__abs(U_3470) ),
inference(clausify,[status(thm)],[f_1116_2]) ).
cnf(f_1116_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3470),U_3472),c_Groups_Ozero__class_Ozero(U_3470)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3470),U_3471),c_Groups_Ozero__class_Ozero(U_3470)))
| hAPP(c_Groups_Oabs__class_Oabs(U_3470),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3470),U_3471),U_3472)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3470),hAPP(c_Groups_Oabs__class_Oabs(U_3470),U_3471)),hAPP(c_Groups_Oabs__class_Oabs(U_3470),U_3472))
| ~ class_Rings_Oordered__ring__abs(U_3470) ),
inference(clausify,[status(thm)],[f_1116_2]) ).
fof(f_1117_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_1117_2,plain,
! [U_3477,U_3476,U_3475,U_3474,U_3473] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3473),hAPP(c_Groups_Oabs__class_Oabs(U_3473),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3473),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3473),U_3474),U_3475)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3473),U_3476),U_3477)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3473),hAPP(c_Groups_Oabs__class_Oabs(U_3473),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3473),U_3474),U_3476))),hAPP(c_Groups_Oabs__class_Oabs(U_3473),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3473),U_3475),U_3477)))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3473) ),
inference(variable_rename,[status(thm)],[f_1117_1]) ).
cnf(f_1117_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3473),hAPP(c_Groups_Oabs__class_Oabs(U_3473),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3473),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3473),U_3474),U_3475)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3473),U_3476),U_3477)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3473),hAPP(c_Groups_Oabs__class_Oabs(U_3473),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3473),U_3474),U_3476))),hAPP(c_Groups_Oabs__class_Oabs(U_3473),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3473),U_3475),U_3477)))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3473) ),
inference(clausify,[status(thm)],[f_1117_2]) ).
fof(f_1118_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_1118_2,plain,
! [U_3480,U_3479,U_3478] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3478),hAPP(c_Groups_Oabs__class_Oabs(U_3478),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3478),U_3479),U_3480))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3478),hAPP(c_Groups_Oabs__class_Oabs(U_3478),U_3479)),hAPP(c_Groups_Oabs__class_Oabs(U_3478),U_3480))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3478) ),
inference(variable_rename,[status(thm)],[f_1118_1]) ).
cnf(f_1118_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3478),hAPP(c_Groups_Oabs__class_Oabs(U_3478),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3478),U_3479),U_3480))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3478),hAPP(c_Groups_Oabs__class_Oabs(U_3478),U_3479)),hAPP(c_Groups_Oabs__class_Oabs(U_3478),U_3480))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3478) ),
inference(clausify,[status(thm)],[f_1118_2]) ).
fof(f_1119_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_1119_2,plain,
! [U_3482,U_3481] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3481),hAPP(c_Groups_Ouminus__class_Ouminus(U_3481),hAPP(c_Groups_Oabs__class_Oabs(U_3481),U_3482))),c_Groups_Ozero__class_Ozero(U_3481)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3481) ),
inference(variable_rename,[status(thm)],[f_1119_1]) ).
cnf(f_1119_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3481),hAPP(c_Groups_Ouminus__class_Ouminus(U_3481),hAPP(c_Groups_Oabs__class_Oabs(U_3481),U_3482))),c_Groups_Ozero__class_Ozero(U_3481)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3481) ),
inference(clausify,[status(thm)],[f_1119_2]) ).
fof(f_1120_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_1120_2,plain,
! [U_3484,U_3483] :
( hAPP(c_Groups_Oabs__class_Oabs(U_3483),U_3484) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3483),U_3484)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3483),U_3484),c_Groups_Ozero__class_Ozero(U_3483)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3483) ),
inference(variable_rename,[status(thm)],[f_1120_1]) ).
cnf(f_1120_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3483),U_3484) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3483),U_3484)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3483),U_3484),c_Groups_Ozero__class_Ozero(U_3483)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3483) ),
inference(clausify,[status(thm)],[f_1120_2]) ).
fof(f_1121_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_1121_2,plain,
! [U_3486,U_3485] :
( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_3485),U_3486) = U_3486
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3485),U_3486),c_Groups_Ozero__class_Ozero(U_3485))) )
& ( hAPP(c_Groups_Oabs__class_Oabs(U_3485),U_3486) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3485),U_3486)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3485),U_3486),c_Groups_Ozero__class_Ozero(U_3485))) ) )
| ~ class_Groups_Oabs__if(U_3485) ),
inference(variable_rename,[status(thm)],[f_1121_1]) ).
cnf(f_1121_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3485),U_3486) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3485),U_3486)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3485),U_3486),c_Groups_Ozero__class_Ozero(U_3485)))
| ~ class_Groups_Oabs__if(U_3485) ),
inference(clausify,[status(thm)],[f_1121_2]) ).
cnf(f_1121_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3485),U_3486) = U_3486
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3485),U_3486),c_Groups_Ozero__class_Ozero(U_3485)))
| ~ class_Groups_Oabs__if(U_3485) ),
inference(clausify,[status(thm)],[f_1121_2]) ).
fof(f_1122_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_1122_2,plain,
! [U_3488,U_3487] :
( hAPP(c_Groups_Oabs__class_Oabs(U_3487),U_3488) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3487),U_3488)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3487),U_3488),c_Groups_Ozero__class_Ozero(U_3487)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3487) ),
inference(variable_rename,[status(thm)],[f_1122_1]) ).
cnf(f_1122_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3487),U_3488) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3487),U_3488)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3487),U_3488),c_Groups_Ozero__class_Ozero(U_3487)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_3487) ),
inference(clausify,[status(thm)],[f_1122_2]) ).
fof(f_1123_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_1123_2,plain,
! [U_3491,U_3490,U_3489] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3489),c_Groups_Ozero__class_Ozero(U_3489)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3489),hAPP(c_Groups_Oabs__class_Oabs(U_3489),U_3490)),U_3491)))
| ~ class_Rings_Olinordered__idom(U_3489) ),
inference(variable_rename,[status(thm)],[f_1123_1]) ).
cnf(f_1123_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3489),c_Groups_Ozero__class_Ozero(U_3489)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3489),hAPP(c_Groups_Oabs__class_Oabs(U_3489),U_3490)),U_3491)))
| ~ class_Rings_Olinordered__idom(U_3489) ),
inference(clausify,[status(thm)],[f_1123_2]) ).
fof(f_1124_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_1124_2,plain,
! [U_3492] :
( hAPP(c_Groups_Oabs__class_Oabs(U_3492),hAPP(c_Int_Onumber__class_Onumber__of(U_3492),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_3492)
| ~ class_Rings_Olinordered__idom(U_3492)
| ~ class_Int_Onumber__ring(U_3492) ),
inference(variable_rename,[status(thm)],[f_1124_1]) ).
cnf(f_1124_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3492),hAPP(c_Int_Onumber__class_Onumber__of(U_3492),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_3492)
| ~ class_Rings_Olinordered__idom(U_3492)
| ~ class_Int_Onumber__ring(U_3492) ),
inference(clausify,[status(thm)],[f_1124_2]) ).
fof(f_1125_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_1125_2,plain,
! [U_3494,U_3493] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3494,U_3493)),U_3493))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3493)) ),
inference(variable_rename,[status(thm)],[f_1125_1]) ).
cnf(f_1125_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3494,U_3493)),U_3493))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3493)) ),
inference(clausify,[status(thm)],[f_1125_2]) ).
fof(f_1126_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_1126_2,plain,
! [U_3495] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3495)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| U_3495 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( U_3495 = 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_3495)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_1126_1]) ).
fof(f_1126_3,plain,
( ! [U_3497] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3497)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| U_3497 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_3496] :
( U_3496 = 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_3496)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_1126_2]) ).
cnf(f_1126_4,plain,
( U_3496 = 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_3496)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1126_3]) ).
cnf(f_1126_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3497)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| U_3497 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1126_3]) ).
fof(f_1127_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_1127_2,plain,
! [U_3498] :
( ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3498) = U_3498
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3498),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3498) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3498)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3498),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_1127_1]) ).
fof(f_1127_3,plain,
( ! [U_3500] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3500) = U_3500
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3500),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_3499] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3499) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3499)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3499),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_1127_2]) ).
cnf(f_1127_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3499) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3499)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3499),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1127_3]) ).
cnf(f_1127_5,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3500) = U_3500
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3500),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1127_3]) ).
fof(f_1128_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_1128_2,plain,
! [U_3503,U_3502,U_3501] : 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_3501),U_3502)),U_3503)),U_3502) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3503),U_3502),
inference(variable_rename,[status(thm)],[f_1128_1]) ).
cnf(f_1128_3,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_3501),U_3502)),U_3503)),U_3502) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3503),U_3502),
inference(clausify,[status(thm)],[f_1128_2]) ).
fof(f_1129_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_1129_2,plain,
! [U_3505,U_3504] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3504),U_3505))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3504))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3505))),
inference(variable_rename,[status(thm)],[f_1129_1]) ).
cnf(f_1129_3,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_3504),U_3505))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3504))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3505))),
inference(clausify,[status(thm)],[f_1129_2]) ).
fof(f_1130_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_1130_2,plain,
! [U_3508,U_3507,U_3506] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3506,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3507),U_3508)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3507),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3506),U_3507),U_3508))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3506,U_3507)),
inference(variable_rename,[status(thm)],[f_1130_1]) ).
cnf(f_1130_3,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3506,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3507),U_3508)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3507),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3506),U_3507),U_3508))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3506,U_3507)),
inference(clausify,[status(thm)],[f_1130_2]) ).
fof(f_1131_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_1131_2,plain,
! [U_3511,U_3510,U_3509] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3509),U_3510)),U_3511) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3509),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3510),U_3511))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3509),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3510,U_3511))),U_3511)),
inference(variable_rename,[status(thm)],[f_1131_1]) ).
cnf(f_1131_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3509),U_3510)),U_3511) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3509),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3510),U_3511))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3509),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3510,U_3511))),U_3511)),
inference(clausify,[status(thm)],[f_1131_2]) ).
fof(f_1132_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_1132_2,plain,
! [U_3513,U_3512] : 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_3512)),U_3513))),
inference(variable_rename,[status(thm)],[f_1132_1]) ).
cnf(f_1132_3,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_3512)),U_3513))),
inference(clausify,[status(thm)],[f_1132_2]) ).
fof(f_1133_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_1133_2,plain,
! [U_3515,U_3514] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3514),U_3515)),U_3515) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3514),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3514,U_3515)),
inference(variable_rename,[status(thm)],[f_1133_1]) ).
cnf(f_1133_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3514),U_3515)),U_3515) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3514),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3514,U_3515)),
inference(clausify,[status(thm)],[f_1133_2]) ).
fof(f_1134_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_1134_2,plain,
! [U_3517,U_3516] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3516),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3517),U_3516)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3517),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3517,U_3516)),
inference(variable_rename,[status(thm)],[f_1134_1]) ).
cnf(f_1134_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3516),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3517),U_3516)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3517),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3517,U_3516)),
inference(clausify,[status(thm)],[f_1134_2]) ).
fof(f_1135_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_1135_2,plain,
! [U_3519,U_3518] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3518,U_3519) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3518),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3518),U_3519)),U_3519)),
inference(variable_rename,[status(thm)],[f_1135_1]) ).
cnf(f_1135_3,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3518,U_3519) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3518),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3518),U_3519)),U_3519)),
inference(clausify,[status(thm)],[f_1135_2]) ).
fof(f_1136_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_1136_2,plain,
! [U_3520] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3520) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3520),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3520),c_Int_OPls))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3520) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1136_1]) ).
fof(f_1136_3,plain,
( ! [U_3522] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3522) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3522),c_Int_OPls)) )
& ! [U_3521] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3521),c_Int_OPls))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3521) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1136_2]) ).
cnf(f_1136_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3521),c_Int_OPls))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3521) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1136_3]) ).
cnf(f_1136_5,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3522) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3522),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1136_3]) ).
fof(f_1137_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_1137_2,plain,
! [U_3523] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3523)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3523),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3523),c_Int_OPls))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3523) ) ),
inference(variable_rename,[status(thm)],[f_1137_1]) ).
fof(f_1137_3,plain,
( ! [U_3525] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3525)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3525),c_Int_OPls)) )
& ! [U_3524] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3524),c_Int_OPls))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3524) ) ),
inference(miniscope,[status(thm)],[f_1137_2]) ).
cnf(f_1137_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3524),c_Int_OPls))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3524) ),
inference(clausify,[status(thm)],[f_1137_3]) ).
cnf(f_1137_5,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3525)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3525),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1137_3]) ).
fof(f_1138_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]) ).
cnf(f_1138_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(clausify,[status(thm)],[f_1138_1]) ).
fof(f_1139_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_1139_2,plain,
! [U_3527,U_3526] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3526)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3527)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3526),U_3527))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3527))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3526),U_3527)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3526),U_3527))
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3527))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3526),U_3527)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3526)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3527))) ) ),
inference(variable_rename,[status(thm)],[f_1139_1]) ).
fof(f_1139_3,plain,
( ! [U_3531,U_3529] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3529)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3531)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3529),U_3531))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3531))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3529),U_3531)) ) )
& ! [U_3530,U_3528] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3528),U_3530))
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3530))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3528),U_3530)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3528)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3530))) ) ),
inference(miniscope,[status(thm)],[f_1139_2]) ).
cnf(f_1139_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3530))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3528),U_3530))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3528)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3530))) ),
inference(clausify,[status(thm)],[f_1139_3]) ).
cnf(f_1139_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3528),U_3530))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3528)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3530))) ),
inference(clausify,[status(thm)],[f_1139_3]) ).
cnf(f_1139_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3529),U_3531))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3529),U_3531))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3529)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3531))) ),
inference(clausify,[status(thm)],[f_1139_3]) ).
cnf(f_1139_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3531))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3529),U_3531))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3529)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3531))) ),
inference(clausify,[status(thm)],[f_1139_3]) ).
fof(f_1140_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_1140_2,plain,
! [U_3533,U_3532] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3532)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3533)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3532),c_Int_OPls))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3532),U_3533)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3532),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3532),U_3533))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3532)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3533))) ) ),
inference(variable_rename,[status(thm)],[f_1140_1]) ).
fof(f_1140_3,plain,
( ! [U_3537,U_3535] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3535)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3537)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3535),c_Int_OPls))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3535),U_3537)) ) )
& ! [U_3536,U_3534] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3534),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3534),U_3536))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3534)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3536))) ) ),
inference(miniscope,[status(thm)],[f_1140_2]) ).
cnf(f_1140_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3534),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3534),U_3536))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3534)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3536))) ),
inference(clausify,[status(thm)],[f_1140_3]) ).
cnf(f_1140_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3535),U_3537))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3535)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3537))) ),
inference(clausify,[status(thm)],[f_1140_3]) ).
cnf(f_1140_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3535),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3535)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3537))) ),
inference(clausify,[status(thm)],[f_1140_3]) ).
fof(f_1141_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_1141_2,plain,
! [U_3539,U_3538] :
( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_3538),hAPP(c_Int_Onumber__class_Onumber__of(U_3538),U_3539)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3538),U_3539)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3538),hAPP(c_Int_Onumber__class_Onumber__of(U_3538),U_3539)),c_Groups_Ozero__class_Ozero(U_3538))) )
& ( hAPP(c_Groups_Oabs__class_Oabs(U_3538),hAPP(c_Int_Onumber__class_Onumber__of(U_3538),U_3539)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3538),hAPP(c_Int_Onumber__class_Onumber__of(U_3538),U_3539))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3538),hAPP(c_Int_Onumber__class_Onumber__of(U_3538),U_3539)),c_Groups_Ozero__class_Ozero(U_3538))) ) )
| ~ class_Rings_Olinordered__idom(U_3538)
| ~ class_Int_Onumber__ring(U_3538) ),
inference(variable_rename,[status(thm)],[f_1141_1]) ).
cnf(f_1141_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3538),hAPP(c_Int_Onumber__class_Onumber__of(U_3538),U_3539)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3538),hAPP(c_Int_Onumber__class_Onumber__of(U_3538),U_3539))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3538),hAPP(c_Int_Onumber__class_Onumber__of(U_3538),U_3539)),c_Groups_Ozero__class_Ozero(U_3538)))
| ~ class_Rings_Olinordered__idom(U_3538)
| ~ class_Int_Onumber__ring(U_3538) ),
inference(clausify,[status(thm)],[f_1141_2]) ).
cnf(f_1141_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3538),hAPP(c_Int_Onumber__class_Onumber__of(U_3538),U_3539)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3538),U_3539)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3538),hAPP(c_Int_Onumber__class_Onumber__of(U_3538),U_3539)),c_Groups_Ozero__class_Ozero(U_3538)))
| ~ class_Rings_Olinordered__idom(U_3538)
| ~ class_Int_Onumber__ring(U_3538) ),
inference(clausify,[status(thm)],[f_1141_2]) ).
fof(f_1142_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_1142_2,plain,
! [U_3541,U_3540] :
( hAPP(c_Groups_Oabs__class_Oabs(U_3540),hAPP(hAPP(c_Power_Opower__class_Opower(U_3540),hAPP(c_Int_Onumber__class_Onumber__of(U_3540),c_Int_OMin)),U_3541)) = c_Groups_Oone__class_Oone(U_3540)
| ~ class_Rings_Olinordered__idom(U_3540)
| ~ class_Int_Onumber__ring(U_3540) ),
inference(variable_rename,[status(thm)],[f_1142_1]) ).
cnf(f_1142_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3540),hAPP(hAPP(c_Power_Opower__class_Opower(U_3540),hAPP(c_Int_Onumber__class_Onumber__of(U_3540),c_Int_OMin)),U_3541)) = c_Groups_Oone__class_Oone(U_3540)
| ~ class_Rings_Olinordered__idom(U_3540)
| ~ class_Int_Onumber__ring(U_3540) ),
inference(clausify,[status(thm)],[f_1142_2]) ).
fof(f_1143_1,plain,
! [V_k_2,V_na_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_na_2,V_k_2)))
| ( ? [B_i,B_j] :
( ~ hBOOL(hAPP(V_P_2,B_j))
& V_na_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_P_2,V_na_2))
& V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( ( ! [B_i,B_j] :
( hBOOL(hAPP(V_P_2,B_j))
| V_na_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_P_2,V_na_2))
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_na_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_split__mod]) ).
fof(f_1143_2,plain,
! [U_3548,U_3547,U_3546] :
( ( hBOOL(hAPP(U_3546,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3547,U_3548)))
| ( ? [U_3545,U_3544] :
( ~ hBOOL(hAPP(U_3546,U_3544))
& U_3547 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3548),U_3545)),U_3544)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3544),U_3548)) )
& U_3548 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_3546,U_3547))
& U_3548 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ( ( ! [U_3543,U_3542] :
( hBOOL(hAPP(U_3546,U_3542))
| U_3547 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3548),U_3543)),U_3542)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3542),U_3548)) )
| U_3548 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_3546,U_3547))
| U_3548 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_3546,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3547,U_3548))) ) ),
inference(variable_rename,[status(thm)],[f_1143_1]) ).
fof(f_1143_3,plain,
( ! [U_3554,U_3552,U_3550] :
( hBOOL(hAPP(U_3550,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3552,U_3554)))
| ( ? [U_3545,U_3544] :
( ~ hBOOL(hAPP(U_3550,U_3544))
& U_3552 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3554),U_3545)),U_3544)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3544),U_3554)) )
& U_3554 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_3550,U_3552))
& U_3554 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_3553,U_3551,U_3549] :
( ( ( ! [U_3543,U_3542] :
( hBOOL(hAPP(U_3549,U_3542))
| U_3551 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3553),U_3543)),U_3542)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3542),U_3553)) )
| U_3553 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_3549,U_3551))
| U_3553 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_3549,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3551,U_3553))) ) ),
inference(miniscope,[status(thm)],[f_1143_2]) ).
fof(f_1143_4,plain,
( ! [U_3554,U_3552,U_3550] :
( hBOOL(hAPP(U_3550,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3552,U_3554)))
| ( ? [U_3544] :
( ~ hBOOL(hAPP(U_3550,U_3544))
& U_3552 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3554),sK53(U_3554,U_3552,U_3550))),U_3544)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3544),U_3554)) )
& U_3554 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_3550,U_3552))
& U_3554 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_3553,U_3551,U_3549] :
( ( ( ! [U_3543,U_3542] :
( hBOOL(hAPP(U_3549,U_3542))
| U_3551 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3553),U_3543)),U_3542)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3542),U_3553)) )
| U_3553 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_3549,U_3551))
| U_3553 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_3549,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3551,U_3553))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_3545,sK53(U_3554,U_3552,U_3550))],[f_1143_3]) ).
fof(f_1143_5,plain,
( ! [U_3554,U_3552,U_3550] :
( hBOOL(hAPP(U_3550,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3552,U_3554)))
| ( ~ hBOOL(hAPP(U_3550,sK54(U_3554,U_3552,U_3550)))
& U_3552 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3554),sK53(U_3554,U_3552,U_3550))),sK54(U_3554,U_3552,U_3550))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK54(U_3554,U_3552,U_3550)),U_3554))
& U_3554 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( ~ hBOOL(hAPP(U_3550,U_3552))
& U_3554 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_3553,U_3551,U_3549] :
( ( ( ! [U_3543,U_3542] :
( hBOOL(hAPP(U_3549,U_3542))
| U_3551 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3553),U_3543)),U_3542)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3542),U_3553)) )
| U_3553 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(U_3549,U_3551))
| U_3553 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(U_3549,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3551,U_3553))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_3544,sK54(U_3554,U_3552,U_3550))],[f_1143_4]) ).
cnf(f_1143_6,plain,
( hBOOL(hAPP(U_3549,U_3551))
| U_3553 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_3549,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3551,U_3553))) ),
inference(clausify,[status(thm)],[f_1143_5]) ).
cnf(f_1143_7,plain,
( hBOOL(hAPP(U_3549,U_3542))
| U_3551 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3553),U_3543)),U_3542)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3542),U_3553))
| U_3553 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_3549,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3551,U_3553))) ),
inference(clausify,[status(thm)],[f_1143_5]) ).
cnf(f_1143_8,plain,
( U_3554 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3554 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_3550,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3552,U_3554))) ),
inference(clausify,[status(thm)],[f_1143_5]) ).
cnf(f_1143_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK54(U_3554,U_3552,U_3550)),U_3554))
| U_3554 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_3550,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3552,U_3554))) ),
inference(clausify,[status(thm)],[f_1143_5]) ).
cnf(f_1143_10,plain,
( U_3552 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3554),sK53(U_3554,U_3552,U_3550))),sK54(U_3554,U_3552,U_3550))
| U_3554 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_3550,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3552,U_3554))) ),
inference(clausify,[status(thm)],[f_1143_5]) ).
cnf(f_1143_11,plain,
( ~ hBOOL(hAPP(U_3550,sK54(U_3554,U_3552,U_3550)))
| U_3554 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(U_3550,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3552,U_3554))) ),
inference(clausify,[status(thm)],[f_1143_5]) ).
cnf(f_1143_12,plain,
( U_3554 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(U_3550,U_3552))
| hBOOL(hAPP(U_3550,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3552,U_3554))) ),
inference(clausify,[status(thm)],[f_1143_5]) ).
cnf(f_1143_13,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK54(U_3554,U_3552,U_3550)),U_3554))
| ~ hBOOL(hAPP(U_3550,U_3552))
| hBOOL(hAPP(U_3550,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3552,U_3554))) ),
inference(clausify,[status(thm)],[f_1143_5]) ).
cnf(f_1143_14,plain,
( U_3552 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3554),sK53(U_3554,U_3552,U_3550))),sK54(U_3554,U_3552,U_3550))
| ~ hBOOL(hAPP(U_3550,U_3552))
| hBOOL(hAPP(U_3550,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3552,U_3554))) ),
inference(clausify,[status(thm)],[f_1143_5]) ).
cnf(f_1143_15,plain,
( ~ hBOOL(hAPP(U_3550,sK54(U_3554,U_3552,U_3550)))
| ~ hBOOL(hAPP(U_3550,U_3552))
| hBOOL(hAPP(U_3550,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3552,U_3554))) ),
inference(clausify,[status(thm)],[f_1143_5]) ).
fof(f_1144_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_1144_2,plain,
! [U_3558,U_3557,U_3556,U_3555] :
( 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_3557),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3558,U_3555))),U_3556)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3557),U_3555)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3556),U_3557))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3555)) ),
inference(variable_rename,[status(thm)],[f_1144_1]) ).
cnf(f_1144_3,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_3557),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3558,U_3555))),U_3556)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3557),U_3555)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3556),U_3557))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3555)) ),
inference(clausify,[status(thm)],[f_1144_2]) ).
fof(f_1145_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_1145_2,plain,
! [U_3560,U_3559] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3559),U_3560)),U_3559) = 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_3559)) ),
inference(variable_rename,[status(thm)],[f_1145_1]) ).
cnf(f_1145_3,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3559),U_3560)),U_3559) = 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_3559)) ),
inference(clausify,[status(thm)],[f_1145_2]) ).
fof(f_1146_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_1146_2,plain,
! [U_3562,U_3561] :
( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3561,U_3562)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3561),hAPP(c_Int_Onat,U_3562))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3562))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3561)) ),
inference(variable_rename,[status(thm)],[f_1146_1]) ).
cnf(f_1146_3,plain,
( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3561,U_3562)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3561),hAPP(c_Int_Onat,U_3562))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3562))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3561)) ),
inference(clausify,[status(thm)],[f_1146_2]) ).
fof(f_1147_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_1147_2,plain,
! [U_3564,U_3563] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3563),hAPP(c_Int_Onat,U_3564)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3563,U_3564))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3564))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3563)) ),
inference(variable_rename,[status(thm)],[f_1147_1]) ).
cnf(f_1147_3,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3563),hAPP(c_Int_Onat,U_3564)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3563,U_3564))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3564))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3563)) ),
inference(clausify,[status(thm)],[f_1147_2]) ).
fof(f_1148_1,plain,
! [V_na_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_na_2)))
| ( V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_x_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( V_na_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_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff]) ).
fof(f_1148_2,plain,
! [U_3566,U_3565] :
( ( 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_3565)),U_3566)))
| ( U_3566 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_3565 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( U_3566 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3565 != 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_3565)),U_3566))) ) ),
inference(variable_rename,[status(thm)],[f_1148_1]) ).
fof(f_1148_3,plain,
( ! [U_3570,U_3568] :
( 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_3568)),U_3570)))
| ( U_3570 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_3568 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_3569,U_3567] :
( U_3569 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3567 != 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_3567)),U_3569))) ) ),
inference(miniscope,[status(thm)],[f_1148_2]) ).
cnf(f_1148_4,plain,
( U_3569 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_3567 != 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_3567)),U_3569))) ),
inference(clausify,[status(thm)],[f_1148_3]) ).
cnf(f_1148_5,plain,
( U_3568 = 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_3568)),U_3570))) ),
inference(clausify,[status(thm)],[f_1148_3]) ).
cnf(f_1148_6,plain,
( U_3570 != 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)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_3568)),U_3570))) ),
inference(clausify,[status(thm)],[f_1148_3]) ).
fof(f_1149_1,plain,
! [V_y_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
| ~ class_Rings_Olinordered__idom(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__special_I1_J]) ).
fof(f_1149_2,plain,
! [U_3572,U_3571] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3571),c_Groups_Ozero__class_Ozero(U_3571)),hAPP(c_Int_Onumber__class_Onumber__of(U_3571),U_3572)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3572)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3572))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3571),c_Groups_Ozero__class_Ozero(U_3571)),hAPP(c_Int_Onumber__class_Onumber__of(U_3571),U_3572))) ) )
| ~ class_Rings_Olinordered__idom(U_3571)
| ~ class_Int_Onumber__ring(U_3571) ),
inference(variable_rename,[status(thm)],[f_1149_1]) ).
cnf(f_1149_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3572))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3571),c_Groups_Ozero__class_Ozero(U_3571)),hAPP(c_Int_Onumber__class_Onumber__of(U_3571),U_3572)))
| ~ class_Rings_Olinordered__idom(U_3571)
| ~ class_Int_Onumber__ring(U_3571) ),
inference(clausify,[status(thm)],[f_1149_2]) ).
cnf(f_1149_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3571),c_Groups_Ozero__class_Ozero(U_3571)),hAPP(c_Int_Onumber__class_Onumber__of(U_3571),U_3572)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3572))
| ~ class_Rings_Olinordered__idom(U_3571)
| ~ class_Int_Onumber__ring(U_3571) ),
inference(clausify,[status(thm)],[f_1149_2]) ).
fof(f_1150_1,plain,
! [V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
| ~ class_Rings_Olinordered__idom(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__special_I3_J]) ).
fof(f_1150_2,plain,
! [U_3574,U_3573] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3573),hAPP(c_Int_Onumber__class_Onumber__of(U_3573),U_3574)),c_Groups_Ozero__class_Ozero(U_3573)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3574),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3574),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3573),hAPP(c_Int_Onumber__class_Onumber__of(U_3573),U_3574)),c_Groups_Ozero__class_Ozero(U_3573))) ) )
| ~ class_Rings_Olinordered__idom(U_3573)
| ~ class_Int_Onumber__ring(U_3573) ),
inference(variable_rename,[status(thm)],[f_1150_1]) ).
cnf(f_1150_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3574),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3573),hAPP(c_Int_Onumber__class_Onumber__of(U_3573),U_3574)),c_Groups_Ozero__class_Ozero(U_3573)))
| ~ class_Rings_Olinordered__idom(U_3573)
| ~ class_Int_Onumber__ring(U_3573) ),
inference(clausify,[status(thm)],[f_1150_2]) ).
cnf(f_1150_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3573),hAPP(c_Int_Onumber__class_Onumber__of(U_3573),U_3574)),c_Groups_Ozero__class_Ozero(U_3573)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3574),c_Int_OPls))
| ~ class_Rings_Olinordered__idom(U_3573)
| ~ class_Int_Onumber__ring(U_3573) ),
inference(clausify,[status(thm)],[f_1150_2]) ).
fof(f_1151_1,plain,
! [V_y_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
| ~ class_Rings_Olinordered__idom(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__special_I1_J]) ).
fof(f_1151_2,plain,
! [U_3576,U_3575] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3575),c_Groups_Ozero__class_Ozero(U_3575)),hAPP(c_Int_Onumber__class_Onumber__of(U_3575),U_3576)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3576)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3576))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3575),c_Groups_Ozero__class_Ozero(U_3575)),hAPP(c_Int_Onumber__class_Onumber__of(U_3575),U_3576))) ) )
| ~ class_Rings_Olinordered__idom(U_3575)
| ~ class_Int_Onumber__ring(U_3575) ),
inference(variable_rename,[status(thm)],[f_1151_1]) ).
cnf(f_1151_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3576))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3575),c_Groups_Ozero__class_Ozero(U_3575)),hAPP(c_Int_Onumber__class_Onumber__of(U_3575),U_3576)))
| ~ class_Rings_Olinordered__idom(U_3575)
| ~ class_Int_Onumber__ring(U_3575) ),
inference(clausify,[status(thm)],[f_1151_2]) ).
cnf(f_1151_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3575),c_Groups_Ozero__class_Ozero(U_3575)),hAPP(c_Int_Onumber__class_Onumber__of(U_3575),U_3576)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3576))
| ~ class_Rings_Olinordered__idom(U_3575)
| ~ class_Int_Onumber__ring(U_3575) ),
inference(clausify,[status(thm)],[f_1151_2]) ).
fof(f_1152_1,plain,
! [V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
| ~ class_Rings_Olinordered__idom(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__special_I3_J]) ).
fof(f_1152_2,plain,
! [U_3578,U_3577] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3577),hAPP(c_Int_Onumber__class_Onumber__of(U_3577),U_3578)),c_Groups_Ozero__class_Ozero(U_3577)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3578),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3578),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3577),hAPP(c_Int_Onumber__class_Onumber__of(U_3577),U_3578)),c_Groups_Ozero__class_Ozero(U_3577))) ) )
| ~ class_Rings_Olinordered__idom(U_3577)
| ~ class_Int_Onumber__ring(U_3577) ),
inference(variable_rename,[status(thm)],[f_1152_1]) ).
cnf(f_1152_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3578),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3577),hAPP(c_Int_Onumber__class_Onumber__of(U_3577),U_3578)),c_Groups_Ozero__class_Ozero(U_3577)))
| ~ class_Rings_Olinordered__idom(U_3577)
| ~ class_Int_Onumber__ring(U_3577) ),
inference(clausify,[status(thm)],[f_1152_2]) ).
cnf(f_1152_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3577),hAPP(c_Int_Onumber__class_Onumber__of(U_3577),U_3578)),c_Groups_Ozero__class_Ozero(U_3577)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3578),c_Int_OPls))
| ~ class_Rings_Olinordered__idom(U_3577)
| ~ class_Int_Onumber__ring(U_3577) ),
inference(clausify,[status(thm)],[f_1152_2]) ).
fof(f_1153_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_1153_2,plain,
! [U_3579] :
( ( 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_3579)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3579)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3579))
| ~ 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_3579))) ) ),
inference(variable_rename,[status(thm)],[f_1153_1]) ).
fof(f_1153_3,plain,
( ! [U_3581] :
( 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_3581)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3581)) )
& ! [U_3580] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3580))
| ~ 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_3580))) ) ),
inference(miniscope,[status(thm)],[f_1153_2]) ).
cnf(f_1153_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3580))
| ~ 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_3580))) ),
inference(clausify,[status(thm)],[f_1153_3]) ).
cnf(f_1153_5,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_3581)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3581)) ),
inference(clausify,[status(thm)],[f_1153_3]) ).
fof(f_1154_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_1154_2,plain,
! [U_3583,U_3582] :
( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3582)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3583)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3582),U_3583))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3583),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3582)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3583)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3582)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3583),c_Int_OPls)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3582),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3582)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3583)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3583)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3582),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1154_1]) ).
fof(f_1154_3,plain,
( ! [U_3587,U_3585] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3585)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3587)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3585),U_3587))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3587),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3585)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3587)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3585)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3587),c_Int_OPls)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3585),c_Int_OPls)) )
& ! [U_3586,U_3584] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3584)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3586)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3586)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3584),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1154_2]) ).
cnf(f_1154_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3584)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3586)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3586)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3584),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1154_3]) ).
cnf(f_1154_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3585)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3587)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3585)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3587),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3585),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1154_3]) ).
cnf(f_1154_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3585)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3587)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3585),U_3587))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3587),c_Int_OPls))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3585),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1154_3]) ).
fof(f_1155_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_1155_2,plain,
! [U_3589,U_3588] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3588)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3589)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3588),U_3589))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3588),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3588)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3589)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3588),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1155_1]) ).
fof(f_1155_3,plain,
( ! [U_3593,U_3591] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3591)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3593)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3591),U_3593))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3591),c_Int_OPls)) )
& ! [U_3592,U_3590] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3590)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3592)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3590),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1155_2]) ).
cnf(f_1155_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3590)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3592)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3590),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1155_3]) ).
cnf(f_1155_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3591)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3593)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3591),U_3593))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3591),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1155_3]) ).
fof(f_1156_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_1156_2,plain,
! [U_3596,U_3595,U_3594] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3594)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3595)),U_3596)) = 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_3594),U_3595))),U_3596)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3594),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3594)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3595)),U_3596)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3594),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1156_1]) ).
fof(f_1156_3,plain,
( ! [U_3602,U_3600,U_3598] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3598)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3600)),U_3602)) = 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_3598),U_3600))),U_3602)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3598),c_Int_OPls)) )
& ! [U_3601,U_3599,U_3597] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3597)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3599)),U_3601)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3597),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1156_2]) ).
cnf(f_1156_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3597)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3599)),U_3601)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3597),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1156_3]) ).
cnf(f_1156_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3598)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3600)),U_3602)) = 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_3598),U_3600))),U_3602)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3598),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1156_3]) ).
fof(f_1157_1,plain,
! [V_x_2,T_b] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
| ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) )
& ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__special_I3_J]) ).
fof(f_1157_2,plain,
! [U_3604,U_3603] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_3603),U_3604) = c_Groups_Ozero__class_Ozero(U_3603)
| ~ c_Int_Oiszero(U_3603,hAPP(c_Int_Onumber__class_Onumber__of(U_3603),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3604),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) )
& ( c_Int_Oiszero(U_3603,hAPP(c_Int_Onumber__class_Onumber__of(U_3603),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3604),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_3603),U_3604) != c_Groups_Ozero__class_Ozero(U_3603) ) )
| ~ class_Int_Onumber__ring(U_3603) ),
inference(variable_rename,[status(thm)],[f_1157_1]) ).
cnf(f_1157_3,plain,
( c_Int_Oiszero(U_3603,hAPP(c_Int_Onumber__class_Onumber__of(U_3603),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3604),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_3603),U_3604) != c_Groups_Ozero__class_Ozero(U_3603)
| ~ class_Int_Onumber__ring(U_3603) ),
inference(clausify,[status(thm)],[f_1157_2]) ).
cnf(f_1157_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_3603),U_3604) = c_Groups_Ozero__class_Ozero(U_3603)
| ~ c_Int_Oiszero(U_3603,hAPP(c_Int_Onumber__class_Onumber__of(U_3603),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3604),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| ~ class_Int_Onumber__ring(U_3603) ),
inference(clausify,[status(thm)],[f_1157_2]) ).
fof(f_1158_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_1158_2,plain,
! [U_3605] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3605)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_3605))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3605),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3605)),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_3605),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1158_1]) ).
fof(f_1158_3,plain,
( ! [U_3607] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3607)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_3607))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3607),c_Int_OPls)) )
& ! [U_3606] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3606)),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_3606),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1158_2]) ).
cnf(f_1158_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3606)),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_3606),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1158_3]) ).
cnf(f_1158_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3607)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_3607))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3607),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1158_3]) ).
fof(f_1159_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_1159_2,plain,
! [U_3609,U_3608] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3609)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3608)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3609),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_3608)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3608)) ),
inference(variable_rename,[status(thm)],[f_1159_1]) ).
cnf(f_1159_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3609)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3608)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3609),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_3608)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3608)) ),
inference(clausify,[status(thm)],[f_1159_2]) ).
fof(f_1160_1,plain,
! [V_y_2,T_b] :
( ( ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
| ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2)))) )
& ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_y_2))))
| c_Groups_Oone__class_Oone(T_b) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2) ) )
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__special_I2_J]) ).
fof(f_1160_2,plain,
! [U_3611,U_3610] :
( ( ( c_Groups_Oone__class_Oone(U_3610) = hAPP(c_Int_Onumber__class_Onumber__of(U_3610),U_3611)
| ~ c_Int_Oiszero(U_3610,hAPP(c_Int_Onumber__class_Onumber__of(U_3610),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_3611)))) )
& ( c_Int_Oiszero(U_3610,hAPP(c_Int_Onumber__class_Onumber__of(U_3610),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_3611))))
| c_Groups_Oone__class_Oone(U_3610) != hAPP(c_Int_Onumber__class_Onumber__of(U_3610),U_3611) ) )
| ~ class_Int_Onumber__ring(U_3610) ),
inference(variable_rename,[status(thm)],[f_1160_1]) ).
cnf(f_1160_3,plain,
( c_Int_Oiszero(U_3610,hAPP(c_Int_Onumber__class_Onumber__of(U_3610),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_3611))))
| c_Groups_Oone__class_Oone(U_3610) != hAPP(c_Int_Onumber__class_Onumber__of(U_3610),U_3611)
| ~ class_Int_Onumber__ring(U_3610) ),
inference(clausify,[status(thm)],[f_1160_2]) ).
cnf(f_1160_4,plain,
( c_Groups_Oone__class_Oone(U_3610) = hAPP(c_Int_Onumber__class_Onumber__of(U_3610),U_3611)
| ~ c_Int_Oiszero(U_3610,hAPP(c_Int_Onumber__class_Onumber__of(U_3610),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_3611))))
| ~ class_Int_Onumber__ring(U_3610) ),
inference(clausify,[status(thm)],[f_1160_2]) ).
fof(f_1161_1,plain,
! [V_x_2,T_b] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
| ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) )
& ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) != c_Groups_Oone__class_Oone(T_b) ) )
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__special_I4_J]) ).
fof(f_1161_2,plain,
! [U_3613,U_3612] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_3612),U_3613) = c_Groups_Oone__class_Oone(U_3612)
| ~ c_Int_Oiszero(U_3612,hAPP(c_Int_Onumber__class_Onumber__of(U_3612),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3613),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) )
& ( c_Int_Oiszero(U_3612,hAPP(c_Int_Onumber__class_Onumber__of(U_3612),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3613),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_3612),U_3613) != c_Groups_Oone__class_Oone(U_3612) ) )
| ~ class_Int_Onumber__ring(U_3612) ),
inference(variable_rename,[status(thm)],[f_1161_1]) ).
cnf(f_1161_3,plain,
( c_Int_Oiszero(U_3612,hAPP(c_Int_Onumber__class_Onumber__of(U_3612),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3613),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| hAPP(c_Int_Onumber__class_Onumber__of(U_3612),U_3613) != c_Groups_Oone__class_Oone(U_3612)
| ~ class_Int_Onumber__ring(U_3612) ),
inference(clausify,[status(thm)],[f_1161_2]) ).
cnf(f_1161_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_3612),U_3613) = c_Groups_Oone__class_Oone(U_3612)
| ~ c_Int_Oiszero(U_3612,hAPP(c_Int_Onumber__class_Onumber__of(U_3612),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3613),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(U_3612) ),
inference(clausify,[status(thm)],[f_1161_2]) ).
fof(f_1162_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_1162_2,plain,
! [U_3615,U_3614] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3614),c_Groups_Oone__class_Oone(U_3614)),hAPP(c_Int_Onumber__class_Onumber__of(U_3614),U_3615)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3614),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_3615)))
| ~ class_Int_Onumber__ring(U_3614) ),
inference(variable_rename,[status(thm)],[f_1162_1]) ).
cnf(f_1162_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3614),c_Groups_Oone__class_Oone(U_3614)),hAPP(c_Int_Onumber__class_Onumber__of(U_3614),U_3615)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3614),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_3615)))
| ~ class_Int_Onumber__ring(U_3614) ),
inference(clausify,[status(thm)],[f_1162_2]) ).
fof(f_1163_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_1163_2,plain,
! [U_3617,U_3616] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3616),hAPP(c_Int_Onumber__class_Onumber__of(U_3616),U_3617)),c_Groups_Oone__class_Oone(U_3616)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3616),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3617),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
| ~ class_Int_Onumber__ring(U_3616) ),
inference(variable_rename,[status(thm)],[f_1163_1]) ).
cnf(f_1163_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3616),hAPP(c_Int_Onumber__class_Onumber__of(U_3616),U_3617)),c_Groups_Oone__class_Oone(U_3616)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3616),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3617),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
| ~ class_Int_Onumber__ring(U_3616) ),
inference(clausify,[status(thm)],[f_1163_2]) ).
fof(f_1164_1,plain,
! [V_k_2,V_f_2,V_na_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_na_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_na_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_na_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_int__val__lemma]) ).
fof(f_1164_2,plain,
! [U_3622,U_3621,U_3620] :
( ? [U_3619] :
( hAPP(U_3621,U_3619) = U_3622
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3619),U_3620)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3622),hAPP(U_3621,U_3620)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_3621,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_3622))
| ? [U_3618] :
( ~ 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_3621,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3618),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_3621,U_3618)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3618),U_3620)) ) ),
inference(variable_rename,[status(thm)],[f_1164_1]) ).
fof(f_1164_3,plain,
! [U_3622,U_3621,U_3620] :
( ? [U_3619] :
( hAPP(U_3621,U_3619) = U_3622
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3619),U_3620)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3622),hAPP(U_3621,U_3620)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_3621,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_3622))
| ( ~ 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_3621,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK55(U_3622,U_3621,U_3620)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_3621,sK55(U_3622,U_3621,U_3620))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK55(U_3622,U_3621,U_3620)),U_3620)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_3618,sK55(U_3622,U_3621,U_3620))],[f_1164_2]) ).
fof(f_1164_4,plain,
! [U_3622,U_3621,U_3620] :
( ( hAPP(U_3621,sK56(U_3622,U_3621,U_3620)) = U_3622
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK56(U_3622,U_3621,U_3620)),U_3620)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3622),hAPP(U_3621,U_3620)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_3621,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_3622))
| ( ~ 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_3621,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK55(U_3622,U_3621,U_3620)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_3621,sK55(U_3622,U_3621,U_3620))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK55(U_3622,U_3621,U_3620)),U_3620)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_3619,sK56(U_3622,U_3621,U_3620))],[f_1164_3]) ).
cnf(f_1164_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK56(U_3622,U_3621,U_3620)),U_3620))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3622),hAPP(U_3621,U_3620)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_3621,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_3622))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK55(U_3622,U_3621,U_3620)),U_3620)) ),
inference(clausify,[status(thm)],[f_1164_4]) ).
cnf(f_1164_6,plain,
( hAPP(U_3621,sK56(U_3622,U_3621,U_3620)) = U_3622
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3622),hAPP(U_3621,U_3620)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_3621,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_3622))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK55(U_3622,U_3621,U_3620)),U_3620)) ),
inference(clausify,[status(thm)],[f_1164_4]) ).
cnf(f_1164_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK56(U_3622,U_3621,U_3620)),U_3620))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3622),hAPP(U_3621,U_3620)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_3621,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_3622))
| ~ 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_3621,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK55(U_3622,U_3621,U_3620)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_3621,sK55(U_3622,U_3621,U_3620))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1164_4]) ).
cnf(f_1164_8,plain,
( hAPP(U_3621,sK56(U_3622,U_3621,U_3620)) = U_3622
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3622),hAPP(U_3621,U_3620)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_3621,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_3622))
| ~ 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_3621,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK55(U_3622,U_3621,U_3620)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_3621,sK55(U_3622,U_3621,U_3620))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1164_4]) ).
fof(f_1165_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_1165_2,plain,
! [U_3623] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_3623)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3623))),
inference(variable_rename,[status(thm)],[f_1165_1]) ).
cnf(f_1165_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_3623)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3623))),
inference(clausify,[status(thm)],[f_1165_2]) ).
fof(f_1166_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_1166_2,plain,
! [U_3625,U_3624] :
( ( c_Int_OBit1(U_3624) = c_Int_OBit1(U_3625)
| U_3624 != U_3625 )
& ( U_3624 = U_3625
| c_Int_OBit1(U_3624) != c_Int_OBit1(U_3625) ) ),
inference(variable_rename,[status(thm)],[f_1166_1]) ).
fof(f_1166_3,plain,
( ! [U_3629,U_3627] :
( c_Int_OBit1(U_3627) = c_Int_OBit1(U_3629)
| U_3627 != U_3629 )
& ! [U_3628,U_3626] :
( U_3626 = U_3628
| c_Int_OBit1(U_3626) != c_Int_OBit1(U_3628) ) ),
inference(miniscope,[status(thm)],[f_1166_2]) ).
cnf(f_1166_4,plain,
( U_3626 = U_3628
| c_Int_OBit1(U_3626) != c_Int_OBit1(U_3628) ),
inference(clausify,[status(thm)],[f_1166_3]) ).
cnf(f_1166_5,plain,
( c_Int_OBit1(U_3627) = c_Int_OBit1(U_3629)
| U_3627 != U_3629 ),
inference(clausify,[status(thm)],[f_1166_3]) ).
fof(f_1167_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_1167_2,plain,
! [U_3631,U_3630] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3630)),c_Int_OBit1(U_3631)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3630),U_3631)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3630),U_3631))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3630)),c_Int_OBit1(U_3631))) ) ),
inference(variable_rename,[status(thm)],[f_1167_1]) ).
fof(f_1167_3,plain,
( ! [U_3635,U_3633] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3633)),c_Int_OBit1(U_3635)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3633),U_3635)) )
& ! [U_3634,U_3632] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3632),U_3634))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3632)),c_Int_OBit1(U_3634))) ) ),
inference(miniscope,[status(thm)],[f_1167_2]) ).
cnf(f_1167_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3632),U_3634))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3632)),c_Int_OBit1(U_3634))) ),
inference(clausify,[status(thm)],[f_1167_3]) ).
cnf(f_1167_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3633)),c_Int_OBit1(U_3635)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3633),U_3635)) ),
inference(clausify,[status(thm)],[f_1167_3]) ).
fof(f_1168_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_1168_2,plain,
! [U_3637,U_3636] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3636)),c_Int_OBit1(U_3637)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3636),U_3637)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3636),U_3637))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3636)),c_Int_OBit1(U_3637))) ) ),
inference(variable_rename,[status(thm)],[f_1168_1]) ).
fof(f_1168_3,plain,
( ! [U_3641,U_3639] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3639)),c_Int_OBit1(U_3641)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3639),U_3641)) )
& ! [U_3640,U_3638] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3638),U_3640))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3638)),c_Int_OBit1(U_3640))) ) ),
inference(miniscope,[status(thm)],[f_1168_2]) ).
cnf(f_1168_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3638),U_3640))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3638)),c_Int_OBit1(U_3640))) ),
inference(clausify,[status(thm)],[f_1168_3]) ).
cnf(f_1168_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3639)),c_Int_OBit1(U_3641)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3639),U_3641)) ),
inference(clausify,[status(thm)],[f_1168_3]) ).
fof(f_1169_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_1169_2,plain,
! [U_3643,U_3642] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3642)),c_Int_OBit1(U_3643)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3642),U_3643)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3642),U_3643))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3642)),c_Int_OBit1(U_3643))) ) ),
inference(variable_rename,[status(thm)],[f_1169_1]) ).
fof(f_1169_3,plain,
( ! [U_3647,U_3645] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3645)),c_Int_OBit1(U_3647)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3645),U_3647)) )
& ! [U_3646,U_3644] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3644),U_3646))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3644)),c_Int_OBit1(U_3646))) ) ),
inference(miniscope,[status(thm)],[f_1169_2]) ).
cnf(f_1169_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3644),U_3646))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3644)),c_Int_OBit1(U_3646))) ),
inference(clausify,[status(thm)],[f_1169_3]) ).
cnf(f_1169_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3645)),c_Int_OBit1(U_3647)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3645),U_3647)) ),
inference(clausify,[status(thm)],[f_1169_3]) ).
fof(f_1170_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_1170_2,plain,
! [U_3649,U_3648] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3648)),c_Int_OBit1(U_3649)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3648),U_3649)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3648),U_3649))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3648)),c_Int_OBit1(U_3649))) ) ),
inference(variable_rename,[status(thm)],[f_1170_1]) ).
fof(f_1170_3,plain,
( ! [U_3653,U_3651] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3651)),c_Int_OBit1(U_3653)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3651),U_3653)) )
& ! [U_3652,U_3650] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3650),U_3652))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3650)),c_Int_OBit1(U_3652))) ) ),
inference(miniscope,[status(thm)],[f_1170_2]) ).
cnf(f_1170_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3650),U_3652))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3650)),c_Int_OBit1(U_3652))) ),
inference(clausify,[status(thm)],[f_1170_3]) ).
cnf(f_1170_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3651)),c_Int_OBit1(U_3653)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3651),U_3653)) ),
inference(clausify,[status(thm)],[f_1170_3]) ).
fof(f_1171_1,plain,
! [V_l] : c_Int_OPls != c_Int_OBit1(V_l),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I39_J]) ).
fof(f_1171_2,plain,
! [U_3654] : c_Int_OPls != c_Int_OBit1(U_3654),
inference(variable_rename,[status(thm)],[f_1171_1]) ).
cnf(f_1171_3,plain,
c_Int_OPls != c_Int_OBit1(U_3654),
inference(clausify,[status(thm)],[f_1171_2]) ).
fof(f_1172_1,plain,
! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I46_J]) ).
fof(f_1172_2,plain,
! [U_3655] : c_Int_OBit1(U_3655) != c_Int_OPls,
inference(variable_rename,[status(thm)],[f_1172_1]) ).
cnf(f_1172_3,plain,
c_Int_OBit1(U_3655) != c_Int_OPls,
inference(clausify,[status(thm)],[f_1172_2]) ).
fof(f_1173_1,plain,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
inference(fof_nnf,[status(thm)],[fact_Bit1__Min]) ).
cnf(f_1173_2,plain,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
inference(clausify,[status(thm)],[f_1173_1]) ).
fof(f_1174_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_1174_2,plain,
! [U_3656] :
( ( c_Int_OMin = c_Int_OBit1(U_3656)
| c_Int_OMin != U_3656 )
& ( c_Int_OMin = U_3656
| c_Int_OMin != c_Int_OBit1(U_3656) ) ),
inference(variable_rename,[status(thm)],[f_1174_1]) ).
fof(f_1174_3,plain,
( ! [U_3658] :
( c_Int_OMin = c_Int_OBit1(U_3658)
| c_Int_OMin != U_3658 )
& ! [U_3657] :
( c_Int_OMin = U_3657
| c_Int_OMin != c_Int_OBit1(U_3657) ) ),
inference(miniscope,[status(thm)],[f_1174_2]) ).
cnf(f_1174_4,plain,
( c_Int_OMin = U_3657
| c_Int_OMin != c_Int_OBit1(U_3657) ),
inference(clausify,[status(thm)],[f_1174_3]) ).
cnf(f_1174_5,plain,
( c_Int_OMin = c_Int_OBit1(U_3658)
| c_Int_OMin != U_3658 ),
inference(clausify,[status(thm)],[f_1174_3]) ).
fof(f_1175_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_1175_2,plain,
! [U_3659] :
( ( c_Int_OBit1(U_3659) = c_Int_OMin
| U_3659 != c_Int_OMin )
& ( U_3659 = c_Int_OMin
| c_Int_OBit1(U_3659) != c_Int_OMin ) ),
inference(variable_rename,[status(thm)],[f_1175_1]) ).
fof(f_1175_3,plain,
( ! [U_3661] :
( c_Int_OBit1(U_3661) = c_Int_OMin
| U_3661 != c_Int_OMin )
& ! [U_3660] :
( U_3660 = c_Int_OMin
| c_Int_OBit1(U_3660) != c_Int_OMin ) ),
inference(miniscope,[status(thm)],[f_1175_2]) ).
cnf(f_1175_4,plain,
( U_3660 = c_Int_OMin
| c_Int_OBit1(U_3660) != c_Int_OMin ),
inference(clausify,[status(thm)],[f_1175_3]) ).
cnf(f_1175_5,plain,
( c_Int_OBit1(U_3661) = c_Int_OMin
| U_3661 != c_Int_OMin ),
inference(clausify,[status(thm)],[f_1175_3]) ).
fof(f_1176_1,plain,
! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
inference(fof_nnf,[status(thm)],[fact_succ__pred]) ).
fof(f_1176_2,plain,
! [U_3662] : c_Int_Osucc(c_Int_Opred(U_3662)) = U_3662,
inference(variable_rename,[status(thm)],[f_1176_1]) ).
cnf(f_1176_3,plain,
c_Int_Osucc(c_Int_Opred(U_3662)) = U_3662,
inference(clausify,[status(thm)],[f_1176_2]) ).
fof(f_1177_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_1177_2,plain,
! [U_3663] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3663)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3663),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3663),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3663)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_1177_1]) ).
fof(f_1177_3,plain,
( ! [U_3665] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3665)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3665),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_3664] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3664),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3664)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_1177_2]) ).
cnf(f_1177_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3664),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3664)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1177_3]) ).
cnf(f_1177_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3665)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3665),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1177_3]) ).
fof(f_1178_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_1178_2,plain,
! [U_3666] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_3666)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3666)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3666))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_3666))) ) ),
inference(variable_rename,[status(thm)],[f_1178_1]) ).
fof(f_1178_3,plain,
( ! [U_3668] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_3668)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3668)) )
& ! [U_3667] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3667))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_3667))) ) ),
inference(miniscope,[status(thm)],[f_1178_2]) ).
cnf(f_1178_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3667))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_3667))) ),
inference(clausify,[status(thm)],[f_1178_3]) ).
cnf(f_1178_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_3668)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3668)) ),
inference(clausify,[status(thm)],[f_1178_3]) ).
fof(f_1179_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_1179_2,plain,
! [U_3669] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3669)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3669),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3669),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3669)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1179_1]) ).
fof(f_1179_3,plain,
( ! [U_3671] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3671)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3671),c_Int_OPls)) )
& ! [U_3670] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3670),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3670)),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1179_2]) ).
cnf(f_1179_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3670),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3670)),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1179_3]) ).
cnf(f_1179_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3671)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3671),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1179_3]) ).
fof(f_1180_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_1180_2,plain,
! [U_3672] : c_Int_OBit1(U_3672) = 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_3672)),U_3672),
inference(variable_rename,[status(thm)],[f_1180_1]) ).
cnf(f_1180_3,plain,
c_Int_OBit1(U_3672) = 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_3672)),U_3672),
inference(clausify,[status(thm)],[f_1180_2]) ).
fof(f_1181_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_1181_2,plain,
! [U_3673] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3673)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3673),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3673),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3673)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[f_1181_1]) ).
fof(f_1181_3,plain,
( ! [U_3675] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3675)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3675),c_Int_OMin)) )
& ! [U_3674] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3674),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3674)),c_Int_OMin)) ) ),
inference(miniscope,[status(thm)],[f_1181_2]) ).
cnf(f_1181_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3674),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3674)),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_1181_3]) ).
cnf(f_1181_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3675)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3675),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_1181_3]) ).
fof(f_1182_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_1182_2,plain,
! [U_3676] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_3676)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_3676)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_3676))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_3676))) ) ),
inference(variable_rename,[status(thm)],[f_1182_1]) ).
fof(f_1182_3,plain,
( ! [U_3678] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_3678)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_3678)) )
& ! [U_3677] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_3677))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_3677))) ) ),
inference(miniscope,[status(thm)],[f_1182_2]) ).
cnf(f_1182_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_3677))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_3677))) ),
inference(clausify,[status(thm)],[f_1182_3]) ).
cnf(f_1182_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_3678)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_3678)) ),
inference(clausify,[status(thm)],[f_1182_3]) ).
fof(f_1183_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_1183_2,plain,
! [U_3679] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_3679)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_3679)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_3679))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_3679))) ) ),
inference(variable_rename,[status(thm)],[f_1183_1]) ).
fof(f_1183_3,plain,
( ! [U_3681] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_3681)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_3681)) )
& ! [U_3680] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_3680))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_3680))) ) ),
inference(miniscope,[status(thm)],[f_1183_2]) ).
cnf(f_1183_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_3680))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_3680))) ),
inference(clausify,[status(thm)],[f_1183_3]) ).
cnf(f_1183_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_3681)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_3681)) ),
inference(clausify,[status(thm)],[f_1183_3]) ).
fof(f_1184_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_1184_2,plain,
! [U_3682] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3682)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3682),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3682),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3682)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[f_1184_1]) ).
fof(f_1184_3,plain,
( ! [U_3684] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3684)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3684),c_Int_OMin)) )
& ! [U_3683] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3683),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3683)),c_Int_OMin)) ) ),
inference(miniscope,[status(thm)],[f_1184_2]) ).
cnf(f_1184_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3683),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3683)),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_1184_3]) ).
cnf(f_1184_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3684)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3684),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_1184_3]) ).
fof(f_1185_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_1185_2,plain,
! [U_3685] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_3685))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3685))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3685)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_3685)))) ) ),
inference(variable_rename,[status(thm)],[f_1185_1]) ).
fof(f_1185_3,plain,
( ! [U_3687] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_3687))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3687))) )
& ! [U_3686] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3686)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_3686)))) ) ),
inference(miniscope,[status(thm)],[f_1185_2]) ).
cnf(f_1185_4,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3686)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_3686)))) ),
inference(clausify,[status(thm)],[f_1185_3]) ).
cnf(f_1185_5,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_3687))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3687))) ),
inference(clausify,[status(thm)],[f_1185_3]) ).
fof(f_1186_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_1186_2,plain,
! [U_3689,U_3688] :
( ~ c_Int_Oiszero(U_3688,hAPP(c_Int_Onumber__class_Onumber__of(U_3688),c_Int_OBit1(U_3689)))
| ~ class_Int_Oring__char__0(U_3688)
| ~ class_Int_Onumber__ring(U_3688) ),
inference(variable_rename,[status(thm)],[f_1186_1]) ).
cnf(f_1186_3,plain,
( ~ c_Int_Oiszero(U_3688,hAPP(c_Int_Onumber__class_Onumber__of(U_3688),c_Int_OBit1(U_3689)))
| ~ class_Int_Oring__char__0(U_3688)
| ~ class_Int_Onumber__ring(U_3688) ),
inference(clausify,[status(thm)],[f_1186_2]) ).
fof(f_1187_1,plain,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
inference(fof_nnf,[status(thm)],[fact_succ__Pls]) ).
cnf(f_1187_2,plain,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
inference(clausify,[status(thm)],[f_1187_1]) ).
fof(f_1188_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_1188_2,plain,
! [U_3691,U_3690] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3690),U_3691))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_3690)),U_3691)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_3690)),U_3691))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3690),U_3691)) ) ),
inference(variable_rename,[status(thm)],[f_1188_1]) ).
fof(f_1188_3,plain,
( ! [U_3695,U_3693] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3693),U_3695))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_3693)),U_3695)) )
& ! [U_3694,U_3692] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_3692)),U_3694))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3692),U_3694)) ) ),
inference(miniscope,[status(thm)],[f_1188_2]) ).
cnf(f_1188_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_3692)),U_3694))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3692),U_3694)) ),
inference(clausify,[status(thm)],[f_1188_3]) ).
cnf(f_1188_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3693),U_3695))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_3693)),U_3695)) ),
inference(clausify,[status(thm)],[f_1188_3]) ).
fof(f_1189_1,plain,
c_Int_Opred(c_Int_OPls) = c_Int_OMin,
inference(fof_nnf,[status(thm)],[fact_pred__Pls]) ).
cnf(f_1189_2,plain,
c_Int_Opred(c_Int_OPls) = c_Int_OMin,
inference(clausify,[status(thm)],[f_1189_1]) ).
fof(f_1190_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_1190_2,plain,
! [U_3696] : c_Int_Opred(U_3696) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3696),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[f_1190_1]) ).
cnf(f_1190_3,plain,
c_Int_Opred(U_3696) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3696),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_1190_2]) ).
fof(f_1191_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_1191_2,plain,
! [U_3697] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3697),c_Int_OMin) = c_Int_Opred(U_3697),
inference(variable_rename,[status(thm)],[f_1191_1]) ).
cnf(f_1191_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3697),c_Int_OMin) = c_Int_Opred(U_3697),
inference(clausify,[status(thm)],[f_1191_2]) ).
fof(f_1192_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_1192_2,plain,
! [U_3698] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_3698) = c_Int_Opred(U_3698),
inference(variable_rename,[status(thm)],[f_1192_1]) ).
cnf(f_1192_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_3698) = c_Int_Opred(U_3698),
inference(clausify,[status(thm)],[f_1192_2]) ).
fof(f_1193_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_1193_2,plain,
! [U_3700,U_3699] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_3699),c_Int_OBit1(U_3700)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3699),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3699),c_Groups_Oone__class_Oone(U_3699)),hAPP(c_Int_Onumber__class_Onumber__of(U_3699),U_3700))),hAPP(c_Int_Onumber__class_Onumber__of(U_3699),U_3700))
| ~ class_Int_Onumber__ring(U_3699) ),
inference(variable_rename,[status(thm)],[f_1193_1]) ).
cnf(f_1193_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_3699),c_Int_OBit1(U_3700)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3699),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3699),c_Groups_Oone__class_Oone(U_3699)),hAPP(c_Int_Onumber__class_Onumber__of(U_3699),U_3700))),hAPP(c_Int_Onumber__class_Onumber__of(U_3699),U_3700))
| ~ class_Int_Onumber__ring(U_3699) ),
inference(clausify,[status(thm)],[f_1193_2]) ).
fof(f_1194_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_1194_2,plain,
! [U_3702,U_3701] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3701),U_3702),hAPP(c_Int_Onumber__class_Onumber__of(U_3701),c_Int_OBit1(c_Int_OPls))) = U_3702
| ~ class_Int_Onumber__ring(U_3701) ),
inference(variable_rename,[status(thm)],[f_1194_1]) ).
cnf(f_1194_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3701),U_3702),hAPP(c_Int_Onumber__class_Onumber__of(U_3701),c_Int_OBit1(c_Int_OPls))) = U_3702
| ~ class_Int_Onumber__ring(U_3701) ),
inference(clausify,[status(thm)],[f_1194_2]) ).
fof(f_1195_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_1195_2,plain,
! [U_3704,U_3703] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3703),hAPP(c_Int_Onumber__class_Onumber__of(U_3703),c_Int_OBit1(c_Int_OPls))),U_3704) = U_3704
| ~ class_Int_Onumber__ring(U_3703) ),
inference(variable_rename,[status(thm)],[f_1195_1]) ).
cnf(f_1195_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3703),hAPP(c_Int_Onumber__class_Onumber__of(U_3703),c_Int_OBit1(c_Int_OPls))),U_3704) = U_3704
| ~ class_Int_Onumber__ring(U_3703) ),
inference(clausify,[status(thm)],[f_1195_2]) ).
fof(f_1196_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_1196_2,plain,
! [U_3705] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_3705),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_3705)
| ~ class_Int_Onumber__ring(U_3705) ),
inference(variable_rename,[status(thm)],[f_1196_1]) ).
cnf(f_1196_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_3705),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_3705)
| ~ class_Int_Onumber__ring(U_3705) ),
inference(clausify,[status(thm)],[f_1196_2]) ).
fof(f_1197_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_1197_2,plain,
! [U_3706] :
( c_Groups_Oone__class_Oone(U_3706) = hAPP(c_Int_Onumber__class_Onumber__of(U_3706),c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(U_3706) ),
inference(variable_rename,[status(thm)],[f_1197_1]) ).
cnf(f_1197_3,plain,
( c_Groups_Oone__class_Oone(U_3706) = hAPP(c_Int_Onumber__class_Onumber__of(U_3706),c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(U_3706) ),
inference(clausify,[status(thm)],[f_1197_2]) ).
fof(f_1198_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_1198_2,plain,
! [U_3707] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3707)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3707),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3707),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3707)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1198_1]) ).
fof(f_1198_3,plain,
( ! [U_3709] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3709)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3709),c_Int_OPls)) )
& ! [U_3708] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3708),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3708)),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1198_2]) ).
cnf(f_1198_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3708),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3708)),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1198_3]) ).
cnf(f_1198_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3709)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3709),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1198_3]) ).
fof(f_1199_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_1199_2,plain,
! [U_3710] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_3710)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3710)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3710))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_3710))) ) ),
inference(variable_rename,[status(thm)],[f_1199_1]) ).
fof(f_1199_3,plain,
( ! [U_3712] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_3712)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3712)) )
& ! [U_3711] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3711))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_3711))) ) ),
inference(miniscope,[status(thm)],[f_1199_2]) ).
cnf(f_1199_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3711))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_3711))) ),
inference(clausify,[status(thm)],[f_1199_3]) ).
cnf(f_1199_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_3712)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3712)) ),
inference(clausify,[status(thm)],[f_1199_3]) ).
fof(f_1200_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]) ).
cnf(f_1200_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(clausify,[status(thm)],[f_1200_1]) ).
fof(f_1201_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]) ).
cnf(f_1201_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(clausify,[status(thm)],[f_1201_1]) ).
fof(f_1202_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]) ).
cnf(f_1202_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(clausify,[status(thm)],[f_1202_1]) ).
fof(f_1203_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_1203_2,plain,
! [U_3713] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_3713)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_3713)),
inference(variable_rename,[status(thm)],[f_1203_1]) ).
cnf(f_1203_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_3713)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_3713)),
inference(clausify,[status(thm)],[f_1203_2]) ).
fof(f_1204_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]) ).
cnf(f_1204_2,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
inference(clausify,[status(thm)],[f_1204_1]) ).
fof(f_1205_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_1205_2,plain,
! [U_3714] :
( ~ c_Int_Oiszero(U_3714,hAPP(c_Int_Onumber__class_Onumber__of(U_3714),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_3714) ),
inference(variable_rename,[status(thm)],[f_1205_1]) ).
cnf(f_1205_3,plain,
( ~ c_Int_Oiszero(U_3714,hAPP(c_Int_Onumber__class_Onumber__of(U_3714),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_3714) ),
inference(clausify,[status(thm)],[f_1205_2]) ).
fof(f_1206_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]) ).
cnf(f_1206_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(clausify,[status(thm)],[f_1206_1]) ).
fof(f_1207_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]) ).
cnf(f_1207_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(clausify,[status(thm)],[f_1207_1]) ).
fof(f_1208_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_1208_2,plain,
! [U_3716,U_3715] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3715),U_3716),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_3715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3715),U_3716),U_3716)),U_3716)
| ~ class_Groups_Omonoid__mult(U_3715) ),
inference(variable_rename,[status(thm)],[f_1208_1]) ).
cnf(f_1208_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3715),U_3716),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_3715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3715),U_3716),U_3716)),U_3716)
| ~ class_Groups_Omonoid__mult(U_3715) ),
inference(clausify,[status(thm)],[f_1208_2]) ).
fof(f_1209_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]) ).
cnf(f_1209_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(clausify,[status(thm)],[f_1209_1]) ).
fof(f_1210_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_1210_2,plain,
! [U_3717] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_3717))) = 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_3717),
inference(variable_rename,[status(thm)],[f_1210_1]) ).
cnf(f_1210_3,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_3717))) = 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_3717),
inference(clausify,[status(thm)],[f_1210_2]) ).
fof(f_1211_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]) ).
cnf(f_1211_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(clausify,[status(thm)],[f_1211_1]) ).
fof(f_1212_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]) ).
cnf(f_1212_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(clausify,[status(thm)],[f_1212_1]) ).
fof(f_1213_1,plain,
! [V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b))) ) )
| ~ class_Rings_Olinordered__idom(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__special_I4_J]) ).
fof(f_1213_2,plain,
! [U_3719,U_3718] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3718),hAPP(c_Int_Onumber__class_Onumber__of(U_3718),U_3719)),c_Groups_Oone__class_Oone(U_3718)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3719),c_Int_OBit1(c_Int_OPls))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3719),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3718),hAPP(c_Int_Onumber__class_Onumber__of(U_3718),U_3719)),c_Groups_Oone__class_Oone(U_3718))) ) )
| ~ class_Rings_Olinordered__idom(U_3718)
| ~ class_Int_Onumber__ring(U_3718) ),
inference(variable_rename,[status(thm)],[f_1213_1]) ).
cnf(f_1213_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3719),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3718),hAPP(c_Int_Onumber__class_Onumber__of(U_3718),U_3719)),c_Groups_Oone__class_Oone(U_3718)))
| ~ class_Rings_Olinordered__idom(U_3718)
| ~ class_Int_Onumber__ring(U_3718) ),
inference(clausify,[status(thm)],[f_1213_2]) ).
cnf(f_1213_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3718),hAPP(c_Int_Onumber__class_Onumber__of(U_3718),U_3719)),c_Groups_Oone__class_Oone(U_3718)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3719),c_Int_OBit1(c_Int_OPls)))
| ~ class_Rings_Olinordered__idom(U_3718)
| ~ class_Int_Onumber__ring(U_3718) ),
inference(clausify,[status(thm)],[f_1213_2]) ).
fof(f_1214_1,plain,
! [V_y_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
| ~ class_Rings_Olinordered__idom(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__special_I2_J]) ).
fof(f_1214_2,plain,
! [U_3721,U_3720] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3720),c_Groups_Oone__class_Oone(U_3720)),hAPP(c_Int_Onumber__class_Onumber__of(U_3720),U_3721)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_3721)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_3721))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3720),c_Groups_Oone__class_Oone(U_3720)),hAPP(c_Int_Onumber__class_Onumber__of(U_3720),U_3721))) ) )
| ~ class_Rings_Olinordered__idom(U_3720)
| ~ class_Int_Onumber__ring(U_3720) ),
inference(variable_rename,[status(thm)],[f_1214_1]) ).
cnf(f_1214_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_3721))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3720),c_Groups_Oone__class_Oone(U_3720)),hAPP(c_Int_Onumber__class_Onumber__of(U_3720),U_3721)))
| ~ class_Rings_Olinordered__idom(U_3720)
| ~ class_Int_Onumber__ring(U_3720) ),
inference(clausify,[status(thm)],[f_1214_2]) ).
cnf(f_1214_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3720),c_Groups_Oone__class_Oone(U_3720)),hAPP(c_Int_Onumber__class_Onumber__of(U_3720),U_3721)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_3721))
| ~ class_Rings_Olinordered__idom(U_3720)
| ~ class_Int_Onumber__ring(U_3720) ),
inference(clausify,[status(thm)],[f_1214_2]) ).
fof(f_1215_1,plain,
! [V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b))) ) )
| ~ class_Rings_Olinordered__idom(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__special_I4_J]) ).
fof(f_1215_2,plain,
! [U_3723,U_3722] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3722),hAPP(c_Int_Onumber__class_Onumber__of(U_3722),U_3723)),c_Groups_Oone__class_Oone(U_3722)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3723),c_Int_OBit1(c_Int_OPls))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3723),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3722),hAPP(c_Int_Onumber__class_Onumber__of(U_3722),U_3723)),c_Groups_Oone__class_Oone(U_3722))) ) )
| ~ class_Rings_Olinordered__idom(U_3722)
| ~ class_Int_Onumber__ring(U_3722) ),
inference(variable_rename,[status(thm)],[f_1215_1]) ).
cnf(f_1215_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3723),c_Int_OBit1(c_Int_OPls)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3722),hAPP(c_Int_Onumber__class_Onumber__of(U_3722),U_3723)),c_Groups_Oone__class_Oone(U_3722)))
| ~ class_Rings_Olinordered__idom(U_3722)
| ~ class_Int_Onumber__ring(U_3722) ),
inference(clausify,[status(thm)],[f_1215_2]) ).
cnf(f_1215_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3722),hAPP(c_Int_Onumber__class_Onumber__of(U_3722),U_3723)),c_Groups_Oone__class_Oone(U_3722)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3723),c_Int_OBit1(c_Int_OPls)))
| ~ class_Rings_Olinordered__idom(U_3722)
| ~ class_Int_Onumber__ring(U_3722) ),
inference(clausify,[status(thm)],[f_1215_2]) ).
fof(f_1216_1,plain,
! [V_y_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
| ~ class_Rings_Olinordered__idom(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__special_I2_J]) ).
fof(f_1216_2,plain,
! [U_3725,U_3724] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3724),c_Groups_Oone__class_Oone(U_3724)),hAPP(c_Int_Onumber__class_Onumber__of(U_3724),U_3725)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_3725)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_3725))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3724),c_Groups_Oone__class_Oone(U_3724)),hAPP(c_Int_Onumber__class_Onumber__of(U_3724),U_3725))) ) )
| ~ class_Rings_Olinordered__idom(U_3724)
| ~ class_Int_Onumber__ring(U_3724) ),
inference(variable_rename,[status(thm)],[f_1216_1]) ).
cnf(f_1216_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_3725))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3724),c_Groups_Oone__class_Oone(U_3724)),hAPP(c_Int_Onumber__class_Onumber__of(U_3724),U_3725)))
| ~ class_Rings_Olinordered__idom(U_3724)
| ~ class_Int_Onumber__ring(U_3724) ),
inference(clausify,[status(thm)],[f_1216_2]) ).
cnf(f_1216_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3724),c_Groups_Oone__class_Oone(U_3724)),hAPP(c_Int_Onumber__class_Onumber__of(U_3724),U_3725)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_3725))
| ~ class_Rings_Olinordered__idom(U_3724)
| ~ class_Int_Onumber__ring(U_3724) ),
inference(clausify,[status(thm)],[f_1216_2]) ).
fof(f_1217_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_1217_2,plain,
! [U_3727,U_3726] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3726),hAPP(c_Int_Onumber__class_Onumber__of(U_3726),U_3727)),c_Groups_Oone__class_Oone(U_3726)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3726),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3727),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_3726) ),
inference(variable_rename,[status(thm)],[f_1217_1]) ).
cnf(f_1217_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3726),hAPP(c_Int_Onumber__class_Onumber__of(U_3726),U_3727)),c_Groups_Oone__class_Oone(U_3726)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3726),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3727),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_3726) ),
inference(clausify,[status(thm)],[f_1217_2]) ).
fof(f_1218_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_1218_2,plain,
! [U_3729,U_3728] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3728),c_Groups_Oone__class_Oone(U_3728)),hAPP(c_Int_Onumber__class_Onumber__of(U_3728),U_3729)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3728),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_3729))
| ~ class_Int_Onumber__ring(U_3728) ),
inference(variable_rename,[status(thm)],[f_1218_1]) ).
cnf(f_1218_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3728),c_Groups_Oone__class_Oone(U_3728)),hAPP(c_Int_Onumber__class_Onumber__of(U_3728),U_3729)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3728),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_3729))
| ~ class_Int_Onumber__ring(U_3728) ),
inference(clausify,[status(thm)],[f_1218_2]) ).
fof(f_1219_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_1219_2,plain,
! [U_3731,U_3730] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3731)),U_3730) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3731),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3730),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_3730)) ),
inference(variable_rename,[status(thm)],[f_1219_1]) ).
cnf(f_1219_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3731)),U_3730) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3731),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3730),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_3730)) ),
inference(clausify,[status(thm)],[f_1219_2]) ).
fof(f_1220_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_1220_2,plain,
! [U_3733,U_3732] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_3732),c_Int_Opred(U_3733)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3732),hAPP(c_Groups_Ouminus__class_Ouminus(U_3732),c_Groups_Oone__class_Oone(U_3732))),hAPP(c_Int_Onumber__class_Onumber__of(U_3732),U_3733))
| ~ class_Int_Onumber__ring(U_3732) ),
inference(variable_rename,[status(thm)],[f_1220_1]) ).
cnf(f_1220_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_3732),c_Int_Opred(U_3733)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3732),hAPP(c_Groups_Ouminus__class_Ouminus(U_3732),c_Groups_Oone__class_Oone(U_3732))),hAPP(c_Int_Onumber__class_Onumber__of(U_3732),U_3733))
| ~ class_Int_Onumber__ring(U_3732) ),
inference(clausify,[status(thm)],[f_1220_2]) ).
fof(f_1221_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_1221_2,plain,
! [U_3735,U_3734] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3734,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_3735)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3734,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_3735)),
inference(variable_rename,[status(thm)],[f_1221_1]) ).
cnf(f_1221_3,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3734,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_3735)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3734,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_3735)),
inference(clausify,[status(thm)],[f_1221_2]) ).
fof(f_1222_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_1222_2,plain,
! [U_3737,U_3736] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_3736))),U_3737) = 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_3736),U_3737),
inference(variable_rename,[status(thm)],[f_1222_1]) ).
cnf(f_1222_3,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_3736))),U_3737) = 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_3736),U_3737),
inference(clausify,[status(thm)],[f_1222_2]) ).
fof(f_1223_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_1223_2,plain,
! [U_3739,U_3738] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_3738))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3739)) = 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_3738),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3739)),
inference(variable_rename,[status(thm)],[f_1223_1]) ).
cnf(f_1223_3,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_3738))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3739)) = 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_3738),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3739)),
inference(clausify,[status(thm)],[f_1223_2]) ).
fof(f_1224_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_1224_2,plain,
! [U_3741,U_3740] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3740),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_3741)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3740),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_3741)),
inference(variable_rename,[status(thm)],[f_1224_1]) ).
cnf(f_1224_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3740),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_3741)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3740),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_3741)),
inference(clausify,[status(thm)],[f_1224_2]) ).
fof(f_1225_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_1225_2,plain,
! [U_3743,U_3742] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_3742)))),U_3743) = 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_3742)),U_3743),
inference(variable_rename,[status(thm)],[f_1225_1]) ).
cnf(f_1225_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_3742)))),U_3743) = 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_3742)),U_3743),
inference(clausify,[status(thm)],[f_1225_2]) ).
fof(f_1226_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_1226_2,plain,
! [U_3745,U_3744] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_3744)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3745)) = 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_3744)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3745)),
inference(variable_rename,[status(thm)],[f_1226_1]) ).
cnf(f_1226_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_3744)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3745)) = 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_3744)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3745)),
inference(clausify,[status(thm)],[f_1226_2]) ).
fof(f_1227_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_1227_2,plain,
! [U_3746] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_3746))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3746) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3746) = 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_3746)))) ) ),
inference(variable_rename,[status(thm)],[f_1227_1]) ).
fof(f_1227_3,plain,
( ! [U_3748] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_3748))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3748) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_3747] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3747) = 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_3747)))) ) ),
inference(miniscope,[status(thm)],[f_1227_2]) ).
cnf(f_1227_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3747) = 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_3747)))) ),
inference(clausify,[status(thm)],[f_1227_3]) ).
cnf(f_1227_5,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_3748))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3748) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1227_3]) ).
fof(f_1228_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_1228_2,plain,
! [U_3750,U_3749] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_3750)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_3749))) = 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_3750)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3749)))),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_3749))) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_3750)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_3749))) = 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_3750),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3749)))),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_3749))) ) ),
inference(variable_rename,[status(thm)],[f_1228_1]) ).
fof(f_1228_3,plain,
( ! [U_3754,U_3752] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_3754)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_3752))) = 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_3754)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3752)))),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_3752))) )
& ! [U_3753,U_3751] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_3753)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_3751))) = 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_3753),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3751)))),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_3751))) ) ),
inference(miniscope,[status(thm)],[f_1228_2]) ).
cnf(f_1228_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_3753)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_3751))) = 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_3753),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3751)))),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_3751))) ),
inference(clausify,[status(thm)],[f_1228_3]) ).
cnf(f_1228_5,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_3754)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_3752))) = 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_3754)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3752)))),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_3752))) ),
inference(clausify,[status(thm)],[f_1228_3]) ).
fof(f_1229_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_1229_2,plain,
! [U_3756,U_3755] :
( 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_3756)),hAPP(hAPP(c_Groups_Otimes__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_3755)) = 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_3756),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_3755))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3755),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1229_1]) ).
cnf(f_1229_3,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_3756)),hAPP(hAPP(c_Groups_Otimes__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_3755)) = 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_3756),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_3755))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3755),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1229_2]) ).
fof(f_1230_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_1230_2,plain,
! [U_3758,U_3757] :
( 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_3758))),hAPP(hAPP(c_Groups_Otimes__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_3757)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3758),U_3757)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3757)) ),
inference(variable_rename,[status(thm)],[f_1230_1]) ).
cnf(f_1230_3,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_3758))),hAPP(hAPP(c_Groups_Otimes__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_3757)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3758),U_3757)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3757)) ),
inference(clausify,[status(thm)],[f_1230_2]) ).
fof(f_1231_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_1231_2,plain,
! [U_3760,U_3759] :
( 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_3760))),hAPP(hAPP(c_Groups_Otimes__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_3759)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3760),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_3759)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3759),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1231_1]) ).
cnf(f_1231_3,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_3760))),hAPP(hAPP(c_Groups_Otimes__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_3759)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3760),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_3759)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3759),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1231_2]) ).
fof(f_1232_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_1232_2,plain,
! [U_3762,U_3761] :
( 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_3762)),hAPP(hAPP(c_Groups_Otimes__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_3761)) = 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_3762,U_3761)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3761)) ),
inference(variable_rename,[status(thm)],[f_1232_1]) ).
cnf(f_1232_3,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_3762)),hAPP(hAPP(c_Groups_Otimes__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_3761)) = 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_3762,U_3761)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3761)) ),
inference(clausify,[status(thm)],[f_1232_2]) ).
fof(f_1233_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_1233_2,plain,
! [U_3764,U_3763] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3763),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_3764))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3763),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3763),hAPP(c_Int_Onat,U_3764))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3763),hAPP(c_Int_Onat,U_3764)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3764))
| ~ class_Rings_Osemiring__1(U_3763) ),
inference(variable_rename,[status(thm)],[f_1233_1]) ).
cnf(f_1233_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3763),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_3764))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3763),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3763),hAPP(c_Int_Onat,U_3764))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3763),hAPP(c_Int_Onat,U_3764)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3764))
| ~ class_Rings_Osemiring__1(U_3763) ),
inference(clausify,[status(thm)],[f_1233_2]) ).
fof(f_1234_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_1234_2,plain,
! [U_3765] :
( 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_3765),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_3765)) ),
inference(variable_rename,[status(thm)],[f_1234_1]) ).
cnf(f_1234_3,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_3765),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_3765)) ),
inference(clausify,[status(thm)],[f_1234_2]) ).
fof(f_1235_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_1235_2,plain,
! [U_3767,U_3766] :
( ( c_Int_OBit0(U_3766) = c_Int_OBit0(U_3767)
| U_3766 != U_3767 )
& ( U_3766 = U_3767
| c_Int_OBit0(U_3766) != c_Int_OBit0(U_3767) ) ),
inference(variable_rename,[status(thm)],[f_1235_1]) ).
fof(f_1235_3,plain,
( ! [U_3771,U_3769] :
( c_Int_OBit0(U_3769) = c_Int_OBit0(U_3771)
| U_3769 != U_3771 )
& ! [U_3770,U_3768] :
( U_3768 = U_3770
| c_Int_OBit0(U_3768) != c_Int_OBit0(U_3770) ) ),
inference(miniscope,[status(thm)],[f_1235_2]) ).
cnf(f_1235_4,plain,
( U_3768 = U_3770
| c_Int_OBit0(U_3768) != c_Int_OBit0(U_3770) ),
inference(clausify,[status(thm)],[f_1235_3]) ).
cnf(f_1235_5,plain,
( c_Int_OBit0(U_3769) = c_Int_OBit0(U_3771)
| U_3769 != U_3771 ),
inference(clausify,[status(thm)],[f_1235_3]) ).
fof(f_1236_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_1236_2,plain,
! [U_3773,U_3772] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3772)),c_Int_OBit0(U_3773)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3772),U_3773)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3772),U_3773))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3772)),c_Int_OBit0(U_3773))) ) ),
inference(variable_rename,[status(thm)],[f_1236_1]) ).
fof(f_1236_3,plain,
( ! [U_3777,U_3775] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3775)),c_Int_OBit0(U_3777)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3775),U_3777)) )
& ! [U_3776,U_3774] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3774),U_3776))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3774)),c_Int_OBit0(U_3776))) ) ),
inference(miniscope,[status(thm)],[f_1236_2]) ).
cnf(f_1236_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3774),U_3776))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3774)),c_Int_OBit0(U_3776))) ),
inference(clausify,[status(thm)],[f_1236_3]) ).
cnf(f_1236_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3775)),c_Int_OBit0(U_3777)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3775),U_3777)) ),
inference(clausify,[status(thm)],[f_1236_3]) ).
fof(f_1237_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_1237_2,plain,
! [U_3779,U_3778] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3778)),c_Int_OBit0(U_3779)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3778),U_3779)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3778),U_3779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3778)),c_Int_OBit0(U_3779))) ) ),
inference(variable_rename,[status(thm)],[f_1237_1]) ).
fof(f_1237_3,plain,
( ! [U_3783,U_3781] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3781)),c_Int_OBit0(U_3783)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3781),U_3783)) )
& ! [U_3782,U_3780] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3780),U_3782))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3780)),c_Int_OBit0(U_3782))) ) ),
inference(miniscope,[status(thm)],[f_1237_2]) ).
cnf(f_1237_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3780),U_3782))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3780)),c_Int_OBit0(U_3782))) ),
inference(clausify,[status(thm)],[f_1237_3]) ).
cnf(f_1237_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3781)),c_Int_OBit0(U_3783)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3781),U_3783)) ),
inference(clausify,[status(thm)],[f_1237_3]) ).
fof(f_1238_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_1238_2,plain,
! [U_3785,U_3784] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3784)),c_Int_OBit0(U_3785)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3784),U_3785)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3784),U_3785))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3784)),c_Int_OBit0(U_3785))) ) ),
inference(variable_rename,[status(thm)],[f_1238_1]) ).
fof(f_1238_3,plain,
( ! [U_3789,U_3787] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3787)),c_Int_OBit0(U_3789)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3787),U_3789)) )
& ! [U_3788,U_3786] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3786),U_3788))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3786)),c_Int_OBit0(U_3788))) ) ),
inference(miniscope,[status(thm)],[f_1238_2]) ).
cnf(f_1238_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3786),U_3788))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3786)),c_Int_OBit0(U_3788))) ),
inference(clausify,[status(thm)],[f_1238_3]) ).
cnf(f_1238_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3787)),c_Int_OBit0(U_3789)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3787),U_3789)) ),
inference(clausify,[status(thm)],[f_1238_3]) ).
fof(f_1239_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_1239_2,plain,
! [U_3791,U_3790] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3790)),c_Int_OBit0(U_3791)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3790),U_3791)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3790),U_3791))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3790)),c_Int_OBit0(U_3791))) ) ),
inference(variable_rename,[status(thm)],[f_1239_1]) ).
fof(f_1239_3,plain,
( ! [U_3795,U_3793] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3793)),c_Int_OBit0(U_3795)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3793),U_3795)) )
& ! [U_3794,U_3792] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3792),U_3794))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3792)),c_Int_OBit0(U_3794))) ) ),
inference(miniscope,[status(thm)],[f_1239_2]) ).
cnf(f_1239_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3792),U_3794))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3792)),c_Int_OBit0(U_3794))) ),
inference(clausify,[status(thm)],[f_1239_3]) ).
cnf(f_1239_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3793)),c_Int_OBit0(U_3795)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3793),U_3795)) ),
inference(clausify,[status(thm)],[f_1239_3]) ).
fof(f_1240_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_1240_2,plain,
! [U_3796] :
( ( c_Int_OBit0(U_3796) = c_Int_OPls
| U_3796 != c_Int_OPls )
& ( U_3796 = c_Int_OPls
| c_Int_OBit0(U_3796) != c_Int_OPls ) ),
inference(variable_rename,[status(thm)],[f_1240_1]) ).
fof(f_1240_3,plain,
( ! [U_3798] :
( c_Int_OBit0(U_3798) = c_Int_OPls
| U_3798 != c_Int_OPls )
& ! [U_3797] :
( U_3797 = c_Int_OPls
| c_Int_OBit0(U_3797) != c_Int_OPls ) ),
inference(miniscope,[status(thm)],[f_1240_2]) ).
cnf(f_1240_4,plain,
( U_3797 = c_Int_OPls
| c_Int_OBit0(U_3797) != c_Int_OPls ),
inference(clausify,[status(thm)],[f_1240_3]) ).
cnf(f_1240_5,plain,
( c_Int_OBit0(U_3798) = c_Int_OPls
| U_3798 != c_Int_OPls ),
inference(clausify,[status(thm)],[f_1240_3]) ).
fof(f_1241_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_1241_2,plain,
! [U_3799] :
( ( c_Int_OPls = c_Int_OBit0(U_3799)
| c_Int_OPls != U_3799 )
& ( c_Int_OPls = U_3799
| c_Int_OPls != c_Int_OBit0(U_3799) ) ),
inference(variable_rename,[status(thm)],[f_1241_1]) ).
fof(f_1241_3,plain,
( ! [U_3801] :
( c_Int_OPls = c_Int_OBit0(U_3801)
| c_Int_OPls != U_3801 )
& ! [U_3800] :
( c_Int_OPls = U_3800
| c_Int_OPls != c_Int_OBit0(U_3800) ) ),
inference(miniscope,[status(thm)],[f_1241_2]) ).
cnf(f_1241_4,plain,
( c_Int_OPls = U_3800
| c_Int_OPls != c_Int_OBit0(U_3800) ),
inference(clausify,[status(thm)],[f_1241_3]) ).
cnf(f_1241_5,plain,
( c_Int_OPls = c_Int_OBit0(U_3801)
| c_Int_OPls != U_3801 ),
inference(clausify,[status(thm)],[f_1241_3]) ).
fof(f_1242_1,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_Bit0__Pls]) ).
cnf(f_1242_2,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(clausify,[status(thm)],[f_1242_1]) ).
fof(f_1243_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_1243_2,plain,
! [U_3803,U_3802] : c_Int_OBit1(U_3802) != c_Int_OBit0(U_3803),
inference(variable_rename,[status(thm)],[f_1243_1]) ).
cnf(f_1243_3,plain,
c_Int_OBit1(U_3802) != c_Int_OBit0(U_3803),
inference(clausify,[status(thm)],[f_1243_2]) ).
fof(f_1244_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_1244_2,plain,
! [U_3805,U_3804] : c_Int_OBit0(U_3804) != c_Int_OBit1(U_3805),
inference(variable_rename,[status(thm)],[f_1244_1]) ).
cnf(f_1244_3,plain,
c_Int_OBit0(U_3804) != c_Int_OBit1(U_3805),
inference(clausify,[status(thm)],[f_1244_2]) ).
fof(f_1245_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_1245_2,plain,
! [U_3807,U_3806] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_3806)),c_Int_OBit0(U_3807)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3806),U_3807)),
inference(variable_rename,[status(thm)],[f_1245_1]) ).
cnf(f_1245_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_3806)),c_Int_OBit0(U_3807)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3806),U_3807)),
inference(clausify,[status(thm)],[f_1245_2]) ).
fof(f_1246_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_1246_2,plain,
! [U_3808] : c_Int_OBit0(U_3808) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3808),U_3808),
inference(variable_rename,[status(thm)],[f_1246_1]) ).
cnf(f_1246_3,plain,
c_Int_OBit0(U_3808) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3808),U_3808),
inference(clausify,[status(thm)],[f_1246_2]) ).
fof(f_1247_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_1247_2,plain,
! [U_3810,U_3809] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_3809)),U_3810) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3809),U_3810)),
inference(variable_rename,[status(thm)],[f_1247_1]) ).
cnf(f_1247_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_3809)),U_3810) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3809),U_3810)),
inference(clausify,[status(thm)],[f_1247_2]) ).
fof(f_1248_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_1248_2,plain,
! [U_3812,U_3811] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_3811)),c_Int_OBit0(U_3812)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3811),U_3812)),
inference(variable_rename,[status(thm)],[f_1248_1]) ).
cnf(f_1248_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_3811)),c_Int_OBit0(U_3812)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3811),U_3812)),
inference(clausify,[status(thm)],[f_1248_2]) ).
fof(f_1249_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_1249_2,plain,
! [U_3813] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_3813)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3813)),
inference(variable_rename,[status(thm)],[f_1249_1]) ).
cnf(f_1249_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_3813)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3813)),
inference(clausify,[status(thm)],[f_1249_2]) ).
fof(f_1250_1,plain,
! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I45_J]) ).
fof(f_1250_2,plain,
! [U_3814] : c_Int_OBit0(U_3814) != c_Int_OMin,
inference(variable_rename,[status(thm)],[f_1250_1]) ).
cnf(f_1250_3,plain,
c_Int_OBit0(U_3814) != c_Int_OMin,
inference(clausify,[status(thm)],[f_1250_2]) ).
fof(f_1251_1,plain,
! [V_l] : c_Int_OMin != c_Int_OBit0(V_l),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I42_J]) ).
fof(f_1251_2,plain,
! [U_3815] : c_Int_OMin != c_Int_OBit0(U_3815),
inference(variable_rename,[status(thm)],[f_1251_1]) ).
cnf(f_1251_3,plain,
c_Int_OMin != c_Int_OBit0(U_3815),
inference(clausify,[status(thm)],[f_1251_2]) ).
fof(f_1252_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_1252_2,plain,
! [U_3816] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3816)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3816),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3816),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3816)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_1252_1]) ).
fof(f_1252_3,plain,
( ! [U_3818] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3818)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3818),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_3817] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3817),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3817)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_1252_2]) ).
cnf(f_1252_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3817),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3817)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1252_3]) ).
cnf(f_1252_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3818)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3818),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1252_3]) ).
fof(f_1253_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_1253_2,plain,
! [U_3819] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_3819)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3819)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3819))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_3819))) ) ),
inference(variable_rename,[status(thm)],[f_1253_1]) ).
fof(f_1253_3,plain,
( ! [U_3821] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_3821)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3821)) )
& ! [U_3820] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3820))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_3820))) ) ),
inference(miniscope,[status(thm)],[f_1253_2]) ).
cnf(f_1253_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3820))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_3820))) ),
inference(clausify,[status(thm)],[f_1253_3]) ).
cnf(f_1253_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_3821)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_3821)) ),
inference(clausify,[status(thm)],[f_1253_3]) ).
fof(f_1254_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_1254_2,plain,
! [U_3822] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3822)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3822),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3822),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3822)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1254_1]) ).
fof(f_1254_3,plain,
( ! [U_3824] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3824)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3824),c_Int_OPls)) )
& ! [U_3823] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3823),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3823)),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1254_2]) ).
cnf(f_1254_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3823),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3823)),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1254_3]) ).
cnf(f_1254_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3824)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3824),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1254_3]) ).
fof(f_1255_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_1255_2,plain,
! [U_3826,U_3825] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3825)),c_Int_OBit1(U_3826)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3825),U_3826)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3825),U_3826))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3825)),c_Int_OBit1(U_3826))) ) ),
inference(variable_rename,[status(thm)],[f_1255_1]) ).
fof(f_1255_3,plain,
( ! [U_3830,U_3828] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3828)),c_Int_OBit1(U_3830)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3828),U_3830)) )
& ! [U_3829,U_3827] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3827),U_3829))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3827)),c_Int_OBit1(U_3829))) ) ),
inference(miniscope,[status(thm)],[f_1255_2]) ).
cnf(f_1255_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3827),U_3829))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3827)),c_Int_OBit1(U_3829))) ),
inference(clausify,[status(thm)],[f_1255_3]) ).
cnf(f_1255_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3828)),c_Int_OBit1(U_3830)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3828),U_3830)) ),
inference(clausify,[status(thm)],[f_1255_3]) ).
fof(f_1256_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_1256_2,plain,
! [U_3832,U_3831] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3831)),c_Int_OBit1(U_3832)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3831),U_3832)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3831),U_3832))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3831)),c_Int_OBit1(U_3832))) ) ),
inference(variable_rename,[status(thm)],[f_1256_1]) ).
fof(f_1256_3,plain,
( ! [U_3836,U_3834] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3834)),c_Int_OBit1(U_3836)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3834),U_3836)) )
& ! [U_3835,U_3833] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3833),U_3835))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3833)),c_Int_OBit1(U_3835))) ) ),
inference(miniscope,[status(thm)],[f_1256_2]) ).
cnf(f_1256_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3833),U_3835))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3833)),c_Int_OBit1(U_3835))) ),
inference(clausify,[status(thm)],[f_1256_3]) ).
cnf(f_1256_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3834)),c_Int_OBit1(U_3836)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3834),U_3836)) ),
inference(clausify,[status(thm)],[f_1256_3]) ).
fof(f_1257_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_1257_2,plain,
! [U_3837] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3837)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3837),c_Int_OPls)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3837),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3837)),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1257_1]) ).
fof(f_1257_3,plain,
( ! [U_3839] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3839)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3839),c_Int_OPls)) )
& ! [U_3838] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3838),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3838)),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1257_2]) ).
cnf(f_1257_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3838),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3838)),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1257_3]) ).
cnf(f_1257_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3839)),c_Int_OPls))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3839),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1257_3]) ).
fof(f_1258_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_1258_2,plain,
! [U_3840] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_3840)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3840)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3840))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_3840))) ) ),
inference(variable_rename,[status(thm)],[f_1258_1]) ).
fof(f_1258_3,plain,
( ! [U_3842] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_3842)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3842)) )
& ! [U_3841] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3841))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_3841))) ) ),
inference(miniscope,[status(thm)],[f_1258_2]) ).
cnf(f_1258_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3841))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_3841))) ),
inference(clausify,[status(thm)],[f_1258_3]) ).
cnf(f_1258_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_3842)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_3842)) ),
inference(clausify,[status(thm)],[f_1258_3]) ).
fof(f_1259_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_1259_2,plain,
! [U_3844,U_3843] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3843)),c_Int_OBit0(U_3844)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3843),U_3844)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3843),U_3844))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3843)),c_Int_OBit0(U_3844))) ) ),
inference(variable_rename,[status(thm)],[f_1259_1]) ).
fof(f_1259_3,plain,
( ! [U_3848,U_3846] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3846)),c_Int_OBit0(U_3848)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3846),U_3848)) )
& ! [U_3847,U_3845] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3845),U_3847))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3845)),c_Int_OBit0(U_3847))) ) ),
inference(miniscope,[status(thm)],[f_1259_2]) ).
cnf(f_1259_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3845),U_3847))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3845)),c_Int_OBit0(U_3847))) ),
inference(clausify,[status(thm)],[f_1259_3]) ).
cnf(f_1259_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3846)),c_Int_OBit0(U_3848)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3846),U_3848)) ),
inference(clausify,[status(thm)],[f_1259_3]) ).
fof(f_1260_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_1260_2,plain,
! [U_3850,U_3849] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3849)),c_Int_OBit0(U_3850)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3849),U_3850)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3849),U_3850))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3849)),c_Int_OBit0(U_3850))) ) ),
inference(variable_rename,[status(thm)],[f_1260_1]) ).
fof(f_1260_3,plain,
( ! [U_3854,U_3852] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3852)),c_Int_OBit0(U_3854)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3852),U_3854)) )
& ! [U_3853,U_3851] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3851),U_3853))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3851)),c_Int_OBit0(U_3853))) ) ),
inference(miniscope,[status(thm)],[f_1260_2]) ).
cnf(f_1260_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3851),U_3853))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3851)),c_Int_OBit0(U_3853))) ),
inference(clausify,[status(thm)],[f_1260_3]) ).
cnf(f_1260_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_3852)),c_Int_OBit0(U_3854)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3852),U_3854)) ),
inference(clausify,[status(thm)],[f_1260_3]) ).
fof(f_1261_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_1261_2,plain,
! [U_3856,U_3855] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_3855)),c_Int_OBit0(U_3856)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3855),U_3856)),
inference(variable_rename,[status(thm)],[f_1261_1]) ).
cnf(f_1261_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_3855)),c_Int_OBit0(U_3856)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3855),U_3856)),
inference(clausify,[status(thm)],[f_1261_2]) ).
fof(f_1262_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_1262_2,plain,
! [U_3858,U_3857] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_3857)),c_Int_OBit1(U_3858)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3857),U_3858)),
inference(variable_rename,[status(thm)],[f_1262_1]) ).
cnf(f_1262_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_3857)),c_Int_OBit1(U_3858)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3857),U_3858)),
inference(clausify,[status(thm)],[f_1262_2]) ).
fof(f_1263_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_1263_2,plain,
! [U_3859] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_3859)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_3859)),
inference(variable_rename,[status(thm)],[f_1263_1]) ).
cnf(f_1263_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_3859)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_3859)),
inference(clausify,[status(thm)],[f_1263_2]) ).
fof(f_1264_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_1264_2,plain,
! [U_3861,U_3860] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_3860)),c_Int_OBit0(U_3861)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3860),U_3861)),
inference(variable_rename,[status(thm)],[f_1264_1]) ).
cnf(f_1264_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_3860)),c_Int_OBit0(U_3861)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3860),U_3861)),
inference(clausify,[status(thm)],[f_1264_2]) ).
fof(f_1265_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_1265_2,plain,
! [U_3863,U_3862] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_3862)),c_Int_OBit1(U_3863)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3862),U_3863)),
inference(variable_rename,[status(thm)],[f_1265_1]) ).
cnf(f_1265_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_3862)),c_Int_OBit1(U_3863)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3862),U_3863)),
inference(clausify,[status(thm)],[f_1265_2]) ).
fof(f_1266_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_1266_2,plain,
! [U_3864] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3864)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3864),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3864),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3864)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[f_1266_1]) ).
fof(f_1266_3,plain,
( ! [U_3866] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3866)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3866),c_Int_OMin)) )
& ! [U_3865] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3865),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3865)),c_Int_OMin)) ) ),
inference(miniscope,[status(thm)],[f_1266_2]) ).
cnf(f_1266_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3865),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3865)),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_1266_3]) ).
cnf(f_1266_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_3866)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3866),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_1266_3]) ).
fof(f_1267_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_1267_2,plain,
! [U_3867] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_3867)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_3867)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_3867))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_3867))) ) ),
inference(variable_rename,[status(thm)],[f_1267_1]) ).
fof(f_1267_3,plain,
( ! [U_3869] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_3869)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_3869)) )
& ! [U_3868] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_3868))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_3868))) ) ),
inference(miniscope,[status(thm)],[f_1267_2]) ).
cnf(f_1267_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_3868))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_3868))) ),
inference(clausify,[status(thm)],[f_1267_3]) ).
cnf(f_1267_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_3869)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_3869)) ),
inference(clausify,[status(thm)],[f_1267_3]) ).
fof(f_1268_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_1268_2,plain,
! [U_3871,U_3870] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_3870))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_3871))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3870)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3871)),
inference(variable_rename,[status(thm)],[f_1268_1]) ).
cnf(f_1268_3,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_3870))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_3871))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3870)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3871)),
inference(clausify,[status(thm)],[f_1268_2]) ).
fof(f_1269_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_1269_2,plain,
! [U_3872] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_3872))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3872))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3872)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_3872)))) ) ),
inference(variable_rename,[status(thm)],[f_1269_1]) ).
fof(f_1269_3,plain,
( ! [U_3874] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_3874))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3874))) )
& ! [U_3873] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3873)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_3873)))) ) ),
inference(miniscope,[status(thm)],[f_1269_2]) ).
cnf(f_1269_4,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3873)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_3873)))) ),
inference(clausify,[status(thm)],[f_1269_3]) ).
cnf(f_1269_5,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_3874))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3874))) ),
inference(clausify,[status(thm)],[f_1269_3]) ).
fof(f_1270_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_1270_2,plain,
! [U_3875] : c_Int_Opred(c_Int_OBit0(U_3875)) = c_Int_OBit1(c_Int_Opred(U_3875)),
inference(variable_rename,[status(thm)],[f_1270_1]) ).
cnf(f_1270_3,plain,
c_Int_Opred(c_Int_OBit0(U_3875)) = c_Int_OBit1(c_Int_Opred(U_3875)),
inference(clausify,[status(thm)],[f_1270_2]) ).
fof(f_1271_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_1271_2,plain,
! [U_3876] : c_Int_Opred(c_Int_OBit1(U_3876)) = c_Int_OBit0(U_3876),
inference(variable_rename,[status(thm)],[f_1271_1]) ).
cnf(f_1271_3,plain,
c_Int_Opred(c_Int_OBit1(U_3876)) = c_Int_OBit0(U_3876),
inference(clausify,[status(thm)],[f_1271_2]) ).
fof(f_1272_1,plain,
c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
inference(fof_nnf,[status(thm)],[fact_pred__Min]) ).
cnf(f_1272_2,plain,
c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
inference(clausify,[status(thm)],[f_1272_1]) ).
fof(f_1273_1,plain,
! [V_w_2,T_b] :
( ( ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
| ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) )
& ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
| ~ c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2))) ) )
| ~ class_Int_Oring__char__0(T_b)
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit0]) ).
fof(f_1273_2,plain,
! [U_3878,U_3877] :
( ( ( c_Int_Oiszero(U_3877,hAPP(c_Int_Onumber__class_Onumber__of(U_3877),c_Int_OBit0(U_3878)))
| ~ c_Int_Oiszero(U_3877,hAPP(c_Int_Onumber__class_Onumber__of(U_3877),U_3878)) )
& ( c_Int_Oiszero(U_3877,hAPP(c_Int_Onumber__class_Onumber__of(U_3877),U_3878))
| ~ c_Int_Oiszero(U_3877,hAPP(c_Int_Onumber__class_Onumber__of(U_3877),c_Int_OBit0(U_3878))) ) )
| ~ class_Int_Oring__char__0(U_3877)
| ~ class_Int_Onumber__ring(U_3877) ),
inference(variable_rename,[status(thm)],[f_1273_1]) ).
cnf(f_1273_3,plain,
( c_Int_Oiszero(U_3877,hAPP(c_Int_Onumber__class_Onumber__of(U_3877),U_3878))
| ~ c_Int_Oiszero(U_3877,hAPP(c_Int_Onumber__class_Onumber__of(U_3877),c_Int_OBit0(U_3878)))
| ~ class_Int_Oring__char__0(U_3877)
| ~ class_Int_Onumber__ring(U_3877) ),
inference(clausify,[status(thm)],[f_1273_2]) ).
cnf(f_1273_4,plain,
( c_Int_Oiszero(U_3877,hAPP(c_Int_Onumber__class_Onumber__of(U_3877),c_Int_OBit0(U_3878)))
| ~ c_Int_Oiszero(U_3877,hAPP(c_Int_Onumber__class_Onumber__of(U_3877),U_3878))
| ~ class_Int_Oring__char__0(U_3877)
| ~ class_Int_Onumber__ring(U_3877) ),
inference(clausify,[status(thm)],[f_1273_2]) ).
fof(f_1274_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_1274_2,plain,
! [U_3879] : c_Int_Osucc(c_Int_OBit0(U_3879)) = c_Int_OBit1(U_3879),
inference(variable_rename,[status(thm)],[f_1274_1]) ).
cnf(f_1274_3,plain,
c_Int_Osucc(c_Int_OBit0(U_3879)) = c_Int_OBit1(U_3879),
inference(clausify,[status(thm)],[f_1274_2]) ).
fof(f_1275_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_1275_2,plain,
! [U_3880] : c_Int_Osucc(c_Int_OBit1(U_3880)) = c_Int_OBit0(c_Int_Osucc(U_3880)),
inference(variable_rename,[status(thm)],[f_1275_1]) ).
cnf(f_1275_3,plain,
c_Int_Osucc(c_Int_OBit1(U_3880)) = c_Int_OBit0(c_Int_Osucc(U_3880)),
inference(clausify,[status(thm)],[f_1275_2]) ).
fof(f_1276_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_1276_2,plain,
! [U_3882,U_3881] :
( hAPP(c_Int_Onumber__class_Onumber__of(U_3881),c_Int_OBit0(U_3882)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3881),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3881),c_Groups_Ozero__class_Ozero(U_3881)),hAPP(c_Int_Onumber__class_Onumber__of(U_3881),U_3882))),hAPP(c_Int_Onumber__class_Onumber__of(U_3881),U_3882))
| ~ class_Int_Onumber__ring(U_3881) ),
inference(variable_rename,[status(thm)],[f_1276_1]) ).
cnf(f_1276_3,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_3881),c_Int_OBit0(U_3882)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3881),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3881),c_Groups_Ozero__class_Ozero(U_3881)),hAPP(c_Int_Onumber__class_Onumber__of(U_3881),U_3882))),hAPP(c_Int_Onumber__class_Onumber__of(U_3881),U_3882))
| ~ class_Int_Onumber__ring(U_3881) ),
inference(clausify,[status(thm)],[f_1276_2]) ).
fof(f_1277_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_1277_2,plain,
! [U_3884,U_3883] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3883)),c_Int_OBit1(U_3884)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3883),U_3884)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3883),U_3884))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3883)),c_Int_OBit1(U_3884))) ) ),
inference(variable_rename,[status(thm)],[f_1277_1]) ).
fof(f_1277_3,plain,
( ! [U_3888,U_3886] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3886)),c_Int_OBit1(U_3888)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3886),U_3888)) )
& ! [U_3887,U_3885] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3885),U_3887))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3885)),c_Int_OBit1(U_3887))) ) ),
inference(miniscope,[status(thm)],[f_1277_2]) ).
cnf(f_1277_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3885),U_3887))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3885)),c_Int_OBit1(U_3887))) ),
inference(clausify,[status(thm)],[f_1277_3]) ).
cnf(f_1277_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3886)),c_Int_OBit1(U_3888)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3886),U_3888)) ),
inference(clausify,[status(thm)],[f_1277_3]) ).
fof(f_1278_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_1278_2,plain,
! [U_3890,U_3889] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3889)),c_Int_OBit1(U_3890)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3889),U_3890)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3889),U_3890))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3889)),c_Int_OBit1(U_3890))) ) ),
inference(variable_rename,[status(thm)],[f_1278_1]) ).
fof(f_1278_3,plain,
( ! [U_3894,U_3892] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3892)),c_Int_OBit1(U_3894)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3892),U_3894)) )
& ! [U_3893,U_3891] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3891),U_3893))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3891)),c_Int_OBit1(U_3893))) ) ),
inference(miniscope,[status(thm)],[f_1278_2]) ).
cnf(f_1278_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3891),U_3893))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3891)),c_Int_OBit1(U_3893))) ),
inference(clausify,[status(thm)],[f_1278_3]) ).
cnf(f_1278_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3892)),c_Int_OBit1(U_3894)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3892),U_3894)) ),
inference(clausify,[status(thm)],[f_1278_3]) ).
fof(f_1279_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_1279_2,plain,
! [U_3896,U_3895] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3895)),c_Int_OBit0(U_3896)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3895),U_3896)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3895),U_3896))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3895)),c_Int_OBit0(U_3896))) ) ),
inference(variable_rename,[status(thm)],[f_1279_1]) ).
fof(f_1279_3,plain,
( ! [U_3900,U_3898] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3898)),c_Int_OBit0(U_3900)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3898),U_3900)) )
& ! [U_3899,U_3897] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3897),U_3899))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3897)),c_Int_OBit0(U_3899))) ) ),
inference(miniscope,[status(thm)],[f_1279_2]) ).
cnf(f_1279_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3897),U_3899))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3897)),c_Int_OBit0(U_3899))) ),
inference(clausify,[status(thm)],[f_1279_3]) ).
cnf(f_1279_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3898)),c_Int_OBit0(U_3900)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3898),U_3900)) ),
inference(clausify,[status(thm)],[f_1279_3]) ).
fof(f_1280_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_1280_2,plain,
! [U_3902,U_3901] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3901)),c_Int_OBit0(U_3902)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3901),U_3902)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3901),U_3902))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3901)),c_Int_OBit0(U_3902))) ) ),
inference(variable_rename,[status(thm)],[f_1280_1]) ).
fof(f_1280_3,plain,
( ! [U_3906,U_3904] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3904)),c_Int_OBit0(U_3906)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3904),U_3906)) )
& ! [U_3905,U_3903] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3903),U_3905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3903)),c_Int_OBit0(U_3905))) ) ),
inference(miniscope,[status(thm)],[f_1280_2]) ).
cnf(f_1280_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3903),U_3905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3903)),c_Int_OBit0(U_3905))) ),
inference(clausify,[status(thm)],[f_1280_3]) ).
cnf(f_1280_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_3904)),c_Int_OBit0(U_3906)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3904),U_3906)) ),
inference(clausify,[status(thm)],[f_1280_3]) ).
fof(f_1281_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_1281_2,plain,
! [U_3908,U_3907] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_3907)),U_3908) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3907),U_3908))),U_3908),
inference(variable_rename,[status(thm)],[f_1281_1]) ).
cnf(f_1281_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_3907)),U_3908) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3907),U_3908))),U_3908),
inference(clausify,[status(thm)],[f_1281_2]) ).
fof(f_1282_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_1282_2,plain,
! [U_3909] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_3909)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_3909)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_3909))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_3909))) ) ),
inference(variable_rename,[status(thm)],[f_1282_1]) ).
fof(f_1282_3,plain,
( ! [U_3911] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_3911)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_3911)) )
& ! [U_3910] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_3910))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_3910))) ) ),
inference(miniscope,[status(thm)],[f_1282_2]) ).
cnf(f_1282_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_3910))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_3910))) ),
inference(clausify,[status(thm)],[f_1282_3]) ).
cnf(f_1282_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_3911)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_3911)) ),
inference(clausify,[status(thm)],[f_1282_3]) ).
fof(f_1283_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_1283_2,plain,
! [U_3912] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3912)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3912),c_Int_OMin)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3912),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3912)),c_Int_OMin)) ) ),
inference(variable_rename,[status(thm)],[f_1283_1]) ).
fof(f_1283_3,plain,
( ! [U_3914] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3914)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3914),c_Int_OMin)) )
& ! [U_3913] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3913),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3913)),c_Int_OMin)) ) ),
inference(miniscope,[status(thm)],[f_1283_2]) ).
cnf(f_1283_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3913),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3913)),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_1283_3]) ).
cnf(f_1283_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_3914)),c_Int_OMin))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3914),c_Int_OMin)) ),
inference(clausify,[status(thm)],[f_1283_3]) ).
fof(f_1284_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_1284_2,plain,
! [U_3915] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_3915)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_3915)),
inference(variable_rename,[status(thm)],[f_1284_1]) ).
cnf(f_1284_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_3915)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_3915)),
inference(clausify,[status(thm)],[f_1284_2]) ).
fof(f_1285_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_1285_2,plain,
! [U_3916] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_3916)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_3916)),
inference(variable_rename,[status(thm)],[f_1285_1]) ).
cnf(f_1285_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_3916)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_3916)),
inference(clausify,[status(thm)],[f_1285_2]) ).
fof(f_1286_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_1286_2,plain,
! [U_3918,U_3917] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_3917)),c_Int_OBit1(U_3918)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_3917)),U_3918)),
inference(variable_rename,[status(thm)],[f_1286_1]) ).
cnf(f_1286_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_3917)),c_Int_OBit1(U_3918)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_3917)),U_3918)),
inference(clausify,[status(thm)],[f_1286_2]) ).
fof(f_1287_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_1287_2,plain,
! [U_3920,U_3919] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_3919)),c_Int_OBit1(U_3920)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3919),c_Int_Osucc(U_3920))),
inference(variable_rename,[status(thm)],[f_1287_1]) ).
cnf(f_1287_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_3919)),c_Int_OBit1(U_3920)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3919),c_Int_Osucc(U_3920))),
inference(clausify,[status(thm)],[f_1287_2]) ).
fof(f_1288_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_1288_2,plain,
! [U_3922,U_3921] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3921),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3921),c_Groups_Oone__class_Oone(U_3921)),c_Groups_Oone__class_Oone(U_3921))),hAPP(c_Int_Onumber__class_Onumber__of(U_3921),U_3922)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3921),c_Int_OBit0(U_3922))
| ~ class_Int_Onumber__ring(U_3921) ),
inference(variable_rename,[status(thm)],[f_1288_1]) ).
cnf(f_1288_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3921),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3921),c_Groups_Oone__class_Oone(U_3921)),c_Groups_Oone__class_Oone(U_3921))),hAPP(c_Int_Onumber__class_Onumber__of(U_3921),U_3922)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3921),c_Int_OBit0(U_3922))
| ~ class_Int_Onumber__ring(U_3921) ),
inference(clausify,[status(thm)],[f_1288_2]) ).
fof(f_1289_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_1289_2,plain,
! [U_3923] :
( ( 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_3923))))
& 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_3923)))) )
| ~ 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_3923))) ),
inference(variable_rename,[status(thm)],[f_1289_1]) ).
cnf(f_1289_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(U_3923))))
| ~ 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_3923))) ),
inference(clausify,[status(thm)],[f_1289_2]) ).
cnf(f_1289_4,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_3923))))
| ~ 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_3923))) ),
inference(clausify,[status(thm)],[f_1289_2]) ).
fof(f_1290_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_1290_2,plain,
! [U_3925,U_3924] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3924),hAPP(c_Int_Onumber__class_Onumber__of(U_3924),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_3925) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3924),U_3925),U_3925)
| ~ class_Int_Onumber__ring(U_3924) ),
inference(variable_rename,[status(thm)],[f_1290_1]) ).
cnf(f_1290_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3924),hAPP(c_Int_Onumber__class_Onumber__of(U_3924),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_3925) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3924),U_3925),U_3925)
| ~ class_Int_Onumber__ring(U_3924) ),
inference(clausify,[status(thm)],[f_1290_2]) ).
fof(f_1291_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_1291_2,plain,
! [U_3927,U_3926] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3926),U_3927),hAPP(c_Int_Onumber__class_Onumber__of(U_3926),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3926),U_3927),U_3927)
| ~ class_Int_Onumber__ring(U_3926) ),
inference(variable_rename,[status(thm)],[f_1291_1]) ).
cnf(f_1291_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3926),U_3927),hAPP(c_Int_Onumber__class_Onumber__of(U_3926),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3926),U_3927),U_3927)
| ~ class_Int_Onumber__ring(U_3926) ),
inference(clausify,[status(thm)],[f_1291_2]) ).
fof(f_1292_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_1292_2,plain,
! [U_3928] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3928),c_Groups_Oone__class_Oone(U_3928)),c_Groups_Oone__class_Oone(U_3928)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3928),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_3928) ),
inference(variable_rename,[status(thm)],[f_1292_1]) ).
cnf(f_1292_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3928),c_Groups_Oone__class_Oone(U_3928)),c_Groups_Oone__class_Oone(U_3928)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3928),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_3928) ),
inference(clausify,[status(thm)],[f_1292_2]) ).
fof(f_1293_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_1293_2,plain,
! [U_3929] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3929),c_Groups_Ozero__class_Ozero(U_3929)),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_3929)
| ~ class_Rings_Osemiring__1(U_3929) ),
inference(variable_rename,[status(thm)],[f_1293_1]) ).
cnf(f_1293_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3929),c_Groups_Ozero__class_Ozero(U_3929)),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_3929)
| ~ class_Rings_Osemiring__1(U_3929) ),
inference(clausify,[status(thm)],[f_1293_2]) ).
fof(f_1294_1,plain,
! [V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_b) ),
inference(fof_nnf,[status(thm)],[fact_zero__eq__power2]) ).
fof(f_1294_2,plain,
! [U_3931,U_3930] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3930),U_3931),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_3930)
| U_3931 != c_Groups_Ozero__class_Ozero(U_3930) )
& ( U_3931 = c_Groups_Ozero__class_Ozero(U_3930)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_3930),U_3931),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_3930) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_3930) ),
inference(variable_rename,[status(thm)],[f_1294_1]) ).
cnf(f_1294_3,plain,
( U_3931 = c_Groups_Ozero__class_Ozero(U_3930)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_3930),U_3931),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_3930)
| ~ class_Rings_Oring__1__no__zero__divisors(U_3930) ),
inference(clausify,[status(thm)],[f_1294_2]) ).
cnf(f_1294_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3930),U_3931),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_3930)
| U_3931 != c_Groups_Ozero__class_Ozero(U_3930)
| ~ class_Rings_Oring__1__no__zero__divisors(U_3930) ),
inference(clausify,[status(thm)],[f_1294_2]) ).
fof(f_1295_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]) ).
cnf(f_1295_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(clausify,[status(thm)],[f_1295_1]) ).
fof(f_1296_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]) ).
cnf(f_1296_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(clausify,[status(thm)],[f_1296_1]) ).
fof(f_1297_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_1297_2,plain,
! [U_3933,U_3932] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3932),U_3933),U_3933) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3932),U_3933),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_3932) ),
inference(variable_rename,[status(thm)],[f_1297_1]) ).
cnf(f_1297_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3932),U_3933),U_3933) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3932),U_3933),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_3932) ),
inference(clausify,[status(thm)],[f_1297_2]) ).
fof(f_1298_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_1298_2,plain,
! [U_3935,U_3934] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3934),U_3935),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_3934),U_3935),U_3935)
| ~ class_Groups_Omonoid__mult(U_3934) ),
inference(variable_rename,[status(thm)],[f_1298_1]) ).
cnf(f_1298_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3934),U_3935),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_3934),U_3935),U_3935)
| ~ class_Groups_Omonoid__mult(U_3934) ),
inference(clausify,[status(thm)],[f_1298_2]) ).
fof(f_1299_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]) ).
cnf(f_1299_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(clausify,[status(thm)],[f_1299_1]) ).
fof(f_1300_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_1300_2,plain,
! [U_3936] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3936),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_3936)),
inference(variable_rename,[status(thm)],[f_1300_1]) ).
cnf(f_1300_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3936),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_3936)),
inference(clausify,[status(thm)],[f_1300_2]) ).
fof(f_1301_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_1301_2,plain,
! [U_3937] : 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_3937) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_3937)),
inference(variable_rename,[status(thm)],[f_1301_1]) ).
cnf(f_1301_3,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_3937) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_3937)),
inference(clausify,[status(thm)],[f_1301_2]) ).
fof(f_1302_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_1302_2,plain,
! [U_3938] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3938),c_Groups_Oone__class_Oone(U_3938)),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_3938)
| ~ class_Rings_Osemiring__1(U_3938) ),
inference(variable_rename,[status(thm)],[f_1302_1]) ).
cnf(f_1302_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3938),c_Groups_Oone__class_Oone(U_3938)),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_3938)
| ~ class_Rings_Osemiring__1(U_3938) ),
inference(clausify,[status(thm)],[f_1302_2]) ).
fof(f_1303_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_1303_2,plain,
! [U_3940,U_3939] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3939),hAPP(c_Groups_Ouminus__class_Ouminus(U_3939),U_3940)),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_3939),U_3940),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Oring__1(U_3939) ),
inference(variable_rename,[status(thm)],[f_1303_1]) ).
cnf(f_1303_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3939),hAPP(c_Groups_Ouminus__class_Ouminus(U_3939),U_3940)),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_3939),U_3940),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Oring__1(U_3939) ),
inference(clausify,[status(thm)],[f_1303_2]) ).
fof(f_1304_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_1304_2,plain,
! [U_3941] : 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_3941) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3941),U_3941),
inference(variable_rename,[status(thm)],[f_1304_1]) ).
cnf(f_1304_3,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_3941) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3941),U_3941),
inference(clausify,[status(thm)],[f_1304_2]) ).
fof(f_1305_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_1305_2,plain,
! [U_3942] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3942),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_3942),U_3942),
inference(variable_rename,[status(thm)],[f_1305_1]) ).
cnf(f_1305_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3942),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_3942),U_3942),
inference(clausify,[status(thm)],[f_1305_2]) ).
fof(f_1306_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_1306_2,plain,
! [U_3945,U_3944,U_3943] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3943),U_3944),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_3945)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3943),hAPP(hAPP(c_Power_Opower__class_Opower(U_3943),U_3944),U_3945)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Groups_Omonoid__mult(U_3943) ),
inference(variable_rename,[status(thm)],[f_1306_1]) ).
cnf(f_1306_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3943),U_3944),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_3945)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3943),hAPP(hAPP(c_Power_Opower__class_Opower(U_3943),U_3944),U_3945)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Groups_Omonoid__mult(U_3943) ),
inference(clausify,[status(thm)],[f_1306_2]) ).
fof(f_1307_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]) ).
cnf(f_1307_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(clausify,[status(thm)],[f_1307_1]) ).
fof(f_1308_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]) ).
cnf(f_1308_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(clausify,[status(thm)],[f_1308_1]) ).
fof(f_1309_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_1309_2,plain,
! [U_3947,U_3946] :
( hAPP(c_Groups_Oabs__class_Oabs(U_3946),hAPP(hAPP(c_Power_Opower__class_Opower(U_3946),U_3947),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_3946),U_3947),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_3946) ),
inference(variable_rename,[status(thm)],[f_1309_1]) ).
cnf(f_1309_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_3946),hAPP(hAPP(c_Power_Opower__class_Opower(U_3946),U_3947),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_3946),U_3947),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_3946) ),
inference(clausify,[status(thm)],[f_1309_2]) ).
fof(f_1310_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_1310_2,plain,
! [U_3949,U_3948] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3948),hAPP(c_Groups_Oabs__class_Oabs(U_3948),U_3949)),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_3948),U_3949),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_3948) ),
inference(variable_rename,[status(thm)],[f_1310_1]) ).
cnf(f_1310_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3948),hAPP(c_Groups_Oabs__class_Oabs(U_3948),U_3949)),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_3948),U_3949),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_3948) ),
inference(clausify,[status(thm)],[f_1310_2]) ).
fof(f_1311_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]) ).
cnf(f_1311_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(clausify,[status(thm)],[f_1311_1]) ).
fof(f_1312_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_1312_2,plain,
! [U_3950] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_3950)),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_3950,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_1312_1]) ).
cnf(f_1312_3,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_3950)),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_3950,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(clausify,[status(thm)],[f_1312_2]) ).
fof(f_1313_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_1313_2,plain,
! [U_3951] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_3951))),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_3951),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_1313_1]) ).
cnf(f_1313_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_3951))),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_3951),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(clausify,[status(thm)],[f_1313_2]) ).
fof(f_1314_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_1314_2,plain,
! [U_3953,U_3952] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_3952)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_3953))) = hAPP(hAPP(c_Groups_Otimes__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_3952),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3953))),
inference(variable_rename,[status(thm)],[f_1314_1]) ).
cnf(f_1314_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_3952)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_3953))) = hAPP(hAPP(c_Groups_Otimes__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_3952),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3953))),
inference(clausify,[status(thm)],[f_1314_2]) ).
fof(f_1315_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_1315_2,plain,
! [U_3954] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3954),U_3954)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_3954,
inference(variable_rename,[status(thm)],[f_1315_1]) ).
cnf(f_1315_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3954),U_3954)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_3954,
inference(clausify,[status(thm)],[f_1315_2]) ).
fof(f_1316_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_1316_2,plain,
! [U_3956,U_3955] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3955),c_Groups_Ozero__class_Ozero(U_3955)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3955),U_3956),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_3955) ),
inference(variable_rename,[status(thm)],[f_1316_1]) ).
cnf(f_1316_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3955),c_Groups_Ozero__class_Ozero(U_3955)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3955),U_3956),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_3955) ),
inference(clausify,[status(thm)],[f_1316_2]) ).
fof(f_1317_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_1317_2,plain,
! [U_3959,U_3958,U_3957] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),U_3958),U_3959))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3959))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Power_Opower__class_Opower(U_3957),U_3958),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_3957),U_3959),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__semidom(U_3957) ),
inference(variable_rename,[status(thm)],[f_1317_1]) ).
cnf(f_1317_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),U_3958),U_3959))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),c_Groups_Ozero__class_Ozero(U_3957)),U_3959))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3957),hAPP(hAPP(c_Power_Opower__class_Opower(U_3957),U_3958),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_3957),U_3959),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__semidom(U_3957) ),
inference(clausify,[status(thm)],[f_1317_2]) ).
fof(f_1318_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_1318_2,plain,
! [U_3962,U_3961,U_3960] :
( U_3961 = U_3962
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3960),c_Groups_Ozero__class_Ozero(U_3960)),U_3962))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3960),c_Groups_Ozero__class_Ozero(U_3960)),U_3961))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_3960),U_3961),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_3960),U_3962),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__semidom(U_3960) ),
inference(variable_rename,[status(thm)],[f_1318_1]) ).
cnf(f_1318_3,plain,
( U_3961 = U_3962
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3960),c_Groups_Ozero__class_Ozero(U_3960)),U_3962))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3960),c_Groups_Ozero__class_Ozero(U_3960)),U_3961))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_3960),U_3961),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_3960),U_3962),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__semidom(U_3960) ),
inference(clausify,[status(thm)],[f_1318_2]) ).
fof(f_1319_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_1319_2,plain,
! [U_3964,U_3963] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3963),hAPP(hAPP(c_Power_Opower__class_Opower(U_3963),U_3964),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_3963)))
| ~ class_Rings_Olinordered__idom(U_3963) ),
inference(variable_rename,[status(thm)],[f_1319_1]) ).
cnf(f_1319_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3963),hAPP(hAPP(c_Power_Opower__class_Opower(U_3963),U_3964),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_3963)))
| ~ class_Rings_Olinordered__idom(U_3963) ),
inference(clausify,[status(thm)],[f_1319_2]) ).
fof(f_1320_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__power2]) ).
fof(f_1320_2,plain,
! [U_3966,U_3965] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3965),c_Groups_Ozero__class_Ozero(U_3965)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3965),U_3966),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| U_3966 = c_Groups_Ozero__class_Ozero(U_3965) )
& ( U_3966 != c_Groups_Ozero__class_Ozero(U_3965)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3965),c_Groups_Ozero__class_Ozero(U_3965)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3965),U_3966),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
| ~ class_Rings_Olinordered__idom(U_3965) ),
inference(variable_rename,[status(thm)],[f_1320_1]) ).
cnf(f_1320_3,plain,
( U_3966 != c_Groups_Ozero__class_Ozero(U_3965)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3965),c_Groups_Ozero__class_Ozero(U_3965)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3965),U_3966),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_3965) ),
inference(clausify,[status(thm)],[f_1320_2]) ).
cnf(f_1320_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3965),c_Groups_Ozero__class_Ozero(U_3965)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3965),U_3966),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| U_3966 = c_Groups_Ozero__class_Ozero(U_3965)
| ~ class_Rings_Olinordered__idom(U_3965) ),
inference(clausify,[status(thm)],[f_1320_2]) ).
fof(f_1321_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_b)
| V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sum__power2__eq__zero__iff]) ).
fof(f_1321_2,plain,
! [U_3969,U_3968,U_3967] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3967),hAPP(hAPP(c_Power_Opower__class_Opower(U_3967),U_3968),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_3967),U_3969),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_3967)
| U_3969 != c_Groups_Ozero__class_Ozero(U_3967)
| U_3968 != c_Groups_Ozero__class_Ozero(U_3967) )
& ( ( U_3969 = c_Groups_Ozero__class_Ozero(U_3967)
& U_3968 = c_Groups_Ozero__class_Ozero(U_3967) )
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3967),hAPP(hAPP(c_Power_Opower__class_Opower(U_3967),U_3968),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_3967),U_3969),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_3967) ) )
| ~ class_Rings_Olinordered__idom(U_3967) ),
inference(variable_rename,[status(thm)],[f_1321_1]) ).
cnf(f_1321_3,plain,
( U_3968 = c_Groups_Ozero__class_Ozero(U_3967)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3967),hAPP(hAPP(c_Power_Opower__class_Opower(U_3967),U_3968),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_3967),U_3969),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_3967)
| ~ class_Rings_Olinordered__idom(U_3967) ),
inference(clausify,[status(thm)],[f_1321_2]) ).
cnf(f_1321_4,plain,
( U_3969 = c_Groups_Ozero__class_Ozero(U_3967)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3967),hAPP(hAPP(c_Power_Opower__class_Opower(U_3967),U_3968),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_3967),U_3969),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_3967)
| ~ class_Rings_Olinordered__idom(U_3967) ),
inference(clausify,[status(thm)],[f_1321_2]) ).
cnf(f_1321_5,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3967),hAPP(hAPP(c_Power_Opower__class_Opower(U_3967),U_3968),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_3967),U_3969),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_3967)
| U_3969 != c_Groups_Ozero__class_Ozero(U_3967)
| U_3968 != c_Groups_Ozero__class_Ozero(U_3967)
| ~ class_Rings_Olinordered__idom(U_3967) ),
inference(clausify,[status(thm)],[f_1321_2]) ).
fof(f_1322_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_1322_2,plain,
! [U_3971,U_3970] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3970),hAPP(c_Int_Onumber__class_Onumber__of(U_3970),U_3971)),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_3970),hAPP(c_Int_Onumber__class_Onumber__of(U_3970),U_3971)),hAPP(c_Int_Onumber__class_Onumber__of(U_3970),U_3971))
| ~ class_Int_Onumber(U_3970)
| ~ class_Groups_Omonoid__mult(U_3970) ),
inference(variable_rename,[status(thm)],[f_1322_1]) ).
cnf(f_1322_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3970),hAPP(c_Int_Onumber__class_Onumber__of(U_3970),U_3971)),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_3970),hAPP(c_Int_Onumber__class_Onumber__of(U_3970),U_3971)),hAPP(c_Int_Onumber__class_Onumber__of(U_3970),U_3971))
| ~ class_Int_Onumber(U_3970)
| ~ class_Groups_Omonoid__mult(U_3970) ),
inference(clausify,[status(thm)],[f_1322_2]) ).
fof(f_1323_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_1323_2,plain,
! [U_3972] :
( U_3972 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_3972 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3972),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_1323_1]) ).
cnf(f_1323_3,plain,
( U_3972 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_3972 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3972),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(clausify,[status(thm)],[f_1323_2]) ).
fof(f_1324_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]) ).
cnf(f_1324_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(clausify,[status(thm)],[f_1324_1]) ).
fof(f_1325_1,plain,
! [V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_b)
| ( V_a_2 != hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
& V_a_2 != c_Groups_Oone__class_Oone(T_b) ) )
& ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
| V_a_2 = c_Groups_Oone__class_Oone(T_b)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(T_b) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power2__eq__1__iff]) ).
fof(f_1325_2,plain,
! [U_3974,U_3973] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3973),U_3974),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_3973)
| ( U_3974 != hAPP(c_Groups_Ouminus__class_Ouminus(U_3973),c_Groups_Oone__class_Oone(U_3973))
& U_3974 != c_Groups_Oone__class_Oone(U_3973) ) )
& ( U_3974 = hAPP(c_Groups_Ouminus__class_Ouminus(U_3973),c_Groups_Oone__class_Oone(U_3973))
| U_3974 = c_Groups_Oone__class_Oone(U_3973)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_3973),U_3974),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_3973) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_3973) ),
inference(variable_rename,[status(thm)],[f_1325_1]) ).
cnf(f_1325_3,plain,
( U_3974 = hAPP(c_Groups_Ouminus__class_Ouminus(U_3973),c_Groups_Oone__class_Oone(U_3973))
| U_3974 = c_Groups_Oone__class_Oone(U_3973)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_3973),U_3974),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_3973)
| ~ class_Rings_Oring__1__no__zero__divisors(U_3973) ),
inference(clausify,[status(thm)],[f_1325_2]) ).
cnf(f_1325_4,plain,
( U_3974 != c_Groups_Oone__class_Oone(U_3973)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_3973),U_3974),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_3973)
| ~ class_Rings_Oring__1__no__zero__divisors(U_3973) ),
inference(clausify,[status(thm)],[f_1325_2]) ).
cnf(f_1325_5,plain,
( U_3974 != hAPP(c_Groups_Ouminus__class_Ouminus(U_3973),c_Groups_Oone__class_Oone(U_3973))
| hAPP(hAPP(c_Power_Opower__class_Opower(U_3973),U_3974),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_3973)
| ~ class_Rings_Oring__1__no__zero__divisors(U_3973) ),
inference(clausify,[status(thm)],[f_1325_2]) ).
fof(f_1326_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_1326_2,plain,
! [U_3977,U_3976,U_3975] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3975),U_3976),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_3977)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3975),hAPP(hAPP(c_Power_Opower__class_Opower(U_3975),U_3976),U_3977)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3975),U_3976),U_3977))
| ~ class_Rings_Ocomm__semiring__1(U_3975) ),
inference(variable_rename,[status(thm)],[f_1326_1]) ).
cnf(f_1326_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3975),U_3976),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_3977)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3975),hAPP(hAPP(c_Power_Opower__class_Opower(U_3975),U_3976),U_3977)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3975),U_3976),U_3977))
| ~ class_Rings_Ocomm__semiring__1(U_3975) ),
inference(clausify,[status(thm)],[f_1326_2]) ).
fof(f_1327_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_1327_2,plain,
! [U_3980,U_3979,U_3978] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3978),hAPP(c_Groups_Ouminus__class_Ouminus(U_3978),U_3979)),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_3980)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3978),U_3979),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_3980))
| ~ class_Rings_Oring__1(U_3978) ),
inference(variable_rename,[status(thm)],[f_1327_1]) ).
cnf(f_1327_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3978),hAPP(c_Groups_Ouminus__class_Ouminus(U_3978),U_3979)),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_3980)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3978),U_3979),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_3980))
| ~ class_Rings_Oring__1(U_3978) ),
inference(clausify,[status(thm)],[f_1327_2]) ).
fof(f_1328_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_1328_2,plain,
! [U_3983,U_3982,U_3981] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3981),U_3982),U_3983))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3981),c_Groups_Ozero__class_Ozero(U_3981)),U_3983))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3981),hAPP(hAPP(c_Power_Opower__class_Opower(U_3981),U_3982),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_3981),U_3983),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__semidom(U_3981) ),
inference(variable_rename,[status(thm)],[f_1328_1]) ).
cnf(f_1328_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3981),U_3982),U_3983))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3981),c_Groups_Ozero__class_Ozero(U_3981)),U_3983))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3981),hAPP(hAPP(c_Power_Opower__class_Opower(U_3981),U_3982),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_3981),U_3983),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__semidom(U_3981) ),
inference(clausify,[status(thm)],[f_1328_2]) ).
fof(f_1329_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_1329_2,plain,
! [U_3986,U_3985,U_3984] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3984),c_Groups_Ozero__class_Ozero(U_3984)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3984),hAPP(hAPP(c_Power_Opower__class_Opower(U_3984),U_3985),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_3984),U_3986),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(U_3984) ),
inference(variable_rename,[status(thm)],[f_1329_1]) ).
cnf(f_1329_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3984),c_Groups_Ozero__class_Ozero(U_3984)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3984),hAPP(hAPP(c_Power_Opower__class_Opower(U_3984),U_3985),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_3984),U_3986),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(U_3984) ),
inference(clausify,[status(thm)],[f_1329_2]) ).
fof(f_1330_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_b)))
| V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(T_b))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sum__power2__le__zero__iff]) ).
fof(f_1330_2,plain,
! [U_3989,U_3988,U_3987] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3987),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3987),hAPP(hAPP(c_Power_Opower__class_Opower(U_3987),U_3988),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_3987),U_3989),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_3987)))
| U_3989 != c_Groups_Ozero__class_Ozero(U_3987)
| U_3988 != c_Groups_Ozero__class_Ozero(U_3987) )
& ( ( U_3989 = c_Groups_Ozero__class_Ozero(U_3987)
& U_3988 = c_Groups_Ozero__class_Ozero(U_3987) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3987),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3987),hAPP(hAPP(c_Power_Opower__class_Opower(U_3987),U_3988),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_3987),U_3989),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_3987))) ) )
| ~ class_Rings_Olinordered__idom(U_3987) ),
inference(variable_rename,[status(thm)],[f_1330_1]) ).
cnf(f_1330_3,plain,
( U_3988 = c_Groups_Ozero__class_Ozero(U_3987)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3987),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3987),hAPP(hAPP(c_Power_Opower__class_Opower(U_3987),U_3988),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_3987),U_3989),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_3987)))
| ~ class_Rings_Olinordered__idom(U_3987) ),
inference(clausify,[status(thm)],[f_1330_2]) ).
cnf(f_1330_4,plain,
( U_3989 = c_Groups_Ozero__class_Ozero(U_3987)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3987),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3987),hAPP(hAPP(c_Power_Opower__class_Opower(U_3987),U_3988),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_3987),U_3989),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_3987)))
| ~ class_Rings_Olinordered__idom(U_3987) ),
inference(clausify,[status(thm)],[f_1330_2]) ).
cnf(f_1330_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3987),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3987),hAPP(hAPP(c_Power_Opower__class_Opower(U_3987),U_3988),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_3987),U_3989),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_3987)))
| U_3989 != c_Groups_Ozero__class_Ozero(U_3987)
| U_3988 != c_Groups_Ozero__class_Ozero(U_3987)
| ~ class_Rings_Olinordered__idom(U_3987) ),
inference(clausify,[status(thm)],[f_1330_2]) ).
fof(f_1331_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_1331_2,plain,
! [U_3992,U_3991,U_3990] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3990),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3990),hAPP(hAPP(c_Power_Opower__class_Opower(U_3990),U_3991),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_3990),U_3992),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_3990)))
| ~ class_Rings_Olinordered__idom(U_3990) ),
inference(variable_rename,[status(thm)],[f_1331_1]) ).
cnf(f_1331_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3990),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3990),hAPP(hAPP(c_Power_Opower__class_Opower(U_3990),U_3991),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_3990),U_3992),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_3990)))
| ~ class_Rings_Olinordered__idom(U_3990) ),
inference(clausify,[status(thm)],[f_1331_2]) ).
fof(f_1332_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
& ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sum__power2__gt__zero__iff]) ).
fof(f_1332_2,plain,
! [U_3995,U_3994,U_3993] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3993),c_Groups_Ozero__class_Ozero(U_3993)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3993),hAPP(hAPP(c_Power_Opower__class_Opower(U_3993),U_3994),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_3993),U_3995),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ( U_3995 = c_Groups_Ozero__class_Ozero(U_3993)
& U_3994 = c_Groups_Ozero__class_Ozero(U_3993) ) )
& ( U_3995 != c_Groups_Ozero__class_Ozero(U_3993)
| U_3994 != c_Groups_Ozero__class_Ozero(U_3993)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3993),c_Groups_Ozero__class_Ozero(U_3993)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3993),hAPP(hAPP(c_Power_Opower__class_Opower(U_3993),U_3994),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_3993),U_3995),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) )
| ~ class_Rings_Olinordered__idom(U_3993) ),
inference(variable_rename,[status(thm)],[f_1332_1]) ).
cnf(f_1332_3,plain,
( U_3995 != c_Groups_Ozero__class_Ozero(U_3993)
| U_3994 != c_Groups_Ozero__class_Ozero(U_3993)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3993),c_Groups_Ozero__class_Ozero(U_3993)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3993),hAPP(hAPP(c_Power_Opower__class_Opower(U_3993),U_3994),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_3993),U_3995),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(U_3993) ),
inference(clausify,[status(thm)],[f_1332_2]) ).
cnf(f_1332_4,plain,
( U_3994 = c_Groups_Ozero__class_Ozero(U_3993)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3993),c_Groups_Ozero__class_Ozero(U_3993)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3993),hAPP(hAPP(c_Power_Opower__class_Opower(U_3993),U_3994),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_3993),U_3995),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(U_3993) ),
inference(clausify,[status(thm)],[f_1332_2]) ).
cnf(f_1332_5,plain,
( U_3995 = c_Groups_Ozero__class_Ozero(U_3993)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3993),c_Groups_Ozero__class_Ozero(U_3993)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3993),hAPP(hAPP(c_Power_Opower__class_Opower(U_3993),U_3994),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_3993),U_3995),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
| ~ class_Rings_Olinordered__idom(U_3993) ),
inference(clausify,[status(thm)],[f_1332_2]) ).
fof(f_1333_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_1333_2,plain,
! [U_3998,U_3997,U_3996] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3996),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3996),U_3997),U_3998)),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_3996),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3996),hAPP(hAPP(c_Power_Opower__class_Opower(U_3996),U_3997),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_3996),U_3998),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_3996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3996),hAPP(c_Int_Onumber__class_Onumber__of(U_3996),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_3997)),U_3998))
| ~ class_Int_Onumber__ring(U_3996) ),
inference(variable_rename,[status(thm)],[f_1333_1]) ).
cnf(f_1333_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_3996),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3996),U_3997),U_3998)),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_3996),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3996),hAPP(hAPP(c_Power_Opower__class_Opower(U_3996),U_3997),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_3996),U_3998),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_3996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3996),hAPP(c_Int_Onumber__class_Onumber__of(U_3996),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_3997)),U_3998))
| ~ class_Int_Onumber__ring(U_3996) ),
inference(clausify,[status(thm)],[f_1333_2]) ).
fof(f_1334_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_1334_2,plain,
! [U_4001,U_4000,U_3999] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3999),c_Groups_Ozero__class_Ozero(U_3999)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3999),U_4000),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_4001))))
| ~ class_Rings_Olinordered__idom(U_3999) ),
inference(variable_rename,[status(thm)],[f_1334_1]) ).
cnf(f_1334_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3999),c_Groups_Ozero__class_Ozero(U_3999)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3999),U_4000),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_4001))))
| ~ class_Rings_Olinordered__idom(U_3999) ),
inference(clausify,[status(thm)],[f_1334_2]) ).
fof(f_1335_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_1335_2,plain,
! [U_4004,U_4003,U_4002] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4002),U_4003),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_4004))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4002),U_4003),hAPP(hAPP(c_Power_Opower__class_Opower(U_4002),hAPP(hAPP(c_Power_Opower__class_Opower(U_4002),U_4003),U_4004)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Groups_Omonoid__mult(U_4002) ),
inference(variable_rename,[status(thm)],[f_1335_1]) ).
cnf(f_1335_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4002),U_4003),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_4004))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4002),U_4003),hAPP(hAPP(c_Power_Opower__class_Opower(U_4002),hAPP(hAPP(c_Power_Opower__class_Opower(U_4002),U_4003),U_4004)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Groups_Omonoid__mult(U_4002) ),
inference(clausify,[status(thm)],[f_1335_2]) ).
fof(f_1336_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_1336_2,plain,
! [U_4007,U_4006,U_4005] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4005),U_4006),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_4007))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4005),U_4006),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4005),hAPP(hAPP(c_Power_Opower__class_Opower(U_4005),U_4006),U_4007)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4005),U_4006),U_4007)))
| ~ class_Rings_Ocomm__semiring__1(U_4005) ),
inference(variable_rename,[status(thm)],[f_1336_1]) ).
cnf(f_1336_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4005),U_4006),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_4007))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4005),U_4006),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4005),hAPP(hAPP(c_Power_Opower__class_Opower(U_4005),U_4006),U_4007)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4005),U_4006),U_4007)))
| ~ class_Rings_Ocomm__semiring__1(U_4005) ),
inference(clausify,[status(thm)],[f_1336_2]) ).
fof(f_1337_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_1337_2,plain,
! [U_4009,U_4008] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4008),hAPP(c_Groups_Ouminus__class_Ouminus(U_4008),c_Groups_Oone__class_Oone(U_4008))),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_4009)) = c_Groups_Oone__class_Oone(U_4008)
| ~ class_Rings_Oring__1(U_4008) ),
inference(variable_rename,[status(thm)],[f_1337_1]) ).
cnf(f_1337_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4008),hAPP(c_Groups_Ouminus__class_Ouminus(U_4008),c_Groups_Oone__class_Oone(U_4008))),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_4009)) = c_Groups_Oone__class_Oone(U_4008)
| ~ class_Rings_Oring__1(U_4008) ),
inference(clausify,[status(thm)],[f_1337_2]) ).
fof(f_1338_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_1338_2,plain,
! [U_4011,U_4010] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4011))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4010))) = 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_4011)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4010))
| 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_4010))) )
& ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4011))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4010))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4011)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4010))
| ~ 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_4010))) ) ),
inference(variable_rename,[status(thm)],[f_1338_1]) ).
fof(f_1338_3,plain,
( ! [U_4015,U_4013] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4015))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4013))) = 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_4015)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4013))
| 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_4013))) )
& ! [U_4014,U_4012] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_4014))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4012))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4014)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4012))
| ~ 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_4012))) ) ),
inference(miniscope,[status(thm)],[f_1338_2]) ).
cnf(f_1338_4,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_4014))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4012))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4014)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4012))
| ~ 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_4012))) ),
inference(clausify,[status(thm)],[f_1338_3]) ).
cnf(f_1338_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_4015))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_4013))) = 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_4015)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4013))
| 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_4013))) ),
inference(clausify,[status(thm)],[f_1338_3]) ).
fof(f_1339_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_1339_2,plain,
! [U_4016] :
( ( 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_4016,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_4016,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_4016,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_4016,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_1339_1]) ).
fof(f_1339_3,plain,
( ! [U_4018] :
( 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_4018,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_4018,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_4017] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4017,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_4017,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
inference(miniscope,[status(thm)],[f_1339_2]) ).
cnf(f_1339_4,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4017,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_4017,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
inference(clausify,[status(thm)],[f_1339_3]) ).
cnf(f_1339_5,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_4018,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_4018,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_1339_3]) ).
fof(f_1340_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_1340_2,plain,
! [U_4019] :
( 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_4019),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_4019)) ),
inference(variable_rename,[status(thm)],[f_1340_1]) ).
cnf(f_1340_3,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_4019),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_4019)) ),
inference(clausify,[status(thm)],[f_1340_2]) ).
fof(f_1341_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_1341_2,plain,
! [U_4022,U_4021,U_4020] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4020),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4020),U_4021),U_4022)),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_4020),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4020),hAPP(hAPP(c_Power_Opower__class_Opower(U_4020),U_4021),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_4020),U_4022),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_4020),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4020),hAPP(c_Int_Onumber__class_Onumber__of(U_4020),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4021)),U_4022))
| ~ class_Int_Onumber__ring(U_4020) ),
inference(variable_rename,[status(thm)],[f_1341_1]) ).
cnf(f_1341_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4020),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4020),U_4021),U_4022)),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_4020),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4020),hAPP(hAPP(c_Power_Opower__class_Opower(U_4020),U_4021),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_4020),U_4022),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_4020),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4020),hAPP(c_Int_Onumber__class_Onumber__of(U_4020),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4021)),U_4022))
| ~ class_Int_Onumber__ring(U_4020) ),
inference(clausify,[status(thm)],[f_1341_2]) ).
fof(f_1342_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_1342_2,plain,
! [U_4025,U_4024,U_4023] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4023),c_Groups_Ozero__class_Ozero(U_4023)),U_4024))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4023),c_Groups_Ozero__class_Ozero(U_4023)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4023),U_4024),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_4025)))))
| ~ class_Rings_Olinordered__idom(U_4023) ),
inference(variable_rename,[status(thm)],[f_1342_1]) ).
cnf(f_1342_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4023),c_Groups_Ozero__class_Ozero(U_4023)),U_4024))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4023),c_Groups_Ozero__class_Ozero(U_4023)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4023),U_4024),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_4025)))))
| ~ class_Rings_Olinordered__idom(U_4023) ),
inference(clausify,[status(thm)],[f_1342_2]) ).
fof(f_1343_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_1343_2,plain,
! [U_4028,U_4027,U_4026] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4026),hAPP(hAPP(c_Power_Opower__class_Opower(U_4026),U_4027),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_4028)))),c_Groups_Ozero__class_Ozero(U_4026)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4026),U_4027),c_Groups_Ozero__class_Ozero(U_4026)))
| ~ class_Rings_Olinordered__idom(U_4026) ),
inference(variable_rename,[status(thm)],[f_1343_1]) ).
cnf(f_1343_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4026),hAPP(hAPP(c_Power_Opower__class_Opower(U_4026),U_4027),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_4028)))),c_Groups_Ozero__class_Ozero(U_4026)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4026),U_4027),c_Groups_Ozero__class_Ozero(U_4026)))
| ~ class_Rings_Olinordered__idom(U_4026) ),
inference(clausify,[status(thm)],[f_1343_2]) ).
fof(f_1344_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_1344_2,plain,
! [U_4030,U_4029] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4029),hAPP(c_Groups_Ouminus__class_Ouminus(U_4029),c_Groups_Oone__class_Oone(U_4029))),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_4030))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4029),c_Groups_Oone__class_Oone(U_4029))
| ~ class_Rings_Oring__1(U_4029) ),
inference(variable_rename,[status(thm)],[f_1344_1]) ).
cnf(f_1344_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4029),hAPP(c_Groups_Ouminus__class_Ouminus(U_4029),c_Groups_Oone__class_Oone(U_4029))),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_4030))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4029),c_Groups_Oone__class_Oone(U_4029))
| ~ class_Rings_Oring__1(U_4029) ),
inference(clausify,[status(thm)],[f_1344_2]) ).
fof(f_1345_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_1345_2,plain,
! [U_4032,U_4031] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4031),hAPP(c_Int_Onumber__class_Onumber__of(U_4031),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_4032)) = c_Groups_Oone__class_Oone(U_4031)
| ~ class_Int_Onumber__ring(U_4031) ),
inference(variable_rename,[status(thm)],[f_1345_1]) ).
cnf(f_1345_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4031),hAPP(c_Int_Onumber__class_Onumber__of(U_4031),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_4032)) = c_Groups_Oone__class_Oone(U_4031)
| ~ class_Int_Onumber__ring(U_4031) ),
inference(clausify,[status(thm)],[f_1345_2]) ).
fof(f_1346_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_1346_2,plain,
! [U_4034,U_4033] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4033),hAPP(c_Int_Onumber__class_Onumber__of(U_4033),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_4034))) = hAPP(c_Int_Onumber__class_Onumber__of(U_4033),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_4033) ),
inference(variable_rename,[status(thm)],[f_1346_1]) ).
cnf(f_1346_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4033),hAPP(c_Int_Onumber__class_Onumber__of(U_4033),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_4034))) = hAPP(c_Int_Onumber__class_Onumber__of(U_4033),c_Int_OMin)
| ~ class_Int_Onumber__ring(U_4033) ),
inference(clausify,[status(thm)],[f_1346_2]) ).
fof(f_1347_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_1347_2,plain,
! [U_4035] :
( ( ( ( hAPP(c_Code__Numeral_Oint__of,U_4035) = 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_4035),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_4035,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_4035) = hAPP(hAPP(c_Groups_Otimes__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_4035),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_4035,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_4035 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( hAPP(c_Code__Numeral_Oint__of,U_4035) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_4035 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(variable_rename,[status(thm)],[f_1347_1]) ).
fof(f_1347_3,plain,
( ! [U_4037] :
( ( ( hAPP(c_Code__Numeral_Oint__of,U_4037) = 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_4037),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_4037,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_4037) = hAPP(hAPP(c_Groups_Otimes__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_4037),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_4037,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_4037 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ! [U_4036] :
( hAPP(c_Code__Numeral_Oint__of,U_4036) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_4036 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(miniscope,[status(thm)],[f_1347_2]) ).
cnf(f_1347_4,plain,
( hAPP(c_Code__Numeral_Oint__of,U_4036) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_4036 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_1347_3]) ).
cnf(f_1347_5,plain,
( hAPP(c_Code__Numeral_Oint__of,U_4037) = hAPP(hAPP(c_Groups_Otimes__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_4037),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_4037,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_4037 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_1347_3]) ).
cnf(f_1347_6,plain,
( hAPP(c_Code__Numeral_Oint__of,U_4037) = 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_4037),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_4037,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_4037 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_1347_3]) ).
fof(f_1348_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]) ).
cnf(f_1348_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(clausify,[status(thm)],[f_1348_1]) ).
fof(f_1349_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_1349_2,plain,
! [U_4039,U_4038] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4038),c_Groups_Ozero__class_Ozero(U_4038)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4038),U_4039),hAPP(c_Int_Onumber__class_Onumber__of(U_4038),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4038),c_Groups_Ozero__class_Ozero(U_4038)),U_4039))
| ~ class_Int_Onumber__ring(U_4038)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4038) ),
inference(variable_rename,[status(thm)],[f_1349_1]) ).
cnf(f_1349_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4038),c_Groups_Ozero__class_Ozero(U_4038)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4038),U_4039),hAPP(c_Int_Onumber__class_Onumber__of(U_4038),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4038),c_Groups_Ozero__class_Ozero(U_4038)),U_4039))
| ~ class_Int_Onumber__ring(U_4038)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4038) ),
inference(clausify,[status(thm)],[f_1349_2]) ).
fof(f_1350_1,plain,
! [V_r_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
| ~ class_Int_Onumber__ring(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_half__gt__zero__iff]) ).
fof(f_1350_2,plain,
! [U_4041,U_4040] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4040),c_Groups_Ozero__class_Ozero(U_4040)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4040),U_4041),hAPP(c_Int_Onumber__class_Onumber__of(U_4040),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4040),c_Groups_Ozero__class_Ozero(U_4040)),U_4041)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4040),c_Groups_Ozero__class_Ozero(U_4040)),U_4041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4040),c_Groups_Ozero__class_Ozero(U_4040)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4040),U_4041),hAPP(c_Int_Onumber__class_Onumber__of(U_4040),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
| ~ class_Int_Onumber__ring(U_4040)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4040) ),
inference(variable_rename,[status(thm)],[f_1350_1]) ).
cnf(f_1350_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4040),c_Groups_Ozero__class_Ozero(U_4040)),U_4041))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4040),c_Groups_Ozero__class_Ozero(U_4040)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4040),U_4041),hAPP(c_Int_Onumber__class_Onumber__of(U_4040),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Int_Onumber__ring(U_4040)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4040) ),
inference(clausify,[status(thm)],[f_1350_2]) ).
cnf(f_1350_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4040),c_Groups_Ozero__class_Ozero(U_4040)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4040),U_4041),hAPP(c_Int_Onumber__class_Onumber__of(U_4040),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4040),c_Groups_Ozero__class_Ozero(U_4040)),U_4041))
| ~ class_Int_Onumber__ring(U_4040)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4040) ),
inference(clausify,[status(thm)],[f_1350_2]) ).
fof(f_1351_1,plain,
! [V_k_2,V_f_2,V_na_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_na_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_na_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_na_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat0__intermed__int__val]) ).
fof(f_1351_2,plain,
! [U_4046,U_4045,U_4044] :
( ? [U_4043] :
( hAPP(U_4045,U_4043) = U_4046
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4043),U_4044)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4046),hAPP(U_4045,U_4044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4045,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4046))
| ? [U_4042] :
( ~ 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_4045,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4042),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4045,U_4042)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4042),U_4044)) ) ),
inference(variable_rename,[status(thm)],[f_1351_1]) ).
fof(f_1351_3,plain,
! [U_4046,U_4045,U_4044] :
( ? [U_4043] :
( hAPP(U_4045,U_4043) = U_4046
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4043),U_4044)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4046),hAPP(U_4045,U_4044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4045,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4046))
| ( ~ 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_4045,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK57(U_4046,U_4045,U_4044)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4045,sK57(U_4046,U_4045,U_4044))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK57(U_4046,U_4045,U_4044)),U_4044)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_4042,sK57(U_4046,U_4045,U_4044))],[f_1351_2]) ).
fof(f_1351_4,plain,
! [U_4046,U_4045,U_4044] :
( ( hAPP(U_4045,sK58(U_4046,U_4045,U_4044)) = U_4046
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK58(U_4046,U_4045,U_4044)),U_4044)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4046),hAPP(U_4045,U_4044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4045,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4046))
| ( ~ 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_4045,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK57(U_4046,U_4045,U_4044)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4045,sK57(U_4046,U_4045,U_4044))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK57(U_4046,U_4045,U_4044)),U_4044)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_4043,sK58(U_4046,U_4045,U_4044))],[f_1351_3]) ).
cnf(f_1351_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK58(U_4046,U_4045,U_4044)),U_4044))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4046),hAPP(U_4045,U_4044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4045,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4046))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK57(U_4046,U_4045,U_4044)),U_4044)) ),
inference(clausify,[status(thm)],[f_1351_4]) ).
cnf(f_1351_6,plain,
( hAPP(U_4045,sK58(U_4046,U_4045,U_4044)) = U_4046
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4046),hAPP(U_4045,U_4044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4045,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4046))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK57(U_4046,U_4045,U_4044)),U_4044)) ),
inference(clausify,[status(thm)],[f_1351_4]) ).
cnf(f_1351_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK58(U_4046,U_4045,U_4044)),U_4044))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4046),hAPP(U_4045,U_4044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4045,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4046))
| ~ 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_4045,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK57(U_4046,U_4045,U_4044)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4045,sK57(U_4046,U_4045,U_4044))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1351_4]) ).
cnf(f_1351_8,plain,
( hAPP(U_4045,sK58(U_4046,U_4045,U_4044)) = U_4046
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4046),hAPP(U_4045,U_4044)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4045,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4046))
| ~ 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_4045,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK57(U_4046,U_4045,U_4044)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4045,sK57(U_4046,U_4045,U_4044))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1351_4]) ).
fof(f_1352_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]) ).
cnf(f_1352_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(clausify,[status(thm)],[f_1352_1]) ).
fof(f_1353_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_1353_2,plain,
! [U_4050,U_4049,U_4048] :
( ? [U_4047] : U_4048 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4050),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4049),U_4047))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4050),U_4048))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4048,U_4049) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4050,U_4049) ),
inference(variable_rename,[status(thm)],[f_1353_1]) ).
fof(f_1353_3,plain,
! [U_4050,U_4049,U_4048] :
( U_4048 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4050),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4049),sK59(U_4050,U_4049,U_4048)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4050),U_4048))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4048,U_4049) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4050,U_4049) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_4047,sK59(U_4050,U_4049,U_4048))],[f_1353_2]) ).
cnf(f_1353_4,plain,
( U_4048 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4050),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4049),sK59(U_4050,U_4049,U_4048)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4050),U_4048))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4048,U_4049) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4050,U_4049) ),
inference(clausify,[status(thm)],[f_1353_3]) ).
fof(f_1354_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]) ).
cnf(f_1354_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(clausify,[status(thm)],[f_1354_1]) ).
fof(f_1355_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_1355_2,plain,
! [U_4052,U_4051] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4051),U_4052),c_Groups_Ozero__class_Ozero(U_4051)) = c_Groups_Ozero__class_Ozero(U_4051)
| ~ class_Rings_Odivision__ring__inverse__zero(U_4051) ),
inference(variable_rename,[status(thm)],[f_1355_1]) ).
cnf(f_1355_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4051),U_4052),c_Groups_Ozero__class_Ozero(U_4051)) = c_Groups_Ozero__class_Ozero(U_4051)
| ~ class_Rings_Odivision__ring__inverse__zero(U_4051) ),
inference(clausify,[status(thm)],[f_1355_2]) ).
fof(f_1356_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_1356_2,plain,
! [U_4054,U_4053] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4053),c_Groups_Ozero__class_Ozero(U_4053)),U_4054) = c_Groups_Ozero__class_Ozero(U_4053)
| ~ class_Rings_Odivision__ring(U_4053) ),
inference(variable_rename,[status(thm)],[f_1356_1]) ).
cnf(f_1356_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4053),c_Groups_Ozero__class_Ozero(U_4053)),U_4054) = c_Groups_Ozero__class_Ozero(U_4053)
| ~ class_Rings_Odivision__ring(U_4053) ),
inference(clausify,[status(thm)],[f_1356_2]) ).
fof(f_1357_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_1357_2,plain,
! [U_4058,U_4057,U_4056,U_4055] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4055),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4055),U_4056),U_4057)),U_4058) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4055),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4055),U_4056),U_4058)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4055),U_4057),U_4058))
| ~ class_Rings_Odivision__ring(U_4055) ),
inference(variable_rename,[status(thm)],[f_1357_1]) ).
cnf(f_1357_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4055),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4055),U_4056),U_4057)),U_4058) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4055),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4055),U_4056),U_4058)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4055),U_4057),U_4058))
| ~ class_Rings_Odivision__ring(U_4055) ),
inference(clausify,[status(thm)],[f_1357_2]) ).
fof(f_1358_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_1358_2,plain,
! [U_4062,U_4061,U_4060,U_4059] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4059),U_4060),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4059),U_4061),U_4062)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4059),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4059),U_4060),U_4061)),U_4062)
| ~ class_Rings_Odivision__ring(U_4059) ),
inference(variable_rename,[status(thm)],[f_1358_1]) ).
cnf(f_1358_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4059),U_4060),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4059),U_4061),U_4062)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4059),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4059),U_4060),U_4061)),U_4062)
| ~ class_Rings_Odivision__ring(U_4059) ),
inference(clausify,[status(thm)],[f_1358_2]) ).
fof(f_1359_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_1359_2,plain,
! [U_4067,U_4066,U_4065,U_4064,U_4063] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4063),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4063),U_4064),U_4065)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4063),U_4066),U_4067)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4063),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4063),U_4064),U_4066)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4063),U_4065),U_4067))
| ~ class_Fields_Ofield__inverse__zero(U_4063) ),
inference(variable_rename,[status(thm)],[f_1359_1]) ).
cnf(f_1359_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4063),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4063),U_4064),U_4065)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4063),U_4066),U_4067)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4063),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4063),U_4064),U_4066)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4063),U_4065),U_4067))
| ~ class_Fields_Ofield__inverse__zero(U_4063) ),
inference(clausify,[status(thm)],[f_1359_2]) ).
fof(f_1360_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_1360_2,plain,
! [U_4071,U_4070,U_4069,U_4068] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4068),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4068),U_4069),U_4070)),U_4071) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4068),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4068),U_4069),U_4071)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4068),U_4070),U_4071))
| ~ class_Rings_Odivision__ring(U_4068) ),
inference(variable_rename,[status(thm)],[f_1360_1]) ).
cnf(f_1360_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4068),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4068),U_4069),U_4070)),U_4071) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4068),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4068),U_4069),U_4071)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4068),U_4070),U_4071))
| ~ class_Rings_Odivision__ring(U_4068) ),
inference(clausify,[status(thm)],[f_1360_2]) ).
fof(f_1361_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_1361_2,plain,
! [U_4073,U_4072] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4072),U_4073),c_Groups_Oone__class_Oone(U_4072)) = U_4073
| ~ class_Rings_Odivision__ring(U_4072) ),
inference(variable_rename,[status(thm)],[f_1361_1]) ).
cnf(f_1361_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4072),U_4073),c_Groups_Oone__class_Oone(U_4072)) = U_4073
| ~ class_Rings_Odivision__ring(U_4072) ),
inference(clausify,[status(thm)],[f_1361_2]) ).
fof(f_1362_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_1362_2,plain,
! [U_4076,U_4075,U_4074] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4074),U_4075),U_4076)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4074),hAPP(c_Groups_Ouminus__class_Ouminus(U_4074),U_4075)),U_4076)
| ~ class_Rings_Odivision__ring(U_4074) ),
inference(variable_rename,[status(thm)],[f_1362_1]) ).
cnf(f_1362_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4074),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4074),U_4075),U_4076)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4074),hAPP(c_Groups_Ouminus__class_Ouminus(U_4074),U_4075)),U_4076)
| ~ class_Rings_Odivision__ring(U_4074) ),
inference(clausify,[status(thm)],[f_1362_2]) ).
fof(f_1363_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_1363_2,plain,
! [U_4079,U_4078,U_4077] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4077),hAPP(c_Groups_Ouminus__class_Ouminus(U_4077),U_4078)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4077),U_4079)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4077),U_4078),U_4079)
| ~ class_Fields_Ofield__inverse__zero(U_4077) ),
inference(variable_rename,[status(thm)],[f_1363_1]) ).
cnf(f_1363_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4077),hAPP(c_Groups_Ouminus__class_Ouminus(U_4077),U_4078)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4077),U_4079)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4077),U_4078),U_4079)
| ~ class_Fields_Ofield__inverse__zero(U_4077) ),
inference(clausify,[status(thm)],[f_1363_2]) ).
fof(f_1364_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_1364_2,plain,
! [U_4082,U_4081,U_4080] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4080),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4080),U_4081),U_4082)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4080),U_4081),hAPP(c_Groups_Ouminus__class_Ouminus(U_4080),U_4082))
| ~ class_Fields_Ofield__inverse__zero(U_4080) ),
inference(variable_rename,[status(thm)],[f_1364_1]) ).
cnf(f_1364_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4080),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4080),U_4081),U_4082)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4080),U_4081),hAPP(c_Groups_Ouminus__class_Ouminus(U_4080),U_4082))
| ~ class_Fields_Ofield__inverse__zero(U_4080) ),
inference(clausify,[status(thm)],[f_1364_2]) ).
fof(f_1365_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_1365_2,plain,
! [U_4086,U_4085,U_4084,U_4083] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4083),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4083),U_4084),U_4085)),U_4086) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4083),hAPP(hAPP(c_Power_Opower__class_Opower(U_4083),U_4084),U_4086)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4083),U_4085),U_4086))
| ~ class_Fields_Ofield__inverse__zero(U_4083) ),
inference(variable_rename,[status(thm)],[f_1365_1]) ).
cnf(f_1365_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4083),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4083),U_4084),U_4085)),U_4086) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4083),hAPP(hAPP(c_Power_Opower__class_Opower(U_4083),U_4084),U_4086)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4083),U_4085),U_4086))
| ~ class_Fields_Ofield__inverse__zero(U_4083) ),
inference(clausify,[status(thm)],[f_1365_2]) ).
fof(f_1366_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_1366_2,plain,
! [U_4089,U_4088,U_4087] :
( hAPP(c_Groups_Oabs__class_Oabs(U_4087),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4087),U_4088),U_4089)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4087),hAPP(c_Groups_Oabs__class_Oabs(U_4087),U_4088)),hAPP(c_Groups_Oabs__class_Oabs(U_4087),U_4089))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4087) ),
inference(variable_rename,[status(thm)],[f_1366_1]) ).
cnf(f_1366_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_4087),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4087),U_4088),U_4089)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4087),hAPP(c_Groups_Oabs__class_Oabs(U_4087),U_4088)),hAPP(c_Groups_Oabs__class_Oabs(U_4087),U_4089))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4087) ),
inference(clausify,[status(thm)],[f_1366_2]) ).
fof(f_1367_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]) ).
cnf(f_1367_2,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_1367_1]) ).
fof(f_1368_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_1368_2,plain,
! [U_4091,U_4090] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4090),U_4091))
| ~ c_Nat__Transfer_Ois__nat(U_4091)
| ~ c_Nat__Transfer_Ois__nat(U_4090) ),
inference(variable_rename,[status(thm)],[f_1368_1]) ).
cnf(f_1368_3,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4090),U_4091))
| ~ c_Nat__Transfer_Ois__nat(U_4091)
| ~ c_Nat__Transfer_Ois__nat(U_4090) ),
inference(clausify,[status(thm)],[f_1368_2]) ).
fof(f_1369_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_1369_2,plain,
! [U_4092] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4092)),
inference(variable_rename,[status(thm)],[f_1369_1]) ).
cnf(f_1369_3,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4092)),
inference(clausify,[status(thm)],[f_1369_2]) ).
fof(f_1370_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]) ).
cnf(f_1370_2,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(clausify,[status(thm)],[f_1370_1]) ).
fof(f_1371_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_1371_2,plain,
! [U_4094,U_4093] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4093),U_4094))
| ~ c_Nat__Transfer_Ois__nat(U_4094)
| ~ c_Nat__Transfer_Ois__nat(U_4093) ),
inference(variable_rename,[status(thm)],[f_1371_1]) ).
cnf(f_1371_3,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4093),U_4094))
| ~ c_Nat__Transfer_Ois__nat(U_4094)
| ~ c_Nat__Transfer_Ois__nat(U_4093) ),
inference(clausify,[status(thm)],[f_1371_2]) ).
fof(f_1372_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_1372_2,plain,
! [U_4096,U_4095] :
( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4095,U_4096))
| ~ c_Nat__Transfer_Ois__nat(U_4096)
| ~ c_Nat__Transfer_Ois__nat(U_4095) ),
inference(variable_rename,[status(thm)],[f_1372_1]) ).
cnf(f_1372_3,plain,
( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4095,U_4096))
| ~ c_Nat__Transfer_Ois__nat(U_4096)
| ~ c_Nat__Transfer_Ois__nat(U_4095) ),
inference(clausify,[status(thm)],[f_1372_2]) ).
fof(f_1373_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_1373_2,plain,
! [U_4098,U_4097] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4097),U_4098))
| ~ c_Nat__Transfer_Ois__nat(U_4098)
| ~ c_Nat__Transfer_Ois__nat(U_4097) ),
inference(variable_rename,[status(thm)],[f_1373_1]) ).
cnf(f_1373_3,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4097),U_4098))
| ~ c_Nat__Transfer_Ois__nat(U_4098)
| ~ c_Nat__Transfer_Ois__nat(U_4097) ),
inference(clausify,[status(thm)],[f_1373_2]) ).
fof(f_1374_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_1374_2,plain,
! [U_4100,U_4099] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4099),U_4100))
| ~ c_Nat__Transfer_Ois__nat(U_4099) ),
inference(variable_rename,[status(thm)],[f_1374_1]) ).
cnf(f_1374_3,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4099),U_4100))
| ~ c_Nat__Transfer_Ois__nat(U_4099) ),
inference(clausify,[status(thm)],[f_1374_2]) ).
fof(f_1375_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_1375_2,plain,
! [U_4104,U_4103,U_4102,U_4101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4101),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4101),U_4103),U_4104)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4101),U_4102),U_4104)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4101),U_4104),c_Groups_Ozero__class_Ozero(U_4101)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4101),U_4102),U_4103))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4101) ),
inference(variable_rename,[status(thm)],[f_1375_1]) ).
cnf(f_1375_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4101),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4101),U_4103),U_4104)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4101),U_4102),U_4104)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4101),U_4104),c_Groups_Ozero__class_Ozero(U_4101)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4101),U_4102),U_4103))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4101) ),
inference(clausify,[status(thm)],[f_1375_2]) ).
fof(f_1376_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_1376_2,plain,
! [U_4108,U_4107,U_4106,U_4105] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4105),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4105),U_4106),U_4108)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4105),U_4107),U_4108)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4105),c_Groups_Ozero__class_Ozero(U_4105)),U_4108))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4105),U_4106),U_4107))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4105) ),
inference(variable_rename,[status(thm)],[f_1376_1]) ).
cnf(f_1376_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4105),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4105),U_4106),U_4108)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4105),U_4107),U_4108)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4105),c_Groups_Ozero__class_Ozero(U_4105)),U_4108))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4105),U_4106),U_4107))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4105) ),
inference(clausify,[status(thm)],[f_1376_2]) ).
fof(f_1377_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__0__iff]) ).
fof(f_1377_2,plain,
! [U_4111,U_4110,U_4109] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4109),U_4110),U_4111)),c_Groups_Ozero__class_Ozero(U_4109)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),c_Groups_Ozero__class_Ozero(U_4109)),U_4111))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),U_4110),c_Groups_Ozero__class_Ozero(U_4109))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),U_4111),c_Groups_Ozero__class_Ozero(U_4109)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),c_Groups_Ozero__class_Ozero(U_4109)),U_4110)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),c_Groups_Ozero__class_Ozero(U_4109)),U_4111))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),U_4110),c_Groups_Ozero__class_Ozero(U_4109))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),U_4111),c_Groups_Ozero__class_Ozero(U_4109)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),c_Groups_Ozero__class_Ozero(U_4109)),U_4110)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4109),U_4110),U_4111)),c_Groups_Ozero__class_Ozero(U_4109))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_4109) ),
inference(variable_rename,[status(thm)],[f_1377_1]) ).
cnf(f_1377_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),U_4110),c_Groups_Ozero__class_Ozero(U_4109)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),c_Groups_Ozero__class_Ozero(U_4109)),U_4110))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4109),U_4110),U_4111)),c_Groups_Ozero__class_Ozero(U_4109)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4109) ),
inference(clausify,[status(thm)],[f_1377_2]) ).
cnf(f_1377_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),c_Groups_Ozero__class_Ozero(U_4109)),U_4111))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),c_Groups_Ozero__class_Ozero(U_4109)),U_4110))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4109),U_4110),U_4111)),c_Groups_Ozero__class_Ozero(U_4109)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4109) ),
inference(clausify,[status(thm)],[f_1377_2]) ).
cnf(f_1377_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),U_4110),c_Groups_Ozero__class_Ozero(U_4109)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),U_4111),c_Groups_Ozero__class_Ozero(U_4109)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4109),U_4110),U_4111)),c_Groups_Ozero__class_Ozero(U_4109)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4109) ),
inference(clausify,[status(thm)],[f_1377_2]) ).
cnf(f_1377_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),c_Groups_Ozero__class_Ozero(U_4109)),U_4111))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),U_4111),c_Groups_Ozero__class_Ozero(U_4109)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4109),U_4110),U_4111)),c_Groups_Ozero__class_Ozero(U_4109)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4109) ),
inference(clausify,[status(thm)],[f_1377_2]) ).
cnf(f_1377_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),U_4111),c_Groups_Ozero__class_Ozero(U_4109)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),c_Groups_Ozero__class_Ozero(U_4109)),U_4110))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4109),U_4110),U_4111)),c_Groups_Ozero__class_Ozero(U_4109)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4109) ),
inference(clausify,[status(thm)],[f_1377_2]) ).
cnf(f_1377_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),c_Groups_Ozero__class_Ozero(U_4109)),U_4111))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),U_4110),c_Groups_Ozero__class_Ozero(U_4109)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4109),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4109),U_4110),U_4111)),c_Groups_Ozero__class_Ozero(U_4109)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4109) ),
inference(clausify,[status(thm)],[f_1377_2]) ).
fof(f_1378_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__divide__iff]) ).
fof(f_1378_2,plain,
! [U_4114,U_4113,U_4112] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),c_Groups_Ozero__class_Ozero(U_4112)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4112),U_4113),U_4114)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),U_4114),c_Groups_Ozero__class_Ozero(U_4112)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),U_4113),c_Groups_Ozero__class_Ozero(U_4112))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),c_Groups_Ozero__class_Ozero(U_4112)),U_4114))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),c_Groups_Ozero__class_Ozero(U_4112)),U_4113)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),U_4114),c_Groups_Ozero__class_Ozero(U_4112)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),U_4113),c_Groups_Ozero__class_Ozero(U_4112))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),c_Groups_Ozero__class_Ozero(U_4112)),U_4114))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),c_Groups_Ozero__class_Ozero(U_4112)),U_4113)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),c_Groups_Ozero__class_Ozero(U_4112)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4112),U_4113),U_4114))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_4112) ),
inference(variable_rename,[status(thm)],[f_1378_1]) ).
cnf(f_1378_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),U_4113),c_Groups_Ozero__class_Ozero(U_4112)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),c_Groups_Ozero__class_Ozero(U_4112)),U_4113))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),c_Groups_Ozero__class_Ozero(U_4112)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4112),U_4113),U_4114)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4112) ),
inference(clausify,[status(thm)],[f_1378_2]) ).
cnf(f_1378_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),U_4114),c_Groups_Ozero__class_Ozero(U_4112)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),c_Groups_Ozero__class_Ozero(U_4112)),U_4113))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),c_Groups_Ozero__class_Ozero(U_4112)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4112),U_4113),U_4114)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4112) ),
inference(clausify,[status(thm)],[f_1378_2]) ).
cnf(f_1378_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),U_4113),c_Groups_Ozero__class_Ozero(U_4112)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),c_Groups_Ozero__class_Ozero(U_4112)),U_4114))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),c_Groups_Ozero__class_Ozero(U_4112)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4112),U_4113),U_4114)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4112) ),
inference(clausify,[status(thm)],[f_1378_2]) ).
cnf(f_1378_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),U_4114),c_Groups_Ozero__class_Ozero(U_4112)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),c_Groups_Ozero__class_Ozero(U_4112)),U_4114))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),c_Groups_Ozero__class_Ozero(U_4112)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4112),U_4113),U_4114)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4112) ),
inference(clausify,[status(thm)],[f_1378_2]) ).
cnf(f_1378_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),c_Groups_Ozero__class_Ozero(U_4112)),U_4114))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),c_Groups_Ozero__class_Ozero(U_4112)),U_4113))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),c_Groups_Ozero__class_Ozero(U_4112)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4112),U_4113),U_4114)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4112) ),
inference(clausify,[status(thm)],[f_1378_2]) ).
cnf(f_1378_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),U_4114),c_Groups_Ozero__class_Ozero(U_4112)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),U_4113),c_Groups_Ozero__class_Ozero(U_4112)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4112),c_Groups_Ozero__class_Ozero(U_4112)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4112),U_4113),U_4114)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4112) ),
inference(clausify,[status(thm)],[f_1378_2]) ).
fof(f_1379_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_1379_2,plain,
! [U_4118,U_4117,U_4116,U_4115] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4115),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4115),U_4117),U_4118)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4115),U_4116),U_4118)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4115),U_4118),c_Groups_Ozero__class_Ozero(U_4115)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4115),U_4116),U_4117))
| ~ class_Fields_Olinordered__field(U_4115) ),
inference(variable_rename,[status(thm)],[f_1379_1]) ).
cnf(f_1379_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4115),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4115),U_4117),U_4118)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4115),U_4116),U_4118)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4115),U_4118),c_Groups_Ozero__class_Ozero(U_4115)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4115),U_4116),U_4117))
| ~ class_Fields_Olinordered__field(U_4115) ),
inference(clausify,[status(thm)],[f_1379_2]) ).
fof(f_1380_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_1380_2,plain,
! [U_4122,U_4121,U_4120,U_4119] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4119),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4119),U_4120),U_4122)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4119),U_4121),U_4122)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4119),c_Groups_Ozero__class_Ozero(U_4119)),U_4122))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4119),U_4120),U_4121))
| ~ class_Fields_Olinordered__field(U_4119) ),
inference(variable_rename,[status(thm)],[f_1380_1]) ).
cnf(f_1380_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4119),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4119),U_4120),U_4122)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4119),U_4121),U_4122)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4119),c_Groups_Ozero__class_Ozero(U_4119)),U_4122))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4119),U_4120),U_4121))
| ~ class_Fields_Olinordered__field(U_4119) ),
inference(clausify,[status(thm)],[f_1380_2]) ).
fof(f_1381_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_1381_2,plain,
! [U_4125,U_4124,U_4123] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4123),c_Groups_Ozero__class_Ozero(U_4123)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4123),U_4124),U_4125)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4123),U_4125),c_Groups_Ozero__class_Ozero(U_4123)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4123),U_4124),c_Groups_Ozero__class_Ozero(U_4123)))
| ~ class_Fields_Olinordered__field(U_4123) ),
inference(variable_rename,[status(thm)],[f_1381_1]) ).
cnf(f_1381_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4123),c_Groups_Ozero__class_Ozero(U_4123)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4123),U_4124),U_4125)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4123),U_4125),c_Groups_Ozero__class_Ozero(U_4123)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4123),U_4124),c_Groups_Ozero__class_Ozero(U_4123)))
| ~ class_Fields_Olinordered__field(U_4123) ),
inference(clausify,[status(thm)],[f_1381_2]) ).
fof(f_1382_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_1382_2,plain,
! [U_4128,U_4127,U_4126] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4126),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4126),U_4127),U_4128)),c_Groups_Ozero__class_Ozero(U_4126)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4126),c_Groups_Ozero__class_Ozero(U_4126)),U_4128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4126),U_4127),c_Groups_Ozero__class_Ozero(U_4126)))
| ~ class_Fields_Olinordered__field(U_4126) ),
inference(variable_rename,[status(thm)],[f_1382_1]) ).
cnf(f_1382_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4126),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4126),U_4127),U_4128)),c_Groups_Ozero__class_Ozero(U_4126)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4126),c_Groups_Ozero__class_Ozero(U_4126)),U_4128))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4126),U_4127),c_Groups_Ozero__class_Ozero(U_4126)))
| ~ class_Fields_Olinordered__field(U_4126) ),
inference(clausify,[status(thm)],[f_1382_2]) ).
fof(f_1383_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_1383_2,plain,
! [U_4131,U_4130,U_4129] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4129),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4129),U_4130),U_4131)),c_Groups_Ozero__class_Ozero(U_4129)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4129),U_4131),c_Groups_Ozero__class_Ozero(U_4129)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4129),c_Groups_Ozero__class_Ozero(U_4129)),U_4130))
| ~ class_Fields_Olinordered__field(U_4129) ),
inference(variable_rename,[status(thm)],[f_1383_1]) ).
cnf(f_1383_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4129),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4129),U_4130),U_4131)),c_Groups_Ozero__class_Ozero(U_4129)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4129),U_4131),c_Groups_Ozero__class_Ozero(U_4129)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4129),c_Groups_Ozero__class_Ozero(U_4129)),U_4130))
| ~ class_Fields_Olinordered__field(U_4129) ),
inference(clausify,[status(thm)],[f_1383_2]) ).
fof(f_1384_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),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_1384_2,plain,
! [U_4134,U_4133,U_4132] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4132),c_Groups_Ozero__class_Ozero(U_4132)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4132),U_4133),U_4134)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4132),c_Groups_Ozero__class_Ozero(U_4132)),U_4134))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4132),c_Groups_Ozero__class_Ozero(U_4132)),U_4133))
| ~ class_Fields_Olinordered__field(U_4132) ),
inference(variable_rename,[status(thm)],[f_1384_1]) ).
cnf(f_1384_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4132),c_Groups_Ozero__class_Ozero(U_4132)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4132),U_4133),U_4134)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4132),c_Groups_Ozero__class_Ozero(U_4132)),U_4134))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4132),c_Groups_Ozero__class_Ozero(U_4132)),U_4133))
| ~ class_Fields_Olinordered__field(U_4132) ),
inference(clausify,[status(thm)],[f_1384_2]) ).
fof(f_1385_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__0__iff]) ).
fof(f_1385_2,plain,
! [U_4137,U_4136,U_4135] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4135),U_4136),U_4137)),c_Groups_Ozero__class_Ozero(U_4135)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),c_Groups_Ozero__class_Ozero(U_4135)),U_4137))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),U_4136),c_Groups_Ozero__class_Ozero(U_4135))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),U_4137),c_Groups_Ozero__class_Ozero(U_4135)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),c_Groups_Ozero__class_Ozero(U_4135)),U_4136)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),c_Groups_Ozero__class_Ozero(U_4135)),U_4137))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),U_4136),c_Groups_Ozero__class_Ozero(U_4135))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),U_4137),c_Groups_Ozero__class_Ozero(U_4135)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),c_Groups_Ozero__class_Ozero(U_4135)),U_4136)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4135),U_4136),U_4137)),c_Groups_Ozero__class_Ozero(U_4135))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_4135) ),
inference(variable_rename,[status(thm)],[f_1385_1]) ).
cnf(f_1385_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),U_4136),c_Groups_Ozero__class_Ozero(U_4135)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),c_Groups_Ozero__class_Ozero(U_4135)),U_4136))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4135),U_4136),U_4137)),c_Groups_Ozero__class_Ozero(U_4135)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4135) ),
inference(clausify,[status(thm)],[f_1385_2]) ).
cnf(f_1385_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),c_Groups_Ozero__class_Ozero(U_4135)),U_4137))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),c_Groups_Ozero__class_Ozero(U_4135)),U_4136))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4135),U_4136),U_4137)),c_Groups_Ozero__class_Ozero(U_4135)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4135) ),
inference(clausify,[status(thm)],[f_1385_2]) ).
cnf(f_1385_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),U_4136),c_Groups_Ozero__class_Ozero(U_4135)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),U_4137),c_Groups_Ozero__class_Ozero(U_4135)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4135),U_4136),U_4137)),c_Groups_Ozero__class_Ozero(U_4135)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4135) ),
inference(clausify,[status(thm)],[f_1385_2]) ).
cnf(f_1385_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),c_Groups_Ozero__class_Ozero(U_4135)),U_4137))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),U_4137),c_Groups_Ozero__class_Ozero(U_4135)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4135),U_4136),U_4137)),c_Groups_Ozero__class_Ozero(U_4135)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4135) ),
inference(clausify,[status(thm)],[f_1385_2]) ).
cnf(f_1385_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),U_4137),c_Groups_Ozero__class_Ozero(U_4135)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),c_Groups_Ozero__class_Ozero(U_4135)),U_4136))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4135),U_4136),U_4137)),c_Groups_Ozero__class_Ozero(U_4135)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4135) ),
inference(clausify,[status(thm)],[f_1385_2]) ).
cnf(f_1385_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),c_Groups_Ozero__class_Ozero(U_4135)),U_4137))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),U_4136),c_Groups_Ozero__class_Ozero(U_4135)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4135),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4135),U_4136),U_4137)),c_Groups_Ozero__class_Ozero(U_4135)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4135) ),
inference(clausify,[status(thm)],[f_1385_2]) ).
fof(f_1386_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__divide__iff]) ).
fof(f_1386_2,plain,
! [U_4140,U_4139,U_4138] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),c_Groups_Ozero__class_Ozero(U_4138)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4138),U_4139),U_4140)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),U_4140),c_Groups_Ozero__class_Ozero(U_4138)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),U_4139),c_Groups_Ozero__class_Ozero(U_4138))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),c_Groups_Ozero__class_Ozero(U_4138)),U_4140))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),c_Groups_Ozero__class_Ozero(U_4138)),U_4139)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),U_4140),c_Groups_Ozero__class_Ozero(U_4138)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),U_4139),c_Groups_Ozero__class_Ozero(U_4138))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),c_Groups_Ozero__class_Ozero(U_4138)),U_4140))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),c_Groups_Ozero__class_Ozero(U_4138)),U_4139)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),c_Groups_Ozero__class_Ozero(U_4138)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4138),U_4139),U_4140))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_4138) ),
inference(variable_rename,[status(thm)],[f_1386_1]) ).
cnf(f_1386_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),U_4139),c_Groups_Ozero__class_Ozero(U_4138)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),c_Groups_Ozero__class_Ozero(U_4138)),U_4139))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),c_Groups_Ozero__class_Ozero(U_4138)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4138),U_4139),U_4140)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4138) ),
inference(clausify,[status(thm)],[f_1386_2]) ).
cnf(f_1386_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),U_4140),c_Groups_Ozero__class_Ozero(U_4138)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),c_Groups_Ozero__class_Ozero(U_4138)),U_4139))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),c_Groups_Ozero__class_Ozero(U_4138)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4138),U_4139),U_4140)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4138) ),
inference(clausify,[status(thm)],[f_1386_2]) ).
cnf(f_1386_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),U_4139),c_Groups_Ozero__class_Ozero(U_4138)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),c_Groups_Ozero__class_Ozero(U_4138)),U_4140))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),c_Groups_Ozero__class_Ozero(U_4138)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4138),U_4139),U_4140)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4138) ),
inference(clausify,[status(thm)],[f_1386_2]) ).
cnf(f_1386_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),U_4140),c_Groups_Ozero__class_Ozero(U_4138)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),c_Groups_Ozero__class_Ozero(U_4138)),U_4140))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),c_Groups_Ozero__class_Ozero(U_4138)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4138),U_4139),U_4140)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4138) ),
inference(clausify,[status(thm)],[f_1386_2]) ).
cnf(f_1386_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),c_Groups_Ozero__class_Ozero(U_4138)),U_4140))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),c_Groups_Ozero__class_Ozero(U_4138)),U_4139))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),c_Groups_Ozero__class_Ozero(U_4138)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4138),U_4139),U_4140)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4138) ),
inference(clausify,[status(thm)],[f_1386_2]) ).
cnf(f_1386_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),U_4140),c_Groups_Ozero__class_Ozero(U_4138)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),U_4139),c_Groups_Ozero__class_Ozero(U_4138)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4138),c_Groups_Ozero__class_Ozero(U_4138)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4138),U_4139),U_4140)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4138) ),
inference(clausify,[status(thm)],[f_1386_2]) ).
fof(f_1387_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) != V_b_2 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2
| V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) ) )
| V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
| ~ class_Rings_Odivision__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq]) ).
fof(f_1387_2,plain,
! [U_4144,U_4143,U_4142,U_4141] :
( ( ( U_4143 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4141),U_4144),U_4142)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4141),U_4143),U_4142) != U_4144 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4141),U_4143),U_4142) = U_4144
| U_4143 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4141),U_4144),U_4142) ) )
| U_4142 = c_Groups_Ozero__class_Ozero(U_4141)
| ~ class_Rings_Odivision__ring(U_4141) ),
inference(variable_rename,[status(thm)],[f_1387_1]) ).
cnf(f_1387_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4141),U_4143),U_4142) = U_4144
| U_4143 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4141),U_4144),U_4142)
| U_4142 = c_Groups_Ozero__class_Ozero(U_4141)
| ~ class_Rings_Odivision__ring(U_4141) ),
inference(clausify,[status(thm)],[f_1387_2]) ).
cnf(f_1387_4,plain,
( U_4143 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4141),U_4144),U_4142)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4141),U_4143),U_4142) != U_4144
| U_4142 = c_Groups_Ozero__class_Ozero(U_4141)
| ~ class_Rings_Odivision__ring(U_4141) ),
inference(clausify,[status(thm)],[f_1387_2]) ).
fof(f_1388_1,plain,
! [V_a_2,V_b_2,V_c_2,T_b] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
| V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) )
& ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) != V_a_2 ) )
| V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
| ~ class_Rings_Odivision__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq]) ).
fof(f_1388_2,plain,
! [U_4148,U_4147,U_4146,U_4145] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4145),U_4147),U_4146) = U_4148
| U_4147 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4145),U_4148),U_4146) )
& ( U_4147 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4145),U_4148),U_4146)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4145),U_4147),U_4146) != U_4148 ) )
| U_4146 = c_Groups_Ozero__class_Ozero(U_4145)
| ~ class_Rings_Odivision__ring(U_4145) ),
inference(variable_rename,[status(thm)],[f_1388_1]) ).
cnf(f_1388_3,plain,
( U_4147 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4145),U_4148),U_4146)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4145),U_4147),U_4146) != U_4148
| U_4146 = c_Groups_Ozero__class_Ozero(U_4145)
| ~ class_Rings_Odivision__ring(U_4145) ),
inference(clausify,[status(thm)],[f_1388_2]) ).
cnf(f_1388_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4145),U_4147),U_4146) = U_4148
| U_4147 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4145),U_4148),U_4146)
| U_4146 = c_Groups_Ozero__class_Ozero(U_4145)
| ~ class_Rings_Odivision__ring(U_4145) ),
inference(clausify,[status(thm)],[f_1388_2]) ).
fof(f_1389_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_1389_2,plain,
! [U_4152,U_4151,U_4150,U_4149] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4149),U_4151),U_4150) = U_4152
| U_4151 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4149),U_4152),U_4150)
| U_4150 = c_Groups_Ozero__class_Ozero(U_4149)
| ~ class_Rings_Odivision__ring(U_4149) ),
inference(variable_rename,[status(thm)],[f_1389_1]) ).
cnf(f_1389_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4149),U_4151),U_4150) = U_4152
| U_4151 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4149),U_4152),U_4150)
| U_4150 = c_Groups_Ozero__class_Ozero(U_4149)
| ~ class_Rings_Odivision__ring(U_4149) ),
inference(clausify,[status(thm)],[f_1389_2]) ).
fof(f_1390_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_1390_2,plain,
! [U_4156,U_4155,U_4154,U_4153] :
( U_4155 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4153),U_4156),U_4154)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4153),U_4155),U_4154) != U_4156
| U_4154 = c_Groups_Ozero__class_Ozero(U_4153)
| ~ class_Rings_Odivision__ring(U_4153) ),
inference(variable_rename,[status(thm)],[f_1390_1]) ).
cnf(f_1390_3,plain,
( U_4155 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4153),U_4156),U_4154)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4153),U_4155),U_4154) != U_4156
| U_4154 = c_Groups_Ozero__class_Ozero(U_4153)
| ~ class_Rings_Odivision__ring(U_4153) ),
inference(clausify,[status(thm)],[f_1390_2]) ).
fof(f_1391_1,plain,
! [V_c_2,V_b_2,V_a_2,T_b] :
( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
& V_c_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) != V_b_2
& V_c_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| V_c_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2
| V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
| V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) ) )
| ~ class_Fields_Ofield__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__eq]) ).
fof(f_1391_2,plain,
! [U_4160,U_4159,U_4158,U_4157] :
( ( ( U_4158 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4157),U_4159),U_4160)
| ( U_4158 != c_Groups_Ozero__class_Ozero(U_4157)
& U_4160 = c_Groups_Ozero__class_Ozero(U_4157) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4157),U_4158),U_4160) != U_4159
& U_4160 != c_Groups_Ozero__class_Ozero(U_4157) ) )
& ( ( ( U_4158 = c_Groups_Ozero__class_Ozero(U_4157)
| U_4160 != c_Groups_Ozero__class_Ozero(U_4157) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4157),U_4158),U_4160) = U_4159
| U_4160 = c_Groups_Ozero__class_Ozero(U_4157) ) )
| U_4158 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4157),U_4159),U_4160) ) )
| ~ class_Fields_Ofield__inverse__zero(U_4157) ),
inference(variable_rename,[status(thm)],[f_1391_1]) ).
cnf(f_1391_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4157),U_4158),U_4160) = U_4159
| U_4160 = c_Groups_Ozero__class_Ozero(U_4157)
| U_4158 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4157),U_4159),U_4160)
| ~ class_Fields_Ofield__inverse__zero(U_4157) ),
inference(clausify,[status(thm)],[f_1391_2]) ).
cnf(f_1391_4,plain,
( U_4158 = c_Groups_Ozero__class_Ozero(U_4157)
| U_4160 != c_Groups_Ozero__class_Ozero(U_4157)
| U_4158 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4157),U_4159),U_4160)
| ~ class_Fields_Ofield__inverse__zero(U_4157) ),
inference(clausify,[status(thm)],[f_1391_2]) ).
cnf(f_1391_5,plain,
( U_4160 = c_Groups_Ozero__class_Ozero(U_4157)
| U_4160 != c_Groups_Ozero__class_Ozero(U_4157)
| U_4158 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4157),U_4159),U_4160)
| ~ class_Fields_Ofield__inverse__zero(U_4157) ),
inference(clausify,[status(thm)],[f_1391_2]) ).
cnf(f_1391_6,plain,
( U_4158 != c_Groups_Ozero__class_Ozero(U_4157)
| U_4160 != c_Groups_Ozero__class_Ozero(U_4157)
| U_4158 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4157),U_4159),U_4160)
| ~ class_Fields_Ofield__inverse__zero(U_4157) ),
inference(clausify,[status(thm)],[f_1391_2]) ).
cnf(f_1391_7,plain,
( U_4160 = c_Groups_Ozero__class_Ozero(U_4157)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4157),U_4158),U_4160) != U_4159
| U_4158 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4157),U_4159),U_4160)
| ~ class_Fields_Ofield__inverse__zero(U_4157) ),
inference(clausify,[status(thm)],[f_1391_2]) ).
cnf(f_1391_8,plain,
( U_4158 != c_Groups_Ozero__class_Ozero(U_4157)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4157),U_4158),U_4160) != U_4159
| U_4158 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4157),U_4159),U_4160)
| ~ class_Fields_Ofield__inverse__zero(U_4157) ),
inference(clausify,[status(thm)],[f_1391_2]) ).
fof(f_1392_1,plain,
! [V_a_2,V_c_2,V_b_2,T_b] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
& V_c_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)
& V_c_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| V_c_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)
| V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) != V_a_2 ) )
| ~ class_Fields_Ofield__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__eq]) ).
fof(f_1392_2,plain,
! [U_4164,U_4163,U_4162,U_4161] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4161),U_4162),U_4163) = U_4164
| ( U_4164 != c_Groups_Ozero__class_Ozero(U_4161)
& U_4163 = c_Groups_Ozero__class_Ozero(U_4161) )
| ( U_4162 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4161),U_4164),U_4163)
& U_4163 != c_Groups_Ozero__class_Ozero(U_4161) ) )
& ( ( ( U_4164 = c_Groups_Ozero__class_Ozero(U_4161)
| U_4163 != c_Groups_Ozero__class_Ozero(U_4161) )
& ( U_4162 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4161),U_4164),U_4163)
| U_4163 = c_Groups_Ozero__class_Ozero(U_4161) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4161),U_4162),U_4163) != U_4164 ) )
| ~ class_Fields_Ofield__inverse__zero(U_4161) ),
inference(variable_rename,[status(thm)],[f_1392_1]) ).
cnf(f_1392_3,plain,
( U_4162 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4161),U_4164),U_4163)
| U_4163 = c_Groups_Ozero__class_Ozero(U_4161)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4161),U_4162),U_4163) != U_4164
| ~ class_Fields_Ofield__inverse__zero(U_4161) ),
inference(clausify,[status(thm)],[f_1392_2]) ).
cnf(f_1392_4,plain,
( U_4164 = c_Groups_Ozero__class_Ozero(U_4161)
| U_4163 != c_Groups_Ozero__class_Ozero(U_4161)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4161),U_4162),U_4163) != U_4164
| ~ class_Fields_Ofield__inverse__zero(U_4161) ),
inference(clausify,[status(thm)],[f_1392_2]) ).
cnf(f_1392_5,plain,
( U_4163 = c_Groups_Ozero__class_Ozero(U_4161)
| U_4163 != c_Groups_Ozero__class_Ozero(U_4161)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4161),U_4162),U_4163) = U_4164
| ~ class_Fields_Ofield__inverse__zero(U_4161) ),
inference(clausify,[status(thm)],[f_1392_2]) ).
cnf(f_1392_6,plain,
( U_4164 != c_Groups_Ozero__class_Ozero(U_4161)
| U_4163 != c_Groups_Ozero__class_Ozero(U_4161)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4161),U_4162),U_4163) = U_4164
| ~ class_Fields_Ofield__inverse__zero(U_4161) ),
inference(clausify,[status(thm)],[f_1392_2]) ).
cnf(f_1392_7,plain,
( U_4163 = c_Groups_Ozero__class_Ozero(U_4161)
| U_4162 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4161),U_4164),U_4163)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4161),U_4162),U_4163) = U_4164
| ~ class_Fields_Ofield__inverse__zero(U_4161) ),
inference(clausify,[status(thm)],[f_1392_2]) ).
cnf(f_1392_8,plain,
( U_4164 != c_Groups_Ozero__class_Ozero(U_4161)
| U_4162 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4161),U_4164),U_4163)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4161),U_4162),U_4163) = U_4164
| ~ class_Fields_Ofield__inverse__zero(U_4161) ),
inference(clausify,[status(thm)],[f_1392_2]) ).
fof(f_1393_1,plain,
! [V_b,V_a,V_c,T_a] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_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_1393_2,plain,
! [U_4168,U_4167,U_4166,U_4165] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4165),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4165),U_4167),U_4166)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4165),U_4168),U_4166)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4165),U_4167),U_4168)
| U_4166 = c_Groups_Ozero__class_Ozero(U_4165)
| ~ class_Fields_Ofield__inverse__zero(U_4165) ),
inference(variable_rename,[status(thm)],[f_1393_1]) ).
cnf(f_1393_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4165),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4165),U_4167),U_4166)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4165),U_4168),U_4166)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4165),U_4167),U_4168)
| U_4166 = c_Groups_Ozero__class_Ozero(U_4165)
| ~ class_Fields_Ofield__inverse__zero(U_4165) ),
inference(clausify,[status(thm)],[f_1393_2]) ).
fof(f_1394_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_1394_2,plain,
! [U_4172,U_4171,U_4170,U_4169] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4169),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4169),U_4170),U_4171)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4169),U_4170),U_4172)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4169),U_4171),U_4172)
| U_4170 = c_Groups_Ozero__class_Ozero(U_4169)
| ~ class_Fields_Ofield__inverse__zero(U_4169) ),
inference(variable_rename,[status(thm)],[f_1394_1]) ).
cnf(f_1394_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4169),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4169),U_4170),U_4171)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4169),U_4170),U_4172)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4169),U_4171),U_4172)
| U_4170 = c_Groups_Ozero__class_Ozero(U_4169)
| ~ class_Fields_Ofield__inverse__zero(U_4169) ),
inference(clausify,[status(thm)],[f_1394_2]) ).
fof(f_1395_1,plain,
! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2) ) )
| V_z_2 = c_Groups_Ozero__class_Ozero(T_b)
| V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
| ~ class_Fields_Ofield(T_b) ),
inference(fof_nnf,[status(thm)],[fact_frac__eq__eq]) ).
fof(f_1395_2,plain,
! [U_4177,U_4176,U_4175,U_4174,U_4173] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4173),U_4176),U_4174) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4173),U_4177),U_4175)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4173),U_4176),U_4175) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4173),U_4177),U_4174) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4173),U_4176),U_4175) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4173),U_4177),U_4174)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4173),U_4176),U_4174) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4173),U_4177),U_4175) ) )
| U_4175 = c_Groups_Ozero__class_Ozero(U_4173)
| U_4174 = c_Groups_Ozero__class_Ozero(U_4173)
| ~ class_Fields_Ofield(U_4173) ),
inference(variable_rename,[status(thm)],[f_1395_1]) ).
cnf(f_1395_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4173),U_4176),U_4175) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4173),U_4177),U_4174)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4173),U_4176),U_4174) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4173),U_4177),U_4175)
| U_4175 = c_Groups_Ozero__class_Ozero(U_4173)
| U_4174 = c_Groups_Ozero__class_Ozero(U_4173)
| ~ class_Fields_Ofield(U_4173) ),
inference(clausify,[status(thm)],[f_1395_2]) ).
cnf(f_1395_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4173),U_4176),U_4174) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4173),U_4177),U_4175)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4173),U_4176),U_4175) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4173),U_4177),U_4174)
| U_4175 = c_Groups_Ozero__class_Ozero(U_4173)
| U_4174 = c_Groups_Ozero__class_Ozero(U_4173)
| ~ class_Fields_Ofield(U_4173) ),
inference(clausify,[status(thm)],[f_1395_2]) ).
fof(f_1396_1,plain,
! [V_a_2,V_b_2,T_b] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) != c_Groups_Oone__class_Oone(T_b) ) )
| V_b_2 = c_Groups_Ozero__class_Ozero(T_b)
| ~ class_Rings_Odivision__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_right__inverse__eq]) ).
fof(f_1396_2,plain,
! [U_4180,U_4179,U_4178] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4178),U_4180),U_4179) = c_Groups_Oone__class_Oone(U_4178)
| U_4180 != U_4179 )
& ( U_4180 = U_4179
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4178),U_4180),U_4179) != c_Groups_Oone__class_Oone(U_4178) ) )
| U_4179 = c_Groups_Ozero__class_Ozero(U_4178)
| ~ class_Rings_Odivision__ring(U_4178) ),
inference(variable_rename,[status(thm)],[f_1396_1]) ).
cnf(f_1396_3,plain,
( U_4180 = U_4179
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4178),U_4180),U_4179) != c_Groups_Oone__class_Oone(U_4178)
| U_4179 = c_Groups_Ozero__class_Ozero(U_4178)
| ~ class_Rings_Odivision__ring(U_4178) ),
inference(clausify,[status(thm)],[f_1396_2]) ).
cnf(f_1396_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4178),U_4180),U_4179) = c_Groups_Oone__class_Oone(U_4178)
| U_4180 != U_4179
| U_4179 = c_Groups_Ozero__class_Ozero(U_4178)
| ~ class_Rings_Odivision__ring(U_4178) ),
inference(clausify,[status(thm)],[f_1396_2]) ).
fof(f_1397_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_1397_2,plain,
! [U_4182,U_4181] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4181),U_4182),U_4182) = c_Groups_Oone__class_Oone(U_4181)
| U_4182 = c_Groups_Ozero__class_Ozero(U_4181)
| ~ class_Rings_Odivision__ring(U_4181) ),
inference(variable_rename,[status(thm)],[f_1397_1]) ).
cnf(f_1397_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4181),U_4182),U_4182) = c_Groups_Oone__class_Oone(U_4181)
| U_4182 = c_Groups_Ozero__class_Ozero(U_4181)
| ~ class_Rings_Odivision__ring(U_4181) ),
inference(clausify,[status(thm)],[f_1397_2]) ).
fof(f_1398_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_1398_2,plain,
! [U_4184,U_4183] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4183),U_4184),U_4184) = c_Groups_Oone__class_Oone(U_4183)
| U_4184 = c_Groups_Ozero__class_Ozero(U_4183) )
& ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4183),U_4184),U_4184) = c_Groups_Ozero__class_Ozero(U_4183)
| U_4184 != c_Groups_Ozero__class_Ozero(U_4183) ) )
| ~ class_Rings_Odivision__ring__inverse__zero(U_4183) ),
inference(variable_rename,[status(thm)],[f_1398_1]) ).
cnf(f_1398_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4183),U_4184),U_4184) = c_Groups_Ozero__class_Ozero(U_4183)
| U_4184 != c_Groups_Ozero__class_Ozero(U_4183)
| ~ class_Rings_Odivision__ring__inverse__zero(U_4183) ),
inference(clausify,[status(thm)],[f_1398_2]) ).
cnf(f_1398_4,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4183),U_4184),U_4184) = c_Groups_Oone__class_Oone(U_4183)
| U_4184 = c_Groups_Ozero__class_Ozero(U_4183)
| ~ class_Rings_Odivision__ring__inverse__zero(U_4183) ),
inference(clausify,[status(thm)],[f_1398_2]) ).
fof(f_1399_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_1399_2,plain,
! [U_4187,U_4186,U_4185] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4185),hAPP(c_Groups_Ouminus__class_Ouminus(U_4185),U_4187)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4185),U_4186)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4185),U_4187),U_4186)
| U_4186 = c_Groups_Ozero__class_Ozero(U_4185)
| ~ class_Rings_Odivision__ring(U_4185) ),
inference(variable_rename,[status(thm)],[f_1399_1]) ).
cnf(f_1399_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4185),hAPP(c_Groups_Ouminus__class_Ouminus(U_4185),U_4187)),hAPP(c_Groups_Ouminus__class_Ouminus(U_4185),U_4186)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4185),U_4187),U_4186)
| U_4186 = c_Groups_Ozero__class_Ozero(U_4185)
| ~ class_Rings_Odivision__ring(U_4185) ),
inference(clausify,[status(thm)],[f_1399_2]) ).
fof(f_1400_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_1400_2,plain,
! [U_4190,U_4189,U_4188] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4188),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4188),U_4190),U_4189)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4188),U_4190),hAPP(c_Groups_Ouminus__class_Ouminus(U_4188),U_4189))
| U_4189 = c_Groups_Ozero__class_Ozero(U_4188)
| ~ class_Rings_Odivision__ring(U_4188) ),
inference(variable_rename,[status(thm)],[f_1400_1]) ).
cnf(f_1400_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_4188),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4188),U_4190),U_4189)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4188),U_4190),hAPP(c_Groups_Ouminus__class_Ouminus(U_4188),U_4189))
| U_4189 = c_Groups_Ozero__class_Ozero(U_4188)
| ~ class_Rings_Odivision__ring(U_4188) ),
inference(clausify,[status(thm)],[f_1400_2]) ).
fof(f_1401_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_1401_2,plain,
! [U_4194,U_4193,U_4192,U_4191] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4191),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4191),U_4193),U_4192)),U_4194) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4191),hAPP(hAPP(c_Power_Opower__class_Opower(U_4191),U_4193),U_4194)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4191),U_4192),U_4194))
| U_4192 = c_Groups_Ozero__class_Ozero(U_4191)
| ~ class_Fields_Ofield(U_4191) ),
inference(variable_rename,[status(thm)],[f_1401_1]) ).
cnf(f_1401_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4191),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4191),U_4193),U_4192)),U_4194) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4191),hAPP(hAPP(c_Power_Opower__class_Opower(U_4191),U_4193),U_4194)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4191),U_4192),U_4194))
| U_4192 = c_Groups_Ozero__class_Ozero(U_4191)
| ~ class_Fields_Ofield(U_4191) ),
inference(clausify,[status(thm)],[f_1401_2]) ).
fof(f_1402_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_1402_2,plain,
! [U_4197,U_4196,U_4195] :
( hAPP(c_Groups_Oabs__class_Oabs(U_4195),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4195),U_4197),U_4196)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4195),hAPP(c_Groups_Oabs__class_Oabs(U_4195),U_4197)),hAPP(c_Groups_Oabs__class_Oabs(U_4195),U_4196))
| U_4196 = c_Groups_Ozero__class_Ozero(U_4195)
| ~ class_Fields_Olinordered__field(U_4195) ),
inference(variable_rename,[status(thm)],[f_1402_1]) ).
cnf(f_1402_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_4195),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4195),U_4197),U_4196)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4195),hAPP(c_Groups_Oabs__class_Oabs(U_4195),U_4197)),hAPP(c_Groups_Oabs__class_Oabs(U_4195),U_4196))
| U_4196 = c_Groups_Ozero__class_Ozero(U_4195)
| ~ class_Fields_Olinordered__field(U_4195) ),
inference(clausify,[status(thm)],[f_1402_2]) ).
fof(f_1403_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_1403_2,plain,
! [U_4200,U_4199,U_4198] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4198),c_Groups_Oone__class_Oone(U_4198)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4198),U_4199),U_4200)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4198),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4198),c_Groups_Oone__class_Oone(U_4198)),U_4199)),U_4200)
| ~ class_Fields_Ofield__inverse__zero(U_4198) ),
inference(variable_rename,[status(thm)],[f_1403_1]) ).
cnf(f_1403_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4198),c_Groups_Oone__class_Oone(U_4198)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4198),U_4199),U_4200)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4198),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4198),c_Groups_Oone__class_Oone(U_4198)),U_4199)),U_4200)
| ~ class_Fields_Ofield__inverse__zero(U_4198) ),
inference(clausify,[status(thm)],[f_1403_2]) ).
fof(f_1404_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_1404_2,plain,
! [U_4202,U_4201] :
( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_4201,U_4202))
| ~ c_Nat__Transfer_Ois__nat(U_4202)
| ~ c_Nat__Transfer_Ois__nat(U_4201) ),
inference(variable_rename,[status(thm)],[f_1404_1]) ).
cnf(f_1404_3,plain,
( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_4201,U_4202))
| ~ c_Nat__Transfer_Ois__nat(U_4202)
| ~ c_Nat__Transfer_Ois__nat(U_4201) ),
inference(clausify,[status(thm)],[f_1404_2]) ).
fof(f_1405_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_1405_2,plain,
! [U_4205,U_4204,U_4203] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4203),c_Groups_Ozero__class_Ozero(U_4203)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4203),U_4204),U_4205)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4203),U_4205),c_Groups_Ozero__class_Ozero(U_4203)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4203),U_4204),c_Groups_Ozero__class_Ozero(U_4203)))
| ~ class_Fields_Olinordered__field(U_4203) ),
inference(variable_rename,[status(thm)],[f_1405_1]) ).
cnf(f_1405_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4203),c_Groups_Ozero__class_Ozero(U_4203)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4203),U_4204),U_4205)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4203),U_4205),c_Groups_Ozero__class_Ozero(U_4203)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4203),U_4204),c_Groups_Ozero__class_Ozero(U_4203)))
| ~ class_Fields_Olinordered__field(U_4203) ),
inference(clausify,[status(thm)],[f_1405_2]) ).
fof(f_1406_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_1406_2,plain,
! [U_4208,U_4207,U_4206] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4206),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4206),U_4207),U_4208)),c_Groups_Ozero__class_Ozero(U_4206)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4206),c_Groups_Ozero__class_Ozero(U_4206)),U_4208))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4206),U_4207),c_Groups_Ozero__class_Ozero(U_4206)))
| ~ class_Fields_Olinordered__field(U_4206) ),
inference(variable_rename,[status(thm)],[f_1406_1]) ).
cnf(f_1406_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4206),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4206),U_4207),U_4208)),c_Groups_Ozero__class_Ozero(U_4206)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4206),c_Groups_Ozero__class_Ozero(U_4206)),U_4208))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4206),U_4207),c_Groups_Ozero__class_Ozero(U_4206)))
| ~ class_Fields_Olinordered__field(U_4206) ),
inference(clausify,[status(thm)],[f_1406_2]) ).
fof(f_1407_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_1407_2,plain,
! [U_4213,U_4212,U_4211,U_4210,U_4209] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4209),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4209),U_4210),U_4213)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4209),U_4211),U_4212)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4209),U_4212),U_4213))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4209),c_Groups_Ozero__class_Ozero(U_4209)),U_4212))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4209),U_4210),U_4211))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4209),c_Groups_Ozero__class_Ozero(U_4209)),U_4210))
| ~ class_Fields_Olinordered__field(U_4209) ),
inference(variable_rename,[status(thm)],[f_1407_1]) ).
cnf(f_1407_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4209),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4209),U_4210),U_4213)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4209),U_4211),U_4212)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4209),U_4212),U_4213))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4209),c_Groups_Ozero__class_Ozero(U_4209)),U_4212))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4209),U_4210),U_4211))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4209),c_Groups_Ozero__class_Ozero(U_4209)),U_4210))
| ~ class_Fields_Olinordered__field(U_4209) ),
inference(clausify,[status(thm)],[f_1407_2]) ).
fof(f_1408_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_1408_2,plain,
! [U_4218,U_4217,U_4216,U_4215,U_4214] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4214),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4214),U_4215),U_4218)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4214),U_4216),U_4217)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4214),U_4217),U_4218))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4214),c_Groups_Ozero__class_Ozero(U_4214)),U_4217))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4214),U_4215),U_4216))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4214),c_Groups_Ozero__class_Ozero(U_4214)),U_4215))
| ~ class_Fields_Olinordered__field(U_4214) ),
inference(variable_rename,[status(thm)],[f_1408_1]) ).
cnf(f_1408_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4214),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4214),U_4215),U_4218)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4214),U_4216),U_4217)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4214),U_4217),U_4218))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4214),c_Groups_Ozero__class_Ozero(U_4214)),U_4217))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4214),U_4215),U_4216))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4214),c_Groups_Ozero__class_Ozero(U_4214)),U_4215))
| ~ class_Fields_Olinordered__field(U_4214) ),
inference(clausify,[status(thm)],[f_1408_2]) ).
fof(f_1409_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_1409_2,plain,
! [U_4223,U_4222,U_4221,U_4220,U_4219] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4219),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4219),U_4220),U_4223)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4219),U_4221),U_4222)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4219),U_4222),U_4223))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4219),c_Groups_Ozero__class_Ozero(U_4219)),U_4222))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4219),U_4220),U_4221))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4219),c_Groups_Ozero__class_Ozero(U_4219)),U_4220))
| ~ class_Fields_Olinordered__field(U_4219) ),
inference(variable_rename,[status(thm)],[f_1409_1]) ).
cnf(f_1409_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4219),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4219),U_4220),U_4223)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4219),U_4221),U_4222)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4219),U_4222),U_4223))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4219),c_Groups_Ozero__class_Ozero(U_4219)),U_4222))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4219),U_4220),U_4221))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4219),c_Groups_Ozero__class_Ozero(U_4219)),U_4220))
| ~ class_Fields_Olinordered__field(U_4219) ),
inference(clausify,[status(thm)],[f_1409_2]) ).
fof(f_1410_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_1410_2,plain,
! [U_4226,U_4225,U_4224] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4224),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4224),U_4225),U_4226)),c_Groups_Ozero__class_Ozero(U_4224)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4224),U_4226),c_Groups_Ozero__class_Ozero(U_4224)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4224),c_Groups_Ozero__class_Ozero(U_4224)),U_4225))
| ~ class_Fields_Olinordered__field(U_4224) ),
inference(variable_rename,[status(thm)],[f_1410_1]) ).
cnf(f_1410_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4224),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4224),U_4225),U_4226)),c_Groups_Ozero__class_Ozero(U_4224)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4224),U_4226),c_Groups_Ozero__class_Ozero(U_4224)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4224),c_Groups_Ozero__class_Ozero(U_4224)),U_4225))
| ~ class_Fields_Olinordered__field(U_4224) ),
inference(clausify,[status(thm)],[f_1410_2]) ).
fof(f_1411_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_1411_2,plain,
! [U_4229,U_4228,U_4227] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4227),c_Groups_Ozero__class_Ozero(U_4227)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4227),U_4228),U_4229)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4227),c_Groups_Ozero__class_Ozero(U_4227)),U_4229))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4227),c_Groups_Ozero__class_Ozero(U_4227)),U_4228))
| ~ class_Fields_Olinordered__field(U_4227) ),
inference(variable_rename,[status(thm)],[f_1411_1]) ).
cnf(f_1411_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4227),c_Groups_Ozero__class_Ozero(U_4227)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4227),U_4228),U_4229)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4227),c_Groups_Ozero__class_Ozero(U_4227)),U_4229))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4227),c_Groups_Ozero__class_Ozero(U_4227)),U_4228))
| ~ class_Fields_Olinordered__field(U_4227) ),
inference(clausify,[status(thm)],[f_1411_2]) ).
fof(f_1412_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_1412_2,plain,
! [U_4233,U_4232,U_4231,U_4230] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4230),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4230),U_4233),U_4231)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4230),U_4233),U_4232)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4230),c_Groups_Ozero__class_Ozero(U_4230)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4230),U_4231),U_4232)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4230),U_4233),c_Groups_Ozero__class_Ozero(U_4230)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4230),U_4231),U_4232))
| ~ class_Fields_Olinordered__field(U_4230) ),
inference(variable_rename,[status(thm)],[f_1412_1]) ).
cnf(f_1412_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4230),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4230),U_4233),U_4231)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4230),U_4233),U_4232)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4230),c_Groups_Ozero__class_Ozero(U_4230)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4230),U_4231),U_4232)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4230),U_4233),c_Groups_Ozero__class_Ozero(U_4230)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4230),U_4231),U_4232))
| ~ class_Fields_Olinordered__field(U_4230) ),
inference(clausify,[status(thm)],[f_1412_2]) ).
fof(f_1413_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_1413_2,plain,
! [U_4237,U_4236,U_4235,U_4234] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4234),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4234),U_4237),U_4236)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4234),U_4237),U_4235)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4234),c_Groups_Ozero__class_Ozero(U_4234)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4234),U_4236),U_4235)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4234),c_Groups_Ozero__class_Ozero(U_4234)),U_4237))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4234),U_4235),U_4236))
| ~ class_Fields_Olinordered__field(U_4234) ),
inference(variable_rename,[status(thm)],[f_1413_1]) ).
cnf(f_1413_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4234),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4234),U_4237),U_4236)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4234),U_4237),U_4235)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4234),c_Groups_Ozero__class_Ozero(U_4234)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4234),U_4236),U_4235)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4234),c_Groups_Ozero__class_Ozero(U_4234)),U_4237))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4234),U_4235),U_4236))
| ~ class_Fields_Olinordered__field(U_4234) ),
inference(clausify,[status(thm)],[f_1413_2]) ).
fof(f_1414_1,plain,
! [V_a_2,V_b_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__divide__less__eq]) ).
fof(f_1414_2,plain,
! [U_4241,U_4240,U_4239,U_4238] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4238),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4238),U_4240),U_4239)),U_4241))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4238),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4238),U_4241),U_4239)),U_4240)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4238),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4238),U_4241),U_4239)),U_4240))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4238),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4238),U_4240),U_4239)),U_4241)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4238),U_4239),c_Groups_Ozero__class_Ozero(U_4238)))
| ~ class_Fields_Olinordered__field(U_4238) ),
inference(variable_rename,[status(thm)],[f_1414_1]) ).
cnf(f_1414_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4238),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4238),U_4241),U_4239)),U_4240))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4238),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4238),U_4240),U_4239)),U_4241))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4238),U_4239),c_Groups_Ozero__class_Ozero(U_4238)))
| ~ class_Fields_Olinordered__field(U_4238) ),
inference(clausify,[status(thm)],[f_1414_2]) ).
cnf(f_1414_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4238),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4238),U_4240),U_4239)),U_4241))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4238),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4238),U_4241),U_4239)),U_4240))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4238),U_4239),c_Groups_Ozero__class_Ozero(U_4238)))
| ~ class_Fields_Olinordered__field(U_4238) ),
inference(clausify,[status(thm)],[f_1414_2]) ).
fof(f_1415_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__divide__eq]) ).
fof(f_1415_2,plain,
! [U_4245,U_4244,U_4243,U_4242] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4242),U_4244),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4242),U_4245),U_4243)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4242),U_4245),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4242),U_4244),U_4243))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4242),U_4245),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4242),U_4244),U_4243)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4242),U_4244),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4242),U_4245),U_4243))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4242),U_4243),c_Groups_Ozero__class_Ozero(U_4242)))
| ~ class_Fields_Olinordered__field(U_4242) ),
inference(variable_rename,[status(thm)],[f_1415_1]) ).
cnf(f_1415_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4242),U_4245),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4242),U_4244),U_4243)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4242),U_4244),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4242),U_4245),U_4243)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4242),U_4243),c_Groups_Ozero__class_Ozero(U_4242)))
| ~ class_Fields_Olinordered__field(U_4242) ),
inference(clausify,[status(thm)],[f_1415_2]) ).
cnf(f_1415_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4242),U_4244),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4242),U_4245),U_4243)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4242),U_4245),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4242),U_4244),U_4243)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4242),U_4243),c_Groups_Ozero__class_Ozero(U_4242)))
| ~ class_Fields_Olinordered__field(U_4242) ),
inference(clausify,[status(thm)],[f_1415_2]) ).
fof(f_1416_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_1416_2,plain,
! [U_4249,U_4248,U_4247,U_4246] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4246),U_4248),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4246),U_4249),U_4247)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4246),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4246),U_4248),U_4247)),U_4249))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4246),c_Groups_Ozero__class_Ozero(U_4246)),U_4247))
| ~ class_Fields_Olinordered__field(U_4246) ),
inference(variable_rename,[status(thm)],[f_1416_1]) ).
cnf(f_1416_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4246),U_4248),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4246),U_4249),U_4247)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4246),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4246),U_4248),U_4247)),U_4249))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4246),c_Groups_Ozero__class_Ozero(U_4246)),U_4247))
| ~ class_Fields_Olinordered__field(U_4246) ),
inference(clausify,[status(thm)],[f_1416_2]) ).
fof(f_1417_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_1417_2,plain,
! [U_4253,U_4252,U_4251,U_4250] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4250),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4250),U_4252),U_4251)),U_4253))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4250),U_4252),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4250),U_4253),U_4251)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4250),c_Groups_Ozero__class_Ozero(U_4250)),U_4251))
| ~ class_Fields_Olinordered__field(U_4250) ),
inference(variable_rename,[status(thm)],[f_1417_1]) ).
cnf(f_1417_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4250),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4250),U_4252),U_4251)),U_4253))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4250),U_4252),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4250),U_4253),U_4251)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4250),c_Groups_Ozero__class_Ozero(U_4250)),U_4251))
| ~ class_Fields_Olinordered__field(U_4250) ),
inference(clausify,[status(thm)],[f_1417_2]) ).
fof(f_1418_1,plain,
! [V_a_2,V_b_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq]) ).
fof(f_1418_2,plain,
! [U_4257,U_4256,U_4255,U_4254] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4254),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4254),U_4256),U_4255)),U_4257))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4254),U_4256),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4254),U_4257),U_4255))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4254),U_4256),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4254),U_4257),U_4255)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4254),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4254),U_4256),U_4255)),U_4257)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4254),c_Groups_Ozero__class_Ozero(U_4254)),U_4255))
| ~ class_Fields_Olinordered__field(U_4254) ),
inference(variable_rename,[status(thm)],[f_1418_1]) ).
cnf(f_1418_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4254),U_4256),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4254),U_4257),U_4255)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4254),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4254),U_4256),U_4255)),U_4257))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4254),c_Groups_Ozero__class_Ozero(U_4254)),U_4255))
| ~ class_Fields_Olinordered__field(U_4254) ),
inference(clausify,[status(thm)],[f_1418_2]) ).
cnf(f_1418_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4254),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4254),U_4256),U_4255)),U_4257))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4254),U_4256),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4254),U_4257),U_4255)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4254),c_Groups_Ozero__class_Ozero(U_4254)),U_4255))
| ~ class_Fields_Olinordered__field(U_4254) ),
inference(clausify,[status(thm)],[f_1418_2]) ).
fof(f_1419_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq]) ).
fof(f_1419_2,plain,
! [U_4261,U_4260,U_4259,U_4258] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4258),U_4260),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4258),U_4261),U_4259)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4258),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4258),U_4260),U_4259)),U_4261)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4258),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4258),U_4260),U_4259)),U_4261))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4258),U_4260),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4258),U_4261),U_4259))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4258),c_Groups_Ozero__class_Ozero(U_4258)),U_4259))
| ~ class_Fields_Olinordered__field(U_4258) ),
inference(variable_rename,[status(thm)],[f_1419_1]) ).
cnf(f_1419_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4258),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4258),U_4260),U_4259)),U_4261))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4258),U_4260),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4258),U_4261),U_4259)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4258),c_Groups_Ozero__class_Ozero(U_4258)),U_4259))
| ~ class_Fields_Olinordered__field(U_4258) ),
inference(clausify,[status(thm)],[f_1419_2]) ).
cnf(f_1419_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4258),U_4260),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4258),U_4261),U_4259)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4258),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4258),U_4260),U_4259)),U_4261))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4258),c_Groups_Ozero__class_Ozero(U_4258)),U_4259))
| ~ class_Fields_Olinordered__field(U_4258) ),
inference(clausify,[status(thm)],[f_1419_2]) ).
fof(f_1420_1,plain,
! [V_a_2,V_c_2,V_b_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__eq]) ).
fof(f_1420_2,plain,
! [U_4265,U_4264,U_4263,U_4262] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4262),U_4263),U_4264)),U_4265))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4265))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4264),c_Groups_Ozero__class_Ozero(U_4262))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4262),U_4265),U_4264)),U_4263))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4264),c_Groups_Ozero__class_Ozero(U_4262))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4264)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4263),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4262),U_4265),U_4264)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4264)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4265))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4264),c_Groups_Ozero__class_Ozero(U_4262))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4262),U_4265),U_4264)),U_4263))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4264),c_Groups_Ozero__class_Ozero(U_4262))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4264)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4263),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4262),U_4265),U_4264)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4264)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4262),U_4263),U_4264)),U_4265)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_4262) ),
inference(variable_rename,[status(thm)],[f_1420_1]) ).
cnf(f_1420_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4263),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4262),U_4265),U_4264)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4264))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4262),U_4263),U_4264)),U_4265))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4262) ),
inference(clausify,[status(thm)],[f_1420_2]) ).
cnf(f_1420_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4262),U_4265),U_4264)),U_4263))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4264),c_Groups_Ozero__class_Ozero(U_4262)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4264))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4262),U_4263),U_4264)),U_4265))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4262) ),
inference(clausify,[status(thm)],[f_1420_2]) ).
cnf(f_1420_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4265))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4264),c_Groups_Ozero__class_Ozero(U_4262)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4264))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4262),U_4263),U_4264)),U_4265))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4262) ),
inference(clausify,[status(thm)],[f_1420_2]) ).
cnf(f_1420_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4264))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4264))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4262),U_4263),U_4264)),U_4265))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4262) ),
inference(clausify,[status(thm)],[f_1420_2]) ).
cnf(f_1420_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4264),c_Groups_Ozero__class_Ozero(U_4262)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4264),c_Groups_Ozero__class_Ozero(U_4262)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4264))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4262),U_4263),U_4264)),U_4265))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4262) ),
inference(clausify,[status(thm)],[f_1420_2]) ).
cnf(f_1420_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4265))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4264),c_Groups_Ozero__class_Ozero(U_4262)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4264))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4262),U_4263),U_4264)),U_4265))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4262) ),
inference(clausify,[status(thm)],[f_1420_2]) ).
cnf(f_1420_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4264),c_Groups_Ozero__class_Ozero(U_4262)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4262),U_4265),U_4264)),U_4263))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4264))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4262),U_4263),U_4264)),U_4265))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4262) ),
inference(clausify,[status(thm)],[f_1420_2]) ).
cnf(f_1420_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4265))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4262),U_4265),U_4264)),U_4263))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4264))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4262),U_4263),U_4264)),U_4265))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4262) ),
inference(clausify,[status(thm)],[f_1420_2]) ).
cnf(f_1420_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4264))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4263),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4262),U_4265),U_4264)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4262),U_4263),U_4264)),U_4265))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4262) ),
inference(clausify,[status(thm)],[f_1420_2]) ).
cnf(f_1420_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4264),c_Groups_Ozero__class_Ozero(U_4262)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4264),c_Groups_Ozero__class_Ozero(U_4262)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4263),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4262),U_4265),U_4264)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4262),U_4263),U_4264)),U_4265))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4262) ),
inference(clausify,[status(thm)],[f_1420_2]) ).
cnf(f_1420_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4265))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4264),c_Groups_Ozero__class_Ozero(U_4262)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4263),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4262),U_4265),U_4264)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4262),U_4263),U_4264)),U_4265))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4262) ),
inference(clausify,[status(thm)],[f_1420_2]) ).
cnf(f_1420_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4264),c_Groups_Ozero__class_Ozero(U_4262)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4262),U_4265),U_4264)),U_4263))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4263),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4262),U_4265),U_4264)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4262),U_4263),U_4264)),U_4265))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4262) ),
inference(clausify,[status(thm)],[f_1420_2]) ).
cnf(f_1420_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),c_Groups_Ozero__class_Ozero(U_4262)),U_4265))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4262),U_4265),U_4264)),U_4263))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),U_4263),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4262),U_4265),U_4264)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4262),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4262),U_4263),U_4264)),U_4265))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4262) ),
inference(clausify,[status(thm)],[f_1420_2]) ).
fof(f_1421_1,plain,
! [V_c_2,V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__divide__eq]) ).
fof(f_1421_2,plain,
! [U_4269,U_4268,U_4267,U_4266] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4266),U_4268),U_4269)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),c_Groups_Ozero__class_Ozero(U_4266)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4269),c_Groups_Ozero__class_Ozero(U_4266))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4268),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4266),U_4267),U_4269)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4269),c_Groups_Ozero__class_Ozero(U_4266))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),c_Groups_Ozero__class_Ozero(U_4266)),U_4269)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4266),U_4267),U_4269)),U_4268))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),c_Groups_Ozero__class_Ozero(U_4266)),U_4269)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),c_Groups_Ozero__class_Ozero(U_4266)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4269),c_Groups_Ozero__class_Ozero(U_4266))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4268),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4266),U_4267),U_4269)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4269),c_Groups_Ozero__class_Ozero(U_4266))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),c_Groups_Ozero__class_Ozero(U_4266)),U_4269)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4266),U_4267),U_4269)),U_4268))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),c_Groups_Ozero__class_Ozero(U_4266)),U_4269)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4266),U_4268),U_4269))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_4266) ),
inference(variable_rename,[status(thm)],[f_1421_1]) ).
cnf(f_1421_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4266),U_4267),U_4269)),U_4268))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),c_Groups_Ozero__class_Ozero(U_4266)),U_4269))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4266),U_4268),U_4269)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4266) ),
inference(clausify,[status(thm)],[f_1421_2]) ).
cnf(f_1421_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4268),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4266),U_4267),U_4269)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4269),c_Groups_Ozero__class_Ozero(U_4266)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),c_Groups_Ozero__class_Ozero(U_4266)),U_4269))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4266),U_4268),U_4269)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4266) ),
inference(clausify,[status(thm)],[f_1421_2]) ).
cnf(f_1421_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),c_Groups_Ozero__class_Ozero(U_4266)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4269),c_Groups_Ozero__class_Ozero(U_4266)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),c_Groups_Ozero__class_Ozero(U_4266)),U_4269))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4266),U_4268),U_4269)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4266) ),
inference(clausify,[status(thm)],[f_1421_2]) ).
cnf(f_1421_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),c_Groups_Ozero__class_Ozero(U_4266)),U_4269))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),c_Groups_Ozero__class_Ozero(U_4266)),U_4269))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4266),U_4268),U_4269)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4266) ),
inference(clausify,[status(thm)],[f_1421_2]) ).
cnf(f_1421_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4269),c_Groups_Ozero__class_Ozero(U_4266)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4269),c_Groups_Ozero__class_Ozero(U_4266)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),c_Groups_Ozero__class_Ozero(U_4266)),U_4269))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4266),U_4268),U_4269)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4266) ),
inference(clausify,[status(thm)],[f_1421_2]) ).
cnf(f_1421_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),c_Groups_Ozero__class_Ozero(U_4266)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4269),c_Groups_Ozero__class_Ozero(U_4266)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),c_Groups_Ozero__class_Ozero(U_4266)),U_4269))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4266),U_4268),U_4269)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4266) ),
inference(clausify,[status(thm)],[f_1421_2]) ).
cnf(f_1421_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4269),c_Groups_Ozero__class_Ozero(U_4266)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4268),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4266),U_4267),U_4269)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),c_Groups_Ozero__class_Ozero(U_4266)),U_4269))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4266),U_4268),U_4269)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4266) ),
inference(clausify,[status(thm)],[f_1421_2]) ).
cnf(f_1421_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),c_Groups_Ozero__class_Ozero(U_4266)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4268),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4266),U_4267),U_4269)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),c_Groups_Ozero__class_Ozero(U_4266)),U_4269))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4266),U_4268),U_4269)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4266) ),
inference(clausify,[status(thm)],[f_1421_2]) ).
cnf(f_1421_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),c_Groups_Ozero__class_Ozero(U_4266)),U_4269))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4266),U_4267),U_4269)),U_4268))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4266),U_4268),U_4269)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4266) ),
inference(clausify,[status(thm)],[f_1421_2]) ).
cnf(f_1421_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4269),c_Groups_Ozero__class_Ozero(U_4266)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4269),c_Groups_Ozero__class_Ozero(U_4266)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4266),U_4267),U_4269)),U_4268))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4266),U_4268),U_4269)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4266) ),
inference(clausify,[status(thm)],[f_1421_2]) ).
cnf(f_1421_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),c_Groups_Ozero__class_Ozero(U_4266)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4269),c_Groups_Ozero__class_Ozero(U_4266)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4266),U_4267),U_4269)),U_4268))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4266),U_4268),U_4269)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4266) ),
inference(clausify,[status(thm)],[f_1421_2]) ).
cnf(f_1421_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4269),c_Groups_Ozero__class_Ozero(U_4266)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4268),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4266),U_4267),U_4269)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4266),U_4267),U_4269)),U_4268))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4266),U_4268),U_4269)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4266) ),
inference(clausify,[status(thm)],[f_1421_2]) ).
cnf(f_1421_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),c_Groups_Ozero__class_Ozero(U_4266)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4268),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4266),U_4267),U_4269)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4266),U_4267),U_4269)),U_4268))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4266),U_4267),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4266),U_4268),U_4269)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4266) ),
inference(clausify,[status(thm)],[f_1421_2]) ).
fof(f_1422_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_1422_2,plain,
! [U_4270] :
( ( c_Nat__Transfer_Ois__nat(U_4270)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4270)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4270))
| ~ c_Nat__Transfer_Ois__nat(U_4270) ) ),
inference(variable_rename,[status(thm)],[f_1422_1]) ).
fof(f_1422_3,plain,
( ! [U_4272] :
( c_Nat__Transfer_Ois__nat(U_4272)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4272)) )
& ! [U_4271] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4271))
| ~ c_Nat__Transfer_Ois__nat(U_4271) ) ),
inference(miniscope,[status(thm)],[f_1422_2]) ).
cnf(f_1422_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4271))
| ~ c_Nat__Transfer_Ois__nat(U_4271) ),
inference(clausify,[status(thm)],[f_1422_3]) ).
cnf(f_1422_5,plain,
( c_Nat__Transfer_Ois__nat(U_4272)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4272)) ),
inference(clausify,[status(thm)],[f_1422_3]) ).
fof(f_1423_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_1423_2,plain,
! [U_4276,U_4275,U_4274,U_4273] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4273),U_4275),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4273),U_4276),U_4274)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4273),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4273),U_4276),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4273),U_4275),U_4274))),U_4274)
| U_4274 = c_Groups_Ozero__class_Ozero(U_4273)
| ~ class_Fields_Ofield__inverse__zero(U_4273) ),
inference(variable_rename,[status(thm)],[f_1423_1]) ).
cnf(f_1423_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4273),U_4275),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4273),U_4276),U_4274)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4273),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4273),U_4276),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4273),U_4275),U_4274))),U_4274)
| U_4274 = c_Groups_Ozero__class_Ozero(U_4273)
| ~ class_Fields_Ofield__inverse__zero(U_4273) ),
inference(clausify,[status(thm)],[f_1423_2]) ).
fof(f_1424_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_1424_2,plain,
! [U_4280,U_4279,U_4278,U_4277] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4277),U_4279),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4277),U_4280),U_4278)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4277),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4277),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4277),U_4278),U_4279)),U_4280)),U_4278)
| U_4278 = c_Groups_Ozero__class_Ozero(U_4277)
| ~ class_Fields_Ofield(U_4277) ),
inference(variable_rename,[status(thm)],[f_1424_1]) ).
cnf(f_1424_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4277),U_4279),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4277),U_4280),U_4278)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4277),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4277),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4277),U_4278),U_4279)),U_4280)),U_4278)
| U_4278 = c_Groups_Ozero__class_Ozero(U_4277)
| ~ class_Fields_Ofield(U_4277) ),
inference(clausify,[status(thm)],[f_1424_2]) ).
fof(f_1425_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_1425_2,plain,
! [U_4284,U_4283,U_4282,U_4281] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4281),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4281),U_4283),U_4282)),U_4284) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4281),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4281),U_4283),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4281),U_4284),U_4282))),U_4282)
| U_4282 = c_Groups_Ozero__class_Ozero(U_4281)
| ~ class_Fields_Ofield__inverse__zero(U_4281) ),
inference(variable_rename,[status(thm)],[f_1425_1]) ).
cnf(f_1425_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4281),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4281),U_4283),U_4282)),U_4284) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4281),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4281),U_4283),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4281),U_4284),U_4282))),U_4282)
| U_4282 = c_Groups_Ozero__class_Ozero(U_4281)
| ~ class_Fields_Ofield__inverse__zero(U_4281) ),
inference(clausify,[status(thm)],[f_1425_2]) ).
fof(f_1426_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_1426_2,plain,
! [U_4288,U_4287,U_4286,U_4285] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4285),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4285),U_4287),U_4286)),U_4288) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4285),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4285),U_4287),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4285),U_4286),U_4288))),U_4286)
| U_4286 = c_Groups_Ozero__class_Ozero(U_4285)
| ~ class_Fields_Ofield(U_4285) ),
inference(variable_rename,[status(thm)],[f_1426_1]) ).
cnf(f_1426_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4285),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4285),U_4287),U_4286)),U_4288) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4285),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4285),U_4287),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4285),U_4286),U_4288))),U_4286)
| U_4286 = c_Groups_Ozero__class_Ozero(U_4285)
| ~ class_Fields_Ofield(U_4285) ),
inference(clausify,[status(thm)],[f_1426_2]) ).
fof(f_1427_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_1427_2,plain,
! [U_4293,U_4292,U_4291,U_4290,U_4289] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4289),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4289),U_4292),U_4290)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4289),U_4293),U_4291)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4289),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4289),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4289),U_4292),U_4291)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4289),U_4293),U_4290))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4289),U_4290),U_4291))
| U_4291 = c_Groups_Ozero__class_Ozero(U_4289)
| U_4290 = c_Groups_Ozero__class_Ozero(U_4289)
| ~ class_Fields_Ofield(U_4289) ),
inference(variable_rename,[status(thm)],[f_1427_1]) ).
cnf(f_1427_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4289),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4289),U_4292),U_4290)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4289),U_4293),U_4291)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4289),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4289),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4289),U_4292),U_4291)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4289),U_4293),U_4290))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4289),U_4290),U_4291))
| U_4291 = c_Groups_Ozero__class_Ozero(U_4289)
| U_4290 = c_Groups_Ozero__class_Ozero(U_4289)
| ~ class_Fields_Ofield(U_4289) ),
inference(clausify,[status(thm)],[f_1427_2]) ).
fof(f_1428_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_1428_2,plain,
! [U_4297,U_4296,U_4295,U_4294] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4294),U_4296),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4294),U_4297),U_4295)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4294),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4294),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4294),U_4295),U_4296)),U_4297)),U_4295)
| U_4295 = c_Groups_Ozero__class_Ozero(U_4294)
| ~ class_Fields_Ofield(U_4294) ),
inference(variable_rename,[status(thm)],[f_1428_1]) ).
cnf(f_1428_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4294),U_4296),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4294),U_4297),U_4295)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4294),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4294),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4294),U_4295),U_4296)),U_4297)),U_4295)
| U_4295 = c_Groups_Ozero__class_Ozero(U_4294)
| ~ class_Fields_Ofield(U_4294) ),
inference(clausify,[status(thm)],[f_1428_2]) ).
fof(f_1429_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_1429_2,plain,
! [U_4301,U_4300,U_4299,U_4298] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4298),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4298),U_4300),U_4299)),U_4301) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4298),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4298),U_4300),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4298),U_4299),U_4301))),U_4299)
| U_4299 = c_Groups_Ozero__class_Ozero(U_4298)
| ~ class_Fields_Ofield(U_4298) ),
inference(variable_rename,[status(thm)],[f_1429_1]) ).
cnf(f_1429_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4298),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4298),U_4300),U_4299)),U_4301) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4298),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4298),U_4300),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4298),U_4299),U_4301))),U_4299)
| U_4299 = c_Groups_Ozero__class_Ozero(U_4298)
| ~ class_Fields_Ofield(U_4298) ),
inference(clausify,[status(thm)],[f_1429_2]) ).
fof(f_1430_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_1430_2,plain,
! [U_4306,U_4305,U_4304,U_4303,U_4302] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4302),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4302),U_4305),U_4303)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4302),U_4306),U_4304)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4302),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4302),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4302),U_4305),U_4304)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4302),U_4306),U_4303))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4302),U_4303),U_4304))
| U_4304 = c_Groups_Ozero__class_Ozero(U_4302)
| U_4303 = c_Groups_Ozero__class_Ozero(U_4302)
| ~ class_Fields_Ofield(U_4302) ),
inference(variable_rename,[status(thm)],[f_1430_1]) ).
cnf(f_1430_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4302),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4302),U_4305),U_4303)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4302),U_4306),U_4304)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4302),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4302),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4302),U_4305),U_4304)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4302),U_4306),U_4303))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4302),U_4303),U_4304))
| U_4304 = c_Groups_Ozero__class_Ozero(U_4302)
| U_4303 = c_Groups_Ozero__class_Ozero(U_4302)
| ~ class_Fields_Ofield(U_4302) ),
inference(clausify,[status(thm)],[f_1430_2]) ).
fof(f_1431_1,plain,
! [V_w_2,V_b_2,V_a_2,T_b] :
( ( ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
& hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) != V_b_2
& hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_b_2
| hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) )
| V_a_2 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Ofield__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of1]) ).
fof(f_1431_2,plain,
! [U_4310,U_4309,U_4308,U_4307] :
( ( ( U_4308 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4307),U_4309),hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310))
| ( U_4308 != c_Groups_Ozero__class_Ozero(U_4307)
& hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310) = c_Groups_Ozero__class_Ozero(U_4307) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4307),U_4308),hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310)) != U_4309
& hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310) != c_Groups_Ozero__class_Ozero(U_4307) ) )
& ( ( ( U_4308 = c_Groups_Ozero__class_Ozero(U_4307)
| hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310) != c_Groups_Ozero__class_Ozero(U_4307) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4307),U_4308),hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310)) = U_4309
| hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310) = c_Groups_Ozero__class_Ozero(U_4307) ) )
| U_4308 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4307),U_4309),hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310)) ) )
| ~ class_Int_Onumber(U_4307)
| ~ class_Fields_Ofield__inverse__zero(U_4307) ),
inference(variable_rename,[status(thm)],[f_1431_1]) ).
cnf(f_1431_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4307),U_4308),hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310)) = U_4309
| hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310) = c_Groups_Ozero__class_Ozero(U_4307)
| U_4308 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4307),U_4309),hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310))
| ~ class_Int_Onumber(U_4307)
| ~ class_Fields_Ofield__inverse__zero(U_4307) ),
inference(clausify,[status(thm)],[f_1431_2]) ).
cnf(f_1431_4,plain,
( U_4308 = c_Groups_Ozero__class_Ozero(U_4307)
| hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310) != c_Groups_Ozero__class_Ozero(U_4307)
| U_4308 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4307),U_4309),hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310))
| ~ class_Int_Onumber(U_4307)
| ~ class_Fields_Ofield__inverse__zero(U_4307) ),
inference(clausify,[status(thm)],[f_1431_2]) ).
cnf(f_1431_5,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310) = c_Groups_Ozero__class_Ozero(U_4307)
| hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310) != c_Groups_Ozero__class_Ozero(U_4307)
| U_4308 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4307),U_4309),hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310))
| ~ class_Int_Onumber(U_4307)
| ~ class_Fields_Ofield__inverse__zero(U_4307) ),
inference(clausify,[status(thm)],[f_1431_2]) ).
cnf(f_1431_6,plain,
( U_4308 != c_Groups_Ozero__class_Ozero(U_4307)
| hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310) != c_Groups_Ozero__class_Ozero(U_4307)
| U_4308 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4307),U_4309),hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310))
| ~ class_Int_Onumber(U_4307)
| ~ class_Fields_Ofield__inverse__zero(U_4307) ),
inference(clausify,[status(thm)],[f_1431_2]) ).
cnf(f_1431_7,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310) = c_Groups_Ozero__class_Ozero(U_4307)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4307),U_4308),hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310)) != U_4309
| U_4308 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4307),U_4309),hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310))
| ~ class_Int_Onumber(U_4307)
| ~ class_Fields_Ofield__inverse__zero(U_4307) ),
inference(clausify,[status(thm)],[f_1431_2]) ).
cnf(f_1431_8,plain,
( U_4308 != c_Groups_Ozero__class_Ozero(U_4307)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4307),U_4308),hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310)) != U_4309
| U_4308 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4307),U_4309),hAPP(c_Int_Onumber__class_Onumber__of(U_4307),U_4310))
| ~ class_Int_Onumber(U_4307)
| ~ class_Fields_Ofield__inverse__zero(U_4307) ),
inference(clausify,[status(thm)],[f_1431_2]) ).
fof(f_1432_1,plain,
! [V_c_2,V_b_2,V_w_2,T_b] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
| ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
& V_c_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) != V_b_2
& V_c_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
& ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_c_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) = V_b_2
| V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
| hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Ofield__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of]) ).
fof(f_1432_2,plain,
! [U_4314,U_4313,U_4312,U_4311] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4311),U_4312) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4311),U_4313),U_4314)
| ( hAPP(c_Int_Onumber__class_Onumber__of(U_4311),U_4312) != c_Groups_Ozero__class_Ozero(U_4311)
& U_4314 = c_Groups_Ozero__class_Ozero(U_4311) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4311),hAPP(c_Int_Onumber__class_Onumber__of(U_4311),U_4312)),U_4314) != U_4313
& U_4314 != c_Groups_Ozero__class_Ozero(U_4311) ) )
& ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4311),U_4312) = c_Groups_Ozero__class_Ozero(U_4311)
| U_4314 != c_Groups_Ozero__class_Ozero(U_4311) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4311),hAPP(c_Int_Onumber__class_Onumber__of(U_4311),U_4312)),U_4314) = U_4313
| U_4314 = c_Groups_Ozero__class_Ozero(U_4311) ) )
| hAPP(c_Int_Onumber__class_Onumber__of(U_4311),U_4312) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4311),U_4313),U_4314) ) )
| ~ class_Int_Onumber(U_4311)
| ~ class_Fields_Ofield__inverse__zero(U_4311) ),
inference(variable_rename,[status(thm)],[f_1432_1]) ).
cnf(f_1432_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4311),hAPP(c_Int_Onumber__class_Onumber__of(U_4311),U_4312)),U_4314) = U_4313
| U_4314 = c_Groups_Ozero__class_Ozero(U_4311)
| hAPP(c_Int_Onumber__class_Onumber__of(U_4311),U_4312) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4311),U_4313),U_4314)
| ~ class_Int_Onumber(U_4311)
| ~ class_Fields_Ofield__inverse__zero(U_4311) ),
inference(clausify,[status(thm)],[f_1432_2]) ).
cnf(f_1432_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_4311),U_4312) = c_Groups_Ozero__class_Ozero(U_4311)
| U_4314 != c_Groups_Ozero__class_Ozero(U_4311)
| hAPP(c_Int_Onumber__class_Onumber__of(U_4311),U_4312) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4311),U_4313),U_4314)
| ~ class_Int_Onumber(U_4311)
| ~ class_Fields_Ofield__inverse__zero(U_4311) ),
inference(clausify,[status(thm)],[f_1432_2]) ).
cnf(f_1432_5,plain,
( U_4314 = c_Groups_Ozero__class_Ozero(U_4311)
| U_4314 != c_Groups_Ozero__class_Ozero(U_4311)
| hAPP(c_Int_Onumber__class_Onumber__of(U_4311),U_4312) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4311),U_4313),U_4314)
| ~ class_Int_Onumber(U_4311)
| ~ class_Fields_Ofield__inverse__zero(U_4311) ),
inference(clausify,[status(thm)],[f_1432_2]) ).
cnf(f_1432_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_4311),U_4312) != c_Groups_Ozero__class_Ozero(U_4311)
| U_4314 != c_Groups_Ozero__class_Ozero(U_4311)
| hAPP(c_Int_Onumber__class_Onumber__of(U_4311),U_4312) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4311),U_4313),U_4314)
| ~ class_Int_Onumber(U_4311)
| ~ class_Fields_Ofield__inverse__zero(U_4311) ),
inference(clausify,[status(thm)],[f_1432_2]) ).
cnf(f_1432_7,plain,
( U_4314 = c_Groups_Ozero__class_Ozero(U_4311)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4311),hAPP(c_Int_Onumber__class_Onumber__of(U_4311),U_4312)),U_4314) != U_4313
| hAPP(c_Int_Onumber__class_Onumber__of(U_4311),U_4312) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4311),U_4313),U_4314)
| ~ class_Int_Onumber(U_4311)
| ~ class_Fields_Ofield__inverse__zero(U_4311) ),
inference(clausify,[status(thm)],[f_1432_2]) ).
cnf(f_1432_8,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_4311),U_4312) != c_Groups_Ozero__class_Ozero(U_4311)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4311),hAPP(c_Int_Onumber__class_Onumber__of(U_4311),U_4312)),U_4314) != U_4313
| hAPP(c_Int_Onumber__class_Onumber__of(U_4311),U_4312) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4311),U_4313),U_4314)
| ~ class_Int_Onumber(U_4311)
| ~ class_Fields_Ofield__inverse__zero(U_4311) ),
inference(clausify,[status(thm)],[f_1432_2]) ).
fof(f_1433_1,plain,
! [V_w_2,V_c_2,V_b_2,T_b] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
| ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
& V_c_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)
& V_c_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
& ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_c_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)
| V_c_2 = c_Groups_Ozero__class_Ozero(T_b) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) != hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Ofield__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of]) ).
fof(f_1433_2,plain,
! [U_4318,U_4317,U_4316,U_4315] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4315),U_4316),U_4317) = hAPP(c_Int_Onumber__class_Onumber__of(U_4315),U_4318)
| ( hAPP(c_Int_Onumber__class_Onumber__of(U_4315),U_4318) != c_Groups_Ozero__class_Ozero(U_4315)
& U_4317 = c_Groups_Ozero__class_Ozero(U_4315) )
| ( U_4316 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4315),hAPP(c_Int_Onumber__class_Onumber__of(U_4315),U_4318)),U_4317)
& U_4317 != c_Groups_Ozero__class_Ozero(U_4315) ) )
& ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4315),U_4318) = c_Groups_Ozero__class_Ozero(U_4315)
| U_4317 != c_Groups_Ozero__class_Ozero(U_4315) )
& ( U_4316 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4315),hAPP(c_Int_Onumber__class_Onumber__of(U_4315),U_4318)),U_4317)
| U_4317 = c_Groups_Ozero__class_Ozero(U_4315) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4315),U_4316),U_4317) != hAPP(c_Int_Onumber__class_Onumber__of(U_4315),U_4318) ) )
| ~ class_Int_Onumber(U_4315)
| ~ class_Fields_Ofield__inverse__zero(U_4315) ),
inference(variable_rename,[status(thm)],[f_1433_1]) ).
cnf(f_1433_3,plain,
( U_4316 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4315),hAPP(c_Int_Onumber__class_Onumber__of(U_4315),U_4318)),U_4317)
| U_4317 = c_Groups_Ozero__class_Ozero(U_4315)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4315),U_4316),U_4317) != hAPP(c_Int_Onumber__class_Onumber__of(U_4315),U_4318)
| ~ class_Int_Onumber(U_4315)
| ~ class_Fields_Ofield__inverse__zero(U_4315) ),
inference(clausify,[status(thm)],[f_1433_2]) ).
cnf(f_1433_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_4315),U_4318) = c_Groups_Ozero__class_Ozero(U_4315)
| U_4317 != c_Groups_Ozero__class_Ozero(U_4315)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4315),U_4316),U_4317) != hAPP(c_Int_Onumber__class_Onumber__of(U_4315),U_4318)
| ~ class_Int_Onumber(U_4315)
| ~ class_Fields_Ofield__inverse__zero(U_4315) ),
inference(clausify,[status(thm)],[f_1433_2]) ).
cnf(f_1433_5,plain,
( U_4317 = c_Groups_Ozero__class_Ozero(U_4315)
| U_4317 != c_Groups_Ozero__class_Ozero(U_4315)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4315),U_4316),U_4317) = hAPP(c_Int_Onumber__class_Onumber__of(U_4315),U_4318)
| ~ class_Int_Onumber(U_4315)
| ~ class_Fields_Ofield__inverse__zero(U_4315) ),
inference(clausify,[status(thm)],[f_1433_2]) ).
cnf(f_1433_6,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_4315),U_4318) != c_Groups_Ozero__class_Ozero(U_4315)
| U_4317 != c_Groups_Ozero__class_Ozero(U_4315)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4315),U_4316),U_4317) = hAPP(c_Int_Onumber__class_Onumber__of(U_4315),U_4318)
| ~ class_Int_Onumber(U_4315)
| ~ class_Fields_Ofield__inverse__zero(U_4315) ),
inference(clausify,[status(thm)],[f_1433_2]) ).
cnf(f_1433_7,plain,
( U_4317 = c_Groups_Ozero__class_Ozero(U_4315)
| U_4316 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4315),hAPP(c_Int_Onumber__class_Onumber__of(U_4315),U_4318)),U_4317)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4315),U_4316),U_4317) = hAPP(c_Int_Onumber__class_Onumber__of(U_4315),U_4318)
| ~ class_Int_Onumber(U_4315)
| ~ class_Fields_Ofield__inverse__zero(U_4315) ),
inference(clausify,[status(thm)],[f_1433_2]) ).
cnf(f_1433_8,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_4315),U_4318) != c_Groups_Ozero__class_Ozero(U_4315)
| U_4316 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4315),hAPP(c_Int_Onumber__class_Onumber__of(U_4315),U_4318)),U_4317)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4315),U_4316),U_4317) = hAPP(c_Int_Onumber__class_Onumber__of(U_4315),U_4318)
| ~ class_Int_Onumber(U_4315)
| ~ class_Fields_Ofield__inverse__zero(U_4315) ),
inference(clausify,[status(thm)],[f_1433_2]) ).
fof(f_1434_1,plain,
! [V_a_2,V_w_2,V_b_2,T_b] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_a_2
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
& hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) )
| ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
& hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
| hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) != V_a_2 ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Ofield__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of1]) ).
fof(f_1434_2,plain,
! [U_4322,U_4321,U_4320,U_4319] :
( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4319),U_4320),hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321)) = U_4322
| ( U_4322 != c_Groups_Ozero__class_Ozero(U_4319)
& hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321) = c_Groups_Ozero__class_Ozero(U_4319) )
| ( U_4320 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4319),U_4322),hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321))
& hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321) != c_Groups_Ozero__class_Ozero(U_4319) ) )
& ( ( ( U_4322 = c_Groups_Ozero__class_Ozero(U_4319)
| hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321) != c_Groups_Ozero__class_Ozero(U_4319) )
& ( U_4320 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4319),U_4322),hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321))
| hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321) = c_Groups_Ozero__class_Ozero(U_4319) ) )
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4319),U_4320),hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321)) != U_4322 ) )
| ~ class_Int_Onumber(U_4319)
| ~ class_Fields_Ofield__inverse__zero(U_4319) ),
inference(variable_rename,[status(thm)],[f_1434_1]) ).
cnf(f_1434_3,plain,
( U_4320 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4319),U_4322),hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321))
| hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321) = c_Groups_Ozero__class_Ozero(U_4319)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4319),U_4320),hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321)) != U_4322
| ~ class_Int_Onumber(U_4319)
| ~ class_Fields_Ofield__inverse__zero(U_4319) ),
inference(clausify,[status(thm)],[f_1434_2]) ).
cnf(f_1434_4,plain,
( U_4322 = c_Groups_Ozero__class_Ozero(U_4319)
| hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321) != c_Groups_Ozero__class_Ozero(U_4319)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4319),U_4320),hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321)) != U_4322
| ~ class_Int_Onumber(U_4319)
| ~ class_Fields_Ofield__inverse__zero(U_4319) ),
inference(clausify,[status(thm)],[f_1434_2]) ).
cnf(f_1434_5,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321) = c_Groups_Ozero__class_Ozero(U_4319)
| hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321) != c_Groups_Ozero__class_Ozero(U_4319)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4319),U_4320),hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321)) = U_4322
| ~ class_Int_Onumber(U_4319)
| ~ class_Fields_Ofield__inverse__zero(U_4319) ),
inference(clausify,[status(thm)],[f_1434_2]) ).
cnf(f_1434_6,plain,
( U_4322 != c_Groups_Ozero__class_Ozero(U_4319)
| hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321) != c_Groups_Ozero__class_Ozero(U_4319)
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4319),U_4320),hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321)) = U_4322
| ~ class_Int_Onumber(U_4319)
| ~ class_Fields_Ofield__inverse__zero(U_4319) ),
inference(clausify,[status(thm)],[f_1434_2]) ).
cnf(f_1434_7,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321) = c_Groups_Ozero__class_Ozero(U_4319)
| U_4320 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4319),U_4322),hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321))
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4319),U_4320),hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321)) = U_4322
| ~ class_Int_Onumber(U_4319)
| ~ class_Fields_Ofield__inverse__zero(U_4319) ),
inference(clausify,[status(thm)],[f_1434_2]) ).
cnf(f_1434_8,plain,
( U_4322 != c_Groups_Ozero__class_Ozero(U_4319)
| U_4320 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4319),U_4322),hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321))
| hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4319),U_4320),hAPP(c_Int_Onumber__class_Onumber__of(U_4319),U_4321)) = U_4322
| ~ class_Int_Onumber(U_4319)
| ~ class_Fields_Ofield__inverse__zero(U_4319) ),
inference(clausify,[status(thm)],[f_1434_2]) ).
fof(f_1435_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_1435_2,plain,
! [U_4325,U_4324,U_4323] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4323),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4323),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4323),U_4324),U_4325)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4323),c_Groups_Oone__class_Oone(U_4323)),c_Groups_Oone__class_Oone(U_4323)))),U_4325))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4323),U_4324),U_4325))
| ~ class_Fields_Olinordered__field(U_4323) ),
inference(variable_rename,[status(thm)],[f_1435_1]) ).
cnf(f_1435_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4323),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4323),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4323),U_4324),U_4325)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4323),c_Groups_Oone__class_Oone(U_4323)),c_Groups_Oone__class_Oone(U_4323)))),U_4325))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4323),U_4324),U_4325))
| ~ class_Fields_Olinordered__field(U_4323) ),
inference(clausify,[status(thm)],[f_1435_2]) ).
fof(f_1436_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_1436_2,plain,
! [U_4328,U_4327,U_4326] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4326),U_4327),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4326),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4326),U_4327),U_4328)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4326),c_Groups_Oone__class_Oone(U_4326)),c_Groups_Oone__class_Oone(U_4326)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4326),U_4327),U_4328))
| ~ class_Fields_Olinordered__field(U_4326) ),
inference(variable_rename,[status(thm)],[f_1436_1]) ).
cnf(f_1436_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4326),U_4327),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4326),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4326),U_4327),U_4328)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4326),c_Groups_Oone__class_Oone(U_4326)),c_Groups_Oone__class_Oone(U_4326)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4326),U_4327),U_4328))
| ~ class_Fields_Olinordered__field(U_4326) ),
inference(clausify,[status(thm)],[f_1436_2]) ).
fof(f_1437_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_1437_2,plain,
! [U_4330,U_4329] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4329),U_4330),hAPP(c_Int_Onumber__class_Onumber__of(U_4329),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_4329)
| ~ class_Int_Onumber__ring(U_4329)
| ~ class_Fields_Ofield__inverse__zero(U_4329) ),
inference(variable_rename,[status(thm)],[f_1437_1]) ).
cnf(f_1437_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4329),U_4330),hAPP(c_Int_Onumber__class_Onumber__of(U_4329),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_4329)
| ~ class_Int_Onumber__ring(U_4329)
| ~ class_Fields_Ofield__inverse__zero(U_4329) ),
inference(clausify,[status(thm)],[f_1437_2]) ).
fof(f_1438_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_1438_2,plain,
! [U_4333,U_4332,U_4331] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4331),hAPP(c_Groups_Oabs__class_Oabs(U_4331),U_4333)),U_4332) = hAPP(c_Groups_Oabs__class_Oabs(U_4331),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4331),U_4333),U_4332))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4331),c_Groups_Ozero__class_Ozero(U_4331)),U_4332))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4331) ),
inference(variable_rename,[status(thm)],[f_1438_1]) ).
cnf(f_1438_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4331),hAPP(c_Groups_Oabs__class_Oabs(U_4331),U_4333)),U_4332) = hAPP(c_Groups_Oabs__class_Oabs(U_4331),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4331),U_4333),U_4332))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4331),c_Groups_Ozero__class_Ozero(U_4331)),U_4332))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4331) ),
inference(clausify,[status(thm)],[f_1438_2]) ).
fof(f_1439_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_1439_2,plain,
! [U_4335,U_4334] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4334),U_4335),hAPP(c_Int_Onumber__class_Onumber__of(U_4334),c_Int_OBit1(c_Int_OPls))) = U_4335
| ~ class_Int_Onumber__ring(U_4334)
| ~ class_Fields_Ofield(U_4334) ),
inference(variable_rename,[status(thm)],[f_1439_1]) ).
cnf(f_1439_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4334),U_4335),hAPP(c_Int_Onumber__class_Onumber__of(U_4334),c_Int_OBit1(c_Int_OPls))) = U_4335
| ~ class_Int_Onumber__ring(U_4334)
| ~ class_Fields_Ofield(U_4334) ),
inference(clausify,[status(thm)],[f_1439_2]) ).
fof(f_1440_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_1440_2,plain,
! [U_4337,U_4336] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4336),U_4337),hAPP(c_Int_Onumber__class_Onumber__of(U_4336),c_Int_OBit1(c_Int_OPls))) = U_4337
| ~ class_Int_Onumber__ring(U_4336)
| ~ class_Fields_Ofield(U_4336) ),
inference(variable_rename,[status(thm)],[f_1440_1]) ).
cnf(f_1440_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4336),U_4337),hAPP(c_Int_Onumber__class_Onumber__of(U_4336),c_Int_OBit1(c_Int_OPls))) = U_4337
| ~ class_Int_Onumber__ring(U_4336)
| ~ class_Fields_Ofield(U_4336) ),
inference(clausify,[status(thm)],[f_1440_2]) ).
fof(f_1441_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_1441_2,plain,
! [U_4339,U_4338] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4338),U_4339),hAPP(c_Int_Onumber__class_Onumber__of(U_4338),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4338),U_4339)
| ~ class_Int_Onumber__ring(U_4338)
| ~ class_Fields_Ofield__inverse__zero(U_4338) ),
inference(variable_rename,[status(thm)],[f_1441_1]) ).
cnf(f_1441_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4338),U_4339),hAPP(c_Int_Onumber__class_Onumber__of(U_4338),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4338),U_4339)
| ~ class_Int_Onumber__ring(U_4338)
| ~ class_Fields_Ofield__inverse__zero(U_4338) ),
inference(clausify,[status(thm)],[f_1441_2]) ).
fof(f_1442_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]) ).
cnf(f_1442_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(clausify,[status(thm)],[f_1442_1]) ).
fof(f_1443_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_1443_2,plain,
! [U_4343,U_4342,U_4341,U_4340] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4340),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4340),U_4343),U_4341)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4340),U_4343),U_4342)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4340),c_Groups_Ozero__class_Ozero(U_4340)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4340),U_4341),U_4342)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4340),U_4343),c_Groups_Ozero__class_Ozero(U_4340)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4340),U_4341),U_4342))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4340) ),
inference(variable_rename,[status(thm)],[f_1443_1]) ).
cnf(f_1443_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4340),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4340),U_4343),U_4341)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4340),U_4343),U_4342)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4340),c_Groups_Ozero__class_Ozero(U_4340)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4340),U_4341),U_4342)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4340),U_4343),c_Groups_Ozero__class_Ozero(U_4340)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4340),U_4341),U_4342))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4340) ),
inference(clausify,[status(thm)],[f_1443_2]) ).
fof(f_1444_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_1444_2,plain,
! [U_4347,U_4346,U_4345,U_4344] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4344),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4344),U_4347),U_4346)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4344),U_4347),U_4345)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4344),c_Groups_Ozero__class_Ozero(U_4344)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4344),U_4346),U_4345)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4344),c_Groups_Ozero__class_Ozero(U_4344)),U_4347))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4344),U_4345),U_4346))
| ~ class_Fields_Olinordered__field(U_4344) ),
inference(variable_rename,[status(thm)],[f_1444_1]) ).
cnf(f_1444_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4344),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4344),U_4347),U_4346)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4344),U_4347),U_4345)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4344),c_Groups_Ozero__class_Ozero(U_4344)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4344),U_4346),U_4345)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4344),c_Groups_Ozero__class_Ozero(U_4344)),U_4347))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4344),U_4345),U_4346))
| ~ class_Fields_Olinordered__field(U_4344) ),
inference(clausify,[status(thm)],[f_1444_2]) ).
fof(f_1445_1,plain,
! [V_a_2,V_b_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__divide__le__eq]) ).
fof(f_1445_2,plain,
! [U_4351,U_4350,U_4349,U_4348] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4348),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4348),U_4350),U_4349)),U_4351))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4348),U_4351),U_4349)),U_4350)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4348),U_4351),U_4349)),U_4350))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4348),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4348),U_4350),U_4349)),U_4351)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4348),U_4349),c_Groups_Ozero__class_Ozero(U_4348)))
| ~ class_Fields_Olinordered__field(U_4348) ),
inference(variable_rename,[status(thm)],[f_1445_1]) ).
cnf(f_1445_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4348),U_4351),U_4349)),U_4350))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4348),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4348),U_4350),U_4349)),U_4351))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4348),U_4349),c_Groups_Ozero__class_Ozero(U_4348)))
| ~ class_Fields_Olinordered__field(U_4348) ),
inference(clausify,[status(thm)],[f_1445_2]) ).
cnf(f_1445_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4348),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4348),U_4350),U_4349)),U_4351))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4348),U_4351),U_4349)),U_4350))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4348),U_4349),c_Groups_Ozero__class_Ozero(U_4348)))
| ~ class_Fields_Olinordered__field(U_4348) ),
inference(clausify,[status(thm)],[f_1445_2]) ).
fof(f_1446_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_neg__le__divide__eq]) ).
fof(f_1446_2,plain,
! [U_4355,U_4354,U_4353,U_4352] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4352),U_4354),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4352),U_4355),U_4353)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4352),U_4355),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4352),U_4354),U_4353))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4352),U_4355),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4352),U_4354),U_4353)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4352),U_4354),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4352),U_4355),U_4353))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4352),U_4353),c_Groups_Ozero__class_Ozero(U_4352)))
| ~ class_Fields_Olinordered__field(U_4352) ),
inference(variable_rename,[status(thm)],[f_1446_1]) ).
cnf(f_1446_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4352),U_4355),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4352),U_4354),U_4353)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4352),U_4354),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4352),U_4355),U_4353)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4352),U_4353),c_Groups_Ozero__class_Ozero(U_4352)))
| ~ class_Fields_Olinordered__field(U_4352) ),
inference(clausify,[status(thm)],[f_1446_2]) ).
cnf(f_1446_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4352),U_4354),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4352),U_4355),U_4353)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4352),U_4355),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4352),U_4354),U_4353)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4352),U_4353),c_Groups_Ozero__class_Ozero(U_4352)))
| ~ class_Fields_Olinordered__field(U_4352) ),
inference(clausify,[status(thm)],[f_1446_2]) ).
fof(f_1447_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_1447_2,plain,
! [U_4359,U_4358,U_4357,U_4356] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4356),U_4358),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4356),U_4359),U_4357)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4356),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4356),U_4358),U_4357)),U_4359))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4356),c_Groups_Ozero__class_Ozero(U_4356)),U_4357))
| ~ class_Fields_Olinordered__field(U_4356) ),
inference(variable_rename,[status(thm)],[f_1447_1]) ).
cnf(f_1447_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4356),U_4358),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4356),U_4359),U_4357)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4356),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4356),U_4358),U_4357)),U_4359))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4356),c_Groups_Ozero__class_Ozero(U_4356)),U_4357))
| ~ class_Fields_Olinordered__field(U_4356) ),
inference(clausify,[status(thm)],[f_1447_2]) ).
fof(f_1448_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_1448_2,plain,
! [U_4363,U_4362,U_4361,U_4360] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4360),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4360),U_4362),U_4361)),U_4363))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4360),U_4362),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4360),U_4363),U_4361)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4360),c_Groups_Ozero__class_Ozero(U_4360)),U_4361))
| ~ class_Fields_Olinordered__field(U_4360) ),
inference(variable_rename,[status(thm)],[f_1448_1]) ).
cnf(f_1448_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4360),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4360),U_4362),U_4361)),U_4363))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4360),U_4362),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4360),U_4363),U_4361)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4360),c_Groups_Ozero__class_Ozero(U_4360)),U_4361))
| ~ class_Fields_Olinordered__field(U_4360) ),
inference(clausify,[status(thm)],[f_1448_2]) ).
fof(f_1449_1,plain,
! [V_a_2,V_b_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_pos__divide__le__eq]) ).
fof(f_1449_2,plain,
! [U_4367,U_4366,U_4365,U_4364] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4364),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4364),U_4366),U_4365)),U_4367))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4364),U_4366),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4364),U_4367),U_4365))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4364),U_4366),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4364),U_4367),U_4365)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4364),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4364),U_4366),U_4365)),U_4367)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4364),c_Groups_Ozero__class_Ozero(U_4364)),U_4365))
| ~ class_Fields_Olinordered__field(U_4364) ),
inference(variable_rename,[status(thm)],[f_1449_1]) ).
cnf(f_1449_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4364),U_4366),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4364),U_4367),U_4365)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4364),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4364),U_4366),U_4365)),U_4367))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4364),c_Groups_Ozero__class_Ozero(U_4364)),U_4365))
| ~ class_Fields_Olinordered__field(U_4364) ),
inference(clausify,[status(thm)],[f_1449_2]) ).
cnf(f_1449_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4364),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4364),U_4366),U_4365)),U_4367))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4364),U_4366),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4364),U_4367),U_4365)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4364),c_Groups_Ozero__class_Ozero(U_4364)),U_4365))
| ~ class_Fields_Olinordered__field(U_4364) ),
inference(clausify,[status(thm)],[f_1449_2]) ).
fof(f_1450_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq]) ).
fof(f_1450_2,plain,
! [U_4371,U_4370,U_4369,U_4368] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4368),U_4370),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4368),U_4371),U_4369)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4368),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4368),U_4370),U_4369)),U_4371)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4368),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4368),U_4370),U_4369)),U_4371))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4368),U_4370),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4368),U_4371),U_4369))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4368),c_Groups_Ozero__class_Ozero(U_4368)),U_4369))
| ~ class_Fields_Olinordered__field(U_4368) ),
inference(variable_rename,[status(thm)],[f_1450_1]) ).
cnf(f_1450_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4368),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4368),U_4370),U_4369)),U_4371))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4368),U_4370),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4368),U_4371),U_4369)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4368),c_Groups_Ozero__class_Ozero(U_4368)),U_4369))
| ~ class_Fields_Olinordered__field(U_4368) ),
inference(clausify,[status(thm)],[f_1450_2]) ).
cnf(f_1450_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4368),U_4370),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4368),U_4371),U_4369)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4368),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4368),U_4370),U_4369)),U_4371))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4368),c_Groups_Ozero__class_Ozero(U_4368)),U_4369))
| ~ class_Fields_Olinordered__field(U_4368) ),
inference(clausify,[status(thm)],[f_1450_2]) ).
fof(f_1451_1,plain,
! [V_a_2,V_c_2,V_b_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__eq]) ).
fof(f_1451_2,plain,
! [U_4375,U_4374,U_4373,U_4372] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4372),U_4373),U_4374)),U_4375))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4375))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),U_4374),c_Groups_Ozero__class_Ozero(U_4372))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4372),U_4375),U_4374)),U_4373))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),U_4374),c_Groups_Ozero__class_Ozero(U_4372))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4374)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),U_4373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4372),U_4375),U_4374)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4374)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4375))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),U_4374),c_Groups_Ozero__class_Ozero(U_4372))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4372),U_4375),U_4374)),U_4373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),U_4374),c_Groups_Ozero__class_Ozero(U_4372))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4374)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),U_4373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4372),U_4375),U_4374)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4374)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4372),U_4373),U_4374)),U_4375)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_4372) ),
inference(variable_rename,[status(thm)],[f_1451_1]) ).
cnf(f_1451_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),U_4373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4372),U_4375),U_4374)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4374))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4372),U_4373),U_4374)),U_4375))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4372) ),
inference(clausify,[status(thm)],[f_1451_2]) ).
cnf(f_1451_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4372),U_4375),U_4374)),U_4373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),U_4374),c_Groups_Ozero__class_Ozero(U_4372)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4374))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4372),U_4373),U_4374)),U_4375))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4372) ),
inference(clausify,[status(thm)],[f_1451_2]) ).
cnf(f_1451_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4375))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),U_4374),c_Groups_Ozero__class_Ozero(U_4372)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4374))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4372),U_4373),U_4374)),U_4375))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4372) ),
inference(clausify,[status(thm)],[f_1451_2]) ).
cnf(f_1451_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4374))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4374))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4372),U_4373),U_4374)),U_4375))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4372) ),
inference(clausify,[status(thm)],[f_1451_2]) ).
cnf(f_1451_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),U_4374),c_Groups_Ozero__class_Ozero(U_4372)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),U_4374),c_Groups_Ozero__class_Ozero(U_4372)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4374))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4372),U_4373),U_4374)),U_4375))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4372) ),
inference(clausify,[status(thm)],[f_1451_2]) ).
cnf(f_1451_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4375))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),U_4374),c_Groups_Ozero__class_Ozero(U_4372)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4374))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4372),U_4373),U_4374)),U_4375))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4372) ),
inference(clausify,[status(thm)],[f_1451_2]) ).
cnf(f_1451_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),U_4374),c_Groups_Ozero__class_Ozero(U_4372)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4372),U_4375),U_4374)),U_4373))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4374))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4372),U_4373),U_4374)),U_4375))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4372) ),
inference(clausify,[status(thm)],[f_1451_2]) ).
cnf(f_1451_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4375))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4372),U_4375),U_4374)),U_4373))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4374))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4372),U_4373),U_4374)),U_4375))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4372) ),
inference(clausify,[status(thm)],[f_1451_2]) ).
cnf(f_1451_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4374))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),U_4373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4372),U_4375),U_4374)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4372),U_4373),U_4374)),U_4375))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4372) ),
inference(clausify,[status(thm)],[f_1451_2]) ).
cnf(f_1451_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),U_4374),c_Groups_Ozero__class_Ozero(U_4372)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),U_4374),c_Groups_Ozero__class_Ozero(U_4372)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),U_4373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4372),U_4375),U_4374)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4372),U_4373),U_4374)),U_4375))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4372) ),
inference(clausify,[status(thm)],[f_1451_2]) ).
cnf(f_1451_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4375))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),U_4374),c_Groups_Ozero__class_Ozero(U_4372)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),U_4373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4372),U_4375),U_4374)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4372),U_4373),U_4374)),U_4375))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4372) ),
inference(clausify,[status(thm)],[f_1451_2]) ).
cnf(f_1451_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4372),U_4374),c_Groups_Ozero__class_Ozero(U_4372)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4372),U_4375),U_4374)),U_4373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),U_4373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4372),U_4375),U_4374)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4372),U_4373),U_4374)),U_4375))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4372) ),
inference(clausify,[status(thm)],[f_1451_2]) ).
cnf(f_1451_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),c_Groups_Ozero__class_Ozero(U_4372)),U_4375))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4372),U_4375),U_4374)),U_4373))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),U_4373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4372),U_4375),U_4374)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4372),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4372),U_4373),U_4374)),U_4375))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4372) ),
inference(clausify,[status(thm)],[f_1451_2]) ).
fof(f_1452_1,plain,
! [V_c_2,V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__divide__eq]) ).
fof(f_1452_2,plain,
! [U_4379,U_4378,U_4377,U_4376] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4376),U_4378),U_4379)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),c_Groups_Ozero__class_Ozero(U_4376)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),U_4379),c_Groups_Ozero__class_Ozero(U_4376))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4376),U_4377),U_4379)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),U_4379),c_Groups_Ozero__class_Ozero(U_4376))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),c_Groups_Ozero__class_Ozero(U_4376)),U_4379)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4376),U_4377),U_4379)),U_4378))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),c_Groups_Ozero__class_Ozero(U_4376)),U_4379)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),c_Groups_Ozero__class_Ozero(U_4376)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),U_4379),c_Groups_Ozero__class_Ozero(U_4376))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4376),U_4377),U_4379)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),U_4379),c_Groups_Ozero__class_Ozero(U_4376))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),c_Groups_Ozero__class_Ozero(U_4376)),U_4379)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4376),U_4377),U_4379)),U_4378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),c_Groups_Ozero__class_Ozero(U_4376)),U_4379)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4376),U_4378),U_4379))) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_4376) ),
inference(variable_rename,[status(thm)],[f_1452_1]) ).
cnf(f_1452_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4376),U_4377),U_4379)),U_4378))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),c_Groups_Ozero__class_Ozero(U_4376)),U_4379))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4376),U_4378),U_4379)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4376) ),
inference(clausify,[status(thm)],[f_1452_2]) ).
cnf(f_1452_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4376),U_4377),U_4379)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),U_4379),c_Groups_Ozero__class_Ozero(U_4376)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),c_Groups_Ozero__class_Ozero(U_4376)),U_4379))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4376),U_4378),U_4379)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4376) ),
inference(clausify,[status(thm)],[f_1452_2]) ).
cnf(f_1452_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),c_Groups_Ozero__class_Ozero(U_4376)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),U_4379),c_Groups_Ozero__class_Ozero(U_4376)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),c_Groups_Ozero__class_Ozero(U_4376)),U_4379))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4376),U_4378),U_4379)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4376) ),
inference(clausify,[status(thm)],[f_1452_2]) ).
cnf(f_1452_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),c_Groups_Ozero__class_Ozero(U_4376)),U_4379))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),c_Groups_Ozero__class_Ozero(U_4376)),U_4379))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4376),U_4378),U_4379)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4376) ),
inference(clausify,[status(thm)],[f_1452_2]) ).
cnf(f_1452_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),U_4379),c_Groups_Ozero__class_Ozero(U_4376)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),U_4379),c_Groups_Ozero__class_Ozero(U_4376)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),c_Groups_Ozero__class_Ozero(U_4376)),U_4379))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4376),U_4378),U_4379)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4376) ),
inference(clausify,[status(thm)],[f_1452_2]) ).
cnf(f_1452_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),c_Groups_Ozero__class_Ozero(U_4376)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),U_4379),c_Groups_Ozero__class_Ozero(U_4376)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),c_Groups_Ozero__class_Ozero(U_4376)),U_4379))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4376),U_4378),U_4379)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4376) ),
inference(clausify,[status(thm)],[f_1452_2]) ).
cnf(f_1452_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),U_4379),c_Groups_Ozero__class_Ozero(U_4376)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4376),U_4377),U_4379)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),c_Groups_Ozero__class_Ozero(U_4376)),U_4379))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4376),U_4378),U_4379)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4376) ),
inference(clausify,[status(thm)],[f_1452_2]) ).
cnf(f_1452_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),c_Groups_Ozero__class_Ozero(U_4376)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4376),U_4377),U_4379)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),c_Groups_Ozero__class_Ozero(U_4376)),U_4379))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4376),U_4378),U_4379)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4376) ),
inference(clausify,[status(thm)],[f_1452_2]) ).
cnf(f_1452_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),c_Groups_Ozero__class_Ozero(U_4376)),U_4379))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4376),U_4377),U_4379)),U_4378))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4376),U_4378),U_4379)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4376) ),
inference(clausify,[status(thm)],[f_1452_2]) ).
cnf(f_1452_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),U_4379),c_Groups_Ozero__class_Ozero(U_4376)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),U_4379),c_Groups_Ozero__class_Ozero(U_4376)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4376),U_4377),U_4379)),U_4378))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4376),U_4378),U_4379)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4376) ),
inference(clausify,[status(thm)],[f_1452_2]) ).
cnf(f_1452_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),c_Groups_Ozero__class_Ozero(U_4376)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),U_4379),c_Groups_Ozero__class_Ozero(U_4376)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4376),U_4377),U_4379)),U_4378))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4376),U_4378),U_4379)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4376) ),
inference(clausify,[status(thm)],[f_1452_2]) ).
cnf(f_1452_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4376),U_4379),c_Groups_Ozero__class_Ozero(U_4376)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4376),U_4377),U_4379)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4376),U_4377),U_4379)),U_4378))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4376),U_4378),U_4379)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4376) ),
inference(clausify,[status(thm)],[f_1452_2]) ).
cnf(f_1452_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),c_Groups_Ozero__class_Ozero(U_4376)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4378),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4376),U_4377),U_4379)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4376),U_4377),U_4379)),U_4378))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4376),U_4377),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4376),U_4378),U_4379)))
| ~ class_Fields_Olinordered__field__inverse__zero(U_4376) ),
inference(clausify,[status(thm)],[f_1452_2]) ).
fof(f_1453_1,plain,
! [V_w_2,V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__divide__eq__number__of1]) ).
fof(f_1453_2,plain,
! [U_4383,U_4382,U_4381,U_4380] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4380),U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),c_Groups_Ozero__class_Ozero(U_4380)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)),c_Groups_Ozero__class_Ozero(U_4380))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4380),U_4381),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)),c_Groups_Ozero__class_Ozero(U_4380))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),c_Groups_Ozero__class_Ozero(U_4380)),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4380),U_4381),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))),U_4382))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),c_Groups_Ozero__class_Ozero(U_4380)),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),c_Groups_Ozero__class_Ozero(U_4380)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)),c_Groups_Ozero__class_Ozero(U_4380))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4380),U_4381),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)),c_Groups_Ozero__class_Ozero(U_4380))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),c_Groups_Ozero__class_Ozero(U_4380)),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4380),U_4381),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))),U_4382))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),c_Groups_Ozero__class_Ozero(U_4380)),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4380),U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)))) ) )
| ~ class_Int_Onumber(U_4380)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4380) ),
inference(variable_rename,[status(thm)],[f_1453_1]) ).
cnf(f_1453_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4380),U_4381),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))),U_4382))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),c_Groups_Ozero__class_Ozero(U_4380)),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4380),U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
| ~ class_Int_Onumber(U_4380)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4380) ),
inference(clausify,[status(thm)],[f_1453_2]) ).
cnf(f_1453_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4380),U_4381),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)),c_Groups_Ozero__class_Ozero(U_4380)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),c_Groups_Ozero__class_Ozero(U_4380)),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4380),U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
| ~ class_Int_Onumber(U_4380)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4380) ),
inference(clausify,[status(thm)],[f_1453_2]) ).
cnf(f_1453_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),c_Groups_Ozero__class_Ozero(U_4380)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)),c_Groups_Ozero__class_Ozero(U_4380)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),c_Groups_Ozero__class_Ozero(U_4380)),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4380),U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
| ~ class_Int_Onumber(U_4380)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4380) ),
inference(clausify,[status(thm)],[f_1453_2]) ).
cnf(f_1453_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),c_Groups_Ozero__class_Ozero(U_4380)),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),c_Groups_Ozero__class_Ozero(U_4380)),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4380),U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
| ~ class_Int_Onumber(U_4380)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4380) ),
inference(clausify,[status(thm)],[f_1453_2]) ).
cnf(f_1453_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)),c_Groups_Ozero__class_Ozero(U_4380)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)),c_Groups_Ozero__class_Ozero(U_4380)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),c_Groups_Ozero__class_Ozero(U_4380)),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4380),U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
| ~ class_Int_Onumber(U_4380)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4380) ),
inference(clausify,[status(thm)],[f_1453_2]) ).
cnf(f_1453_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),c_Groups_Ozero__class_Ozero(U_4380)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)),c_Groups_Ozero__class_Ozero(U_4380)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),c_Groups_Ozero__class_Ozero(U_4380)),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4380),U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
| ~ class_Int_Onumber(U_4380)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4380) ),
inference(clausify,[status(thm)],[f_1453_2]) ).
cnf(f_1453_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)),c_Groups_Ozero__class_Ozero(U_4380)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4380),U_4381),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),c_Groups_Ozero__class_Ozero(U_4380)),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4380),U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
| ~ class_Int_Onumber(U_4380)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4380) ),
inference(clausify,[status(thm)],[f_1453_2]) ).
cnf(f_1453_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),c_Groups_Ozero__class_Ozero(U_4380)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4380),U_4381),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),c_Groups_Ozero__class_Ozero(U_4380)),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4380),U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
| ~ class_Int_Onumber(U_4380)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4380) ),
inference(clausify,[status(thm)],[f_1453_2]) ).
cnf(f_1453_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),c_Groups_Ozero__class_Ozero(U_4380)),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4380),U_4381),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))),U_4382))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4380),U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
| ~ class_Int_Onumber(U_4380)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4380) ),
inference(clausify,[status(thm)],[f_1453_2]) ).
cnf(f_1453_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)),c_Groups_Ozero__class_Ozero(U_4380)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)),c_Groups_Ozero__class_Ozero(U_4380)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4380),U_4381),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))),U_4382))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4380),U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
| ~ class_Int_Onumber(U_4380)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4380) ),
inference(clausify,[status(thm)],[f_1453_2]) ).
cnf(f_1453_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),c_Groups_Ozero__class_Ozero(U_4380)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)),c_Groups_Ozero__class_Ozero(U_4380)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4380),U_4381),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))),U_4382))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4380),U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
| ~ class_Int_Onumber(U_4380)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4380) ),
inference(clausify,[status(thm)],[f_1453_2]) ).
cnf(f_1453_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383)),c_Groups_Ozero__class_Ozero(U_4380)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4380),U_4381),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4380),U_4381),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))),U_4382))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4380),U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
| ~ class_Int_Onumber(U_4380)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4380) ),
inference(clausify,[status(thm)],[f_1453_2]) ).
cnf(f_1453_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),c_Groups_Ozero__class_Ozero(U_4380)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4380),U_4381),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4380),U_4381),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))),U_4382))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4380),U_4381),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4380),U_4382),hAPP(c_Int_Onumber__class_Onumber__of(U_4380),U_4383))))
| ~ class_Int_Onumber(U_4380)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4380) ),
inference(clausify,[status(thm)],[f_1453_2]) ).
fof(f_1454_1,plain,
! [V_c_2,V_b_2,V_w_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__divide__eq__number__of]) ).
fof(f_1454_2,plain,
! [U_4387,U_4386,U_4385,U_4384] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4384),U_4386),U_4387)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),c_Groups_Ozero__class_Ozero(U_4384)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4387),c_Groups_Ozero__class_Ozero(U_4384))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),U_4387)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4387),c_Groups_Ozero__class_Ozero(U_4384))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),c_Groups_Ozero__class_Ozero(U_4384)),U_4387)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),U_4387)),U_4386))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),c_Groups_Ozero__class_Ozero(U_4384)),U_4387)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),c_Groups_Ozero__class_Ozero(U_4384)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4387),c_Groups_Ozero__class_Ozero(U_4384))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),U_4387)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4387),c_Groups_Ozero__class_Ozero(U_4384))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),c_Groups_Ozero__class_Ozero(U_4384)),U_4387)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),U_4387)),U_4386))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),c_Groups_Ozero__class_Ozero(U_4384)),U_4387)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4384),U_4386),U_4387))) ) )
| ~ class_Int_Onumber(U_4384)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4384) ),
inference(variable_rename,[status(thm)],[f_1454_1]) ).
cnf(f_1454_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),U_4387)),U_4386))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),c_Groups_Ozero__class_Ozero(U_4384)),U_4387))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4384),U_4386),U_4387)))
| ~ class_Int_Onumber(U_4384)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4384) ),
inference(clausify,[status(thm)],[f_1454_2]) ).
cnf(f_1454_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),U_4387)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4387),c_Groups_Ozero__class_Ozero(U_4384)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),c_Groups_Ozero__class_Ozero(U_4384)),U_4387))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4384),U_4386),U_4387)))
| ~ class_Int_Onumber(U_4384)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4384) ),
inference(clausify,[status(thm)],[f_1454_2]) ).
cnf(f_1454_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),c_Groups_Ozero__class_Ozero(U_4384)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4387),c_Groups_Ozero__class_Ozero(U_4384)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),c_Groups_Ozero__class_Ozero(U_4384)),U_4387))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4384),U_4386),U_4387)))
| ~ class_Int_Onumber(U_4384)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4384) ),
inference(clausify,[status(thm)],[f_1454_2]) ).
cnf(f_1454_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),c_Groups_Ozero__class_Ozero(U_4384)),U_4387))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),c_Groups_Ozero__class_Ozero(U_4384)),U_4387))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4384),U_4386),U_4387)))
| ~ class_Int_Onumber(U_4384)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4384) ),
inference(clausify,[status(thm)],[f_1454_2]) ).
cnf(f_1454_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4387),c_Groups_Ozero__class_Ozero(U_4384)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4387),c_Groups_Ozero__class_Ozero(U_4384)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),c_Groups_Ozero__class_Ozero(U_4384)),U_4387))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4384),U_4386),U_4387)))
| ~ class_Int_Onumber(U_4384)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4384) ),
inference(clausify,[status(thm)],[f_1454_2]) ).
cnf(f_1454_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),c_Groups_Ozero__class_Ozero(U_4384)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4387),c_Groups_Ozero__class_Ozero(U_4384)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),c_Groups_Ozero__class_Ozero(U_4384)),U_4387))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4384),U_4386),U_4387)))
| ~ class_Int_Onumber(U_4384)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4384) ),
inference(clausify,[status(thm)],[f_1454_2]) ).
cnf(f_1454_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4387),c_Groups_Ozero__class_Ozero(U_4384)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),U_4387)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),c_Groups_Ozero__class_Ozero(U_4384)),U_4387))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4384),U_4386),U_4387)))
| ~ class_Int_Onumber(U_4384)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4384) ),
inference(clausify,[status(thm)],[f_1454_2]) ).
cnf(f_1454_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),c_Groups_Ozero__class_Ozero(U_4384)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),U_4387)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),c_Groups_Ozero__class_Ozero(U_4384)),U_4387))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4384),U_4386),U_4387)))
| ~ class_Int_Onumber(U_4384)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4384) ),
inference(clausify,[status(thm)],[f_1454_2]) ).
cnf(f_1454_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),c_Groups_Ozero__class_Ozero(U_4384)),U_4387))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),U_4387)),U_4386))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4384),U_4386),U_4387)))
| ~ class_Int_Onumber(U_4384)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4384) ),
inference(clausify,[status(thm)],[f_1454_2]) ).
cnf(f_1454_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4387),c_Groups_Ozero__class_Ozero(U_4384)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4387),c_Groups_Ozero__class_Ozero(U_4384)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),U_4387)),U_4386))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4384),U_4386),U_4387)))
| ~ class_Int_Onumber(U_4384)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4384) ),
inference(clausify,[status(thm)],[f_1454_2]) ).
cnf(f_1454_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),c_Groups_Ozero__class_Ozero(U_4384)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4387),c_Groups_Ozero__class_Ozero(U_4384)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),U_4387)),U_4386))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4384),U_4386),U_4387)))
| ~ class_Int_Onumber(U_4384)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4384) ),
inference(clausify,[status(thm)],[f_1454_2]) ).
cnf(f_1454_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4387),c_Groups_Ozero__class_Ozero(U_4384)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),U_4387)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),U_4387)),U_4386))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4384),U_4386),U_4387)))
| ~ class_Int_Onumber(U_4384)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4384) ),
inference(clausify,[status(thm)],[f_1454_2]) ).
cnf(f_1454_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),c_Groups_Ozero__class_Ozero(U_4384)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),U_4386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),U_4387)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),U_4387)),U_4386))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4384),hAPP(c_Int_Onumber__class_Onumber__of(U_4384),U_4385)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4384),U_4386),U_4387)))
| ~ class_Int_Onumber(U_4384)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4384) ),
inference(clausify,[status(thm)],[f_1454_2]) ).
fof(f_1455_1,plain,
! [V_w_2,V_c_2,V_b_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__eq__number__of]) ).
fof(f_1455_2,plain,
! [U_4391,U_4390,U_4389,U_4388] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4388),U_4389),U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4390),c_Groups_Ozero__class_Ozero(U_4388))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4388),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)),U_4390)),U_4389))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4390),c_Groups_Ozero__class_Ozero(U_4388))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),U_4390)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4389),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4388),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)),U_4390)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),U_4390)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4390),c_Groups_Ozero__class_Ozero(U_4388))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4388),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)),U_4390)),U_4389))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4390),c_Groups_Ozero__class_Ozero(U_4388))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),U_4390)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4389),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4388),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)),U_4390)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),U_4390)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4388),U_4389),U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391))) ) )
| ~ class_Int_Onumber(U_4388)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4388) ),
inference(variable_rename,[status(thm)],[f_1455_1]) ).
cnf(f_1455_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4389),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4388),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)),U_4390)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),U_4390))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4388),U_4389),U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
| ~ class_Int_Onumber(U_4388)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4388) ),
inference(clausify,[status(thm)],[f_1455_2]) ).
cnf(f_1455_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4388),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)),U_4390)),U_4389))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4390),c_Groups_Ozero__class_Ozero(U_4388)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),U_4390))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4388),U_4389),U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
| ~ class_Int_Onumber(U_4388)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4388) ),
inference(clausify,[status(thm)],[f_1455_2]) ).
cnf(f_1455_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4390),c_Groups_Ozero__class_Ozero(U_4388)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),U_4390))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4388),U_4389),U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
| ~ class_Int_Onumber(U_4388)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4388) ),
inference(clausify,[status(thm)],[f_1455_2]) ).
cnf(f_1455_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),U_4390))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),U_4390))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4388),U_4389),U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
| ~ class_Int_Onumber(U_4388)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4388) ),
inference(clausify,[status(thm)],[f_1455_2]) ).
cnf(f_1455_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4390),c_Groups_Ozero__class_Ozero(U_4388)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4390),c_Groups_Ozero__class_Ozero(U_4388)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),U_4390))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4388),U_4389),U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
| ~ class_Int_Onumber(U_4388)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4388) ),
inference(clausify,[status(thm)],[f_1455_2]) ).
cnf(f_1455_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4390),c_Groups_Ozero__class_Ozero(U_4388)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),U_4390))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4388),U_4389),U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
| ~ class_Int_Onumber(U_4388)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4388) ),
inference(clausify,[status(thm)],[f_1455_2]) ).
cnf(f_1455_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4390),c_Groups_Ozero__class_Ozero(U_4388)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4388),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)),U_4390)),U_4389))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),U_4390))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4388),U_4389),U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
| ~ class_Int_Onumber(U_4388)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4388) ),
inference(clausify,[status(thm)],[f_1455_2]) ).
cnf(f_1455_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4388),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)),U_4390)),U_4389))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),U_4390))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4388),U_4389),U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
| ~ class_Int_Onumber(U_4388)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4388) ),
inference(clausify,[status(thm)],[f_1455_2]) ).
cnf(f_1455_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),U_4390))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4389),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4388),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)),U_4390)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4388),U_4389),U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
| ~ class_Int_Onumber(U_4388)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4388) ),
inference(clausify,[status(thm)],[f_1455_2]) ).
cnf(f_1455_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4390),c_Groups_Ozero__class_Ozero(U_4388)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4390),c_Groups_Ozero__class_Ozero(U_4388)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4389),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4388),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)),U_4390)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4388),U_4389),U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
| ~ class_Int_Onumber(U_4388)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4388) ),
inference(clausify,[status(thm)],[f_1455_2]) ).
cnf(f_1455_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4390),c_Groups_Ozero__class_Ozero(U_4388)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4389),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4388),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)),U_4390)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4388),U_4389),U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
| ~ class_Int_Onumber(U_4388)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4388) ),
inference(clausify,[status(thm)],[f_1455_2]) ).
cnf(f_1455_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4390),c_Groups_Ozero__class_Ozero(U_4388)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4388),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)),U_4390)),U_4389))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4389),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4388),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)),U_4390)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4388),U_4389),U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
| ~ class_Int_Onumber(U_4388)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4388) ),
inference(clausify,[status(thm)],[f_1455_2]) ).
cnf(f_1455_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),c_Groups_Ozero__class_Ozero(U_4388)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4388),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)),U_4390)),U_4389))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),U_4389),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4388),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)),U_4390)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4388),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4388),U_4389),U_4390)),hAPP(c_Int_Onumber__class_Onumber__of(U_4388),U_4391)))
| ~ class_Int_Onumber(U_4388)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4388) ),
inference(clausify,[status(thm)],[f_1455_2]) ).
fof(f_1456_1,plain,
! [V_a_2,V_w_2,V_b_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2)) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__eq__number__of1]) ).
fof(f_1456_2,plain,
! [U_4395,U_4394,U_4393,U_4392] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4392),U_4393),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4395))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),U_4395))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)),c_Groups_Ozero__class_Ozero(U_4392))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4392),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4393))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)),c_Groups_Ozero__class_Ozero(U_4392))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),U_4393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4392),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),U_4395))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)),c_Groups_Ozero__class_Ozero(U_4392))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4392),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4393))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)),c_Groups_Ozero__class_Ozero(U_4392))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),U_4393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4392),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4392),U_4393),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4395)) ) )
| ~ class_Int_Onumber(U_4392)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4392) ),
inference(variable_rename,[status(thm)],[f_1456_1]) ).
cnf(f_1456_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),U_4393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4392),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4392),U_4393),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4395))
| ~ class_Int_Onumber(U_4392)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4392) ),
inference(clausify,[status(thm)],[f_1456_2]) ).
cnf(f_1456_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4392),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4393))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)),c_Groups_Ozero__class_Ozero(U_4392)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4392),U_4393),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4395))
| ~ class_Int_Onumber(U_4392)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4392) ),
inference(clausify,[status(thm)],[f_1456_2]) ).
cnf(f_1456_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),U_4395))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)),c_Groups_Ozero__class_Ozero(U_4392)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4392),U_4393),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4395))
| ~ class_Int_Onumber(U_4392)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4392) ),
inference(clausify,[status(thm)],[f_1456_2]) ).
cnf(f_1456_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4392),U_4393),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4395))
| ~ class_Int_Onumber(U_4392)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4392) ),
inference(clausify,[status(thm)],[f_1456_2]) ).
cnf(f_1456_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)),c_Groups_Ozero__class_Ozero(U_4392)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)),c_Groups_Ozero__class_Ozero(U_4392)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4392),U_4393),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4395))
| ~ class_Int_Onumber(U_4392)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4392) ),
inference(clausify,[status(thm)],[f_1456_2]) ).
cnf(f_1456_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),U_4395))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)),c_Groups_Ozero__class_Ozero(U_4392)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4392),U_4393),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4395))
| ~ class_Int_Onumber(U_4392)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4392) ),
inference(clausify,[status(thm)],[f_1456_2]) ).
cnf(f_1456_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)),c_Groups_Ozero__class_Ozero(U_4392)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4392),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4393))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4392),U_4393),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4395))
| ~ class_Int_Onumber(U_4392)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4392) ),
inference(clausify,[status(thm)],[f_1456_2]) ).
cnf(f_1456_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),U_4395))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4392),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4393))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4392),U_4393),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4395))
| ~ class_Int_Onumber(U_4392)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4392) ),
inference(clausify,[status(thm)],[f_1456_2]) ).
cnf(f_1456_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),U_4393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4392),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4392),U_4393),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4395))
| ~ class_Int_Onumber(U_4392)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4392) ),
inference(clausify,[status(thm)],[f_1456_2]) ).
cnf(f_1456_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)),c_Groups_Ozero__class_Ozero(U_4392)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)),c_Groups_Ozero__class_Ozero(U_4392)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),U_4393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4392),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4392),U_4393),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4395))
| ~ class_Int_Onumber(U_4392)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4392) ),
inference(clausify,[status(thm)],[f_1456_2]) ).
cnf(f_1456_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),U_4395))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)),c_Groups_Ozero__class_Ozero(U_4392)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),U_4393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4392),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4392),U_4393),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4395))
| ~ class_Int_Onumber(U_4392)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4392) ),
inference(clausify,[status(thm)],[f_1456_2]) ).
cnf(f_1456_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394)),c_Groups_Ozero__class_Ozero(U_4392)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4392),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4393))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),U_4393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4392),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4392),U_4393),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4395))
| ~ class_Int_Onumber(U_4392)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4392) ),
inference(clausify,[status(thm)],[f_1456_2]) ).
cnf(f_1456_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),c_Groups_Ozero__class_Ozero(U_4392)),U_4395))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4392),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4393))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),U_4393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4392),U_4395),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4392),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4392),U_4393),hAPP(c_Int_Onumber__class_Onumber__of(U_4392),U_4394))),U_4395))
| ~ class_Int_Onumber(U_4392)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4392) ),
inference(clausify,[status(thm)],[f_1456_2]) ).
fof(f_1457_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_1457_2,plain,
! [U_4399,U_4398,U_4397,U_4396] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4396),U_4397),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4399),U_4398)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4396),hAPP(hAPP(c_Power_Opower__class_Opower(U_4396),U_4397),U_4399)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4396),U_4397),U_4398))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4398),U_4399))
| U_4397 = c_Groups_Ozero__class_Ozero(U_4396)
| ~ class_Fields_Ofield(U_4396) ),
inference(variable_rename,[status(thm)],[f_1457_1]) ).
cnf(f_1457_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4396),U_4397),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4399),U_4398)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4396),hAPP(hAPP(c_Power_Opower__class_Opower(U_4396),U_4397),U_4399)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4396),U_4397),U_4398))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4398),U_4399))
| U_4397 = c_Groups_Ozero__class_Ozero(U_4396)
| ~ class_Fields_Ofield(U_4396) ),
inference(clausify,[status(thm)],[f_1457_2]) ).
fof(f_1458_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_1458_2,plain,
! [U_4401,U_4400] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4400),hAPP(c_Int_Onumber__class_Onumber__of(U_4400),c_Int_OMin)),U_4401) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4400),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4400),c_Groups_Oone__class_Oone(U_4400)),U_4401))
| ~ class_Int_Onumber__ring(U_4400)
| ~ class_Fields_Ofield__inverse__zero(U_4400) ),
inference(variable_rename,[status(thm)],[f_1458_1]) ).
cnf(f_1458_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4400),hAPP(c_Int_Onumber__class_Onumber__of(U_4400),c_Int_OMin)),U_4401) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4400),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4400),c_Groups_Oone__class_Oone(U_4400)),U_4401))
| ~ class_Int_Onumber__ring(U_4400)
| ~ class_Fields_Ofield__inverse__zero(U_4400) ),
inference(clausify,[status(thm)],[f_1458_2]) ).
fof(f_1459_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]) ).
cnf(f_1459_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(clausify,[status(thm)],[f_1459_1]) ).
fof(f_1460_1,plain,
! [V_a_2,V_w_2,V_b_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2)) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__eq__number__of1]) ).
fof(f_1460_2,plain,
! [U_4405,U_4404,U_4403,U_4402] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4405))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4405))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)),c_Groups_Ozero__class_Ozero(U_4402))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),U_4405),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4403))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)),c_Groups_Ozero__class_Ozero(U_4402))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),U_4403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),U_4405),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4405))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)),c_Groups_Ozero__class_Ozero(U_4402))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),U_4405),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4403))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)),c_Groups_Ozero__class_Ozero(U_4402))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),U_4403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),U_4405),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4405)) ) )
| ~ class_Int_Onumber(U_4402)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
inference(variable_rename,[status(thm)],[f_1460_1]) ).
cnf(f_1460_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),U_4403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),U_4405),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4405))
| ~ class_Int_Onumber(U_4402)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
inference(clausify,[status(thm)],[f_1460_2]) ).
cnf(f_1460_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),U_4405),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4403))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)),c_Groups_Ozero__class_Ozero(U_4402)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4405))
| ~ class_Int_Onumber(U_4402)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
inference(clausify,[status(thm)],[f_1460_2]) ).
cnf(f_1460_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4405))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)),c_Groups_Ozero__class_Ozero(U_4402)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4405))
| ~ class_Int_Onumber(U_4402)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
inference(clausify,[status(thm)],[f_1460_2]) ).
cnf(f_1460_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4405))
| ~ class_Int_Onumber(U_4402)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
inference(clausify,[status(thm)],[f_1460_2]) ).
cnf(f_1460_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)),c_Groups_Ozero__class_Ozero(U_4402)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)),c_Groups_Ozero__class_Ozero(U_4402)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4405))
| ~ class_Int_Onumber(U_4402)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
inference(clausify,[status(thm)],[f_1460_2]) ).
cnf(f_1460_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4405))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)),c_Groups_Ozero__class_Ozero(U_4402)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4405))
| ~ class_Int_Onumber(U_4402)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
inference(clausify,[status(thm)],[f_1460_2]) ).
cnf(f_1460_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)),c_Groups_Ozero__class_Ozero(U_4402)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),U_4405),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4403))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4405))
| ~ class_Int_Onumber(U_4402)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
inference(clausify,[status(thm)],[f_1460_2]) ).
cnf(f_1460_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4405))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),U_4405),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4403))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4405))
| ~ class_Int_Onumber(U_4402)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
inference(clausify,[status(thm)],[f_1460_2]) ).
cnf(f_1460_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),U_4403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),U_4405),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4405))
| ~ class_Int_Onumber(U_4402)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
inference(clausify,[status(thm)],[f_1460_2]) ).
cnf(f_1460_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)),c_Groups_Ozero__class_Ozero(U_4402)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)),c_Groups_Ozero__class_Ozero(U_4402)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),U_4403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),U_4405),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4405))
| ~ class_Int_Onumber(U_4402)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
inference(clausify,[status(thm)],[f_1460_2]) ).
cnf(f_1460_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4405))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)),c_Groups_Ozero__class_Ozero(U_4402)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),U_4403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),U_4405),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4405))
| ~ class_Int_Onumber(U_4402)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
inference(clausify,[status(thm)],[f_1460_2]) ).
cnf(f_1460_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4402),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404)),c_Groups_Ozero__class_Ozero(U_4402)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),U_4405),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4403))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),U_4403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),U_4405),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4405))
| ~ class_Int_Onumber(U_4402)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
inference(clausify,[status(thm)],[f_1460_2]) ).
cnf(f_1460_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),c_Groups_Ozero__class_Ozero(U_4402)),U_4405))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),U_4405),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4403))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),U_4403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4402),U_4405),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4402),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4402),U_4403),hAPP(c_Int_Onumber__class_Onumber__of(U_4402),U_4404))),U_4405))
| ~ class_Int_Onumber(U_4402)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4402) ),
inference(clausify,[status(thm)],[f_1460_2]) ).
fof(f_1461_1,plain,
! [V_w_2,V_c_2,V_b_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__eq__number__of]) ).
fof(f_1461_2,plain,
! [U_4409,U_4408,U_4407,U_4406] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4407),U_4408)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4408),c_Groups_Ozero__class_Ozero(U_4406))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)),U_4408)),U_4407))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4408),c_Groups_Ozero__class_Ozero(U_4406))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4408)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),U_4407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)),U_4408)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4408)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4408),c_Groups_Ozero__class_Ozero(U_4406))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)),U_4408)),U_4407))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4408),c_Groups_Ozero__class_Ozero(U_4406))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4408)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),U_4407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)),U_4408)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4408)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4407),U_4408)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409))) ) )
| ~ class_Int_Onumber(U_4406)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
inference(variable_rename,[status(thm)],[f_1461_1]) ).
cnf(f_1461_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),U_4407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)),U_4408)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4407),U_4408)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
| ~ class_Int_Onumber(U_4406)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
inference(clausify,[status(thm)],[f_1461_2]) ).
cnf(f_1461_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)),U_4408)),U_4407))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4408),c_Groups_Ozero__class_Ozero(U_4406)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4407),U_4408)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
| ~ class_Int_Onumber(U_4406)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
inference(clausify,[status(thm)],[f_1461_2]) ).
cnf(f_1461_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4408),c_Groups_Ozero__class_Ozero(U_4406)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4407),U_4408)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
| ~ class_Int_Onumber(U_4406)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
inference(clausify,[status(thm)],[f_1461_2]) ).
cnf(f_1461_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4408))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4408))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4407),U_4408)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
| ~ class_Int_Onumber(U_4406)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
inference(clausify,[status(thm)],[f_1461_2]) ).
cnf(f_1461_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4408),c_Groups_Ozero__class_Ozero(U_4406)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4408),c_Groups_Ozero__class_Ozero(U_4406)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4408))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4407),U_4408)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
| ~ class_Int_Onumber(U_4406)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
inference(clausify,[status(thm)],[f_1461_2]) ).
cnf(f_1461_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4408),c_Groups_Ozero__class_Ozero(U_4406)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4408))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4407),U_4408)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
| ~ class_Int_Onumber(U_4406)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
inference(clausify,[status(thm)],[f_1461_2]) ).
cnf(f_1461_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4408),c_Groups_Ozero__class_Ozero(U_4406)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)),U_4408)),U_4407))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4408))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4407),U_4408)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
| ~ class_Int_Onumber(U_4406)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
inference(clausify,[status(thm)],[f_1461_2]) ).
cnf(f_1461_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)),U_4408)),U_4407))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4408))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4407),U_4408)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
| ~ class_Int_Onumber(U_4406)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
inference(clausify,[status(thm)],[f_1461_2]) ).
cnf(f_1461_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),U_4408))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),U_4407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)),U_4408)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4407),U_4408)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
| ~ class_Int_Onumber(U_4406)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
inference(clausify,[status(thm)],[f_1461_2]) ).
cnf(f_1461_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4408),c_Groups_Ozero__class_Ozero(U_4406)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4408),c_Groups_Ozero__class_Ozero(U_4406)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),U_4407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)),U_4408)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4407),U_4408)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
| ~ class_Int_Onumber(U_4406)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
inference(clausify,[status(thm)],[f_1461_2]) ).
cnf(f_1461_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4408),c_Groups_Ozero__class_Ozero(U_4406)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),U_4407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)),U_4408)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4407),U_4408)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
| ~ class_Int_Onumber(U_4406)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
inference(clausify,[status(thm)],[f_1461_2]) ).
cnf(f_1461_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4406),U_4408),c_Groups_Ozero__class_Ozero(U_4406)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)),U_4408)),U_4407))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),U_4407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)),U_4408)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4407),U_4408)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
| ~ class_Int_Onumber(U_4406)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
inference(clausify,[status(thm)],[f_1461_2]) ).
cnf(f_1461_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),c_Groups_Ozero__class_Ozero(U_4406)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)),U_4408)),U_4407))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),U_4407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4406),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)),U_4408)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4406),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4406),U_4407),U_4408)),hAPP(c_Int_Onumber__class_Onumber__of(U_4406),U_4409)))
| ~ class_Int_Onumber(U_4406)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4406) ),
inference(clausify,[status(thm)],[f_1461_2]) ).
fof(f_1462_1,plain,
! [V_c_2,V_b_2,V_w_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2))) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__divide__eq__number__of]) ).
fof(f_1462_2,plain,
! [U_4413,U_4412,U_4411,U_4410] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),U_4413)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),c_Groups_Ozero__class_Ozero(U_4410)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),U_4413),c_Groups_Ozero__class_Ozero(U_4410))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),U_4413)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),U_4413),c_Groups_Ozero__class_Ozero(U_4410))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),U_4413)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),U_4413)),U_4412))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),U_4413)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),c_Groups_Ozero__class_Ozero(U_4410)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),U_4413),c_Groups_Ozero__class_Ozero(U_4410))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),U_4413)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),U_4413),c_Groups_Ozero__class_Ozero(U_4410))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),U_4413)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),U_4413)),U_4412))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),U_4413)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),U_4413))) ) )
| ~ class_Int_Onumber(U_4410)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
inference(variable_rename,[status(thm)],[f_1462_1]) ).
cnf(f_1462_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),U_4413)),U_4412))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),U_4413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),U_4413)))
| ~ class_Int_Onumber(U_4410)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
inference(clausify,[status(thm)],[f_1462_2]) ).
cnf(f_1462_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),U_4413)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),U_4413),c_Groups_Ozero__class_Ozero(U_4410)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),U_4413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),U_4413)))
| ~ class_Int_Onumber(U_4410)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
inference(clausify,[status(thm)],[f_1462_2]) ).
cnf(f_1462_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),c_Groups_Ozero__class_Ozero(U_4410)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),U_4413),c_Groups_Ozero__class_Ozero(U_4410)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),U_4413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),U_4413)))
| ~ class_Int_Onumber(U_4410)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
inference(clausify,[status(thm)],[f_1462_2]) ).
cnf(f_1462_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),U_4413))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),U_4413))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),U_4413)))
| ~ class_Int_Onumber(U_4410)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
inference(clausify,[status(thm)],[f_1462_2]) ).
cnf(f_1462_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),U_4413),c_Groups_Ozero__class_Ozero(U_4410)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),U_4413),c_Groups_Ozero__class_Ozero(U_4410)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),U_4413))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),U_4413)))
| ~ class_Int_Onumber(U_4410)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
inference(clausify,[status(thm)],[f_1462_2]) ).
cnf(f_1462_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),c_Groups_Ozero__class_Ozero(U_4410)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),U_4413),c_Groups_Ozero__class_Ozero(U_4410)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),U_4413))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),U_4413)))
| ~ class_Int_Onumber(U_4410)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
inference(clausify,[status(thm)],[f_1462_2]) ).
cnf(f_1462_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),U_4413),c_Groups_Ozero__class_Ozero(U_4410)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),U_4413)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),U_4413))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),U_4413)))
| ~ class_Int_Onumber(U_4410)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
inference(clausify,[status(thm)],[f_1462_2]) ).
cnf(f_1462_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),c_Groups_Ozero__class_Ozero(U_4410)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),U_4413)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),U_4413))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),U_4413)))
| ~ class_Int_Onumber(U_4410)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
inference(clausify,[status(thm)],[f_1462_2]) ).
cnf(f_1462_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),c_Groups_Ozero__class_Ozero(U_4410)),U_4413))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),U_4413)),U_4412))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),U_4413)))
| ~ class_Int_Onumber(U_4410)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
inference(clausify,[status(thm)],[f_1462_2]) ).
cnf(f_1462_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),U_4413),c_Groups_Ozero__class_Ozero(U_4410)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),U_4413),c_Groups_Ozero__class_Ozero(U_4410)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),U_4413)),U_4412))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),U_4413)))
| ~ class_Int_Onumber(U_4410)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
inference(clausify,[status(thm)],[f_1462_2]) ).
cnf(f_1462_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),c_Groups_Ozero__class_Ozero(U_4410)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),U_4413),c_Groups_Ozero__class_Ozero(U_4410)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),U_4413)),U_4412))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),U_4413)))
| ~ class_Int_Onumber(U_4410)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
inference(clausify,[status(thm)],[f_1462_2]) ).
cnf(f_1462_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4410),U_4413),c_Groups_Ozero__class_Ozero(U_4410)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),U_4413)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),U_4413)),U_4412))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),U_4413)))
| ~ class_Int_Onumber(U_4410)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
inference(clausify,[status(thm)],[f_1462_2]) ).
cnf(f_1462_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),c_Groups_Ozero__class_Ozero(U_4410)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),U_4412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),U_4413)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),U_4413)),U_4412))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4410),hAPP(c_Int_Onumber__class_Onumber__of(U_4410),U_4411)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4410),U_4412),U_4413)))
| ~ class_Int_Onumber(U_4410)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4410) ),
inference(clausify,[status(thm)],[f_1462_2]) ).
fof(f_1463_1,plain,
! [V_w_2,V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__divide__eq__number__of1]) ).
fof(f_1463_2,plain,
! [U_4417,U_4416,U_4415,U_4414] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4414),U_4416),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),c_Groups_Ozero__class_Ozero(U_4414)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)),c_Groups_Ozero__class_Ozero(U_4414))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4414),U_4415),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)),c_Groups_Ozero__class_Ozero(U_4414))) ) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),c_Groups_Ozero__class_Ozero(U_4414)),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4414),U_4415),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))),U_4416))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),c_Groups_Ozero__class_Ozero(U_4414)),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),c_Groups_Ozero__class_Ozero(U_4414)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)),c_Groups_Ozero__class_Ozero(U_4414))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4414),U_4415),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)),c_Groups_Ozero__class_Ozero(U_4414))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),c_Groups_Ozero__class_Ozero(U_4414)),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4414),U_4415),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))),U_4416))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),c_Groups_Ozero__class_Ozero(U_4414)),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4414),U_4416),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)))) ) )
| ~ class_Int_Onumber(U_4414)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4414) ),
inference(variable_rename,[status(thm)],[f_1463_1]) ).
cnf(f_1463_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4414),U_4415),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))),U_4416))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),c_Groups_Ozero__class_Ozero(U_4414)),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4414),U_4416),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
| ~ class_Int_Onumber(U_4414)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4414) ),
inference(clausify,[status(thm)],[f_1463_2]) ).
cnf(f_1463_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4414),U_4415),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)),c_Groups_Ozero__class_Ozero(U_4414)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),c_Groups_Ozero__class_Ozero(U_4414)),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4414),U_4416),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
| ~ class_Int_Onumber(U_4414)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4414) ),
inference(clausify,[status(thm)],[f_1463_2]) ).
cnf(f_1463_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),c_Groups_Ozero__class_Ozero(U_4414)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)),c_Groups_Ozero__class_Ozero(U_4414)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),c_Groups_Ozero__class_Ozero(U_4414)),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4414),U_4416),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
| ~ class_Int_Onumber(U_4414)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4414) ),
inference(clausify,[status(thm)],[f_1463_2]) ).
cnf(f_1463_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),c_Groups_Ozero__class_Ozero(U_4414)),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),c_Groups_Ozero__class_Ozero(U_4414)),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4414),U_4416),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
| ~ class_Int_Onumber(U_4414)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4414) ),
inference(clausify,[status(thm)],[f_1463_2]) ).
cnf(f_1463_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)),c_Groups_Ozero__class_Ozero(U_4414)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)),c_Groups_Ozero__class_Ozero(U_4414)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),c_Groups_Ozero__class_Ozero(U_4414)),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4414),U_4416),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
| ~ class_Int_Onumber(U_4414)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4414) ),
inference(clausify,[status(thm)],[f_1463_2]) ).
cnf(f_1463_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),c_Groups_Ozero__class_Ozero(U_4414)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)),c_Groups_Ozero__class_Ozero(U_4414)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),c_Groups_Ozero__class_Ozero(U_4414)),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4414),U_4416),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
| ~ class_Int_Onumber(U_4414)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4414) ),
inference(clausify,[status(thm)],[f_1463_2]) ).
cnf(f_1463_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)),c_Groups_Ozero__class_Ozero(U_4414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4414),U_4415),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),c_Groups_Ozero__class_Ozero(U_4414)),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4414),U_4416),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
| ~ class_Int_Onumber(U_4414)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4414) ),
inference(clausify,[status(thm)],[f_1463_2]) ).
cnf(f_1463_10,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),c_Groups_Ozero__class_Ozero(U_4414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4414),U_4415),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),c_Groups_Ozero__class_Ozero(U_4414)),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4414),U_4416),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
| ~ class_Int_Onumber(U_4414)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4414) ),
inference(clausify,[status(thm)],[f_1463_2]) ).
cnf(f_1463_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),c_Groups_Ozero__class_Ozero(U_4414)),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4414),U_4415),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))),U_4416))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4414),U_4416),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
| ~ class_Int_Onumber(U_4414)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4414) ),
inference(clausify,[status(thm)],[f_1463_2]) ).
cnf(f_1463_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)),c_Groups_Ozero__class_Ozero(U_4414)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)),c_Groups_Ozero__class_Ozero(U_4414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4414),U_4415),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))),U_4416))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4414),U_4416),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
| ~ class_Int_Onumber(U_4414)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4414) ),
inference(clausify,[status(thm)],[f_1463_2]) ).
cnf(f_1463_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),c_Groups_Ozero__class_Ozero(U_4414)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)),c_Groups_Ozero__class_Ozero(U_4414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4414),U_4415),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))),U_4416))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4414),U_4416),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
| ~ class_Int_Onumber(U_4414)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4414) ),
inference(clausify,[status(thm)],[f_1463_2]) ).
cnf(f_1463_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417)),c_Groups_Ozero__class_Ozero(U_4414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4414),U_4415),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4414),U_4415),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))),U_4416))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4414),U_4416),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
| ~ class_Int_Onumber(U_4414)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4414) ),
inference(clausify,[status(thm)],[f_1463_2]) ).
cnf(f_1463_15,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),c_Groups_Ozero__class_Ozero(U_4414)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4414),U_4415),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4414),U_4415),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))),U_4416))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4414),U_4415),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_4414),U_4416),hAPP(c_Int_Onumber__class_Onumber__of(U_4414),U_4417))))
| ~ class_Int_Onumber(U_4414)
| ~ class_Fields_Olinordered__field__inverse__zero(U_4414) ),
inference(clausify,[status(thm)],[f_1463_2]) ).
fof(f_1464_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_1464_2,plain,
! [U_4419,U_4418] :
( ( c_Code__Numeral_Onat__of__aux(U_4418,U_4419) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_4418),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_4419))
| U_4418 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( c_Code__Numeral_Onat__of__aux(U_4418,U_4419) = U_4419
| U_4418 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(variable_rename,[status(thm)],[f_1464_1]) ).
fof(f_1464_3,plain,
( ! [U_4423,U_4421] :
( c_Code__Numeral_Onat__of__aux(U_4421,U_4423) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_4421),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_4423))
| U_4421 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ! [U_4422,U_4420] :
( c_Code__Numeral_Onat__of__aux(U_4420,U_4422) = U_4422
| U_4420 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(miniscope,[status(thm)],[f_1464_2]) ).
cnf(f_1464_4,plain,
( c_Code__Numeral_Onat__of__aux(U_4420,U_4422) = U_4422
| U_4420 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_1464_3]) ).
cnf(f_1464_5,plain,
( c_Code__Numeral_Onat__of__aux(U_4421,U_4423) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_4421),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_4423))
| U_4421 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_1464_3]) ).
fof(f_1465_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]) ).
cnf(f_1465_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(clausify,[status(thm)],[f_1465_1]) ).
fof(f_1466_1,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_code__numeral_Osize_I3_J]) ).
cnf(f_1466_2,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1466_1]) ).
fof(f_1467_1,plain,
! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2,
inference(fof_nnf,[status(thm)],[fact_code__numeral_Osimps_I4_J]) ).
fof(f_1467_2,plain,
! [U_4426,U_4425,U_4424] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_4424,U_4425,U_4426,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_4425,
inference(variable_rename,[status(thm)],[f_1467_1]) ).
cnf(f_1467_3,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_4424,U_4425,U_4426,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_4425,
inference(clausify,[status(thm)],[f_1467_2]) ).
fof(f_1468_1,plain,
! [V_i_2,V_P_2,V_p_2] :
( hBOOL(hAPP(V_P_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_P_2,V_i_2))
| ? [B_i] :
( ~ hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2)))
& hBOOL(hAPP(V_P_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_1468_2,plain,
! [U_4430,U_4429,U_4428] :
( hBOOL(hAPP(U_4429,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4430),U_4428))
| ~ hBOOL(hAPP(U_4429,U_4430))
| ? [U_4427] :
( ~ hBOOL(hAPP(U_4429,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_4427),U_4428)))
& hBOOL(hAPP(U_4429,U_4427))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4427),U_4428)) ) ),
inference(variable_rename,[status(thm)],[f_1468_1]) ).
fof(f_1468_3,plain,
! [U_4430,U_4429,U_4428] :
( hBOOL(hAPP(U_4429,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4430),U_4428))
| ~ hBOOL(hAPP(U_4429,U_4430))
| ( ~ hBOOL(hAPP(U_4429,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK60(U_4430,U_4429,U_4428)),U_4428)))
& hBOOL(hAPP(U_4429,sK60(U_4430,U_4429,U_4428)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK60(U_4430,U_4429,U_4428)),U_4428)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_4427,sK60(U_4430,U_4429,U_4428))],[f_1468_2]) ).
cnf(f_1468_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK60(U_4430,U_4429,U_4428)),U_4428))
| hBOOL(hAPP(U_4429,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4430),U_4428))
| ~ hBOOL(hAPP(U_4429,U_4430)) ),
inference(clausify,[status(thm)],[f_1468_3]) ).
cnf(f_1468_5,plain,
( hBOOL(hAPP(U_4429,sK60(U_4430,U_4429,U_4428)))
| hBOOL(hAPP(U_4429,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4430),U_4428))
| ~ hBOOL(hAPP(U_4429,U_4430)) ),
inference(clausify,[status(thm)],[f_1468_3]) ).
cnf(f_1468_6,plain,
( ~ hBOOL(hAPP(U_4429,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK60(U_4430,U_4429,U_4428)),U_4428)))
| hBOOL(hAPP(U_4429,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4430),U_4428))
| ~ hBOOL(hAPP(U_4429,U_4430)) ),
inference(clausify,[status(thm)],[f_1468_3]) ).
fof(f_1469_1,plain,
! [V_k_2,V_f_2,V_na_2,V_m_2] :
( ? [B_i] :
( hAPP(V_f_2,B_i) = V_k_2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_na_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_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_na_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__intermed__int__val]) ).
fof(f_1469_2,plain,
! [U_4436,U_4435,U_4434,U_4433] :
( ? [U_4432] :
( hAPP(U_4435,U_4432) = U_4436
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4432),U_4434))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4433),U_4432)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4436),hAPP(U_4435,U_4434)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4435,U_4433)),U_4436))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4433),U_4434))
| ? [U_4431] :
( ~ 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_4435,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4431),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4435,U_4431)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4431),U_4434))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4433),U_4431)) ) ),
inference(variable_rename,[status(thm)],[f_1469_1]) ).
fof(f_1469_3,plain,
! [U_4436,U_4435,U_4434,U_4433] :
( ? [U_4432] :
( hAPP(U_4435,U_4432) = U_4436
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4432),U_4434))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4433),U_4432)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4436),hAPP(U_4435,U_4434)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4435,U_4433)),U_4436))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4433),U_4434))
| ( ~ 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_4435,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK61(U_4436,U_4435,U_4434,U_4433)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4435,sK61(U_4436,U_4435,U_4434,U_4433))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK61(U_4436,U_4435,U_4434,U_4433)),U_4434))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4433),sK61(U_4436,U_4435,U_4434,U_4433))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_4431,sK61(U_4436,U_4435,U_4434,U_4433))],[f_1469_2]) ).
fof(f_1469_4,plain,
! [U_4436,U_4435,U_4434,U_4433] :
( ( hAPP(U_4435,sK62(U_4436,U_4435,U_4434,U_4433)) = U_4436
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK62(U_4436,U_4435,U_4434,U_4433)),U_4434))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4433),sK62(U_4436,U_4435,U_4434,U_4433))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4436),hAPP(U_4435,U_4434)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4435,U_4433)),U_4436))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4433),U_4434))
| ( ~ 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_4435,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK61(U_4436,U_4435,U_4434,U_4433)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4435,sK61(U_4436,U_4435,U_4434,U_4433))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK61(U_4436,U_4435,U_4434,U_4433)),U_4434))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4433),sK61(U_4436,U_4435,U_4434,U_4433))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_4432,sK62(U_4436,U_4435,U_4434,U_4433))],[f_1469_3]) ).
cnf(f_1469_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4433),sK62(U_4436,U_4435,U_4434,U_4433)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4436),hAPP(U_4435,U_4434)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4435,U_4433)),U_4436))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4433),U_4434))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4433),sK61(U_4436,U_4435,U_4434,U_4433))) ),
inference(clausify,[status(thm)],[f_1469_4]) ).
cnf(f_1469_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK62(U_4436,U_4435,U_4434,U_4433)),U_4434))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4436),hAPP(U_4435,U_4434)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4435,U_4433)),U_4436))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4433),U_4434))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4433),sK61(U_4436,U_4435,U_4434,U_4433))) ),
inference(clausify,[status(thm)],[f_1469_4]) ).
cnf(f_1469_7,plain,
( hAPP(U_4435,sK62(U_4436,U_4435,U_4434,U_4433)) = U_4436
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4436),hAPP(U_4435,U_4434)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4435,U_4433)),U_4436))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4433),U_4434))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4433),sK61(U_4436,U_4435,U_4434,U_4433))) ),
inference(clausify,[status(thm)],[f_1469_4]) ).
cnf(f_1469_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4433),sK62(U_4436,U_4435,U_4434,U_4433)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4436),hAPP(U_4435,U_4434)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4435,U_4433)),U_4436))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4433),U_4434))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK61(U_4436,U_4435,U_4434,U_4433)),U_4434)) ),
inference(clausify,[status(thm)],[f_1469_4]) ).
cnf(f_1469_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK62(U_4436,U_4435,U_4434,U_4433)),U_4434))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4436),hAPP(U_4435,U_4434)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4435,U_4433)),U_4436))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4433),U_4434))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK61(U_4436,U_4435,U_4434,U_4433)),U_4434)) ),
inference(clausify,[status(thm)],[f_1469_4]) ).
cnf(f_1469_10,plain,
( hAPP(U_4435,sK62(U_4436,U_4435,U_4434,U_4433)) = U_4436
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4436),hAPP(U_4435,U_4434)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4435,U_4433)),U_4436))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4433),U_4434))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK61(U_4436,U_4435,U_4434,U_4433)),U_4434)) ),
inference(clausify,[status(thm)],[f_1469_4]) ).
cnf(f_1469_11,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4433),sK62(U_4436,U_4435,U_4434,U_4433)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4436),hAPP(U_4435,U_4434)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4435,U_4433)),U_4436))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4433),U_4434))
| ~ 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_4435,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK61(U_4436,U_4435,U_4434,U_4433)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4435,sK61(U_4436,U_4435,U_4434,U_4433))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1469_4]) ).
cnf(f_1469_12,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK62(U_4436,U_4435,U_4434,U_4433)),U_4434))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4436),hAPP(U_4435,U_4434)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4435,U_4433)),U_4436))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4433),U_4434))
| ~ 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_4435,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK61(U_4436,U_4435,U_4434,U_4433)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4435,sK61(U_4436,U_4435,U_4434,U_4433))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1469_4]) ).
cnf(f_1469_13,plain,
( hAPP(U_4435,sK62(U_4436,U_4435,U_4434,U_4433)) = U_4436
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4436),hAPP(U_4435,U_4434)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4435,U_4433)),U_4436))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4433),U_4434))
| ~ 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_4435,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK61(U_4436,U_4435,U_4434,U_4433)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4435,sK61(U_4436,U_4435,U_4434,U_4433))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1469_4]) ).
fof(f_1470_1,plain,
! [V_code__numeral] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_code__numeral_Osize_I4_J]) ).
fof(f_1470_2,plain,
! [U_4437] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_4437)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_4437)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_1470_1]) ).
cnf(f_1470_3,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_4437)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_4437)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_1470_2]) ).
fof(f_1471_1,plain,
! [V_code__numeral] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(V_code__numeral)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(V_code__numeral)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_code__numeral_Osize_I2_J]) ).
fof(f_1471_2,plain,
! [U_4438] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_4438)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_4438)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_1471_1]) ).
cnf(f_1471_3,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_4438)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_4438)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_1471_2]) ).
fof(f_1472_1,plain,
! [V_i,V_b] :
( ( c_Random_Olog(V_b,V_i) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(V_b,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_i),V_b)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
& ( c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
inference(fof_nnf,[status(thm)],[fact_log_Osimps]) ).
fof(f_1472_2,plain,
! [U_4440,U_4439] :
( ( c_Random_Olog(U_4439,U_4440) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(U_4439,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_4440),U_4439)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_4440),U_4439))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_4439),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
& ( c_Random_Olog(U_4439,U_4440) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_4440),U_4439))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_4439),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
inference(variable_rename,[status(thm)],[f_1472_1]) ).
fof(f_1472_3,plain,
( ! [U_4444,U_4442] :
( c_Random_Olog(U_4442,U_4444) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(U_4442,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_4444),U_4442)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_4444),U_4442))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_4442),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
& ! [U_4443,U_4441] :
( c_Random_Olog(U_4441,U_4443) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_4443),U_4441))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_4441),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
inference(miniscope,[status(thm)],[f_1472_2]) ).
cnf(f_1472_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_4441),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
| c_Random_Olog(U_4441,U_4443) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_1472_3]) ).
cnf(f_1472_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_4443),U_4441))
| c_Random_Olog(U_4441,U_4443) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_1472_3]) ).
cnf(f_1472_6,plain,
( c_Random_Olog(U_4442,U_4444) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(U_4442,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_4444),U_4442)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_4444),U_4442))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_4442),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ),
inference(clausify,[status(thm)],[f_1472_3]) ).
fof(f_1473_1,plain,
! [V_b,V_a,T_a] :
( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_b)),V_b)),c_Divides_Odiv__class_Omod(T_a,V_a,V_b))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__div__decomp]) ).
fof(f_1473_2,plain,
! [U_4447,U_4446,U_4445] :
( U_4446 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4445),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4445),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_4445),U_4446),U_4447)),U_4447)),c_Divides_Odiv__class_Omod(U_4445,U_4446,U_4447))
| ~ class_Divides_Osemiring__div(U_4445) ),
inference(variable_rename,[status(thm)],[f_1473_1]) ).
cnf(f_1473_3,plain,
( U_4446 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4445),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4445),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_4445),U_4446),U_4447)),U_4447)),c_Divides_Odiv__class_Omod(U_4445,U_4446,U_4447))
| ~ class_Divides_Osemiring__div(U_4445) ),
inference(clausify,[status(thm)],[f_1473_2]) ).
fof(f_1474_1,plain,
! [V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
| ? [B_e] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),B_e)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e)) )
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_field__le__epsilon]) ).
fof(f_1474_2,plain,
! [U_4451,U_4450,U_4449] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4449),U_4450),U_4451))
| ? [U_4448] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4449),U_4450),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4449),U_4451),U_4448)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4449),c_Groups_Ozero__class_Ozero(U_4449)),U_4448)) )
| ~ class_Fields_Olinordered__field(U_4449) ),
inference(variable_rename,[status(thm)],[f_1474_1]) ).
fof(f_1474_3,plain,
! [U_4451,U_4450,U_4449] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4449),U_4450),U_4451))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4449),U_4450),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4449),U_4451),sK63(U_4451,U_4450,U_4449))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4449),c_Groups_Ozero__class_Ozero(U_4449)),sK63(U_4451,U_4450,U_4449))) )
| ~ class_Fields_Olinordered__field(U_4449) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_4448,sK63(U_4451,U_4450,U_4449))],[f_1474_2]) ).
cnf(f_1474_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4449),c_Groups_Ozero__class_Ozero(U_4449)),sK63(U_4451,U_4450,U_4449)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4449),U_4450),U_4451))
| ~ class_Fields_Olinordered__field(U_4449) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
cnf(f_1474_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4449),U_4450),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4449),U_4451),sK63(U_4451,U_4450,U_4449))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4449),U_4450),U_4451))
| ~ class_Fields_Olinordered__field(U_4449) ),
inference(clausify,[status(thm)],[f_1474_3]) ).
fof(f_1475_1,plain,
! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,V_n),V_m),
inference(fof_nnf,[status(thm)],[fact_minus__code__numeral__code]) ).
fof(f_1475_2,plain,
! [U_4453,U_4452] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_4452),U_4453) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_4452),U_4453),
inference(variable_rename,[status(thm)],[f_1475_1]) ).
cnf(f_1475_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_4452),U_4453) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_4452),U_4453),
inference(clausify,[status(thm)],[f_1475_2]) ).
fof(f_1476_1,plain,
! [V_code__numeral_H_2,V_code__numeral_2] :
( ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
| V_code__numeral_2 != V_code__numeral_H_2 )
& ( V_code__numeral_2 = V_code__numeral_H_2
| c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) ) ),
inference(fof_nnf,[status(thm)],[fact_code__numeral_Oinject]) ).
fof(f_1476_2,plain,
! [U_4455,U_4454] :
( ( c_Code__Numeral_OSuc__code__numeral(U_4454) = c_Code__Numeral_OSuc__code__numeral(U_4455)
| U_4454 != U_4455 )
& ( U_4454 = U_4455
| c_Code__Numeral_OSuc__code__numeral(U_4454) != c_Code__Numeral_OSuc__code__numeral(U_4455) ) ),
inference(variable_rename,[status(thm)],[f_1476_1]) ).
fof(f_1476_3,plain,
( ! [U_4459,U_4457] :
( c_Code__Numeral_OSuc__code__numeral(U_4457) = c_Code__Numeral_OSuc__code__numeral(U_4459)
| U_4457 != U_4459 )
& ! [U_4458,U_4456] :
( U_4456 = U_4458
| c_Code__Numeral_OSuc__code__numeral(U_4456) != c_Code__Numeral_OSuc__code__numeral(U_4458) ) ),
inference(miniscope,[status(thm)],[f_1476_2]) ).
cnf(f_1476_4,plain,
( U_4456 = U_4458
| c_Code__Numeral_OSuc__code__numeral(U_4456) != c_Code__Numeral_OSuc__code__numeral(U_4458) ),
inference(clausify,[status(thm)],[f_1476_3]) ).
cnf(f_1476_5,plain,
( c_Code__Numeral_OSuc__code__numeral(U_4457) = c_Code__Numeral_OSuc__code__numeral(U_4459)
| U_4457 != U_4459 ),
inference(clausify,[status(thm)],[f_1476_3]) ).
fof(f_1477_1,plain,
! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H),
inference(fof_nnf,[status(thm)],[fact_code__numeral_Osimps_I2_J]) ).
fof(f_1477_2,plain,
! [U_4460] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_4460),
inference(variable_rename,[status(thm)],[f_1477_1]) ).
cnf(f_1477_3,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_4460),
inference(clausify,[status(thm)],[f_1477_2]) ).
fof(f_1478_1,plain,
! [V_code__numeral_H_1] : c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_1) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[fact_code__numeral_Osimps_I3_J]) ).
fof(f_1478_2,plain,
! [U_4461] : c_Code__Numeral_OSuc__code__numeral(U_4461) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(variable_rename,[status(thm)],[f_1478_1]) ).
cnf(f_1478_3,plain,
c_Code__Numeral_OSuc__code__numeral(U_4461) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1478_2]) ).
fof(f_1479_1,plain,
! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2),
inference(fof_nnf,[status(thm)],[fact_code__numeral_Osimps_I5_J]) ).
fof(f_1479_2,plain,
! [U_4465,U_4464,U_4463,U_4462] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_4462,U_4463,U_4464,c_Code__Numeral_OSuc__code__numeral(U_4465)) = hAPP(U_4464,U_4465),
inference(variable_rename,[status(thm)],[f_1479_1]) ).
cnf(f_1479_3,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_4462,U_4463,U_4464,c_Code__Numeral_OSuc__code__numeral(U_4465)) = hAPP(U_4464,U_4465),
inference(clausify,[status(thm)],[f_1479_2]) ).
fof(f_1480_1,plain,
! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(V_n)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = V_n,
inference(fof_nnf,[status(thm)],[fact_Suc__code__numeral__minus__one]) ).
fof(f_1480_2,plain,
! [U_4466] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_4466)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_4466,
inference(variable_rename,[status(thm)],[f_1480_1]) ).
cnf(f_1480_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_4466)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_4466,
inference(clausify,[status(thm)],[f_1480_2]) ).
fof(f_1481_1,plain,
c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[fact_subtract__code__numeral__def]) ).
cnf(f_1481_2,plain,
c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1481_1]) ).
fof(f_1482_1,plain,
! [V_r,V_l,V_k] :
( ( c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k),V_l)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) )
& ( c_Random_Ominus__shift(V_r,V_k,V_l) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_r),V_k)),V_l)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) ) ),
inference(fof_nnf,[status(thm)],[fact_minus__shift__def]) ).
fof(f_1482_2,plain,
! [U_4469,U_4468,U_4467] :
( ( c_Random_Ominus__shift(U_4469,U_4467,U_4468) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_4467),U_4468)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_4467),U_4468)) )
& ( c_Random_Ominus__shift(U_4469,U_4467,U_4468) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_4469),U_4467)),U_4468)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_4467),U_4468)) ) ),
inference(variable_rename,[status(thm)],[f_1482_1]) ).
fof(f_1482_3,plain,
( ! [U_4475,U_4473,U_4471] :
( c_Random_Ominus__shift(U_4475,U_4471,U_4473) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_4471),U_4473)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_4471),U_4473)) )
& ! [U_4474,U_4472,U_4470] :
( c_Random_Ominus__shift(U_4474,U_4470,U_4472) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_4474),U_4470)),U_4472)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_4470),U_4472)) ) ),
inference(miniscope,[status(thm)],[f_1482_2]) ).
cnf(f_1482_4,plain,
( c_Random_Ominus__shift(U_4474,U_4470,U_4472) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_4474),U_4470)),U_4472)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_4470),U_4472)) ),
inference(clausify,[status(thm)],[f_1482_3]) ).
cnf(f_1482_5,plain,
( c_Random_Ominus__shift(U_4475,U_4471,U_4473) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_4471),U_4473)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_4471),U_4473)) ),
inference(clausify,[status(thm)],[f_1482_3]) ).
fof(f_1483_1,plain,
! [V_k,V_v] :
( ( c_Random_Oinc__shift(V_v,V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),V_k),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
| V_v = V_k )
& ( c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| V_v != V_k ) ),
inference(fof_nnf,[status(thm)],[fact_inc__shift__def]) ).
fof(f_1483_2,plain,
! [U_4477,U_4476] :
( ( c_Random_Oinc__shift(U_4476,U_4477) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_4477),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
| U_4476 = U_4477 )
& ( c_Random_Oinc__shift(U_4476,U_4477) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| U_4476 != U_4477 ) ),
inference(variable_rename,[status(thm)],[f_1483_1]) ).
fof(f_1483_3,plain,
( ! [U_4481,U_4479] :
( c_Random_Oinc__shift(U_4479,U_4481) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_4481),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
| U_4479 = U_4481 )
& ! [U_4480,U_4478] :
( c_Random_Oinc__shift(U_4478,U_4480) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| U_4478 != U_4480 ) ),
inference(miniscope,[status(thm)],[f_1483_2]) ).
cnf(f_1483_4,plain,
( c_Random_Oinc__shift(U_4478,U_4480) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
| U_4478 != U_4480 ),
inference(clausify,[status(thm)],[f_1483_3]) ).
cnf(f_1483_5,plain,
( c_Random_Oinc__shift(U_4479,U_4481) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_4481),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
| U_4479 = U_4481 ),
inference(clausify,[status(thm)],[f_1483_3]) ).
fof(f_1484_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_1484_2,plain,
! [U_4482] :
( ( ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4482)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4482)),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_4482))))
| 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_4482)))) )
& ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4482)) = 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_4482)))
| ~ 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_4482)))) ) )
| ~ 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_4482))) ),
inference(variable_rename,[status(thm)],[f_1484_1]) ).
cnf(f_1484_3,plain,
( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4482)) = 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_4482)))
| ~ 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_4482))))
| ~ 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_4482))) ),
inference(clausify,[status(thm)],[f_1484_2]) ).
cnf(f_1484_4,plain,
( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4482)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4482)),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_4482))))
| 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_4482))))
| ~ 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_4482))) ),
inference(clausify,[status(thm)],[f_1484_2]) ).
fof(f_1485_1,plain,
! [V_nat] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_nat_Osize_I2_J]) ).
fof(f_1485_2,plain,
! [U_4483] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_4483)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_4483)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_1485_1]) ).
cnf(f_1485_3,plain,
c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_4483)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_4483)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_1485_2]) ).
fof(f_1486_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_1486_2,plain,
! [U_4485,U_4484] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4485)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4484)) = 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_4485),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4484)))),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_4484),c_Int_OPls)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4485)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4484)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4485)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4484),c_Int_OPls)) ) ),
inference(variable_rename,[status(thm)],[f_1486_1]) ).
fof(f_1486_3,plain,
( ! [U_4489,U_4487] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4489)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4487)) = 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_4489),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4487)))),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_4487),c_Int_OPls)) )
& ! [U_4488,U_4486] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4488)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4486)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4488)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4486),c_Int_OPls)) ) ),
inference(miniscope,[status(thm)],[f_1486_2]) ).
cnf(f_1486_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4488)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4486)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4488)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4486),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1486_3]) ).
cnf(f_1486_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4489)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4487)) = 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_4489),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4487)))),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_4487),c_Int_OPls)) ),
inference(clausify,[status(thm)],[f_1486_3]) ).
fof(f_1487_1,plain,
! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(hAPP(V_f2_2,V_code__numeral_2),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,V_code__numeral_2)),
inference(fof_nnf,[status(thm)],[fact_code__numeral_Orecs_I2_J]) ).
fof(f_1487_2,plain,
! [U_4493,U_4492,U_4491,U_4490] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_4490,U_4491,U_4492,c_Code__Numeral_OSuc__code__numeral(U_4493)) = hAPP(hAPP(U_4492,U_4493),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_4490,U_4491,U_4492,U_4493)),
inference(variable_rename,[status(thm)],[f_1487_1]) ).
cnf(f_1487_3,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_4490,U_4491,U_4492,c_Code__Numeral_OSuc__code__numeral(U_4493)) = hAPP(hAPP(U_4492,U_4493),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_4490,U_4491,U_4492,U_4493)),
inference(clausify,[status(thm)],[f_1487_2]) ).
fof(f_1488_1,plain,
! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_f_2)),V_a_2))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_f_2)),V_a_2)) ) )
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_INF__less__iff]) ).
fof(f_1488_2,plain,
! [U_4500,U_4499,U_4498,U_4497,U_4496] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4496),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4497,U_4496),U_4498),U_4499)),U_4500))
| ! [U_4495] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4496),hAPP(U_4499,U_4495)),U_4500))
| ~ hBOOL(hAPP(hAPP(c_member(U_4497),U_4495),U_4498)) ) )
& ( ? [U_4494] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4496),hAPP(U_4499,U_4494)),U_4500))
& hBOOL(hAPP(hAPP(c_member(U_4497),U_4494),U_4498)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4496),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4497,U_4496),U_4498),U_4499)),U_4500)) ) )
| ~ class_Orderings_Olinorder(U_4496)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4496) ),
inference(variable_rename,[status(thm)],[f_1488_1]) ).
fof(f_1488_3,plain,
! [U_4500,U_4499,U_4498,U_4497,U_4496] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4496),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4497,U_4496),U_4498),U_4499)),U_4500))
| ! [U_4495] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4496),hAPP(U_4499,U_4495)),U_4500))
| ~ hBOOL(hAPP(hAPP(c_member(U_4497),U_4495),U_4498)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4496),hAPP(U_4499,sK64(U_4500,U_4499,U_4498,U_4497,U_4496))),U_4500))
& hBOOL(hAPP(hAPP(c_member(U_4497),sK64(U_4500,U_4499,U_4498,U_4497,U_4496)),U_4498)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4496),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4497,U_4496),U_4498),U_4499)),U_4500)) ) )
| ~ class_Orderings_Olinorder(U_4496)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4496) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_4494,sK64(U_4500,U_4499,U_4498,U_4497,U_4496))],[f_1488_2]) ).
cnf(f_1488_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_4497),sK64(U_4500,U_4499,U_4498,U_4497,U_4496)),U_4498))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4496),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4497,U_4496),U_4498),U_4499)),U_4500))
| ~ class_Orderings_Olinorder(U_4496)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4496) ),
inference(clausify,[status(thm)],[f_1488_3]) ).
cnf(f_1488_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4496),hAPP(U_4499,sK64(U_4500,U_4499,U_4498,U_4497,U_4496))),U_4500))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4496),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4497,U_4496),U_4498),U_4499)),U_4500))
| ~ class_Orderings_Olinorder(U_4496)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4496) ),
inference(clausify,[status(thm)],[f_1488_3]) ).
cnf(f_1488_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4496),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4497,U_4496),U_4498),U_4499)),U_4500))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4496),hAPP(U_4499,U_4495)),U_4500))
| ~ hBOOL(hAPP(hAPP(c_member(U_4497),U_4495),U_4498))
| ~ class_Orderings_Olinorder(U_4496)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4496) ),
inference(clausify,[status(thm)],[f_1488_3]) ).
fof(f_1489_1,plain,
! [V_na_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_na_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_na_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_na_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_na_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I2_J]) ).
fof(f_1489_2,plain,
! [U_4502,U_4501] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4501)),U_4502))
| ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4501),U_4502)) )
& ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4501),U_4502))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4501)),U_4502)) ) ),
inference(variable_rename,[status(thm)],[f_1489_1]) ).
fof(f_1489_3,plain,
( ! [U_4506,U_4504] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4504)),U_4506))
| ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4504),U_4506)) )
& ! [U_4505,U_4503] :
( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4503),U_4505))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4503)),U_4505)) ) ),
inference(miniscope,[status(thm)],[f_1489_2]) ).
cnf(f_1489_4,plain,
( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4503),U_4505))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4503)),U_4505)) ),
inference(clausify,[status(thm)],[f_1489_3]) ).
cnf(f_1489_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4504)),U_4506))
| ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4504),U_4506)) ),
inference(clausify,[status(thm)],[f_1489_3]) ).
fof(f_1490_1,plain,
! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__subset__iff]) ).
fof(f_1490_2,plain,
! [U_4513,U_4512,U_4511,U_4510,U_4509] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4509,tc_HOL_Obool)),U_4510),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4511,tc_fun(U_4509,tc_HOL_Obool)),U_4512),U_4513)))
| ? [U_4508] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4509,tc_HOL_Obool)),U_4510),hAPP(U_4513,U_4508)))
& hBOOL(hAPP(hAPP(c_member(U_4511),U_4508),U_4512)) ) )
& ( ! [U_4507] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4509,tc_HOL_Obool)),U_4510),hAPP(U_4513,U_4507)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4511),U_4507),U_4512)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4509,tc_HOL_Obool)),U_4510),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4511,tc_fun(U_4509,tc_HOL_Obool)),U_4512),U_4513))) ) ),
inference(variable_rename,[status(thm)],[f_1490_1]) ).
fof(f_1490_3,plain,
( ! [U_4523,U_4521,U_4519,U_4517,U_4515] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4515,tc_HOL_Obool)),U_4517),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4519,tc_fun(U_4515,tc_HOL_Obool)),U_4521),U_4523)))
| ? [U_4508] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4515,tc_HOL_Obool)),U_4517),hAPP(U_4523,U_4508)))
& hBOOL(hAPP(hAPP(c_member(U_4519),U_4508),U_4521)) ) )
& ! [U_4522,U_4520,U_4518,U_4516,U_4514] :
( ! [U_4507] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4514,tc_HOL_Obool)),U_4516),hAPP(U_4522,U_4507)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4518),U_4507),U_4520)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4514,tc_HOL_Obool)),U_4516),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4518,tc_fun(U_4514,tc_HOL_Obool)),U_4520),U_4522))) ) ),
inference(miniscope,[status(thm)],[f_1490_2]) ).
fof(f_1490_4,plain,
( ! [U_4523,U_4521,U_4519,U_4517,U_4515] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4515,tc_HOL_Obool)),U_4517),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4519,tc_fun(U_4515,tc_HOL_Obool)),U_4521),U_4523)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4515,tc_HOL_Obool)),U_4517),hAPP(U_4523,sK65(U_4523,U_4521,U_4519,U_4517,U_4515))))
& hBOOL(hAPP(hAPP(c_member(U_4519),sK65(U_4523,U_4521,U_4519,U_4517,U_4515)),U_4521)) ) )
& ! [U_4522,U_4520,U_4518,U_4516,U_4514] :
( ! [U_4507] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4514,tc_HOL_Obool)),U_4516),hAPP(U_4522,U_4507)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4518),U_4507),U_4520)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4514,tc_HOL_Obool)),U_4516),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4518,tc_fun(U_4514,tc_HOL_Obool)),U_4520),U_4522))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_4508,sK65(U_4523,U_4521,U_4519,U_4517,U_4515))],[f_1490_3]) ).
cnf(f_1490_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4514,tc_HOL_Obool)),U_4516),hAPP(U_4522,U_4507)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4518),U_4507),U_4520))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4514,tc_HOL_Obool)),U_4516),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4518,tc_fun(U_4514,tc_HOL_Obool)),U_4520),U_4522))) ),
inference(clausify,[status(thm)],[f_1490_4]) ).
cnf(f_1490_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_4519),sK65(U_4523,U_4521,U_4519,U_4517,U_4515)),U_4521))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4515,tc_HOL_Obool)),U_4517),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4519,tc_fun(U_4515,tc_HOL_Obool)),U_4521),U_4523))) ),
inference(clausify,[status(thm)],[f_1490_4]) ).
cnf(f_1490_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4515,tc_HOL_Obool)),U_4517),hAPP(U_4523,sK65(U_4523,U_4521,U_4519,U_4517,U_4515))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4515,tc_HOL_Obool)),U_4517),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4519,tc_fun(U_4515,tc_HOL_Obool)),U_4521),U_4523))) ),
inference(clausify,[status(thm)],[f_1490_4]) ).
fof(f_1491_1,plain,
! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_M_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_M_2))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__INF__iff]) ).
fof(f_1491_2,plain,
! [U_4530,U_4529,U_4528,U_4527,U_4526] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4526),U_4527),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4528,U_4526),U_4529),U_4530)))
| ? [U_4525] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4526),U_4527),hAPP(U_4530,U_4525)))
& hBOOL(hAPP(hAPP(c_member(U_4528),U_4525),U_4529)) ) )
& ( ! [U_4524] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4526),U_4527),hAPP(U_4530,U_4524)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4528),U_4524),U_4529)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4526),U_4527),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4528,U_4526),U_4529),U_4530))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4526) ),
inference(variable_rename,[status(thm)],[f_1491_1]) ).
fof(f_1491_3,plain,
! [U_4530,U_4529,U_4528,U_4527,U_4526] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4526),U_4527),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4528,U_4526),U_4529),U_4530)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4526),U_4527),hAPP(U_4530,sK66(U_4530,U_4529,U_4528,U_4527,U_4526))))
& hBOOL(hAPP(hAPP(c_member(U_4528),sK66(U_4530,U_4529,U_4528,U_4527,U_4526)),U_4529)) ) )
& ( ! [U_4524] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4526),U_4527),hAPP(U_4530,U_4524)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4528),U_4524),U_4529)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4526),U_4527),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4528,U_4526),U_4529),U_4530))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4526) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_4525,sK66(U_4530,U_4529,U_4528,U_4527,U_4526))],[f_1491_2]) ).
cnf(f_1491_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4526),U_4527),hAPP(U_4530,U_4524)))
| ~ hBOOL(hAPP(hAPP(c_member(U_4528),U_4524),U_4529))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4526),U_4527),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4528,U_4526),U_4529),U_4530)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4526) ),
inference(clausify,[status(thm)],[f_1491_3]) ).
cnf(f_1491_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_4528),sK66(U_4530,U_4529,U_4528,U_4527,U_4526)),U_4529))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4526),U_4527),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4528,U_4526),U_4529),U_4530)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4526) ),
inference(clausify,[status(thm)],[f_1491_3]) ).
cnf(f_1491_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4526),U_4527),hAPP(U_4530,sK66(U_4530,U_4529,U_4528,U_4527,U_4526))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4526),U_4527),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4528,U_4526),U_4529),U_4530)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4526) ),
inference(clausify,[status(thm)],[f_1491_3]) ).
fof(f_1492_1,plain,
! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_INFI__apply]) ).
fof(f_1492_2,plain,
! [U_4536,U_4535,U_4534,U_4533,U_4532,U_4531] :
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4532,tc_fun(U_4533,U_4531)),U_4534),U_4535),U_4536) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4532,U_4531),U_4534),hAPP(hAPP(c_COMBC(U_4532,U_4533,U_4531),U_4535),U_4536))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4531) ),
inference(variable_rename,[status(thm)],[f_1492_1]) ).
cnf(f_1492_3,plain,
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4532,tc_fun(U_4533,U_4531)),U_4534),U_4535),U_4536) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4532,U_4531),U_4534),hAPP(hAPP(c_COMBC(U_4532,U_4533,U_4531),U_4535),U_4536))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4531) ),
inference(clausify,[status(thm)],[f_1492_2]) ).
fof(f_1493_1,plain,
! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2)))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_INF__commute]) ).
fof(f_1493_2,plain,
! [U_4542,U_4541,U_4540,U_4539,U_4538,U_4537] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4538,U_4537),U_4539),hAPP(hAPP(c_COMBB(tc_fun(U_4540,U_4537),U_4537,U_4538),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4540,U_4537),U_4541)),U_4542)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4540,U_4537),U_4541),hAPP(hAPP(c_COMBB(tc_fun(U_4538,U_4537),U_4537,U_4540),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4538,U_4537),U_4539)),hAPP(c_COMBC(U_4538,U_4540,U_4537),U_4542)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4537) ),
inference(variable_rename,[status(thm)],[f_1493_1]) ).
cnf(f_1493_3,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4538,U_4537),U_4539),hAPP(hAPP(c_COMBB(tc_fun(U_4540,U_4537),U_4537,U_4538),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4540,U_4537),U_4541)),U_4542)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4540,U_4537),U_4541),hAPP(hAPP(c_COMBB(tc_fun(U_4538,U_4537),U_4537,U_4540),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_4538,U_4537),U_4539)),hAPP(c_COMBC(U_4538,U_4540,U_4537),U_4542)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_4537) ),
inference(clausify,[status(thm)],[f_1493_2]) ).
fof(f_1494_1,plain,
! [V_x_2,V_A_2,T_c,T_b] :
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2))
| ~ class_Groups_Ouminus(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fun__Compl__def]) ).
fof(f_1494_2,plain,
! [U_4546,U_4545,U_4544,U_4543] :
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4544,U_4543)),U_4545),U_4546) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4543),hAPP(U_4545,U_4546))
| ~ class_Groups_Ouminus(U_4543) ),
inference(variable_rename,[status(thm)],[f_1494_1]) ).
cnf(f_1494_3,plain,
( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_4544,U_4543)),U_4545),U_4546) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4543),hAPP(U_4545,U_4546))
| ~ class_Groups_Ouminus(U_4543) ),
inference(clausify,[status(thm)],[f_1494_2]) ).
fof(f_1495_1,plain,
! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2))
| ~ class_Groups_Ominus(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fun__diff__def]) ).
fof(f_1495_2,plain,
! [U_4551,U_4550,U_4549,U_4548,U_4547] :
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4548,U_4547)),U_4549),U_4550),U_4551) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4547),hAPP(U_4549,U_4551)),hAPP(U_4550,U_4551))
| ~ class_Groups_Ominus(U_4547) ),
inference(variable_rename,[status(thm)],[f_1495_1]) ).
cnf(f_1495_3,plain,
( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4548,U_4547)),U_4549),U_4550),U_4551) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4547),hAPP(U_4549,U_4551)),hAPP(U_4550,U_4551))
| ~ class_Groups_Ominus(U_4547) ),
inference(clausify,[status(thm)],[f_1495_2]) ).
fof(f_1496_1,plain,
! [V_na_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),
inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le__raw]) ).
fof(f_1496_2,plain,
! [U_4552] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4552) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4552)),
inference(variable_rename,[status(thm)],[f_1496_1]) ).
cnf(f_1496_3,plain,
hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4552) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4552)),
inference(clausify,[status(thm)],[f_1496_2]) ).
fof(f_1497_1,plain,
! [V_na_2,V_m_2] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_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_na_2)),
inference(fof_nnf,[status(thm)],[fact_diff__Suc]) ).
fof(f_1497_2,plain,
! [U_4554,U_4553] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4553),hAPP(c_Nat_OSuc,U_4554)) = 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_4553),U_4554)),
inference(variable_rename,[status(thm)],[f_1497_1]) ).
cnf(f_1497_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4553),hAPP(c_Nat_OSuc,U_4554)) = 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_4553),U_4554)),
inference(clausify,[status(thm)],[f_1497_2]) ).
fof(f_1498_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_1498_2,plain,
! [U_4555] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_4555)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4555)),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_1498_1]) ).
cnf(f_1498_3,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_4555)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4555)),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_1498_2]) ).
fof(f_1499_1,plain,
c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_nat_Osize_I1_J]) ).
cnf(f_1499_2,plain,
c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1499_1]) ).
fof(f_1500_1,plain,
! [V_w_2,V_z_2,T_b] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b)))
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power__number__of__even]) ).
fof(f_1500_2,plain,
! [U_4558,U_4557,U_4556] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4556),U_4557),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_4558))) = hAPP(hAPP(c_HOL_OLet(U_4556,U_4556),hAPP(hAPP(c_Power_Opower__class_Opower(U_4556),U_4557),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4558))),hAPP(hAPP(c_COMBS(U_4556,U_4556,U_4556),c_Groups_Otimes__class_Otimes(U_4556)),c_COMBI(U_4556)))
| ~ class_Int_Onumber__ring(U_4556) ),
inference(variable_rename,[status(thm)],[f_1500_1]) ).
cnf(f_1500_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4556),U_4557),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_4558))) = hAPP(hAPP(c_HOL_OLet(U_4556,U_4556),hAPP(hAPP(c_Power_Opower__class_Opower(U_4556),U_4557),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4558))),hAPP(hAPP(c_COMBS(U_4556,U_4556,U_4556),c_Groups_Otimes__class_Otimes(U_4556)),c_COMBI(U_4556)))
| ~ class_Int_Onumber__ring(U_4556) ),
inference(clausify,[status(thm)],[f_1500_2]) ).
fof(f_1501_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_1501_2,plain,
! [U_4560,U_4559] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4559),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_4560))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4559),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4560))),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_1501_1]) ).
cnf(f_1501_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4559),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_4560))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4559),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4560))),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_1501_2]) ).
fof(f_1502_1,plain,
! [V_w_2,V_v_2,T_b] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b)))
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power__number__of__even__number__of]) ).
fof(f_1502_2,plain,
! [U_4563,U_4562,U_4561] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4561),hAPP(c_Int_Onumber__class_Onumber__of(U_4561),U_4562)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_4563))) = hAPP(hAPP(c_HOL_OLet(U_4561,U_4561),hAPP(hAPP(c_Power_Opower__class_Opower(U_4561),hAPP(c_Int_Onumber__class_Onumber__of(U_4561),U_4562)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4563))),hAPP(hAPP(c_COMBS(U_4561,U_4561,U_4561),c_Groups_Otimes__class_Otimes(U_4561)),c_COMBI(U_4561)))
| ~ class_Int_Onumber__ring(U_4561) ),
inference(variable_rename,[status(thm)],[f_1502_1]) ).
cnf(f_1502_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4561),hAPP(c_Int_Onumber__class_Onumber__of(U_4561),U_4562)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_4563))) = hAPP(hAPP(c_HOL_OLet(U_4561,U_4561),hAPP(hAPP(c_Power_Opower__class_Opower(U_4561),hAPP(c_Int_Onumber__class_Onumber__of(U_4561),U_4562)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4563))),hAPP(hAPP(c_COMBS(U_4561,U_4561,U_4561),c_Groups_Otimes__class_Otimes(U_4561)),c_COMBI(U_4561)))
| ~ class_Int_Onumber__ring(U_4561) ),
inference(clausify,[status(thm)],[f_1502_2]) ).
fof(f_1503_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_1503_2,plain,
! [U_4565,U_4564] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_4565)),hAPP(c_Int_Onat,U_4564)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4565),U_4564)),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_4564)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_4565)),hAPP(c_Int_Onat,U_4564)) = hAPP(c_Int_Onat,U_4565)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4564)) ) ),
inference(variable_rename,[status(thm)],[f_1503_1]) ).
fof(f_1503_3,plain,
( ! [U_4569,U_4567] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_4569)),hAPP(c_Int_Onat,U_4567)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4569),U_4567)),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_4567)) )
& ! [U_4568,U_4566] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_4568)),hAPP(c_Int_Onat,U_4566)) = hAPP(c_Int_Onat,U_4568)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4566)) ) ),
inference(miniscope,[status(thm)],[f_1503_2]) ).
cnf(f_1503_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_4568)),hAPP(c_Int_Onat,U_4566)) = hAPP(c_Int_Onat,U_4568)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_4566)) ),
inference(clausify,[status(thm)],[f_1503_3]) ).
cnf(f_1503_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_4569)),hAPP(c_Int_Onat,U_4567)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4569),U_4567)),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_4567)) ),
inference(clausify,[status(thm)],[f_1503_3]) ).
fof(f_1504_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_1504_2,plain,
! [U_4571,U_4570] :
( c_Divides_OnegDivAlg(U_4570,U_4571) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4570),U_4571)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4570,U_4571))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4571))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4570),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1504_1]) ).
cnf(f_1504_3,plain,
( c_Divides_OnegDivAlg(U_4570,U_4571) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4570),U_4571)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4570,U_4571))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4571))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4570),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1504_2]) ).
fof(f_1505_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_1505_2,plain,
! [U_4572] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_4572) = 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_4572),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_1505_1]) ).
cnf(f_1505_3,plain,
c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_4572) = 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_4572),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_1505_2]) ).
fof(f_1506_1,plain,
! [V_na_2,T_b] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_Groups_Oone__class_Oone(T_b)),V_na_2,c_Groups_Ozero__class_Ozero(T_b))
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_semiring__1__class_Oof__nat__code]) ).
fof(f_1506_2,plain,
! [U_4574,U_4573] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4573),U_4574) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_4573,hAPP(hAPP(c_COMBC(U_4573,U_4573,U_4573),c_Groups_Oplus__class_Oplus(U_4573)),c_Groups_Oone__class_Oone(U_4573)),U_4574,c_Groups_Ozero__class_Ozero(U_4573))
| ~ class_Rings_Osemiring__1(U_4573) ),
inference(variable_rename,[status(thm)],[f_1506_1]) ).
cnf(f_1506_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4573),U_4574) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_4573,hAPP(hAPP(c_COMBC(U_4573,U_4573,U_4573),c_Groups_Oplus__class_Oplus(U_4573)),c_Groups_Oone__class_Oone(U_4573)),U_4574,c_Groups_Ozero__class_Ozero(U_4573))
| ~ class_Rings_Osemiring__1(U_4573) ),
inference(clausify,[status(thm)],[f_1506_2]) ).
fof(f_1507_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_1507_2,plain,
! [U_4577,U_4576,U_4575] : hAPP(c_Divides_Oadjust(U_4575),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4576),U_4577)) = 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_4577),U_4575)),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_4576)),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_4576)),U_4577))),
inference(variable_rename,[status(thm)],[f_1507_1]) ).
cnf(f_1507_3,plain,
hAPP(c_Divides_Oadjust(U_4575),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4576),U_4577)) = 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_4577),U_4575)),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_4576)),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_4576)),U_4577))),
inference(clausify,[status(thm)],[f_1507_2]) ).
fof(f_1508_1,plain,
! [V_na_2,V_v_2] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_na_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_na_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_na_2)))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) != hAPP(c_Nat_OSuc,V_na_2) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__number__of__Suc]) ).
fof(f_1508_2,plain,
! [U_4579,U_4578] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4578) = hAPP(c_Nat_OSuc,U_4579)
| ~ 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_4578))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4579))))) )
& ( 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_4578))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4579)))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4578) != hAPP(c_Nat_OSuc,U_4579) ) ),
inference(variable_rename,[status(thm)],[f_1508_1]) ).
fof(f_1508_3,plain,
( ! [U_4583,U_4581] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4581) = hAPP(c_Nat_OSuc,U_4583)
| ~ 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_4581))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4583))))) )
& ! [U_4582,U_4580] :
( 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_4580))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4582)))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4580) != hAPP(c_Nat_OSuc,U_4582) ) ),
inference(miniscope,[status(thm)],[f_1508_2]) ).
cnf(f_1508_4,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_4580))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4582)))))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4580) != hAPP(c_Nat_OSuc,U_4582) ),
inference(clausify,[status(thm)],[f_1508_3]) ).
cnf(f_1508_5,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4581) = hAPP(c_Nat_OSuc,U_4583)
| ~ 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_4581))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4583))))) ),
inference(clausify,[status(thm)],[f_1508_3]) ).
fof(f_1509_1,plain,
! [V_v_2,V_na_2] :
( ( hAPP(c_Nat_OSuc,V_na_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_na_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_na_2)))))
| hAPP(c_Nat_OSuc,V_na_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_1509_2,plain,
! [U_4585,U_4584] :
( ( hAPP(c_Nat_OSuc,U_4584) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4585)
| ~ 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_4585))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4584))))) )
& ( 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_4585))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4584)))))
| hAPP(c_Nat_OSuc,U_4584) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4585) ) ),
inference(variable_rename,[status(thm)],[f_1509_1]) ).
fof(f_1509_3,plain,
( ! [U_4589,U_4587] :
( hAPP(c_Nat_OSuc,U_4587) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4589)
| ~ 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_4589))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4587))))) )
& ! [U_4588,U_4586] :
( 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_4588))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4586)))))
| hAPP(c_Nat_OSuc,U_4586) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4588) ) ),
inference(miniscope,[status(thm)],[f_1509_2]) ).
cnf(f_1509_4,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_4588))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4586)))))
| hAPP(c_Nat_OSuc,U_4586) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4588) ),
inference(clausify,[status(thm)],[f_1509_3]) ).
cnf(f_1509_5,plain,
( hAPP(c_Nat_OSuc,U_4587) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4589)
| ~ 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_4589))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4587))))) ),
inference(clausify,[status(thm)],[f_1509_3]) ).
fof(f_1510_1,plain,
! [V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat))),
inference(fof_nnf,[status(thm)],[fact_nat__case__number__of]) ).
fof(f_1510_2,plain,
! [U_4593,U_4592,U_4591,U_4590] : c_Nat_Onat_Onat__case(U_4590,U_4591,U_4592,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4593)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_4590),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_4593))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_4590,U_4590),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_4590,tc_fun(U_4590,U_4590)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4590,tc_fun(U_4590,U_4590)),tc_Int_Oint),c_If(U_4590)),c_Nat__Numeral_Oneg)),U_4591)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_4590,tc_Int_Oint),U_4592),c_Int_Onat))),
inference(variable_rename,[status(thm)],[f_1510_1]) ).
cnf(f_1510_3,plain,
c_Nat_Onat_Onat__case(U_4590,U_4591,U_4592,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4593)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_4590),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_4593))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_4590,U_4590),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_4590,tc_fun(U_4590,U_4590)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4590,tc_fun(U_4590,U_4590)),tc_Int_Oint),c_If(U_4590)),c_Nat__Numeral_Oneg)),U_4591)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_4590,tc_Int_Oint),U_4592),c_Int_Onat))),
inference(clausify,[status(thm)],[f_1510_2]) ).
fof(f_1511_1,plain,
! [V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),c_Int_Onat)))),
inference(fof_nnf,[status(thm)],[fact_nat__rec__number__of]) ).
fof(f_1511_2,plain,
! [U_4597,U_4596,U_4595,U_4594] : hAPP(c_Nat_Onat_Onat__rec(U_4594,U_4595,U_4596),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4597)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_4594),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_4597))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_4594,U_4594),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_4594,tc_fun(U_4594,U_4594)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4594,tc_fun(U_4594,U_4594)),tc_Int_Oint),c_If(U_4594)),c_Nat__Numeral_Oneg)),U_4595)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_4594,U_4594),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_4594,U_4594),tc_Int_Oint),U_4596),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_4594,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_4594,U_4595,U_4596)),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[f_1511_1]) ).
cnf(f_1511_3,plain,
hAPP(c_Nat_Onat_Onat__rec(U_4594,U_4595,U_4596),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4597)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_4594),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_4597))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_4594,U_4594),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_4594,tc_fun(U_4594,U_4594)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4594,tc_fun(U_4594,U_4594)),tc_Int_Oint),c_If(U_4594)),c_Nat__Numeral_Oneg)),U_4595)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_4594,U_4594),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_4594,U_4594),tc_Int_Oint),U_4596),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_4594,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_4594,U_4595,U_4596)),c_Int_Onat)))),
inference(clausify,[status(thm)],[f_1511_2]) ).
fof(f_1512_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_1512_2,plain,
! [U_4598] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_4598)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4598)),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_4598))) )
& ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_4598)) = 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_4598))) ) ),
inference(variable_rename,[status(thm)],[f_1512_1]) ).
fof(f_1512_3,plain,
( ! [U_4600] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_4600)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4600)),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_4600))) )
& ! [U_4599] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_4599)) = 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_4599))) ) ),
inference(miniscope,[status(thm)],[f_1512_2]) ).
cnf(f_1512_4,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_4599)) = 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_4599))) ),
inference(clausify,[status(thm)],[f_1512_3]) ).
cnf(f_1512_5,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_4600)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4600)),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_4600))) ),
inference(clausify,[status(thm)],[f_1512_3]) ).
fof(f_1513_1,plain,
! [V_v_2,V_na_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_na_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_na_2)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_1513_2,plain,
! [U_4602,U_4601] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4601)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4602)))
| ~ 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_4602))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4601)),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_4602))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4601)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4601)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4602))) ) ),
inference(variable_rename,[status(thm)],[f_1513_1]) ).
fof(f_1513_3,plain,
( ! [U_4606,U_4604] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4604)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4606)))
| ~ 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_4606))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4604)),c_Int_Onat))))) )
& ! [U_4605,U_4603] :
( 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_4605))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4603)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4603)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4605))) ) ),
inference(miniscope,[status(thm)],[f_1513_2]) ).
cnf(f_1513_4,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_4605))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4603)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4603)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4605))) ),
inference(clausify,[status(thm)],[f_1513_3]) ).
cnf(f_1513_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4604)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4606)))
| ~ 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_4606))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4604)),c_Int_Onat))))) ),
inference(clausify,[status(thm)],[f_1513_3]) ).
fof(f_1514_1,plain,
! [V_na_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_na_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_na_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_na_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_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__number__of__Suc]) ).
fof(f_1514_2,plain,
! [U_4608,U_4607] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4607)),hAPP(c_Nat_OSuc,U_4608)))
| ~ 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_4607))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4608)))) )
& ( 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_4607))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4608))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4607)),hAPP(c_Nat_OSuc,U_4608))) ) ),
inference(variable_rename,[status(thm)],[f_1514_1]) ).
fof(f_1514_3,plain,
( ! [U_4612,U_4610] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4610)),hAPP(c_Nat_OSuc,U_4612)))
| ~ 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_4610))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4612)))) )
& ! [U_4611,U_4609] :
( 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_4609))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4611))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4609)),hAPP(c_Nat_OSuc,U_4611))) ) ),
inference(miniscope,[status(thm)],[f_1514_2]) ).
cnf(f_1514_4,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_4609))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4611))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4609)),hAPP(c_Nat_OSuc,U_4611))) ),
inference(clausify,[status(thm)],[f_1514_3]) ).
cnf(f_1514_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4610)),hAPP(c_Nat_OSuc,U_4612)))
| ~ 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_4610))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4612)))) ),
inference(clausify,[status(thm)],[f_1514_3]) ).
fof(f_1515_1,plain,
! [V_na_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_na_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_na_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_na_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_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_le__number__of__Suc]) ).
fof(f_1515_2,plain,
! [U_4614,U_4613] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4613)),hAPP(c_Nat_OSuc,U_4614)))
| ~ 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_4613))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4614)))) )
& ( 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_4613))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4614))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4613)),hAPP(c_Nat_OSuc,U_4614))) ) ),
inference(variable_rename,[status(thm)],[f_1515_1]) ).
fof(f_1515_3,plain,
( ! [U_4618,U_4616] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4616)),hAPP(c_Nat_OSuc,U_4618)))
| ~ 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_4616))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4618)))) )
& ! [U_4617,U_4615] :
( 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_4615))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4617))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4615)),hAPP(c_Nat_OSuc,U_4617))) ) ),
inference(miniscope,[status(thm)],[f_1515_2]) ).
cnf(f_1515_4,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_4615))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4617))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4615)),hAPP(c_Nat_OSuc,U_4617))) ),
inference(clausify,[status(thm)],[f_1515_3]) ).
cnf(f_1515_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4616)),hAPP(c_Nat_OSuc,U_4618)))
| ~ 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_4616))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4618)))) ),
inference(clausify,[status(thm)],[f_1515_3]) ).
fof(f_1516_1,plain,
! [V_v_2,V_na_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_na_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_na_2)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_1516_2,plain,
! [U_4620,U_4619] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4619)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4620)))
| ~ 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_4620))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4619)),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_4620))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4619)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4619)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4620))) ) ),
inference(variable_rename,[status(thm)],[f_1516_1]) ).
fof(f_1516_3,plain,
( ! [U_4624,U_4622] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4622)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4624)))
| ~ 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_4624))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4622)),c_Int_Onat))))) )
& ! [U_4623,U_4621] :
( 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_4623))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4621)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4621)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4623))) ) ),
inference(miniscope,[status(thm)],[f_1516_2]) ).
cnf(f_1516_4,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_4623))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4621)),c_Int_Onat)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4621)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4623))) ),
inference(clausify,[status(thm)],[f_1516_3]) ).
cnf(f_1516_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4622)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4624)))
| ~ 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_4624))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4622)),c_Int_Onat))))) ),
inference(clausify,[status(thm)],[f_1516_3]) ).
fof(f_1517_1,plain,
! [V_na_2,V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_na_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,V_na_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_na_2)))),
inference(fof_nnf,[status(thm)],[fact_nat__case__add__eq__if]) ).
fof(f_1517_2,plain,
! [U_4629,U_4628,U_4627,U_4626,U_4625] : c_Nat_Onat_Onat__case(U_4625,U_4626,U_4627,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4628)),U_4629)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_4625),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_4628))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_4625,U_4625),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_4625,tc_fun(U_4625,U_4625)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4625,tc_fun(U_4625,U_4625)),tc_Int_Oint),c_If(U_4625)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_4625,U_4626,U_4627,U_4629))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_4625,tc_Int_Oint),U_4627),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_4629)))),
inference(variable_rename,[status(thm)],[f_1517_1]) ).
cnf(f_1517_3,plain,
c_Nat_Onat_Onat__case(U_4625,U_4626,U_4627,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4628)),U_4629)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_4625),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_4628))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_4625,U_4625),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_4625,tc_fun(U_4625,U_4625)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4625,tc_fun(U_4625,U_4625)),tc_Int_Oint),c_If(U_4625)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_4625,U_4626,U_4627,U_4629))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_4625,tc_Int_Oint),U_4627),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_4629)))),
inference(clausify,[status(thm)],[f_1517_2]) ).
fof(f_1518_1,plain,
! [V_na_2,V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_na_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),V_na_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_na_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_na_2))))),
inference(fof_nnf,[status(thm)],[fact_nat__rec__add__eq__if]) ).
fof(f_1518_2,plain,
! [U_4634,U_4633,U_4632,U_4631,U_4630] : hAPP(c_Nat_Onat_Onat__rec(U_4630,U_4631,U_4632),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4633)),U_4634)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_4630),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_4633))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_4630,U_4630),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_4630,tc_fun(U_4630,U_4630)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4630,tc_fun(U_4630,U_4630)),tc_Int_Oint),c_If(U_4630)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_4630,U_4631,U_4632),U_4634))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_4630,U_4630),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_4630,U_4630),tc_Int_Oint),U_4632),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_4634))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_4630,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_4630,U_4631,U_4632)),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_4634))))),
inference(variable_rename,[status(thm)],[f_1518_1]) ).
cnf(f_1518_3,plain,
hAPP(c_Nat_Onat_Onat__rec(U_4630,U_4631,U_4632),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4633)),U_4634)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_4630),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_4633))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_4630,U_4630),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_4630,tc_fun(U_4630,U_4630)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4630,tc_fun(U_4630,U_4630)),tc_Int_Oint),c_If(U_4630)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_4630,U_4631,U_4632),U_4634))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_4630,U_4630),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_4630,U_4630),tc_Int_Oint),U_4632),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_4634))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_4630,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_4630,U_4631,U_4632)),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_4634))))),
inference(clausify,[status(thm)],[f_1518_2]) ).
fof(f_1519_1,plain,
! [V_z_2,V_w_2,T_b] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2))),c_COMBI(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) )
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power__number__of__odd]) ).
fof(f_1519_2,plain,
! [U_4637,U_4636,U_4635] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4635),U_4637),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_4636))) = c_Groups_Oone__class_Oone(U_4635)
| 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_4636))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4635),U_4637),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_4636))) = hAPP(hAPP(c_HOL_OLet(U_4635,U_4635),hAPP(hAPP(c_Power_Opower__class_Opower(U_4635),U_4637),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4636))),hAPP(hAPP(c_COMBS(U_4635,U_4635,U_4635),hAPP(hAPP(c_COMBB(U_4635,tc_fun(U_4635,U_4635),U_4635),c_Groups_Otimes__class_Otimes(U_4635)),hAPP(c_Groups_Otimes__class_Otimes(U_4635),U_4637))),c_COMBI(U_4635)))
| ~ 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_4636))) ) )
| ~ class_Int_Onumber__ring(U_4635) ),
inference(variable_rename,[status(thm)],[f_1519_1]) ).
cnf(f_1519_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4635),U_4637),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_4636))) = hAPP(hAPP(c_HOL_OLet(U_4635,U_4635),hAPP(hAPP(c_Power_Opower__class_Opower(U_4635),U_4637),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4636))),hAPP(hAPP(c_COMBS(U_4635,U_4635,U_4635),hAPP(hAPP(c_COMBB(U_4635,tc_fun(U_4635,U_4635),U_4635),c_Groups_Otimes__class_Otimes(U_4635)),hAPP(c_Groups_Otimes__class_Otimes(U_4635),U_4637))),c_COMBI(U_4635)))
| ~ 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_4636)))
| ~ class_Int_Onumber__ring(U_4635) ),
inference(clausify,[status(thm)],[f_1519_2]) ).
cnf(f_1519_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4635),U_4637),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_4636))) = c_Groups_Oone__class_Oone(U_4635)
| 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_4636)))
| ~ class_Int_Onumber__ring(U_4635) ),
inference(clausify,[status(thm)],[f_1519_2]) ).
fof(f_1520_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_1520_2,plain,
! [U_4639,U_4638] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4639),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_4638))) = 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_4638))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4639),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_4638))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4639),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4638))),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_4639))),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_4638))) ) ),
inference(variable_rename,[status(thm)],[f_1520_1]) ).
fof(f_1520_3,plain,
( ! [U_4643,U_4641] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4643),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_4641))) = 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_4641))) )
& ! [U_4642,U_4640] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4642),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_4640))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4642),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4640))),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_4642))),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_4640))) ) ),
inference(miniscope,[status(thm)],[f_1520_2]) ).
cnf(f_1520_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4642),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_4640))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4642),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4640))),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_4642))),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_4640))) ),
inference(clausify,[status(thm)],[f_1520_3]) ).
cnf(f_1520_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4643),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_4641))) = 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_4641))) ),
inference(clausify,[status(thm)],[f_1520_3]) ).
fof(f_1521_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_1521_2,plain,
! [U_4645,U_4644] :
( ( c_Divides_OnegDivAlg(U_4644,U_4645) = hAPP(c_Divides_Oadjust(U_4645),c_Divides_OnegDivAlg(U_4644,hAPP(hAPP(c_Groups_Otimes__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_4645)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4645),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_4644),U_4645))) )
& ( c_Divides_OnegDivAlg(U_4644,U_4645) = 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_4644),U_4645))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4645),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_4644),U_4645))) ) ) ),
inference(variable_rename,[status(thm)],[f_1521_1]) ).
fof(f_1521_3,plain,
( ! [U_4649,U_4647] :
( c_Divides_OnegDivAlg(U_4647,U_4649) = hAPP(c_Divides_Oadjust(U_4649),c_Divides_OnegDivAlg(U_4647,hAPP(hAPP(c_Groups_Otimes__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_4649)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4649),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_4647),U_4649))) )
& ! [U_4648,U_4646] :
( c_Divides_OnegDivAlg(U_4646,U_4648) = 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_4646),U_4648))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4648),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_4646),U_4648))) ) ) ),
inference(miniscope,[status(thm)],[f_1521_2]) ).
cnf(f_1521_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_4646),U_4648)))
| c_Divides_OnegDivAlg(U_4646,U_4648) = 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_4646),U_4648)) ),
inference(clausify,[status(thm)],[f_1521_3]) ).
cnf(f_1521_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4648),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OnegDivAlg(U_4646,U_4648) = 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_4646),U_4648)) ),
inference(clausify,[status(thm)],[f_1521_3]) ).
cnf(f_1521_6,plain,
( c_Divides_OnegDivAlg(U_4647,U_4649) = hAPP(c_Divides_Oadjust(U_4649),c_Divides_OnegDivAlg(U_4647,hAPP(hAPP(c_Groups_Otimes__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_4649)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4649),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_4647),U_4649))) ),
inference(clausify,[status(thm)],[f_1521_3]) ).
fof(f_1522_1,plain,
! [V_v_2,V_w_2,T_b] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(T_b)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)))),c_COMBI(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) )
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power__number__of__odd__number__of]) ).
fof(f_1522_2,plain,
! [U_4652,U_4651,U_4650] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4650),hAPP(c_Int_Onumber__class_Onumber__of(U_4650),U_4652)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_4651))) = c_Groups_Oone__class_Oone(U_4650)
| 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_4651))) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4650),hAPP(c_Int_Onumber__class_Onumber__of(U_4650),U_4652)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_4651))) = hAPP(hAPP(c_HOL_OLet(U_4650,U_4650),hAPP(hAPP(c_Power_Opower__class_Opower(U_4650),hAPP(c_Int_Onumber__class_Onumber__of(U_4650),U_4652)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4651))),hAPP(hAPP(c_COMBS(U_4650,U_4650,U_4650),hAPP(hAPP(c_COMBB(U_4650,tc_fun(U_4650,U_4650),U_4650),c_Groups_Otimes__class_Otimes(U_4650)),hAPP(c_Groups_Otimes__class_Otimes(U_4650),hAPP(c_Int_Onumber__class_Onumber__of(U_4650),U_4652)))),c_COMBI(U_4650)))
| ~ 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_4651))) ) )
| ~ class_Int_Onumber__ring(U_4650) ),
inference(variable_rename,[status(thm)],[f_1522_1]) ).
cnf(f_1522_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4650),hAPP(c_Int_Onumber__class_Onumber__of(U_4650),U_4652)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_4651))) = hAPP(hAPP(c_HOL_OLet(U_4650,U_4650),hAPP(hAPP(c_Power_Opower__class_Opower(U_4650),hAPP(c_Int_Onumber__class_Onumber__of(U_4650),U_4652)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4651))),hAPP(hAPP(c_COMBS(U_4650,U_4650,U_4650),hAPP(hAPP(c_COMBB(U_4650,tc_fun(U_4650,U_4650),U_4650),c_Groups_Otimes__class_Otimes(U_4650)),hAPP(c_Groups_Otimes__class_Otimes(U_4650),hAPP(c_Int_Onumber__class_Onumber__of(U_4650),U_4652)))),c_COMBI(U_4650)))
| ~ 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_4651)))
| ~ class_Int_Onumber__ring(U_4650) ),
inference(clausify,[status(thm)],[f_1522_2]) ).
cnf(f_1522_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_4650),hAPP(c_Int_Onumber__class_Onumber__of(U_4650),U_4652)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_4651))) = c_Groups_Oone__class_Oone(U_4650)
| 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_4651)))
| ~ class_Int_Onumber__ring(U_4650) ),
inference(clausify,[status(thm)],[f_1522_2]) ).
fof(f_1523_1,plain,
! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2,
inference(fof_nnf,[status(thm)],[fact_code__numeral_Orecs_I1_J]) ).
fof(f_1523_2,plain,
! [U_4655,U_4654,U_4653] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_4653,U_4654,U_4655,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_4654,
inference(variable_rename,[status(thm)],[f_1523_1]) ).
cnf(f_1523_3,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_4653,U_4654,U_4655,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_4654,
inference(clausify,[status(thm)],[f_1523_2]) ).
fof(f_1524_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_1524_2,plain,
! [U_4657,U_4656] :
( ( ( c_Divides_OnegDivAlg(U_4657,U_4656) = hAPP(c_Divides_Oadjust(U_4656),c_Divides_OnegDivAlg(U_4657,hAPP(hAPP(c_Groups_Otimes__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_4656)))
| 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_4657),U_4656))) )
& ( c_Divides_OnegDivAlg(U_4657,U_4656) = 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_4657),U_4656))
| ~ 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_4657),U_4656))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4656)) ),
inference(variable_rename,[status(thm)],[f_1524_1]) ).
cnf(f_1524_3,plain,
( c_Divides_OnegDivAlg(U_4657,U_4656) = 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_4657),U_4656))
| ~ 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_4657),U_4656)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4656)) ),
inference(clausify,[status(thm)],[f_1524_2]) ).
cnf(f_1524_4,plain,
( c_Divides_OnegDivAlg(U_4657,U_4656) = hAPP(c_Divides_Oadjust(U_4656),c_Divides_OnegDivAlg(U_4657,hAPP(hAPP(c_Groups_Otimes__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_4656)))
| 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_4657),U_4656)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4656)) ),
inference(clausify,[status(thm)],[f_1524_2]) ).
fof(f_1525_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_1525_2,plain,
! [U_4659,U_4658] :
( ( ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4659),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4658)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4658)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4659),hAPP(hAPP(c_Groups_Otimes__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_4658))))
| 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_4659)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4658)))) )
& ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4659),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4658)) = 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_4659)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4658)))
| ~ 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_4659)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4658)))) ) )
| ~ 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_4658))) ),
inference(variable_rename,[status(thm)],[f_1525_1]) ).
cnf(f_1525_3,plain,
( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4659),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4658)) = 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_4659)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4658)))
| ~ 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_4659)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4658))))
| ~ 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_4658))) ),
inference(clausify,[status(thm)],[f_1525_2]) ).
cnf(f_1525_4,plain,
( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4659),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4658)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4658)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4659),hAPP(hAPP(c_Groups_Otimes__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_4658))))
| 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_4659)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4658))))
| ~ 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_4658))) ),
inference(clausify,[status(thm)],[f_1525_2]) ).
fof(f_1526_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_1526_2,plain,
! [U_4660] :
( ( ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4660)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4660)),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_4660))))
| 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_4660))) )
& ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4660)) = 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_4660))) ) )
| ~ 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_4660))) ),
inference(variable_rename,[status(thm)],[f_1526_1]) ).
cnf(f_1526_3,plain,
( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4660)) = 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_4660)))
| ~ 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_4660))) ),
inference(clausify,[status(thm)],[f_1526_2]) ).
cnf(f_1526_4,plain,
( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4660)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4660)),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_4660))))
| 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_4660)))
| ~ 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_4660))) ),
inference(clausify,[status(thm)],[f_1526_2]) ).
fof(f_1527_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_1527_2,plain,
! [U_4662,U_4661] :
( ( c_Divides_OposDivAlg(U_4661,U_4662) = hAPP(c_Divides_Oadjust(U_4662),c_Divides_OposDivAlg(U_4661,hAPP(hAPP(c_Groups_Otimes__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_4662)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4662),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4661),U_4662)) )
& ( c_Divides_OposDivAlg(U_4661,U_4662) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4661)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4662),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4661),U_4662)) ) ) ),
inference(variable_rename,[status(thm)],[f_1527_1]) ).
fof(f_1527_3,plain,
( ! [U_4666,U_4664] :
( c_Divides_OposDivAlg(U_4664,U_4666) = hAPP(c_Divides_Oadjust(U_4666),c_Divides_OposDivAlg(U_4664,hAPP(hAPP(c_Groups_Otimes__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_4666)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4666),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4664),U_4666)) )
& ! [U_4665,U_4663] :
( c_Divides_OposDivAlg(U_4663,U_4665) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4663)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4665),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4663),U_4665)) ) ) ),
inference(miniscope,[status(thm)],[f_1527_2]) ).
cnf(f_1527_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4663),U_4665))
| c_Divides_OposDivAlg(U_4663,U_4665) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4663) ),
inference(clausify,[status(thm)],[f_1527_3]) ).
cnf(f_1527_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4665),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OposDivAlg(U_4663,U_4665) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4663) ),
inference(clausify,[status(thm)],[f_1527_3]) ).
cnf(f_1527_6,plain,
( c_Divides_OposDivAlg(U_4664,U_4666) = hAPP(c_Divides_Oadjust(U_4666),c_Divides_OposDivAlg(U_4664,hAPP(hAPP(c_Groups_Otimes__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_4666)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4666),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4664),U_4666)) ),
inference(clausify,[status(thm)],[f_1527_3]) ).
fof(f_1528_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_1528_2,plain,
! [U_4667] : c_Divides_Oadjust(U_4667) = 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_4667))))),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_4667))))),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_1528_1]) ).
cnf(f_1528_3,plain,
c_Divides_Oadjust(U_4667) = 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_4667))))),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_4667))))),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_1528_2]) ).
fof(f_1529_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_1529_2,plain,
! [U_4669,U_4668] :
( ( ( c_Divides_OposDivAlg(U_4669,U_4668) = hAPP(c_Divides_Oadjust(U_4668),c_Divides_OposDivAlg(U_4669,hAPP(hAPP(c_Groups_Otimes__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_4668)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4669),U_4668)) )
& ( c_Divides_OposDivAlg(U_4669,U_4668) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4669)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4669),U_4668)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4668)) ),
inference(variable_rename,[status(thm)],[f_1529_1]) ).
cnf(f_1529_3,plain,
( c_Divides_OposDivAlg(U_4669,U_4668) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4669)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4669),U_4668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4668)) ),
inference(clausify,[status(thm)],[f_1529_2]) ).
cnf(f_1529_4,plain,
( c_Divides_OposDivAlg(U_4669,U_4668) = hAPP(c_Divides_Oadjust(U_4668),c_Divides_OposDivAlg(U_4669,hAPP(hAPP(c_Groups_Otimes__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_4668)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4669),U_4668))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4668)) ),
inference(clausify,[status(thm)],[f_1529_2]) ).
fof(f_1530_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_1530_2,plain,
! [U_4671,U_4670] :
( ( ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4671),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4670)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4670)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4671),hAPP(hAPP(c_Groups_Otimes__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_4670))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4671)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4670))) )
& ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4671),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4670)) = 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_4671))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4671)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4670))) ) )
| ~ 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_4670))) ),
inference(variable_rename,[status(thm)],[f_1530_1]) ).
cnf(f_1530_3,plain,
( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4671),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4670)) = 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_4671))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4671)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4670)))
| ~ 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_4670))) ),
inference(clausify,[status(thm)],[f_1530_2]) ).
cnf(f_1530_4,plain,
( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4671),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4670)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4670)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4671),hAPP(hAPP(c_Groups_Otimes__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_4670))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4671)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4670)))
| ~ 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_4670))) ),
inference(clausify,[status(thm)],[f_1530_2]) ).
fof(f_1531_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_1531_2,plain,
! [U_4673,U_4672] :
( ( ( c_Divides_OnegDivAlg(U_4672,U_4673) = hAPP(c_Divides_Oadjust(U_4673),c_Divides_OnegDivAlg(U_4672,hAPP(hAPP(c_Groups_Otimes__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_4673)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4673),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_4672),U_4673))) )
& ( c_Divides_OnegDivAlg(U_4672,U_4673) = 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_4672),U_4673))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4673),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_4672),U_4673))) ) ) )
| ~ 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_4672),U_4673))) ),
inference(variable_rename,[status(thm)],[f_1531_1]) ).
cnf(f_1531_3,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_4672),U_4673)))
| c_Divides_OnegDivAlg(U_4672,U_4673) = 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_4672),U_4673))
| ~ 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_4672),U_4673))) ),
inference(clausify,[status(thm)],[f_1531_2]) ).
cnf(f_1531_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4673),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OnegDivAlg(U_4672,U_4673) = 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_4672),U_4673))
| ~ 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_4672),U_4673))) ),
inference(clausify,[status(thm)],[f_1531_2]) ).
cnf(f_1531_5,plain,
( c_Divides_OnegDivAlg(U_4672,U_4673) = hAPP(c_Divides_Oadjust(U_4673),c_Divides_OnegDivAlg(U_4672,hAPP(hAPP(c_Groups_Otimes__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_4673)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4673),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_4672),U_4673)))
| ~ 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_4672),U_4673))) ),
inference(clausify,[status(thm)],[f_1531_2]) ).
fof(f_1532_1,plain,
! [V_a_2,V_r_2,T_b] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
| ? [B_x] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x))
& hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x))
| ~ hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_accp_Osimps]) ).
fof(f_1532_2,plain,
! [U_4678,U_4677,U_4676] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_4676,U_4677),U_4678))
| ? [U_4675] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_4676,U_4677),U_4675))
& hBOOL(hAPP(hAPP(U_4677,U_4675),U_4678)) ) )
& ( ! [U_4674] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_4676,U_4677),U_4674))
| ~ hBOOL(hAPP(hAPP(U_4677,U_4674),U_4678)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_4676,U_4677),U_4678)) ) ),
inference(variable_rename,[status(thm)],[f_1532_1]) ).
fof(f_1532_3,plain,
( ! [U_4684,U_4682,U_4680] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_4680,U_4682),U_4684))
| ? [U_4675] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_4680,U_4682),U_4675))
& hBOOL(hAPP(hAPP(U_4682,U_4675),U_4684)) ) )
& ! [U_4683,U_4681,U_4679] :
( ! [U_4674] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_4679,U_4681),U_4674))
| ~ hBOOL(hAPP(hAPP(U_4681,U_4674),U_4683)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_4679,U_4681),U_4683)) ) ),
inference(miniscope,[status(thm)],[f_1532_2]) ).
fof(f_1532_4,plain,
( ! [U_4684,U_4682,U_4680] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_4680,U_4682),U_4684))
| ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_4680,U_4682),sK67(U_4684,U_4682,U_4680)))
& hBOOL(hAPP(hAPP(U_4682,sK67(U_4684,U_4682,U_4680)),U_4684)) ) )
& ! [U_4683,U_4681,U_4679] :
( ! [U_4674] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_4679,U_4681),U_4674))
| ~ hBOOL(hAPP(hAPP(U_4681,U_4674),U_4683)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_4679,U_4681),U_4683)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_4675,sK67(U_4684,U_4682,U_4680))],[f_1532_3]) ).
cnf(f_1532_5,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_4679,U_4681),U_4674))
| ~ hBOOL(hAPP(hAPP(U_4681,U_4674),U_4683))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_4679,U_4681),U_4683)) ),
inference(clausify,[status(thm)],[f_1532_4]) ).
cnf(f_1532_6,plain,
( hBOOL(hAPP(hAPP(U_4682,sK67(U_4684,U_4682,U_4680)),U_4684))
| hBOOL(hAPP(c_Wellfounded_Oaccp(U_4680,U_4682),U_4684)) ),
inference(clausify,[status(thm)],[f_1532_4]) ).
cnf(f_1532_7,plain,
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_4680,U_4682),sK67(U_4684,U_4682,U_4680)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(U_4680,U_4682),U_4684)) ),
inference(clausify,[status(thm)],[f_1532_4]) ).
fof(f_1533_1,plain,
! [V_a_2,V_r_2,T_b] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
| ? [B_x] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x))
& hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x))
| ~ hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_accp_Oequations]) ).
fof(f_1533_2,plain,
! [U_4689,U_4688,U_4687] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_4687,U_4688),U_4689))
| ? [U_4686] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_4687,U_4688),U_4686))
& hBOOL(hAPP(hAPP(U_4688,U_4686),U_4689)) ) )
& ( ! [U_4685] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_4687,U_4688),U_4685))
| ~ hBOOL(hAPP(hAPP(U_4688,U_4685),U_4689)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_4687,U_4688),U_4689)) ) ),
inference(variable_rename,[status(thm)],[f_1533_1]) ).
fof(f_1533_3,plain,
( ! [U_4695,U_4693,U_4691] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_4691,U_4693),U_4695))
| ? [U_4686] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_4691,U_4693),U_4686))
& hBOOL(hAPP(hAPP(U_4693,U_4686),U_4695)) ) )
& ! [U_4694,U_4692,U_4690] :
( ! [U_4685] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_4690,U_4692),U_4685))
| ~ hBOOL(hAPP(hAPP(U_4692,U_4685),U_4694)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_4690,U_4692),U_4694)) ) ),
inference(miniscope,[status(thm)],[f_1533_2]) ).
fof(f_1533_4,plain,
( ! [U_4695,U_4693,U_4691] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_4691,U_4693),U_4695))
| ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_4691,U_4693),sK68(U_4695,U_4693,U_4691)))
& hBOOL(hAPP(hAPP(U_4693,sK68(U_4695,U_4693,U_4691)),U_4695)) ) )
& ! [U_4694,U_4692,U_4690] :
( ! [U_4685] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_4690,U_4692),U_4685))
| ~ hBOOL(hAPP(hAPP(U_4692,U_4685),U_4694)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_4690,U_4692),U_4694)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_4686,sK68(U_4695,U_4693,U_4691))],[f_1533_3]) ).
cnf(f_1533_5,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_4690,U_4692),U_4685))
| ~ hBOOL(hAPP(hAPP(U_4692,U_4685),U_4694))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_4690,U_4692),U_4694)) ),
inference(clausify,[status(thm)],[f_1533_4]) ).
cnf(f_1533_6,plain,
( hBOOL(hAPP(hAPP(U_4693,sK68(U_4695,U_4693,U_4691)),U_4695))
| hBOOL(hAPP(c_Wellfounded_Oaccp(U_4691,U_4693),U_4695)) ),
inference(clausify,[status(thm)],[f_1533_4]) ).
cnf(f_1533_7,plain,
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_4691,U_4693),sK68(U_4695,U_4693,U_4691)))
| hBOOL(hAPP(c_Wellfounded_Oaccp(U_4691,U_4693),U_4695)) ),
inference(clausify,[status(thm)],[f_1533_4]) ).
fof(f_1534_1,plain,
! [V_a_2,V_b_2,V_r_2,T_b] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_accp__downward]) ).
fof(f_1534_2,plain,
! [U_4699,U_4698,U_4697,U_4696] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_4696,U_4697),U_4699))
| ~ hBOOL(hAPP(hAPP(U_4697,U_4699),U_4698))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_4696,U_4697),U_4698)) ),
inference(variable_rename,[status(thm)],[f_1534_1]) ).
cnf(f_1534_3,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_4696,U_4697),U_4699))
| ~ hBOOL(hAPP(hAPP(U_4697,U_4699),U_4698))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_4696,U_4697),U_4698)) ),
inference(clausify,[status(thm)],[f_1534_2]) ).
fof(f_1535_1,plain,
! [V_R2_2,V_R1_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_b,V_R2_2)),c_Wellfounded_Oaccp(T_b,V_R1_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_R1_2),V_R2_2)) ),
inference(fof_nnf,[status(thm)],[fact_accp__subset]) ).
fof(f_1535_2,plain,
! [U_4702,U_4701,U_4700] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4700,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_4700,U_4702)),c_Wellfounded_Oaccp(U_4700,U_4701)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4700,tc_fun(U_4700,tc_HOL_Obool))),U_4701),U_4702)) ),
inference(variable_rename,[status(thm)],[f_1535_1]) ).
cnf(f_1535_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4700,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_4700,U_4702)),c_Wellfounded_Oaccp(U_4700,U_4701)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4700,tc_fun(U_4700,tc_HOL_Obool))),U_4701),U_4702)) ),
inference(clausify,[status(thm)],[f_1535_2]) ).
fof(f_1536_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_1536_2,plain,
! [U_4703] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_4703) = 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_1536_1]) ).
cnf(f_1536_3,plain,
c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_4703) = 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_1536_2]) ).
fof(f_1537_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_1537_2,plain,
! [U_4705,U_4704] :
( c_Divides_OposDivAlg(U_4704,U_4705) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4704),U_4705)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4704,U_4705))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4705))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4704)) ),
inference(variable_rename,[status(thm)],[f_1537_1]) ).
cnf(f_1537_3,plain,
( c_Divides_OposDivAlg(U_4704,U_4705) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4704),U_4705)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4704,U_4705))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4705))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4704)) ),
inference(clausify,[status(thm)],[f_1537_2]) ).
fof(f_1538_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_1538_2,plain,
! [U_4707,U_4706] :
( ( ( c_Divides_OposDivAlg(U_4706,U_4707) = hAPP(c_Divides_Oadjust(U_4707),c_Divides_OposDivAlg(U_4706,hAPP(hAPP(c_Groups_Otimes__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_4707)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4707),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4706),U_4707)) )
& ( c_Divides_OposDivAlg(U_4706,U_4707) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4706)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4707),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4706),U_4707)) ) ) )
| ~ 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_4706),U_4707))) ),
inference(variable_rename,[status(thm)],[f_1538_1]) ).
cnf(f_1538_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4706),U_4707))
| c_Divides_OposDivAlg(U_4706,U_4707) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4706)
| ~ 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_4706),U_4707))) ),
inference(clausify,[status(thm)],[f_1538_2]) ).
cnf(f_1538_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4707),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Divides_OposDivAlg(U_4706,U_4707) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4706)
| ~ 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_4706),U_4707))) ),
inference(clausify,[status(thm)],[f_1538_2]) ).
cnf(f_1538_5,plain,
( c_Divides_OposDivAlg(U_4706,U_4707) = hAPP(c_Divides_Oadjust(U_4707),c_Divides_OposDivAlg(U_4706,hAPP(hAPP(c_Groups_Otimes__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_4707)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4707),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4706),U_4707))
| ~ 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_4706),U_4707))) ),
inference(clausify,[status(thm)],[f_1538_2]) ).
fof(f_1539_1,plain,
! [V_k_2,T_b] :
( ( ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),T_b),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),tc_Int_Oint),c_COMBB(tc_fun(T_b,T_b),T_b,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,T_b),T_b),tc_Int_Oint),c_HOL_OLet(T_b,T_b)),c_Int_Oring__1__class_Oof__int(T_b)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,T_b)),tc_Int_Oint),c_COMBS(T_b,T_b,T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),tc_Int_Oint),c_COMBB(T_b,tc_fun(T_b,T_b),T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Oplus__class_Oplus(T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b)))),c_Groups_Oone__class_Oone(T_b))))),c_Divides_Odivmod__int(V_k_2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__num]) ).
fof(f_1539_2,plain,
! [U_4709,U_4708] :
( ( ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_4708),U_4709) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_4708),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_4708,U_4708)),tc_fun(tc_Int_Oint,U_4708)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_4708,U_4708),U_4708),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_4708,U_4708)),tc_fun(tc_Int_Oint,U_4708)),tc_Int_Oint),c_COMBB(tc_fun(U_4708,U_4708),U_4708,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_4708,tc_fun(tc_fun(U_4708,U_4708),U_4708),tc_Int_Oint),c_HOL_OLet(U_4708,U_4708)),c_Int_Oring__1__class_Oof__int(U_4708)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_4708,U_4708),tc_fun(U_4708,U_4708)),hAPP(hAPP(c_COMBB(tc_fun(U_4708,tc_fun(U_4708,U_4708)),tc_fun(tc_fun(U_4708,U_4708),tc_fun(U_4708,U_4708)),tc_Int_Oint),c_COMBS(U_4708,U_4708,U_4708)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_4708,U_4708),tc_fun(U_4708,tc_fun(U_4708,U_4708))),hAPP(hAPP(c_COMBB(tc_fun(U_4708,tc_fun(U_4708,U_4708)),tc_fun(tc_fun(U_4708,U_4708),tc_fun(U_4708,tc_fun(U_4708,U_4708))),tc_Int_Oint),c_COMBB(U_4708,tc_fun(U_4708,U_4708),U_4708)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4708,tc_fun(U_4708,U_4708)),tc_Int_Oint),c_If(U_4708)),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_4708,U_4708,U_4708),c_Groups_Oplus__class_Oplus(U_4708)),c_COMBI(U_4708))))),hAPP(hAPP(c_COMBC(U_4708,U_4708,U_4708),hAPP(hAPP(c_COMBB(U_4708,tc_fun(U_4708,U_4708),U_4708),c_Groups_Oplus__class_Oplus(U_4708)),hAPP(hAPP(c_COMBS(U_4708,U_4708,U_4708),c_Groups_Oplus__class_Oplus(U_4708)),c_COMBI(U_4708)))),c_Groups_Oone__class_Oone(U_4708))))),c_Divides_Odivmod__int(U_4709,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_4709),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hAPP(c_Int_Oring__1__class_Oof__int(U_4708),U_4709) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4708),hAPP(c_Int_Oring__1__class_Oof__int(U_4708),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4709)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4709),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| U_4709 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( hAPP(c_Int_Oring__1__class_Oof__int(U_4708),U_4709) = c_Groups_Ozero__class_Ozero(U_4708)
| U_4709 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| ~ class_Rings_Oring__1(U_4708) ),
inference(variable_rename,[status(thm)],[f_1539_1]) ).
cnf(f_1539_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_4708),U_4709) = c_Groups_Ozero__class_Ozero(U_4708)
| U_4709 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Rings_Oring__1(U_4708) ),
inference(clausify,[status(thm)],[f_1539_2]) ).
cnf(f_1539_4,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_4708),U_4709) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4708),hAPP(c_Int_Oring__1__class_Oof__int(U_4708),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4709)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4709),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_4709 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Rings_Oring__1(U_4708) ),
inference(clausify,[status(thm)],[f_1539_2]) ).
cnf(f_1539_5,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_4708),U_4709) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_4708),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_4708,U_4708)),tc_fun(tc_Int_Oint,U_4708)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_4708,U_4708),U_4708),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_4708,U_4708)),tc_fun(tc_Int_Oint,U_4708)),tc_Int_Oint),c_COMBB(tc_fun(U_4708,U_4708),U_4708,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_4708,tc_fun(tc_fun(U_4708,U_4708),U_4708),tc_Int_Oint),c_HOL_OLet(U_4708,U_4708)),c_Int_Oring__1__class_Oof__int(U_4708)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_4708,U_4708),tc_fun(U_4708,U_4708)),hAPP(hAPP(c_COMBB(tc_fun(U_4708,tc_fun(U_4708,U_4708)),tc_fun(tc_fun(U_4708,U_4708),tc_fun(U_4708,U_4708)),tc_Int_Oint),c_COMBS(U_4708,U_4708,U_4708)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_4708,U_4708),tc_fun(U_4708,tc_fun(U_4708,U_4708))),hAPP(hAPP(c_COMBB(tc_fun(U_4708,tc_fun(U_4708,U_4708)),tc_fun(tc_fun(U_4708,U_4708),tc_fun(U_4708,tc_fun(U_4708,U_4708))),tc_Int_Oint),c_COMBB(U_4708,tc_fun(U_4708,U_4708),U_4708)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_4708,tc_fun(U_4708,U_4708)),tc_Int_Oint),c_If(U_4708)),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_4708,U_4708,U_4708),c_Groups_Oplus__class_Oplus(U_4708)),c_COMBI(U_4708))))),hAPP(hAPP(c_COMBC(U_4708,U_4708,U_4708),hAPP(hAPP(c_COMBB(U_4708,tc_fun(U_4708,U_4708),U_4708),c_Groups_Oplus__class_Oplus(U_4708)),hAPP(hAPP(c_COMBS(U_4708,U_4708,U_4708),c_Groups_Oplus__class_Oplus(U_4708)),c_COMBI(U_4708)))),c_Groups_Oone__class_Oone(U_4708))))),c_Divides_Odivmod__int(U_4709,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_4709),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| U_4709 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ class_Rings_Oring__1(U_4708) ),
inference(clausify,[status(thm)],[f_1539_2]) ).
fof(f_1540_1,plain,
! [V_P_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
| ? [B_a,B_b] :
( ~ hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
& ( hBOOL(hAPP(hAPP(V_P_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_1540_2,plain,
! [U_4714,U_4713,U_4712] :
( hBOOL(hAPP(hAPP(U_4714,U_4712),U_4713))
| ? [U_4711,U_4710] :
( ~ hBOOL(hAPP(hAPP(U_4714,U_4711),U_4710))
& ( hBOOL(hAPP(hAPP(U_4714,U_4711),hAPP(hAPP(c_Groups_Otimes__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_4710)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4710),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_4711),U_4710))) )
& 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_4711),U_4710))) )
| ~ 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_4712),U_4713))) ),
inference(variable_rename,[status(thm)],[f_1540_1]) ).
fof(f_1540_3,plain,
! [U_4714,U_4713,U_4712] :
( hBOOL(hAPP(hAPP(U_4714,U_4712),U_4713))
| ? [U_4710] :
( ~ hBOOL(hAPP(hAPP(U_4714,sK69(U_4714,U_4713,U_4712)),U_4710))
& ( hBOOL(hAPP(hAPP(U_4714,sK69(U_4714,U_4713,U_4712)),hAPP(hAPP(c_Groups_Otimes__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_4710)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4710),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),sK69(U_4714,U_4713,U_4712)),U_4710))) )
& 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),sK69(U_4714,U_4713,U_4712)),U_4710))) )
| ~ 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_4712),U_4713))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_4711,sK69(U_4714,U_4713,U_4712))],[f_1540_2]) ).
fof(f_1540_4,plain,
! [U_4714,U_4713,U_4712] :
( hBOOL(hAPP(hAPP(U_4714,U_4712),U_4713))
| ( ~ hBOOL(hAPP(hAPP(U_4714,sK69(U_4714,U_4713,U_4712)),sK70(U_4714,U_4713,U_4712)))
& ( hBOOL(hAPP(hAPP(U_4714,sK69(U_4714,U_4713,U_4712)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK70(U_4714,U_4713,U_4712))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK70(U_4714,U_4713,U_4712)),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),sK69(U_4714,U_4713,U_4712)),sK70(U_4714,U_4713,U_4712)))) )
& 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),sK69(U_4714,U_4713,U_4712)),sK70(U_4714,U_4713,U_4712)))) )
| ~ 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_4712),U_4713))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_4710,sK70(U_4714,U_4713,U_4712))],[f_1540_3]) ).
cnf(f_1540_5,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),sK69(U_4714,U_4713,U_4712)),sK70(U_4714,U_4713,U_4712))))
| hBOOL(hAPP(hAPP(U_4714,U_4712),U_4713))
| ~ 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_4712),U_4713))) ),
inference(clausify,[status(thm)],[f_1540_4]) ).
cnf(f_1540_6,plain,
( hBOOL(hAPP(hAPP(U_4714,sK69(U_4714,U_4713,U_4712)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK70(U_4714,U_4713,U_4712))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK70(U_4714,U_4713,U_4712)),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),sK69(U_4714,U_4713,U_4712)),sK70(U_4714,U_4713,U_4712))))
| hBOOL(hAPP(hAPP(U_4714,U_4712),U_4713))
| ~ 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_4712),U_4713))) ),
inference(clausify,[status(thm)],[f_1540_4]) ).
cnf(f_1540_7,plain,
( ~ hBOOL(hAPP(hAPP(U_4714,sK69(U_4714,U_4713,U_4712)),sK70(U_4714,U_4713,U_4712)))
| hBOOL(hAPP(hAPP(U_4714,U_4712),U_4713))
| ~ 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_4712),U_4713))) ),
inference(clausify,[status(thm)],[f_1540_4]) ).
fof(f_1541_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_1541_2,plain,
! [U_4716,U_4715] :
( ( c_Divides_Opdivmod(U_4716,U_4715) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4716),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4715))
| U_4715 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Opdivmod(U_4716,U_4715) = 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_4716))
| U_4715 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_1541_1]) ).
fof(f_1541_3,plain,
( ! [U_4720,U_4718] :
( c_Divides_Opdivmod(U_4720,U_4718) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4720),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4718))
| U_4718 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_4719,U_4717] :
( c_Divides_Opdivmod(U_4719,U_4717) = 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_4719))
| U_4717 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_1541_2]) ).
cnf(f_1541_4,plain,
( c_Divides_Opdivmod(U_4719,U_4717) = 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_4719))
| U_4717 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1541_3]) ).
cnf(f_1541_5,plain,
( c_Divides_Opdivmod(U_4720,U_4718) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4720),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4718))
| U_4718 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1541_3]) ).
fof(f_1542_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_1542_2,plain,
! [U_4722,U_4721] : c_Divides_Opdivmod(U_4721,U_4722) = 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_4721)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4722))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4721),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4722))),
inference(variable_rename,[status(thm)],[f_1542_1]) ).
cnf(f_1542_3,plain,
c_Divides_Opdivmod(U_4721,U_4722) = 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_4721)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4722))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4721),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4722))),
inference(clausify,[status(thm)],[f_1542_2]) ).
fof(f_1543_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_1543_2,plain,
! [U_4727,U_4726,U_4725,U_4724,U_4723] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4723,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4724),U_4727)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4725),U_4727)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4724),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4725,U_4727))),U_4726))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4727))
| U_4724 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4723,U_4724),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4725),U_4726))) ),
inference(variable_rename,[status(thm)],[f_1543_1]) ).
cnf(f_1543_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4723,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4724),U_4727)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4725),U_4727)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4724),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4725,U_4727))),U_4726))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4727))
| U_4724 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4723,U_4724),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4725),U_4726))) ),
inference(clausify,[status(thm)],[f_1543_2]) ).
fof(f_1544_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_1544_2,plain,
! [U_4729,U_4728] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4729,U_4728),c_Divides_Odivmod__int(U_4729,U_4728)))
| U_4728 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1544_1]) ).
cnf(f_1544_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4729,U_4728),c_Divides_Odivmod__int(U_4729,U_4728)))
| U_4728 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1544_2]) ).
fof(f_1545_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_1545_2,plain,
! [U_4731,U_4730] : c_Divides_Odivmod__int__rel(U_4730,U_4731) = 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_4730))),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_4731)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4731))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4731))))),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_4731)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4731))),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_1545_1]) ).
cnf(f_1545_3,plain,
c_Divides_Odivmod__int__rel(U_4730,U_4731) = 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_4730))),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_4731)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4731))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4731))))),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_4731)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_4731))),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_1545_2]) ).
fof(f_1546_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_1546_2,plain,
! [U_4737,U_4736,U_4735,U_4734,U_4733,U_4732] :
( U_4735 = U_4737
| U_4733 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4732,U_4733),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4736),U_4737)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4732,U_4733),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4734),U_4735))) ),
inference(variable_rename,[status(thm)],[f_1546_1]) ).
cnf(f_1546_3,plain,
( U_4735 = U_4737
| U_4733 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4732,U_4733),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4736),U_4737)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4732,U_4733),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4734),U_4735))) ),
inference(clausify,[status(thm)],[f_1546_2]) ).
fof(f_1547_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_1547_2,plain,
! [U_4743,U_4742,U_4741,U_4740,U_4739,U_4738] :
( U_4740 = U_4742
| U_4739 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4738,U_4739),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4742),U_4743)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4738,U_4739),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4740),U_4741))) ),
inference(variable_rename,[status(thm)],[f_1547_1]) ).
cnf(f_1547_3,plain,
( U_4740 = U_4742
| U_4739 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4738,U_4739),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4742),U_4743)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4738,U_4739),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4740),U_4741))) ),
inference(clausify,[status(thm)],[f_1547_2]) ).
fof(f_1548_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_1548_2,plain,
! [U_4746,U_4745,U_4744] :
( U_4746 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_4744 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4744,U_4744),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4745),U_4746))) ),
inference(variable_rename,[status(thm)],[f_1548_1]) ).
cnf(f_1548_3,plain,
( U_4746 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_4744 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4744,U_4744),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4745),U_4746))) ),
inference(clausify,[status(thm)],[f_1548_2]) ).
fof(f_1549_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_1549_2,plain,
! [U_4747] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_4747),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_4747 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1549_1]) ).
cnf(f_1549_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_4747),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_4747 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1549_2]) ).
fof(f_1550_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_1550_2,plain,
! [U_4750,U_4749,U_4748] :
( U_4749 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_4748 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4748,U_4748),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4749),U_4750))) ),
inference(variable_rename,[status(thm)],[f_1550_1]) ).
cnf(f_1550_3,plain,
( U_4749 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_4748 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4748,U_4748),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4749),U_4750))) ),
inference(clausify,[status(thm)],[f_1550_2]) ).
fof(f_1551_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_1551_2,plain,
! [U_4754,U_4753,U_4752,U_4751] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4751,U_4752) = U_4754
| U_4752 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4751,U_4752),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4753),U_4754))) ),
inference(variable_rename,[status(thm)],[f_1551_1]) ).
cnf(f_1551_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4751,U_4752) = U_4754
| U_4752 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4751,U_4752),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4753),U_4754))) ),
inference(clausify,[status(thm)],[f_1551_2]) ).
fof(f_1552_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_1552_2,plain,
! [U_4758,U_4757,U_4756,U_4755] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4755),U_4756) = U_4757
| U_4756 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4755,U_4756),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4757),U_4758))) ),
inference(variable_rename,[status(thm)],[f_1552_1]) ).
cnf(f_1552_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4755),U_4756) = U_4757
| U_4756 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4755,U_4756),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4757),U_4758))) ),
inference(clausify,[status(thm)],[f_1552_2]) ).
fof(f_1553_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_1553_2,plain,
! [U_4760,U_4759] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4759,U_4760),c_Divides_OnegDivAlg(U_4759,U_4760)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4759),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1553_1]) ).
cnf(f_1553_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4759,U_4760),c_Divides_OnegDivAlg(U_4759,U_4760)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4760))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4759),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1553_2]) ).
fof(f_1554_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_1554_2,plain,
! [U_4762,U_4761] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4762,U_4761),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4762),U_4761)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4762,U_4761))))
| U_4761 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1554_1]) ).
cnf(f_1554_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4762,U_4761),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4762),U_4761)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4762,U_4761))))
| U_4761 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1554_2]) ).
fof(f_1555_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_1555_2,plain,
! [U_4764,U_4763] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4763,U_4764),c_Divides_OposDivAlg(U_4763,U_4764)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4764))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4763)) ),
inference(variable_rename,[status(thm)],[f_1555_1]) ).
cnf(f_1555_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4763,U_4764),c_Divides_OposDivAlg(U_4763,U_4764)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4764))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4763)) ),
inference(clausify,[status(thm)],[f_1555_2]) ).
fof(f_1556_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_1556_2,plain,
! [U_4766,U_4765] : c_Divides_Odivmod__int(U_4765,U_4766) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4765),U_4766)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4765,U_4766)),
inference(variable_rename,[status(thm)],[f_1556_1]) ).
cnf(f_1556_3,plain,
c_Divides_Odivmod__int(U_4765,U_4766) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4765),U_4766)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4765,U_4766)),
inference(clausify,[status(thm)],[f_1556_2]) ).
fof(f_1557_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_1557_2,plain,
! [U_4773,U_4772,U_4771,U_4770,U_4769,U_4768,U_4767] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4767),U_4771),U_4768),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_4769),U_4772)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4770),U_4773)),U_4768))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4770),U_4773),U_4768))))
| U_4768 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4771,U_4768),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4772),U_4773)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4767,U_4768),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4769),U_4770))) ),
inference(variable_rename,[status(thm)],[f_1557_1]) ).
cnf(f_1557_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4767),U_4771),U_4768),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_4769),U_4772)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4770),U_4773)),U_4768))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4770),U_4773),U_4768))))
| U_4768 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4771,U_4768),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4772),U_4773)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4767,U_4768),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4769),U_4770))) ),
inference(clausify,[status(thm)],[f_1557_2]) ).
fof(f_1558_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_1558_2,plain,
! [U_4777,U_4776,U_4775,U_4774] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4774),U_4775),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_4777),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4776)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4776)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_4777),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_4775),U_4777)))))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4774,U_4775),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4776),U_4777))) ),
inference(variable_rename,[status(thm)],[f_1558_1]) ).
cnf(f_1558_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4774),U_4775),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_4777),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4776)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4776)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_4777),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_4775),U_4777)))))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4774,U_4775),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4776),U_4777))) ),
inference(clausify,[status(thm)],[f_1558_2]) ).
fof(f_1559_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_1559_2,plain,
! [U_4781,U_4780,U_4779,U_4778] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4778,U_4779),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4780),U_4781)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4781),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4779),U_4781)) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4779)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4781),U_4779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4781)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4779)) )
| U_4778 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4779),U_4780)),U_4781) ),
inference(variable_rename,[status(thm)],[f_1559_1]) ).
cnf(f_1559_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4779))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4779))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4778,U_4779),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4780),U_4781)))
| U_4778 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4779),U_4780)),U_4781) ),
inference(clausify,[status(thm)],[f_1559_2]) ).
cnf(f_1559_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4781),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4779),U_4781))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4779))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4778,U_4779),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4780),U_4781)))
| U_4778 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4779),U_4780)),U_4781) ),
inference(clausify,[status(thm)],[f_1559_2]) ).
cnf(f_1559_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4781),U_4779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4781))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4778,U_4779),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4780),U_4781)))
| U_4778 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4779),U_4780)),U_4781) ),
inference(clausify,[status(thm)],[f_1559_2]) ).
cnf(f_1559_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4781),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4779),U_4781))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4781),U_4779))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4781))
| hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4778,U_4779),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4780),U_4781)))
| U_4778 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4779),U_4780)),U_4781) ),
inference(clausify,[status(thm)],[f_1559_2]) ).
fof(f_1560_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_1560_2,plain,
! [U_4786,U_4785,U_4784,U_4783,U_4782] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4786),U_4782),U_4783),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_4786),U_4784)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4786),U_4785)),U_4783))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4786),U_4785),U_4783))))
| U_4783 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4782,U_4783),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4784),U_4785))) ),
inference(variable_rename,[status(thm)],[f_1560_1]) ).
cnf(f_1560_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4786),U_4782),U_4783),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_4786),U_4784)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4786),U_4785)),U_4783))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4786),U_4785),U_4783))))
| U_4783 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4782,U_4783),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4784),U_4785))) ),
inference(clausify,[status(thm)],[f_1560_2]) ).
fof(f_1561_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_1561_2,plain,
! [U_4788,U_4787] :
( ( ( ( c_Divides_Odivmod__int(U_4787,U_4788) = 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_4788))),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_4788)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4787))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4788),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4787),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_4787,U_4788)),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_4788))))),c_Divides_Opdivmod(U_4787,U_4788))))
| U_4788 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_4787,U_4788) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4787)
| U_4788 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_4787 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_4787,U_4788) = 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_4787 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_1561_1]) ).
fof(f_1561_3,plain,
( ! [U_4792,U_4790] :
( ( ( c_Divides_Odivmod__int(U_4790,U_4792) = 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_4792))),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_4792)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4790))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4792),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4790),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_4790,U_4792)),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_4792))))),c_Divides_Opdivmod(U_4790,U_4792))))
| U_4792 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_4790,U_4792) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4790)
| U_4792 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_4790 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_4791,U_4789] :
( c_Divides_Odivmod__int(U_4789,U_4791) = 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_4789 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_1561_2]) ).
cnf(f_1561_4,plain,
( c_Divides_Odivmod__int(U_4789,U_4791) = 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_4789 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1561_3]) ).
cnf(f_1561_5,plain,
( c_Divides_Odivmod__int(U_4790,U_4792) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4790)
| U_4792 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_4790 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1561_3]) ).
cnf(f_1561_6,plain,
( c_Divides_Odivmod__int(U_4790,U_4792) = 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_4792))),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_4792)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4790))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4792),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4790),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_4790,U_4792)),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_4792))))),c_Divides_Opdivmod(U_4790,U_4792))))
| U_4792 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_4790 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1561_3]) ).
fof(f_1562_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_1562_2,plain,
! [U_4794,U_4793] :
( ( ( ( c_Divides_Odivmod__int(U_4793,U_4794) = 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_4794))),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_4793)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_4794))),c_Divides_Opdivmod(U_4793,U_4794)),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_4794))))),c_Divides_Opdivmod(U_4793,U_4794))))
| U_4794 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_4793,U_4794) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4793)
| U_4794 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_4793 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_4793,U_4794) = 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_4793 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_1562_1]) ).
fof(f_1562_3,plain,
( ! [U_4798,U_4796] :
( ( ( c_Divides_Odivmod__int(U_4796,U_4798) = 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_4798))),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_4796)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_4798))),c_Divides_Opdivmod(U_4796,U_4798)),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_4798))))),c_Divides_Opdivmod(U_4796,U_4798))))
| U_4798 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_4796,U_4798) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4796)
| U_4798 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
| U_4796 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_4797,U_4795] :
( c_Divides_Odivmod__int(U_4795,U_4797) = 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_4795 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_1562_2]) ).
cnf(f_1562_4,plain,
( c_Divides_Odivmod__int(U_4795,U_4797) = 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_4795 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1562_3]) ).
cnf(f_1562_5,plain,
( c_Divides_Odivmod__int(U_4796,U_4798) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4796)
| U_4798 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_4796 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1562_3]) ).
cnf(f_1562_6,plain,
( c_Divides_Odivmod__int(U_4796,U_4798) = 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_4798))),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_4796)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_4798))),c_Divides_Opdivmod(U_4796,U_4798)),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_4798))))),c_Divides_Opdivmod(U_4796,U_4798))))
| U_4798 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_4796 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1562_3]) ).
fof(f_1563_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_1563_2,plain,
! [U_4800,U_4799] :
( ( ( ( c_Divides_Odivmod__int(U_4799,U_4800) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4799),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4800)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4800)) )
& ( c_Divides_Odivmod__int(U_4799,U_4800) = c_Divides_OnegDivAlg(U_4799,U_4800)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4800)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4799)) )
& ( ( ( ( ( c_Divides_Odivmod__int(U_4799,U_4800) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4799),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4800)))
| U_4799 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_4799,U_4800) = 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_4799 != 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_4800)) )
& ( c_Divides_Odivmod__int(U_4799,U_4800) = c_Divides_OposDivAlg(U_4799,U_4800)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4800)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4799)) ) ),
inference(variable_rename,[status(thm)],[f_1563_1]) ).
fof(f_1563_3,plain,
( ! [U_4804,U_4802] :
( ( ( c_Divides_Odivmod__int(U_4802,U_4804) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4802),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4804)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4804)) )
& ( c_Divides_Odivmod__int(U_4802,U_4804) = c_Divides_OnegDivAlg(U_4802,U_4804)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4804)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4802)) )
& ! [U_4803,U_4801] :
( ( ( ( ( c_Divides_Odivmod__int(U_4801,U_4803) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4801),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4803)))
| U_4801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odivmod__int(U_4801,U_4803) = 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_4801 != 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_4803)) )
& ( c_Divides_Odivmod__int(U_4801,U_4803) = c_Divides_OposDivAlg(U_4801,U_4803)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4803)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4801)) ) ),
inference(miniscope,[status(thm)],[f_1563_2]) ).
cnf(f_1563_4,plain,
( c_Divides_Odivmod__int(U_4801,U_4803) = c_Divides_OposDivAlg(U_4801,U_4803)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4801)) ),
inference(clausify,[status(thm)],[f_1563_3]) ).
cnf(f_1563_5,plain,
( c_Divides_Odivmod__int(U_4801,U_4803) = 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_4801 != 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_4803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4801)) ),
inference(clausify,[status(thm)],[f_1563_3]) ).
cnf(f_1563_6,plain,
( c_Divides_Odivmod__int(U_4801,U_4803) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4801),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4803)))
| U_4801 = 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_4803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4801)) ),
inference(clausify,[status(thm)],[f_1563_3]) ).
cnf(f_1563_7,plain,
( c_Divides_Odivmod__int(U_4802,U_4804) = c_Divides_OnegDivAlg(U_4802,U_4804)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4804))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4802)) ),
inference(clausify,[status(thm)],[f_1563_3]) ).
cnf(f_1563_8,plain,
( c_Divides_Odivmod__int(U_4802,U_4804) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4802),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4804)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4804))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4802)) ),
inference(clausify,[status(thm)],[f_1563_3]) ).
fof(f_1564_1,plain,
! [V_P_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
| ? [B_a,B_b] :
( ~ hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
& ( hBOOL(hAPP(hAPP(V_P_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_1564_2,plain,
! [U_4809,U_4808,U_4807] :
( hBOOL(hAPP(hAPP(U_4809,U_4807),U_4808))
| ? [U_4806,U_4805] :
( ~ hBOOL(hAPP(hAPP(U_4809,U_4806),U_4805))
& ( hBOOL(hAPP(hAPP(U_4809,U_4806),hAPP(hAPP(c_Groups_Otimes__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_4805)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4805),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4806),U_4805)) )
& 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_4806),U_4805))) )
| ~ 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_4807),U_4808))) ),
inference(variable_rename,[status(thm)],[f_1564_1]) ).
fof(f_1564_3,plain,
! [U_4809,U_4808,U_4807] :
( hBOOL(hAPP(hAPP(U_4809,U_4807),U_4808))
| ? [U_4805] :
( ~ hBOOL(hAPP(hAPP(U_4809,sK71(U_4809,U_4808,U_4807)),U_4805))
& ( hBOOL(hAPP(hAPP(U_4809,sK71(U_4809,U_4808,U_4807)),hAPP(hAPP(c_Groups_Otimes__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_4805)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4805),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK71(U_4809,U_4808,U_4807)),U_4805)) )
& 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),sK71(U_4809,U_4808,U_4807)),U_4805))) )
| ~ 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_4807),U_4808))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_4806,sK71(U_4809,U_4808,U_4807))],[f_1564_2]) ).
fof(f_1564_4,plain,
! [U_4809,U_4808,U_4807] :
( hBOOL(hAPP(hAPP(U_4809,U_4807),U_4808))
| ( ~ hBOOL(hAPP(hAPP(U_4809,sK71(U_4809,U_4808,U_4807)),sK72(U_4809,U_4808,U_4807)))
& ( hBOOL(hAPP(hAPP(U_4809,sK71(U_4809,U_4808,U_4807)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK72(U_4809,U_4808,U_4807))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK72(U_4809,U_4808,U_4807)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK71(U_4809,U_4808,U_4807)),sK72(U_4809,U_4808,U_4807))) )
& 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),sK71(U_4809,U_4808,U_4807)),sK72(U_4809,U_4808,U_4807)))) )
| ~ 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_4807),U_4808))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_4805,sK72(U_4809,U_4808,U_4807))],[f_1564_3]) ).
cnf(f_1564_5,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),sK71(U_4809,U_4808,U_4807)),sK72(U_4809,U_4808,U_4807))))
| hBOOL(hAPP(hAPP(U_4809,U_4807),U_4808))
| ~ 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_4807),U_4808))) ),
inference(clausify,[status(thm)],[f_1564_4]) ).
cnf(f_1564_6,plain,
( hBOOL(hAPP(hAPP(U_4809,sK71(U_4809,U_4808,U_4807)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK72(U_4809,U_4808,U_4807))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK72(U_4809,U_4808,U_4807)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK71(U_4809,U_4808,U_4807)),sK72(U_4809,U_4808,U_4807)))
| hBOOL(hAPP(hAPP(U_4809,U_4807),U_4808))
| ~ 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_4807),U_4808))) ),
inference(clausify,[status(thm)],[f_1564_4]) ).
cnf(f_1564_7,plain,
( ~ hBOOL(hAPP(hAPP(U_4809,sK71(U_4809,U_4808,U_4807)),sK72(U_4809,U_4808,U_4807)))
| hBOOL(hAPP(hAPP(U_4809,U_4807),U_4808))
| ~ 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_4807),U_4808))) ),
inference(clausify,[status(thm)],[f_1564_4]) ).
fof(f_1565_1,plain,
! [V_p_2,V_g_2,T_f,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,tc_prod(T_c,T_d)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(T_f,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_f),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2))),V_g_2)),V_p_2),
inference(fof_nnf,[status(thm)],[fact_split__twice]) ).
fof(f_1565_2,plain,
! [U_4817,U_4816,U_4815,U_4814,U_4813,U_4812,U_4811,U_4810] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4810,U_4811,U_4812),U_4813),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4814,U_4815,tc_prod(U_4810,U_4811)),U_4816),U_4817)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4814,U_4815,U_4812),hAPP(hAPP(c_COMBB(tc_fun(U_4815,tc_prod(U_4810,U_4811)),tc_fun(U_4815,U_4812),U_4814),hAPP(c_COMBB(tc_prod(U_4810,U_4811),U_4812,U_4815),hAPP(c_Product__Type_Oprod_Oprod__case(U_4810,U_4811,U_4812),U_4813))),U_4816)),U_4817),
inference(variable_rename,[status(thm)],[f_1565_1]) ).
cnf(f_1565_3,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4810,U_4811,U_4812),U_4813),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4814,U_4815,tc_prod(U_4810,U_4811)),U_4816),U_4817)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4814,U_4815,U_4812),hAPP(hAPP(c_COMBB(tc_fun(U_4815,tc_prod(U_4810,U_4811)),tc_fun(U_4815,U_4812),U_4814),hAPP(c_COMBB(tc_prod(U_4810,U_4811),U_4812,U_4815),hAPP(c_Product__Type_Oprod_Oprod__case(U_4810,U_4811,U_4812),U_4813))),U_4816)),U_4817),
inference(clausify,[status(thm)],[f_1565_2]) ).
fof(f_1566_1,plain,
! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_d),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_d,T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c))) = V_f_2,
inference(fof_nnf,[status(thm)],[fact_split__eta]) ).
fof(f_1566_2,plain,
! [U_4821,U_4820,U_4819,U_4818] : hAPP(c_Product__Type_Oprod_Oprod__case(U_4818,U_4819,U_4820),hAPP(hAPP(c_COMBB(tc_fun(U_4819,tc_prod(U_4818,U_4819)),tc_fun(U_4819,U_4820),U_4818),hAPP(c_COMBB(tc_prod(U_4818,U_4819),U_4820,U_4819),U_4821)),c_Product__Type_OPair(U_4818,U_4819))) = U_4821,
inference(variable_rename,[status(thm)],[f_1566_1]) ).
cnf(f_1566_3,plain,
hAPP(c_Product__Type_Oprod_Oprod__case(U_4818,U_4819,U_4820),hAPP(hAPP(c_COMBB(tc_fun(U_4819,tc_prod(U_4818,U_4819)),tc_fun(U_4819,U_4820),U_4818),hAPP(c_COMBB(tc_prod(U_4818,U_4819),U_4820,U_4819),U_4821)),c_Product__Type_OPair(U_4818,U_4819))) = U_4821,
inference(clausify,[status(thm)],[f_1566_2]) ).
fof(f_1567_1,plain,
! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_splitI]) ).
fof(f_1567_2,plain,
! [U_4826,U_4825,U_4824,U_4823,U_4822] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4825,U_4826,tc_HOL_Obool),U_4822),hAPP(hAPP(c_Product__Type_OPair(U_4825,U_4826),U_4823),U_4824)))
| ~ hBOOL(hAPP(hAPP(U_4822,U_4823),U_4824)) ),
inference(variable_rename,[status(thm)],[f_1567_1]) ).
cnf(f_1567_3,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4825,U_4826,tc_HOL_Obool),U_4822),hAPP(hAPP(c_Product__Type_OPair(U_4825,U_4826),U_4823),U_4824)))
| ~ hBOOL(hAPP(hAPP(U_4822,U_4823),U_4824)) ),
inference(clausify,[status(thm)],[f_1567_2]) ).
fof(f_1568_1,plain,
! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_prod__caseI]) ).
fof(f_1568_2,plain,
! [U_4831,U_4830,U_4829,U_4828,U_4827] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4830,U_4831,tc_HOL_Obool),U_4827),hAPP(hAPP(c_Product__Type_OPair(U_4830,U_4831),U_4828),U_4829)))
| ~ hBOOL(hAPP(hAPP(U_4827,U_4828),U_4829)) ),
inference(variable_rename,[status(thm)],[f_1568_1]) ).
cnf(f_1568_3,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4830,U_4831,tc_HOL_Obool),U_4827),hAPP(hAPP(c_Product__Type_OPair(U_4830,U_4831),U_4828),U_4829)))
| ~ hBOOL(hAPP(hAPP(U_4827,U_4828),U_4829)) ),
inference(clausify,[status(thm)],[f_1568_2]) ).
fof(f_1569_1,plain,
! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
inference(fof_nnf,[status(thm)],[fact_splitD]) ).
fof(f_1569_2,plain,
! [U_4836,U_4835,U_4834,U_4833,U_4832] :
( hBOOL(hAPP(hAPP(U_4834,U_4835),U_4836))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4832,U_4833,tc_HOL_Obool),U_4834),hAPP(hAPP(c_Product__Type_OPair(U_4832,U_4833),U_4835),U_4836))) ),
inference(variable_rename,[status(thm)],[f_1569_1]) ).
fof(f_1569_3,plain,
! [U_4836,U_4835,U_4834] :
( ! [U_4833,U_4832] : ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4832,U_4833,tc_HOL_Obool),U_4834),hAPP(hAPP(c_Product__Type_OPair(U_4832,U_4833),U_4835),U_4836)))
| hBOOL(hAPP(hAPP(U_4834,U_4835),U_4836)) ),
inference(miniscope,[status(thm)],[f_1569_2]) ).
cnf(f_1569_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4832,U_4833,tc_HOL_Obool),U_4834),hAPP(hAPP(c_Product__Type_OPair(U_4832,U_4833),U_4835),U_4836)))
| hBOOL(hAPP(hAPP(U_4834,U_4835),U_4836)) ),
inference(clausify,[status(thm)],[f_1569_3]) ).
fof(f_1570_1,plain,
! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_c_2)) ),
inference(fof_nnf,[status(thm)],[fact_splitD_H]) ).
fof(f_1570_2,plain,
! [U_4843,U_4842,U_4841,U_4840,U_4839,U_4838,U_4837] :
( hBOOL(hAPP(hAPP(hAPP(U_4840,U_4841),U_4842),U_4843))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4837,U_4838,tc_fun(U_4839,tc_HOL_Obool)),U_4840),hAPP(hAPP(c_Product__Type_OPair(U_4837,U_4838),U_4841),U_4842)),U_4843)) ),
inference(variable_rename,[status(thm)],[f_1570_1]) ).
fof(f_1570_3,plain,
! [U_4843,U_4842,U_4841,U_4840] :
( ! [U_4839,U_4838,U_4837] : ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4837,U_4838,tc_fun(U_4839,tc_HOL_Obool)),U_4840),hAPP(hAPP(c_Product__Type_OPair(U_4837,U_4838),U_4841),U_4842)),U_4843))
| hBOOL(hAPP(hAPP(hAPP(U_4840,U_4841),U_4842),U_4843)) ),
inference(miniscope,[status(thm)],[f_1570_2]) ).
cnf(f_1570_4,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4837,U_4838,tc_fun(U_4839,tc_HOL_Obool)),U_4840),hAPP(hAPP(c_Product__Type_OPair(U_4837,U_4838),U_4841),U_4842)),U_4843))
| hBOOL(hAPP(hAPP(hAPP(U_4840,U_4841),U_4842),U_4843)) ),
inference(clausify,[status(thm)],[f_1570_3]) ).
fof(f_1571_1,plain,
! [V_y_2,V_x_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),hAPP(V_f_2,V_y_2)),
inference(fof_nnf,[status(thm)],[fact_apsnd__conv]) ).
fof(f_1571_2,plain,
! [U_4849,U_4848,U_4847,U_4846,U_4845,U_4844] : hAPP(c_Product__Type_Oapsnd(U_4844,U_4845,U_4846,U_4847),hAPP(hAPP(c_Product__Type_OPair(U_4846,U_4844),U_4848),U_4849)) = hAPP(hAPP(c_Product__Type_OPair(U_4846,U_4845),U_4848),hAPP(U_4847,U_4849)),
inference(variable_rename,[status(thm)],[f_1571_1]) ).
cnf(f_1571_3,plain,
hAPP(c_Product__Type_Oapsnd(U_4844,U_4845,U_4846,U_4847),hAPP(hAPP(c_Product__Type_OPair(U_4846,U_4844),U_4848),U_4849)) = hAPP(hAPP(c_Product__Type_OPair(U_4846,U_4845),U_4848),hAPP(U_4847,U_4849)),
inference(clausify,[status(thm)],[f_1571_2]) ).
fof(f_1572_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]) ).
cnf(f_1572_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(clausify,[status(thm)],[f_1572_1]) ).
fof(f_1573_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_1573_2,plain,
! [U_4855,U_4854,U_4853,U_4852,U_4851,U_4850] :
( ( U_4853 = U_4855
& U_4852 = U_4854 )
| hAPP(hAPP(c_Product__Type_OPair(U_4850,U_4851),U_4852),U_4853) != hAPP(hAPP(c_Product__Type_OPair(U_4850,U_4851),U_4854),U_4855) ),
inference(variable_rename,[status(thm)],[f_1573_1]) ).
fof(f_1573_3,plain,
! [U_4855,U_4854,U_4853,U_4852] :
( ! [U_4851,U_4850] : hAPP(hAPP(c_Product__Type_OPair(U_4850,U_4851),U_4852),U_4853) != hAPP(hAPP(c_Product__Type_OPair(U_4850,U_4851),U_4854),U_4855)
| ( U_4853 = U_4855
& U_4852 = U_4854 ) ),
inference(miniscope,[status(thm)],[f_1573_2]) ).
cnf(f_1573_4,plain,
( U_4852 = U_4854
| hAPP(hAPP(c_Product__Type_OPair(U_4850,U_4851),U_4852),U_4853) != hAPP(hAPP(c_Product__Type_OPair(U_4850,U_4851),U_4854),U_4855) ),
inference(clausify,[status(thm)],[f_1573_3]) ).
cnf(f_1573_5,plain,
( U_4853 = U_4855
| hAPP(hAPP(c_Product__Type_OPair(U_4850,U_4851),U_4852),U_4853) != hAPP(hAPP(c_Product__Type_OPair(U_4850,U_4851),U_4854),U_4855) ),
inference(clausify,[status(thm)],[f_1573_3]) ).
fof(f_1574_1,plain,
! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
( ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2)
| V_b_2 != V_b_H_2
| V_a_2 != V_a_H_2 )
& ( ( V_b_2 = V_b_H_2
& V_a_2 = V_a_H_2 )
| hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2) != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Pair__eq]) ).
fof(f_1574_2,plain,
! [U_4861,U_4860,U_4859,U_4858,U_4857,U_4856] :
( ( hAPP(hAPP(c_Product__Type_OPair(U_4856,U_4857),U_4858),U_4859) = hAPP(hAPP(c_Product__Type_OPair(U_4856,U_4857),U_4860),U_4861)
| U_4859 != U_4861
| U_4858 != U_4860 )
& ( ( U_4859 = U_4861
& U_4858 = U_4860 )
| hAPP(hAPP(c_Product__Type_OPair(U_4856,U_4857),U_4858),U_4859) != hAPP(hAPP(c_Product__Type_OPair(U_4856,U_4857),U_4860),U_4861) ) ),
inference(variable_rename,[status(thm)],[f_1574_1]) ).
fof(f_1574_3,plain,
( ! [U_4873,U_4871,U_4869,U_4867] :
( ! [U_4865,U_4863] : hAPP(hAPP(c_Product__Type_OPair(U_4863,U_4865),U_4867),U_4869) = hAPP(hAPP(c_Product__Type_OPair(U_4863,U_4865),U_4871),U_4873)
| U_4869 != U_4873
| U_4867 != U_4871 )
& ! [U_4872,U_4870,U_4868,U_4866] :
( ! [U_4864,U_4862] : hAPP(hAPP(c_Product__Type_OPair(U_4862,U_4864),U_4866),U_4868) != hAPP(hAPP(c_Product__Type_OPair(U_4862,U_4864),U_4870),U_4872)
| ( U_4868 = U_4872
& U_4866 = U_4870 ) ) ),
inference(miniscope,[status(thm)],[f_1574_2]) ).
cnf(f_1574_4,plain,
( U_4866 = U_4870
| hAPP(hAPP(c_Product__Type_OPair(U_4862,U_4864),U_4866),U_4868) != hAPP(hAPP(c_Product__Type_OPair(U_4862,U_4864),U_4870),U_4872) ),
inference(clausify,[status(thm)],[f_1574_3]) ).
cnf(f_1574_5,plain,
( U_4868 = U_4872
| hAPP(hAPP(c_Product__Type_OPair(U_4862,U_4864),U_4866),U_4868) != hAPP(hAPP(c_Product__Type_OPair(U_4862,U_4864),U_4870),U_4872) ),
inference(clausify,[status(thm)],[f_1574_3]) ).
cnf(f_1574_6,plain,
( hAPP(hAPP(c_Product__Type_OPair(U_4863,U_4865),U_4867),U_4869) = hAPP(hAPP(c_Product__Type_OPair(U_4863,U_4865),U_4871),U_4873)
| U_4869 != U_4873
| U_4867 != U_4871 ),
inference(clausify,[status(thm)],[f_1574_3]) ).
fof(f_1575_1,plain,
! [T_c,T_b,V_P_2] :
( ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
| ? [B_a,B_b] : ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) )
& ( ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)))
| ? [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ) ),
inference(fof_nnf,[status(thm)],[fact_split__paired__All]) ).
fof(f_1575_2,plain,
! [U_4882,U_4881,U_4880] :
( ( ! [U_4879] : hBOOL(hAPP(U_4880,U_4879))
| ? [U_4878,U_4877] : ~ hBOOL(hAPP(U_4880,hAPP(hAPP(c_Product__Type_OPair(U_4881,U_4882),U_4878),U_4877))) )
& ( ! [U_4876,U_4875] : hBOOL(hAPP(U_4880,hAPP(hAPP(c_Product__Type_OPair(U_4881,U_4882),U_4876),U_4875)))
| ? [U_4874] : ~ hBOOL(hAPP(U_4880,U_4874)) ) ),
inference(variable_rename,[status(thm)],[f_1575_1]) ).
fof(f_1575_3,plain,
( ! [U_4888,U_4886,U_4884] :
( ! [U_4879] : hBOOL(hAPP(U_4884,U_4879))
| ? [U_4878,U_4877] : ~ hBOOL(hAPP(U_4884,hAPP(hAPP(c_Product__Type_OPair(U_4886,U_4888),U_4878),U_4877))) )
& ! [U_4887,U_4885,U_4883] :
( ! [U_4876,U_4875] : hBOOL(hAPP(U_4883,hAPP(hAPP(c_Product__Type_OPair(U_4885,U_4887),U_4876),U_4875)))
| ? [U_4874] : ~ hBOOL(hAPP(U_4883,U_4874)) ) ),
inference(miniscope,[status(thm)],[f_1575_2]) ).
fof(f_1575_4,plain,
( ! [U_4888,U_4886,U_4884] :
( ! [U_4879] : hBOOL(hAPP(U_4884,U_4879))
| ? [U_4878,U_4877] : ~ hBOOL(hAPP(U_4884,hAPP(hAPP(c_Product__Type_OPair(U_4886,U_4888),U_4878),U_4877))) )
& ! [U_4887,U_4885,U_4883] :
( ! [U_4876,U_4875] : hBOOL(hAPP(U_4883,hAPP(hAPP(c_Product__Type_OPair(U_4885,U_4887),U_4876),U_4875)))
| ~ hBOOL(hAPP(U_4883,sK73(U_4887,U_4885,U_4883))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_4874,sK73(U_4887,U_4885,U_4883))],[f_1575_3]) ).
fof(f_1575_5,plain,
( ! [U_4888,U_4886,U_4884] :
( ! [U_4879] : hBOOL(hAPP(U_4884,U_4879))
| ? [U_4877] : ~ hBOOL(hAPP(U_4884,hAPP(hAPP(c_Product__Type_OPair(U_4886,U_4888),sK74(U_4888,U_4886,U_4884)),U_4877))) )
& ! [U_4887,U_4885,U_4883] :
( ! [U_4876,U_4875] : hBOOL(hAPP(U_4883,hAPP(hAPP(c_Product__Type_OPair(U_4885,U_4887),U_4876),U_4875)))
| ~ hBOOL(hAPP(U_4883,sK73(U_4887,U_4885,U_4883))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_4878,sK74(U_4888,U_4886,U_4884))],[f_1575_4]) ).
fof(f_1575_6,plain,
( ! [U_4888,U_4886,U_4884] :
( ! [U_4879] : hBOOL(hAPP(U_4884,U_4879))
| ~ hBOOL(hAPP(U_4884,hAPP(hAPP(c_Product__Type_OPair(U_4886,U_4888),sK74(U_4888,U_4886,U_4884)),sK75(U_4888,U_4886,U_4884)))) )
& ! [U_4887,U_4885,U_4883] :
( ! [U_4876,U_4875] : hBOOL(hAPP(U_4883,hAPP(hAPP(c_Product__Type_OPair(U_4885,U_4887),U_4876),U_4875)))
| ~ hBOOL(hAPP(U_4883,sK73(U_4887,U_4885,U_4883))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_4877,sK75(U_4888,U_4886,U_4884))],[f_1575_5]) ).
cnf(f_1575_7,plain,
( hBOOL(hAPP(U_4883,hAPP(hAPP(c_Product__Type_OPair(U_4885,U_4887),U_4876),U_4875)))
| ~ hBOOL(hAPP(U_4883,sK73(U_4887,U_4885,U_4883))) ),
inference(clausify,[status(thm)],[f_1575_6]) ).
cnf(f_1575_8,plain,
( hBOOL(hAPP(U_4884,U_4879))
| ~ hBOOL(hAPP(U_4884,hAPP(hAPP(c_Product__Type_OPair(U_4886,U_4888),sK74(U_4888,U_4886,U_4884)),sK75(U_4888,U_4886,U_4884)))) ),
inference(clausify,[status(thm)],[f_1575_6]) ).
fof(f_1576_1,plain,
! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_q_2)
| V_p_2 != V_q_2 ),
inference(fof_nnf,[status(thm)],[fact_split__weak__cong]) ).
fof(f_1576_2,plain,
! [U_4894,U_4893,U_4892,U_4891,U_4890,U_4889] :
( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4891,U_4892,U_4893),U_4894),U_4889) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4891,U_4892,U_4893),U_4894),U_4890)
| U_4889 != U_4890 ),
inference(variable_rename,[status(thm)],[f_1576_1]) ).
cnf(f_1576_3,plain,
( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4891,U_4892,U_4893),U_4894),U_4889) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4891,U_4892,U_4893),U_4894),U_4890)
| U_4889 != U_4890 ),
inference(clausify,[status(thm)],[f_1576_2]) ).
fof(f_1577_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_1577_2,plain,
! [U_4896,U_4895] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4895),U_4896)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4895),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4896)),
inference(variable_rename,[status(thm)],[f_1577_1]) ).
cnf(f_1577_3,plain,
hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4895),U_4896)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4895),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4896)),
inference(clausify,[status(thm)],[f_1577_2]) ).
fof(f_1578_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_1578_2,plain,
! [U_4899,U_4898,U_4897] :
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4897,U_4898),hAPP(c_Divides_OnegateSnd,U_4899)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4897),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4898)),U_4899)) ),
inference(variable_rename,[status(thm)],[f_1578_1]) ).
cnf(f_1578_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4897,U_4898),hAPP(c_Divides_OnegateSnd,U_4899)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4897),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4898)),U_4899)) ),
inference(clausify,[status(thm)],[f_1578_2]) ).
fof(f_1579_1,plain,
! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2),
inference(fof_nnf,[status(thm)],[fact_split__conv]) ).
fof(f_1579_2,plain,
! [U_4905,U_4904,U_4903,U_4902,U_4901,U_4900] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4900,U_4901,U_4902),U_4903),hAPP(hAPP(c_Product__Type_OPair(U_4900,U_4901),U_4904),U_4905)) = hAPP(hAPP(U_4903,U_4904),U_4905),
inference(variable_rename,[status(thm)],[f_1579_1]) ).
cnf(f_1579_3,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4900,U_4901,U_4902),U_4903),hAPP(hAPP(c_Product__Type_OPair(U_4900,U_4901),U_4904),U_4905)) = hAPP(hAPP(U_4903,U_4904),U_4905),
inference(clausify,[status(thm)],[f_1579_2]) ).
fof(f_1580_1,plain,
! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
inference(fof_nnf,[status(thm)],[fact_prod_Osimps_I2_J]) ).
fof(f_1580_2,plain,
! [U_4911,U_4910,U_4909,U_4908,U_4907,U_4906] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4906,U_4907,U_4908),U_4909),hAPP(hAPP(c_Product__Type_OPair(U_4906,U_4907),U_4910),U_4911)) = hAPP(hAPP(U_4909,U_4910),U_4911),
inference(variable_rename,[status(thm)],[f_1580_1]) ).
cnf(f_1580_3,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4906,U_4907,U_4908),U_4909),hAPP(hAPP(c_Product__Type_OPair(U_4906,U_4907),U_4910),U_4911)) = hAPP(hAPP(U_4909,U_4910),U_4911),
inference(clausify,[status(thm)],[f_1580_2]) ).
fof(f_1581_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_1581_2,plain,
! [U_4913,U_4912] : c_Code__Numeral_Odiv__mod__code__numeral(U_4912,U_4913) = 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_4912),U_4913)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_4912,U_4913)),
inference(variable_rename,[status(thm)],[f_1581_1]) ).
cnf(f_1581_3,plain,
c_Code__Numeral_Odiv__mod__code__numeral(U_4912,U_4913) = 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_4912),U_4913)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_4912,U_4913)),
inference(clausify,[status(thm)],[f_1581_2]) ).
fof(f_1582_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_1582_2,plain,
! [U_4915,U_4914] :
( c_Divides_Odivmod__nat(U_4915,U_4914) = 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_4915),U_4914)),U_4914))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4915),U_4914),U_4914))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4914),U_4915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4914)) ),
inference(variable_rename,[status(thm)],[f_1582_1]) ).
cnf(f_1582_3,plain,
( c_Divides_Odivmod__nat(U_4915,U_4914) = 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_4915),U_4914)),U_4914))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4915),U_4914),U_4914))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4914),U_4915))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4914)) ),
inference(clausify,[status(thm)],[f_1582_2]) ).
fof(f_1583_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_1583_2,plain,
! [U_4916] :
( 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_4916)) = 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_4916)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4916)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1583_1]) ).
cnf(f_1583_3,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_4916)) = 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_4916)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4916)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1583_2]) ).
fof(f_1584_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_1584_2,plain,
! [U_4921,U_4920,U_4919,U_4918,U_4917] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4917,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4918),U_4921)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4919),U_4921)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4918),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4919,U_4921))),U_4920))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4921))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4918))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4917,U_4918),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4919),U_4920))) ),
inference(variable_rename,[status(thm)],[f_1584_1]) ).
cnf(f_1584_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4917,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4918),U_4921)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4919),U_4921)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4918),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4919,U_4921))),U_4920))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4921))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4918))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4917,U_4918),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4919),U_4920))) ),
inference(clausify,[status(thm)],[f_1584_2]) ).
fof(f_1585_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_1585_2,plain,
! [U_4926,U_4925,U_4924,U_4923,U_4922] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4926),U_4922),U_4923),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_4926),U_4924)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4926),U_4925)),U_4923))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4926),U_4925),U_4923))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4923))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4922,U_4923),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4924),U_4925))) ),
inference(variable_rename,[status(thm)],[f_1585_1]) ).
cnf(f_1585_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4926),U_4922),U_4923),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_4926),U_4924)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4926),U_4925)),U_4923))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4926),U_4925),U_4923))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4923))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4922,U_4923),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4924),U_4925))) ),
inference(clausify,[status(thm)],[f_1585_2]) ).
fof(f_1586_1,plain,
! [V_w] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_div__pos__neg__1__number__of]) ).
fof(f_1586_2,plain,
! [U_4927] :
( 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_4927)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4927)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4927)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1586_1]) ).
cnf(f_1586_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4927)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4927)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4927)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1586_2]) ).
fof(f_1587_1,plain,
! [V_p_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)),
inference(fof_nnf,[status(thm)],[fact_split__def]) ).
fof(f_1587_2,plain,
! [U_4932,U_4931,U_4930,U_4929,U_4928] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4928,U_4929,U_4930),U_4931),U_4932) = hAPP(hAPP(U_4931,hAPP(c_Product__Type_Ofst(U_4928,U_4929),U_4932)),hAPP(c_Product__Type_Osnd(U_4928,U_4929),U_4932)),
inference(variable_rename,[status(thm)],[f_1587_1]) ).
cnf(f_1587_3,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4928,U_4929,U_4930),U_4931),U_4932) = hAPP(hAPP(U_4931,hAPP(c_Product__Type_Ofst(U_4928,U_4929),U_4932)),hAPP(c_Product__Type_Osnd(U_4928,U_4929),U_4932)),
inference(clausify,[status(thm)],[f_1587_2]) ).
fof(f_1588_1,plain,
! [V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),tc_prod(T_b,T_c)),V_f_2),hAPP(hAPP(c_COMBB(T_b,T_e,tc_prod(T_b,T_c)),V_g_2),c_Product__Type_Ofst(T_b,T_c)))),c_Product__Type_Osnd(T_b,T_c)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),T_b),V_f_2),V_g_2)),
inference(fof_nnf,[status(thm)],[fact_split__comp__eq]) ).
fof(f_1588_2,plain,
! [U_4938,U_4937,U_4936,U_4935,U_4934,U_4933] : hAPP(hAPP(c_COMBS(tc_prod(U_4933,U_4934),U_4934,U_4935),hAPP(hAPP(c_COMBB(U_4936,tc_fun(U_4934,U_4935),tc_prod(U_4933,U_4934)),U_4937),hAPP(hAPP(c_COMBB(U_4933,U_4936,tc_prod(U_4933,U_4934)),U_4938),c_Product__Type_Ofst(U_4933,U_4934)))),c_Product__Type_Osnd(U_4933,U_4934)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_4933,U_4934,U_4935),hAPP(hAPP(c_COMBB(U_4936,tc_fun(U_4934,U_4935),U_4933),U_4937),U_4938)),
inference(variable_rename,[status(thm)],[f_1588_1]) ).
cnf(f_1588_3,plain,
hAPP(hAPP(c_COMBS(tc_prod(U_4933,U_4934),U_4934,U_4935),hAPP(hAPP(c_COMBB(U_4936,tc_fun(U_4934,U_4935),tc_prod(U_4933,U_4934)),U_4937),hAPP(hAPP(c_COMBB(U_4933,U_4936,tc_prod(U_4933,U_4934)),U_4938),c_Product__Type_Ofst(U_4933,U_4934)))),c_Product__Type_Osnd(U_4933,U_4934)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_4933,U_4934,U_4935),hAPP(hAPP(c_COMBB(U_4936,tc_fun(U_4934,U_4935),U_4933),U_4937),U_4938)),
inference(clausify,[status(thm)],[f_1588_2]) ).
fof(f_1589_1,plain,
! [V_z_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_P_2),V_z_2) = hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)),
inference(fof_nnf,[status(thm)],[fact_split__beta]) ).
fof(f_1589_2,plain,
! [U_4943,U_4942,U_4941,U_4940,U_4939] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4939,U_4940,U_4941),U_4942),U_4943) = hAPP(hAPP(U_4942,hAPP(c_Product__Type_Ofst(U_4939,U_4940),U_4943)),hAPP(c_Product__Type_Osnd(U_4939,U_4940),U_4943)),
inference(variable_rename,[status(thm)],[f_1589_1]) ).
cnf(f_1589_3,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4939,U_4940,U_4941),U_4942),U_4943) = hAPP(hAPP(U_4942,hAPP(c_Product__Type_Ofst(U_4939,U_4940),U_4943)),hAPP(c_Product__Type_Osnd(U_4939,U_4940),U_4943)),
inference(clausify,[status(thm)],[f_1589_2]) ).
fof(f_1590_1,plain,
! [V_p_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)),
inference(fof_nnf,[status(thm)],[fact_prod__case__beta]) ).
fof(f_1590_2,plain,
! [U_4948,U_4947,U_4946,U_4945,U_4944] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4944,U_4945,U_4946),U_4947),U_4948) = hAPP(hAPP(U_4947,hAPP(c_Product__Type_Ofst(U_4944,U_4945),U_4948)),hAPP(c_Product__Type_Osnd(U_4944,U_4945),U_4948)),
inference(variable_rename,[status(thm)],[f_1590_1]) ).
cnf(f_1590_3,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_4944,U_4945,U_4946),U_4947),U_4948) = hAPP(hAPP(U_4947,hAPP(c_Product__Type_Ofst(U_4944,U_4945),U_4948)),hAPP(c_Product__Type_Osnd(U_4944,U_4945),U_4948)),
inference(clausify,[status(thm)],[f_1590_2]) ).
fof(f_1591_1,plain,
! [T_b,T_a,V_t] : V_t = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_t)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_t)),
inference(fof_nnf,[status(thm)],[fact_surjective__pairing]) ).
fof(f_1591_2,plain,
! [U_4951,U_4950,U_4949] : U_4949 = hAPP(hAPP(c_Product__Type_OPair(U_4950,U_4951),hAPP(c_Product__Type_Ofst(U_4950,U_4951),U_4949)),hAPP(c_Product__Type_Osnd(U_4950,U_4951),U_4949)),
inference(variable_rename,[status(thm)],[f_1591_1]) ).
cnf(f_1591_3,plain,
U_4949 = hAPP(hAPP(c_Product__Type_OPair(U_4950,U_4951),hAPP(c_Product__Type_Ofst(U_4950,U_4951),U_4949)),hAPP(c_Product__Type_Osnd(U_4950,U_4951),U_4949)),
inference(clausify,[status(thm)],[f_1591_2]) ).
fof(f_1592_1,plain,
! [V_p,T_b,T_a] : hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p)) = V_p,
inference(fof_nnf,[status(thm)],[fact_pair__collapse]) ).
fof(f_1592_2,plain,
! [U_4954,U_4953,U_4952] : hAPP(hAPP(c_Product__Type_OPair(U_4952,U_4953),hAPP(c_Product__Type_Ofst(U_4952,U_4953),U_4954)),hAPP(c_Product__Type_Osnd(U_4952,U_4953),U_4954)) = U_4954,
inference(variable_rename,[status(thm)],[f_1592_1]) ).
cnf(f_1592_3,plain,
hAPP(hAPP(c_Product__Type_OPair(U_4952,U_4953),hAPP(c_Product__Type_Ofst(U_4952,U_4953),U_4954)),hAPP(c_Product__Type_Osnd(U_4952,U_4953),U_4954)) = U_4954,
inference(clausify,[status(thm)],[f_1592_2]) ).
fof(f_1593_1,plain,
! [V_q,V_p,T_b,T_a] :
( V_p = V_q
| hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) != hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
| hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) != hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) ),
inference(fof_nnf,[status(thm)],[fact_prod__eqI]) ).
fof(f_1593_2,plain,
! [U_4958,U_4957,U_4956,U_4955] :
( U_4957 = U_4958
| hAPP(c_Product__Type_Osnd(U_4955,U_4956),U_4957) != hAPP(c_Product__Type_Osnd(U_4955,U_4956),U_4958)
| hAPP(c_Product__Type_Ofst(U_4955,U_4956),U_4957) != hAPP(c_Product__Type_Ofst(U_4955,U_4956),U_4958) ),
inference(variable_rename,[status(thm)],[f_1593_1]) ).
cnf(f_1593_3,plain,
( U_4957 = U_4958
| hAPP(c_Product__Type_Osnd(U_4955,U_4956),U_4957) != hAPP(c_Product__Type_Osnd(U_4955,U_4956),U_4958)
| hAPP(c_Product__Type_Ofst(U_4955,U_4956),U_4957) != hAPP(c_Product__Type_Ofst(U_4955,U_4956),U_4958) ),
inference(clausify,[status(thm)],[f_1593_2]) ).
fof(f_1594_1,plain,
! [T_c,T_b,V_t_2,V_s_2] :
( ( V_s_2 = V_t_2
| hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) != hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2)
| hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) != hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) )
& ( ( hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2)
& hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) )
| V_s_2 != V_t_2 ) ),
inference(fof_nnf,[status(thm)],[fact_Pair__fst__snd__eq]) ).
fof(f_1594_2,plain,
! [U_4962,U_4961,U_4960,U_4959] :
( ( U_4959 = U_4960
| hAPP(c_Product__Type_Osnd(U_4961,U_4962),U_4959) != hAPP(c_Product__Type_Osnd(U_4961,U_4962),U_4960)
| hAPP(c_Product__Type_Ofst(U_4961,U_4962),U_4959) != hAPP(c_Product__Type_Ofst(U_4961,U_4962),U_4960) )
& ( ( hAPP(c_Product__Type_Osnd(U_4961,U_4962),U_4959) = hAPP(c_Product__Type_Osnd(U_4961,U_4962),U_4960)
& hAPP(c_Product__Type_Ofst(U_4961,U_4962),U_4959) = hAPP(c_Product__Type_Ofst(U_4961,U_4962),U_4960) )
| U_4959 != U_4960 ) ),
inference(variable_rename,[status(thm)],[f_1594_1]) ).
fof(f_1594_3,plain,
( ! [U_4970,U_4968,U_4966,U_4964] :
( U_4964 = U_4966
| hAPP(c_Product__Type_Osnd(U_4968,U_4970),U_4964) != hAPP(c_Product__Type_Osnd(U_4968,U_4970),U_4966)
| hAPP(c_Product__Type_Ofst(U_4968,U_4970),U_4964) != hAPP(c_Product__Type_Ofst(U_4968,U_4970),U_4966) )
& ! [U_4969,U_4967,U_4965,U_4963] :
( ( hAPP(c_Product__Type_Osnd(U_4967,U_4969),U_4963) = hAPP(c_Product__Type_Osnd(U_4967,U_4969),U_4965)
& hAPP(c_Product__Type_Ofst(U_4967,U_4969),U_4963) = hAPP(c_Product__Type_Ofst(U_4967,U_4969),U_4965) )
| U_4963 != U_4965 ) ),
inference(miniscope,[status(thm)],[f_1594_2]) ).
cnf(f_1594_4,plain,
( hAPP(c_Product__Type_Ofst(U_4967,U_4969),U_4963) = hAPP(c_Product__Type_Ofst(U_4967,U_4969),U_4965)
| U_4963 != U_4965 ),
inference(clausify,[status(thm)],[f_1594_3]) ).
cnf(f_1594_5,plain,
( hAPP(c_Product__Type_Osnd(U_4967,U_4969),U_4963) = hAPP(c_Product__Type_Osnd(U_4967,U_4969),U_4965)
| U_4963 != U_4965 ),
inference(clausify,[status(thm)],[f_1594_3]) ).
cnf(f_1594_6,plain,
( U_4964 = U_4966
| hAPP(c_Product__Type_Osnd(U_4968,U_4970),U_4964) != hAPP(c_Product__Type_Osnd(U_4968,U_4970),U_4966)
| hAPP(c_Product__Type_Ofst(U_4968,U_4970),U_4964) != hAPP(c_Product__Type_Ofst(U_4968,U_4970),U_4966) ),
inference(clausify,[status(thm)],[f_1594_3]) ).
fof(f_1595_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_1595_2,plain,
! [U_4974,U_4973,U_4972,U_4971] :
( U_4973 = U_4974
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4971,U_4972),U_4974))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4971,U_4972),U_4973)) ),
inference(variable_rename,[status(thm)],[f_1595_1]) ).
cnf(f_1595_3,plain,
( U_4973 = U_4974
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4971,U_4972),U_4974))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4971,U_4972),U_4973)) ),
inference(clausify,[status(thm)],[f_1595_2]) ).
fof(f_1596_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_1596_2,plain,
! [U_4977,U_4976,U_4975] :
( c_Divides_Odivmod__nat(U_4975,U_4976) = U_4977
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4975,U_4976),U_4977)) ),
inference(variable_rename,[status(thm)],[f_1596_1]) ).
cnf(f_1596_3,plain,
( c_Divides_Odivmod__nat(U_4975,U_4976) = U_4977
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4975,U_4976),U_4977)) ),
inference(clausify,[status(thm)],[f_1596_2]) ).
fof(f_1597_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_1597_2,plain,
! [U_4979,U_4978] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4978,U_4979),c_Divides_Odivmod__nat(U_4978,U_4979))),
inference(variable_rename,[status(thm)],[f_1597_1]) ).
cnf(f_1597_3,plain,
hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4978,U_4979),c_Divides_Odivmod__nat(U_4978,U_4979))),
inference(clausify,[status(thm)],[f_1597_2]) ).
fof(f_1598_1,plain,
! [V_a,V_y,V_x,T_b,T_a] :
( V_x = V_a
| hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) != V_a ),
inference(fof_nnf,[status(thm)],[fact_fst__eqD]) ).
fof(f_1598_2,plain,
! [U_4984,U_4983,U_4982,U_4981,U_4980] :
( U_4982 = U_4984
| hAPP(c_Product__Type_Ofst(U_4980,U_4981),hAPP(hAPP(c_Product__Type_OPair(U_4980,U_4981),U_4982),U_4983)) != U_4984 ),
inference(variable_rename,[status(thm)],[f_1598_1]) ).
fof(f_1598_3,plain,
! [U_4984,U_4983,U_4982] :
( ! [U_4981,U_4980] : hAPP(c_Product__Type_Ofst(U_4980,U_4981),hAPP(hAPP(c_Product__Type_OPair(U_4980,U_4981),U_4982),U_4983)) != U_4984
| U_4982 = U_4984 ),
inference(miniscope,[status(thm)],[f_1598_2]) ).
cnf(f_1598_4,plain,
( hAPP(c_Product__Type_Ofst(U_4980,U_4981),hAPP(hAPP(c_Product__Type_OPair(U_4980,U_4981),U_4982),U_4983)) != U_4984
| U_4982 = U_4984 ),
inference(clausify,[status(thm)],[f_1598_3]) ).
fof(f_1599_1,plain,
! [V_b,V_a,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b)) = V_a,
inference(fof_nnf,[status(thm)],[fact_fst__conv]) ).
fof(f_1599_2,plain,
! [U_4988,U_4987,U_4986,U_4985] : hAPP(c_Product__Type_Ofst(U_4985,U_4986),hAPP(hAPP(c_Product__Type_OPair(U_4985,U_4986),U_4987),U_4988)) = U_4987,
inference(variable_rename,[status(thm)],[f_1599_1]) ).
cnf(f_1599_3,plain,
hAPP(c_Product__Type_Ofst(U_4985,U_4986),hAPP(hAPP(c_Product__Type_OPair(U_4985,U_4986),U_4987),U_4988)) = U_4987,
inference(clausify,[status(thm)],[f_1599_2]) ).
fof(f_1600_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_1600_2,plain,
! [U_4993,U_4992,U_4991,U_4990,U_4989] :
( U_4992 = U_4993
| hAPP(c_Product__Type_Osnd(U_4989,U_4990),hAPP(hAPP(c_Product__Type_OPair(U_4989,U_4990),U_4991),U_4992)) != U_4993 ),
inference(variable_rename,[status(thm)],[f_1600_1]) ).
fof(f_1600_3,plain,
! [U_4993,U_4992] :
( ! [U_4991,U_4990,U_4989] : hAPP(c_Product__Type_Osnd(U_4989,U_4990),hAPP(hAPP(c_Product__Type_OPair(U_4989,U_4990),U_4991),U_4992)) != U_4993
| U_4992 = U_4993 ),
inference(miniscope,[status(thm)],[f_1600_2]) ).
cnf(f_1600_4,plain,
( hAPP(c_Product__Type_Osnd(U_4989,U_4990),hAPP(hAPP(c_Product__Type_OPair(U_4989,U_4990),U_4991),U_4992)) != U_4993
| U_4992 = U_4993 ),
inference(clausify,[status(thm)],[f_1600_3]) ).
fof(f_1601_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_1601_2,plain,
! [U_4997,U_4996,U_4995,U_4994] : hAPP(c_Product__Type_Osnd(U_4994,U_4995),hAPP(hAPP(c_Product__Type_OPair(U_4994,U_4995),U_4996),U_4997)) = U_4997,
inference(variable_rename,[status(thm)],[f_1601_1]) ).
cnf(f_1601_3,plain,
hAPP(c_Product__Type_Osnd(U_4994,U_4995),hAPP(hAPP(c_Product__Type_OPair(U_4994,U_4995),U_4996),U_4997)) = U_4997,
inference(clausify,[status(thm)],[f_1601_2]) ).
fof(f_1602_1,plain,
! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_b,T_d),V_x_2),
inference(fof_nnf,[status(thm)],[fact_fst__apsnd]) ).
fof(f_1602_2,plain,
! [U_5002,U_5001,U_5000,U_4999,U_4998] : hAPP(c_Product__Type_Ofst(U_4998,U_4999),hAPP(c_Product__Type_Oapsnd(U_5000,U_4999,U_4998,U_5001),U_5002)) = hAPP(c_Product__Type_Ofst(U_4998,U_5000),U_5002),
inference(variable_rename,[status(thm)],[f_1602_1]) ).
cnf(f_1602_3,plain,
hAPP(c_Product__Type_Ofst(U_4998,U_4999),hAPP(c_Product__Type_Oapsnd(U_5000,U_4999,U_4998,U_5001),U_5002)) = hAPP(c_Product__Type_Ofst(U_4998,U_5000),U_5002),
inference(clausify,[status(thm)],[f_1602_2]) ).
fof(f_1603_1,plain,
! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)),
inference(fof_nnf,[status(thm)],[fact_snd__apsnd]) ).
fof(f_1603_2,plain,
! [U_5007,U_5006,U_5005,U_5004,U_5003] : hAPP(c_Product__Type_Osnd(U_5003,U_5004),hAPP(c_Product__Type_Oapsnd(U_5005,U_5004,U_5003,U_5006),U_5007)) = hAPP(U_5006,hAPP(c_Product__Type_Osnd(U_5003,U_5005),U_5007)),
inference(variable_rename,[status(thm)],[f_1603_1]) ).
cnf(f_1603_3,plain,
hAPP(c_Product__Type_Osnd(U_5003,U_5004),hAPP(c_Product__Type_Oapsnd(U_5005,U_5004,U_5003,U_5006),U_5007)) = hAPP(U_5006,hAPP(c_Product__Type_Osnd(U_5003,U_5005),U_5007)),
inference(clausify,[status(thm)],[f_1603_2]) ).
fof(f_1604_1,plain,
! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
( ( hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2)
| hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) != hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) )
& ( hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2))
| hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2) != hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2) ) ),
inference(fof_nnf,[status(thm)],[fact_apsnd__eq__conv]) ).
fof(f_1604_2,plain,
! [U_5013,U_5012,U_5011,U_5010,U_5009,U_5008] :
( ( hAPP(c_Product__Type_Oapsnd(U_5008,U_5009,U_5010,U_5011),U_5012) = hAPP(c_Product__Type_Oapsnd(U_5008,U_5009,U_5010,U_5013),U_5012)
| hAPP(U_5011,hAPP(c_Product__Type_Osnd(U_5010,U_5008),U_5012)) != hAPP(U_5013,hAPP(c_Product__Type_Osnd(U_5010,U_5008),U_5012)) )
& ( hAPP(U_5011,hAPP(c_Product__Type_Osnd(U_5010,U_5008),U_5012)) = hAPP(U_5013,hAPP(c_Product__Type_Osnd(U_5010,U_5008),U_5012))
| hAPP(c_Product__Type_Oapsnd(U_5008,U_5009,U_5010,U_5011),U_5012) != hAPP(c_Product__Type_Oapsnd(U_5008,U_5009,U_5010,U_5013),U_5012) ) ),
inference(variable_rename,[status(thm)],[f_1604_1]) ).
fof(f_1604_3,plain,
( ! [U_5025,U_5023,U_5021,U_5019,U_5017,U_5015] :
( hAPP(c_Product__Type_Oapsnd(U_5015,U_5017,U_5019,U_5021),U_5023) = hAPP(c_Product__Type_Oapsnd(U_5015,U_5017,U_5019,U_5025),U_5023)
| hAPP(U_5021,hAPP(c_Product__Type_Osnd(U_5019,U_5015),U_5023)) != hAPP(U_5025,hAPP(c_Product__Type_Osnd(U_5019,U_5015),U_5023)) )
& ! [U_5024,U_5022,U_5020,U_5018,U_5016,U_5014] :
( hAPP(U_5020,hAPP(c_Product__Type_Osnd(U_5018,U_5014),U_5022)) = hAPP(U_5024,hAPP(c_Product__Type_Osnd(U_5018,U_5014),U_5022))
| hAPP(c_Product__Type_Oapsnd(U_5014,U_5016,U_5018,U_5020),U_5022) != hAPP(c_Product__Type_Oapsnd(U_5014,U_5016,U_5018,U_5024),U_5022) ) ),
inference(miniscope,[status(thm)],[f_1604_2]) ).
cnf(f_1604_4,plain,
( hAPP(U_5020,hAPP(c_Product__Type_Osnd(U_5018,U_5014),U_5022)) = hAPP(U_5024,hAPP(c_Product__Type_Osnd(U_5018,U_5014),U_5022))
| hAPP(c_Product__Type_Oapsnd(U_5014,U_5016,U_5018,U_5020),U_5022) != hAPP(c_Product__Type_Oapsnd(U_5014,U_5016,U_5018,U_5024),U_5022) ),
inference(clausify,[status(thm)],[f_1604_3]) ).
cnf(f_1604_5,plain,
( hAPP(c_Product__Type_Oapsnd(U_5015,U_5017,U_5019,U_5021),U_5023) = hAPP(c_Product__Type_Oapsnd(U_5015,U_5017,U_5019,U_5025),U_5023)
| hAPP(U_5021,hAPP(c_Product__Type_Osnd(U_5019,U_5015),U_5023)) != hAPP(U_5025,hAPP(c_Product__Type_Osnd(U_5019,U_5015),U_5023)) ),
inference(clausify,[status(thm)],[f_1604_3]) ).
fof(f_1605_1,plain,
! [V_p_2,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_b),c_COMBK(T_b,T_c)),V_p_2),
inference(fof_nnf,[status(thm)],[fact_fst__def]) ).
fof(f_1605_2,plain,
! [U_5028,U_5027,U_5026] : hAPP(c_Product__Type_Ofst(U_5026,U_5027),U_5028) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5026,U_5027,U_5026),c_COMBK(U_5026,U_5027)),U_5028),
inference(variable_rename,[status(thm)],[f_1605_1]) ).
cnf(f_1605_3,plain,
hAPP(c_Product__Type_Ofst(U_5026,U_5027),U_5028) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5026,U_5027,U_5026),c_COMBK(U_5026,U_5027)),U_5028),
inference(clausify,[status(thm)],[f_1605_2]) ).
fof(f_1606_1,plain,
! [V_p_2,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_b),hAPP(c_COMBK(tc_fun(T_b,T_b),T_c),c_COMBI(T_b))),V_p_2),
inference(fof_nnf,[status(thm)],[fact_snd__def]) ).
fof(f_1606_2,plain,
! [U_5031,U_5030,U_5029] : hAPP(c_Product__Type_Osnd(U_5029,U_5030),U_5031) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5029,U_5030,U_5030),hAPP(c_COMBK(tc_fun(U_5030,U_5030),U_5029),c_COMBI(U_5030))),U_5031),
inference(variable_rename,[status(thm)],[f_1606_1]) ).
cnf(f_1606_3,plain,
hAPP(c_Product__Type_Osnd(U_5029,U_5030),U_5031) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5029,U_5030,U_5030),hAPP(c_COMBK(tc_fun(U_5030,U_5030),U_5029),c_COMBI(U_5030))),U_5031),
inference(clausify,[status(thm)],[f_1606_2]) ).
fof(f_1607_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_1607_2,plain,
! [U_5035,U_5034,U_5033,U_5032] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5032,U_5033) = U_5035
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5032,U_5033),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5034),U_5035))) ),
inference(variable_rename,[status(thm)],[f_1607_1]) ).
cnf(f_1607_3,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5032,U_5033) = U_5035
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5032,U_5033),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5034),U_5035))) ),
inference(clausify,[status(thm)],[f_1607_2]) ).
fof(f_1608_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_1608_2,plain,
! [U_5039,U_5038,U_5037,U_5036] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5036),U_5037) = U_5038
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5036,U_5037),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5038),U_5039))) ),
inference(variable_rename,[status(thm)],[f_1608_1]) ).
cnf(f_1608_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5036),U_5037) = U_5038
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5036,U_5037),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5038),U_5039))) ),
inference(clausify,[status(thm)],[f_1608_2]) ).
fof(f_1609_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_1609_2,plain,
! [U_5040] : c_Divides_Odivmod__nat(U_5040,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_5040),
inference(variable_rename,[status(thm)],[f_1609_1]) ).
cnf(f_1609_3,plain,
c_Divides_Odivmod__nat(U_5040,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_5040),
inference(clausify,[status(thm)],[f_1609_2]) ).
fof(f_1610_1,plain,
! [V_b,V_a] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(V_a,V_b)),
inference(fof_nnf,[status(thm)],[fact_div__int__def]) ).
fof(f_1610_2,plain,
! [U_5042,U_5041] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5041),U_5042) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_5041,U_5042)),
inference(variable_rename,[status(thm)],[f_1610_1]) ).
cnf(f_1610_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5041),U_5042) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_5041,U_5042)),
inference(clausify,[status(thm)],[f_1610_2]) ).
fof(f_1611_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_1611_2,plain,
! [U_5044,U_5043] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5043,U_5044) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_5043,U_5044)),
inference(variable_rename,[status(thm)],[f_1611_1]) ).
cnf(f_1611_3,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5043,U_5044) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_5043,U_5044)),
inference(clausify,[status(thm)],[f_1611_2]) ).
fof(f_1612_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_1612_2,plain,
! [U_5046,U_5045] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5045,U_5046),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5045),U_5046)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5045,U_5046)))),
inference(variable_rename,[status(thm)],[f_1612_1]) ).
cnf(f_1612_3,plain,
hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5045,U_5046),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5045),U_5046)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5045,U_5046)))),
inference(clausify,[status(thm)],[f_1612_2]) ).
fof(f_1613_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_1613_2,plain,
! [U_5048,U_5047] :
( c_Divides_Odivmod__nat(U_5047,U_5048) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5047)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5047),U_5048)) ),
inference(variable_rename,[status(thm)],[f_1613_1]) ).
cnf(f_1613_3,plain,
( c_Divides_Odivmod__nat(U_5047,U_5048) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5047)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5047),U_5048)) ),
inference(clausify,[status(thm)],[f_1613_2]) ).
fof(f_1614_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_1614_2,plain,
! [U_5050,U_5049] : c_Divides_Odivmod__nat(U_5049,U_5050) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5049),U_5050)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5049,U_5050)),
inference(variable_rename,[status(thm)],[f_1614_1]) ).
cnf(f_1614_3,plain,
c_Divides_Odivmod__nat(U_5049,U_5050) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5049),U_5050)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5049,U_5050)),
inference(clausify,[status(thm)],[f_1614_2]) ).
fof(f_1615_1,plain,
! [V_b,V_a] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(V_a,V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_div__neg__pos]) ).
fof(f_1615_2,plain,
! [U_5052,U_5051] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5051),U_5052) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_5051,U_5052))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5052))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5051),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1615_1]) ).
cnf(f_1615_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5051),U_5052) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_5051,U_5052))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5052))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5051),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1615_2]) ).
fof(f_1616_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_1616_2,plain,
! [U_5054,U_5053] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5053,U_5054) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_5053,U_5054))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5054))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5053),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1616_1]) ).
cnf(f_1616_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5053,U_5054) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_5053,U_5054))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5054))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5053),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1616_2]) ).
fof(f_1617_1,plain,
! [V_b,V_a] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(V_a,V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_div__pos__pos]) ).
fof(f_1617_2,plain,
! [U_5056,U_5055] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5055),U_5056) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_5055,U_5056))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5056))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5055)) ),
inference(variable_rename,[status(thm)],[f_1617_1]) ).
cnf(f_1617_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5055),U_5056) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_5055,U_5056))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5056))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5055)) ),
inference(clausify,[status(thm)],[f_1617_2]) ).
fof(f_1618_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_1618_2,plain,
! [U_5058,U_5057] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5057,U_5058) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_5057,U_5058))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5058))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5057)) ),
inference(variable_rename,[status(thm)],[f_1618_1]) ).
cnf(f_1618_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5057,U_5058) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_5057,U_5058))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5058))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5057)) ),
inference(clausify,[status(thm)],[f_1618_2]) ).
fof(f_1619_1,plain,
! [V_w] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ),
inference(fof_nnf,[status(thm)],[fact_div__pos__pos__1__number__of]) ).
fof(f_1619_2,plain,
! [U_5059] :
( 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_5059)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5059)))
| ~ 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_5059))) ),
inference(variable_rename,[status(thm)],[f_1619_1]) ).
cnf(f_1619_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5059)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5059)))
| ~ 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_5059))) ),
inference(clausify,[status(thm)],[f_1619_2]) ).
fof(f_1620_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_1620_2,plain,
! [U_5060] :
( 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_5060)) = 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_5060)))
| ~ 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_5060))) ),
inference(variable_rename,[status(thm)],[f_1620_1]) ).
cnf(f_1620_3,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_5060)) = 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_5060)))
| ~ 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_5060))) ),
inference(clausify,[status(thm)],[f_1620_2]) ).
fof(f_1621_1,plain,
! [V_b,V_a] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) ),
inference(fof_nnf,[status(thm)],[fact_div__pos__neg]) ).
fof(f_1621_2,plain,
! [U_5062,U_5061] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5061),U_5062) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5061),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5062))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5062),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_5061)) ),
inference(variable_rename,[status(thm)],[f_1621_1]) ).
cnf(f_1621_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5061),U_5062) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5061),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5062))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5062),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_5061)) ),
inference(clausify,[status(thm)],[f_1621_2]) ).
fof(f_1622_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_1622_2,plain,
! [U_5064,U_5063] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5063,U_5064) = 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_5063),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5064))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5064),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_5063)) ),
inference(variable_rename,[status(thm)],[f_1622_1]) ).
cnf(f_1622_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5063,U_5064) = 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_5063),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5064))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5064),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_5063)) ),
inference(clausify,[status(thm)],[f_1622_2]) ).
fof(f_1623_1,plain,
! [V_m_2,V_na_2] :
( ( c_Divides_Odivmod__nat(V_m_2,V_na_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_na_2),V_na_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
| V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Divides_Odivmod__nat(V_m_2,V_na_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_na_2))
& V_na_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(fof_nnf,[status(thm)],[fact_divmod__nat__if]) ).
fof(f_1623_2,plain,
! [U_5066,U_5065] :
( ( c_Divides_Odivmod__nat(U_5066,U_5065) = 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_5066),U_5065),U_5065))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5066),U_5065))
| U_5065 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Divides_Odivmod__nat(U_5066,U_5065) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5066)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5066),U_5065))
& U_5065 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(variable_rename,[status(thm)],[f_1623_1]) ).
fof(f_1623_3,plain,
( ! [U_5070,U_5068] :
( c_Divides_Odivmod__nat(U_5070,U_5068) = 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_5070),U_5068),U_5068))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5070),U_5068))
| U_5068 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_5069,U_5067] :
( c_Divides_Odivmod__nat(U_5069,U_5067) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5069)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5069),U_5067))
& U_5067 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
inference(miniscope,[status(thm)],[f_1623_2]) ).
cnf(f_1623_4,plain,
( U_5067 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Divides_Odivmod__nat(U_5069,U_5067) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5069) ),
inference(clausify,[status(thm)],[f_1623_3]) ).
cnf(f_1623_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5069),U_5067))
| c_Divides_Odivmod__nat(U_5069,U_5067) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5069) ),
inference(clausify,[status(thm)],[f_1623_3]) ).
cnf(f_1623_6,plain,
( c_Divides_Odivmod__nat(U_5070,U_5068) = 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_5070),U_5068),U_5068))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5070),U_5068))
| U_5068 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1623_3]) ).
fof(f_1624_1,plain,
! [V_b,V_a] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(fof_nnf,[status(thm)],[fact_div__neg__neg]) ).
fof(f_1624_2,plain,
! [U_5072,U_5071] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5071),U_5072) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5071),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5072))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5072),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5071),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1624_1]) ).
cnf(f_1624_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5071),U_5072) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5071),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5072))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5072),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5071),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1624_2]) ).
fof(f_1625_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_1625_2,plain,
! [U_5079,U_5078,U_5077,U_5076,U_5075,U_5074,U_5073] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5073),U_5077),U_5074),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_5075),U_5078)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5076),U_5079)),U_5074))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5076),U_5079),U_5074))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5074))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5077,U_5074),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5078),U_5079)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5073,U_5074),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5075),U_5076))) ),
inference(variable_rename,[status(thm)],[f_1625_1]) ).
cnf(f_1625_3,plain,
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5073),U_5077),U_5074),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_5075),U_5078)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5076),U_5079)),U_5074))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5076),U_5079),U_5074))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5074))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5077,U_5074),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5078),U_5079)))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5073,U_5074),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5075),U_5076))) ),
inference(clausify,[status(thm)],[f_1625_2]) ).
fof(f_1626_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_1626_2,plain,
! [U_5081,U_5080] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5080,U_5081) = 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_5080),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5081))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5081),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5080),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(variable_rename,[status(thm)],[f_1626_1]) ).
cnf(f_1626_3,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_5080,U_5081) = 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_5080),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5081))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5081),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5080),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1626_2]) ).
fof(f_1627_1,plain,
! [V_p_2,V_g_2,V_f_2,T_c,T_b] : c_Product__Type_Oprod_Oprod__size(T_b,T_c,V_f_2,V_g_2,V_p_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_prod__size__simp]) ).
fof(f_1627_2,plain,
! [U_5086,U_5085,U_5084,U_5083,U_5082] : c_Product__Type_Oprod_Oprod__size(U_5082,U_5083,U_5084,U_5085,U_5086) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_5084,hAPP(c_Product__Type_Ofst(U_5082,U_5083),U_5086))),hAPP(U_5085,hAPP(c_Product__Type_Osnd(U_5082,U_5083),U_5086)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_1627_1]) ).
cnf(f_1627_3,plain,
c_Product__Type_Oprod_Oprod__size(U_5082,U_5083,U_5084,U_5085,U_5086) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_5084,hAPP(c_Product__Type_Ofst(U_5082,U_5083),U_5086))),hAPP(U_5085,hAPP(c_Product__Type_Osnd(U_5082,U_5083),U_5086)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_1627_2]) ).
fof(f_1628_1,plain,
! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_P_2] :
( ( hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2))))
& hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) )
| ~ hBOOL(hAPP(V_Q_2,V_q_2))
| ~ hBOOL(hAPP(V_P_2,V_p_2)) ),
inference(fof_nnf,[status(thm)],[fact_conjI__realizer]) ).
fof(f_1628_2,plain,
! [U_5092,U_5091,U_5090,U_5089,U_5088,U_5087] :
( ( hBOOL(hAPP(U_5089,hAPP(c_Product__Type_Osnd(U_5091,U_5092),hAPP(hAPP(c_Product__Type_OPair(U_5091,U_5092),U_5088),U_5090))))
& hBOOL(hAPP(U_5087,hAPP(c_Product__Type_Ofst(U_5091,U_5092),hAPP(hAPP(c_Product__Type_OPair(U_5091,U_5092),U_5088),U_5090)))) )
| ~ hBOOL(hAPP(U_5089,U_5090))
| ~ hBOOL(hAPP(U_5087,U_5088)) ),
inference(variable_rename,[status(thm)],[f_1628_1]) ).
cnf(f_1628_3,plain,
( hBOOL(hAPP(U_5087,hAPP(c_Product__Type_Ofst(U_5091,U_5092),hAPP(hAPP(c_Product__Type_OPair(U_5091,U_5092),U_5088),U_5090))))
| ~ hBOOL(hAPP(U_5089,U_5090))
| ~ hBOOL(hAPP(U_5087,U_5088)) ),
inference(clausify,[status(thm)],[f_1628_2]) ).
cnf(f_1628_4,plain,
( hBOOL(hAPP(U_5089,hAPP(c_Product__Type_Osnd(U_5091,U_5092),hAPP(hAPP(c_Product__Type_OPair(U_5091,U_5092),U_5088),U_5090))))
| ~ hBOOL(hAPP(U_5089,U_5090))
| ~ hBOOL(hAPP(U_5087,U_5088)) ),
inference(clausify,[status(thm)],[f_1628_2]) ).
fof(f_1629_1,plain,
! [T_b,T_c,V_x_2,V_y_2,V_P_2] :
( hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))))
| ~ hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_exI__realizer]) ).
fof(f_1629_2,plain,
! [U_5097,U_5096,U_5095,U_5094,U_5093] :
( hBOOL(hAPP(hAPP(U_5093,hAPP(c_Product__Type_Osnd(U_5096,U_5097),hAPP(hAPP(c_Product__Type_OPair(U_5096,U_5097),U_5095),U_5094))),hAPP(c_Product__Type_Ofst(U_5096,U_5097),hAPP(hAPP(c_Product__Type_OPair(U_5096,U_5097),U_5095),U_5094))))
| ~ hBOOL(hAPP(hAPP(U_5093,U_5094),U_5095)) ),
inference(variable_rename,[status(thm)],[f_1629_1]) ).
cnf(f_1629_3,plain,
( hBOOL(hAPP(hAPP(U_5093,hAPP(c_Product__Type_Osnd(U_5096,U_5097),hAPP(hAPP(c_Product__Type_OPair(U_5096,U_5097),U_5095),U_5094))),hAPP(c_Product__Type_Ofst(U_5096,U_5097),hAPP(hAPP(c_Product__Type_OPair(U_5096,U_5097),U_5095),U_5094))))
| ~ hBOOL(hAPP(hAPP(U_5093,U_5094),U_5095)) ),
inference(clausify,[status(thm)],[f_1629_2]) ).
fof(f_1630_1,plain,
! [V_nat] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_nat_Osize_I4_J]) ).
fof(f_1630_2,plain,
! [U_5098] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5098)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_5098)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_1630_1]) ).
cnf(f_1630_3,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5098)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_5098)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_1630_2]) ).
fof(f_1631_1,plain,
! [V_na_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_na_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_na_2)))),
inference(fof_nnf,[status(thm)],[fact_min__Suc__number__of]) ).
fof(f_1631_2,plain,
! [U_5100,U_5099] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5099)),hAPP(c_Nat_OSuc,U_5100)) = 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_5099))),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_5100)))),
inference(variable_rename,[status(thm)],[f_1631_1]) ).
cnf(f_1631_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5099)),hAPP(c_Nat_OSuc,U_5100)) = 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_5099))),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_5100)))),
inference(clausify,[status(thm)],[f_1631_2]) ).
fof(f_1632_1,plain,
! [V_v_2,V_na_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_na_2)),c_Int_Onat)))),
inference(fof_nnf,[status(thm)],[fact_min__number__of__Suc]) ).
fof(f_1632_2,plain,
! [U_5102,U_5101] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5101)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5102)) = 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_5102))),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_5101)),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[f_1632_1]) ).
cnf(f_1632_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5101)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5102)) = 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_5102))),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_5101)),c_Int_Onat)))),
inference(clausify,[status(thm)],[f_1632_2]) ).
fof(f_1633_1,plain,
! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n,
inference(fof_nnf,[status(thm)],[fact_nat__size]) ).
fof(f_1633_2,plain,
! [U_5103] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_5103) = U_5103,
inference(variable_rename,[status(thm)],[f_1633_1]) ).
cnf(f_1633_3,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_5103) = U_5103,
inference(clausify,[status(thm)],[f_1633_2]) ).
fof(f_1634_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_1634_2,plain,
! [U_5105,U_5104] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5104),U_5105),U_5105) = U_5105
| ~ class_Orderings_Olinorder(U_5104) ),
inference(variable_rename,[status(thm)],[f_1634_1]) ).
cnf(f_1634_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5104),U_5105),U_5105) = U_5105
| ~ class_Orderings_Olinorder(U_5104) ),
inference(clausify,[status(thm)],[f_1634_2]) ).
fof(f_1635_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_1635_2,plain,
! [U_5108,U_5107,U_5106] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5106),U_5107),U_5108) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5106),U_5108),U_5107)
| ~ class_Orderings_Olinorder(U_5106) ),
inference(variable_rename,[status(thm)],[f_1635_1]) ).
cnf(f_1635_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5106),U_5107),U_5108) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5106),U_5108),U_5107)
| ~ class_Orderings_Olinorder(U_5106) ),
inference(clausify,[status(thm)],[f_1635_2]) ).
fof(f_1636_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_1636_2,plain,
! [U_5111,U_5110,U_5109] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5109),U_5110),U_5111) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5109),U_5111),U_5110)
| ~ class_Orderings_Olinorder(U_5109) ),
inference(variable_rename,[status(thm)],[f_1636_1]) ).
cnf(f_1636_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5109),U_5110),U_5111) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5109),U_5111),U_5110)
| ~ class_Orderings_Olinorder(U_5109) ),
inference(clausify,[status(thm)],[f_1636_2]) ).
fof(f_1637_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_1637_2,plain,
! [U_5114,U_5113,U_5112] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5112),U_5113),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5112),U_5113),U_5114)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5112),U_5113),U_5114)
| ~ class_Orderings_Olinorder(U_5112) ),
inference(variable_rename,[status(thm)],[f_1637_1]) ).
cnf(f_1637_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5112),U_5113),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5112),U_5113),U_5114)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5112),U_5113),U_5114)
| ~ class_Orderings_Olinorder(U_5112) ),
inference(clausify,[status(thm)],[f_1637_2]) ).
fof(f_1638_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_1638_2,plain,
! [U_5117,U_5116,U_5115] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5115),U_5116),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5115),U_5116),U_5117)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5115),U_5116),U_5117)
| ~ class_Orderings_Olinorder(U_5115) ),
inference(variable_rename,[status(thm)],[f_1638_1]) ).
cnf(f_1638_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5115),U_5116),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5115),U_5116),U_5117)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5115),U_5116),U_5117)
| ~ class_Orderings_Olinorder(U_5115) ),
inference(clausify,[status(thm)],[f_1638_2]) ).
fof(f_1639_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_1639_2,plain,
! [U_5121,U_5120,U_5119,U_5118] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5118),U_5119),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5118),U_5120),U_5121)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5118),U_5120),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5118),U_5119),U_5121))
| ~ class_Orderings_Olinorder(U_5118) ),
inference(variable_rename,[status(thm)],[f_1639_1]) ).
cnf(f_1639_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5118),U_5119),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5118),U_5120),U_5121)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5118),U_5120),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5118),U_5119),U_5121))
| ~ class_Orderings_Olinorder(U_5118) ),
inference(clausify,[status(thm)],[f_1639_2]) ).
fof(f_1640_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_1640_2,plain,
! [U_5125,U_5124,U_5123,U_5122] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5122),U_5123),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5122),U_5124),U_5125)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5122),U_5124),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5122),U_5123),U_5125))
| ~ class_Orderings_Olinorder(U_5122) ),
inference(variable_rename,[status(thm)],[f_1640_1]) ).
cnf(f_1640_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5122),U_5123),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5122),U_5124),U_5125)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5122),U_5124),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5122),U_5123),U_5125))
| ~ class_Orderings_Olinorder(U_5122) ),
inference(clausify,[status(thm)],[f_1640_2]) ).
fof(f_1641_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_1641_2,plain,
! [U_5129,U_5128,U_5127,U_5126] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5126),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5126),U_5127),U_5128)),U_5129) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5126),U_5127),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5126),U_5128),U_5129))
| ~ class_Orderings_Olinorder(U_5126) ),
inference(variable_rename,[status(thm)],[f_1641_1]) ).
cnf(f_1641_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5126),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5126),U_5127),U_5128)),U_5129) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5126),U_5127),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5126),U_5128),U_5129))
| ~ class_Orderings_Olinorder(U_5126) ),
inference(clausify,[status(thm)],[f_1641_2]) ).
fof(f_1642_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_1642_2,plain,
! [U_5133,U_5132,U_5131,U_5130] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5130),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5130),U_5131),U_5132)),U_5133) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5130),U_5131),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5130),U_5132),U_5133))
| ~ class_Orderings_Olinorder(U_5130) ),
inference(variable_rename,[status(thm)],[f_1642_1]) ).
cnf(f_1642_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5130),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5130),U_5131),U_5132)),U_5133) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5130),U_5131),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5130),U_5132),U_5133))
| ~ class_Orderings_Olinorder(U_5130) ),
inference(clausify,[status(thm)],[f_1642_2]) ).
fof(f_1643_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_1643_2,plain,
! [U_5136,U_5135,U_5134] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5134),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5134),U_5135),U_5136)),U_5135))
| ~ class_Orderings_Olinorder(U_5134) ),
inference(variable_rename,[status(thm)],[f_1643_1]) ).
cnf(f_1643_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5134),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5134),U_5135),U_5136)),U_5135))
| ~ class_Orderings_Olinorder(U_5134) ),
inference(clausify,[status(thm)],[f_1643_2]) ).
fof(f_1644_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_1644_2,plain,
! [U_5139,U_5138,U_5137] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5137),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5137),U_5138),U_5139)),U_5139))
| ~ class_Orderings_Olinorder(U_5137) ),
inference(variable_rename,[status(thm)],[f_1644_1]) ).
cnf(f_1644_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5137),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5137),U_5138),U_5139)),U_5139))
| ~ class_Orderings_Olinorder(U_5137) ),
inference(clausify,[status(thm)],[f_1644_2]) ).
fof(f_1645_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) != V_x_2 )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__inf]) ).
fof(f_1645_2,plain,
! [U_5142,U_5141,U_5140] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5140),U_5141),U_5142))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5140),U_5141),U_5142) != U_5141 )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5140),U_5141),U_5142) = U_5141
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5140),U_5141),U_5142)) ) )
| ~ class_Orderings_Olinorder(U_5140) ),
inference(variable_rename,[status(thm)],[f_1645_1]) ).
cnf(f_1645_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5140),U_5141),U_5142) = U_5141
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5140),U_5141),U_5142))
| ~ class_Orderings_Olinorder(U_5140) ),
inference(clausify,[status(thm)],[f_1645_2]) ).
cnf(f_1645_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5140),U_5141),U_5142))
| hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5140),U_5141),U_5142) != U_5141
| ~ class_Orderings_Olinorder(U_5140) ),
inference(clausify,[status(thm)],[f_1645_2]) ).
fof(f_1646_1,plain,
! [V_z_2,V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_y_2),V_z_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_y_2),V_z_2))) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ole__inf__iff]) ).
fof(f_1646_2,plain,
! [U_5146,U_5145,U_5144,U_5143] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5143),U_5144),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5143),U_5145),U_5146)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5143),U_5144),U_5146))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5143),U_5144),U_5145)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5143),U_5144),U_5146))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5143),U_5144),U_5145)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5143),U_5144),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5143),U_5145),U_5146))) ) )
| ~ class_Orderings_Olinorder(U_5143) ),
inference(variable_rename,[status(thm)],[f_1646_1]) ).
cnf(f_1646_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5143),U_5144),U_5145))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5143),U_5144),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5143),U_5145),U_5146)))
| ~ class_Orderings_Olinorder(U_5143) ),
inference(clausify,[status(thm)],[f_1646_2]) ).
cnf(f_1646_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5143),U_5144),U_5146))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5143),U_5144),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5143),U_5145),U_5146)))
| ~ class_Orderings_Olinorder(U_5143) ),
inference(clausify,[status(thm)],[f_1646_2]) ).
cnf(f_1646_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5143),U_5144),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5143),U_5145),U_5146)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5143),U_5144),U_5146))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5143),U_5144),U_5145))
| ~ class_Orderings_Olinorder(U_5143) ),
inference(clausify,[status(thm)],[f_1646_2]) ).
fof(f_1647_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_1647_2,plain,
! [U_5150,U_5149,U_5148,U_5147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5147),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5147),U_5148),U_5150)),U_5149))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5147),U_5148),U_5149))
| ~ class_Orderings_Olinorder(U_5147) ),
inference(variable_rename,[status(thm)],[f_1647_1]) ).
cnf(f_1647_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5147),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5147),U_5148),U_5150)),U_5149))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5147),U_5148),U_5149))
| ~ class_Orderings_Olinorder(U_5147) ),
inference(clausify,[status(thm)],[f_1647_2]) ).
fof(f_1648_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_1648_2,plain,
! [U_5154,U_5153,U_5152,U_5151] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5151),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5151),U_5154),U_5152)),U_5153))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5151),U_5152),U_5153))
| ~ class_Orderings_Olinorder(U_5151) ),
inference(variable_rename,[status(thm)],[f_1648_1]) ).
cnf(f_1648_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5151),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5151),U_5154),U_5152)),U_5153))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5151),U_5152),U_5153))
| ~ class_Orderings_Olinorder(U_5151) ),
inference(clausify,[status(thm)],[f_1648_2]) ).
fof(f_1649_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_1649_2,plain,
! [U_5157,U_5156,U_5155] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5155),U_5156),U_5157) = U_5156
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5155),U_5156),U_5157))
| ~ class_Orderings_Olinorder(U_5155) ),
inference(variable_rename,[status(thm)],[f_1649_1]) ).
cnf(f_1649_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5155),U_5156),U_5157) = U_5156
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5155),U_5156),U_5157))
| ~ class_Orderings_Olinorder(U_5155) ),
inference(clausify,[status(thm)],[f_1649_2]) ).
fof(f_1650_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_1650_2,plain,
! [U_5160,U_5159,U_5158] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5158),U_5160),U_5159) = U_5159
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5158),U_5159),U_5160))
| ~ class_Orderings_Olinorder(U_5158) ),
inference(variable_rename,[status(thm)],[f_1650_1]) ).
cnf(f_1650_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5158),U_5160),U_5159) = U_5159
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5158),U_5159),U_5160))
| ~ class_Orderings_Olinorder(U_5158) ),
inference(clausify,[status(thm)],[f_1650_2]) ).
fof(f_1651_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_1651_2,plain,
! [U_5164,U_5163,U_5162,U_5161] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5161),U_5162),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5161),U_5163),U_5164)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5161),U_5162),U_5164))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5161),U_5162),U_5163))
| ~ class_Orderings_Olinorder(U_5161) ),
inference(variable_rename,[status(thm)],[f_1651_1]) ).
cnf(f_1651_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5161),U_5162),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5161),U_5163),U_5164)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5161),U_5162),U_5164))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5161),U_5162),U_5163))
| ~ class_Orderings_Olinorder(U_5161) ),
inference(clausify,[status(thm)],[f_1651_2]) ).
fof(f_1652_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_1652_2,plain,
! [U_5168,U_5167,U_5166,U_5165] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5165),U_5166),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5165),U_5167),U_5168)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5165),U_5166),U_5168))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5165),U_5166),U_5167))
| ~ class_Orderings_Olinorder(U_5165) ),
inference(variable_rename,[status(thm)],[f_1652_1]) ).
cnf(f_1652_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5165),U_5166),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5165),U_5167),U_5168)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5165),U_5166),U_5168))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5165),U_5166),U_5167))
| ~ class_Orderings_Olinorder(U_5165) ),
inference(clausify,[status(thm)],[f_1652_2]) ).
fof(f_1653_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_1653_2,plain,
! [U_5173,U_5172,U_5171,U_5170,U_5169] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5169),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5169),U_5170),U_5172)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5169),U_5171),U_5173)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5169),U_5172),U_5173))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5169),U_5170),U_5171))
| ~ class_Orderings_Olinorder(U_5169) ),
inference(variable_rename,[status(thm)],[f_1653_1]) ).
cnf(f_1653_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5169),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5169),U_5170),U_5172)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5169),U_5171),U_5173)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5169),U_5172),U_5173))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5169),U_5170),U_5171))
| ~ class_Orderings_Olinorder(U_5169) ),
inference(clausify,[status(thm)],[f_1653_2]) ).
fof(f_1654_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_1654_2,plain,
! [U_5177,U_5176,U_5175,U_5174] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5174),U_5175),U_5177))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5174),U_5175),U_5176)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5174),U_5175),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5174),U_5176),U_5177)))
| ~ class_Orderings_Olinorder(U_5174) ),
inference(variable_rename,[status(thm)],[f_1654_1]) ).
cnf(f_1654_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5174),U_5175),U_5176))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5174),U_5175),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5174),U_5176),U_5177)))
| ~ class_Orderings_Olinorder(U_5174) ),
inference(clausify,[status(thm)],[f_1654_2]) ).
cnf(f_1654_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5174),U_5175),U_5177))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5174),U_5175),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5174),U_5176),U_5177)))
| ~ class_Orderings_Olinorder(U_5174) ),
inference(clausify,[status(thm)],[f_1654_2]) ).
fof(f_1655_1,plain,
! [V_z_2,V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2)) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__le__iff__disj]) ).
fof(f_1655_2,plain,
! [U_5181,U_5180,U_5179,U_5178] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5178),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5178),U_5179),U_5180)),U_5181))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5178),U_5180),U_5181))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5178),U_5179),U_5181)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5178),U_5180),U_5181))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5178),U_5179),U_5181))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5178),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5178),U_5179),U_5180)),U_5181)) ) )
| ~ class_Orderings_Olinorder(U_5178) ),
inference(variable_rename,[status(thm)],[f_1655_1]) ).
cnf(f_1655_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5178),U_5180),U_5181))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5178),U_5179),U_5181))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5178),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5178),U_5179),U_5180)),U_5181))
| ~ class_Orderings_Olinorder(U_5178) ),
inference(clausify,[status(thm)],[f_1655_2]) ).
cnf(f_1655_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5178),U_5179),U_5181))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5178),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5178),U_5179),U_5180)),U_5181))
| ~ class_Orderings_Olinorder(U_5178) ),
inference(clausify,[status(thm)],[f_1655_2]) ).
cnf(f_1655_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5178),U_5180),U_5181))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5178),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5178),U_5179),U_5180)),U_5181))
| ~ class_Orderings_Olinorder(U_5178) ),
inference(clausify,[status(thm)],[f_1655_2]) ).
fof(f_1656_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_1656_2,plain,
! [U_5185,U_5184,U_5183,U_5182] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5182),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5182),U_5185),U_5183)),U_5184))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5182),U_5183),U_5184))
| ~ class_Orderings_Olinorder(U_5182) ),
inference(variable_rename,[status(thm)],[f_1656_1]) ).
cnf(f_1656_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5182),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5182),U_5185),U_5183)),U_5184))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5182),U_5183),U_5184))
| ~ class_Orderings_Olinorder(U_5182) ),
inference(clausify,[status(thm)],[f_1656_2]) ).
fof(f_1657_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_1657_2,plain,
! [U_5189,U_5188,U_5187,U_5186] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5186),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5186),U_5187),U_5189)),U_5188))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5186),U_5187),U_5188))
| ~ class_Orderings_Olinorder(U_5186) ),
inference(variable_rename,[status(thm)],[f_1657_1]) ).
cnf(f_1657_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5186),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5186),U_5187),U_5189)),U_5188))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5186),U_5187),U_5188))
| ~ class_Orderings_Olinorder(U_5186) ),
inference(clausify,[status(thm)],[f_1657_2]) ).
fof(f_1658_1,plain,
! [V_z_2,V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2)) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__less__iff__disj]) ).
fof(f_1658_2,plain,
! [U_5193,U_5192,U_5191,U_5190] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5190),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5190),U_5191),U_5192)),U_5193))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5190),U_5192),U_5193))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5190),U_5191),U_5193)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5190),U_5192),U_5193))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5190),U_5191),U_5193))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5190),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5190),U_5191),U_5192)),U_5193)) ) )
| ~ class_Orderings_Olinorder(U_5190) ),
inference(variable_rename,[status(thm)],[f_1658_1]) ).
cnf(f_1658_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5190),U_5192),U_5193))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5190),U_5191),U_5193))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5190),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5190),U_5191),U_5192)),U_5193))
| ~ class_Orderings_Olinorder(U_5190) ),
inference(clausify,[status(thm)],[f_1658_2]) ).
cnf(f_1658_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5190),U_5191),U_5193))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5190),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5190),U_5191),U_5192)),U_5193))
| ~ class_Orderings_Olinorder(U_5190) ),
inference(clausify,[status(thm)],[f_1658_2]) ).
cnf(f_1658_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5190),U_5192),U_5193))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5190),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5190),U_5191),U_5192)),U_5193))
| ~ class_Orderings_Olinorder(U_5190) ),
inference(clausify,[status(thm)],[f_1658_2]) ).
fof(f_1659_1,plain,
! [V_y_2,V_x_2,V_z_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2))) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__less__iff__conj]) ).
fof(f_1659_2,plain,
! [U_5197,U_5196,U_5195,U_5194] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5194),U_5195),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5194),U_5196),U_5197)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5194),U_5195),U_5197))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5194),U_5195),U_5196)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5194),U_5195),U_5197))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5194),U_5195),U_5196)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5194),U_5195),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5194),U_5196),U_5197))) ) )
| ~ class_Orderings_Olinorder(U_5194) ),
inference(variable_rename,[status(thm)],[f_1659_1]) ).
cnf(f_1659_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5194),U_5195),U_5196))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5194),U_5195),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5194),U_5196),U_5197)))
| ~ class_Orderings_Olinorder(U_5194) ),
inference(clausify,[status(thm)],[f_1659_2]) ).
cnf(f_1659_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5194),U_5195),U_5197))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5194),U_5195),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5194),U_5196),U_5197)))
| ~ class_Orderings_Olinorder(U_5194) ),
inference(clausify,[status(thm)],[f_1659_2]) ).
cnf(f_1659_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5194),U_5195),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5194),U_5196),U_5197)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5194),U_5195),U_5197))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5194),U_5195),U_5196))
| ~ class_Orderings_Olinorder(U_5194) ),
inference(clausify,[status(thm)],[f_1659_2]) ).
fof(f_1660_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_1660_2,plain,
! [U_5201,U_5200,U_5199,U_5198] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5198),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5198),U_5199),U_5200)),U_5201) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5198),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5198),U_5199),U_5201)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5198),U_5200),U_5201))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_5198) ),
inference(variable_rename,[status(thm)],[f_1660_1]) ).
cnf(f_1660_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5198),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5198),U_5199),U_5200)),U_5201) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5198),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5198),U_5199),U_5201)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5198),U_5200),U_5201))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_5198) ),
inference(clausify,[status(thm)],[f_1660_2]) ).
fof(f_1661_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_1661_2,plain,
! [U_5205,U_5204,U_5203,U_5202] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5202),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5202),U_5203),U_5204)),U_5205) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5202),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5202),U_5203),U_5205)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5202),U_5204),U_5205))
| ~ class_Groups_Oordered__ab__group__add(U_5202) ),
inference(variable_rename,[status(thm)],[f_1661_1]) ).
cnf(f_1661_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5202),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5202),U_5203),U_5204)),U_5205) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5202),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5202),U_5203),U_5205)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5202),U_5204),U_5205))
| ~ class_Groups_Oordered__ab__group__add(U_5202) ),
inference(clausify,[status(thm)],[f_1661_2]) ).
fof(f_1662_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_1662_2,plain,
! [U_5206] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5206) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1662_1]) ).
cnf(f_1662_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5206) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1662_2]) ).
fof(f_1663_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_1663_2,plain,
! [U_5207] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_5207),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1663_1]) ).
cnf(f_1663_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_5207),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1663_2]) ).
fof(f_1664_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_1664_2,plain,
! [U_5209,U_5208] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5208)),hAPP(c_Nat_OSuc,U_5209)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_5208),U_5209)),
inference(variable_rename,[status(thm)],[f_1664_1]) ).
cnf(f_1664_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5208)),hAPP(c_Nat_OSuc,U_5209)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_5208),U_5209)),
inference(clausify,[status(thm)],[f_1664_2]) ).
fof(f_1665_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_1665_2,plain,
! [U_5212,U_5211,U_5210] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5210),U_5211)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5212),U_5211)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_5210),U_5212)),U_5211),
inference(variable_rename,[status(thm)],[f_1665_1]) ).
cnf(f_1665_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5210),U_5211)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5212),U_5211)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_5210),U_5212)),U_5211),
inference(clausify,[status(thm)],[f_1665_2]) ).
fof(f_1666_1,plain,
! [V_na_2,V_m_2,V_f_2,T_b,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,V_na_2)) = hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_m_2),V_na_2))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__of__mono]) ).
fof(f_1666_2,plain,
! [U_5217,U_5216,U_5215,U_5214,U_5213] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5213),hAPP(U_5215,U_5216)),hAPP(U_5215,U_5217)) = hAPP(U_5215,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5214),U_5216),U_5217))
| ~ c_Orderings_Oorder__class_Omono(U_5214,U_5213,U_5215)
| ~ class_Orderings_Olinorder(U_5214)
| ~ class_Orderings_Olinorder(U_5213) ),
inference(variable_rename,[status(thm)],[f_1666_1]) ).
cnf(f_1666_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5213),hAPP(U_5215,U_5216)),hAPP(U_5215,U_5217)) = hAPP(U_5215,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5214),U_5216),U_5217))
| ~ c_Orderings_Oorder__class_Omono(U_5214,U_5213,U_5215)
| ~ class_Orderings_Olinorder(U_5214)
| ~ class_Orderings_Olinorder(U_5213) ),
inference(clausify,[status(thm)],[f_1666_2]) ).
fof(f_1667_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_1667_2,plain,
! [U_5220,U_5219,U_5218] :
( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5218),hAPP(c_Int_Onumber__class_Onumber__of(U_5218),U_5219)),hAPP(c_Int_Onumber__class_Onumber__of(U_5218),U_5220)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5218),U_5220)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5218),hAPP(c_Int_Onumber__class_Onumber__of(U_5218),U_5219)),hAPP(c_Int_Onumber__class_Onumber__of(U_5218),U_5220))) )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5218),hAPP(c_Int_Onumber__class_Onumber__of(U_5218),U_5219)),hAPP(c_Int_Onumber__class_Onumber__of(U_5218),U_5220)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5218),U_5219)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5218),hAPP(c_Int_Onumber__class_Onumber__of(U_5218),U_5219)),hAPP(c_Int_Onumber__class_Onumber__of(U_5218),U_5220))) ) )
| ~ class_Orderings_Oord(U_5218)
| ~ class_Int_Onumber(U_5218) ),
inference(variable_rename,[status(thm)],[f_1667_1]) ).
cnf(f_1667_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5218),hAPP(c_Int_Onumber__class_Onumber__of(U_5218),U_5219)),hAPP(c_Int_Onumber__class_Onumber__of(U_5218),U_5220)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5218),U_5219)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5218),hAPP(c_Int_Onumber__class_Onumber__of(U_5218),U_5219)),hAPP(c_Int_Onumber__class_Onumber__of(U_5218),U_5220)))
| ~ class_Orderings_Oord(U_5218)
| ~ class_Int_Onumber(U_5218) ),
inference(clausify,[status(thm)],[f_1667_2]) ).
cnf(f_1667_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5218),hAPP(c_Int_Onumber__class_Onumber__of(U_5218),U_5219)),hAPP(c_Int_Onumber__class_Onumber__of(U_5218),U_5220)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5218),U_5220)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5218),hAPP(c_Int_Onumber__class_Onumber__of(U_5218),U_5219)),hAPP(c_Int_Onumber__class_Onumber__of(U_5218),U_5220)))
| ~ class_Orderings_Oord(U_5218)
| ~ class_Int_Onumber(U_5218) ),
inference(clausify,[status(thm)],[f_1667_2]) ).
fof(f_1668_1,plain,
! [V_n,V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)),
inference(fof_nnf,[status(thm)],[fact_div__nat__def]) ).
fof(f_1668_2,plain,
! [U_5222,U_5221] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5221),U_5222) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_5221,U_5222)),
inference(variable_rename,[status(thm)],[f_1668_1]) ).
cnf(f_1668_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5221),U_5222) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_5221,U_5222)),
inference(clausify,[status(thm)],[f_1668_2]) ).
fof(f_1669_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_1669_2,plain,
! [U_5224,U_5223] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5223,U_5224) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_5223,U_5224)),
inference(variable_rename,[status(thm)],[f_1669_1]) ).
cnf(f_1669_3,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5223,U_5224) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_5223,U_5224)),
inference(clausify,[status(thm)],[f_1669_2]) ).
fof(f_1670_1,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_nat_Osize_I3_J]) ).
cnf(f_1670_2,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1670_1]) ).
fof(f_1671_1,plain,
! [V_qr_2,V_na_2,V_m_2] :
( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_na_2),V_qr_2))
| ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_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_na_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_na_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) )
& V_na_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_na_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_na_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)) )
& ( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_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_na_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_na_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) ) )
| V_na_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_na_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_na_2)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),V_qr_2)) )
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_na_2),V_qr_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__def]) ).
fof(f_1671_2,plain,
! [U_5227,U_5226,U_5225] :
( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5225,U_5226),U_5227))
| ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5227)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5226),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5227))) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5226)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5227)),U_5226))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5227))) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5226)) ) )
& U_5226 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5227) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_5226 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| U_5225 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5227)),U_5226)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5227)) )
& ( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5227)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5226),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5227))) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5226)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5227)),U_5226))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5227))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5226)) ) )
| U_5226 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5227) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5226 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& U_5225 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5227)),U_5226)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5227)) )
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5225,U_5226),U_5227)) ) ),
inference(variable_rename,[status(thm)],[f_1671_1]) ).
fof(f_1671_3,plain,
( ! [U_5233,U_5231,U_5229] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5229,U_5231),U_5233))
| ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5231),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233))) )
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5231)) )
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233)),U_5231))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233))) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5231)) ) )
& U_5231 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5233) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_5231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| U_5229 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5233)),U_5231)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233)) )
& ! [U_5232,U_5230,U_5228] :
( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5232)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5230),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5232))) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5230)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5232)),U_5230))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5232))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5230)) ) )
| U_5230 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5232) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5230 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& U_5228 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5232)),U_5230)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5232)) )
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5228,U_5230),U_5232)) ) ),
inference(miniscope,[status(thm)],[f_1671_2]) ).
cnf(f_1671_4,plain,
( U_5228 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5232)),U_5230)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5232))
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5228,U_5230),U_5232)) ),
inference(clausify,[status(thm)],[f_1671_3]) ).
cnf(f_1671_5,plain,
( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5232) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5230 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5228,U_5230),U_5232)) ),
inference(clausify,[status(thm)],[f_1671_3]) ).
cnf(f_1671_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5232)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5230))
| U_5230 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5228,U_5230),U_5232)) ),
inference(clausify,[status(thm)],[f_1671_3]) ).
cnf(f_1671_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5232)),U_5230))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5230))
| U_5230 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5228,U_5230),U_5232)) ),
inference(clausify,[status(thm)],[f_1671_3]) ).
cnf(f_1671_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5230),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5232)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5230))
| U_5230 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5228,U_5230),U_5232)) ),
inference(clausify,[status(thm)],[f_1671_3]) ).
cnf(f_1671_9,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5232)),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_5230))
| U_5230 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5228,U_5230),U_5232)) ),
inference(clausify,[status(thm)],[f_1671_3]) ).
cnf(f_1671_10,plain,
( U_5231 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5229 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5233)),U_5231)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5229,U_5231),U_5233)) ),
inference(clausify,[status(thm)],[f_1671_3]) ).
cnf(f_1671_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5231))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5231))
| U_5231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5229 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5233)),U_5231)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5229,U_5231),U_5233)) ),
inference(clausify,[status(thm)],[f_1671_3]) ).
cnf(f_1671_12,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5231),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5231))
| U_5231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5229 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5233)),U_5231)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5229,U_5231),U_5233)) ),
inference(clausify,[status(thm)],[f_1671_3]) ).
cnf(f_1671_13,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5231))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233)),U_5231))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233)))
| U_5231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5229 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5233)),U_5231)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5229,U_5231),U_5233)) ),
inference(clausify,[status(thm)],[f_1671_3]) ).
cnf(f_1671_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5231),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233)),U_5231))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233)))
| U_5231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5229 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5233)),U_5231)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5229,U_5231),U_5233)) ),
inference(clausify,[status(thm)],[f_1671_3]) ).
cnf(f_1671_15,plain,
( U_5231 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5233) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5229 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5233)),U_5231)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5229,U_5231),U_5233)) ),
inference(clausify,[status(thm)],[f_1671_3]) ).
cnf(f_1671_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5231))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5231))
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5233) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5229 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5233)),U_5231)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5229,U_5231),U_5233)) ),
inference(clausify,[status(thm)],[f_1671_3]) ).
cnf(f_1671_17,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5231),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5231))
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5233) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5229 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5233)),U_5231)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5229,U_5231),U_5233)) ),
inference(clausify,[status(thm)],[f_1671_3]) ).
cnf(f_1671_18,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5231))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233)),U_5231))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233)))
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5233) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5229 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5233)),U_5231)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5229,U_5231),U_5233)) ),
inference(clausify,[status(thm)],[f_1671_3]) ).
cnf(f_1671_19,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5231),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233)),U_5231))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233)))
| hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5233) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_5229 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_5233)),U_5231)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_5233))
| hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_5229,U_5231),U_5233)) ),
inference(clausify,[status(thm)],[f_1671_3]) ).
fof(f_1672_1,plain,
! [V_na_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_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_na_2)),V_m_2),
inference(fof_nnf,[status(thm)],[fact_min__Suc2]) ).
fof(f_1672_2,plain,
! [U_5235,U_5234] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_5234),hAPP(c_Nat_OSuc,U_5235)) = 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_5235)),U_5234),
inference(variable_rename,[status(thm)],[f_1672_1]) ).
cnf(f_1672_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_5234),hAPP(c_Nat_OSuc,U_5235)) = 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_5235)),U_5234),
inference(clausify,[status(thm)],[f_1672_2]) ).
fof(f_1673_1,plain,
! [V_m_2,V_na_2] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_na_2)),V_m_2),
inference(fof_nnf,[status(thm)],[fact_min__Suc1]) ).
fof(f_1673_2,plain,
! [U_5237,U_5236] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5236)),U_5237) = 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_5236)),U_5237),
inference(variable_rename,[status(thm)],[f_1673_1]) ).
cnf(f_1673_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5236)),U_5237) = 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_5236)),U_5237),
inference(clausify,[status(thm)],[f_1673_2]) ).
fof(f_1674_1,plain,
! [V_s,V_k] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(V_k),V_s))),V_k))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_k)) ),
inference(fof_nnf,[status(thm)],[fact_range]) ).
fof(f_1674_2,plain,
! [U_5239,U_5238] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(U_5238),U_5239))),U_5238))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_5238)) ),
inference(variable_rename,[status(thm)],[f_1674_1]) ).
cnf(f_1674_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Orange(U_5238),U_5239))),U_5238))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_5238)) ),
inference(clausify,[status(thm)],[f_1674_2]) ).
fof(f_1675_1,plain,
! [T_b] :
( c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b))
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__ord__min]) ).
fof(f_1675_2,plain,
! [U_5240] :
( c_Orderings_Oord__class_Omin(U_5240) = c_Orderings_Oord_Omin(U_5240,c_Orderings_Oord__class_Oless__eq(U_5240))
| ~ class_Orderings_Oord(U_5240) ),
inference(variable_rename,[status(thm)],[f_1675_1]) ).
cnf(f_1675_3,plain,
( c_Orderings_Oord__class_Omin(U_5240) = c_Orderings_Oord_Omin(U_5240,c_Orderings_Oord__class_Oless__eq(U_5240))
| ~ class_Orderings_Oord(U_5240) ),
inference(clausify,[status(thm)],[f_1675_2]) ).
fof(f_1676_1,plain,
! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Product__Type_Oprod_Oprod__rec(T_c,T_d,T_b,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
inference(fof_nnf,[status(thm)],[fact_prod_Orecs]) ).
fof(f_1676_2,plain,
! [U_5246,U_5245,U_5244,U_5243,U_5242,U_5241] : c_Product__Type_Oprod_Oprod__rec(U_5241,U_5242,U_5243,U_5244,hAPP(hAPP(c_Product__Type_OPair(U_5241,U_5242),U_5245),U_5246)) = hAPP(hAPP(U_5244,U_5245),U_5246),
inference(variable_rename,[status(thm)],[f_1676_1]) ).
cnf(f_1676_3,plain,
c_Product__Type_Oprod_Oprod__rec(U_5241,U_5242,U_5243,U_5244,hAPP(hAPP(c_Product__Type_OPair(U_5241,U_5242),U_5245),U_5246)) = hAPP(hAPP(U_5244,U_5245),U_5246),
inference(clausify,[status(thm)],[f_1676_2]) ).
fof(f_1677_1,plain,
! [V_v_2,V_na_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_na_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_na_2)),c_Int_Onat)))),
inference(fof_nnf,[status(thm)],[fact_max__number__of__Suc]) ).
fof(f_1677_2,plain,
! [U_5248,U_5247] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5247)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5248)) = 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_5248))),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_5247))),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_5247)),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[f_1677_1]) ).
cnf(f_1677_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5247)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5248)) = 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_5248))),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_5247))),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_5247)),c_Int_Onat)))),
inference(clausify,[status(thm)],[f_1677_2]) ).
fof(f_1678_1,plain,
! [V_na_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_na_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_na_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_na_2)))),
inference(fof_nnf,[status(thm)],[fact_max__Suc__number__of]) ).
fof(f_1678_2,plain,
! [U_5250,U_5249] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5249)),hAPP(c_Nat_OSuc,U_5250)) = 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_5249))),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_5250))),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_5250)))),
inference(variable_rename,[status(thm)],[f_1678_1]) ).
cnf(f_1678_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5249)),hAPP(c_Nat_OSuc,U_5250)) = 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_5249))),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_5250))),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_5250)))),
inference(clausify,[status(thm)],[f_1678_2]) ).
fof(f_1679_1,plain,
! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_e,T_d),V_x_2))),
inference(fof_nnf,[status(thm)],[fact_apsnd__apfst]) ).
fof(f_1679_2,plain,
! [U_5257,U_5256,U_5255,U_5254,U_5253,U_5252,U_5251] : hAPP(c_Product__Type_Oapsnd(U_5251,U_5252,U_5253,U_5254),hAPP(c_Product__Type_Oapfst(U_5255,U_5253,U_5251,U_5256),U_5257)) = hAPP(hAPP(c_Product__Type_OPair(U_5253,U_5252),hAPP(U_5256,hAPP(c_Product__Type_Ofst(U_5255,U_5251),U_5257))),hAPP(U_5254,hAPP(c_Product__Type_Osnd(U_5255,U_5251),U_5257))),
inference(variable_rename,[status(thm)],[f_1679_1]) ).
cnf(f_1679_3,plain,
hAPP(c_Product__Type_Oapsnd(U_5251,U_5252,U_5253,U_5254),hAPP(c_Product__Type_Oapfst(U_5255,U_5253,U_5251,U_5256),U_5257)) = hAPP(hAPP(c_Product__Type_OPair(U_5253,U_5252),hAPP(U_5256,hAPP(c_Product__Type_Ofst(U_5255,U_5251),U_5257))),hAPP(U_5254,hAPP(c_Product__Type_Osnd(U_5255,U_5251),U_5257))),
inference(clausify,[status(thm)],[f_1679_2]) ).
fof(f_1680_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_1680_2,plain,
! [U_5261,U_5260,U_5259,U_5258] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5258),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5258),U_5259),U_5260)),U_5261) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5258),U_5259),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5258),U_5260),U_5261))
| ~ class_Orderings_Olinorder(U_5258) ),
inference(variable_rename,[status(thm)],[f_1680_1]) ).
cnf(f_1680_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5258),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5258),U_5259),U_5260)),U_5261) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5258),U_5259),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5258),U_5260),U_5261))
| ~ class_Orderings_Olinorder(U_5258) ),
inference(clausify,[status(thm)],[f_1680_2]) ).
fof(f_1681_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_1681_2,plain,
! [U_5265,U_5264,U_5263,U_5262] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5262),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5262),U_5263),U_5264)),U_5265) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5262),U_5263),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5262),U_5264),U_5265))
| ~ class_Orderings_Olinorder(U_5262) ),
inference(variable_rename,[status(thm)],[f_1681_1]) ).
cnf(f_1681_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5262),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5262),U_5263),U_5264)),U_5265) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5262),U_5263),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5262),U_5264),U_5265))
| ~ class_Orderings_Olinorder(U_5262) ),
inference(clausify,[status(thm)],[f_1681_2]) ).
fof(f_1682_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_1682_2,plain,
! [U_5269,U_5268,U_5267,U_5266] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5266),U_5267),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5266),U_5268),U_5269)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5266),U_5268),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5266),U_5267),U_5269))
| ~ class_Orderings_Olinorder(U_5266) ),
inference(variable_rename,[status(thm)],[f_1682_1]) ).
cnf(f_1682_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5266),U_5267),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5266),U_5268),U_5269)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5266),U_5268),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5266),U_5267),U_5269))
| ~ class_Orderings_Olinorder(U_5266) ),
inference(clausify,[status(thm)],[f_1682_2]) ).
fof(f_1683_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_1683_2,plain,
! [U_5273,U_5272,U_5271,U_5270] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5270),U_5271),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5270),U_5272),U_5273)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5270),U_5272),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5270),U_5271),U_5273))
| ~ class_Orderings_Olinorder(U_5270) ),
inference(variable_rename,[status(thm)],[f_1683_1]) ).
cnf(f_1683_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5270),U_5271),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5270),U_5272),U_5273)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5270),U_5272),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5270),U_5271),U_5273))
| ~ class_Orderings_Olinorder(U_5270) ),
inference(clausify,[status(thm)],[f_1683_2]) ).
fof(f_1684_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_1684_2,plain,
! [U_5276,U_5275,U_5274] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5274),U_5275),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5274),U_5275),U_5276)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5274),U_5275),U_5276)
| ~ class_Orderings_Olinorder(U_5274) ),
inference(variable_rename,[status(thm)],[f_1684_1]) ).
cnf(f_1684_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5274),U_5275),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5274),U_5275),U_5276)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5274),U_5275),U_5276)
| ~ class_Orderings_Olinorder(U_5274) ),
inference(clausify,[status(thm)],[f_1684_2]) ).
fof(f_1685_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_1685_2,plain,
! [U_5279,U_5278,U_5277] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5277),U_5278),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5277),U_5278),U_5279)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5277),U_5278),U_5279)
| ~ class_Orderings_Olinorder(U_5277) ),
inference(variable_rename,[status(thm)],[f_1685_1]) ).
cnf(f_1685_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5277),U_5278),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5277),U_5278),U_5279)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5277),U_5278),U_5279)
| ~ class_Orderings_Olinorder(U_5277) ),
inference(clausify,[status(thm)],[f_1685_2]) ).
fof(f_1686_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_1686_2,plain,
! [U_5282,U_5281,U_5280] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5280),U_5281),U_5282) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5280),U_5282),U_5281)
| ~ class_Orderings_Olinorder(U_5280) ),
inference(variable_rename,[status(thm)],[f_1686_1]) ).
cnf(f_1686_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5280),U_5281),U_5282) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5280),U_5282),U_5281)
| ~ class_Orderings_Olinorder(U_5280) ),
inference(clausify,[status(thm)],[f_1686_2]) ).
fof(f_1687_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_1687_2,plain,
! [U_5285,U_5284,U_5283] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5283),U_5284),U_5285) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5283),U_5285),U_5284)
| ~ class_Orderings_Olinorder(U_5283) ),
inference(variable_rename,[status(thm)],[f_1687_1]) ).
cnf(f_1687_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5283),U_5284),U_5285) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5283),U_5285),U_5284)
| ~ class_Orderings_Olinorder(U_5283) ),
inference(clausify,[status(thm)],[f_1687_2]) ).
fof(f_1688_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_1688_2,plain,
! [U_5287,U_5286] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5286),U_5287),U_5287) = U_5287
| ~ class_Orderings_Olinorder(U_5286) ),
inference(variable_rename,[status(thm)],[f_1688_1]) ).
cnf(f_1688_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5286),U_5287),U_5287) = U_5287
| ~ class_Orderings_Olinorder(U_5286) ),
inference(clausify,[status(thm)],[f_1688_2]) ).
fof(f_1689_1,plain,
! [V_y_2,V_x_2,V_z_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2))) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__max__iff__disj]) ).
fof(f_1689_2,plain,
! [U_5291,U_5290,U_5289,U_5288] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5288),U_5289),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5288),U_5290),U_5291)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5288),U_5289),U_5291))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5288),U_5289),U_5290)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5288),U_5289),U_5291))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5288),U_5289),U_5290))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5288),U_5289),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5288),U_5290),U_5291))) ) )
| ~ class_Orderings_Olinorder(U_5288) ),
inference(variable_rename,[status(thm)],[f_1689_1]) ).
cnf(f_1689_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5288),U_5289),U_5291))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5288),U_5289),U_5290))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5288),U_5289),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5288),U_5290),U_5291)))
| ~ class_Orderings_Olinorder(U_5288) ),
inference(clausify,[status(thm)],[f_1689_2]) ).
cnf(f_1689_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5288),U_5289),U_5290))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5288),U_5289),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5288),U_5290),U_5291)))
| ~ class_Orderings_Olinorder(U_5288) ),
inference(clausify,[status(thm)],[f_1689_2]) ).
cnf(f_1689_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5288),U_5289),U_5291))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5288),U_5289),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5288),U_5290),U_5291)))
| ~ class_Orderings_Olinorder(U_5288) ),
inference(clausify,[status(thm)],[f_1689_2]) ).
fof(f_1690_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_1690_2,plain,
! [U_5295,U_5294,U_5293,U_5292] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5292),U_5294),U_5295))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5292),U_5293),U_5295)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5292),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5292),U_5293),U_5294)),U_5295))
| ~ class_Orderings_Olinorder(U_5292) ),
inference(variable_rename,[status(thm)],[f_1690_1]) ).
cnf(f_1690_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5292),U_5293),U_5295))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5292),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5292),U_5293),U_5294)),U_5295))
| ~ class_Orderings_Olinorder(U_5292) ),
inference(clausify,[status(thm)],[f_1690_2]) ).
cnf(f_1690_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5292),U_5294),U_5295))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5292),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5292),U_5293),U_5294)),U_5295))
| ~ class_Orderings_Olinorder(U_5292) ),
inference(clausify,[status(thm)],[f_1690_2]) ).
fof(f_1691_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_1691_2,plain,
! [U_5300,U_5299,U_5298,U_5297,U_5296] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5296),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5296),U_5297),U_5299)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5296),U_5298),U_5300)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5296),U_5299),U_5300))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5296),U_5297),U_5298))
| ~ class_Orderings_Olinorder(U_5296) ),
inference(variable_rename,[status(thm)],[f_1691_1]) ).
cnf(f_1691_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5296),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5296),U_5297),U_5299)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5296),U_5298),U_5300)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5296),U_5299),U_5300))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5296),U_5297),U_5298))
| ~ class_Orderings_Olinorder(U_5296) ),
inference(clausify,[status(thm)],[f_1691_2]) ).
fof(f_1692_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_1692_2,plain,
! [U_5304,U_5303,U_5302,U_5301] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5301),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5301),U_5302),U_5304)),U_5303))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5301),U_5304),U_5303))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5301),U_5302),U_5303))
| ~ class_Orderings_Olinorder(U_5301) ),
inference(variable_rename,[status(thm)],[f_1692_1]) ).
cnf(f_1692_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5301),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5301),U_5302),U_5304)),U_5303))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5301),U_5304),U_5303))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5301),U_5302),U_5303))
| ~ class_Orderings_Olinorder(U_5301) ),
inference(clausify,[status(thm)],[f_1692_2]) ).
fof(f_1693_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_1693_2,plain,
! [U_5308,U_5307,U_5306,U_5305] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5305),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5305),U_5306),U_5308)),U_5307))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5305),U_5308),U_5307))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5305),U_5306),U_5307))
| ~ class_Orderings_Olinorder(U_5305) ),
inference(variable_rename,[status(thm)],[f_1693_1]) ).
cnf(f_1693_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5305),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5305),U_5306),U_5308)),U_5307))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5305),U_5308),U_5307))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5305),U_5306),U_5307))
| ~ class_Orderings_Olinorder(U_5305) ),
inference(clausify,[status(thm)],[f_1693_2]) ).
fof(f_1694_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_1694_2,plain,
! [U_5311,U_5310,U_5309] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5309),U_5311),U_5310) = U_5311
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5309),U_5310),U_5311))
| ~ class_Orderings_Olinorder(U_5309) ),
inference(variable_rename,[status(thm)],[f_1694_1]) ).
cnf(f_1694_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5309),U_5311),U_5310) = U_5311
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5309),U_5310),U_5311))
| ~ class_Orderings_Olinorder(U_5309) ),
inference(clausify,[status(thm)],[f_1694_2]) ).
fof(f_1695_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_1695_2,plain,
! [U_5314,U_5313,U_5312] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5312),U_5313),U_5314) = U_5314
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5312),U_5313),U_5314))
| ~ class_Orderings_Olinorder(U_5312) ),
inference(variable_rename,[status(thm)],[f_1695_1]) ).
cnf(f_1695_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5312),U_5313),U_5314) = U_5314
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5312),U_5313),U_5314))
| ~ class_Orderings_Olinorder(U_5312) ),
inference(clausify,[status(thm)],[f_1695_2]) ).
fof(f_1696_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_1696_2,plain,
! [U_5318,U_5317,U_5316,U_5315] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5315),U_5316),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5315),U_5318),U_5317)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5315),U_5316),U_5317))
| ~ class_Orderings_Olinorder(U_5315) ),
inference(variable_rename,[status(thm)],[f_1696_1]) ).
cnf(f_1696_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5315),U_5316),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5315),U_5318),U_5317)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5315),U_5316),U_5317))
| ~ class_Orderings_Olinorder(U_5315) ),
inference(clausify,[status(thm)],[f_1696_2]) ).
fof(f_1697_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_1697_2,plain,
! [U_5322,U_5321,U_5320,U_5319] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5319),U_5320),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5319),U_5321),U_5322)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5319),U_5320),U_5321))
| ~ class_Orderings_Olinorder(U_5319) ),
inference(variable_rename,[status(thm)],[f_1697_1]) ).
cnf(f_1697_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5319),U_5320),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5319),U_5321),U_5322)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5319),U_5320),U_5321))
| ~ class_Orderings_Olinorder(U_5319) ),
inference(clausify,[status(thm)],[f_1697_2]) ).
fof(f_1698_1,plain,
! [V_z_2,V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2)) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ole__sup__iff]) ).
fof(f_1698_2,plain,
! [U_5326,U_5325,U_5324,U_5323] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5323),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5323),U_5324),U_5325)),U_5326))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5323),U_5325),U_5326))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5323),U_5324),U_5326)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5323),U_5325),U_5326))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5323),U_5324),U_5326)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5323),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5323),U_5324),U_5325)),U_5326)) ) )
| ~ class_Orderings_Olinorder(U_5323) ),
inference(variable_rename,[status(thm)],[f_1698_1]) ).
cnf(f_1698_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5323),U_5324),U_5326))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5323),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5323),U_5324),U_5325)),U_5326))
| ~ class_Orderings_Olinorder(U_5323) ),
inference(clausify,[status(thm)],[f_1698_2]) ).
cnf(f_1698_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5323),U_5325),U_5326))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5323),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5323),U_5324),U_5325)),U_5326))
| ~ class_Orderings_Olinorder(U_5323) ),
inference(clausify,[status(thm)],[f_1698_2]) ).
cnf(f_1698_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5323),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5323),U_5324),U_5325)),U_5326))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5323),U_5325),U_5326))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5323),U_5324),U_5326))
| ~ class_Orderings_Olinorder(U_5323) ),
inference(clausify,[status(thm)],[f_1698_2]) ).
fof(f_1699_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) != V_y_2 )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__sup]) ).
fof(f_1699_2,plain,
! [U_5329,U_5328,U_5327] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5327),U_5328),U_5329))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5327),U_5328),U_5329) != U_5329 )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5327),U_5328),U_5329) = U_5329
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5327),U_5328),U_5329)) ) )
| ~ class_Orderings_Olinorder(U_5327) ),
inference(variable_rename,[status(thm)],[f_1699_1]) ).
cnf(f_1699_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5327),U_5328),U_5329) = U_5329
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5327),U_5328),U_5329))
| ~ class_Orderings_Olinorder(U_5327) ),
inference(clausify,[status(thm)],[f_1699_2]) ).
cnf(f_1699_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5327),U_5328),U_5329))
| hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5327),U_5328),U_5329) != U_5329
| ~ class_Orderings_Olinorder(U_5327) ),
inference(clausify,[status(thm)],[f_1699_2]) ).
fof(f_1700_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_1700_2,plain,
! [U_5332,U_5331,U_5330] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5330),U_5331),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5330),U_5332),U_5331)))
| ~ class_Orderings_Olinorder(U_5330) ),
inference(variable_rename,[status(thm)],[f_1700_1]) ).
cnf(f_1700_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5330),U_5331),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5330),U_5332),U_5331)))
| ~ class_Orderings_Olinorder(U_5330) ),
inference(clausify,[status(thm)],[f_1700_2]) ).
fof(f_1701_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_1701_2,plain,
! [U_5335,U_5334,U_5333] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5333),U_5334),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5333),U_5334),U_5335)))
| ~ class_Orderings_Olinorder(U_5333) ),
inference(variable_rename,[status(thm)],[f_1701_1]) ).
cnf(f_1701_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5333),U_5334),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5333),U_5334),U_5335)))
| ~ class_Orderings_Olinorder(U_5333) ),
inference(clausify,[status(thm)],[f_1701_2]) ).
fof(f_1702_1,plain,
! [V_y_2,V_x_2,V_z_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2))) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__max__iff__disj]) ).
fof(f_1702_2,plain,
! [U_5339,U_5338,U_5337,U_5336] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5336),U_5337),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5336),U_5338),U_5339)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5336),U_5337),U_5339))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5336),U_5337),U_5338)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5336),U_5337),U_5339))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5336),U_5337),U_5338))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5336),U_5337),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5336),U_5338),U_5339))) ) )
| ~ class_Orderings_Olinorder(U_5336) ),
inference(variable_rename,[status(thm)],[f_1702_1]) ).
cnf(f_1702_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5336),U_5337),U_5339))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5336),U_5337),U_5338))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5336),U_5337),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5336),U_5338),U_5339)))
| ~ class_Orderings_Olinorder(U_5336) ),
inference(clausify,[status(thm)],[f_1702_2]) ).
cnf(f_1702_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5336),U_5337),U_5338))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5336),U_5337),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5336),U_5338),U_5339)))
| ~ class_Orderings_Olinorder(U_5336) ),
inference(clausify,[status(thm)],[f_1702_2]) ).
cnf(f_1702_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5336),U_5337),U_5339))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5336),U_5337),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5336),U_5338),U_5339)))
| ~ class_Orderings_Olinorder(U_5336) ),
inference(clausify,[status(thm)],[f_1702_2]) ).
fof(f_1703_1,plain,
! [V_z_2,V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2)) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_max__less__iff__conj]) ).
fof(f_1703_2,plain,
! [U_5343,U_5342,U_5341,U_5340] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5340),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5340),U_5341),U_5342)),U_5343))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5340),U_5342),U_5343))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5340),U_5341),U_5343)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5340),U_5342),U_5343))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5340),U_5341),U_5343)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5340),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5340),U_5341),U_5342)),U_5343)) ) )
| ~ class_Orderings_Olinorder(U_5340) ),
inference(variable_rename,[status(thm)],[f_1703_1]) ).
cnf(f_1703_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5340),U_5341),U_5343))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5340),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5340),U_5341),U_5342)),U_5343))
| ~ class_Orderings_Olinorder(U_5340) ),
inference(clausify,[status(thm)],[f_1703_2]) ).
cnf(f_1703_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5340),U_5342),U_5343))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5340),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5340),U_5341),U_5342)),U_5343))
| ~ class_Orderings_Olinorder(U_5340) ),
inference(clausify,[status(thm)],[f_1703_2]) ).
cnf(f_1703_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5340),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5340),U_5341),U_5342)),U_5343))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5340),U_5342),U_5343))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5340),U_5341),U_5343))
| ~ class_Orderings_Olinorder(U_5340) ),
inference(clausify,[status(thm)],[f_1703_2]) ).
fof(f_1704_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_1704_2,plain,
! [U_5347,U_5346,U_5345,U_5344] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5344),U_5345),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5344),U_5346),U_5347)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5344),U_5345),U_5346))
| ~ class_Orderings_Olinorder(U_5344) ),
inference(variable_rename,[status(thm)],[f_1704_1]) ).
cnf(f_1704_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5344),U_5345),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5344),U_5346),U_5347)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5344),U_5345),U_5346))
| ~ class_Orderings_Olinorder(U_5344) ),
inference(clausify,[status(thm)],[f_1704_2]) ).
fof(f_1705_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_1705_2,plain,
! [U_5351,U_5350,U_5349,U_5348] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5348),U_5349),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5348),U_5351),U_5350)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5348),U_5349),U_5350))
| ~ class_Orderings_Olinorder(U_5348) ),
inference(variable_rename,[status(thm)],[f_1705_1]) ).
cnf(f_1705_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5348),U_5349),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5348),U_5351),U_5350)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5348),U_5349),U_5350))
| ~ class_Orderings_Olinorder(U_5348) ),
inference(clausify,[status(thm)],[f_1705_2]) ).
fof(f_1706_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_1706_2,plain,
! [U_5355,U_5354,U_5353,U_5352] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5352),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5352),U_5353),U_5354)),U_5355) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5352),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5352),U_5353),U_5355)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5352),U_5354),U_5355))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_5352) ),
inference(variable_rename,[status(thm)],[f_1706_1]) ).
cnf(f_1706_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5352),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5352),U_5353),U_5354)),U_5355) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5352),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5352),U_5353),U_5355)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5352),U_5354),U_5355))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_5352) ),
inference(clausify,[status(thm)],[f_1706_2]) ).
fof(f_1707_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_1707_2,plain,
! [U_5359,U_5358,U_5357,U_5356] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5356),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5356),U_5357),U_5358)),U_5359) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5356),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5356),U_5357),U_5359)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5356),U_5358),U_5359))
| ~ class_Groups_Oordered__ab__group__add(U_5356) ),
inference(variable_rename,[status(thm)],[f_1707_1]) ).
cnf(f_1707_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5356),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5356),U_5357),U_5358)),U_5359) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5356),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5356),U_5357),U_5359)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5356),U_5358),U_5359))
| ~ class_Groups_Oordered__ab__group__add(U_5356) ),
inference(clausify,[status(thm)],[f_1707_2]) ).
fof(f_1708_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_1708_2,plain,
! [U_5360] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_5360),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_5360,
inference(variable_rename,[status(thm)],[f_1708_1]) ).
cnf(f_1708_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_5360),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_5360,
inference(clausify,[status(thm)],[f_1708_2]) ).
fof(f_1709_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_1709_2,plain,
! [U_5361] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5361) = U_5361,
inference(variable_rename,[status(thm)],[f_1709_1]) ).
cnf(f_1709_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5361) = U_5361,
inference(clausify,[status(thm)],[f_1709_2]) ).
fof(f_1710_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_1710_2,plain,
! [U_5363,U_5362] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5362)),hAPP(c_Nat_OSuc,U_5363)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_5362),U_5363)),
inference(variable_rename,[status(thm)],[f_1710_1]) ).
cnf(f_1710_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5362)),hAPP(c_Nat_OSuc,U_5363)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_5362),U_5363)),
inference(clausify,[status(thm)],[f_1710_2]) ).
fof(f_1711_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_1711_2,plain,
! [U_5367,U_5366,U_5365,U_5364] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5364),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5364),U_5365),U_5366)),U_5367) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5364),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5364),U_5365),U_5367)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5364),U_5366),U_5367))
| ~ class_Orderings_Olinorder(U_5364) ),
inference(variable_rename,[status(thm)],[f_1711_1]) ).
cnf(f_1711_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5364),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5364),U_5365),U_5366)),U_5367) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5364),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5364),U_5365),U_5367)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5364),U_5366),U_5367))
| ~ class_Orderings_Olinorder(U_5364) ),
inference(clausify,[status(thm)],[f_1711_2]) ).
fof(f_1712_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_1712_2,plain,
! [U_5371,U_5370,U_5369,U_5368] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5368),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5368),U_5369),U_5370)),U_5371) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5368),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5368),U_5369),U_5371)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5368),U_5370),U_5371))
| ~ class_Orderings_Olinorder(U_5368) ),
inference(variable_rename,[status(thm)],[f_1712_1]) ).
cnf(f_1712_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5368),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5368),U_5369),U_5370)),U_5371) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5368),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5368),U_5369),U_5371)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5368),U_5370),U_5371))
| ~ class_Orderings_Olinorder(U_5368) ),
inference(clausify,[status(thm)],[f_1712_2]) ).
fof(f_1713_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_1713_2,plain,
! [U_5375,U_5374,U_5373,U_5372] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5372),U_5373),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5372),U_5374),U_5375)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5372),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5372),U_5373),U_5374)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5372),U_5373),U_5375))
| ~ class_Orderings_Olinorder(U_5372) ),
inference(variable_rename,[status(thm)],[f_1713_1]) ).
cnf(f_1713_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5372),U_5373),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5372),U_5374),U_5375)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5372),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5372),U_5373),U_5374)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5372),U_5373),U_5375))
| ~ class_Orderings_Olinorder(U_5372) ),
inference(clausify,[status(thm)],[f_1713_2]) ).
fof(f_1714_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_1714_2,plain,
! [U_5379,U_5378,U_5377,U_5376] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5376),U_5377),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5376),U_5378),U_5379)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5376),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5376),U_5377),U_5378)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5376),U_5377),U_5379))
| ~ class_Orderings_Olinorder(U_5376) ),
inference(variable_rename,[status(thm)],[f_1714_1]) ).
cnf(f_1714_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5376),U_5377),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5376),U_5378),U_5379)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5376),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5376),U_5377),U_5378)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5376),U_5377),U_5379))
| ~ class_Orderings_Olinorder(U_5376) ),
inference(clausify,[status(thm)],[f_1714_2]) ).
fof(f_1715_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_1715_2,plain,
! [U_5382,U_5381,U_5380] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5380),U_5381),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5380),U_5381),U_5382)) = U_5381
| ~ class_Orderings_Olinorder(U_5380) ),
inference(variable_rename,[status(thm)],[f_1715_1]) ).
cnf(f_1715_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5380),U_5381),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5380),U_5381),U_5382)) = U_5381
| ~ class_Orderings_Olinorder(U_5380) ),
inference(clausify,[status(thm)],[f_1715_2]) ).
fof(f_1716_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_1716_2,plain,
! [U_5385,U_5384,U_5383] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5383),U_5384),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5383),U_5384),U_5385)) = U_5384
| ~ class_Orderings_Olinorder(U_5383) ),
inference(variable_rename,[status(thm)],[f_1716_1]) ).
cnf(f_1716_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5383),U_5384),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5383),U_5384),U_5385)) = U_5384
| ~ class_Orderings_Olinorder(U_5383) ),
inference(clausify,[status(thm)],[f_1716_2]) ).
fof(f_1717_1,plain,
! [V_na_2,V_m_2,V_f_2,T_b,T_c] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,V_na_2)) = hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_m_2),V_na_2))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Orderings_Olinorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_max__of__mono]) ).
fof(f_1717_2,plain,
! [U_5390,U_5389,U_5388,U_5387,U_5386] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5386),hAPP(U_5388,U_5389)),hAPP(U_5388,U_5390)) = hAPP(U_5388,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5387),U_5389),U_5390))
| ~ c_Orderings_Oorder__class_Omono(U_5387,U_5386,U_5388)
| ~ class_Orderings_Olinorder(U_5387)
| ~ class_Orderings_Olinorder(U_5386) ),
inference(variable_rename,[status(thm)],[f_1717_1]) ).
cnf(f_1717_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5386),hAPP(U_5388,U_5389)),hAPP(U_5388,U_5390)) = hAPP(U_5388,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5387),U_5389),U_5390))
| ~ c_Orderings_Oorder__class_Omono(U_5387,U_5386,U_5388)
| ~ class_Orderings_Olinorder(U_5387)
| ~ class_Orderings_Olinorder(U_5386) ),
inference(clausify,[status(thm)],[f_1717_2]) ).
fof(f_1718_1,plain,
! [V_y_2,V_x_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_x_2)),V_y_2),
inference(fof_nnf,[status(thm)],[fact_apfst__conv]) ).
fof(f_1718_2,plain,
! [U_5396,U_5395,U_5394,U_5393,U_5392,U_5391] : hAPP(c_Product__Type_Oapfst(U_5391,U_5392,U_5393,U_5394),hAPP(hAPP(c_Product__Type_OPair(U_5391,U_5393),U_5395),U_5396)) = hAPP(hAPP(c_Product__Type_OPair(U_5392,U_5393),hAPP(U_5394,U_5395)),U_5396),
inference(variable_rename,[status(thm)],[f_1718_1]) ).
cnf(f_1718_3,plain,
hAPP(c_Product__Type_Oapfst(U_5391,U_5392,U_5393,U_5394),hAPP(hAPP(c_Product__Type_OPair(U_5391,U_5393),U_5395),U_5396)) = hAPP(hAPP(c_Product__Type_OPair(U_5392,U_5393),hAPP(U_5394,U_5395)),U_5396),
inference(clausify,[status(thm)],[f_1718_2]) ).
fof(f_1719_1,plain,
! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
( ( hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2)
| hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) != hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) )
& ( hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2))
| hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2) != hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2) ) ),
inference(fof_nnf,[status(thm)],[fact_apfst__eq__conv]) ).
fof(f_1719_2,plain,
! [U_5402,U_5401,U_5400,U_5399,U_5398,U_5397] :
( ( hAPP(c_Product__Type_Oapfst(U_5397,U_5398,U_5399,U_5400),U_5401) = hAPP(c_Product__Type_Oapfst(U_5397,U_5398,U_5399,U_5402),U_5401)
| hAPP(U_5400,hAPP(c_Product__Type_Ofst(U_5397,U_5399),U_5401)) != hAPP(U_5402,hAPP(c_Product__Type_Ofst(U_5397,U_5399),U_5401)) )
& ( hAPP(U_5400,hAPP(c_Product__Type_Ofst(U_5397,U_5399),U_5401)) = hAPP(U_5402,hAPP(c_Product__Type_Ofst(U_5397,U_5399),U_5401))
| hAPP(c_Product__Type_Oapfst(U_5397,U_5398,U_5399,U_5400),U_5401) != hAPP(c_Product__Type_Oapfst(U_5397,U_5398,U_5399,U_5402),U_5401) ) ),
inference(variable_rename,[status(thm)],[f_1719_1]) ).
fof(f_1719_3,plain,
( ! [U_5414,U_5412,U_5410,U_5408,U_5406,U_5404] :
( hAPP(c_Product__Type_Oapfst(U_5404,U_5406,U_5408,U_5410),U_5412) = hAPP(c_Product__Type_Oapfst(U_5404,U_5406,U_5408,U_5414),U_5412)
| hAPP(U_5410,hAPP(c_Product__Type_Ofst(U_5404,U_5408),U_5412)) != hAPP(U_5414,hAPP(c_Product__Type_Ofst(U_5404,U_5408),U_5412)) )
& ! [U_5413,U_5411,U_5409,U_5407,U_5405,U_5403] :
( hAPP(U_5409,hAPP(c_Product__Type_Ofst(U_5403,U_5407),U_5411)) = hAPP(U_5413,hAPP(c_Product__Type_Ofst(U_5403,U_5407),U_5411))
| hAPP(c_Product__Type_Oapfst(U_5403,U_5405,U_5407,U_5409),U_5411) != hAPP(c_Product__Type_Oapfst(U_5403,U_5405,U_5407,U_5413),U_5411) ) ),
inference(miniscope,[status(thm)],[f_1719_2]) ).
cnf(f_1719_4,plain,
( hAPP(U_5409,hAPP(c_Product__Type_Ofst(U_5403,U_5407),U_5411)) = hAPP(U_5413,hAPP(c_Product__Type_Ofst(U_5403,U_5407),U_5411))
| hAPP(c_Product__Type_Oapfst(U_5403,U_5405,U_5407,U_5409),U_5411) != hAPP(c_Product__Type_Oapfst(U_5403,U_5405,U_5407,U_5413),U_5411) ),
inference(clausify,[status(thm)],[f_1719_3]) ).
cnf(f_1719_5,plain,
( hAPP(c_Product__Type_Oapfst(U_5404,U_5406,U_5408,U_5410),U_5412) = hAPP(c_Product__Type_Oapfst(U_5404,U_5406,U_5408,U_5414),U_5412)
| hAPP(U_5410,hAPP(c_Product__Type_Ofst(U_5404,U_5408),U_5412)) != hAPP(U_5414,hAPP(c_Product__Type_Ofst(U_5404,U_5408),U_5412)) ),
inference(clausify,[status(thm)],[f_1719_3]) ).
fof(f_1720_1,plain,
! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)),
inference(fof_nnf,[status(thm)],[fact_fst__apfst]) ).
fof(f_1720_2,plain,
! [U_5419,U_5418,U_5417,U_5416,U_5415] : hAPP(c_Product__Type_Ofst(U_5415,U_5416),hAPP(c_Product__Type_Oapfst(U_5417,U_5415,U_5416,U_5418),U_5419)) = hAPP(U_5418,hAPP(c_Product__Type_Ofst(U_5417,U_5416),U_5419)),
inference(variable_rename,[status(thm)],[f_1720_1]) ).
cnf(f_1720_3,plain,
hAPP(c_Product__Type_Ofst(U_5415,U_5416),hAPP(c_Product__Type_Oapfst(U_5417,U_5415,U_5416,U_5418),U_5419)) = hAPP(U_5418,hAPP(c_Product__Type_Ofst(U_5417,U_5416),U_5419)),
inference(clausify,[status(thm)],[f_1720_2]) ).
fof(f_1721_1,plain,
! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_d,T_b),V_x_2),
inference(fof_nnf,[status(thm)],[fact_snd__apfst]) ).
fof(f_1721_2,plain,
! [U_5424,U_5423,U_5422,U_5421,U_5420] : hAPP(c_Product__Type_Osnd(U_5420,U_5421),hAPP(c_Product__Type_Oapfst(U_5422,U_5420,U_5421,U_5423),U_5424)) = hAPP(c_Product__Type_Osnd(U_5422,U_5421),U_5424),
inference(variable_rename,[status(thm)],[f_1721_1]) ).
cnf(f_1721_3,plain,
hAPP(c_Product__Type_Osnd(U_5420,U_5421),hAPP(c_Product__Type_Oapfst(U_5422,U_5420,U_5421,U_5423),U_5424)) = hAPP(c_Product__Type_Osnd(U_5422,U_5421),U_5424),
inference(clausify,[status(thm)],[f_1721_2]) ).
fof(f_1722_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_1722_2,plain,
! [U_5427,U_5426,U_5425] :
( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5425),hAPP(c_Int_Onumber__class_Onumber__of(U_5425),U_5426)),hAPP(c_Int_Onumber__class_Onumber__of(U_5425),U_5427)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5425),U_5426)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5425),hAPP(c_Int_Onumber__class_Onumber__of(U_5425),U_5426)),hAPP(c_Int_Onumber__class_Onumber__of(U_5425),U_5427))) )
& ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5425),hAPP(c_Int_Onumber__class_Onumber__of(U_5425),U_5426)),hAPP(c_Int_Onumber__class_Onumber__of(U_5425),U_5427)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5425),U_5427)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5425),hAPP(c_Int_Onumber__class_Onumber__of(U_5425),U_5426)),hAPP(c_Int_Onumber__class_Onumber__of(U_5425),U_5427))) ) )
| ~ class_Orderings_Oord(U_5425)
| ~ class_Int_Onumber(U_5425) ),
inference(variable_rename,[status(thm)],[f_1722_1]) ).
cnf(f_1722_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5425),hAPP(c_Int_Onumber__class_Onumber__of(U_5425),U_5426)),hAPP(c_Int_Onumber__class_Onumber__of(U_5425),U_5427)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5425),U_5427)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5425),hAPP(c_Int_Onumber__class_Onumber__of(U_5425),U_5426)),hAPP(c_Int_Onumber__class_Onumber__of(U_5425),U_5427)))
| ~ class_Orderings_Oord(U_5425)
| ~ class_Int_Onumber(U_5425) ),
inference(clausify,[status(thm)],[f_1722_2]) ).
cnf(f_1722_4,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5425),hAPP(c_Int_Onumber__class_Onumber__of(U_5425),U_5426)),hAPP(c_Int_Onumber__class_Onumber__of(U_5425),U_5427)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5425),U_5426)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5425),hAPP(c_Int_Onumber__class_Onumber__of(U_5425),U_5426)),hAPP(c_Int_Onumber__class_Onumber__of(U_5425),U_5427)))
| ~ class_Orderings_Oord(U_5425)
| ~ class_Int_Onumber(U_5425) ),
inference(clausify,[status(thm)],[f_1722_2]) ).
fof(f_1723_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_1723_2,plain,
! [U_5431,U_5430,U_5429,U_5428] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5428),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5428),U_5429),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5428),U_5430),U_5431))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5428),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5428),U_5429),U_5430)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5428),U_5429),U_5431))))
| ~ class_Orderings_Olinorder(U_5428) ),
inference(variable_rename,[status(thm)],[f_1723_1]) ).
cnf(f_1723_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5428),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5428),U_5429),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5428),U_5430),U_5431))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5428),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5428),U_5429),U_5430)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5428),U_5429),U_5431))))
| ~ class_Orderings_Olinorder(U_5428) ),
inference(clausify,[status(thm)],[f_1723_2]) ).
fof(f_1724_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_1724_2,plain,
! [U_5435,U_5434,U_5433,U_5432] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5432),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5432),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5432),U_5433),U_5434)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5432),U_5433),U_5435))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5432),U_5433),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5432),U_5434),U_5435))))
| ~ class_Orderings_Olinorder(U_5432) ),
inference(variable_rename,[status(thm)],[f_1724_1]) ).
cnf(f_1724_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5432),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5432),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5432),U_5433),U_5434)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5432),U_5433),U_5435))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5432),U_5433),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5432),U_5434),U_5435))))
| ~ class_Orderings_Olinorder(U_5432) ),
inference(clausify,[status(thm)],[f_1724_2]) ).
fof(f_1725_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_1725_2,plain,
! [U_5438,U_5437,U_5436] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5436),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5436),U_5437),U_5438)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5436),hAPP(c_Groups_Ouminus__class_Ouminus(U_5436),U_5437)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5436),U_5438))
| ~ class_Groups_Olinordered__ab__group__add(U_5436) ),
inference(variable_rename,[status(thm)],[f_1725_1]) ).
cnf(f_1725_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5436),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5436),U_5437),U_5438)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5436),hAPP(c_Groups_Ouminus__class_Ouminus(U_5436),U_5437)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5436),U_5438))
| ~ class_Groups_Olinordered__ab__group__add(U_5436) ),
inference(clausify,[status(thm)],[f_1725_2]) ).
fof(f_1726_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_1726_2,plain,
! [U_5441,U_5440,U_5439] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5439),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5439),U_5440),U_5441)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5439),hAPP(c_Groups_Ouminus__class_Ouminus(U_5439),U_5440)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5439),U_5441))
| ~ class_Groups_Olinordered__ab__group__add(U_5439) ),
inference(variable_rename,[status(thm)],[f_1726_1]) ).
cnf(f_1726_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_5439),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5439),U_5440),U_5441)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5439),hAPP(c_Groups_Ouminus__class_Ouminus(U_5439),U_5440)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5439),U_5441))
| ~ class_Groups_Olinordered__ab__group__add(U_5439) ),
inference(clausify,[status(thm)],[f_1726_2]) ).
fof(f_1727_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_1727_2,plain,
! [U_5443,U_5442] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5442),U_5443)),U_5443) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_5442),U_5443),
inference(variable_rename,[status(thm)],[f_1727_1]) ).
cnf(f_1727_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5442),U_5443)),U_5443) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_5442),U_5443),
inference(clausify,[status(thm)],[f_1727_2]) ).
fof(f_1728_1,plain,
! [V_p_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,V_g_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_e,V_f_2),V_p_2)),
inference(fof_nnf,[status(thm)],[fact_apsnd__apfst__commute]) ).
fof(f_1728_2,plain,
! [U_5450,U_5449,U_5448,U_5447,U_5446,U_5445,U_5444] : hAPP(c_Product__Type_Oapsnd(U_5444,U_5445,U_5446,U_5447),hAPP(c_Product__Type_Oapfst(U_5448,U_5446,U_5444,U_5449),U_5450)) = hAPP(c_Product__Type_Oapfst(U_5448,U_5446,U_5445,U_5449),hAPP(c_Product__Type_Oapsnd(U_5444,U_5445,U_5448,U_5447),U_5450)),
inference(variable_rename,[status(thm)],[f_1728_1]) ).
cnf(f_1728_3,plain,
hAPP(c_Product__Type_Oapsnd(U_5444,U_5445,U_5446,U_5447),hAPP(c_Product__Type_Oapfst(U_5448,U_5446,U_5444,U_5449),U_5450)) = hAPP(c_Product__Type_Oapfst(U_5448,U_5446,U_5445,U_5449),hAPP(c_Product__Type_Oapsnd(U_5444,U_5445,U_5448,U_5447),U_5450)),
inference(clausify,[status(thm)],[f_1728_2]) ).
fof(f_1729_1,plain,
! [V_m_2,V_na_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_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_na_2)),V_m_2),
inference(fof_nnf,[status(thm)],[fact_max__Suc1]) ).
fof(f_1729_2,plain,
! [U_5452,U_5451] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5451)),U_5452) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_5451),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_5451)),U_5452),
inference(variable_rename,[status(thm)],[f_1729_1]) ).
cnf(f_1729_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5451)),U_5452) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_5451),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_5451)),U_5452),
inference(clausify,[status(thm)],[f_1729_2]) ).
fof(f_1730_1,plain,
! [V_na_2,V_m_2] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_na_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_na_2)),V_m_2),
inference(fof_nnf,[status(thm)],[fact_max__Suc2]) ).
fof(f_1730_2,plain,
! [U_5454,U_5453] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_5453),hAPP(c_Nat_OSuc,U_5454)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_5454),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_5454)),U_5453),
inference(variable_rename,[status(thm)],[f_1730_1]) ).
cnf(f_1730_3,plain,
hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_5453),hAPP(c_Nat_OSuc,U_5454)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_5454),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_5454)),U_5453),
inference(clausify,[status(thm)],[f_1730_2]) ).
fof(f_1731_1,plain,
! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2))),
inference(fof_nnf,[status(thm)],[fact_apfst__apsnd]) ).
fof(f_1731_2,plain,
! [U_5461,U_5460,U_5459,U_5458,U_5457,U_5456,U_5455] : hAPP(c_Product__Type_Oapfst(U_5455,U_5456,U_5457,U_5458),hAPP(c_Product__Type_Oapsnd(U_5459,U_5457,U_5455,U_5460),U_5461)) = hAPP(hAPP(c_Product__Type_OPair(U_5456,U_5457),hAPP(U_5458,hAPP(c_Product__Type_Ofst(U_5455,U_5459),U_5461))),hAPP(U_5460,hAPP(c_Product__Type_Osnd(U_5455,U_5459),U_5461))),
inference(variable_rename,[status(thm)],[f_1731_1]) ).
cnf(f_1731_3,plain,
hAPP(c_Product__Type_Oapfst(U_5455,U_5456,U_5457,U_5458),hAPP(c_Product__Type_Oapsnd(U_5459,U_5457,U_5455,U_5460),U_5461)) = hAPP(hAPP(c_Product__Type_OPair(U_5456,U_5457),hAPP(U_5458,hAPP(c_Product__Type_Ofst(U_5455,U_5459),U_5461))),hAPP(U_5460,hAPP(c_Product__Type_Osnd(U_5455,U_5459),U_5461))),
inference(clausify,[status(thm)],[f_1731_2]) ).
fof(f_1732_1,plain,
! [T_b] :
( c_Orderings_Oord_Omin(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omax(T_b)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_dual__min]) ).
fof(f_1732_2,plain,
! [U_5462] :
( c_Orderings_Oord_Omin(U_5462,hAPP(c_COMBC(U_5462,U_5462,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_5462))) = c_Orderings_Oord__class_Omax(U_5462)
| ~ class_Orderings_Olinorder(U_5462) ),
inference(variable_rename,[status(thm)],[f_1732_1]) ).
cnf(f_1732_3,plain,
( c_Orderings_Oord_Omin(U_5462,hAPP(c_COMBC(U_5462,U_5462,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_5462))) = c_Orderings_Oord__class_Omax(U_5462)
| ~ class_Orderings_Olinorder(U_5462) ),
inference(clausify,[status(thm)],[f_1732_2]) ).
fof(f_1733_1,plain,
! [T_b] :
( c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b))
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_max__ord__max]) ).
fof(f_1733_2,plain,
! [U_5463] :
( c_Orderings_Oord__class_Omax(U_5463) = c_Orderings_Oord_Omax(U_5463,c_Orderings_Oord__class_Oless__eq(U_5463))
| ~ class_Orderings_Oord(U_5463) ),
inference(variable_rename,[status(thm)],[f_1733_1]) ).
cnf(f_1733_3,plain,
( c_Orderings_Oord__class_Omax(U_5463) = c_Orderings_Oord_Omax(U_5463,c_Orderings_Oord__class_Oless__eq(U_5463))
| ~ class_Orderings_Oord(U_5463) ),
inference(clausify,[status(thm)],[f_1733_2]) ).
fof(f_1734_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]) ).
cnf(f_1734_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(clausify,[status(thm)],[f_1734_1]) ).
fof(f_1735_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_1735_2,plain,
! [U_5465,U_5464] :
( ( ( ( c_Nitpick_Onorm__frac(U_5465,U_5464) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_5465),U_5464)),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_5465))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5464)))
| U_5464 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_5465 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Nitpick_Onorm__frac(U_5465,U_5464) = 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_5464 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& U_5465 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5464),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( c_Nitpick_Onorm__frac(U_5465,U_5464) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5465),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5464))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5464),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_1735_1]) ).
fof(f_1735_3,plain,
( ! [U_5469,U_5467] :
( ( ( c_Nitpick_Onorm__frac(U_5469,U_5467) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_5469),U_5467)),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_5469))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5467)))
| U_5467 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_5469 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Nitpick_Onorm__frac(U_5469,U_5467) = 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_5467 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& U_5469 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5467),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_5468,U_5466] :
( c_Nitpick_Onorm__frac(U_5468,U_5466) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5468),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5466))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5466),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_1735_2]) ).
cnf(f_1735_4,plain,
( c_Nitpick_Onorm__frac(U_5468,U_5466) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5468),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5466))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5466),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1735_3]) ).
cnf(f_1735_5,plain,
( U_5469 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(U_5469,U_5467) = 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),U_5467),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1735_3]) ).
cnf(f_1735_6,plain,
( U_5467 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(U_5469,U_5467) = 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),U_5467),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1735_3]) ).
cnf(f_1735_7,plain,
( c_Nitpick_Onorm__frac(U_5469,U_5467) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_5469),U_5467)),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_5469))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5467)))
| U_5467 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_5469 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5467),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1735_3]) ).
fof(f_1736_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_1736_2,plain,
! [U_5471,U_5470] :
( ( ( ( ( c_Nitpick_Onorm__frac(U_5470,U_5471) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_5470),U_5471)),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_5470))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5471)))
| U_5471 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_5470 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Nitpick_Onorm__frac(U_5470,U_5471) = 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_5471 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& U_5470 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5471),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( c_Nitpick_Onorm__frac(U_5470,U_5471) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5470),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5471))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5471),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_5470),U_5471))) ),
inference(variable_rename,[status(thm)],[f_1736_1]) ).
cnf(f_1736_3,plain,
( c_Nitpick_Onorm__frac(U_5470,U_5471) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5470),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5471))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5471),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_5470),U_5471))) ),
inference(clausify,[status(thm)],[f_1736_2]) ).
cnf(f_1736_4,plain,
( U_5470 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(U_5470,U_5471) = 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),U_5471),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_5470),U_5471))) ),
inference(clausify,[status(thm)],[f_1736_2]) ).
cnf(f_1736_5,plain,
( U_5471 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Nitpick_Onorm__frac(U_5470,U_5471) = 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),U_5471),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_5470),U_5471))) ),
inference(clausify,[status(thm)],[f_1736_2]) ).
cnf(f_1736_6,plain,
( c_Nitpick_Onorm__frac(U_5470,U_5471) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_5470),U_5471)),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_5470))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5471)))
| U_5471 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_5470 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5471),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_5470),U_5471))) ),
inference(clausify,[status(thm)],[f_1736_2]) ).
fof(f_1737_1,plain,
! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
( ( hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_b,tc_prod(T_c,T_b)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_c,T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_f_2))
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2)
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(fof_nnf,[status(thm)],[fact_iterate_Osimps]) ).
fof(f_1737_2,plain,
! [U_5476,U_5475,U_5474,U_5473,U_5472] :
( ( hAPP(c_Random_Oiterate(U_5473,U_5474,U_5472,U_5475),U_5476) = hAPP(hAPP(c_Product__Type_Oscomp(U_5474,U_5473,U_5474,tc_prod(U_5473,U_5474)),hAPP(U_5475,U_5476)),c_Random_Oiterate(U_5473,U_5474,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5472),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_5475))
| U_5472 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( hAPP(c_Random_Oiterate(U_5473,U_5474,U_5472,U_5475),U_5476) = hAPP(c_Product__Type_OPair(U_5473,U_5474),U_5476)
| U_5472 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(variable_rename,[status(thm)],[f_1737_1]) ).
fof(f_1737_3,plain,
( ! [U_5486,U_5484,U_5482,U_5480,U_5478] :
( hAPP(c_Random_Oiterate(U_5480,U_5482,U_5478,U_5484),U_5486) = hAPP(hAPP(c_Product__Type_Oscomp(U_5482,U_5480,U_5482,tc_prod(U_5480,U_5482)),hAPP(U_5484,U_5486)),c_Random_Oiterate(U_5480,U_5482,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5478),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_5484))
| U_5478 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ! [U_5485,U_5483,U_5481,U_5479,U_5477] :
( hAPP(c_Random_Oiterate(U_5479,U_5481,U_5477,U_5483),U_5485) = hAPP(c_Product__Type_OPair(U_5479,U_5481),U_5485)
| U_5477 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(miniscope,[status(thm)],[f_1737_2]) ).
cnf(f_1737_4,plain,
( hAPP(c_Random_Oiterate(U_5479,U_5481,U_5477,U_5483),U_5485) = hAPP(c_Product__Type_OPair(U_5479,U_5481),U_5485)
| U_5477 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_1737_3]) ).
cnf(f_1737_5,plain,
( hAPP(c_Random_Oiterate(U_5480,U_5482,U_5478,U_5484),U_5486) = hAPP(hAPP(c_Product__Type_Oscomp(U_5482,U_5480,U_5482,tc_prod(U_5480,U_5482)),hAPP(U_5484,U_5486)),c_Random_Oiterate(U_5480,U_5482,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5478),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_5484))
| U_5478 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_1737_3]) ).
fof(f_1738_1,plain,
! [V_h_2,V_g_2,V_f_2,T_g,T_f,T_c,T_e,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_e,T_c),hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,tc_prod(T_d,T_e)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,T_c),V_f_2),hAPP(hAPP(c_COMBC(T_f,tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_g,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),T_f),c_Product__Type_Oscomp(T_g,T_d,T_e,T_c)),V_g_2)),V_h_2)),
inference(fof_nnf,[status(thm)],[fact_scomp__scomp]) ).
fof(f_1738_2,plain,
! [U_5495,U_5494,U_5493,U_5492,U_5491,U_5490,U_5489,U_5488,U_5487] : hAPP(hAPP(c_Product__Type_Oscomp(U_5487,U_5488,U_5489,U_5490),hAPP(hAPP(c_Product__Type_Oscomp(U_5487,U_5491,U_5492,tc_prod(U_5488,U_5489)),U_5493),U_5494)),U_5495) = hAPP(hAPP(c_Product__Type_Oscomp(U_5487,U_5491,U_5492,U_5490),U_5493),hAPP(hAPP(c_COMBC(U_5491,tc_fun(U_5488,tc_fun(U_5489,U_5490)),tc_fun(U_5492,U_5490)),hAPP(hAPP(c_COMBB(tc_fun(U_5492,tc_prod(U_5488,U_5489)),tc_fun(tc_fun(U_5488,tc_fun(U_5489,U_5490)),tc_fun(U_5492,U_5490)),U_5491),c_Product__Type_Oscomp(U_5492,U_5488,U_5489,U_5490)),U_5494)),U_5495)),
inference(variable_rename,[status(thm)],[f_1738_1]) ).
cnf(f_1738_3,plain,
hAPP(hAPP(c_Product__Type_Oscomp(U_5487,U_5488,U_5489,U_5490),hAPP(hAPP(c_Product__Type_Oscomp(U_5487,U_5491,U_5492,tc_prod(U_5488,U_5489)),U_5493),U_5494)),U_5495) = hAPP(hAPP(c_Product__Type_Oscomp(U_5487,U_5491,U_5492,U_5490),U_5493),hAPP(hAPP(c_COMBC(U_5491,tc_fun(U_5488,tc_fun(U_5489,U_5490)),tc_fun(U_5492,U_5490)),hAPP(hAPP(c_COMBB(tc_fun(U_5492,tc_prod(U_5488,U_5489)),tc_fun(tc_fun(U_5488,tc_fun(U_5489,U_5490)),tc_fun(U_5492,U_5490)),U_5491),c_Product__Type_Oscomp(U_5492,U_5488,U_5489,U_5490)),U_5494)),U_5495)),
inference(clausify,[status(thm)],[f_1738_2]) ).
fof(f_1739_1,plain,
! [V_x_2,T_d,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,tc_prod(T_c,T_d)),V_x_2),c_Product__Type_OPair(T_c,T_d)) = V_x_2,
inference(fof_nnf,[status(thm)],[fact_scomp__Pair]) ).
fof(f_1739_2,plain,
! [U_5499,U_5498,U_5497,U_5496] : hAPP(hAPP(c_Product__Type_Oscomp(U_5496,U_5497,U_5498,tc_prod(U_5497,U_5498)),U_5499),c_Product__Type_OPair(U_5497,U_5498)) = U_5499,
inference(variable_rename,[status(thm)],[f_1739_1]) ).
cnf(f_1739_3,plain,
hAPP(hAPP(c_Product__Type_Oscomp(U_5496,U_5497,U_5498,tc_prod(U_5497,U_5498)),U_5499),c_Product__Type_OPair(U_5497,U_5498)) = U_5499,
inference(clausify,[status(thm)],[f_1739_2]) ).
fof(f_1740_1,plain,
! [V_f_2,V_x_2,T_c,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_b,T_c),hAPP(c_Product__Type_OPair(T_d,T_b),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2),
inference(fof_nnf,[status(thm)],[fact_Pair__scomp]) ).
fof(f_1740_2,plain,
! [U_5504,U_5503,U_5502,U_5501,U_5500] : hAPP(hAPP(c_Product__Type_Oscomp(U_5500,U_5501,U_5500,U_5502),hAPP(c_Product__Type_OPair(U_5501,U_5500),U_5503)),U_5504) = hAPP(U_5504,U_5503),
inference(variable_rename,[status(thm)],[f_1740_1]) ).
cnf(f_1740_3,plain,
hAPP(hAPP(c_Product__Type_Oscomp(U_5500,U_5501,U_5500,U_5502),hAPP(c_Product__Type_OPair(U_5501,U_5500),U_5503)),U_5504) = hAPP(U_5504,U_5503),
inference(clausify,[status(thm)],[f_1740_2]) ).
fof(f_1741_1,plain,
! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)),
inference(fof_nnf,[status(thm)],[fact_scomp__apply]) ).
fof(f_1741_2,plain,
! [U_5511,U_5510,U_5509,U_5508,U_5507,U_5506,U_5505] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_5505,U_5506,U_5507,U_5508),U_5509),U_5510),U_5511) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5506,U_5507,U_5508),U_5510),hAPP(U_5509,U_5511)),
inference(variable_rename,[status(thm)],[f_1741_1]) ).
cnf(f_1741_3,plain,
hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_5505,U_5506,U_5507,U_5508),U_5509),U_5510),U_5511) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5506,U_5507,U_5508),U_5510),hAPP(U_5509,U_5511)),
inference(clausify,[status(thm)],[f_1741_2]) ).
fof(f_1742_1,plain,
! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)),
inference(fof_nnf,[status(thm)],[fact_scomp__def]) ).
fof(f_1742_2,plain,
! [U_5518,U_5517,U_5516,U_5515,U_5514,U_5513,U_5512] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_5512,U_5513,U_5514,U_5515),U_5516),U_5517),U_5518) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5513,U_5514,U_5515),U_5517),hAPP(U_5516,U_5518)),
inference(variable_rename,[status(thm)],[f_1742_1]) ).
cnf(f_1742_3,plain,
hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_5512,U_5513,U_5514,U_5515),U_5516),U_5517),U_5518) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5513,U_5514,U_5515),U_5517),hAPP(U_5516,U_5518)),
inference(clausify,[status(thm)],[f_1742_2]) ).
fof(f_1743_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_1743_2,plain,
! [U_5520,U_5519] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5519),U_5520),U_5520) = U_5520
| ~ class_Orderings_Olinorder(U_5519) ),
inference(variable_rename,[status(thm)],[f_1743_1]) ).
cnf(f_1743_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_5519),U_5520),U_5520) = U_5520
| ~ class_Orderings_Olinorder(U_5519) ),
inference(clausify,[status(thm)],[f_1743_2]) ).
fof(f_1744_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_1744_2,plain,
! [U_5522,U_5521] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5521),U_5522),U_5522) = U_5522
| ~ class_Orderings_Olinorder(U_5521) ),
inference(variable_rename,[status(thm)],[f_1744_1]) ).
cnf(f_1744_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_5521),U_5522),U_5522) = U_5522
| ~ class_Orderings_Olinorder(U_5521) ),
inference(clausify,[status(thm)],[f_1744_2]) ).
fof(f_1745_1,plain,
! [T_b] :
( c_Orderings_Oord_Omax(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omin(T_b)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_dual__max]) ).
fof(f_1745_2,plain,
! [U_5523] :
( c_Orderings_Oord_Omax(U_5523,hAPP(c_COMBC(U_5523,U_5523,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_5523))) = c_Orderings_Oord__class_Omin(U_5523)
| ~ class_Orderings_Olinorder(U_5523) ),
inference(variable_rename,[status(thm)],[f_1745_1]) ).
cnf(f_1745_3,plain,
( c_Orderings_Oord_Omax(U_5523,hAPP(c_COMBC(U_5523,U_5523,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_5523))) = c_Orderings_Oord__class_Omin(U_5523)
| ~ class_Orderings_Olinorder(U_5523) ),
inference(clausify,[status(thm)],[f_1745_2]) ).
fof(f_1746_1,plain,
! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_e),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_d,T_e),hAPP(V_f_2,V_x_2))),
inference(fof_nnf,[status(thm)],[fact_scomp__unfold]) ).
fof(f_1746_2,plain,
! [U_5530,U_5529,U_5528,U_5527,U_5526,U_5525,U_5524] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_5524,U_5525,U_5526,U_5527),U_5528),U_5529),U_5530) = hAPP(hAPP(U_5529,hAPP(c_Product__Type_Ofst(U_5525,U_5526),hAPP(U_5528,U_5530))),hAPP(c_Product__Type_Osnd(U_5525,U_5526),hAPP(U_5528,U_5530))),
inference(variable_rename,[status(thm)],[f_1746_1]) ).
cnf(f_1746_3,plain,
hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_5524,U_5525,U_5526,U_5527),U_5528),U_5529),U_5530) = hAPP(hAPP(U_5529,hAPP(c_Product__Type_Ofst(U_5525,U_5526),hAPP(U_5528,U_5530))),hAPP(c_Product__Type_Osnd(U_5525,U_5526),hAPP(U_5528,U_5530))),
inference(clausify,[status(thm)],[f_1746_2]) ).
fof(f_1747_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_1747_2,plain,
! [U_5532,U_5531] : hAPP(hAPP(c_Nitpick_Oint__gcd,U_5531),U_5532) = 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_5531)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5532)))),
inference(variable_rename,[status(thm)],[f_1747_1]) ).
cnf(f_1747_3,plain,
hAPP(hAPP(c_Nitpick_Oint__gcd,U_5531),U_5532) = 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_5531)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5532)))),
inference(clausify,[status(thm)],[f_1747_2]) ).
fof(f_1748_1,plain,
! [V_P_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
| ? [B_a,B_b] :
( ~ hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
& ( hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_a)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),B_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),B_a),B_b))) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_a0_2),V_a1_2))) ),
inference(fof_nnf,[status(thm)],[fact_norm__frac_Opinduct]) ).
fof(f_1748_2,plain,
! [U_5537,U_5536,U_5535] :
( hBOOL(hAPP(hAPP(U_5537,U_5535),U_5536))
| ? [U_5534,U_5533] :
( ~ hBOOL(hAPP(hAPP(U_5537,U_5534),U_5533))
& ( hBOOL(hAPP(hAPP(U_5537,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5534)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5533)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5533),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_5534),U_5533))) )
| ~ 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_5535),U_5536))) ),
inference(variable_rename,[status(thm)],[f_1748_1]) ).
fof(f_1748_3,plain,
! [U_5537,U_5536,U_5535] :
( hBOOL(hAPP(hAPP(U_5537,U_5535),U_5536))
| ? [U_5533] :
( ~ hBOOL(hAPP(hAPP(U_5537,sK76(U_5537,U_5536,U_5535)),U_5533))
& ( hBOOL(hAPP(hAPP(U_5537,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK76(U_5537,U_5536,U_5535))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5533)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5533),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),sK76(U_5537,U_5536,U_5535)),U_5533))) )
| ~ 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_5535),U_5536))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_5534,sK76(U_5537,U_5536,U_5535))],[f_1748_2]) ).
fof(f_1748_4,plain,
! [U_5537,U_5536,U_5535] :
( hBOOL(hAPP(hAPP(U_5537,U_5535),U_5536))
| ( ~ hBOOL(hAPP(hAPP(U_5537,sK76(U_5537,U_5536,U_5535)),sK77(U_5537,U_5536,U_5535)))
& ( hBOOL(hAPP(hAPP(U_5537,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK76(U_5537,U_5536,U_5535))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK77(U_5537,U_5536,U_5535))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK77(U_5537,U_5536,U_5535)),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),sK76(U_5537,U_5536,U_5535)),sK77(U_5537,U_5536,U_5535)))) )
| ~ 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_5535),U_5536))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_5533,sK77(U_5537,U_5536,U_5535))],[f_1748_3]) ).
cnf(f_1748_5,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK76(U_5537,U_5536,U_5535)),sK77(U_5537,U_5536,U_5535))))
| hBOOL(hAPP(hAPP(U_5537,U_5535),U_5536))
| ~ 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_5535),U_5536))) ),
inference(clausify,[status(thm)],[f_1748_4]) ).
cnf(f_1748_6,plain,
( hBOOL(hAPP(hAPP(U_5537,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK76(U_5537,U_5536,U_5535))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK77(U_5537,U_5536,U_5535))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK77(U_5537,U_5536,U_5535)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(U_5537,U_5535),U_5536))
| ~ 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_5535),U_5536))) ),
inference(clausify,[status(thm)],[f_1748_4]) ).
cnf(f_1748_7,plain,
( ~ hBOOL(hAPP(hAPP(U_5537,sK76(U_5537,U_5536,U_5535)),sK77(U_5537,U_5536,U_5535)))
| hBOOL(hAPP(hAPP(U_5537,U_5535),U_5536))
| ~ 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_5535),U_5536))) ),
inference(clausify,[status(thm)],[f_1748_4]) ).
fof(f_1749_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_1749_2,plain,
! [U_5539,U_5538] : c_Nitpick_Oint__lcm(U_5538,U_5539) = 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_5538)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5539)))),
inference(variable_rename,[status(thm)],[f_1749_1]) ).
cnf(f_1749_3,plain,
c_Nitpick_Oint__lcm(U_5538,U_5539) = 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_5538)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_5539)))),
inference(clausify,[status(thm)],[f_1749_2]) ).
fof(f_1750_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Ozero__frac__def]) ).
fof(f_1750_2,plain,
! [U_5540] : c_Nitpick_Ozero__frac(U_5540) = c_Nitpick_OAbs__Frac(U_5540,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))),
inference(variable_rename,[status(thm)],[f_1750_1]) ).
cnf(f_1750_3,plain,
c_Nitpick_Ozero__frac(U_5540) = c_Nitpick_OAbs__Frac(U_5540,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))),
inference(clausify,[status(thm)],[f_1750_2]) ).
fof(f_1751_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_1751_2,plain,
! [U_5542,U_5541] :
( ( c_Nitpick_Onat__gcd(U_5542,U_5541) = c_Nitpick_Onat__gcd(U_5541,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5542,U_5541))
| U_5541 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Nitpick_Onat__gcd(U_5542,U_5541) = U_5542
| U_5541 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_1751_1]) ).
fof(f_1751_3,plain,
( ! [U_5546,U_5544] :
( c_Nitpick_Onat__gcd(U_5546,U_5544) = c_Nitpick_Onat__gcd(U_5544,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5546,U_5544))
| U_5544 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_5545,U_5543] :
( c_Nitpick_Onat__gcd(U_5545,U_5543) = U_5545
| U_5543 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_1751_2]) ).
cnf(f_1751_4,plain,
( c_Nitpick_Onat__gcd(U_5545,U_5543) = U_5545
| U_5543 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1751_3]) ).
cnf(f_1751_5,plain,
( c_Nitpick_Onat__gcd(U_5546,U_5544) = c_Nitpick_Onat__gcd(U_5544,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5546,U_5544))
| U_5544 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1751_3]) ).
fof(f_1752_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_1752_2,plain,
! [U_5548,U_5547] : c_Nitpick_Onat__lcm(U_5547,U_5548) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5547),U_5548)),c_Nitpick_Onat__gcd(U_5547,U_5548)),
inference(variable_rename,[status(thm)],[f_1752_1]) ).
cnf(f_1752_3,plain,
c_Nitpick_Onat__lcm(U_5547,U_5548) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5547),U_5548)),c_Nitpick_Onat__gcd(U_5547,U_5548)),
inference(clausify,[status(thm)],[f_1752_2]) ).
fof(f_1753_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Oone__frac__def]) ).
fof(f_1753_2,plain,
! [U_5549] : c_Nitpick_Oone__frac(U_5549) = c_Nitpick_OAbs__Frac(U_5549,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))),
inference(variable_rename,[status(thm)],[f_1753_1]) ).
cnf(f_1753_3,plain,
c_Nitpick_Oone__frac(U_5549) = c_Nitpick_OAbs__Frac(U_5549,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))),
inference(clausify,[status(thm)],[f_1753_2]) ).
fof(f_1754_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Onumber__of__frac__def]) ).
fof(f_1754_2,plain,
! [U_5551,U_5550] : c_Nitpick_Onumber__of__frac(U_5550,U_5551) = c_Nitpick_OAbs__Frac(U_5550,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5551),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_1754_1]) ).
cnf(f_1754_3,plain,
c_Nitpick_Onumber__of__frac(U_5550,U_5551) = c_Nitpick_OAbs__Frac(U_5550,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5551),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_1754_2]) ).
fof(f_1755_1,plain,
! [V_y_2,V_x_2] :
( ( ( c_Nitpick_Onat__gcd(V_x_2,V_y_2) = c_Nitpick_Onat__gcd(V_y_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,V_y_2))
| V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2
| V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2))) ),
inference(fof_nnf,[status(thm)],[fact_nat__gcd_Opsimps]) ).
fof(f_1755_2,plain,
! [U_5553,U_5552] :
( ( ( c_Nitpick_Onat__gcd(U_5552,U_5553) = c_Nitpick_Onat__gcd(U_5553,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5552,U_5553))
| U_5553 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Nitpick_Onat__gcd(U_5552,U_5553) = U_5552
| U_5553 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5552),U_5553))) ),
inference(variable_rename,[status(thm)],[f_1755_1]) ).
cnf(f_1755_3,plain,
( c_Nitpick_Onat__gcd(U_5552,U_5553) = U_5552
| U_5553 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5552),U_5553))) ),
inference(clausify,[status(thm)],[f_1755_2]) ).
cnf(f_1755_4,plain,
( c_Nitpick_Onat__gcd(U_5552,U_5553) = c_Nitpick_Onat__gcd(U_5553,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5552,U_5553))
| U_5553 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5552),U_5553))) ),
inference(clausify,[status(thm)],[f_1755_2]) ).
fof(f_1756_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Ofrac__def]) ).
fof(f_1756_2,plain,
! [U_5556,U_5555,U_5554] : hAPP(hAPP(c_Nitpick_Ofrac(U_5554),U_5555),U_5556) = c_Nitpick_OAbs__Frac(U_5554,c_Nitpick_Onorm__frac(U_5555,U_5556)),
inference(variable_rename,[status(thm)],[f_1756_1]) ).
cnf(f_1756_3,plain,
hAPP(hAPP(c_Nitpick_Ofrac(U_5554),U_5555),U_5556) = c_Nitpick_OAbs__Frac(U_5554,c_Nitpick_Onorm__frac(U_5555,U_5556)),
inference(clausify,[status(thm)],[f_1756_2]) ).
fof(f_1757_1,plain,
! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_INF1__iff]) ).
fof(f_1757_2,plain,
! [U_5563,U_5562,U_5561,U_5560,U_5559] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5559,tc_fun(U_5560,tc_HOL_Obool)),U_5561),U_5562),U_5563))
| ? [U_5558] :
( ~ hBOOL(hAPP(hAPP(U_5562,U_5558),U_5563))
& hBOOL(hAPP(hAPP(c_member(U_5559),U_5558),U_5561)) ) )
& ( ! [U_5557] :
( hBOOL(hAPP(hAPP(U_5562,U_5557),U_5563))
| ~ hBOOL(hAPP(hAPP(c_member(U_5559),U_5557),U_5561)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5559,tc_fun(U_5560,tc_HOL_Obool)),U_5561),U_5562),U_5563)) ) ),
inference(variable_rename,[status(thm)],[f_1757_1]) ).
fof(f_1757_3,plain,
( ! [U_5573,U_5571,U_5569,U_5567,U_5565] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5565,tc_fun(U_5567,tc_HOL_Obool)),U_5569),U_5571),U_5573))
| ? [U_5558] :
( ~ hBOOL(hAPP(hAPP(U_5571,U_5558),U_5573))
& hBOOL(hAPP(hAPP(c_member(U_5565),U_5558),U_5569)) ) )
& ! [U_5572,U_5570,U_5568,U_5566,U_5564] :
( ! [U_5557] :
( hBOOL(hAPP(hAPP(U_5570,U_5557),U_5572))
| ~ hBOOL(hAPP(hAPP(c_member(U_5564),U_5557),U_5568)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5564,tc_fun(U_5566,tc_HOL_Obool)),U_5568),U_5570),U_5572)) ) ),
inference(miniscope,[status(thm)],[f_1757_2]) ).
fof(f_1757_4,plain,
( ! [U_5573,U_5571,U_5569,U_5567,U_5565] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5565,tc_fun(U_5567,tc_HOL_Obool)),U_5569),U_5571),U_5573))
| ( ~ hBOOL(hAPP(hAPP(U_5571,sK78(U_5573,U_5571,U_5569,U_5567,U_5565)),U_5573))
& hBOOL(hAPP(hAPP(c_member(U_5565),sK78(U_5573,U_5571,U_5569,U_5567,U_5565)),U_5569)) ) )
& ! [U_5572,U_5570,U_5568,U_5566,U_5564] :
( ! [U_5557] :
( hBOOL(hAPP(hAPP(U_5570,U_5557),U_5572))
| ~ hBOOL(hAPP(hAPP(c_member(U_5564),U_5557),U_5568)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5564,tc_fun(U_5566,tc_HOL_Obool)),U_5568),U_5570),U_5572)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_5558,sK78(U_5573,U_5571,U_5569,U_5567,U_5565))],[f_1757_3]) ).
cnf(f_1757_5,plain,
( hBOOL(hAPP(hAPP(U_5570,U_5557),U_5572))
| ~ hBOOL(hAPP(hAPP(c_member(U_5564),U_5557),U_5568))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5564,tc_fun(U_5566,tc_HOL_Obool)),U_5568),U_5570),U_5572)) ),
inference(clausify,[status(thm)],[f_1757_4]) ).
cnf(f_1757_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5565),sK78(U_5573,U_5571,U_5569,U_5567,U_5565)),U_5569))
| hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5565,tc_fun(U_5567,tc_HOL_Obool)),U_5569),U_5571),U_5573)) ),
inference(clausify,[status(thm)],[f_1757_4]) ).
cnf(f_1757_7,plain,
( ~ hBOOL(hAPP(hAPP(U_5571,sK78(U_5573,U_5571,U_5569,U_5567,U_5565)),U_5573))
| hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_5565,tc_fun(U_5567,tc_HOL_Obool)),U_5569),U_5571),U_5573)) ),
inference(clausify,[status(thm)],[f_1757_4]) ).
fof(f_1758_1,plain,
! [V_Q_2,T_b,V_x_2,V_P_2] :
( hBOOL(hAPP(V_Q_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
| ~ hBOOL(hAPP(V_P_2,V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_rev__predicate1D]) ).
fof(f_1758_2,plain,
! [U_5577,U_5576,U_5575,U_5574] :
( hBOOL(hAPP(U_5577,U_5575))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5576,tc_HOL_Obool)),U_5574),U_5577))
| ~ hBOOL(hAPP(U_5574,U_5575)) ),
inference(variable_rename,[status(thm)],[f_1758_1]) ).
cnf(f_1758_3,plain,
( hBOOL(hAPP(U_5577,U_5575))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5576,tc_HOL_Obool)),U_5574),U_5577))
| ~ hBOOL(hAPP(U_5574,U_5575)) ),
inference(clausify,[status(thm)],[f_1758_2]) ).
fof(f_1759_1,plain,
! [V_x_2,V_Q_2,V_P_2,T_b] :
( hBOOL(hAPP(V_Q_2,V_x_2))
| ~ hBOOL(hAPP(V_P_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2)) ),
inference(fof_nnf,[status(thm)],[fact_predicate1D]) ).
fof(f_1759_2,plain,
! [U_5581,U_5580,U_5579,U_5578] :
( hBOOL(hAPP(U_5580,U_5581))
| ~ hBOOL(hAPP(U_5579,U_5581))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5578,tc_HOL_Obool)),U_5579),U_5580)) ),
inference(variable_rename,[status(thm)],[f_1759_1]) ).
fof(f_1759_3,plain,
! [U_5581,U_5580,U_5579] :
( ! [U_5578] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5578,tc_HOL_Obool)),U_5579),U_5580))
| hBOOL(hAPP(U_5580,U_5581))
| ~ hBOOL(hAPP(U_5579,U_5581)) ),
inference(miniscope,[status(thm)],[f_1759_2]) ).
cnf(f_1759_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5578,tc_HOL_Obool)),U_5579),U_5580))
| hBOOL(hAPP(U_5580,U_5581))
| ~ hBOOL(hAPP(U_5579,U_5581)) ),
inference(clausify,[status(thm)],[f_1759_3]) ).
fof(f_1760_1,plain,
! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_P_2] :
( hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2))
| ~ hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_rev__predicate2D]) ).
fof(f_1760_2,plain,
! [U_5587,U_5586,U_5585,U_5584,U_5583,U_5582] :
( hBOOL(hAPP(hAPP(U_5587,U_5583),U_5584))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5585,tc_fun(U_5586,tc_HOL_Obool))),U_5582),U_5587))
| ~ hBOOL(hAPP(hAPP(U_5582,U_5583),U_5584)) ),
inference(variable_rename,[status(thm)],[f_1760_1]) ).
cnf(f_1760_3,plain,
( hBOOL(hAPP(hAPP(U_5587,U_5583),U_5584))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5585,tc_fun(U_5586,tc_HOL_Obool))),U_5582),U_5587))
| ~ hBOOL(hAPP(hAPP(U_5582,U_5583),U_5584)) ),
inference(clausify,[status(thm)],[f_1760_2]) ).
fof(f_1761_1,plain,
! [V_y_2,V_x_2,V_Q_2,V_P_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2)) ),
inference(fof_nnf,[status(thm)],[fact_predicate2D]) ).
fof(f_1761_2,plain,
! [U_5593,U_5592,U_5591,U_5590,U_5589,U_5588] :
( hBOOL(hAPP(hAPP(U_5591,U_5592),U_5593))
| ~ hBOOL(hAPP(hAPP(U_5590,U_5592),U_5593))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5588,tc_fun(U_5589,tc_HOL_Obool))),U_5590),U_5591)) ),
inference(variable_rename,[status(thm)],[f_1761_1]) ).
fof(f_1761_3,plain,
! [U_5593,U_5592,U_5591,U_5590] :
( ! [U_5589,U_5588] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5588,tc_fun(U_5589,tc_HOL_Obool))),U_5590),U_5591))
| hBOOL(hAPP(hAPP(U_5591,U_5592),U_5593))
| ~ hBOOL(hAPP(hAPP(U_5590,U_5592),U_5593)) ),
inference(miniscope,[status(thm)],[f_1761_2]) ).
cnf(f_1761_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5588,tc_fun(U_5589,tc_HOL_Obool))),U_5590),U_5591))
| hBOOL(hAPP(hAPP(U_5591,U_5592),U_5593))
| ~ hBOOL(hAPP(hAPP(U_5590,U_5592),U_5593)) ),
inference(clausify,[status(thm)],[f_1761_3]) ).
fof(f_1762_1,plain,
! [V_P_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
| ? [B_x,B_y] :
( ~ hBOOL(hAPP(hAPP(V_P_2,B_x),B_y))
& ( hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y)))
| B_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),B_x),B_y))) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a0_2),V_a1_2))) ),
inference(fof_nnf,[status(thm)],[fact_nat__gcd_Opinduct]) ).
fof(f_1762_2,plain,
! [U_5598,U_5597,U_5596] :
( hBOOL(hAPP(hAPP(U_5598,U_5596),U_5597))
| ? [U_5595,U_5594] :
( ~ hBOOL(hAPP(hAPP(U_5598,U_5595),U_5594))
& ( hBOOL(hAPP(hAPP(U_5598,U_5594),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5595,U_5594)))
| U_5594 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5595),U_5594))) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5596),U_5597))) ),
inference(variable_rename,[status(thm)],[f_1762_1]) ).
fof(f_1762_3,plain,
! [U_5598,U_5597,U_5596] :
( hBOOL(hAPP(hAPP(U_5598,U_5596),U_5597))
| ? [U_5594] :
( ~ hBOOL(hAPP(hAPP(U_5598,sK79(U_5598,U_5597,U_5596)),U_5594))
& ( hBOOL(hAPP(hAPP(U_5598,U_5594),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK79(U_5598,U_5597,U_5596),U_5594)))
| U_5594 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),sK79(U_5598,U_5597,U_5596)),U_5594))) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5596),U_5597))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_5595,sK79(U_5598,U_5597,U_5596))],[f_1762_2]) ).
fof(f_1762_4,plain,
! [U_5598,U_5597,U_5596] :
( hBOOL(hAPP(hAPP(U_5598,U_5596),U_5597))
| ( ~ hBOOL(hAPP(hAPP(U_5598,sK79(U_5598,U_5597,U_5596)),sK80(U_5598,U_5597,U_5596)))
& ( hBOOL(hAPP(hAPP(U_5598,sK80(U_5598,U_5597,U_5596)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK79(U_5598,U_5597,U_5596),sK80(U_5598,U_5597,U_5596))))
| sK80(U_5598,U_5597,U_5596) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),sK79(U_5598,U_5597,U_5596)),sK80(U_5598,U_5597,U_5596)))) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5596),U_5597))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_5594,sK80(U_5598,U_5597,U_5596))],[f_1762_3]) ).
cnf(f_1762_5,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),sK79(U_5598,U_5597,U_5596)),sK80(U_5598,U_5597,U_5596))))
| hBOOL(hAPP(hAPP(U_5598,U_5596),U_5597))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5596),U_5597))) ),
inference(clausify,[status(thm)],[f_1762_4]) ).
cnf(f_1762_6,plain,
( hBOOL(hAPP(hAPP(U_5598,sK80(U_5598,U_5597,U_5596)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK79(U_5598,U_5597,U_5596),sK80(U_5598,U_5597,U_5596))))
| sK80(U_5598,U_5597,U_5596) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(U_5598,U_5596),U_5597))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5596),U_5597))) ),
inference(clausify,[status(thm)],[f_1762_4]) ).
cnf(f_1762_7,plain,
( ~ hBOOL(hAPP(hAPP(U_5598,sK79(U_5598,U_5597,U_5596)),sK80(U_5598,U_5597,U_5596)))
| hBOOL(hAPP(hAPP(U_5598,U_5596),U_5597))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_5596),U_5597))) ),
inference(clausify,[status(thm)],[f_1762_4]) ).
fof(f_1763_1,plain,
! [V_r_2,V_q_2,T_b] : c_Nitpick_Oplus__frac(T_b,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_b),V_q_2),hAPP(c_Nitpick_Odenom(T_b),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_b),tc_Int_Oint),c_Nitpick_Ofrac(T_b)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_q_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_q_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),V_r_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint)),hAPP(c_Nitpick_Odenom(T_b),V_r_2)))))),c_COMBI(tc_Int_Oint))),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Oplus__frac__def]) ).
fof(f_1763_2,plain,
! [U_5601,U_5600,U_5599] : c_Nitpick_Oplus__frac(U_5599,U_5600,U_5601) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5599),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(U_5599),U_5600),hAPP(c_Nitpick_Odenom(U_5599),U_5601))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,U_5599),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,U_5599),tc_Int_Oint),c_Nitpick_Ofrac(U_5599)),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(U_5599),U_5600))),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(U_5599),U_5600))))),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(U_5599),U_5601))),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(U_5599),U_5601)))))),c_COMBI(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_1763_1]) ).
cnf(f_1763_3,plain,
c_Nitpick_Oplus__frac(U_5599,U_5600,U_5601) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5599),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(U_5599),U_5600),hAPP(c_Nitpick_Odenom(U_5599),U_5601))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,U_5599),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,U_5599),tc_Int_Oint),c_Nitpick_Ofrac(U_5599)),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(U_5599),U_5600))),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(U_5599),U_5600))))),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(U_5599),U_5601))),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(U_5599),U_5601)))))),c_COMBI(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_1763_2]) ).
fof(f_1764_1,plain,
! [T_d,T_c,T_b] : c_Product__Type_Ointernal__split(T_b,T_c,T_d) = c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),
inference(fof_nnf,[status(thm)],[fact_internal__split__def]) ).
fof(f_1764_2,plain,
! [U_5604,U_5603,U_5602] : c_Product__Type_Ointernal__split(U_5602,U_5603,U_5604) = c_Product__Type_Oprod_Oprod__case(U_5602,U_5603,U_5604),
inference(variable_rename,[status(thm)],[f_1764_1]) ).
cnf(f_1764_3,plain,
c_Product__Type_Ointernal__split(U_5602,U_5603,U_5604) = c_Product__Type_Oprod_Oprod__case(U_5602,U_5603,U_5604),
inference(clausify,[status(thm)],[f_1764_2]) ).
fof(f_1765_1,plain,
c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_bool_Osize_I2_J]) ).
cnf(f_1765_2,plain,
c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1765_1]) ).
fof(f_1766_1,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_bool_Osize_I1_J]) ).
cnf(f_1766_2,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1766_1]) ).
fof(f_1767_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2),
inference(fof_nnf,[status(thm)],[fact_internal__split__conv]) ).
fof(f_1767_2,plain,
! [U_5610,U_5609,U_5608,U_5607,U_5606,U_5605] : hAPP(hAPP(c_Product__Type_Ointernal__split(U_5605,U_5606,U_5607),U_5608),hAPP(hAPP(c_Product__Type_OPair(U_5605,U_5606),U_5609),U_5610)) = hAPP(hAPP(U_5608,U_5609),U_5610),
inference(variable_rename,[status(thm)],[f_1767_1]) ).
cnf(f_1767_3,plain,
hAPP(hAPP(c_Product__Type_Ointernal__split(U_5605,U_5606,U_5607),U_5608),hAPP(hAPP(c_Product__Type_OPair(U_5605,U_5606),U_5609),U_5610)) = hAPP(hAPP(U_5608,U_5609),U_5610),
inference(clausify,[status(thm)],[f_1767_2]) ).
fof(f_1768_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Otimes__frac__def]) ).
fof(f_1768_2,plain,
! [U_5613,U_5612,U_5611] : c_Nitpick_Otimes__frac(U_5611,U_5612,U_5613) = hAPP(hAPP(c_Nitpick_Ofrac(U_5611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_5611),U_5612)),hAPP(c_Nitpick_Onum(U_5611),U_5613))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(U_5611),U_5612)),hAPP(c_Nitpick_Odenom(U_5611),U_5613))),
inference(variable_rename,[status(thm)],[f_1768_1]) ).
cnf(f_1768_3,plain,
c_Nitpick_Otimes__frac(U_5611,U_5612,U_5613) = hAPP(hAPP(c_Nitpick_Ofrac(U_5611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_5611),U_5612)),hAPP(c_Nitpick_Onum(U_5611),U_5613))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(U_5611),U_5612)),hAPP(c_Nitpick_Odenom(U_5611),U_5613))),
inference(clausify,[status(thm)],[f_1768_2]) ).
fof(f_1769_1,plain,
! [V_q,T_a,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)))
| ~ class_Rings_Oring__1(T_b)
| ~ class_Rings_Oinverse(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Oof__frac__def]) ).
fof(f_1769_2,plain,
! [U_5616,U_5615,U_5614] :
( c_Nitpick_Oof__frac(U_5615,U_5614,U_5616) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5614),hAPP(c_Int_Oring__1__class_Oof__int(U_5614),hAPP(c_Nitpick_Onum(U_5615),U_5616))),hAPP(c_Int_Oring__1__class_Oof__int(U_5614),hAPP(c_Nitpick_Odenom(U_5615),U_5616)))
| ~ class_Rings_Oring__1(U_5614)
| ~ class_Rings_Oinverse(U_5614) ),
inference(variable_rename,[status(thm)],[f_1769_1]) ).
cnf(f_1769_3,plain,
( c_Nitpick_Oof__frac(U_5615,U_5614,U_5616) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5614),hAPP(c_Int_Oring__1__class_Oof__int(U_5614),hAPP(c_Nitpick_Onum(U_5615),U_5616))),hAPP(c_Int_Oring__1__class_Oof__int(U_5614),hAPP(c_Nitpick_Odenom(U_5615),U_5616)))
| ~ class_Rings_Oring__1(U_5614)
| ~ class_Rings_Oinverse(U_5614) ),
inference(clausify,[status(thm)],[f_1769_2]) ).
fof(f_1770_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Oinverse__frac__def]) ).
fof(f_1770_2,plain,
! [U_5618,U_5617] : c_Nitpick_Oinverse__frac(U_5617,U_5618) = hAPP(hAPP(c_Nitpick_Ofrac(U_5617),hAPP(c_Nitpick_Odenom(U_5617),U_5618)),hAPP(c_Nitpick_Onum(U_5617),U_5618)),
inference(variable_rename,[status(thm)],[f_1770_1]) ).
cnf(f_1770_3,plain,
c_Nitpick_Oinverse__frac(U_5617,U_5618) = hAPP(hAPP(c_Nitpick_Ofrac(U_5617),hAPP(c_Nitpick_Odenom(U_5617),U_5618)),hAPP(c_Nitpick_Onum(U_5617),U_5618)),
inference(clausify,[status(thm)],[f_1770_2]) ).
fof(f_1771_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Ouminus__frac__def]) ).
fof(f_1771_2,plain,
! [U_5620,U_5619] : c_Nitpick_Ouminus__frac(U_5619,U_5620) = c_Nitpick_OAbs__Frac(U_5619,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(U_5619),U_5620))),hAPP(c_Nitpick_Odenom(U_5619),U_5620))),
inference(variable_rename,[status(thm)],[f_1771_1]) ).
cnf(f_1771_3,plain,
c_Nitpick_Ouminus__frac(U_5619,U_5620) = c_Nitpick_OAbs__Frac(U_5619,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(U_5619),U_5620))),hAPP(c_Nitpick_Odenom(U_5619),U_5620))),
inference(clausify,[status(thm)],[f_1771_2]) ).
fof(f_1772_1,plain,
! [V_r_2,V_q_2,T_b] :
( ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__frac__def]) ).
fof(f_1772_2,plain,
! [U_5623,U_5622,U_5621] :
( ( c_Nitpick_Oless__frac(U_5621,U_5622,U_5623)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_5621),c_Nitpick_Oplus__frac(U_5621,U_5622,c_Nitpick_Ouminus__frac(U_5621,U_5623)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_5621),c_Nitpick_Oplus__frac(U_5621,U_5622,c_Nitpick_Ouminus__frac(U_5621,U_5623)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ c_Nitpick_Oless__frac(U_5621,U_5622,U_5623) ) ),
inference(variable_rename,[status(thm)],[f_1772_1]) ).
fof(f_1772_3,plain,
( ! [U_5629,U_5627,U_5625] :
( c_Nitpick_Oless__frac(U_5625,U_5627,U_5629)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_5625),c_Nitpick_Oplus__frac(U_5625,U_5627,c_Nitpick_Ouminus__frac(U_5625,U_5629)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_5628,U_5626,U_5624] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_5624),c_Nitpick_Oplus__frac(U_5624,U_5626,c_Nitpick_Ouminus__frac(U_5624,U_5628)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ c_Nitpick_Oless__frac(U_5624,U_5626,U_5628) ) ),
inference(miniscope,[status(thm)],[f_1772_2]) ).
cnf(f_1772_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_5624),c_Nitpick_Oplus__frac(U_5624,U_5626,c_Nitpick_Ouminus__frac(U_5624,U_5628)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ c_Nitpick_Oless__frac(U_5624,U_5626,U_5628) ),
inference(clausify,[status(thm)],[f_1772_3]) ).
cnf(f_1772_5,plain,
( c_Nitpick_Oless__frac(U_5625,U_5627,U_5629)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_5625),c_Nitpick_Oplus__frac(U_5625,U_5627,c_Nitpick_Ouminus__frac(U_5625,U_5629)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1772_3]) ).
fof(f_1773_1,plain,
! [V_r_2,V_q_2,T_b] :
( ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__eq__frac__def]) ).
fof(f_1773_2,plain,
! [U_5632,U_5631,U_5630] :
( ( c_Nitpick_Oless__eq__frac(U_5630,U_5631,U_5632)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_5630),c_Nitpick_Oplus__frac(U_5630,U_5631,c_Nitpick_Ouminus__frac(U_5630,U_5632)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_5630),c_Nitpick_Oplus__frac(U_5630,U_5631,c_Nitpick_Ouminus__frac(U_5630,U_5632)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ c_Nitpick_Oless__eq__frac(U_5630,U_5631,U_5632) ) ),
inference(variable_rename,[status(thm)],[f_1773_1]) ).
fof(f_1773_3,plain,
( ! [U_5638,U_5636,U_5634] :
( c_Nitpick_Oless__eq__frac(U_5634,U_5636,U_5638)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_5634),c_Nitpick_Oplus__frac(U_5634,U_5636,c_Nitpick_Ouminus__frac(U_5634,U_5638)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [U_5637,U_5635,U_5633] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_5633),c_Nitpick_Oplus__frac(U_5633,U_5635,c_Nitpick_Ouminus__frac(U_5633,U_5637)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ c_Nitpick_Oless__eq__frac(U_5633,U_5635,U_5637) ) ),
inference(miniscope,[status(thm)],[f_1773_2]) ).
cnf(f_1773_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_5633),c_Nitpick_Oplus__frac(U_5633,U_5635,c_Nitpick_Ouminus__frac(U_5633,U_5637)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ c_Nitpick_Oless__eq__frac(U_5633,U_5635,U_5637) ),
inference(clausify,[status(thm)],[f_1773_3]) ).
cnf(f_1773_5,plain,
( c_Nitpick_Oless__eq__frac(U_5634,U_5636,U_5638)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_5634),c_Nitpick_Oplus__frac(U_5634,U_5636,c_Nitpick_Ouminus__frac(U_5634,U_5638)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1773_3]) ).
fof(f_1774_1,plain,
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)),
inference(fof_nnf,[status(thm)],[fact_transfer__morphism__int__nat]) ).
cnf(f_1774_2,plain,
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)),
inference(clausify,[status(thm)],[f_1774_1]) ).
fof(f_1775_1,plain,
! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__size(T_b,T_c,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(fof_nnf,[status(thm)],[fact_pair__box_Osize_I1_J]) ).
fof(f_1775_2,plain,
! [U_5644,U_5643,U_5642,U_5641,U_5640,U_5639] : c_Nitpick_Opair__box_Opair__box__size(U_5639,U_5640,U_5641,U_5642,c_Nitpick_Opair__box_OPairBox(U_5639,U_5640,U_5643,U_5644)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_5641,U_5643)),hAPP(U_5642,U_5644))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_1775_1]) ).
cnf(f_1775_3,plain,
c_Nitpick_Opair__box_Opair__box__size(U_5639,U_5640,U_5641,U_5642,c_Nitpick_Opair__box_OPairBox(U_5639,U_5640,U_5643,U_5644)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_5641,U_5643)),hAPP(U_5642,U_5644))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_1775_2]) ).
fof(f_1776_1,plain,
! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))),
inference(fof_nnf,[status(thm)],[fact_The__split]) ).
fof(f_1776_2,plain,
! [U_5647,U_5646,U_5645] : c_HOL_OThe(tc_prod(U_5645,U_5646),hAPP(c_Product__Type_Oprod_Oprod__case(U_5645,U_5646,tc_HOL_Obool),U_5647)) = c_HOL_OThe(tc_prod(U_5645,U_5646),hAPP(hAPP(c_COMBS(tc_prod(U_5645,U_5646),U_5646,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_5645,tc_fun(U_5646,tc_HOL_Obool),tc_prod(U_5645,U_5646)),U_5647),c_Product__Type_Ofst(U_5645,U_5646))),c_Product__Type_Osnd(U_5645,U_5646))),
inference(variable_rename,[status(thm)],[f_1776_1]) ).
cnf(f_1776_3,plain,
c_HOL_OThe(tc_prod(U_5645,U_5646),hAPP(c_Product__Type_Oprod_Oprod__case(U_5645,U_5646,tc_HOL_Obool),U_5647)) = c_HOL_OThe(tc_prod(U_5645,U_5646),hAPP(hAPP(c_COMBS(tc_prod(U_5645,U_5646),U_5646,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_5645,tc_fun(U_5646,tc_HOL_Obool),tc_prod(U_5645,U_5646)),U_5647),c_Product__Type_Ofst(U_5645,U_5646))),c_Product__Type_Osnd(U_5645,U_5646))),
inference(clausify,[status(thm)],[f_1776_2]) ).
fof(f_1777_1,plain,
! [V_size_2,V_g_2,T_b,V_nrandom_2] :
( ( c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(V_g_2,V_size_2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_b,V_g_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_size_2))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_b)),c_Product__Type_Ofst(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) )
& ( c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b))
| ~ 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))) ) ),
inference(fof_nnf,[status(thm)],[fact_Random_Osimps]) ).
fof(f_1777_2,plain,
! [U_5651,U_5650,U_5649,U_5648] :
( ( c_Random__Sequence_ORandom(U_5649,U_5650,U_5648,U_5651) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_5649,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(U_5649)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_5650,U_5651)),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(U_5649)))),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(U_5649)))),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(U_5649)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_5649,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(U_5649)))),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(U_5649)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_5649,U_5650,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5648),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_5651))),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(U_5649)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_5649))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_5649)))),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(U_5649)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_5649,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(U_5649)))),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(U_5649)))),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(U_5649))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_5649)))),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(U_5649)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_5649)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_5649))))),tc_prod(U_5649,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_5649)),hAPP(hAPP(c_COMBB(U_5649,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_5649)))),tc_prod(U_5649,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_5649)),c_Product__Type_Ofst(U_5649,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5648),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) )
& ( c_Random__Sequence_ORandom(U_5649,U_5650,U_5648,U_5651) = 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(U_5649)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_5649))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5648),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ) ),
inference(variable_rename,[status(thm)],[f_1777_1]) ).
fof(f_1777_3,plain,
( ! [U_5659,U_5657,U_5655,U_5653] :
( c_Random__Sequence_ORandom(U_5655,U_5657,U_5653,U_5659) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_5655,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(U_5655)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_5657,U_5659)),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(U_5655)))),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(U_5655)))),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(U_5655)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_5655,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(U_5655)))),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(U_5655)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_5655,U_5657,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5653),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_5659))),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(U_5655)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_5655))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_5655)))),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(U_5655)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_5655,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(U_5655)))),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(U_5655)))),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(U_5655))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_5655)))),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(U_5655)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_5655)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_5655))))),tc_prod(U_5655,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_5655)),hAPP(hAPP(c_COMBB(U_5655,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_5655)))),tc_prod(U_5655,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_5655)),c_Product__Type_Ofst(U_5655,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5653),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) )
& ! [U_5658,U_5656,U_5654,U_5652] :
( c_Random__Sequence_ORandom(U_5654,U_5656,U_5652,U_5658) = 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(U_5654)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_5654))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5652),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ) ),
inference(miniscope,[status(thm)],[f_1777_2]) ).
cnf(f_1777_4,plain,
( c_Random__Sequence_ORandom(U_5654,U_5656,U_5652,U_5658) = 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(U_5654)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_5654))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5652),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ),
inference(clausify,[status(thm)],[f_1777_3]) ).
cnf(f_1777_5,plain,
( c_Random__Sequence_ORandom(U_5655,U_5657,U_5653,U_5659) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_5655,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(U_5655)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_5657,U_5659)),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(U_5655)))),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(U_5655)))),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(U_5655)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_5655,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(U_5655)))),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(U_5655)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_5655,U_5657,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5653),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_5659))),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(U_5655)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_5655))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_5655)))),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(U_5655)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_5655,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(U_5655)))),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(U_5655)))),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(U_5655))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_5655)))),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(U_5655)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_5655)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_5655))))),tc_prod(U_5655,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_5655)),hAPP(hAPP(c_COMBB(U_5655,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_5655)))),tc_prod(U_5655,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_5655)),c_Product__Type_Ofst(U_5655,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5653),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ),
inference(clausify,[status(thm)],[f_1777_3]) ).
fof(f_1778_1,plain,
! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
( ( c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2)
| V_b_2 != V_b_H_2
| V_a_2 != V_a_H_2 )
& ( ( V_b_2 = V_b_H_2
& V_a_2 = V_a_H_2 )
| c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2) != c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2) ) ),
inference(fof_nnf,[status(thm)],[fact_pair__box_Oinject]) ).
fof(f_1778_2,plain,
! [U_5665,U_5664,U_5663,U_5662,U_5661,U_5660] :
( ( c_Nitpick_Opair__box_OPairBox(U_5660,U_5661,U_5662,U_5663) = c_Nitpick_Opair__box_OPairBox(U_5660,U_5661,U_5664,U_5665)
| U_5663 != U_5665
| U_5662 != U_5664 )
& ( ( U_5663 = U_5665
& U_5662 = U_5664 )
| c_Nitpick_Opair__box_OPairBox(U_5660,U_5661,U_5662,U_5663) != c_Nitpick_Opair__box_OPairBox(U_5660,U_5661,U_5664,U_5665) ) ),
inference(variable_rename,[status(thm)],[f_1778_1]) ).
fof(f_1778_3,plain,
( ! [U_5677,U_5675,U_5673,U_5671] :
( ! [U_5669,U_5667] : c_Nitpick_Opair__box_OPairBox(U_5667,U_5669,U_5671,U_5673) = c_Nitpick_Opair__box_OPairBox(U_5667,U_5669,U_5675,U_5677)
| U_5673 != U_5677
| U_5671 != U_5675 )
& ! [U_5676,U_5674,U_5672,U_5670] :
( ! [U_5668,U_5666] : c_Nitpick_Opair__box_OPairBox(U_5666,U_5668,U_5670,U_5672) != c_Nitpick_Opair__box_OPairBox(U_5666,U_5668,U_5674,U_5676)
| ( U_5672 = U_5676
& U_5670 = U_5674 ) ) ),
inference(miniscope,[status(thm)],[f_1778_2]) ).
cnf(f_1778_4,plain,
( U_5670 = U_5674
| c_Nitpick_Opair__box_OPairBox(U_5666,U_5668,U_5670,U_5672) != c_Nitpick_Opair__box_OPairBox(U_5666,U_5668,U_5674,U_5676) ),
inference(clausify,[status(thm)],[f_1778_3]) ).
cnf(f_1778_5,plain,
( U_5672 = U_5676
| c_Nitpick_Opair__box_OPairBox(U_5666,U_5668,U_5670,U_5672) != c_Nitpick_Opair__box_OPairBox(U_5666,U_5668,U_5674,U_5676) ),
inference(clausify,[status(thm)],[f_1778_3]) ).
cnf(f_1778_6,plain,
( c_Nitpick_Opair__box_OPairBox(U_5667,U_5669,U_5671,U_5673) = c_Nitpick_Opair__box_OPairBox(U_5667,U_5669,U_5675,U_5677)
| U_5673 != U_5677
| U_5671 != U_5675 ),
inference(clausify,[status(thm)],[f_1778_3]) ).
fof(f_1779_1,plain,
! [V_y_2,V_x_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2),
inference(fof_nnf,[status(thm)],[fact_The__split__eq]) ).
fof(f_1779_2,plain,
! [U_5681,U_5680,U_5679,U_5678] : c_HOL_OThe(tc_prod(U_5678,U_5679),hAPP(c_Product__Type_Oprod_Oprod__case(U_5678,U_5679,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_5678,tc_fun(U_5679,tc_HOL_Obool),tc_fun(U_5679,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_5679,tc_HOL_Obool),tc_fun(U_5679,tc_HOL_Obool)),U_5678),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_5679)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_5678),c_fconj),hAPP(c_fequal,U_5680)))),hAPP(c_fequal,U_5681)))) = hAPP(hAPP(c_Product__Type_OPair(U_5678,U_5679),U_5680),U_5681),
inference(variable_rename,[status(thm)],[f_1779_1]) ).
cnf(f_1779_3,plain,
c_HOL_OThe(tc_prod(U_5678,U_5679),hAPP(c_Product__Type_Oprod_Oprod__case(U_5678,U_5679,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_5678,tc_fun(U_5679,tc_HOL_Obool),tc_fun(U_5679,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_5679,tc_HOL_Obool),tc_fun(U_5679,tc_HOL_Obool)),U_5678),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_5679)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_5678),c_fconj),hAPP(c_fequal,U_5680)))),hAPP(c_fequal,U_5681)))) = hAPP(hAPP(c_Product__Type_OPair(U_5678,U_5679),U_5680),U_5681),
inference(clausify,[status(thm)],[f_1779_2]) ).
fof(f_1780_1,plain,
! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_P_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))),
inference(fof_nnf,[status(thm)],[fact_split__paired__The]) ).
fof(f_1780_2,plain,
! [U_5684,U_5683,U_5682] : c_HOL_OThe(tc_prod(U_5682,U_5683),U_5684) = c_HOL_OThe(tc_prod(U_5682,U_5683),hAPP(c_Product__Type_Oprod_Oprod__case(U_5682,U_5683,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_5683,tc_prod(U_5682,U_5683)),tc_fun(U_5683,tc_HOL_Obool),U_5682),hAPP(c_COMBB(tc_prod(U_5682,U_5683),tc_HOL_Obool,U_5683),U_5684)),c_Product__Type_OPair(U_5682,U_5683)))),
inference(variable_rename,[status(thm)],[f_1780_1]) ).
cnf(f_1780_3,plain,
c_HOL_OThe(tc_prod(U_5682,U_5683),U_5684) = c_HOL_OThe(tc_prod(U_5682,U_5683),hAPP(c_Product__Type_Oprod_Oprod__case(U_5682,U_5683,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_5683,tc_prod(U_5682,U_5683)),tc_fun(U_5683,tc_HOL_Obool),U_5682),hAPP(c_COMBB(tc_prod(U_5682,U_5683),tc_HOL_Obool,U_5683),U_5684)),c_Product__Type_OPair(U_5682,U_5683)))),
inference(clausify,[status(thm)],[f_1780_2]) ).
fof(f_1781_1,plain,
! [V_na_2,V_m_2] : c_Divides_Odivmod__nat(V_m_2,V_na_2) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(V_m_2,V_na_2)),
inference(fof_nnf,[status(thm)],[fact_divmod__nat__def]) ).
fof(f_1781_2,plain,
! [U_5686,U_5685] : c_Divides_Odivmod__nat(U_5685,U_5686) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_5685,U_5686)),
inference(variable_rename,[status(thm)],[f_1781_1]) ).
cnf(f_1781_3,plain,
c_Divides_Odivmod__nat(U_5685,U_5686) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_5685,U_5686)),
inference(clausify,[status(thm)],[f_1781_2]) ).
fof(f_1782_1,plain,
! [V_size_2,V_nrandom_2,T_b] : c_Random__Sequence_Oempty(T_b,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)),
inference(fof_nnf,[status(thm)],[fact_Random__Sequence_Oempty__def]) ).
fof(f_1782_2,plain,
! [U_5689,U_5688,U_5687] : c_Random__Sequence_Oempty(U_5687,U_5688,U_5689) = 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(U_5687)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_5687)),
inference(variable_rename,[status(thm)],[f_1782_1]) ).
cnf(f_1782_3,plain,
c_Random__Sequence_Oempty(U_5687,U_5688,U_5689) = 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(U_5687)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_5687)),
inference(clausify,[status(thm)],[f_1782_2]) ).
fof(f_1783_1,plain,
! [V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_b),V_x_2),V_nrandom_2),V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_b),V_x_2)),
inference(fof_nnf,[status(thm)],[fact_Random__Sequence_Osingle__def]) ).
fof(f_1783_2,plain,
! [U_5693,U_5692,U_5691,U_5690] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(U_5690),U_5691),U_5692),U_5693) = 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(U_5690)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(U_5690),U_5691)),
inference(variable_rename,[status(thm)],[f_1783_1]) ).
cnf(f_1783_3,plain,
hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(U_5690),U_5691),U_5692),U_5693) = 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(U_5690)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(U_5690),U_5691)),
inference(clausify,[status(thm)],[f_1783_2]) ).
fof(f_1784_1,plain,
! [V_b,V_a,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(T_a,T_b)),c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a,V_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_pair__box_Osize_I2_J]) ).
fof(f_1784_2,plain,
! [U_5697,U_5696,U_5695,U_5694] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(U_5694,U_5695)),c_Nitpick_Opair__box_OPairBox(U_5694,U_5695,U_5696,U_5697)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_1784_1]) ).
cnf(f_1784_3,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(U_5694,U_5695)),c_Nitpick_Opair__box_OPairBox(U_5694,U_5695,U_5696,U_5697)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1784_2]) ).
fof(f_1785_1,plain,
! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__case(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
inference(fof_nnf,[status(thm)],[fact_pair__box_Osimps_I2_J]) ).
fof(f_1785_2,plain,
! [U_5703,U_5702,U_5701,U_5700,U_5699,U_5698] : c_Nitpick_Opair__box_Opair__box__case(U_5698,U_5699,U_5700,U_5701,c_Nitpick_Opair__box_OPairBox(U_5698,U_5699,U_5702,U_5703)) = hAPP(hAPP(U_5701,U_5702),U_5703),
inference(variable_rename,[status(thm)],[f_1785_1]) ).
cnf(f_1785_3,plain,
c_Nitpick_Opair__box_Opair__box__case(U_5698,U_5699,U_5700,U_5701,c_Nitpick_Opair__box_OPairBox(U_5698,U_5699,U_5702,U_5703)) = hAPP(hAPP(U_5701,U_5702),U_5703),
inference(clausify,[status(thm)],[f_1785_2]) ).
fof(f_1786_1,plain,
! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__rec(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2),
inference(fof_nnf,[status(thm)],[fact_pair__box_Orecs]) ).
fof(f_1786_2,plain,
! [U_5709,U_5708,U_5707,U_5706,U_5705,U_5704] : c_Nitpick_Opair__box_Opair__box__rec(U_5704,U_5705,U_5706,U_5707,c_Nitpick_Opair__box_OPairBox(U_5704,U_5705,U_5708,U_5709)) = hAPP(hAPP(U_5707,U_5708),U_5709),
inference(variable_rename,[status(thm)],[f_1786_1]) ).
cnf(f_1786_3,plain,
c_Nitpick_Opair__box_Opair__box__rec(U_5704,U_5705,U_5706,U_5707,c_Nitpick_Opair__box_OPairBox(U_5704,U_5705,U_5708,U_5709)) = hAPP(hAPP(U_5707,U_5708),U_5709),
inference(clausify,[status(thm)],[f_1786_2]) ).
fof(f_1787_1,plain,
! [V_a_2,T_b] : c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2,
inference(fof_nnf,[status(thm)],[fact_the__eq__trivial]) ).
fof(f_1787_2,plain,
! [U_5711,U_5710] : c_HOL_OThe(U_5710,hAPP(hAPP(c_COMBC(U_5710,U_5710,tc_HOL_Obool),c_fequal),U_5711)) = U_5711,
inference(variable_rename,[status(thm)],[f_1787_1]) ).
cnf(f_1787_3,plain,
c_HOL_OThe(U_5710,hAPP(hAPP(c_COMBC(U_5710,U_5710,tc_HOL_Obool),c_fequal),U_5711)) = U_5711,
inference(clausify,[status(thm)],[f_1787_2]) ).
fof(f_1788_1,plain,
! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2,
inference(fof_nnf,[status(thm)],[fact_the__sym__eq__trivial]) ).
fof(f_1788_2,plain,
! [U_5713,U_5712] : c_HOL_OThe(U_5712,hAPP(c_fequal,U_5713)) = U_5713,
inference(variable_rename,[status(thm)],[f_1788_1]) ).
cnf(f_1788_3,plain,
c_HOL_OThe(U_5712,hAPP(c_fequal,U_5713)) = U_5713,
inference(clausify,[status(thm)],[f_1788_2]) ).
fof(f_1789_1,plain,
! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_P_2] :
( hBOOL(hAPP(V_Q_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2)))
| ? [B_x,B_y] :
( ~ hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y)))
& hBOOL(hAPP(hAPP(V_P_2,B_y),B_x)) )
| ~ hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2))) ),
inference(fof_nnf,[status(thm)],[fact_exE__realizer]) ).
fof(f_1789_2,plain,
! [U_5722,U_5721,U_5720,U_5719,U_5718,U_5717,U_5716] :
( hBOOL(hAPP(U_5720,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5717,U_5718,U_5722),U_5721),U_5719)))
| ? [U_5715,U_5714] :
( ~ hBOOL(hAPP(U_5720,hAPP(hAPP(U_5721,U_5715),U_5714)))
& hBOOL(hAPP(hAPP(U_5716,U_5714),U_5715)) )
| ~ hBOOL(hAPP(hAPP(U_5716,hAPP(c_Product__Type_Osnd(U_5717,U_5718),U_5719)),hAPP(c_Product__Type_Ofst(U_5717,U_5718),U_5719))) ),
inference(variable_rename,[status(thm)],[f_1789_1]) ).
fof(f_1789_3,plain,
! [U_5722,U_5721,U_5720,U_5719,U_5718,U_5717,U_5716] :
( hBOOL(hAPP(U_5720,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5717,U_5718,U_5722),U_5721),U_5719)))
| ? [U_5714] :
( ~ hBOOL(hAPP(U_5720,hAPP(hAPP(U_5721,sK81(U_5722,U_5721,U_5720,U_5719,U_5718,U_5717,U_5716)),U_5714)))
& hBOOL(hAPP(hAPP(U_5716,U_5714),sK81(U_5722,U_5721,U_5720,U_5719,U_5718,U_5717,U_5716))) )
| ~ hBOOL(hAPP(hAPP(U_5716,hAPP(c_Product__Type_Osnd(U_5717,U_5718),U_5719)),hAPP(c_Product__Type_Ofst(U_5717,U_5718),U_5719))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_5715,sK81(U_5722,U_5721,U_5720,U_5719,U_5718,U_5717,U_5716))],[f_1789_2]) ).
fof(f_1789_4,plain,
! [U_5722,U_5721,U_5720,U_5719,U_5718,U_5717,U_5716] :
( hBOOL(hAPP(U_5720,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5717,U_5718,U_5722),U_5721),U_5719)))
| ( ~ hBOOL(hAPP(U_5720,hAPP(hAPP(U_5721,sK81(U_5722,U_5721,U_5720,U_5719,U_5718,U_5717,U_5716)),sK82(U_5722,U_5721,U_5720,U_5719,U_5718,U_5717,U_5716))))
& hBOOL(hAPP(hAPP(U_5716,sK82(U_5722,U_5721,U_5720,U_5719,U_5718,U_5717,U_5716)),sK81(U_5722,U_5721,U_5720,U_5719,U_5718,U_5717,U_5716))) )
| ~ hBOOL(hAPP(hAPP(U_5716,hAPP(c_Product__Type_Osnd(U_5717,U_5718),U_5719)),hAPP(c_Product__Type_Ofst(U_5717,U_5718),U_5719))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_5714,sK82(U_5722,U_5721,U_5720,U_5719,U_5718,U_5717,U_5716))],[f_1789_3]) ).
cnf(f_1789_5,plain,
( hBOOL(hAPP(hAPP(U_5716,sK82(U_5722,U_5721,U_5720,U_5719,U_5718,U_5717,U_5716)),sK81(U_5722,U_5721,U_5720,U_5719,U_5718,U_5717,U_5716)))
| hBOOL(hAPP(U_5720,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5717,U_5718,U_5722),U_5721),U_5719)))
| ~ hBOOL(hAPP(hAPP(U_5716,hAPP(c_Product__Type_Osnd(U_5717,U_5718),U_5719)),hAPP(c_Product__Type_Ofst(U_5717,U_5718),U_5719))) ),
inference(clausify,[status(thm)],[f_1789_4]) ).
cnf(f_1789_6,plain,
( ~ hBOOL(hAPP(U_5720,hAPP(hAPP(U_5721,sK81(U_5722,U_5721,U_5720,U_5719,U_5718,U_5717,U_5716)),sK82(U_5722,U_5721,U_5720,U_5719,U_5718,U_5717,U_5716))))
| hBOOL(hAPP(U_5720,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5717,U_5718,U_5722),U_5721),U_5719)))
| ~ hBOOL(hAPP(hAPP(U_5716,hAPP(c_Product__Type_Osnd(U_5717,U_5718),U_5719)),hAPP(c_Product__Type_Ofst(U_5717,U_5718),U_5719))) ),
inference(clausify,[status(thm)],[f_1789_4]) ).
fof(f_1790_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__not__seq__def]) ).
fof(f_1790_2,plain,
! [U_5724,U_5723] : hAPP(c_New__DSequence_Opos__not__seq(U_5723),U_5724) = c_Lazy__Sequence_Ohb__not__seq(hAPP(U_5723,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)))),U_5724))),
inference(variable_rename,[status(thm)],[f_1790_1]) ).
cnf(f_1790_3,plain,
hAPP(c_New__DSequence_Opos__not__seq(U_5723),U_5724) = c_Lazy__Sequence_Ohb__not__seq(hAPP(U_5723,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)))),U_5724))),
inference(clausify,[status(thm)],[f_1790_2]) ).
fof(f_1791_1,plain,
! [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)) )
& ( 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))
| V_i_2 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[fact_code__numeral__not__eq__zero]) ).
fof(f_1791_2,plain,
! [U_5725] :
( ( U_5725 != 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)),U_5725)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_5725))
| U_5725 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_1791_1]) ).
fof(f_1791_3,plain,
( ! [U_5727] :
( U_5727 != 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)),U_5727)) )
& ! [U_5726] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_5726))
| U_5726 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_1791_2]) ).
cnf(f_1791_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_5726))
| U_5726 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_1791_3]) ).
cnf(f_1791_5,plain,
( U_5727 != 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)),U_5727)) ),
inference(clausify,[status(thm)],[f_1791_3]) ).
fof(f_1792_1,plain,
! [V_m_2,V_na_2] :
( ( hAPP(c_Code__Numeral_Oof__nat,V_na_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
| V_na_2 != V_m_2 )
& ( V_na_2 = V_m_2
| hAPP(c_Code__Numeral_Oof__nat,V_na_2) != hAPP(c_Code__Numeral_Oof__nat,V_m_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Oof__nat__inject]) ).
fof(f_1792_2,plain,
! [U_5729,U_5728] :
( ( hAPP(c_Code__Numeral_Oof__nat,U_5728) = hAPP(c_Code__Numeral_Oof__nat,U_5729)
| U_5728 != U_5729 )
& ( U_5728 = U_5729
| hAPP(c_Code__Numeral_Oof__nat,U_5728) != hAPP(c_Code__Numeral_Oof__nat,U_5729) ) ),
inference(variable_rename,[status(thm)],[f_1792_1]) ).
fof(f_1792_3,plain,
( ! [U_5733,U_5731] :
( hAPP(c_Code__Numeral_Oof__nat,U_5731) = hAPP(c_Code__Numeral_Oof__nat,U_5733)
| U_5731 != U_5733 )
& ! [U_5732,U_5730] :
( U_5730 = U_5732
| hAPP(c_Code__Numeral_Oof__nat,U_5730) != hAPP(c_Code__Numeral_Oof__nat,U_5732) ) ),
inference(miniscope,[status(thm)],[f_1792_2]) ).
cnf(f_1792_4,plain,
( U_5730 = U_5732
| hAPP(c_Code__Numeral_Oof__nat,U_5730) != hAPP(c_Code__Numeral_Oof__nat,U_5732) ),
inference(clausify,[status(thm)],[f_1792_3]) ).
cnf(f_1792_5,plain,
( hAPP(c_Code__Numeral_Oof__nat,U_5731) = hAPP(c_Code__Numeral_Oof__nat,U_5733)
| U_5731 != U_5733 ),
inference(clausify,[status(thm)],[f_1792_3]) ).
fof(f_1793_1,plain,
c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Oof__nat__code]) ).
cnf(f_1793_2,plain,
c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1793_1]) ).
fof(f_1794_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_times__code__numeral__code]) ).
fof(f_1794_2,plain,
! [U_5735,U_5734] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5734)),hAPP(c_Code__Numeral_Oof__nat,U_5735)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5734),U_5735)),
inference(variable_rename,[status(thm)],[f_1794_1]) ).
cnf(f_1794_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5734)),hAPP(c_Code__Numeral_Oof__nat,U_5735)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5734),U_5735)),
inference(clausify,[status(thm)],[f_1794_2]) ).
fof(f_1795_1,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[fact_zero__code__numeral__def]) ).
cnf(f_1795_2,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_1795_1]) ).
fof(f_1796_1,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[fact_one__code__numeral__def]) ).
cnf(f_1796_2,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_1796_1]) ).
fof(f_1797_1,plain,
! [V_m_2,V_na_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_na_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_na_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__code__numeral__code]) ).
fof(f_1797_2,plain,
! [U_5737,U_5736] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5736)),hAPP(c_Code__Numeral_Oof__nat,U_5737)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5736),U_5737)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5736),U_5737))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5736)),hAPP(c_Code__Numeral_Oof__nat,U_5737))) ) ),
inference(variable_rename,[status(thm)],[f_1797_1]) ).
fof(f_1797_3,plain,
( ! [U_5741,U_5739] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5739)),hAPP(c_Code__Numeral_Oof__nat,U_5741)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5739),U_5741)) )
& ! [U_5740,U_5738] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5738),U_5740))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5738)),hAPP(c_Code__Numeral_Oof__nat,U_5740))) ) ),
inference(miniscope,[status(thm)],[f_1797_2]) ).
cnf(f_1797_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5738),U_5740))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5738)),hAPP(c_Code__Numeral_Oof__nat,U_5740))) ),
inference(clausify,[status(thm)],[f_1797_3]) ).
cnf(f_1797_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5739)),hAPP(c_Code__Numeral_Oof__nat,U_5741)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5739),U_5741)) ),
inference(clausify,[status(thm)],[f_1797_3]) ).
fof(f_1798_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_plus__code__numeral__code]) ).
fof(f_1798_2,plain,
! [U_5743,U_5742] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5742)),hAPP(c_Code__Numeral_Oof__nat,U_5743)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5742),U_5743)),
inference(variable_rename,[status(thm)],[f_1798_1]) ).
cnf(f_1798_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5742)),hAPP(c_Code__Numeral_Oof__nat,U_5743)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5742),U_5743)),
inference(clausify,[status(thm)],[f_1798_2]) ).
fof(f_1799_1,plain,
! [V_m_2,V_na_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_na_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_m_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_m_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_na_2)),hAPP(c_Code__Numeral_Oof__nat,V_m_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__code]) ).
fof(f_1799_2,plain,
! [U_5745,U_5744] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5744)),hAPP(c_Code__Numeral_Oof__nat,U_5745)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5744),U_5745)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5744),U_5745))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5744)),hAPP(c_Code__Numeral_Oof__nat,U_5745))) ) ),
inference(variable_rename,[status(thm)],[f_1799_1]) ).
fof(f_1799_3,plain,
( ! [U_5749,U_5747] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5747)),hAPP(c_Code__Numeral_Oof__nat,U_5749)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5747),U_5749)) )
& ! [U_5748,U_5746] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5746),U_5748))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5746)),hAPP(c_Code__Numeral_Oof__nat,U_5748))) ) ),
inference(miniscope,[status(thm)],[f_1799_2]) ).
cnf(f_1799_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5746),U_5748))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5746)),hAPP(c_Code__Numeral_Oof__nat,U_5748))) ),
inference(clausify,[status(thm)],[f_1799_3]) ).
cnf(f_1799_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_5747)),hAPP(c_Code__Numeral_Oof__nat,U_5749)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5747),U_5749)) ),
inference(clausify,[status(thm)],[f_1799_3]) ).
fof(f_1800_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_subtract__code__numeral__code]) ).
fof(f_1800_2,plain,
! [U_5751,U_5750] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,U_5750)),hAPP(c_Code__Numeral_Oof__nat,U_5751)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5750),U_5751)),
inference(variable_rename,[status(thm)],[f_1800_1]) ).
cnf(f_1800_3,plain,
hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,U_5750)),hAPP(c_Code__Numeral_Oof__nat,U_5751)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5750),U_5751)),
inference(clausify,[status(thm)],[f_1800_2]) ).
fof(f_1801_1,plain,
! [V_k] :
( 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)))
| V_k = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(fof_nnf,[status(thm)],[fact_code__numeral__decr]) ).
fof(f_1801_2,plain,
! [U_5752] :
( 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,U_5752)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,U_5752)))
| U_5752 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[f_1801_1]) ).
cnf(f_1801_3,plain,
( 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,U_5752)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,U_5752)))
| U_5752 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_1801_2]) ).
fof(f_1802_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_pos__not__random__dseq__def]) ).
fof(f_1802_2,plain,
! [U_5756,U_5755,U_5754,U_5753] : c_New__Random__Sequence_Opos__not__random__dseq(U_5753,U_5754,U_5755,U_5756) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(U_5753,U_5754),U_5755),U_5756)),
inference(variable_rename,[status(thm)],[f_1802_1]) ).
cnf(f_1802_3,plain,
c_New__Random__Sequence_Opos__not__random__dseq(U_5753,U_5754,U_5755,U_5756) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(U_5753,U_5754),U_5755),U_5756)),
inference(clausify,[status(thm)],[f_1802_2]) ).
fof(f_1803_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_mod__code__numeral__def]) ).
fof(f_1803_2,plain,
! [U_5758,U_5757] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_5757,U_5758) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,U_5757),hAPP(c_Code__Numeral_Onat__of,U_5758))),
inference(variable_rename,[status(thm)],[f_1803_1]) ).
cnf(f_1803_3,plain,
c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_5757,U_5758) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,U_5757),hAPP(c_Code__Numeral_Onat__of,U_5758))),
inference(clausify,[status(thm)],[f_1803_2]) ).
fof(f_1804_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_times__code__numeral__def]) ).
fof(f_1804_2,plain,
! [U_5760,U_5759] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),U_5759),U_5760) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5759)),hAPP(c_Code__Numeral_Onat__of,U_5760))),
inference(variable_rename,[status(thm)],[f_1804_1]) ).
cnf(f_1804_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),U_5759),U_5760) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5759)),hAPP(c_Code__Numeral_Onat__of,U_5760))),
inference(clausify,[status(thm)],[f_1804_2]) ).
fof(f_1805_1,plain,
! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
( ( hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2))
| V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_b)
| V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__decr__bind__def]) ).
fof(f_1805_2,plain,
! [U_5765,U_5764,U_5763,U_5762,U_5761] :
( ( hAPP(c_New__DSequence_Opos__decr__bind(U_5762,U_5763,U_5764,U_5765),U_5761) = hAPP(c_Lazy__Sequence_Obind(U_5762,U_5763,hAPP(U_5764,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5761),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(U_5762,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_5763)),U_5765),U_5761))
| U_5761 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( hAPP(c_New__DSequence_Opos__decr__bind(U_5762,U_5763,U_5764,U_5765),U_5761) = c_Lazy__Sequence_Oempty(U_5763)
| U_5761 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(variable_rename,[status(thm)],[f_1805_1]) ).
fof(f_1805_3,plain,
( ! [U_5775,U_5773,U_5771,U_5769,U_5767] :
( hAPP(c_New__DSequence_Opos__decr__bind(U_5769,U_5771,U_5773,U_5775),U_5767) = hAPP(c_Lazy__Sequence_Obind(U_5769,U_5771,hAPP(U_5773,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5767),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(U_5769,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_5771)),U_5775),U_5767))
| U_5767 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ! [U_5774,U_5772,U_5770,U_5768,U_5766] :
( hAPP(c_New__DSequence_Opos__decr__bind(U_5768,U_5770,U_5772,U_5774),U_5766) = c_Lazy__Sequence_Oempty(U_5770)
| U_5766 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(miniscope,[status(thm)],[f_1805_2]) ).
cnf(f_1805_4,plain,
( hAPP(c_New__DSequence_Opos__decr__bind(U_5768,U_5770,U_5772,U_5774),U_5766) = c_Lazy__Sequence_Oempty(U_5770)
| U_5766 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_1805_3]) ).
cnf(f_1805_5,plain,
( hAPP(c_New__DSequence_Opos__decr__bind(U_5769,U_5771,U_5773,U_5775),U_5767) = hAPP(c_Lazy__Sequence_Obind(U_5769,U_5771,hAPP(U_5773,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5767),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(U_5769,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_5771)),U_5775),U_5767))
| U_5767 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_1805_3]) ).
fof(f_1806_1,plain,
! [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 )
& ( V_k_2 = V_l_2
| hAPP(c_Code__Numeral_Onat__of,V_k_2) != hAPP(c_Code__Numeral_Onat__of,V_l_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Onat__of__inject]) ).
fof(f_1806_2,plain,
! [U_5777,U_5776] :
( ( hAPP(c_Code__Numeral_Onat__of,U_5776) = hAPP(c_Code__Numeral_Onat__of,U_5777)
| U_5776 != U_5777 )
& ( U_5776 = U_5777
| hAPP(c_Code__Numeral_Onat__of,U_5776) != hAPP(c_Code__Numeral_Onat__of,U_5777) ) ),
inference(variable_rename,[status(thm)],[f_1806_1]) ).
fof(f_1806_3,plain,
( ! [U_5781,U_5779] :
( hAPP(c_Code__Numeral_Onat__of,U_5779) = hAPP(c_Code__Numeral_Onat__of,U_5781)
| U_5779 != U_5781 )
& ! [U_5780,U_5778] :
( U_5778 = U_5780
| hAPP(c_Code__Numeral_Onat__of,U_5778) != hAPP(c_Code__Numeral_Onat__of,U_5780) ) ),
inference(miniscope,[status(thm)],[f_1806_2]) ).
cnf(f_1806_4,plain,
( U_5778 = U_5780
| hAPP(c_Code__Numeral_Onat__of,U_5778) != hAPP(c_Code__Numeral_Onat__of,U_5780) ),
inference(clausify,[status(thm)],[f_1806_3]) ).
cnf(f_1806_5,plain,
( hAPP(c_Code__Numeral_Onat__of,U_5779) = hAPP(c_Code__Numeral_Onat__of,U_5781)
| U_5779 != U_5781 ),
inference(clausify,[status(thm)],[f_1806_3]) ).
fof(f_1807_1,plain,
! [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 )
& ( V_x_2 = V_y_2
| hAPP(c_Code__Numeral_Onat__of,V_x_2) != hAPP(c_Code__Numeral_Onat__of,V_y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_code__numeral_Onat__of__inject]) ).
fof(f_1807_2,plain,
! [U_5783,U_5782] :
( ( hAPP(c_Code__Numeral_Onat__of,U_5782) = hAPP(c_Code__Numeral_Onat__of,U_5783)
| U_5782 != U_5783 )
& ( U_5782 = U_5783
| hAPP(c_Code__Numeral_Onat__of,U_5782) != hAPP(c_Code__Numeral_Onat__of,U_5783) ) ),
inference(variable_rename,[status(thm)],[f_1807_1]) ).
fof(f_1807_3,plain,
( ! [U_5787,U_5785] :
( hAPP(c_Code__Numeral_Onat__of,U_5785) = hAPP(c_Code__Numeral_Onat__of,U_5787)
| U_5785 != U_5787 )
& ! [U_5786,U_5784] :
( U_5784 = U_5786
| hAPP(c_Code__Numeral_Onat__of,U_5784) != hAPP(c_Code__Numeral_Onat__of,U_5786) ) ),
inference(miniscope,[status(thm)],[f_1807_2]) ).
cnf(f_1807_4,plain,
( U_5784 = U_5786
| hAPP(c_Code__Numeral_Onat__of,U_5784) != hAPP(c_Code__Numeral_Onat__of,U_5786) ),
inference(clausify,[status(thm)],[f_1807_3]) ).
cnf(f_1807_5,plain,
( hAPP(c_Code__Numeral_Onat__of,U_5785) = hAPP(c_Code__Numeral_Onat__of,U_5787)
| U_5785 != U_5787 ),
inference(clausify,[status(thm)],[f_1807_3]) ).
fof(f_1808_1,plain,
! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n,
inference(fof_nnf,[status(thm)],[fact_nat__of__of__nat]) ).
fof(f_1808_2,plain,
! [U_5788] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_5788)) = U_5788,
inference(variable_rename,[status(thm)],[f_1808_1]) ).
cnf(f_1808_3,plain,
hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_5788)) = U_5788,
inference(clausify,[status(thm)],[f_1808_2]) ).
fof(f_1809_1,plain,
! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k,
inference(fof_nnf,[status(thm)],[fact_of__nat__nat__of]) ).
fof(f_1809_2,plain,
! [U_5789] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_5789)) = U_5789,
inference(variable_rename,[status(thm)],[f_1809_1]) ).
cnf(f_1809_3,plain,
hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_5789)) = U_5789,
inference(clausify,[status(thm)],[f_1809_2]) ).
fof(f_1810_1,plain,
! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x,
inference(fof_nnf,[status(thm)],[fact_nat__of__inverse]) ).
fof(f_1810_2,plain,
! [U_5790] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_5790)) = U_5790,
inference(variable_rename,[status(thm)],[f_1810_1]) ).
cnf(f_1810_3,plain,
hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_5790)) = U_5790,
inference(clausify,[status(thm)],[f_1810_2]) ).
fof(f_1811_1,plain,
! [V_m_2,V_na_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_na_2),V_m_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_na_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_na_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_na_2),V_m_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__code__numeral__def]) ).
fof(f_1811_2,plain,
! [U_5792,U_5791] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5791),U_5792))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5791)),hAPP(c_Code__Numeral_Onat__of,U_5792))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5791)),hAPP(c_Code__Numeral_Onat__of,U_5792)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5791),U_5792)) ) ),
inference(variable_rename,[status(thm)],[f_1811_1]) ).
fof(f_1811_3,plain,
( ! [U_5796,U_5794] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5794),U_5796))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5794)),hAPP(c_Code__Numeral_Onat__of,U_5796))) )
& ! [U_5795,U_5793] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5793)),hAPP(c_Code__Numeral_Onat__of,U_5795)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5793),U_5795)) ) ),
inference(miniscope,[status(thm)],[f_1811_2]) ).
cnf(f_1811_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5793)),hAPP(c_Code__Numeral_Onat__of,U_5795)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5793),U_5795)) ),
inference(clausify,[status(thm)],[f_1811_3]) ).
cnf(f_1811_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5794),U_5796))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5794)),hAPP(c_Code__Numeral_Onat__of,U_5796))) ),
inference(clausify,[status(thm)],[f_1811_3]) ).
fof(f_1812_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_nat__of__number]) ).
fof(f_1812_2,plain,
! [U_5797] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),U_5797)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5797),
inference(variable_rename,[status(thm)],[f_1812_1]) ).
cnf(f_1812_3,plain,
hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),U_5797)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5797),
inference(clausify,[status(thm)],[f_1812_2]) ).
fof(f_1813_1,plain,
! [V_m_2,V_na_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_na_2),V_m_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_na_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_na_2)),hAPP(c_Code__Numeral_Onat__of,V_m_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_na_2),V_m_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__def]) ).
fof(f_1813_2,plain,
! [U_5799,U_5798] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5798),U_5799))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5798)),hAPP(c_Code__Numeral_Onat__of,U_5799))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5798)),hAPP(c_Code__Numeral_Onat__of,U_5799)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5798),U_5799)) ) ),
inference(variable_rename,[status(thm)],[f_1813_1]) ).
fof(f_1813_3,plain,
( ! [U_5803,U_5801] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5801),U_5803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5801)),hAPP(c_Code__Numeral_Onat__of,U_5803))) )
& ! [U_5802,U_5800] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5800)),hAPP(c_Code__Numeral_Onat__of,U_5802)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5800),U_5802)) ) ),
inference(miniscope,[status(thm)],[f_1813_2]) ).
cnf(f_1813_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5800)),hAPP(c_Code__Numeral_Onat__of,U_5802)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5800),U_5802)) ),
inference(clausify,[status(thm)],[f_1813_3]) ).
cnf(f_1813_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_5801),U_5803))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5801)),hAPP(c_Code__Numeral_Onat__of,U_5803))) ),
inference(clausify,[status(thm)],[f_1813_3]) ).
fof(f_1814_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_nat__of__code]) ).
fof(f_1814_2,plain,
! [U_5804] : hAPP(c_Code__Numeral_Onat__of,U_5804) = c_Code__Numeral_Onat__of__aux(U_5804,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_1814_1]) ).
cnf(f_1814_3,plain,
hAPP(c_Code__Numeral_Onat__of,U_5804) = c_Code__Numeral_Onat__of__aux(U_5804,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_1814_2]) ).
fof(f_1815_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_nat__of__aux__def]) ).
fof(f_1815_2,plain,
! [U_5806,U_5805] : c_Code__Numeral_Onat__of__aux(U_5805,U_5806) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5805)),U_5806),
inference(variable_rename,[status(thm)],[f_1815_1]) ).
cnf(f_1815_3,plain,
c_Code__Numeral_Onat__of__aux(U_5805,U_5806) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5805)),U_5806),
inference(clausify,[status(thm)],[f_1815_2]) ).
fof(f_1816_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_Suc__code__numeral__def]) ).
fof(f_1816_2,plain,
! [U_5807] : c_Code__Numeral_OSuc__code__numeral(U_5807) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,U_5807))),
inference(variable_rename,[status(thm)],[f_1816_1]) ).
cnf(f_1816_3,plain,
c_Code__Numeral_OSuc__code__numeral(U_5807) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,U_5807))),
inference(clausify,[status(thm)],[f_1816_2]) ).
fof(f_1817_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_minus__code__numeral__def]) ).
fof(f_1817_2,plain,
! [U_5809,U_5808] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5808),U_5809) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5808)),hAPP(c_Code__Numeral_Onat__of,U_5809))),
inference(variable_rename,[status(thm)],[f_1817_1]) ).
cnf(f_1817_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5808),U_5809) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5808)),hAPP(c_Code__Numeral_Onat__of,U_5809))),
inference(clausify,[status(thm)],[f_1817_2]) ).
fof(f_1818_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_plus__code__numeral__def]) ).
fof(f_1818_2,plain,
! [U_5811,U_5810] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_5810),U_5811) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5810)),hAPP(c_Code__Numeral_Onat__of,U_5811))),
inference(variable_rename,[status(thm)],[f_1818_1]) ).
cnf(f_1818_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_5810),U_5811) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5810)),hAPP(c_Code__Numeral_Onat__of,U_5811))),
inference(clausify,[status(thm)],[f_1818_2]) ).
fof(f_1819_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_div__code__numeral__def]) ).
fof(f_1819_2,plain,
! [U_5813,U_5812] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_5812),U_5813) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5812)),hAPP(c_Code__Numeral_Onat__of,U_5813))),
inference(variable_rename,[status(thm)],[f_1819_1]) ).
cnf(f_1819_3,plain,
hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_5812),U_5813) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_5812)),hAPP(c_Code__Numeral_Onat__of,U_5813))),
inference(clausify,[status(thm)],[f_1819_2]) ).
fof(f_1820_1,plain,
! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Opos__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
inference(fof_nnf,[status(thm)],[fact_New__Random__Sequence_Opos__decr__bind__def]) ).
fof(f_1820_2,plain,
! [U_5820,U_5819,U_5818,U_5817,U_5816,U_5815,U_5814] : c_New__Random__Sequence_Opos__decr__bind(U_5814,U_5815,U_5816,U_5817,U_5818,U_5819,U_5820) = c_New__DSequence_Opos__decr__bind(U_5814,U_5815,hAPP(hAPP(hAPP(U_5816,U_5818),U_5819),U_5820),hAPP(hAPP(c_COMBC(U_5814,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_5815))),hAPP(hAPP(c_COMBC(U_5814,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(U_5815)))),hAPP(hAPP(c_COMBC(U_5814,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(U_5815))))),U_5817),U_5818)),U_5819)),U_5820)),
inference(variable_rename,[status(thm)],[f_1820_1]) ).
cnf(f_1820_3,plain,
c_New__Random__Sequence_Opos__decr__bind(U_5814,U_5815,U_5816,U_5817,U_5818,U_5819,U_5820) = c_New__DSequence_Opos__decr__bind(U_5814,U_5815,hAPP(hAPP(hAPP(U_5816,U_5818),U_5819),U_5820),hAPP(hAPP(c_COMBC(U_5814,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_5815))),hAPP(hAPP(c_COMBC(U_5814,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(U_5815)))),hAPP(hAPP(c_COMBC(U_5814,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(U_5815))))),U_5817),U_5818)),U_5819)),U_5820)),
inference(clausify,[status(thm)],[f_1820_2]) ).
fof(f_1821_1,plain,
! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a),
inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__empty__def]) ).
fof(f_1821_2,plain,
! [U_5822,U_5821] : hAPP(c_New__DSequence_Opos__empty(U_5821),U_5822) = c_Lazy__Sequence_Oempty(U_5821),
inference(variable_rename,[status(thm)],[f_1821_1]) ).
cnf(f_1821_3,plain,
hAPP(c_New__DSequence_Opos__empty(U_5821),U_5822) = c_Lazy__Sequence_Oempty(U_5821),
inference(clausify,[status(thm)],[f_1821_2]) ).
fof(f_1822_1,plain,
! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Opos__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)),
inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__bind__def]) ).
fof(f_1822_2,plain,
! [U_5827,U_5826,U_5825,U_5824,U_5823] : hAPP(c_New__DSequence_Opos__bind(U_5823,U_5824,U_5825,U_5826),U_5827) = hAPP(c_Lazy__Sequence_Obind(U_5823,U_5824,hAPP(U_5825,U_5827)),hAPP(hAPP(c_COMBC(U_5823,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_5824)),U_5826),U_5827)),
inference(variable_rename,[status(thm)],[f_1822_1]) ).
cnf(f_1822_3,plain,
hAPP(c_New__DSequence_Opos__bind(U_5823,U_5824,U_5825,U_5826),U_5827) = hAPP(c_Lazy__Sequence_Obind(U_5823,U_5824,hAPP(U_5825,U_5827)),hAPP(hAPP(c_COMBC(U_5823,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_5824)),U_5826),U_5827)),
inference(clausify,[status(thm)],[f_1822_2]) ).
fof(f_1823_1,plain,
! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
( ( hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2))
| V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_b)
| V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(fof_nnf,[status(thm)],[fact_New__DSequence_Oneg__decr__bind__def]) ).
fof(f_1823_2,plain,
! [U_5832,U_5831,U_5830,U_5829,U_5828] :
( ( hAPP(c_New__DSequence_Oneg__decr__bind(U_5829,U_5830,U_5831,U_5832),U_5828) = c_Lazy__Sequence_Ohb__bind(U_5829,U_5830,hAPP(U_5831,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5828),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_5829,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_5830))),U_5832),U_5828))
| U_5828 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ( hAPP(c_New__DSequence_Oneg__decr__bind(U_5829,U_5830,U_5831,U_5832),U_5828) = c_Lazy__Sequence_Ohit__bound(U_5830)
| U_5828 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(variable_rename,[status(thm)],[f_1823_1]) ).
fof(f_1823_3,plain,
( ! [U_5842,U_5840,U_5838,U_5836,U_5834] :
( hAPP(c_New__DSequence_Oneg__decr__bind(U_5836,U_5838,U_5840,U_5842),U_5834) = c_Lazy__Sequence_Ohb__bind(U_5836,U_5838,hAPP(U_5840,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5834),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_5836,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_5838))),U_5842),U_5834))
| U_5834 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
& ! [U_5841,U_5839,U_5837,U_5835,U_5833] :
( hAPP(c_New__DSequence_Oneg__decr__bind(U_5835,U_5837,U_5839,U_5841),U_5833) = c_Lazy__Sequence_Ohit__bound(U_5837)
| U_5833 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
inference(miniscope,[status(thm)],[f_1823_2]) ).
cnf(f_1823_4,plain,
( hAPP(c_New__DSequence_Oneg__decr__bind(U_5835,U_5837,U_5839,U_5841),U_5833) = c_Lazy__Sequence_Ohit__bound(U_5837)
| U_5833 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_1823_3]) ).
cnf(f_1823_5,plain,
( hAPP(c_New__DSequence_Oneg__decr__bind(U_5836,U_5838,U_5840,U_5842),U_5834) = c_Lazy__Sequence_Ohb__bind(U_5836,U_5838,hAPP(U_5840,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_5834),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_5836,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_5838))),U_5842),U_5834))
| U_5834 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
inference(clausify,[status(thm)],[f_1823_3]) ).
fof(f_1824_1,plain,
! [V_l,V_k] :
( ( 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
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) ) ),
inference(fof_nnf,[status(thm)],[fact_beyond__def]) ).
fof(f_1824_2,plain,
! [U_5844,U_5843] :
( ( c_Quickcheck_Obeyond(U_5843,U_5844) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5843),U_5844)) )
& ( c_Quickcheck_Obeyond(U_5843,U_5844) = U_5844
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5843),U_5844)) ) ),
inference(variable_rename,[status(thm)],[f_1824_1]) ).
fof(f_1824_3,plain,
( ! [U_5848,U_5846] :
( c_Quickcheck_Obeyond(U_5846,U_5848) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5846),U_5848)) )
& ! [U_5847,U_5845] :
( c_Quickcheck_Obeyond(U_5845,U_5847) = U_5847
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5845),U_5847)) ) ),
inference(miniscope,[status(thm)],[f_1824_2]) ).
cnf(f_1824_4,plain,
( c_Quickcheck_Obeyond(U_5845,U_5847) = U_5847
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5845),U_5847)) ),
inference(clausify,[status(thm)],[f_1824_3]) ).
cnf(f_1824_5,plain,
( c_Quickcheck_Obeyond(U_5846,U_5848) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_5846),U_5848)) ),
inference(clausify,[status(thm)],[f_1824_3]) ).
fof(f_1825_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_beyond__zero]) ).
fof(f_1825_2,plain,
! [U_5849] : c_Quickcheck_Obeyond(U_5849,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(variable_rename,[status(thm)],[f_1825_1]) ).
cnf(f_1825_3,plain,
c_Quickcheck_Obeyond(U_5849,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(clausify,[status(thm)],[f_1825_2]) ).
fof(f_1826_1,plain,
! [V_seed_2,V_size_2,V_nrandom_2,T_b] : c_New__Random__Sequence_Opos__empty(T_b,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_b),
inference(fof_nnf,[status(thm)],[fact_pos__empty__def]) ).
fof(f_1826_2,plain,
! [U_5853,U_5852,U_5851,U_5850] : c_New__Random__Sequence_Opos__empty(U_5850,U_5851,U_5852,U_5853) = c_New__DSequence_Opos__empty(U_5850),
inference(variable_rename,[status(thm)],[f_1826_1]) ).
cnf(f_1826_3,plain,
c_New__Random__Sequence_Opos__empty(U_5850,U_5851,U_5852,U_5853) = c_New__DSequence_Opos__empty(U_5850),
inference(clausify,[status(thm)],[f_1826_2]) ).
fof(f_1827_1,plain,
! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Oneg__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
inference(fof_nnf,[status(thm)],[fact_New__Random__Sequence_Oneg__decr__bind__def]) ).
fof(f_1827_2,plain,
! [U_5860,U_5859,U_5858,U_5857,U_5856,U_5855,U_5854] : c_New__Random__Sequence_Oneg__decr__bind(U_5854,U_5855,U_5856,U_5857,U_5858,U_5859,U_5860) = c_New__DSequence_Oneg__decr__bind(U_5854,U_5855,hAPP(hAPP(hAPP(U_5856,U_5858),U_5859),U_5860),hAPP(hAPP(c_COMBC(U_5854,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(U_5855)))),hAPP(hAPP(c_COMBC(U_5854,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(U_5855))))),hAPP(hAPP(c_COMBC(U_5854,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(U_5855)))))),U_5857),U_5858)),U_5859)),U_5860)),
inference(variable_rename,[status(thm)],[f_1827_1]) ).
cnf(f_1827_3,plain,
c_New__Random__Sequence_Oneg__decr__bind(U_5854,U_5855,U_5856,U_5857,U_5858,U_5859,U_5860) = c_New__DSequence_Oneg__decr__bind(U_5854,U_5855,hAPP(hAPP(hAPP(U_5856,U_5858),U_5859),U_5860),hAPP(hAPP(c_COMBC(U_5854,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(U_5855)))),hAPP(hAPP(c_COMBC(U_5854,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(U_5855))))),hAPP(hAPP(c_COMBC(U_5854,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(U_5855)))))),U_5857),U_5858)),U_5859)),U_5860)),
inference(clausify,[status(thm)],[f_1827_2]) ).
fof(f_1828_1,plain,
! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
inference(fof_nnf,[status(thm)],[fact_pos__bind__def]) ).
fof(f_1828_2,plain,
! [U_5867,U_5866,U_5865,U_5864,U_5863,U_5862,U_5861] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(U_5861,U_5862,U_5863,U_5864),U_5865),U_5866),U_5867) = c_New__DSequence_Opos__bind(U_5861,U_5862,hAPP(hAPP(hAPP(U_5863,U_5865),U_5866),U_5867),hAPP(hAPP(c_COMBC(U_5861,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_5862))),hAPP(hAPP(c_COMBC(U_5861,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(U_5862)))),hAPP(hAPP(c_COMBC(U_5861,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(U_5862))))),U_5864),U_5865)),U_5866)),U_5867)),
inference(variable_rename,[status(thm)],[f_1828_1]) ).
cnf(f_1828_3,plain,
hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(U_5861,U_5862,U_5863,U_5864),U_5865),U_5866),U_5867) = c_New__DSequence_Opos__bind(U_5861,U_5862,hAPP(hAPP(hAPP(U_5863,U_5865),U_5866),U_5867),hAPP(hAPP(c_COMBC(U_5861,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_5862))),hAPP(hAPP(c_COMBC(U_5861,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(U_5862)))),hAPP(hAPP(c_COMBC(U_5861,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(U_5862))))),U_5864),U_5865)),U_5866)),U_5867)),
inference(clausify,[status(thm)],[f_1828_2]) ).
fof(f_1829_1,plain,
! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Oneg__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)),
inference(fof_nnf,[status(thm)],[fact_New__DSequence_Oneg__bind__def]) ).
fof(f_1829_2,plain,
! [U_5872,U_5871,U_5870,U_5869,U_5868] : hAPP(c_New__DSequence_Oneg__bind(U_5868,U_5869,U_5870,U_5871),U_5872) = c_Lazy__Sequence_Ohb__bind(U_5868,U_5869,hAPP(U_5870,U_5872),hAPP(hAPP(c_COMBC(U_5868,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_5869))),U_5871),U_5872)),
inference(variable_rename,[status(thm)],[f_1829_1]) ).
cnf(f_1829_3,plain,
hAPP(c_New__DSequence_Oneg__bind(U_5868,U_5869,U_5870,U_5871),U_5872) = c_Lazy__Sequence_Ohb__bind(U_5868,U_5869,hAPP(U_5870,U_5872),hAPP(hAPP(c_COMBC(U_5868,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_5869))),U_5871),U_5872)),
inference(clausify,[status(thm)],[f_1829_2]) ).
fof(f_1830_1,plain,
! [V_y_2,V_x_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_c_2),V_x_2),V_y_2) = hAPP(V_c_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),
inference(fof_nnf,[status(thm)],[fact_curry__def]) ).
fof(f_1830_2,plain,
! [U_5878,U_5877,U_5876,U_5875,U_5874,U_5873] : hAPP(hAPP(c_Product__Type_Ocurry(U_5873,U_5874,U_5875,U_5876),U_5877),U_5878) = hAPP(U_5876,hAPP(hAPP(c_Product__Type_OPair(U_5873,U_5874),U_5877),U_5878)),
inference(variable_rename,[status(thm)],[f_1830_1]) ).
cnf(f_1830_3,plain,
hAPP(hAPP(c_Product__Type_Ocurry(U_5873,U_5874,U_5875,U_5876),U_5877),U_5878) = hAPP(U_5876,hAPP(hAPP(c_Product__Type_OPair(U_5873,U_5874),U_5877),U_5878)),
inference(clausify,[status(thm)],[f_1830_2]) ).
fof(f_1831_1,plain,
! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
| ~ hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ),
inference(fof_nnf,[status(thm)],[fact_curryI]) ).
fof(f_1831_2,plain,
! [U_5883,U_5882,U_5881,U_5880,U_5879] :
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_5880,U_5881,tc_HOL_Obool,U_5879),U_5882),U_5883))
| ~ hBOOL(hAPP(U_5879,hAPP(hAPP(c_Product__Type_OPair(U_5880,U_5881),U_5882),U_5883))) ),
inference(variable_rename,[status(thm)],[f_1831_1]) ).
cnf(f_1831_3,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_5880,U_5881,tc_HOL_Obool,U_5879),U_5882),U_5883))
| ~ hBOOL(hAPP(U_5879,hAPP(hAPP(c_Product__Type_OPair(U_5880,U_5881),U_5882),U_5883))) ),
inference(clausify,[status(thm)],[f_1831_2]) ).
fof(f_1832_1,plain,
! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_curryE]) ).
fof(f_1832_2,plain,
! [U_5888,U_5887,U_5886,U_5885,U_5884] :
( hBOOL(hAPP(U_5886,hAPP(hAPP(c_Product__Type_OPair(U_5884,U_5885),U_5887),U_5888)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_5884,U_5885,tc_HOL_Obool,U_5886),U_5887),U_5888)) ),
inference(variable_rename,[status(thm)],[f_1832_1]) ).
cnf(f_1832_3,plain,
( hBOOL(hAPP(U_5886,hAPP(hAPP(c_Product__Type_OPair(U_5884,U_5885),U_5887),U_5888)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_5884,U_5885,tc_HOL_Obool,U_5886),U_5887),U_5888)) ),
inference(clausify,[status(thm)],[f_1832_2]) ).
fof(f_1833_1,plain,
! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_curryD]) ).
fof(f_1833_2,plain,
! [U_5893,U_5892,U_5891,U_5890,U_5889] :
( hBOOL(hAPP(U_5891,hAPP(hAPP(c_Product__Type_OPair(U_5889,U_5890),U_5892),U_5893)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_5889,U_5890,tc_HOL_Obool,U_5891),U_5892),U_5893)) ),
inference(variable_rename,[status(thm)],[f_1833_1]) ).
cnf(f_1833_3,plain,
( hBOOL(hAPP(U_5891,hAPP(hAPP(c_Product__Type_OPair(U_5889,U_5890),U_5892),U_5893)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_5889,U_5890,tc_HOL_Obool,U_5891),U_5892),U_5893)) ),
inference(clausify,[status(thm)],[f_1833_2]) ).
fof(f_1834_1,plain,
! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_f_2),V_a_2),V_b_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)),
inference(fof_nnf,[status(thm)],[fact_curry__conv]) ).
fof(f_1834_2,plain,
! [U_5899,U_5898,U_5897,U_5896,U_5895,U_5894] : hAPP(hAPP(c_Product__Type_Ocurry(U_5894,U_5895,U_5896,U_5897),U_5898),U_5899) = hAPP(U_5897,hAPP(hAPP(c_Product__Type_OPair(U_5894,U_5895),U_5898),U_5899)),
inference(variable_rename,[status(thm)],[f_1834_1]) ).
cnf(f_1834_3,plain,
hAPP(hAPP(c_Product__Type_Ocurry(U_5894,U_5895,U_5896,U_5897),U_5898),U_5899) = hAPP(U_5897,hAPP(hAPP(c_Product__Type_OPair(U_5894,U_5895),U_5898),U_5899)),
inference(clausify,[status(thm)],[f_1834_2]) ).
fof(f_1835_1,plain,
! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),c_Product__Type_Ocurry(T_b,T_c,T_d,V_f_2)) = V_f_2,
inference(fof_nnf,[status(thm)],[fact_split__curry]) ).
fof(f_1835_2,plain,
! [U_5903,U_5902,U_5901,U_5900] : hAPP(c_Product__Type_Oprod_Oprod__case(U_5900,U_5901,U_5902),c_Product__Type_Ocurry(U_5900,U_5901,U_5902,U_5903)) = U_5903,
inference(variable_rename,[status(thm)],[f_1835_1]) ).
cnf(f_1835_3,plain,
hAPP(c_Product__Type_Oprod_Oprod__case(U_5900,U_5901,U_5902),c_Product__Type_Ocurry(U_5900,U_5901,U_5902,U_5903)) = U_5903,
inference(clausify,[status(thm)],[f_1835_2]) ).
fof(f_1836_1,plain,
! [V_f_2,T_d,T_c,T_b] : c_Product__Type_Ocurry(T_b,T_c,T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)) = V_f_2,
inference(fof_nnf,[status(thm)],[fact_curry__split]) ).
fof(f_1836_2,plain,
! [U_5907,U_5906,U_5905,U_5904] : c_Product__Type_Ocurry(U_5904,U_5905,U_5906,hAPP(c_Product__Type_Oprod_Oprod__case(U_5904,U_5905,U_5906),U_5907)) = U_5907,
inference(variable_rename,[status(thm)],[f_1836_1]) ).
cnf(f_1836_3,plain,
c_Product__Type_Ocurry(U_5904,U_5905,U_5906,hAPP(c_Product__Type_Oprod_Oprod__case(U_5904,U_5905,U_5906),U_5907)) = U_5907,
inference(clausify,[status(thm)],[f_1836_2]) ).
fof(f_1837_1,plain,
! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
inference(fof_nnf,[status(thm)],[fact_neg__bind__def]) ).
fof(f_1837_2,plain,
! [U_5914,U_5913,U_5912,U_5911,U_5910,U_5909,U_5908] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(U_5908,U_5909,U_5910,U_5911),U_5912),U_5913),U_5914) = c_New__DSequence_Oneg__bind(U_5908,U_5909,hAPP(hAPP(hAPP(U_5910,U_5912),U_5913),U_5914),hAPP(hAPP(c_COMBC(U_5908,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(U_5909)))),hAPP(hAPP(c_COMBC(U_5908,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(U_5909))))),hAPP(hAPP(c_COMBC(U_5908,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(U_5909)))))),U_5911),U_5912)),U_5913)),U_5914)),
inference(variable_rename,[status(thm)],[f_1837_1]) ).
cnf(f_1837_3,plain,
hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(U_5908,U_5909,U_5910,U_5911),U_5912),U_5913),U_5914) = c_New__DSequence_Oneg__bind(U_5908,U_5909,hAPP(hAPP(hAPP(U_5910,U_5912),U_5913),U_5914),hAPP(hAPP(c_COMBC(U_5908,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(U_5909)))),hAPP(hAPP(c_COMBC(U_5908,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(U_5909))))),hAPP(hAPP(c_COMBC(U_5908,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(U_5909)))))),U_5911),U_5912)),U_5913)),U_5914)),
inference(clausify,[status(thm)],[f_1837_2]) ).
fof(f_1838_1,plain,
! [V_B_2,V_A_2,T_b] :
( ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
| ? [B_x] :
( ~ hBOOL(hAPP(V_A_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(V_A_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
| ~ hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Powp__def]) ).
fof(f_1838_2,plain,
! [U_5919,U_5918,U_5917] :
( ( hBOOL(hAPP(c_Predicate_OPowp(U_5917,U_5918),U_5919))
| ? [U_5916] :
( ~ hBOOL(hAPP(U_5918,U_5916))
& hBOOL(hAPP(hAPP(c_member(U_5917),U_5916),U_5919)) ) )
& ( ! [U_5915] :
( hBOOL(hAPP(U_5918,U_5915))
| ~ hBOOL(hAPP(hAPP(c_member(U_5917),U_5915),U_5919)) )
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_5917,U_5918),U_5919)) ) ),
inference(variable_rename,[status(thm)],[f_1838_1]) ).
fof(f_1838_3,plain,
( ! [U_5925,U_5923,U_5921] :
( hBOOL(hAPP(c_Predicate_OPowp(U_5921,U_5923),U_5925))
| ? [U_5916] :
( ~ hBOOL(hAPP(U_5923,U_5916))
& hBOOL(hAPP(hAPP(c_member(U_5921),U_5916),U_5925)) ) )
& ! [U_5924,U_5922,U_5920] :
( ! [U_5915] :
( hBOOL(hAPP(U_5922,U_5915))
| ~ hBOOL(hAPP(hAPP(c_member(U_5920),U_5915),U_5924)) )
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_5920,U_5922),U_5924)) ) ),
inference(miniscope,[status(thm)],[f_1838_2]) ).
fof(f_1838_4,plain,
( ! [U_5925,U_5923,U_5921] :
( hBOOL(hAPP(c_Predicate_OPowp(U_5921,U_5923),U_5925))
| ( ~ hBOOL(hAPP(U_5923,sK83(U_5925,U_5923,U_5921)))
& hBOOL(hAPP(hAPP(c_member(U_5921),sK83(U_5925,U_5923,U_5921)),U_5925)) ) )
& ! [U_5924,U_5922,U_5920] :
( ! [U_5915] :
( hBOOL(hAPP(U_5922,U_5915))
| ~ hBOOL(hAPP(hAPP(c_member(U_5920),U_5915),U_5924)) )
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_5920,U_5922),U_5924)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_5916,sK83(U_5925,U_5923,U_5921))],[f_1838_3]) ).
cnf(f_1838_5,plain,
( hBOOL(hAPP(U_5922,U_5915))
| ~ hBOOL(hAPP(hAPP(c_member(U_5920),U_5915),U_5924))
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_5920,U_5922),U_5924)) ),
inference(clausify,[status(thm)],[f_1838_4]) ).
cnf(f_1838_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_5921),sK83(U_5925,U_5923,U_5921)),U_5925))
| hBOOL(hAPP(c_Predicate_OPowp(U_5921,U_5923),U_5925)) ),
inference(clausify,[status(thm)],[f_1838_4]) ).
cnf(f_1838_7,plain,
( ~ hBOOL(hAPP(U_5923,sK83(U_5925,U_5923,U_5921)))
| hBOOL(hAPP(c_Predicate_OPowp(U_5921,U_5923),U_5925)) ),
inference(clausify,[status(thm)],[f_1838_4]) ).
fof(f_1839_1,plain,
! [V_n,V_m,V_i] :
( 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_Oone__class_Oone(tc_Nat_Onat)),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))) ),
inference(fof_nnf,[status(thm)],[fact_power__dvd__imp__le]) ).
fof(f_1839_2,plain,
! [U_5928,U_5927,U_5926] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5927),U_5928))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_5926))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5926),U_5927)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5926),U_5928))) ),
inference(variable_rename,[status(thm)],[f_1839_1]) ).
cnf(f_1839_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5927),U_5928))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_5926))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5926),U_5927)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_5926),U_5928))) ),
inference(clausify,[status(thm)],[f_1839_2]) ).
fof(f_1840_1,plain,
! [V_na_2,V_m_2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_na_2)),V_m_2))
| V_na_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( V_na_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_na_2)),V_m_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel1]) ).
fof(f_1840_2,plain,
! [U_5930,U_5929] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5929),U_5930)),U_5929))
| U_5930 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( U_5930 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5929),U_5930)),U_5929)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5929)) ),
inference(variable_rename,[status(thm)],[f_1840_1]) ).
cnf(f_1840_3,plain,
( U_5930 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5929),U_5930)),U_5929))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5929)) ),
inference(clausify,[status(thm)],[f_1840_2]) ).
cnf(f_1840_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5929),U_5930)),U_5929))
| U_5930 != 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_5929)) ),
inference(clausify,[status(thm)],[f_1840_2]) ).
fof(f_1841_1,plain,
! [V_na_2,V_m_2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_na_2),V_m_2)),V_m_2))
| V_na_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( V_na_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_na_2),V_m_2)),V_m_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel2]) ).
fof(f_1841_2,plain,
! [U_5932,U_5931] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5932),U_5931)),U_5931))
| U_5932 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( U_5932 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5932),U_5931)),U_5931)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5931)) ),
inference(variable_rename,[status(thm)],[f_1841_1]) ).
cnf(f_1841_3,plain,
( U_5932 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5932),U_5931)),U_5931))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_5931)) ),
inference(clausify,[status(thm)],[f_1841_2]) ).
cnf(f_1841_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5932),U_5931)),U_5931))
| U_5932 != 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_5931)) ),
inference(clausify,[status(thm)],[f_1841_2]) ).
fof(f_1842_1,plain,
! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)),
inference(fof_nnf,[status(thm)],[fact_dvd_Oorder__refl]) ).
fof(f_1842_2,plain,
! [U_5933] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5933),U_5933)),
inference(variable_rename,[status(thm)],[f_1842_1]) ).
cnf(f_1842_3,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5933),U_5933)),
inference(clausify,[status(thm)],[f_1842_2]) ).
fof(f_1843_1,plain,
! [V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__0__right]) ).
fof(f_1843_2,plain,
! [U_5935,U_5934] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5934),U_5935),c_Groups_Ozero__class_Ozero(U_5934)))
| ~ class_Rings_Ocomm__semiring__1(U_5934) ),
inference(variable_rename,[status(thm)],[f_1843_1]) ).
cnf(f_1843_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5934),U_5935),c_Groups_Ozero__class_Ozero(U_5934)))
| ~ class_Rings_Ocomm__semiring__1(U_5934) ),
inference(clausify,[status(thm)],[f_1843_2]) ).
fof(f_1844_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_dvd__1__left]) ).
fof(f_1844_2,plain,
! [U_5936] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5936)),
inference(variable_rename,[status(thm)],[f_1844_1]) ).
cnf(f_1844_3,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_5936)),
inference(clausify,[status(thm)],[f_1844_2]) ).
fof(f_1845_1,plain,
! [V_k_2,V_m_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2))) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_dvd__abs__iff]) ).
fof(f_1845_2,plain,
! [U_5939,U_5938,U_5937] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5937),U_5938),hAPP(c_Groups_Oabs__class_Oabs(U_5937),U_5939)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5937),U_5938),U_5939)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5937),U_5938),U_5939))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5937),U_5938),hAPP(c_Groups_Oabs__class_Oabs(U_5937),U_5939))) ) )
| ~ class_Rings_Olinordered__idom(U_5937) ),
inference(variable_rename,[status(thm)],[f_1845_1]) ).
cnf(f_1845_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5937),U_5938),U_5939))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5937),U_5938),hAPP(c_Groups_Oabs__class_Oabs(U_5937),U_5939)))
| ~ class_Rings_Olinordered__idom(U_5937) ),
inference(clausify,[status(thm)],[f_1845_2]) ).
cnf(f_1845_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5937),U_5938),hAPP(c_Groups_Oabs__class_Oabs(U_5937),U_5939)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5937),U_5938),U_5939))
| ~ class_Rings_Olinordered__idom(U_5937) ),
inference(clausify,[status(thm)],[f_1845_2]) ).
fof(f_1846_1,plain,
! [V_k_2,V_m_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2)) ) )
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_abs__dvd__iff]) ).
fof(f_1846_2,plain,
! [U_5942,U_5941,U_5940] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5940),hAPP(c_Groups_Oabs__class_Oabs(U_5940),U_5941)),U_5942))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5940),U_5941),U_5942)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5940),U_5941),U_5942))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5940),hAPP(c_Groups_Oabs__class_Oabs(U_5940),U_5941)),U_5942)) ) )
| ~ class_Rings_Olinordered__idom(U_5940) ),
inference(variable_rename,[status(thm)],[f_1846_1]) ).
cnf(f_1846_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5940),U_5941),U_5942))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5940),hAPP(c_Groups_Oabs__class_Oabs(U_5940),U_5941)),U_5942))
| ~ class_Rings_Olinordered__idom(U_5940) ),
inference(clausify,[status(thm)],[f_1846_2]) ).
cnf(f_1846_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5940),hAPP(c_Groups_Oabs__class_Oabs(U_5940),U_5941)),U_5942))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5940),U_5941),U_5942))
| ~ class_Rings_Olinordered__idom(U_5940) ),
inference(clausify,[status(thm)],[f_1846_2]) ).
fof(f_1847_1,plain,
! [V_k,V_l,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k))
| hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) != hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__if__abs__eq]) ).
fof(f_1847_2,plain,
! [U_5945,U_5944,U_5943] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5943),U_5944),U_5945))
| hAPP(c_Groups_Oabs__class_Oabs(U_5943),U_5944) != hAPP(c_Groups_Oabs__class_Oabs(U_5943),U_5945)
| ~ class_Rings_Olinordered__idom(U_5943) ),
inference(variable_rename,[status(thm)],[f_1847_1]) ).
cnf(f_1847_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5943),U_5944),U_5945))
| hAPP(c_Groups_Oabs__class_Oabs(U_5943),U_5944) != hAPP(c_Groups_Oabs__class_Oabs(U_5943),U_5945)
| ~ class_Rings_Olinordered__idom(U_5943) ),
inference(clausify,[status(thm)],[f_1847_2]) ).
fof(f_1848_1,plain,
! [V_c_2,V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_c_2),V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_c_2),V_a_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
| ~ class_Divides_Osemiring__div(T_b) ),
inference(fof_nnf,[status(thm)],[fact_div__dvd__div]) ).
fof(f_1848_2,plain,
! [U_5949,U_5948,U_5947,U_5946] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5946),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_5946),U_5948),U_5947)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_5946),U_5949),U_5947)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5946),U_5948),U_5949)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5946),U_5948),U_5949))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5946),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_5946),U_5948),U_5947)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_5946),U_5949),U_5947))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5946),U_5947),U_5949))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5946),U_5947),U_5948))
| ~ class_Divides_Osemiring__div(U_5946) ),
inference(variable_rename,[status(thm)],[f_1848_1]) ).
cnf(f_1848_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5946),U_5948),U_5949))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5946),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_5946),U_5948),U_5947)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_5946),U_5949),U_5947)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5946),U_5947),U_5949))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5946),U_5947),U_5948))
| ~ class_Divides_Osemiring__div(U_5946) ),
inference(clausify,[status(thm)],[f_1848_2]) ).
cnf(f_1848_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5946),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_5946),U_5948),U_5947)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_5946),U_5949),U_5947)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5946),U_5948),U_5949))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5946),U_5947),U_5949))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5946),U_5947),U_5948))
| ~ class_Divides_Osemiring__div(U_5946) ),
inference(clausify,[status(thm)],[f_1848_2]) ).
fof(f_1849_1,plain,
! [V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__dvd]) ).
fof(f_1849_2,plain,
! [U_5951,U_5950] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5950),c_Groups_Oone__class_Oone(U_5950)),U_5951))
| ~ class_Rings_Ocomm__semiring__1(U_5950) ),
inference(variable_rename,[status(thm)],[f_1849_1]) ).
cnf(f_1849_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5950),c_Groups_Oone__class_Oone(U_5950)),U_5951))
| ~ class_Rings_Ocomm__semiring__1(U_5950) ),
inference(clausify,[status(thm)],[f_1849_2]) ).
fof(f_1850_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2))) ) )
| ~ class_Rings_Ocomm__ring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_dvd__minus__iff]) ).
fof(f_1850_2,plain,
! [U_5954,U_5953,U_5952] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5952),U_5953),hAPP(c_Groups_Ouminus__class_Ouminus(U_5952),U_5954)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5952),U_5953),U_5954)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5952),U_5953),U_5954))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5952),U_5953),hAPP(c_Groups_Ouminus__class_Ouminus(U_5952),U_5954))) ) )
| ~ class_Rings_Ocomm__ring__1(U_5952) ),
inference(variable_rename,[status(thm)],[f_1850_1]) ).
cnf(f_1850_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5952),U_5953),U_5954))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5952),U_5953),hAPP(c_Groups_Ouminus__class_Ouminus(U_5952),U_5954)))
| ~ class_Rings_Ocomm__ring__1(U_5952) ),
inference(clausify,[status(thm)],[f_1850_2]) ).
cnf(f_1850_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5952),U_5953),hAPP(c_Groups_Ouminus__class_Ouminus(U_5952),U_5954)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5952),U_5953),U_5954))
| ~ class_Rings_Ocomm__ring__1(U_5952) ),
inference(clausify,[status(thm)],[f_1850_2]) ).
fof(f_1851_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2)) ) )
| ~ class_Rings_Ocomm__ring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_minus__dvd__iff]) ).
fof(f_1851_2,plain,
! [U_5957,U_5956,U_5955] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5955),hAPP(c_Groups_Ouminus__class_Ouminus(U_5955),U_5956)),U_5957))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5955),U_5956),U_5957)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5955),U_5956),U_5957))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5955),hAPP(c_Groups_Ouminus__class_Ouminus(U_5955),U_5956)),U_5957)) ) )
| ~ class_Rings_Ocomm__ring__1(U_5955) ),
inference(variable_rename,[status(thm)],[f_1851_1]) ).
cnf(f_1851_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5955),U_5956),U_5957))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5955),hAPP(c_Groups_Ouminus__class_Ouminus(U_5955),U_5956)),U_5957))
| ~ class_Rings_Ocomm__ring__1(U_5955) ),
inference(clausify,[status(thm)],[f_1851_2]) ).
cnf(f_1851_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5955),hAPP(c_Groups_Ouminus__class_Ouminus(U_5955),U_5956)),U_5957))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5955),U_5956),U_5957))
| ~ class_Rings_Ocomm__ring__1(U_5955) ),
inference(clausify,[status(thm)],[f_1851_2]) ).
fof(f_1852_1,plain,
! [V_m_2,V_na_2,V_k_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_na_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_na_2))
| ~ class_Divides_Osemiring__div(T_b) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mod__iff]) ).
fof(f_1852_2,plain,
! [U_5961,U_5960,U_5959,U_5958] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5958),U_5959),c_Divides_Odiv__class_Omod(U_5958,U_5961,U_5960)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5958),U_5959),U_5961)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5958),U_5959),U_5961))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5958),U_5959),c_Divides_Odiv__class_Omod(U_5958,U_5961,U_5960))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5958),U_5959),U_5960))
| ~ class_Divides_Osemiring__div(U_5958) ),
inference(variable_rename,[status(thm)],[f_1852_1]) ).
cnf(f_1852_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5958),U_5959),U_5961))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5958),U_5959),c_Divides_Odiv__class_Omod(U_5958,U_5961,U_5960)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5958),U_5959),U_5960))
| ~ class_Divides_Osemiring__div(U_5958) ),
inference(clausify,[status(thm)],[f_1852_2]) ).
cnf(f_1852_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5958),U_5959),c_Divides_Odiv__class_Omod(U_5958,U_5961,U_5960)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5958),U_5959),U_5961))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5958),U_5959),U_5960))
| ~ class_Divides_Osemiring__div(U_5958) ),
inference(clausify,[status(thm)],[f_1852_2]) ).
fof(f_1853_1,plain,
! [V_a,V_b,V_c,T_a] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mod__mod__cancel]) ).
fof(f_1853_2,plain,
! [U_5965,U_5964,U_5963,U_5962] :
( c_Divides_Odiv__class_Omod(U_5962,c_Divides_Odiv__class_Omod(U_5962,U_5965,U_5964),U_5963) = c_Divides_Odiv__class_Omod(U_5962,U_5965,U_5963)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5962),U_5963),U_5964))
| ~ class_Divides_Osemiring__div(U_5962) ),
inference(variable_rename,[status(thm)],[f_1853_1]) ).
cnf(f_1853_3,plain,
( c_Divides_Odiv__class_Omod(U_5962,c_Divides_Odiv__class_Omod(U_5962,U_5965,U_5964),U_5963) = c_Divides_Odiv__class_Omod(U_5962,U_5965,U_5963)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5962),U_5963),U_5964))
| ~ class_Divides_Osemiring__div(U_5962) ),
inference(clausify,[status(thm)],[f_1853_2]) ).
fof(f_1854_1,plain,
! [V_n,V_m,V_k,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))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mod]) ).
fof(f_1854_2,plain,
! [U_5969,U_5968,U_5967,U_5966] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5966),U_5967),c_Divides_Odiv__class_Omod(U_5966,U_5968,U_5969)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5966),U_5967),U_5969))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5966),U_5967),U_5968))
| ~ class_Divides_Osemiring__div(U_5966) ),
inference(variable_rename,[status(thm)],[f_1854_1]) ).
cnf(f_1854_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5966),U_5967),c_Divides_Odiv__class_Omod(U_5966,U_5968,U_5969)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5966),U_5967),U_5969))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5966),U_5967),U_5968))
| ~ class_Divides_Osemiring__div(U_5966) ),
inference(clausify,[status(thm)],[f_1854_2]) ).
fof(f_1855_1,plain,
! [V_n,V_m,V_k,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)))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mod__imp__dvd]) ).
fof(f_1855_2,plain,
! [U_5973,U_5972,U_5971,U_5970] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5970),U_5971),U_5972))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5970),U_5971),U_5973))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5970),U_5971),c_Divides_Odiv__class_Omod(U_5970,U_5972,U_5973)))
| ~ class_Divides_Osemiring__div(U_5970) ),
inference(variable_rename,[status(thm)],[f_1855_1]) ).
cnf(f_1855_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5970),U_5971),U_5972))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5970),U_5971),U_5973))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5970),U_5971),c_Divides_Odiv__class_Omod(U_5970,U_5972,U_5973)))
| ~ class_Divides_Osemiring__div(U_5970) ),
inference(clausify,[status(thm)],[f_1855_2]) ).
fof(f_1856_1,plain,
! [V_a,T_a] :
( V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__0__left]) ).
fof(f_1856_2,plain,
! [U_5975,U_5974] :
( U_5975 = c_Groups_Ozero__class_Ozero(U_5974)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5974),c_Groups_Ozero__class_Ozero(U_5974)),U_5975))
| ~ class_Rings_Ocomm__semiring__1(U_5974) ),
inference(variable_rename,[status(thm)],[f_1856_1]) ).
cnf(f_1856_3,plain,
( U_5975 = c_Groups_Ozero__class_Ozero(U_5974)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_5974),c_Groups_Ozero__class_Ozero(U_5974)),U_5975))
| ~ class_Rings_Ocomm__semiring__1(U_5974) ),
inference(clausify,[status(thm)],[f_1856_2]) ).
fof(f_1857_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
| 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)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__asym]) ).
fof(f_1857_2,plain,
! [U_5977,U_5976] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5976),U_5977))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5977),U_5976))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5977),U_5976))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5976),U_5977)) ),
inference(variable_rename,[status(thm)],[f_1857_1]) ).
cnf(f_1857_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5976),U_5977))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5977),U_5976))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5977),U_5976))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5976),U_5977)) ),
inference(clausify,[status(thm)],[f_1857_2]) ).
fof(f_1858_1,plain,
! [V_z,V_y,V_x] :
( ( ~ 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)) )
| 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_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__trans]) ).
fof(f_1858_2,plain,
! [U_5980,U_5979,U_5978] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5980),U_5978))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5978),U_5980)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5980),U_5979))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5979),U_5980))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5979),U_5978))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5978),U_5979)) ),
inference(variable_rename,[status(thm)],[f_1858_1]) ).
cnf(f_1858_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5978),U_5980))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5980),U_5979))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5979),U_5980))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5979),U_5978))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5978),U_5979)) ),
inference(clausify,[status(thm)],[f_1858_2]) ).
cnf(f_1858_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5980),U_5978))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5980),U_5979))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5979),U_5980))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5979),U_5978))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5978),U_5979)) ),
inference(clausify,[status(thm)],[f_1858_2]) ).
fof(f_1859_1,plain,
! [V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__asym_H]) ).
fof(f_1859_2,plain,
! [U_5982,U_5981] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5981),U_5982))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5982),U_5981))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5982),U_5981))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5981),U_5982)) ),
inference(variable_rename,[status(thm)],[f_1859_1]) ).
cnf(f_1859_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5981),U_5982))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5982),U_5981))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5982),U_5981))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5981),U_5982)) ),
inference(clausify,[status(thm)],[f_1859_2]) ).
fof(f_1860_1,plain,
! [V_z,V_y,V_x] :
( ( ~ 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)) )
| ~ 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_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__le__trans]) ).
fof(f_1860_2,plain,
! [U_5985,U_5984,U_5983] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5985),U_5983))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5983),U_5985)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5984),U_5985))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5984),U_5983))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5983),U_5984)) ),
inference(variable_rename,[status(thm)],[f_1860_1]) ).
cnf(f_1860_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5983),U_5985))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5984),U_5985))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5984),U_5983))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5983),U_5984)) ),
inference(clausify,[status(thm)],[f_1860_2]) ).
cnf(f_1860_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5985),U_5983))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5984),U_5985))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5984),U_5983))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5983),U_5984)) ),
inference(clausify,[status(thm)],[f_1860_2]) ).
fof(f_1861_1,plain,
! [V_c,V_b,V_a] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) )
| V_b != V_c
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oord__less__eq__trans]) ).
fof(f_1861_2,plain,
! [U_5988,U_5987,U_5986] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5988),U_5986))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5986),U_5988)) )
| U_5987 != U_5988
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5987),U_5986))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5986),U_5987)) ),
inference(variable_rename,[status(thm)],[f_1861_1]) ).
cnf(f_1861_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5986),U_5988))
| U_5987 != U_5988
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5987),U_5986))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5986),U_5987)) ),
inference(clausify,[status(thm)],[f_1861_2]) ).
cnf(f_1861_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5988),U_5986))
| U_5987 != U_5988
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5987),U_5986))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5986),U_5987)) ),
inference(clausify,[status(thm)],[f_1861_2]) ).
fof(f_1862_1,plain,
! [V_y,V_x] :
( 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)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__not__eq2]) ).
fof(f_1862_2,plain,
! [U_5990,U_5989] :
( U_5990 != U_5989
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5990),U_5989))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5989),U_5990)) ),
inference(variable_rename,[status(thm)],[f_1862_1]) ).
cnf(f_1862_3,plain,
( U_5990 != U_5989
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5990),U_5989))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5989),U_5990)) ),
inference(clausify,[status(thm)],[f_1862_2]) ).
fof(f_1863_1,plain,
! [V_y,V_x] :
( V_x != V_y
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__not__eq]) ).
fof(f_1863_2,plain,
! [U_5992,U_5991] :
( U_5991 != U_5992
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5992),U_5991))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5991),U_5992)) ),
inference(variable_rename,[status(thm)],[f_1863_1]) ).
cnf(f_1863_3,plain,
( U_5991 != U_5992
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5992),U_5991))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5991),U_5992)) ),
inference(clausify,[status(thm)],[f_1863_2]) ).
fof(f_1864_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
| 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)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__not__less]) ).
fof(f_1864_2,plain,
! [U_5994,U_5993] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5993),U_5994))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5994),U_5993))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5994),U_5993))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5993),U_5994)) ),
inference(variable_rename,[status(thm)],[f_1864_1]) ).
cnf(f_1864_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5993),U_5994))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5994),U_5993))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5994),U_5993))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5993),U_5994)) ),
inference(clausify,[status(thm)],[f_1864_2]) ).
fof(f_1865_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__le]) ).
fof(f_1865_2,plain,
! [U_5996,U_5995] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5995),U_5996))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5996),U_5995))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5995),U_5996)) ),
inference(variable_rename,[status(thm)],[f_1865_1]) ).
cnf(f_1865_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5995),U_5996))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5996),U_5995))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5995),U_5996)) ),
inference(clausify,[status(thm)],[f_1865_2]) ).
fof(f_1866_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
| 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)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__not__sym]) ).
fof(f_1866_2,plain,
! [U_5998,U_5997] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5997),U_5998))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5998),U_5997))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5998),U_5997))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5997),U_5998)) ),
inference(variable_rename,[status(thm)],[f_1866_1]) ).
cnf(f_1866_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5997),U_5998))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5998),U_5997))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5998),U_5997))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5997),U_5998)) ),
inference(clausify,[status(thm)],[f_1866_2]) ).
fof(f_1867_1,plain,
! [V_y,V_x] :
( V_x != V_y
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__neq]) ).
fof(f_1867_2,plain,
! [U_6000,U_5999] :
( U_5999 != U_6000
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6000),U_5999))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5999),U_6000)) ),
inference(variable_rename,[status(thm)],[f_1867_1]) ).
cnf(f_1867_3,plain,
( U_5999 != U_6000
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6000),U_5999))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_5999),U_6000)) ),
inference(clausify,[status(thm)],[f_1867_2]) ).
fof(f_1868_1,plain,
! [V_z,V_y,V_x] :
( ( ~ 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)) )
| 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_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Ole__less__trans]) ).
fof(f_1868_2,plain,
! [U_6003,U_6002,U_6001] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6003),U_6001))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6001),U_6003)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6003),U_6002))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6002),U_6003))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6001),U_6002)) ),
inference(variable_rename,[status(thm)],[f_1868_1]) ).
cnf(f_1868_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6001),U_6003))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6003),U_6002))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6002),U_6003))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6001),U_6002)) ),
inference(clausify,[status(thm)],[f_1868_2]) ).
cnf(f_1868_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6003),U_6001))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6003),U_6002))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6002),U_6003))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6001),U_6002)) ),
inference(clausify,[status(thm)],[f_1868_2]) ).
fof(f_1869_1,plain,
! [V_c,V_b,V_a] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
| V_a != V_b ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oord__eq__less__trans]) ).
fof(f_1869_2,plain,
! [U_6006,U_6005,U_6004] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6006),U_6004))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6004),U_6006)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6006),U_6005))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6005),U_6006))
| U_6004 != U_6005 ),
inference(variable_rename,[status(thm)],[f_1869_1]) ).
cnf(f_1869_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6004),U_6006))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6006),U_6005))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6005),U_6006))
| U_6004 != U_6005 ),
inference(clausify,[status(thm)],[f_1869_2]) ).
cnf(f_1869_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6006),U_6004))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6006),U_6005))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6005),U_6006))
| U_6004 != U_6005 ),
inference(clausify,[status(thm)],[f_1869_2]) ).
fof(f_1870_1,plain,
! [V_z,V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
| ~ 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_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oorder__trans]) ).
fof(f_1870_2,plain,
! [U_6009,U_6008,U_6007] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6007),U_6009))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6008),U_6009))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6007),U_6008)) ),
inference(variable_rename,[status(thm)],[f_1870_1]) ).
cnf(f_1870_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6007),U_6009))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6008),U_6009))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6007),U_6008)) ),
inference(clausify,[status(thm)],[f_1870_2]) ).
fof(f_1871_1,plain,
! [V_y,V_x] :
( V_x = V_y
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym]) ).
fof(f_1871_2,plain,
! [U_6011,U_6010] :
( U_6010 = U_6011
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6011),U_6010))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6010),U_6011)) ),
inference(variable_rename,[status(thm)],[f_1871_1]) ).
cnf(f_1871_3,plain,
( U_6010 = U_6011
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6011),U_6010))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6010),U_6011)) ),
inference(clausify,[status(thm)],[f_1871_2]) ).
fof(f_1872_1,plain,
! [V_n,V_m] :
( V_m = V_n
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_dvd__antisym]) ).
fof(f_1872_2,plain,
! [U_6013,U_6012] :
( U_6012 = U_6013
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6013),U_6012))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6012),U_6013)) ),
inference(variable_rename,[status(thm)],[f_1872_1]) ).
cnf(f_1872_3,plain,
( U_6012 = U_6013
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6013),U_6012))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6012),U_6013)) ),
inference(clausify,[status(thm)],[f_1872_2]) ).
fof(f_1873_1,plain,
! [V_c,V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
| V_b != V_c
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oord__le__eq__trans]) ).
fof(f_1873_2,plain,
! [U_6016,U_6015,U_6014] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6014),U_6016))
| U_6015 != U_6016
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6014),U_6015)) ),
inference(variable_rename,[status(thm)],[f_1873_1]) ).
cnf(f_1873_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6014),U_6016))
| U_6015 != U_6016
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6014),U_6015)) ),
inference(clausify,[status(thm)],[f_1873_2]) ).
fof(f_1874_1,plain,
! [V_c,V_b,V_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
| V_a != V_b ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oord__eq__le__trans]) ).
fof(f_1874_2,plain,
! [U_6019,U_6018,U_6017] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6017),U_6019))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6018),U_6019))
| U_6017 != U_6018 ),
inference(variable_rename,[status(thm)],[f_1874_1]) ).
cnf(f_1874_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6017),U_6019))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6018),U_6019))
| U_6017 != U_6018 ),
inference(clausify,[status(thm)],[f_1874_2]) ).
fof(f_1875_1,plain,
! [V_b,V_a] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) )
| V_a = V_b
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Ole__neq__trans]) ).
fof(f_1875_2,plain,
! [U_6021,U_6020] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6021),U_6020))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6020),U_6021)) )
| U_6020 = U_6021
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6020),U_6021)) ),
inference(variable_rename,[status(thm)],[f_1875_1]) ).
cnf(f_1875_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6020),U_6021))
| U_6020 = U_6021
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6020),U_6021)) ),
inference(clausify,[status(thm)],[f_1875_2]) ).
cnf(f_1875_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6021),U_6020))
| U_6020 = U_6021
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6020),U_6021)) ),
inference(clausify,[status(thm)],[f_1875_2]) ).
fof(f_1876_1,plain,
! [V_y,V_x] :
( V_x = V_y
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Ole__imp__less__or__eq]) ).
fof(f_1876_2,plain,
! [U_6023,U_6022] :
( U_6022 = U_6023
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6023),U_6022))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6022),U_6023)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6022),U_6023)) ),
inference(variable_rename,[status(thm)],[f_1876_1]) ).
cnf(f_1876_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6022),U_6023))
| U_6022 = U_6023
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6022),U_6023)) ),
inference(clausify,[status(thm)],[f_1876_2]) ).
cnf(f_1876_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6023),U_6022))
| U_6022 = U_6023
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6022),U_6023)) ),
inference(clausify,[status(thm)],[f_1876_2]) ).
fof(f_1877_1,plain,
! [V_x_2,V_y_2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym__conv]) ).
fof(f_1877_2,plain,
! [U_6025,U_6024] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6025),U_6024))
| U_6025 != U_6024 )
& ( U_6025 = U_6024
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6025),U_6024)) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6024),U_6025)) ),
inference(variable_rename,[status(thm)],[f_1877_1]) ).
cnf(f_1877_3,plain,
( U_6025 = U_6024
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6025),U_6024))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6024),U_6025)) ),
inference(clausify,[status(thm)],[f_1877_2]) ).
cnf(f_1877_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6025),U_6024))
| U_6025 != U_6024
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6024),U_6025)) ),
inference(clausify,[status(thm)],[f_1877_2]) ).
fof(f_1878_1,plain,
! [V_y,V_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
| V_x != V_y ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__refl]) ).
fof(f_1878_2,plain,
! [U_6027,U_6026] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6026),U_6027))
| U_6026 != U_6027 ),
inference(variable_rename,[status(thm)],[f_1878_1]) ).
cnf(f_1878_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6026),U_6027))
| U_6026 != U_6027 ),
inference(clausify,[status(thm)],[f_1878_2]) ).
fof(f_1879_1,plain,
! [V_b,V_a] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
| V_a = V_b ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oneq__le__trans]) ).
fof(f_1879_2,plain,
! [U_6029,U_6028] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6029),U_6028))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6028),U_6029)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6028),U_6029))
| U_6028 = U_6029 ),
inference(variable_rename,[status(thm)],[f_1879_1]) ).
cnf(f_1879_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6028),U_6029))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6028),U_6029))
| U_6028 = U_6029 ),
inference(clausify,[status(thm)],[f_1879_2]) ).
cnf(f_1879_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6029),U_6028))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6028),U_6029))
| U_6028 = U_6029 ),
inference(clausify,[status(thm)],[f_1879_2]) ).
fof(f_1880_1,plain,
! [V_y_2,V_x_2] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
| V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
& ( ( V_x_2 != V_y_2
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__le]) ).
fof(f_1880_2,plain,
! [U_6031,U_6030] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6031),U_6030))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6030),U_6031)) )
| U_6030 = U_6031
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6030),U_6031)) )
& ( ( U_6030 != U_6031
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6030),U_6031)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6031),U_6030))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6030),U_6031)) ) ),
inference(variable_rename,[status(thm)],[f_1880_1]) ).
fof(f_1880_3,plain,
( ! [U_6035,U_6033] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6035),U_6033))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6033),U_6035)) )
| U_6033 = U_6035
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6033),U_6035)) )
& ! [U_6034,U_6032] :
( ( U_6032 != U_6034
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6032),U_6034)) )
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6034),U_6032))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6032),U_6034)) ) ),
inference(miniscope,[status(thm)],[f_1880_2]) ).
cnf(f_1880_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6032),U_6034))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6034),U_6032))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6032),U_6034)) ),
inference(clausify,[status(thm)],[f_1880_3]) ).
cnf(f_1880_5,plain,
( U_6032 != U_6034
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6034),U_6032))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6032),U_6034)) ),
inference(clausify,[status(thm)],[f_1880_3]) ).
cnf(f_1880_6,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6033),U_6035))
| U_6033 = U_6035
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6033),U_6035)) ),
inference(clausify,[status(thm)],[f_1880_3]) ).
cnf(f_1880_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6035),U_6033))
| U_6033 = U_6035
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6033),U_6035)) ),
inference(clausify,[status(thm)],[f_1880_3]) ).
fof(f_1881_1,plain,
! [V_y_2,V_x_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
| ( V_x_2 != V_y_2
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ) )
& ( V_x_2 = V_y_2
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Ole__less]) ).
fof(f_1881_2,plain,
! [U_6037,U_6036] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6036),U_6037))
| ( U_6036 != U_6037
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6037),U_6036))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6036),U_6037)) ) ) )
& ( U_6036 = U_6037
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6037),U_6036))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6036),U_6037)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6036),U_6037)) ) ),
inference(variable_rename,[status(thm)],[f_1881_1]) ).
fof(f_1881_3,plain,
( ! [U_6041,U_6039] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6039),U_6041))
| ( U_6039 != U_6041
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6041),U_6039))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6039),U_6041)) ) ) )
& ! [U_6040,U_6038] :
( U_6038 = U_6040
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6040),U_6038))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6038),U_6040)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6038),U_6040)) ) ),
inference(miniscope,[status(thm)],[f_1881_2]) ).
cnf(f_1881_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6038),U_6040))
| U_6038 = U_6040
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6038),U_6040)) ),
inference(clausify,[status(thm)],[f_1881_3]) ).
cnf(f_1881_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6040),U_6038))
| U_6038 = U_6040
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6038),U_6040)) ),
inference(clausify,[status(thm)],[f_1881_3]) ).
cnf(f_1881_6,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6041),U_6039))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6039),U_6041))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6039),U_6041)) ),
inference(clausify,[status(thm)],[f_1881_3]) ).
cnf(f_1881_7,plain,
( U_6039 != U_6041
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6039),U_6041)) ),
inference(clausify,[status(thm)],[f_1881_3]) ).
fof(f_1882_1,plain,
! [V_y_2,V_x_2] :
( ( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
| V_x_2 != V_y_2 ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__iff]) ).
fof(f_1882_2,plain,
! [U_6043,U_6042] :
( ( U_6042 = U_6043
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6043),U_6042))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6042),U_6043)) )
& ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6043),U_6042))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6042),U_6043)) )
| U_6042 != U_6043 ) ),
inference(variable_rename,[status(thm)],[f_1882_1]) ).
fof(f_1882_3,plain,
( ! [U_6047,U_6045] :
( U_6045 = U_6047
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6047),U_6045))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6045),U_6047)) )
& ! [U_6046,U_6044] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6046),U_6044))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6044),U_6046)) )
| U_6044 != U_6046 ) ),
inference(miniscope,[status(thm)],[f_1882_2]) ).
cnf(f_1882_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6044),U_6046))
| U_6044 != U_6046 ),
inference(clausify,[status(thm)],[f_1882_3]) ).
cnf(f_1882_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6046),U_6044))
| U_6044 != U_6046 ),
inference(clausify,[status(thm)],[f_1882_3]) ).
cnf(f_1882_6,plain,
( U_6045 = U_6047
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6047),U_6045))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6045),U_6047)) ),
inference(clausify,[status(thm)],[f_1882_3]) ).
fof(f_1883_1,plain,
! [V_c,V_b,V_a,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_b),V_c))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__trans]) ).
fof(f_1883_2,plain,
! [U_6051,U_6050,U_6049,U_6048] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6048),U_6049),U_6051))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6048),U_6050),U_6051))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6048),U_6049),U_6050))
| ~ class_Rings_Ocomm__semiring__1(U_6048) ),
inference(variable_rename,[status(thm)],[f_1883_1]) ).
cnf(f_1883_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6048),U_6049),U_6051))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6048),U_6050),U_6051))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6048),U_6049),U_6050))
| ~ class_Rings_Ocomm__semiring__1(U_6048) ),
inference(clausify,[status(thm)],[f_1883_2]) ).
fof(f_1884_1,plain,
! [V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__refl]) ).
fof(f_1884_2,plain,
! [U_6053,U_6052] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6052),U_6053),U_6053))
| ~ class_Rings_Ocomm__semiring__1(U_6052) ),
inference(variable_rename,[status(thm)],[f_1884_1]) ).
cnf(f_1884_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6052),U_6053),U_6053))
| ~ class_Rings_Ocomm__semiring__1(U_6052) ),
inference(clausify,[status(thm)],[f_1884_2]) ).
fof(f_1885_1,plain,
! [V_z,V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__diff]) ).
fof(f_1885_2,plain,
! [U_6057,U_6056,U_6055,U_6054] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6054),U_6055),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6054),U_6056),U_6057)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6054),U_6055),U_6057))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6054),U_6055),U_6056))
| ~ class_Rings_Ocomm__ring__1(U_6054) ),
inference(variable_rename,[status(thm)],[f_1885_1]) ).
cnf(f_1885_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6054),U_6055),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6054),U_6056),U_6057)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6054),U_6055),U_6057))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6054),U_6055),U_6056))
| ~ class_Rings_Ocomm__ring__1(U_6054) ),
inference(clausify,[status(thm)],[f_1885_2]) ).
fof(f_1886_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)))
| ~ 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),V_b))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__add]) ).
fof(f_1886_2,plain,
! [U_6061,U_6060,U_6059,U_6058] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6058),U_6059),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6058),U_6060),U_6061)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6058),U_6059),U_6061))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6058),U_6059),U_6060))
| ~ class_Rings_Ocomm__semiring__1(U_6058) ),
inference(variable_rename,[status(thm)],[f_1886_1]) ).
cnf(f_1886_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6058),U_6059),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6058),U_6060),U_6061)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6058),U_6059),U_6061))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6058),U_6059),U_6060))
| ~ class_Rings_Ocomm__semiring__1(U_6058) ),
inference(clausify,[status(thm)],[f_1886_2]) ).
fof(f_1887_1,plain,
! [V_n,V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__power__same]) ).
fof(f_1887_2,plain,
! [U_6065,U_6064,U_6063,U_6062] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6062),hAPP(hAPP(c_Power_Opower__class_Opower(U_6062),U_6063),U_6065)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6062),U_6064),U_6065)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6062),U_6063),U_6064))
| ~ class_Rings_Ocomm__semiring__1(U_6062) ),
inference(variable_rename,[status(thm)],[f_1887_1]) ).
cnf(f_1887_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6062),hAPP(hAPP(c_Power_Opower__class_Opower(U_6062),U_6063),U_6065)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6062),U_6064),U_6065)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6062),U_6063),U_6064))
| ~ class_Rings_Ocomm__semiring__1(U_6062) ),
inference(clausify,[status(thm)],[f_1887_2]) ).
fof(f_1888_1,plain,
! [V_b,V_a,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)))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__triv__left]) ).
fof(f_1888_2,plain,
! [U_6068,U_6067,U_6066] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6066),U_6067),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6066),U_6067),U_6068)))
| ~ class_Rings_Ocomm__semiring__1(U_6066) ),
inference(variable_rename,[status(thm)],[f_1888_1]) ).
cnf(f_1888_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6066),U_6067),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6066),U_6067),U_6068)))
| ~ class_Rings_Ocomm__semiring__1(U_6066) ),
inference(clausify,[status(thm)],[f_1888_2]) ).
fof(f_1889_1,plain,
! [V_b,V_a,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)))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__triv__right]) ).
fof(f_1889_2,plain,
! [U_6071,U_6070,U_6069] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6069),U_6070),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6069),U_6071),U_6070)))
| ~ class_Rings_Ocomm__semiring__1(U_6069) ),
inference(variable_rename,[status(thm)],[f_1889_1]) ).
cnf(f_1889_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6069),U_6070),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6069),U_6071),U_6070)))
| ~ class_Rings_Ocomm__semiring__1(U_6069) ),
inference(clausify,[status(thm)],[f_1889_2]) ).
fof(f_1890_1,plain,
! [V_c,V_b,V_a,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_c)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult2]) ).
fof(f_1890_2,plain,
! [U_6075,U_6074,U_6073,U_6072] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6072),U_6073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6072),U_6074),U_6075)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6072),U_6073),U_6074))
| ~ class_Rings_Ocomm__semiring__1(U_6072) ),
inference(variable_rename,[status(thm)],[f_1890_1]) ).
cnf(f_1890_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6072),U_6073),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6072),U_6074),U_6075)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6072),U_6073),U_6074))
| ~ class_Rings_Ocomm__semiring__1(U_6072) ),
inference(clausify,[status(thm)],[f_1890_2]) ).
fof(f_1891_1,plain,
! [V_b,V_c,V_a,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_c)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult]) ).
fof(f_1891_2,plain,
! [U_6079,U_6078,U_6077,U_6076] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6076),U_6077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6076),U_6079),U_6078)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6076),U_6077),U_6078))
| ~ class_Rings_Ocomm__semiring__1(U_6076) ),
inference(variable_rename,[status(thm)],[f_1891_1]) ).
cnf(f_1891_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6076),U_6077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6076),U_6079),U_6078)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6076),U_6077),U_6078))
| ~ class_Rings_Ocomm__semiring__1(U_6076) ),
inference(clausify,[status(thm)],[f_1891_2]) ).
fof(f_1892_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( 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)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__dvd__mono]) ).
fof(f_1892_2,plain,
! [U_6084,U_6083,U_6082,U_6081,U_6080] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6080),U_6081),U_6083)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6080),U_6082),U_6084)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6080),U_6083),U_6084))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6080),U_6081),U_6082))
| ~ class_Rings_Ocomm__semiring__1(U_6080) ),
inference(variable_rename,[status(thm)],[f_1892_1]) ).
cnf(f_1892_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6080),U_6081),U_6083)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6080),U_6082),U_6084)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6080),U_6083),U_6084))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6080),U_6081),U_6082))
| ~ class_Rings_Ocomm__semiring__1(U_6080) ),
inference(clausify,[status(thm)],[f_1892_2]) ).
fof(f_1893_1,plain,
! [V_k,V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a))
| V_a != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
| ~ class_Rings_Odvd(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvdI]) ).
fof(f_1893_2,plain,
! [U_6088,U_6087,U_6086,U_6085] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6085),U_6087),U_6086))
| U_6086 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6085),U_6087),U_6088)
| ~ class_Rings_Odvd(U_6085) ),
inference(variable_rename,[status(thm)],[f_1893_1]) ).
cnf(f_1893_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6085),U_6087),U_6086))
| U_6086 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6085),U_6087),U_6088)
| ~ class_Rings_Odvd(U_6085) ),
inference(clausify,[status(thm)],[f_1893_2]) ).
fof(f_1894_1,plain,
! [V_c,V_b,V_a,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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__left]) ).
fof(f_1894_2,plain,
! [U_6092,U_6091,U_6090,U_6089] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6089),U_6090),U_6092))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6089),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6089),U_6090),U_6091)),U_6092))
| ~ class_Rings_Ocomm__semiring__1(U_6089) ),
inference(variable_rename,[status(thm)],[f_1894_1]) ).
cnf(f_1894_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6089),U_6090),U_6092))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6089),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6089),U_6090),U_6091)),U_6092))
| ~ class_Rings_Ocomm__semiring__1(U_6089) ),
inference(clausify,[status(thm)],[f_1894_2]) ).
fof(f_1895_1,plain,
! [V_c,V_b,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
| ~ 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))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__right]) ).
fof(f_1895_2,plain,
! [U_6096,U_6095,U_6094,U_6093] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6093),U_6095),U_6096))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6093),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6093),U_6094),U_6095)),U_6096))
| ~ class_Rings_Ocomm__semiring__1(U_6093) ),
inference(variable_rename,[status(thm)],[f_1895_1]) ).
cnf(f_1895_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6093),U_6095),U_6096))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6093),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6093),U_6094),U_6095)),U_6096))
| ~ class_Rings_Ocomm__semiring__1(U_6093) ),
inference(clausify,[status(thm)],[f_1895_2]) ).
fof(f_1896_1,plain,
! [V_na_2,V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_na_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd__reduce]) ).
fof(f_1896_2,plain,
! [U_6098,U_6097] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6097),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6098),U_6097)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6097),U_6098)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6097),U_6098))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6097),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6098),U_6097))) ) ),
inference(variable_rename,[status(thm)],[f_1896_1]) ).
fof(f_1896_3,plain,
( ! [U_6102,U_6100] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6100),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6102),U_6100)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6100),U_6102)) )
& ! [U_6101,U_6099] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6099),U_6101))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6099),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6101),U_6099))) ) ),
inference(miniscope,[status(thm)],[f_1896_2]) ).
cnf(f_1896_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6099),U_6101))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6099),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6101),U_6099))) ),
inference(clausify,[status(thm)],[f_1896_3]) ).
cnf(f_1896_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6100),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6102),U_6100)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6100),U_6102)) ),
inference(clausify,[status(thm)],[f_1896_3]) ).
fof(f_1897_1,plain,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_dvd__diff__nat]) ).
fof(f_1897_2,plain,
! [U_6105,U_6104,U_6103] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6103),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6104),U_6105)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6103),U_6105))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6103),U_6104)) ),
inference(variable_rename,[status(thm)],[f_1897_1]) ).
cnf(f_1897_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6103),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6104),U_6105)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6103),U_6105))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6103),U_6104)) ),
inference(clausify,[status(thm)],[f_1897_2]) ).
fof(f_1898_1,plain,
! [V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__dvd__1__iff__1]) ).
fof(f_1898_2,plain,
! [U_6106] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6106),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| U_6106 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( U_6106 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6106),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[f_1898_1]) ).
fof(f_1898_3,plain,
( ! [U_6108] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6108),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| U_6108 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_6107] :
( U_6107 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6107),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(miniscope,[status(thm)],[f_1898_2]) ).
cnf(f_1898_4,plain,
( U_6107 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6107),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_1898_3]) ).
cnf(f_1898_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6108),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| U_6108 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1898_3]) ).
fof(f_1899_1,plain,
! [V_b_2,V_a_2,V_c_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
& V_c_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
| V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2))) ) )
| ~ class_Rings_Oidom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__left]) ).
fof(f_1899_2,plain,
! [U_6112,U_6111,U_6110,U_6109] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6109),U_6110),U_6111)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6109),U_6110),U_6112)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6109),U_6111),U_6112))
& U_6110 != c_Groups_Ozero__class_Ozero(U_6109) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6109),U_6111),U_6112))
| U_6110 = c_Groups_Ozero__class_Ozero(U_6109)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6109),U_6110),U_6111)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6109),U_6110),U_6112))) ) )
| ~ class_Rings_Oidom(U_6109) ),
inference(variable_rename,[status(thm)],[f_1899_1]) ).
cnf(f_1899_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6109),U_6111),U_6112))
| U_6110 = c_Groups_Ozero__class_Ozero(U_6109)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6109),U_6110),U_6111)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6109),U_6110),U_6112)))
| ~ class_Rings_Oidom(U_6109) ),
inference(clausify,[status(thm)],[f_1899_2]) ).
cnf(f_1899_4,plain,
( U_6110 != c_Groups_Ozero__class_Ozero(U_6109)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6109),U_6110),U_6111)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6109),U_6110),U_6112)))
| ~ class_Rings_Oidom(U_6109) ),
inference(clausify,[status(thm)],[f_1899_2]) ).
cnf(f_1899_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6109),U_6111),U_6112))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6109),U_6110),U_6111)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6109),U_6110),U_6112)))
| ~ class_Rings_Oidom(U_6109) ),
inference(clausify,[status(thm)],[f_1899_2]) ).
fof(f_1900_1,plain,
! [V_b_2,V_c_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
& V_c_2 != c_Groups_Ozero__class_Ozero(T_b) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
| V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2))) ) )
| ~ class_Rings_Oidom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__right]) ).
fof(f_1900_2,plain,
! [U_6116,U_6115,U_6114,U_6113] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6113),U_6114),U_6115)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6113),U_6116),U_6115)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6113),U_6114),U_6116))
& U_6115 != c_Groups_Ozero__class_Ozero(U_6113) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6113),U_6114),U_6116))
| U_6115 = c_Groups_Ozero__class_Ozero(U_6113)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6113),U_6114),U_6115)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6113),U_6116),U_6115))) ) )
| ~ class_Rings_Oidom(U_6113) ),
inference(variable_rename,[status(thm)],[f_1900_1]) ).
cnf(f_1900_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6113),U_6114),U_6116))
| U_6115 = c_Groups_Ozero__class_Ozero(U_6113)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6113),U_6114),U_6115)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6113),U_6116),U_6115)))
| ~ class_Rings_Oidom(U_6113) ),
inference(clausify,[status(thm)],[f_1900_2]) ).
cnf(f_1900_4,plain,
( U_6115 != c_Groups_Ozero__class_Ozero(U_6113)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6113),U_6114),U_6115)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6113),U_6116),U_6115)))
| ~ class_Rings_Oidom(U_6113) ),
inference(clausify,[status(thm)],[f_1900_2]) ).
cnf(f_1900_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6113),U_6114),U_6116))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6113),U_6114),U_6115)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6113),U_6116),U_6115)))
| ~ class_Rings_Oidom(U_6113) ),
inference(clausify,[status(thm)],[f_1900_2]) ).
fof(f_1901_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
| c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b) )
& ( c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) )
| ~ class_Divides_Osemiring__div(T_b) ),
inference(fof_nnf,[status(thm)],[fact_dvd__eq__mod__eq__0]) ).
fof(f_1901_2,plain,
! [U_6119,U_6118,U_6117] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6117),U_6118),U_6119))
| c_Divides_Odiv__class_Omod(U_6117,U_6119,U_6118) != c_Groups_Ozero__class_Ozero(U_6117) )
& ( c_Divides_Odiv__class_Omod(U_6117,U_6119,U_6118) = c_Groups_Ozero__class_Ozero(U_6117)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6117),U_6118),U_6119)) ) )
| ~ class_Divides_Osemiring__div(U_6117) ),
inference(variable_rename,[status(thm)],[f_1901_1]) ).
cnf(f_1901_3,plain,
( c_Divides_Odiv__class_Omod(U_6117,U_6119,U_6118) = c_Groups_Ozero__class_Ozero(U_6117)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6117),U_6118),U_6119))
| ~ class_Divides_Osemiring__div(U_6117) ),
inference(clausify,[status(thm)],[f_1901_2]) ).
cnf(f_1901_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6117),U_6118),U_6119))
| c_Divides_Odiv__class_Omod(U_6117,U_6119,U_6118) != c_Groups_Ozero__class_Ozero(U_6117)
| ~ class_Divides_Osemiring__div(U_6117) ),
inference(clausify,[status(thm)],[f_1901_2]) ).
fof(f_1902_1,plain,
! [V_b,V_a,T_a] :
( c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__imp__mod__0]) ).
fof(f_1902_2,plain,
! [U_6122,U_6121,U_6120] :
( c_Divides_Odiv__class_Omod(U_6120,U_6122,U_6121) = c_Groups_Ozero__class_Ozero(U_6120)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6120),U_6121),U_6122))
| ~ class_Divides_Osemiring__div(U_6120) ),
inference(variable_rename,[status(thm)],[f_1902_1]) ).
cnf(f_1902_3,plain,
( c_Divides_Odiv__class_Omod(U_6120,U_6122,U_6121) = c_Groups_Ozero__class_Ozero(U_6120)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6120),U_6121),U_6122))
| ~ class_Divides_Osemiring__div(U_6120) ),
inference(clausify,[status(thm)],[f_1902_2]) ).
fof(f_1903_1,plain,
! [V_y,V_x,V_z,T_a] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_z)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_y),V_z))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__add]) ).
fof(f_1903_2,plain,
! [U_6126,U_6125,U_6124,U_6123] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6123),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6123),U_6125),U_6126)),U_6124) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6123),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6123),U_6125),U_6124)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6123),U_6126),U_6124))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6123),U_6124),U_6126))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6123),U_6124),U_6125))
| ~ class_Divides_Osemiring__div(U_6123) ),
inference(variable_rename,[status(thm)],[f_1903_1]) ).
cnf(f_1903_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6123),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6123),U_6125),U_6126)),U_6124) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6123),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6123),U_6125),U_6124)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6123),U_6126),U_6124))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6123),U_6124),U_6126))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6123),U_6124),U_6125))
| ~ class_Divides_Osemiring__div(U_6123) ),
inference(clausify,[status(thm)],[f_1903_2]) ).
fof(f_1904_1,plain,
! [V_b,V_a,T_a] :
( 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
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__div__cancel]) ).
fof(f_1904_2,plain,
! [U_6129,U_6128,U_6127] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6127),U_6128),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6127),U_6129),U_6128)) = U_6129
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6127),U_6128),U_6129))
| ~ class_Divides_Osemiring__div(U_6127) ),
inference(variable_rename,[status(thm)],[f_1904_1]) ).
cnf(f_1904_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6127),U_6128),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6127),U_6129),U_6128)) = U_6129
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6127),U_6128),U_6129))
| ~ class_Divides_Osemiring__div(U_6127) ),
inference(clausify,[status(thm)],[f_1904_2]) ).
fof(f_1905_1,plain,
! [V_a,V_b,V_c,T_a] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__mult__swap]) ).
fof(f_1905_2,plain,
! [U_6133,U_6132,U_6131,U_6130] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6130),U_6133),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6130),U_6132),U_6131)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6130),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6130),U_6133),U_6132)),U_6131)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6130),U_6131),U_6132))
| ~ class_Divides_Osemiring__div(U_6130) ),
inference(variable_rename,[status(thm)],[f_1905_1]) ).
cnf(f_1905_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6130),U_6133),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6130),U_6132),U_6131)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6130),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6130),U_6133),U_6132)),U_6131)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6130),U_6131),U_6132))
| ~ class_Divides_Osemiring__div(U_6130) ),
inference(clausify,[status(thm)],[f_1905_2]) ).
fof(f_1906_1,plain,
! [V_b,V_a,T_a] :
( 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
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__div__mult__self]) ).
fof(f_1906_2,plain,
! [U_6136,U_6135,U_6134] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6134),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6134),U_6136),U_6135)),U_6135) = U_6136
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6134),U_6135),U_6136))
| ~ class_Divides_Osemiring__div(U_6134) ),
inference(variable_rename,[status(thm)],[f_1906_1]) ).
cnf(f_1906_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6134),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6134),U_6136),U_6135)),U_6135) = U_6136
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6134),U_6135),U_6136))
| ~ class_Divides_Osemiring__div(U_6134) ),
inference(clausify,[status(thm)],[f_1906_2]) ).
fof(f_1907_1,plain,
! [V_c,V_b,V_a,T_a] :
( 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)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__div__mult]) ).
fof(f_1907_2,plain,
! [U_6140,U_6139,U_6138,U_6137] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6137),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6137),U_6139),U_6138)),U_6140) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6137),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6137),U_6139),U_6140)),U_6138)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6137),U_6138),U_6139))
| ~ class_Divides_Osemiring__div(U_6137) ),
inference(variable_rename,[status(thm)],[f_1907_1]) ).
cnf(f_1907_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6137),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6137),U_6139),U_6138)),U_6140) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6137),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6137),U_6139),U_6140)),U_6138)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6137),U_6138),U_6139))
| ~ class_Divides_Osemiring__div(U_6137) ),
inference(clausify,[status(thm)],[f_1907_2]) ).
fof(f_1908_1,plain,
! [V_w,V_z,V_x,V_y,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__mult__div__if__dvd]) ).
fof(f_1908_2,plain,
! [U_6145,U_6144,U_6143,U_6142,U_6141] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6141),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6141),U_6143),U_6142)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6141),U_6145),U_6144)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6141),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6141),U_6143),U_6145)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6141),U_6142),U_6144))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6141),U_6144),U_6145))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6141),U_6142),U_6143))
| ~ class_Divides_Osemiring__div(U_6141) ),
inference(variable_rename,[status(thm)],[f_1908_1]) ).
cnf(f_1908_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6141),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6141),U_6143),U_6142)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6141),U_6145),U_6144)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6141),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6141),U_6143),U_6145)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6141),U_6142),U_6144))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6141),U_6144),U_6145))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6141),U_6142),U_6143))
| ~ class_Divides_Osemiring__div(U_6141) ),
inference(clausify,[status(thm)],[f_1908_2]) ).
fof(f_1909_1,plain,
! [V_x,V_y,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
| ~ class_Divides_Oring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__div__neg]) ).
fof(f_1909_2,plain,
! [U_6148,U_6147,U_6146] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6146),U_6148),hAPP(c_Groups_Ouminus__class_Ouminus(U_6146),U_6147)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6146),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6146),U_6148),U_6147))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6146),U_6147),U_6148))
| ~ class_Divides_Oring__div(U_6146) ),
inference(variable_rename,[status(thm)],[f_1909_1]) ).
cnf(f_1909_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6146),U_6148),hAPP(c_Groups_Ouminus__class_Ouminus(U_6146),U_6147)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6146),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6146),U_6148),U_6147))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6146),U_6147),U_6148))
| ~ class_Divides_Oring__div(U_6146) ),
inference(clausify,[status(thm)],[f_1909_2]) ).
fof(f_1910_1,plain,
! [V_x,V_y,T_a] :
( 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))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
| ~ class_Divides_Oring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__neg__div]) ).
fof(f_1910_2,plain,
! [U_6151,U_6150,U_6149] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6149),hAPP(c_Groups_Ouminus__class_Ouminus(U_6149),U_6151)),U_6150) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6149),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6149),U_6151),U_6150))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6149),U_6150),U_6151))
| ~ class_Divides_Oring__div(U_6149) ),
inference(variable_rename,[status(thm)],[f_1910_1]) ).
cnf(f_1910_3,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6149),hAPP(c_Groups_Ouminus__class_Ouminus(U_6149),U_6151)),U_6150) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6149),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6149),U_6151),U_6150))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6149),U_6150),U_6151))
| ~ class_Divides_Oring__div(U_6149) ),
inference(clausify,[status(thm)],[f_1910_2]) ).
fof(f_1911_1,plain,
! [V_a,V_n,V_m,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__power__dvd]) ).
fof(f_1911_2,plain,
! [U_6155,U_6154,U_6153,U_6152] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6152),hAPP(hAPP(c_Power_Opower__class_Opower(U_6152),U_6155),U_6153)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6152),U_6155),U_6154)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6153),U_6154))
| ~ class_Rings_Ocomm__semiring__1(U_6152) ),
inference(variable_rename,[status(thm)],[f_1911_1]) ).
cnf(f_1911_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6152),hAPP(hAPP(c_Power_Opower__class_Opower(U_6152),U_6155),U_6153)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6152),U_6155),U_6154)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6153),U_6154))
| ~ class_Rings_Ocomm__semiring__1(U_6152) ),
inference(clausify,[status(thm)],[f_1911_2]) ).
fof(f_1912_1,plain,
! [V_m,V_n,V_y,V_x,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__power__le]) ).
fof(f_1912_2,plain,
! [U_6160,U_6159,U_6158,U_6157,U_6156] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6156),hAPP(hAPP(c_Power_Opower__class_Opower(U_6156),U_6157),U_6159)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6156),U_6158),U_6160)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6159),U_6160))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6156),U_6157),U_6158))
| ~ class_Rings_Ocomm__semiring__1(U_6156) ),
inference(variable_rename,[status(thm)],[f_1912_1]) ).
cnf(f_1912_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6156),hAPP(hAPP(c_Power_Opower__class_Opower(U_6156),U_6157),U_6159)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6156),U_6158),U_6160)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6159),U_6160))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6156),U_6157),U_6158))
| ~ class_Rings_Ocomm__semiring__1(U_6156) ),
inference(clausify,[status(thm)],[f_1912_2]) ).
fof(f_1913_1,plain,
! [V_m,V_b,V_n,V_a,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_b))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_b))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__le__dvd]) ).
fof(f_1913_2,plain,
! [U_6165,U_6164,U_6163,U_6162,U_6161] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6161),hAPP(hAPP(c_Power_Opower__class_Opower(U_6161),U_6162),U_6165)),U_6164))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6165),U_6163))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6161),hAPP(hAPP(c_Power_Opower__class_Opower(U_6161),U_6162),U_6163)),U_6164))
| ~ class_Rings_Ocomm__semiring__1(U_6161) ),
inference(variable_rename,[status(thm)],[f_1913_1]) ).
cnf(f_1913_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6161),hAPP(hAPP(c_Power_Opower__class_Opower(U_6161),U_6162),U_6165)),U_6164))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6165),U_6163))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6161),hAPP(hAPP(c_Power_Opower__class_Opower(U_6161),U_6162),U_6163)),U_6164))
| ~ class_Rings_Ocomm__semiring__1(U_6161) ),
inference(clausify,[status(thm)],[f_1913_2]) ).
fof(f_1914_1,plain,
! [V_n,V_x,V_y,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
| ~ class_Divides_Osemiring__div(T_a) ),
inference(fof_nnf,[status(thm)],[fact_div__power]) ).
fof(f_1914_2,plain,
! [U_6169,U_6168,U_6167,U_6166] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6166),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6166),U_6168),U_6167)),U_6169) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6166),hAPP(hAPP(c_Power_Opower__class_Opower(U_6166),U_6168),U_6169)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6166),U_6167),U_6169))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6166),U_6167),U_6168))
| ~ class_Divides_Osemiring__div(U_6166) ),
inference(variable_rename,[status(thm)],[f_1914_1]) ).
cnf(f_1914_3,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_6166),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6166),U_6168),U_6167)),U_6169) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6166),hAPP(hAPP(c_Power_Opower__class_Opower(U_6166),U_6168),U_6169)),hAPP(hAPP(c_Power_Opower__class_Opower(U_6166),U_6167),U_6169))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6166),U_6167),U_6168))
| ~ class_Divides_Osemiring__div(U_6166) ),
inference(clausify,[status(thm)],[f_1914_2]) ).
fof(f_1915_1,plain,
! [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)) )
& ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ 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)))) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd__1__iff__1]) ).
fof(f_1915_2,plain,
! [U_6170] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6170),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_6170 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( U_6170 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6170),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(variable_rename,[status(thm)],[f_1915_1]) ).
fof(f_1915_3,plain,
( ! [U_6172] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6172),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_6172 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ! [U_6171] :
( U_6171 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6171),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(miniscope,[status(thm)],[f_1915_2]) ).
cnf(f_1915_4,plain,
( U_6171 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6171),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(clausify,[status(thm)],[f_1915_3]) ).
cnf(f_1915_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6172),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| U_6172 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_1915_3]) ).
fof(f_1916_1,plain,
! [V_n,V_m] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),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),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_nat__dvd__not__less]) ).
fof(f_1916_2,plain,
! [U_6174,U_6173] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6174),U_6173))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6173),U_6174))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6173)) ),
inference(variable_rename,[status(thm)],[f_1916_1]) ).
cnf(f_1916_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6174),U_6173))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6173),U_6174))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6173)) ),
inference(clausify,[status(thm)],[f_1916_2]) ).
fof(f_1917_1,plain,
! [V_na_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_na_2)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_na_2))
& V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_na_2))
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ 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_na_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel__disj]) ).
fof(f_1917_2,plain,
! [U_6177,U_6176,U_6175] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6175),U_6176)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6175),U_6177)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6176),U_6177))
& U_6175 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6176),U_6177))
| U_6175 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6175),U_6176)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6175),U_6177))) ) ),
inference(variable_rename,[status(thm)],[f_1917_1]) ).
fof(f_1917_3,plain,
( ! [U_6183,U_6181,U_6179] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6179),U_6181)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6179),U_6183)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6181),U_6183))
& U_6179 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_6182,U_6180,U_6178] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6180),U_6182))
| U_6178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6178),U_6180)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6178),U_6182))) ) ),
inference(miniscope,[status(thm)],[f_1917_2]) ).
cnf(f_1917_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6180),U_6182))
| U_6178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6178),U_6180)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6178),U_6182))) ),
inference(clausify,[status(thm)],[f_1917_3]) ).
cnf(f_1917_5,plain,
( U_6179 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6179),U_6181)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6179),U_6183))) ),
inference(clausify,[status(thm)],[f_1917_3]) ).
cnf(f_1917_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6181),U_6183))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6179),U_6181)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6179),U_6183))) ),
inference(clausify,[status(thm)],[f_1917_3]) ).
fof(f_1918_1,plain,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))) ),
inference(fof_nnf,[status(thm)],[fact_dvd__diffD]) ).
fof(f_1918_2,plain,
! [U_6186,U_6185,U_6184] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6184),U_6185))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6186),U_6185))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6184),U_6186))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6184),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6185),U_6186))) ),
inference(variable_rename,[status(thm)],[f_1918_1]) ).
cnf(f_1918_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6184),U_6185))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6186),U_6185))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6184),U_6186))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6184),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6185),U_6186))) ),
inference(clausify,[status(thm)],[f_1918_2]) ).
fof(f_1919_1,plain,
! [V_n,V_m,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__eq(tc_Nat_Onat),V_n),V_m))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))) ),
inference(fof_nnf,[status(thm)],[fact_dvd__diffD1]) ).
fof(f_1919_2,plain,
! [U_6189,U_6188,U_6187] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6187),U_6189))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6189),U_6188))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6187),U_6188))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6187),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6188),U_6189))) ),
inference(variable_rename,[status(thm)],[f_1919_1]) ).
cnf(f_1919_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6187),U_6189))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6189),U_6188))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6187),U_6188))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6187),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6188),U_6189))) ),
inference(clausify,[status(thm)],[f_1919_2]) ).
fof(f_1920_1,plain,
! [V_l_2,V_P_2,T_b] :
( ( ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
| ! [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b)))) ) )
& ( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b)))) )
| ! [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x))) ) )
| ~ class_Rings_Osemiring__0(T_b)
| ~ class_Rings_Odvd(T_b) ),
inference(fof_nnf,[status(thm)],[fact_unity__coeff__ex]) ).
fof(f_1920_2,plain,
! [U_6196,U_6195,U_6194] :
( ( ( ? [U_6193] : hBOOL(hAPP(U_6195,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),U_6196),U_6193)))
| ! [U_6192] :
( ~ hBOOL(hAPP(U_6195,U_6192))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6194),U_6196),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6194),U_6192),c_Groups_Ozero__class_Ozero(U_6194)))) ) )
& ( ? [U_6191] :
( hBOOL(hAPP(U_6195,U_6191))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6194),U_6196),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6194),U_6191),c_Groups_Ozero__class_Ozero(U_6194)))) )
| ! [U_6190] : ~ hBOOL(hAPP(U_6195,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),U_6196),U_6190))) ) )
| ~ class_Rings_Osemiring__0(U_6194)
| ~ class_Rings_Odvd(U_6194) ),
inference(variable_rename,[status(thm)],[f_1920_1]) ).
fof(f_1920_3,plain,
! [U_6196,U_6195,U_6194] :
( ( ( ? [U_6193] : hBOOL(hAPP(U_6195,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),U_6196),U_6193)))
| ! [U_6192] :
( ~ hBOOL(hAPP(U_6195,U_6192))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6194),U_6196),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6194),U_6192),c_Groups_Ozero__class_Ozero(U_6194)))) ) )
& ( ( hBOOL(hAPP(U_6195,sK84(U_6196,U_6195,U_6194)))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6194),U_6196),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6194),sK84(U_6196,U_6195,U_6194)),c_Groups_Ozero__class_Ozero(U_6194)))) )
| ! [U_6190] : ~ hBOOL(hAPP(U_6195,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),U_6196),U_6190))) ) )
| ~ class_Rings_Osemiring__0(U_6194)
| ~ class_Rings_Odvd(U_6194) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_6191,sK84(U_6196,U_6195,U_6194))],[f_1920_2]) ).
fof(f_1920_4,plain,
! [U_6196,U_6195,U_6194] :
( ( ( hBOOL(hAPP(U_6195,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),U_6196),sK85(U_6196,U_6195,U_6194))))
| ! [U_6192] :
( ~ hBOOL(hAPP(U_6195,U_6192))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6194),U_6196),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6194),U_6192),c_Groups_Ozero__class_Ozero(U_6194)))) ) )
& ( ( hBOOL(hAPP(U_6195,sK84(U_6196,U_6195,U_6194)))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6194),U_6196),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6194),sK84(U_6196,U_6195,U_6194)),c_Groups_Ozero__class_Ozero(U_6194)))) )
| ! [U_6190] : ~ hBOOL(hAPP(U_6195,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),U_6196),U_6190))) ) )
| ~ class_Rings_Osemiring__0(U_6194)
| ~ class_Rings_Odvd(U_6194) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_6193,sK85(U_6196,U_6195,U_6194))],[f_1920_3]) ).
cnf(f_1920_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6194),U_6196),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6194),sK84(U_6196,U_6195,U_6194)),c_Groups_Ozero__class_Ozero(U_6194))))
| ~ hBOOL(hAPP(U_6195,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),U_6196),U_6190)))
| ~ class_Rings_Osemiring__0(U_6194)
| ~ class_Rings_Odvd(U_6194) ),
inference(clausify,[status(thm)],[f_1920_4]) ).
cnf(f_1920_6,plain,
( hBOOL(hAPP(U_6195,sK84(U_6196,U_6195,U_6194)))
| ~ hBOOL(hAPP(U_6195,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),U_6196),U_6190)))
| ~ class_Rings_Osemiring__0(U_6194)
| ~ class_Rings_Odvd(U_6194) ),
inference(clausify,[status(thm)],[f_1920_4]) ).
cnf(f_1920_7,plain,
( hBOOL(hAPP(U_6195,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6194),U_6196),sK85(U_6196,U_6195,U_6194))))
| ~ hBOOL(hAPP(U_6195,U_6192))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6194),U_6196),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6194),U_6192),c_Groups_Ozero__class_Ozero(U_6194))))
| ~ class_Rings_Osemiring__0(U_6194)
| ~ class_Rings_Odvd(U_6194) ),
inference(clausify,[status(thm)],[f_1920_4]) ).
fof(f_1921_1,plain,
! [V_t_2,V_D_2,V_d_2,T_b] :
( ! [B_x,B_k] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
| ~ class_Rings_Odvd(T_b)
| ~ class_Rings_Ocomm__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__period_I3_J]) ).
fof(f_1921_2,plain,
! [U_6202,U_6201,U_6200,U_6199] :
( ! [U_6198,U_6197] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6199),U_6200),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6199),U_6198),U_6202)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6199),U_6200),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6199),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6199),U_6198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6199),U_6197),U_6201))),U_6202))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6199),U_6200),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6199),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6199),U_6198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6199),U_6197),U_6201))),U_6202)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6199),U_6200),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6199),U_6198),U_6202))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6199),U_6200),U_6201))
| ~ class_Rings_Odvd(U_6199)
| ~ class_Rings_Ocomm__ring(U_6199) ),
inference(variable_rename,[status(thm)],[f_1921_1]) ).
fof(f_1921_3,plain,
! [U_6202,U_6201,U_6200,U_6199] :
( ( ! [U_6206] :
( ! [U_6204] : ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6199),U_6200),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6199),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6199),U_6206),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6199),U_6204),U_6201))),U_6202)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6199),U_6200),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6199),U_6206),U_6202))) )
& ! [U_6205] :
( ! [U_6203] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6199),U_6200),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6199),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6199),U_6205),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6199),U_6203),U_6201))),U_6202)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6199),U_6200),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6199),U_6205),U_6202))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6199),U_6200),U_6201))
| ~ class_Rings_Odvd(U_6199)
| ~ class_Rings_Ocomm__ring(U_6199) ),
inference(miniscope,[status(thm)],[f_1921_2]) ).
cnf(f_1921_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6199),U_6200),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6199),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6199),U_6205),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6199),U_6203),U_6201))),U_6202)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6199),U_6200),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6199),U_6205),U_6202)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6199),U_6200),U_6201))
| ~ class_Rings_Odvd(U_6199)
| ~ class_Rings_Ocomm__ring(U_6199) ),
inference(clausify,[status(thm)],[f_1921_3]) ).
cnf(f_1921_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6199),U_6200),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6199),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6199),U_6206),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6199),U_6204),U_6201))),U_6202)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6199),U_6200),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6199),U_6206),U_6202)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6199),U_6200),U_6201))
| ~ class_Rings_Odvd(U_6199)
| ~ class_Rings_Ocomm__ring(U_6199) ),
inference(clausify,[status(thm)],[f_1921_3]) ).
fof(f_1922_1,plain,
! [V_t_2,V_D_2,V_d_2,T_b] :
( ! [B_x,B_k] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
| ~ class_Rings_Odvd(T_b)
| ~ class_Rings_Ocomm__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__period_I4_J]) ).
fof(f_1922_2,plain,
! [U_6212,U_6211,U_6210,U_6209] :
( ! [U_6208,U_6207] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6209),U_6210),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6209),U_6208),U_6212)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6209),U_6210),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6209),U_6208),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6209),U_6207),U_6211))),U_6212))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6209),U_6210),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6209),U_6208),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6209),U_6207),U_6211))),U_6212)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6209),U_6210),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6209),U_6208),U_6212))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6209),U_6210),U_6211))
| ~ class_Rings_Odvd(U_6209)
| ~ class_Rings_Ocomm__ring(U_6209) ),
inference(variable_rename,[status(thm)],[f_1922_1]) ).
fof(f_1922_3,plain,
! [U_6212,U_6211,U_6210,U_6209] :
( ( ! [U_6216] :
( ! [U_6214] : ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6209),U_6210),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6209),U_6216),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6209),U_6214),U_6211))),U_6212)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6209),U_6210),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6209),U_6216),U_6212))) )
& ! [U_6215] :
( ! [U_6213] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6209),U_6210),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6209),U_6215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6209),U_6213),U_6211))),U_6212)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6209),U_6210),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6209),U_6215),U_6212))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6209),U_6210),U_6211))
| ~ class_Rings_Odvd(U_6209)
| ~ class_Rings_Ocomm__ring(U_6209) ),
inference(miniscope,[status(thm)],[f_1922_2]) ).
cnf(f_1922_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6209),U_6210),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6209),U_6215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6209),U_6213),U_6211))),U_6212)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6209),U_6210),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6209),U_6215),U_6212)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6209),U_6210),U_6211))
| ~ class_Rings_Odvd(U_6209)
| ~ class_Rings_Ocomm__ring(U_6209) ),
inference(clausify,[status(thm)],[f_1922_3]) ).
cnf(f_1922_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6209),U_6210),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6209),U_6216),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6209),U_6214),U_6211))),U_6212)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6209),U_6210),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6209),U_6216),U_6212)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6209),U_6210),U_6211))
| ~ class_Rings_Odvd(U_6209)
| ~ class_Rings_Ocomm__ring(U_6209) ),
inference(clausify,[status(thm)],[f_1922_3]) ).
fof(f_1923_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
| c_Divides_Odiv__class_Omod(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)) != c_Groups_Ozero__class_Ozero(T_b) )
& ( c_Divides_Odiv__class_Omod(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)) = c_Groups_Ozero__class_Ozero(T_b)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2))) ) )
| ~ class_Int_Onumber(T_b)
| ~ class_Divides_Osemiring__div(T_b) ),
inference(fof_nnf,[status(thm)],[fact_dvd__eq__mod__eq__0__number__of]) ).
fof(f_1923_2,plain,
! [U_6219,U_6218,U_6217] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6217),hAPP(c_Int_Onumber__class_Onumber__of(U_6217),U_6218)),hAPP(c_Int_Onumber__class_Onumber__of(U_6217),U_6219)))
| c_Divides_Odiv__class_Omod(U_6217,hAPP(c_Int_Onumber__class_Onumber__of(U_6217),U_6219),hAPP(c_Int_Onumber__class_Onumber__of(U_6217),U_6218)) != c_Groups_Ozero__class_Ozero(U_6217) )
& ( c_Divides_Odiv__class_Omod(U_6217,hAPP(c_Int_Onumber__class_Onumber__of(U_6217),U_6219),hAPP(c_Int_Onumber__class_Onumber__of(U_6217),U_6218)) = c_Groups_Ozero__class_Ozero(U_6217)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6217),hAPP(c_Int_Onumber__class_Onumber__of(U_6217),U_6218)),hAPP(c_Int_Onumber__class_Onumber__of(U_6217),U_6219))) ) )
| ~ class_Int_Onumber(U_6217)
| ~ class_Divides_Osemiring__div(U_6217) ),
inference(variable_rename,[status(thm)],[f_1923_1]) ).
cnf(f_1923_3,plain,
( c_Divides_Odiv__class_Omod(U_6217,hAPP(c_Int_Onumber__class_Onumber__of(U_6217),U_6219),hAPP(c_Int_Onumber__class_Onumber__of(U_6217),U_6218)) = c_Groups_Ozero__class_Ozero(U_6217)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6217),hAPP(c_Int_Onumber__class_Onumber__of(U_6217),U_6218)),hAPP(c_Int_Onumber__class_Onumber__of(U_6217),U_6219)))
| ~ class_Int_Onumber(U_6217)
| ~ class_Divides_Osemiring__div(U_6217) ),
inference(clausify,[status(thm)],[f_1923_2]) ).
cnf(f_1923_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6217),hAPP(c_Int_Onumber__class_Onumber__of(U_6217),U_6218)),hAPP(c_Int_Onumber__class_Onumber__of(U_6217),U_6219)))
| c_Divides_Odiv__class_Omod(U_6217,hAPP(c_Int_Onumber__class_Onumber__of(U_6217),U_6219),hAPP(c_Int_Onumber__class_Onumber__of(U_6217),U_6218)) != c_Groups_Ozero__class_Ozero(U_6217)
| ~ class_Int_Onumber(U_6217)
| ~ class_Divides_Osemiring__div(U_6217) ),
inference(clausify,[status(thm)],[f_1923_2]) ).
fof(f_1924_1,plain,
! [V_c_2,V_b_2,V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_c_2
| V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2) )
& ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) != V_c_2 ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
| V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| ~ class_Divides_Osemiring__div(T_b) ),
inference(fof_nnf,[status(thm)],[fact_dvd__div__eq__mult]) ).
fof(f_1924_2,plain,
! [U_6223,U_6222,U_6221,U_6220] :
( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6220),U_6222),U_6221) = U_6223
| U_6222 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6220),U_6223),U_6221) )
& ( U_6222 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6220),U_6223),U_6221)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6220),U_6222),U_6221) != U_6223 ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6220),U_6221),U_6222))
| U_6221 = c_Groups_Ozero__class_Ozero(U_6220)
| ~ class_Divides_Osemiring__div(U_6220) ),
inference(variable_rename,[status(thm)],[f_1924_1]) ).
cnf(f_1924_3,plain,
( U_6222 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6220),U_6223),U_6221)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6220),U_6222),U_6221) != U_6223
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6220),U_6221),U_6222))
| U_6221 = c_Groups_Ozero__class_Ozero(U_6220)
| ~ class_Divides_Osemiring__div(U_6220) ),
inference(clausify,[status(thm)],[f_1924_2]) ).
cnf(f_1924_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6220),U_6222),U_6221) = U_6223
| U_6222 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6220),U_6223),U_6221)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6220),U_6221),U_6222))
| U_6221 = c_Groups_Ozero__class_Ozero(U_6220)
| ~ class_Divides_Osemiring__div(U_6220) ),
inference(clausify,[status(thm)],[f_1924_2]) ).
fof(f_1925_1,plain,
! [V_d_2,V_b_2,V_c_2,V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_c_2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_c_2) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_c_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
| V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| ~ class_Divides_Osemiring__div(T_b) ),
inference(fof_nnf,[status(thm)],[fact_dvd__div__div__eq__mult]) ).
fof(f_1925_2,plain,
! [U_6228,U_6227,U_6226,U_6225,U_6224] :
( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6224),U_6227),U_6225) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6224),U_6228),U_6226)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6224),U_6227),U_6226) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6224),U_6225),U_6228) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6224),U_6227),U_6226) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6224),U_6225),U_6228)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6224),U_6227),U_6225) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6224),U_6228),U_6226) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6224),U_6226),U_6228))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6224),U_6225),U_6227))
| U_6226 = c_Groups_Ozero__class_Ozero(U_6224)
| U_6225 = c_Groups_Ozero__class_Ozero(U_6224)
| ~ class_Divides_Osemiring__div(U_6224) ),
inference(variable_rename,[status(thm)],[f_1925_1]) ).
cnf(f_1925_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6224),U_6227),U_6226) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6224),U_6225),U_6228)
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6224),U_6227),U_6225) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6224),U_6228),U_6226)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6224),U_6226),U_6228))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6224),U_6225),U_6227))
| U_6226 = c_Groups_Ozero__class_Ozero(U_6224)
| U_6225 = c_Groups_Ozero__class_Ozero(U_6224)
| ~ class_Divides_Osemiring__div(U_6224) ),
inference(clausify,[status(thm)],[f_1925_2]) ).
cnf(f_1925_4,plain,
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6224),U_6227),U_6225) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_6224),U_6228),U_6226)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6224),U_6227),U_6226) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6224),U_6225),U_6228)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6224),U_6226),U_6228))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6224),U_6225),U_6227))
| U_6226 = c_Groups_Ozero__class_Ozero(U_6224)
| U_6225 = c_Groups_Ozero__class_Ozero(U_6224)
| ~ class_Divides_Osemiring__div(U_6224) ),
inference(clausify,[status(thm)],[f_1925_2]) ).
fof(f_1926_1,plain,
! [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(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_dvd__imp__le]) ).
fof(f_1926_2,plain,
! [U_6230,U_6229] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6229),U_6230))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6230))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6229),U_6230)) ),
inference(variable_rename,[status(thm)],[f_1926_1]) ).
cnf(f_1926_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6229),U_6230))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6230))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6229),U_6230)) ),
inference(clausify,[status(thm)],[f_1926_2]) ).
fof(f_1927_1,plain,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))
| ~ 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))) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel]) ).
fof(f_1927_2,plain,
! [U_6233,U_6232,U_6231] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6232),U_6233))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6231))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6231),U_6232)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6231),U_6233))) ),
inference(variable_rename,[status(thm)],[f_1927_1]) ).
cnf(f_1927_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6232),U_6233))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6231))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6231),U_6232)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6231),U_6233))) ),
inference(clausify,[status(thm)],[f_1927_2]) ).
fof(f_1928_1,plain,
! [V_na_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_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_na_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_na_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__dvd__cancel1]) ).
fof(f_1928_2,plain,
! [U_6236,U_6235,U_6234] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6234),U_6235)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6234),U_6236)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6235),U_6236)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6235),U_6236))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6234),U_6235)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6234),U_6236))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6234)) ),
inference(variable_rename,[status(thm)],[f_1928_1]) ).
cnf(f_1928_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6235),U_6236))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6234),U_6235)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6234),U_6236)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6234)) ),
inference(clausify,[status(thm)],[f_1928_2]) ).
cnf(f_1928_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6234),U_6235)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6234),U_6236)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6235),U_6236))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6234)) ),
inference(clausify,[status(thm)],[f_1928_2]) ).
fof(f_1929_1,plain,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_b,V_A_2)),c_Predicate_OPowp(T_b,V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Powp__mono]) ).
fof(f_1929_2,plain,
! [U_6239,U_6238,U_6237] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_6237,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_6237,U_6238)),c_Predicate_OPowp(U_6237,U_6239)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6237,tc_HOL_Obool)),U_6238),U_6239)) ),
inference(variable_rename,[status(thm)],[f_1929_1]) ).
cnf(f_1929_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_6237,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_6237,U_6238)),c_Predicate_OPowp(U_6237,U_6239)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6237,tc_HOL_Obool)),U_6238),U_6239)) ),
inference(clausify,[status(thm)],[f_1929_2]) ).
fof(f_1930_1,plain,
! [V_x,V_n,T_a] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)))
| ( V_x != c_Groups_Oone__class_Oone(T_a)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) )
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__power]) ).
fof(f_1930_2,plain,
! [U_6242,U_6241,U_6240] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6240),U_6242),hAPP(hAPP(c_Power_Opower__class_Opower(U_6240),U_6242),U_6241)))
| ( U_6242 != c_Groups_Oone__class_Oone(U_6240)
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6241)) )
| ~ class_Rings_Ocomm__semiring__1(U_6240) ),
inference(variable_rename,[status(thm)],[f_1930_1]) ).
cnf(f_1930_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6241))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6240),U_6242),hAPP(hAPP(c_Power_Opower__class_Opower(U_6240),U_6242),U_6241)))
| ~ class_Rings_Ocomm__semiring__1(U_6240) ),
inference(clausify,[status(thm)],[f_1930_2]) ).
cnf(f_1930_4,plain,
( U_6242 != c_Groups_Oone__class_Oone(U_6240)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_6240),U_6242),hAPP(hAPP(c_Power_Opower__class_Opower(U_6240),U_6242),U_6241)))
| ~ class_Rings_Ocomm__semiring__1(U_6240) ),
inference(clausify,[status(thm)],[f_1930_2]) ).
fof(f_1931_1,plain,
! [V_y_2,V_x_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
| ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Ostrict__monoD]) ).
fof(f_1931_2,plain,
! [U_6246,U_6245,U_6244,U_6243] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6243),hAPP(U_6244,U_6245)),hAPP(U_6244,U_6246)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6246),U_6245))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6245),U_6246))
| ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_6243,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)))),U_6244)
| ~ class_Orderings_Oorder(U_6243) ),
inference(variable_rename,[status(thm)],[f_1931_1]) ).
cnf(f_1931_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6243),hAPP(U_6244,U_6245)),hAPP(U_6244,U_6246)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6246),U_6245))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6245),U_6246))
| ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_6243,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)))),U_6244)
| ~ class_Orderings_Oorder(U_6243) ),
inference(clausify,[status(thm)],[f_1931_2]) ).
fof(f_1932_1,plain,
! [V_y_2,V_x_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
| ~ c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_dvd_OmonoD]) ).
fof(f_1932_2,plain,
! [U_6250,U_6249,U_6248,U_6247] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6247),hAPP(U_6248,U_6249)),hAPP(U_6248,U_6250)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6249),U_6250))
| ~ c_Orderings_Oorder_Omono(tc_Nat_Onat,U_6247,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6248)
| ~ class_Orderings_Oorder(U_6247) ),
inference(variable_rename,[status(thm)],[f_1932_1]) ).
cnf(f_1932_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6247),hAPP(U_6248,U_6249)),hAPP(U_6248,U_6250)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6249),U_6250))
| ~ c_Orderings_Oorder_Omono(tc_Nat_Onat,U_6247,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6248)
| ~ class_Orderings_Oorder(U_6247) ),
inference(clausify,[status(thm)],[f_1932_2]) ).
fof(f_1933_1,plain,
! [V_m_2,V_z_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_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_z_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))
& 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 = 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_z_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))
| ~ 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_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),V_m_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__dvd__iff]) ).
fof(f_1933_2,plain,
! [U_6252,U_6251] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_6251)),U_6252))
| ( U_6252 != 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_6251)) )
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6251),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6252)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6251)) ) )
& ( ( ( U_6252 = 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_6251)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6251),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6252)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6251)) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_6251)),U_6252)) ) ),
inference(variable_rename,[status(thm)],[f_1933_1]) ).
fof(f_1933_3,plain,
( ! [U_6256,U_6254] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_6254)),U_6256))
| ( U_6256 != 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_6254)) )
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6254),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6256)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6254)) ) )
& ! [U_6255,U_6253] :
( ( ( U_6255 = 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_6253)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6253),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6255)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6253)) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_6253)),U_6255)) ) ),
inference(miniscope,[status(thm)],[f_1933_2]) ).
cnf(f_1933_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6253),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6255)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6253))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_6253)),U_6255)) ),
inference(clausify,[status(thm)],[f_1933_3]) ).
cnf(f_1933_5,plain,
( U_6255 = 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_6253))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_6253)),U_6255)) ),
inference(clausify,[status(thm)],[f_1933_3]) ).
cnf(f_1933_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6254))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6254))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_6254)),U_6256)) ),
inference(clausify,[status(thm)],[f_1933_3]) ).
cnf(f_1933_7,plain,
( U_6256 != 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_6254))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_6254)),U_6256)) ),
inference(clausify,[status(thm)],[f_1933_3]) ).
cnf(f_1933_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6254))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6254),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6256)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_6254)),U_6256)) ),
inference(clausify,[status(thm)],[f_1933_3]) ).
cnf(f_1933_9,plain,
( U_6256 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6254),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6256)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_6254)),U_6256)) ),
inference(clausify,[status(thm)],[f_1933_3]) ).
fof(f_1934_1,plain,
! [V_z_2,V_m_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_int__dvd__iff]) ).
fof(f_1934_2,plain,
! [U_6258,U_6257] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6257)),U_6258))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6257),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6258)))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6257),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6258))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6257)),U_6258)) ) ),
inference(variable_rename,[status(thm)],[f_1934_1]) ).
fof(f_1934_3,plain,
( ! [U_6262,U_6260] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6260)),U_6262))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6260),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6262)))) )
& ! [U_6261,U_6259] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6259),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6261))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6259)),U_6261)) ) ),
inference(miniscope,[status(thm)],[f_1934_2]) ).
cnf(f_1934_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6259),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6261))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6259)),U_6261)) ),
inference(clausify,[status(thm)],[f_1934_3]) ).
cnf(f_1934_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6260)),U_6262))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6260),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6262)))) ),
inference(clausify,[status(thm)],[f_1934_3]) ).
fof(f_1935_1,plain,
! [V_m_2,V_z_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2))),V_m_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2))),V_m_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd__int__iff]) ).
fof(f_1935_2,plain,
! [U_6264,U_6263] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6263),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6264)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6263))),U_6264)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6263))),U_6264))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6263),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6264))) ) ),
inference(variable_rename,[status(thm)],[f_1935_1]) ).
fof(f_1935_3,plain,
( ! [U_6268,U_6266] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6266),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6268)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6266))),U_6268)) )
& ! [U_6267,U_6265] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6265))),U_6267))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6265),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6267))) ) ),
inference(miniscope,[status(thm)],[f_1935_2]) ).
cnf(f_1935_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6265))),U_6267))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6265),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6267))) ),
inference(clausify,[status(thm)],[f_1935_3]) ).
cnf(f_1935_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6266),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6268)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6266))),U_6268)) ),
inference(clausify,[status(thm)],[f_1935_3]) ).
fof(f_1936_1,plain,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_m),V_n))) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__zdiffD]) ).
fof(f_1936_2,plain,
! [U_6271,U_6270,U_6269] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6269),U_6270))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6269),U_6271))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6269),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6270),U_6271))) ),
inference(variable_rename,[status(thm)],[f_1936_1]) ).
cnf(f_1936_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6269),U_6270))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6269),U_6271))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6269),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6270),U_6271))) ),
inference(clausify,[status(thm)],[f_1936_2]) ).
fof(f_1937_1,plain,
! [V_t_2,V_d_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_t_2))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_t_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_uminus__dvd__conv_I2_J]) ).
fof(f_1937_2,plain,
! [U_6273,U_6272] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6272),U_6273))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6272),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6273))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6272),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6273)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6272),U_6273)) ) ),
inference(variable_rename,[status(thm)],[f_1937_1]) ).
fof(f_1937_3,plain,
( ! [U_6277,U_6275] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6275),U_6277))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6275),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6277))) )
& ! [U_6276,U_6274] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6274),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6276)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6274),U_6276)) ) ),
inference(miniscope,[status(thm)],[f_1937_2]) ).
cnf(f_1937_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6274),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6276)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6274),U_6276)) ),
inference(clausify,[status(thm)],[f_1937_3]) ).
cnf(f_1937_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6275),U_6277))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6275),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6277))) ),
inference(clausify,[status(thm)],[f_1937_3]) ).
fof(f_1938_1,plain,
! [V_t_2,V_d_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d_2)),V_t_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d_2)),V_t_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_uminus__dvd__conv_I1_J]) ).
fof(f_1938_2,plain,
! [U_6279,U_6278] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6278),U_6279))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6278)),U_6279)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6278)),U_6279))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6278),U_6279)) ) ),
inference(variable_rename,[status(thm)],[f_1938_1]) ).
fof(f_1938_3,plain,
( ! [U_6283,U_6281] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6281),U_6283))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6281)),U_6283)) )
& ! [U_6282,U_6280] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6280)),U_6282))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6280),U_6282)) ) ),
inference(miniscope,[status(thm)],[f_1938_2]) ).
cnf(f_1938_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6280)),U_6282))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6280),U_6282)) ),
inference(clausify,[status(thm)],[f_1938_3]) ).
cnf(f_1938_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6281),U_6283))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6281)),U_6283)) ),
inference(clausify,[status(thm)],[f_1938_3]) ).
fof(f_1939_1,plain,
! [V_n,V_m,V_f] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_n))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_f),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__zmod]) ).
fof(f_1939_2,plain,
! [U_6286,U_6285,U_6284] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6284),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6285,U_6286)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6284),U_6286))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6284),U_6285)) ),
inference(variable_rename,[status(thm)],[f_1939_1]) ).
cnf(f_1939_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6284),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6285,U_6286)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6284),U_6286))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6284),U_6285)) ),
inference(clausify,[status(thm)],[f_1939_2]) ).
fof(f_1940_1,plain,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_m))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),V_n))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m,V_n))) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__zmod__imp__zdvd]) ).
fof(f_1940_2,plain,
! [U_6289,U_6288,U_6287] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6287),U_6288))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6287),U_6289))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6287),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6288,U_6289))) ),
inference(variable_rename,[status(thm)],[f_1940_1]) ).
cnf(f_1940_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6287),U_6288))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6287),U_6289))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6287),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6288,U_6289))) ),
inference(clausify,[status(thm)],[f_1940_2]) ).
fof(f_1941_1,plain,
! [V_b,V_a] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_a) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_b)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_b),V_a))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a),V_b)) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__antisym__abs]) ).
fof(f_1941_2,plain,
! [U_6291,U_6290] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6290) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6291)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6291),U_6290))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6290),U_6291)) ),
inference(variable_rename,[status(thm)],[f_1941_1]) ).
cnf(f_1941_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6290) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6291)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6291),U_6290))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6290),U_6291)) ),
inference(clausify,[status(thm)],[f_1941_2]) ).
fof(f_1942_1,plain,
! [V_n,V_m] :
( V_m = V_n
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(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)),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__antisym__nonneg]) ).
fof(f_1942_2,plain,
! [U_6293,U_6292] :
( U_6292 = U_6293
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6293),U_6292))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6292),U_6293))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6293))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6292)) ),
inference(variable_rename,[status(thm)],[f_1942_1]) ).
cnf(f_1942_3,plain,
( U_6292 = U_6293
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6293),U_6292))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6292),U_6293))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6293))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6292)) ),
inference(clausify,[status(thm)],[f_1942_2]) ).
fof(f_1943_1,plain,
! [V_n,V_m] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_m),V_n))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__not__zless]) ).
fof(f_1943_2,plain,
! [U_6295,U_6294] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6295),U_6294))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6294),U_6295))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6294)) ),
inference(variable_rename,[status(thm)],[f_1943_1]) ).
cnf(f_1943_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6295),U_6294))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6294),U_6295))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6294)) ),
inference(clausify,[status(thm)],[f_1943_2]) ).
fof(f_1944_1,plain,
! [V_n,V_m,V_k] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m),V_n))
| V_k = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n))) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__mult__cancel]) ).
fof(f_1944_2,plain,
! [U_6298,U_6297,U_6296] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6297),U_6298))
| U_6296 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6296),U_6297)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6296),U_6298))) ),
inference(variable_rename,[status(thm)],[f_1944_1]) ).
cnf(f_1944_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6297),U_6298))
| U_6296 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6296),U_6297)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6296),U_6298))) ),
inference(clausify,[status(thm)],[f_1944_2]) ).
fof(f_1945_1,plain,
! [V_t_2,V_m_2,V_k_2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_m_2),V_t_2)) ) )
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__mono]) ).
fof(f_1945_2,plain,
! [U_6301,U_6300,U_6299] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6300),U_6301))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6299),U_6300)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6299),U_6301))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6299),U_6300)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6299),U_6301)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6300),U_6301)) ) )
| U_6299 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1945_1]) ).
cnf(f_1945_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6299),U_6300)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6299),U_6301)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6300),U_6301))
| U_6299 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1945_2]) ).
cnf(f_1945_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6300),U_6301))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6299),U_6300)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6299),U_6301)))
| U_6299 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1945_2]) ).
fof(f_1946_1,plain,
! [V_c_2,V_t_2,V_x_2,V_d_2,V_a_2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),V_t_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_c_2),V_d_2))),V_t_2))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_c_2),V_d_2))),V_t_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),V_t_2))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2)) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__period]) ).
fof(f_1946_2,plain,
! [U_6306,U_6305,U_6304,U_6303,U_6302] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6304),U_6305)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6306),U_6303))),U_6305))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6306),U_6303))),U_6305)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6304),U_6305))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6302),U_6303)) ),
inference(variable_rename,[status(thm)],[f_1946_1]) ).
cnf(f_1946_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6306),U_6303))),U_6305)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6304),U_6305)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6302),U_6303)) ),
inference(clausify,[status(thm)],[f_1946_2]) ).
cnf(f_1946_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6304),U_6305)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6302),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6304),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6306),U_6303))),U_6305)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6302),U_6303)) ),
inference(clausify,[status(thm)],[f_1946_2]) ).
fof(f_1947_1,plain,
! [V_m_2,V_na_2,V_k_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_na_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_na_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_na_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)))) ) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__reduce]) ).
fof(f_1947_2,plain,
! [U_6309,U_6308,U_6307] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6307),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6307),U_6309))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6307),U_6308)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6307),U_6308))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6307),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6307),U_6309)))) ) ),
inference(variable_rename,[status(thm)],[f_1947_1]) ).
fof(f_1947_3,plain,
( ! [U_6315,U_6313,U_6311] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6311),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6313),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6311),U_6315))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6311),U_6313)) )
& ! [U_6314,U_6312,U_6310] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6310),U_6312))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6310),U_6314)))) ) ),
inference(miniscope,[status(thm)],[f_1947_2]) ).
cnf(f_1947_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6310),U_6312))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6310),U_6314)))) ),
inference(clausify,[status(thm)],[f_1947_3]) ).
cnf(f_1947_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6311),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6313),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6311),U_6315))))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6311),U_6313)) ),
inference(clausify,[status(thm)],[f_1947_3]) ).
fof(f_1948_1,plain,
! [V_y_2,V_x_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__int]) ).
fof(f_1948_2,plain,
! [U_6317,U_6316] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6316),U_6317))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6316)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6317))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6316)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6317)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6316),U_6317)) ) ),
inference(variable_rename,[status(thm)],[f_1948_1]) ).
fof(f_1948_3,plain,
( ! [U_6321,U_6319] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6319),U_6321))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6319)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6321))) )
& ! [U_6320,U_6318] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6318)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6320)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6318),U_6320)) ) ),
inference(miniscope,[status(thm)],[f_1948_2]) ).
cnf(f_1948_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6318)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6320)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6318),U_6320)) ),
inference(clausify,[status(thm)],[f_1948_3]) ).
cnf(f_1948_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6319),U_6321))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6319)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6321))) ),
inference(clausify,[status(thm)],[f_1948_3]) ).
fof(f_1949_1,plain,
! [V_y_2,V_x_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I4_J]) ).
fof(f_1949_2,plain,
! [U_6323,U_6322] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6322)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6323)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6322),U_6323)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6322),U_6323))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6322)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6323))) ) ),
inference(variable_rename,[status(thm)],[f_1949_1]) ).
fof(f_1949_3,plain,
( ! [U_6327,U_6325] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6325)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6327)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6325),U_6327)) )
& ! [U_6326,U_6324] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6324),U_6326))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6324)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6326))) ) ),
inference(miniscope,[status(thm)],[f_1949_2]) ).
cnf(f_1949_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6324),U_6326))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6324)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6326))) ),
inference(clausify,[status(thm)],[f_1949_3]) ).
cnf(f_1949_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6325)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6327)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6325),U_6327)) ),
inference(clausify,[status(thm)],[f_1949_3]) ).
fof(f_1950_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)) = V_m
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_n),V_m)) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__mult__div__cancel]) ).
fof(f_1950_2,plain,
! [U_6329,U_6328] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6328),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6329),U_6328)) = U_6329
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6328),U_6329)) ),
inference(variable_rename,[status(thm)],[f_1950_1]) ).
cnf(f_1950_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6328),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6329),U_6328)) = U_6329
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6328),U_6329)) ),
inference(clausify,[status(thm)],[f_1950_2]) ).
fof(f_1951_1,plain,
! [V_y_2,V_na_2,V_x_2] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,V_na_2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y_2,V_na_2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_na_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x_2),V_y_2))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_na_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x_2),V_y_2)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x_2,V_na_2) != c_Divides_Odiv__class_Omod(tc_Int_Oint,V_y_2,V_na_2) ) ),
inference(fof_nnf,[status(thm)],[fact_zmod__eq__dvd__iff]) ).
fof(f_1951_2,plain,
! [U_6332,U_6331,U_6330] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6330,U_6331) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6332,U_6331)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6331),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6330),U_6332))) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6331),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6330),U_6332)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6330,U_6331) != c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6332,U_6331) ) ),
inference(variable_rename,[status(thm)],[f_1951_1]) ).
fof(f_1951_3,plain,
( ! [U_6338,U_6336,U_6334] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6334,U_6336) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6338,U_6336)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6336),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6334),U_6338))) )
& ! [U_6337,U_6335,U_6333] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6335),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6333),U_6337)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6333,U_6335) != c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6337,U_6335) ) ),
inference(miniscope,[status(thm)],[f_1951_2]) ).
cnf(f_1951_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6335),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6333),U_6337)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6333,U_6335) != c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6337,U_6335) ),
inference(clausify,[status(thm)],[f_1951_3]) ).
cnf(f_1951_5,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6334,U_6336) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6338,U_6336)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6336),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6334),U_6338))) ),
inference(clausify,[status(thm)],[f_1951_3]) ).
fof(f_1952_1,plain,
! [V_x_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(fof_nnf,[status(thm)],[fact_zdvd1__eq]) ).
fof(f_1952_2,plain,
! [U_6339] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6339),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6339) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6339) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6339),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_1952_1]) ).
fof(f_1952_3,plain,
( ! [U_6341] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6341),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6341) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ! [U_6340] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6340) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6340),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_1952_2]) ).
cnf(f_1952_4,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6340) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6340),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_1952_3]) ).
cnf(f_1952_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6341),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6341) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1952_3]) ).
fof(f_1953_1,plain,
! [V_x,V_y] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_y),V_x)) ),
inference(fof_nnf,[status(thm)],[fact_abs__div]) ).
fof(f_1953_2,plain,
! [U_6343,U_6342] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6343),U_6342)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6343)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6342))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6342),U_6343)) ),
inference(variable_rename,[status(thm)],[f_1953_1]) ).
cnf(f_1953_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6343),U_6342)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6343)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6342))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6342),U_6343)) ),
inference(clausify,[status(thm)],[f_1953_2]) ).
fof(f_1954_1,plain,
! [V_f_2,T_b] :
( c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)
| ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Ostrict__mono__mono]) ).
fof(f_1954_2,plain,
! [U_6345,U_6344] :
( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_6344,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6345)
| ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_6344,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)))),U_6345)
| ~ class_Orderings_Oorder(U_6344) ),
inference(variable_rename,[status(thm)],[f_1954_1]) ).
cnf(f_1954_3,plain,
( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_6344,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6345)
| ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_6344,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)))),U_6345)
| ~ class_Orderings_Oorder(U_6344) ),
inference(clausify,[status(thm)],[f_1954_2]) ).
fof(f_1955_1,plain,
! [V_n,V_z] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_n))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_n))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_z),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__imp__le]) ).
fof(f_1955_2,plain,
! [U_6347,U_6346] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6346),U_6347))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6347))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6346),U_6347)) ),
inference(variable_rename,[status(thm)],[f_1955_1]) ).
cnf(f_1955_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6346),U_6347))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6347))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6346),U_6347)) ),
inference(clausify,[status(thm)],[f_1955_2]) ).
fof(f_1956_1,plain,
! [V_y_2,V_x_2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_y_2)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_x_2)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_x_2)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__iff__zmod__eq__0__number__of]) ).
fof(f_1956_2,plain,
! [U_6349,U_6348] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6348)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6349)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6349),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6348)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6349),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6348)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6348)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6349))) ) ),
inference(variable_rename,[status(thm)],[f_1956_1]) ).
fof(f_1956_3,plain,
( ! [U_6353,U_6351] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6351)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6353)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6353),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6351)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_6352,U_6350] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6352),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6350)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6350)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6352))) ) ),
inference(miniscope,[status(thm)],[f_1956_2]) ).
cnf(f_1956_4,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6352),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6350)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6350)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6352))) ),
inference(clausify,[status(thm)],[f_1956_3]) ).
cnf(f_1956_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6351)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6353)))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6353),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_6351)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1956_3]) ).
fof(f_1957_1,plain,
! [V_d,V_i] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_d)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d),V_i))
| V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(fof_nnf,[status(thm)],[fact_dvd__imp__le__int]) ).
fof(f_1957_2,plain,
! [U_6355,U_6354] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6355)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6354)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6355),U_6354))
| U_6354 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1957_1]) ).
cnf(f_1957_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6355)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6354)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6355),U_6354))
| U_6354 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1957_2]) ).
fof(f_1958_1,plain,
! [V_y_2,V_x_2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2))) ) )
| ~ 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_I4_J]) ).
fof(f_1958_2,plain,
! [U_6357,U_6356] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_6356)),hAPP(c_Int_Onat,U_6357)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6356),U_6357)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6356),U_6357))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_6356)),hAPP(c_Int_Onat,U_6357))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6357))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6356)) ),
inference(variable_rename,[status(thm)],[f_1958_1]) ).
cnf(f_1958_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6356),U_6357))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_6356)),hAPP(c_Int_Onat,U_6357)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6357))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6356)) ),
inference(clausify,[status(thm)],[f_1958_2]) ).
cnf(f_1958_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_6356)),hAPP(c_Int_Onat,U_6357)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6356),U_6357))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6357))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6356)) ),
inference(clausify,[status(thm)],[f_1958_2]) ).
fof(f_1959_1,plain,
! [V_na_2,V_m_2] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_na_2)),V_m_2))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_na_2) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_na_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_na_2)),V_m_2)) ) )
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__mult__cancel1]) ).
fof(f_1959_2,plain,
! [U_6359,U_6358] :
( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6358),U_6359)),U_6358))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6359) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6359) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6358),U_6359)),U_6358)) ) )
| U_6358 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_1959_1]) ).
cnf(f_1959_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6359) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6358),U_6359)),U_6358))
| U_6358 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1959_2]) ).
cnf(f_1959_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6358),U_6359)),U_6358))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6359) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_6358 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_1959_2]) ).
fof(f_1960_1,plain,
! [V_f_2,T_b] :
( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2)
| ? [B_x,B_y] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y)))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_y),B_x))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y)) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Ostrict__monoI]) ).
fof(f_1960_2,plain,
! [U_6363,U_6362] :
( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_6362,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)))),U_6363)
| ? [U_6361,U_6360] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6362),hAPP(U_6363,U_6361)),hAPP(U_6363,U_6360)))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6360),U_6361))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6361),U_6360)) )
| ~ class_Orderings_Oorder(U_6362) ),
inference(variable_rename,[status(thm)],[f_1960_1]) ).
fof(f_1960_3,plain,
! [U_6363,U_6362] :
( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_6362,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)))),U_6363)
| ? [U_6360] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6362),hAPP(U_6363,sK86(U_6363,U_6362))),hAPP(U_6363,U_6360)))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6360),sK86(U_6363,U_6362)))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK86(U_6363,U_6362)),U_6360)) )
| ~ class_Orderings_Oorder(U_6362) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_6361,sK86(U_6363,U_6362))],[f_1960_2]) ).
fof(f_1960_4,plain,
! [U_6363,U_6362] :
( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_6362,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)))),U_6363)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6362),hAPP(U_6363,sK86(U_6363,U_6362))),hAPP(U_6363,sK87(U_6363,U_6362))))
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK87(U_6363,U_6362)),sK86(U_6363,U_6362)))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK86(U_6363,U_6362)),sK87(U_6363,U_6362))) )
| ~ class_Orderings_Oorder(U_6362) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_6360,sK87(U_6363,U_6362))],[f_1960_3]) ).
cnf(f_1960_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK86(U_6363,U_6362)),sK87(U_6363,U_6362)))
| c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_6362,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)))),U_6363)
| ~ class_Orderings_Oorder(U_6362) ),
inference(clausify,[status(thm)],[f_1960_4]) ).
cnf(f_1960_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK87(U_6363,U_6362)),sK86(U_6363,U_6362)))
| c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_6362,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)))),U_6363)
| ~ class_Orderings_Oorder(U_6362) ),
inference(clausify,[status(thm)],[f_1960_4]) ).
cnf(f_1960_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6362),hAPP(U_6363,sK86(U_6363,U_6362))),hAPP(U_6363,sK87(U_6363,U_6362))))
| c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_6362,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)))),U_6363)
| ~ class_Orderings_Oorder(U_6362) ),
inference(clausify,[status(thm)],[f_1960_4]) ).
fof(f_1961_1,plain,
! [V_f_2,T_b] :
( c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)
| ? [B_x,B_y] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y)))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y)) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_dvd_OmonoI]) ).
fof(f_1961_2,plain,
! [U_6367,U_6366] :
( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_6366,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6367)
| ? [U_6365,U_6364] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6366),hAPP(U_6367,U_6365)),hAPP(U_6367,U_6364)))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6365),U_6364)) )
| ~ class_Orderings_Oorder(U_6366) ),
inference(variable_rename,[status(thm)],[f_1961_1]) ).
fof(f_1961_3,plain,
! [U_6367,U_6366] :
( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_6366,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6367)
| ? [U_6364] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6366),hAPP(U_6367,sK88(U_6367,U_6366))),hAPP(U_6367,U_6364)))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK88(U_6367,U_6366)),U_6364)) )
| ~ class_Orderings_Oorder(U_6366) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_6365,sK88(U_6367,U_6366))],[f_1961_2]) ).
fof(f_1961_4,plain,
! [U_6367,U_6366] :
( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_6366,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6367)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6366),hAPP(U_6367,sK88(U_6367,U_6366))),hAPP(U_6367,sK89(U_6367,U_6366))))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK88(U_6367,U_6366)),sK89(U_6367,U_6366))) )
| ~ class_Orderings_Oorder(U_6366) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_6364,sK89(U_6367,U_6366))],[f_1961_3]) ).
cnf(f_1961_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK88(U_6367,U_6366)),sK89(U_6367,U_6366)))
| c_Orderings_Oorder_Omono(tc_Nat_Onat,U_6366,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6367)
| ~ class_Orderings_Oorder(U_6366) ),
inference(clausify,[status(thm)],[f_1961_4]) ).
cnf(f_1961_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6366),hAPP(U_6367,sK88(U_6367,U_6366))),hAPP(U_6367,sK89(U_6367,U_6366))))
| c_Orderings_Oorder_Omono(tc_Nat_Onat,U_6366,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6367)
| ~ class_Orderings_Oorder(U_6366) ),
inference(clausify,[status(thm)],[f_1961_4]) ).
fof(f_1962_1,plain,
! [V_na_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_na_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_na_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_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))),
inference(fof_nnf,[status(thm)],[fact_arith__series__int]) ).
fof(f_1962_2,plain,
! [U_6370,U_6369,U_6368] : hAPP(hAPP(c_Groups_Otimes__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_6368)),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_6369))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6370))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6370)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6368),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6368),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_6370),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_6369)))),
inference(variable_rename,[status(thm)],[f_1962_1]) ).
cnf(f_1962_3,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_6368)),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_6369))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6370))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6370)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6368),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6368),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_6370),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_6369)))),
inference(clausify,[status(thm)],[f_1962_2]) ).
fof(f_1963_1,plain,
! [V_r,V_d,V_m] :
( ? [B_q] : V_m = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),B_q),V_d))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_d) != V_r ),
inference(fof_nnf,[status(thm)],[fact_mod__eqD]) ).
fof(f_1963_2,plain,
! [U_6374,U_6373,U_6372] :
( ? [U_6371] : U_6372 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6371),U_6373))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6372,U_6373) != U_6374 ),
inference(variable_rename,[status(thm)],[f_1963_1]) ).
fof(f_1963_3,plain,
! [U_6374,U_6373,U_6372] :
( U_6372 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),sK90(U_6374,U_6373,U_6372)),U_6373))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6372,U_6373) != U_6374 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_6371,sK90(U_6374,U_6373,U_6372))],[f_1963_2]) ).
cnf(f_1963_4,plain,
( U_6372 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),sK90(U_6374,U_6373,U_6372)),U_6373))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6372,U_6373) != U_6374 ),
inference(clausify,[status(thm)],[f_1963_3]) ).
fof(f_1964_1,plain,
! [V_y_2,V_na_2,V_x_2] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,V_na_2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y_2,V_na_2)
| ! [B_q1,B_q2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_na_2),B_q1)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_na_2),B_q2)) )
& ( ? [B_q1,B_q2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_na_2),B_q1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_na_2),B_q2))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,V_na_2) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y_2,V_na_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__mod__eq__iff]) ).
fof(f_1964_2,plain,
! [U_6381,U_6380,U_6379] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6379,U_6380) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6381,U_6380)
| ! [U_6378,U_6377] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6379),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6380),U_6378)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6381),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6380),U_6377)) )
& ( ? [U_6376,U_6375] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6379),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6380),U_6376)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6381),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6380),U_6375))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6379,U_6380) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6381,U_6380) ) ),
inference(variable_rename,[status(thm)],[f_1964_1]) ).
fof(f_1964_3,plain,
( ! [U_6387,U_6385,U_6383] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6383,U_6385) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6387,U_6385)
| ! [U_6378,U_6377] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6385),U_6378)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6387),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6385),U_6377)) )
& ! [U_6386,U_6384,U_6382] :
( ? [U_6376,U_6375] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6384),U_6376)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6384),U_6375))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6382,U_6384) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6386,U_6384) ) ),
inference(miniscope,[status(thm)],[f_1964_2]) ).
fof(f_1964_4,plain,
( ! [U_6387,U_6385,U_6383] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6383,U_6385) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6387,U_6385)
| ! [U_6378,U_6377] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6385),U_6378)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6387),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6385),U_6377)) )
& ! [U_6386,U_6384,U_6382] :
( ? [U_6375] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6384),sK91(U_6386,U_6384,U_6382))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6384),U_6375))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6382,U_6384) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6386,U_6384) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_6376,sK91(U_6386,U_6384,U_6382))],[f_1964_3]) ).
fof(f_1964_5,plain,
( ! [U_6387,U_6385,U_6383] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6383,U_6385) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6387,U_6385)
| ! [U_6378,U_6377] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6385),U_6378)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6387),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6385),U_6377)) )
& ! [U_6386,U_6384,U_6382] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6384),sK91(U_6386,U_6384,U_6382))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6384),sK92(U_6386,U_6384,U_6382)))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6382,U_6384) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6386,U_6384) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_6375,sK92(U_6386,U_6384,U_6382))],[f_1964_4]) ).
cnf(f_1964_6,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6382),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6384),sK91(U_6386,U_6384,U_6382))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6386),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6384),sK92(U_6386,U_6384,U_6382)))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6382,U_6384) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6386,U_6384) ),
inference(clausify,[status(thm)],[f_1964_5]) ).
cnf(f_1964_7,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6383,U_6385) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6387,U_6385)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6383),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6385),U_6378)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6387),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6385),U_6377)) ),
inference(clausify,[status(thm)],[f_1964_5]) ).
fof(f_1965_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)))
| ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__abs]) ).
fof(f_1965_2,plain,
! [U_6391,U_6390,U_6389,U_6388] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6388),hAPP(c_Groups_Oabs__class_Oabs(U_6388),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6389,U_6388),U_6390),U_6391))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6389,U_6388),hAPP(hAPP(c_COMBB(U_6388,U_6388,U_6389),c_Groups_Oabs__class_Oabs(U_6388)),U_6390)),U_6391)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_6388) ),
inference(variable_rename,[status(thm)],[f_1965_1]) ).
cnf(f_1965_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6388),hAPP(c_Groups_Oabs__class_Oabs(U_6388),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6389,U_6388),U_6390),U_6391))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6389,U_6388),hAPP(hAPP(c_COMBB(U_6388,U_6388,U_6389),c_Groups_Oabs__class_Oabs(U_6388)),U_6390)),U_6391)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_6388) ),
inference(clausify,[status(thm)],[f_1965_2]) ).
fof(f_1966_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)))
| ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__abs__ge__zero]) ).
fof(f_1966_2,plain,
! [U_6395,U_6394,U_6393,U_6392] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6392),c_Groups_Ozero__class_Ozero(U_6392)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6393,U_6392),hAPP(hAPP(c_COMBB(U_6392,U_6392,U_6393),c_Groups_Oabs__class_Oabs(U_6392)),U_6394)),U_6395)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_6392) ),
inference(variable_rename,[status(thm)],[f_1966_1]) ).
cnf(f_1966_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6392),c_Groups_Ozero__class_Ozero(U_6392)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6393,U_6392),hAPP(hAPP(c_COMBB(U_6392,U_6392,U_6393),c_Groups_Oabs__class_Oabs(U_6392)),U_6394)),U_6395)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_6392) ),
inference(clausify,[status(thm)],[f_1966_2]) ).
fof(f_1967_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2)
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__setsum]) ).
fof(f_1967_2,plain,
! [U_6399,U_6398,U_6397,U_6396] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6396),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6397,tc_Nat_Onat),U_6398),U_6399)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6397,U_6396),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6396,U_6397),c_Nat_Osemiring__1__class_Oof__nat(U_6396)),U_6398)),U_6399)
| ~ class_Rings_Osemiring__1(U_6396) ),
inference(variable_rename,[status(thm)],[f_1967_1]) ).
cnf(f_1967_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6396),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6397,tc_Nat_Onat),U_6398),U_6399)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6397,U_6396),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6396,U_6397),c_Nat_Osemiring__1__class_Oof__nat(U_6396)),U_6398)),U_6399)
| ~ class_Rings_Osemiring__1(U_6396) ),
inference(clausify,[status(thm)],[f_1967_2]) ).
fof(f_1968_1,plain,
! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_b),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))),V_A_2)),V_B_2)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__commute]) ).
fof(f_1968_2,plain,
! [U_6405,U_6404,U_6403,U_6402,U_6401,U_6400] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6401,U_6400),hAPP(hAPP(c_COMBC(U_6401,tc_fun(U_6402,tc_HOL_Obool),U_6400),hAPP(hAPP(c_COMBB(tc_fun(U_6402,U_6400),tc_fun(tc_fun(U_6402,tc_HOL_Obool),U_6400),U_6401),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6402,U_6400)),U_6403)),U_6404)),U_6405) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6402,U_6400),hAPP(hAPP(c_COMBC(U_6402,tc_fun(U_6401,tc_HOL_Obool),U_6400),hAPP(hAPP(c_COMBB(tc_fun(U_6401,U_6400),tc_fun(tc_fun(U_6401,tc_HOL_Obool),U_6400),U_6402),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6401,U_6400)),hAPP(c_COMBC(U_6401,U_6402,U_6400),U_6403))),U_6405)),U_6404)
| ~ class_Groups_Ocomm__monoid__add(U_6400) ),
inference(variable_rename,[status(thm)],[f_1968_1]) ).
cnf(f_1968_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6401,U_6400),hAPP(hAPP(c_COMBC(U_6401,tc_fun(U_6402,tc_HOL_Obool),U_6400),hAPP(hAPP(c_COMBB(tc_fun(U_6402,U_6400),tc_fun(tc_fun(U_6402,tc_HOL_Obool),U_6400),U_6401),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6402,U_6400)),U_6403)),U_6404)),U_6405) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6402,U_6400),hAPP(hAPP(c_COMBC(U_6402,tc_fun(U_6401,tc_HOL_Obool),U_6400),hAPP(hAPP(c_COMBB(tc_fun(U_6401,U_6400),tc_fun(tc_fun(U_6401,tc_HOL_Obool),U_6400),U_6402),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6401,U_6400)),hAPP(c_COMBC(U_6401,U_6402,U_6400),U_6403))),U_6405)),U_6404)
| ~ class_Groups_Ocomm__monoid__add(U_6400) ),
inference(clausify,[status(thm)],[f_1968_2]) ).
fof(f_1969_1,plain,
! [V_na_2,V_f_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_2))),hAPP(V_f_2,V_na_2))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__lessThan__Suc]) ).
fof(f_1969_2,plain,
! [U_6408,U_6407,U_6406] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6406),U_6407),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6408))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6406),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6406),U_6407),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6408))),hAPP(U_6407,U_6408))
| ~ class_Groups_Ocomm__monoid__add(U_6406) ),
inference(variable_rename,[status(thm)],[f_1969_1]) ).
cnf(f_1969_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6406),U_6407),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6408))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6406),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6406),U_6407),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6408))),hAPP(U_6407,U_6408))
| ~ class_Groups_Ocomm__monoid__add(U_6406) ),
inference(clausify,[status(thm)],[f_1969_2]) ).
fof(f_1970_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2)
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__setsum]) ).
fof(f_1970_2,plain,
! [U_6412,U_6411,U_6410,U_6409] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_6409),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6410,tc_Int_Oint),U_6411),U_6412)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6410,U_6409),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_6409,U_6410),c_Int_Oring__1__class_Oof__int(U_6409)),U_6411)),U_6412)
| ~ class_Rings_Oring__1(U_6409) ),
inference(variable_rename,[status(thm)],[f_1970_1]) ).
cnf(f_1970_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_6409),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6410,tc_Int_Oint),U_6411),U_6412)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6410,U_6409),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_6409,U_6410),c_Int_Oring__1__class_Oof__int(U_6409)),U_6411)),U_6412)
| ~ class_Rings_Oring__1(U_6409) ),
inference(clausify,[status(thm)],[f_1970_2]) ).
fof(f_1971_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) != hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lessThan__eq__iff]) ).
fof(f_1971_2,plain,
! [U_6415,U_6414,U_6413] :
( ( ( hAPP(c_SetInterval_Oord__class_OlessThan(U_6413),U_6414) = hAPP(c_SetInterval_Oord__class_OlessThan(U_6413),U_6415)
| U_6414 != U_6415 )
& ( U_6414 = U_6415
| hAPP(c_SetInterval_Oord__class_OlessThan(U_6413),U_6414) != hAPP(c_SetInterval_Oord__class_OlessThan(U_6413),U_6415) ) )
| ~ class_Orderings_Olinorder(U_6413) ),
inference(variable_rename,[status(thm)],[f_1971_1]) ).
cnf(f_1971_3,plain,
( U_6414 = U_6415
| hAPP(c_SetInterval_Oord__class_OlessThan(U_6413),U_6414) != hAPP(c_SetInterval_Oord__class_OlessThan(U_6413),U_6415)
| ~ class_Orderings_Olinorder(U_6413) ),
inference(clausify,[status(thm)],[f_1971_2]) ).
cnf(f_1971_4,plain,
( hAPP(c_SetInterval_Oord__class_OlessThan(U_6413),U_6414) = hAPP(c_SetInterval_Oord__class_OlessThan(U_6413),U_6415)
| U_6414 != U_6415
| ~ class_Orderings_Olinorder(U_6413) ),
inference(clausify,[status(thm)],[f_1971_2]) ).
fof(f_1972_1,plain,
! [V_A_2,T_c,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) = c_Groups_Ozero__class_Ozero(T_b)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__0]) ).
fof(f_1972_2,plain,
! [U_6418,U_6417,U_6416] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6417,U_6416),hAPP(c_COMBK(U_6416,U_6417),c_Groups_Ozero__class_Ozero(U_6416))),U_6418) = c_Groups_Ozero__class_Ozero(U_6416)
| ~ class_Groups_Ocomm__monoid__add(U_6416) ),
inference(variable_rename,[status(thm)],[f_1972_1]) ).
cnf(f_1972_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6417,U_6416),hAPP(c_COMBK(U_6416,U_6417),c_Groups_Ozero__class_Ozero(U_6416))),U_6418) = c_Groups_Ozero__class_Ozero(U_6416)
| ~ class_Groups_Ocomm__monoid__add(U_6416) ),
inference(clausify,[status(thm)],[f_1972_2]) ).
fof(f_1973_1,plain,
! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__addf]) ).
fof(f_1973_2,plain,
! [U_6423,U_6422,U_6421,U_6420,U_6419] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6420,U_6419),hAPP(hAPP(c_COMBS(U_6420,U_6419,U_6419),hAPP(hAPP(c_COMBB(U_6419,tc_fun(U_6419,U_6419),U_6420),c_Groups_Oplus__class_Oplus(U_6419)),U_6421)),U_6422)),U_6423) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6419),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6420,U_6419),U_6421),U_6423)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6420,U_6419),U_6422),U_6423))
| ~ class_Groups_Ocomm__monoid__add(U_6419) ),
inference(variable_rename,[status(thm)],[f_1973_1]) ).
cnf(f_1973_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6420,U_6419),hAPP(hAPP(c_COMBS(U_6420,U_6419,U_6419),hAPP(hAPP(c_COMBB(U_6419,tc_fun(U_6419,U_6419),U_6420),c_Groups_Oplus__class_Oplus(U_6419)),U_6421)),U_6422)),U_6423) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6419),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6420,U_6419),U_6421),U_6423)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6420,U_6419),U_6422),U_6423))
| ~ class_Groups_Ocomm__monoid__add(U_6419) ),
inference(clausify,[status(thm)],[f_1973_2]) ).
fof(f_1974_1,plain,
! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_b),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,T_b)),T_c),c_COMBB(T_b,T_b,T_d)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2))),V_g_2))),V_B_2)),V_A_2)
| ~ class_Rings_Osemiring__0(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__product]) ).
fof(f_1974_2,plain,
! [U_6430,U_6429,U_6428,U_6427,U_6426,U_6425,U_6424] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6424),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6425,U_6424),U_6426),U_6427)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6428,U_6424),U_6429),U_6430)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6425,U_6424),hAPP(hAPP(c_COMBC(U_6425,tc_fun(U_6428,tc_HOL_Obool),U_6424),hAPP(hAPP(c_COMBB(tc_fun(U_6428,U_6424),tc_fun(tc_fun(U_6428,tc_HOL_Obool),U_6424),U_6425),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6428,U_6424)),hAPP(hAPP(c_COMBC(U_6425,tc_fun(U_6428,U_6424),tc_fun(U_6428,U_6424)),hAPP(hAPP(c_COMBB(tc_fun(U_6424,U_6424),tc_fun(tc_fun(U_6428,U_6424),tc_fun(U_6428,U_6424)),U_6425),c_COMBB(U_6424,U_6424,U_6428)),hAPP(hAPP(c_COMBB(U_6424,tc_fun(U_6424,U_6424),U_6425),c_Groups_Otimes__class_Otimes(U_6424)),U_6426))),U_6429))),U_6430)),U_6427)
| ~ class_Rings_Osemiring__0(U_6424) ),
inference(variable_rename,[status(thm)],[f_1974_1]) ).
cnf(f_1974_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6424),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6425,U_6424),U_6426),U_6427)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6428,U_6424),U_6429),U_6430)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6425,U_6424),hAPP(hAPP(c_COMBC(U_6425,tc_fun(U_6428,tc_HOL_Obool),U_6424),hAPP(hAPP(c_COMBB(tc_fun(U_6428,U_6424),tc_fun(tc_fun(U_6428,tc_HOL_Obool),U_6424),U_6425),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6428,U_6424)),hAPP(hAPP(c_COMBC(U_6425,tc_fun(U_6428,U_6424),tc_fun(U_6428,U_6424)),hAPP(hAPP(c_COMBB(tc_fun(U_6424,U_6424),tc_fun(tc_fun(U_6428,U_6424),tc_fun(U_6428,U_6424)),U_6425),c_COMBB(U_6424,U_6424,U_6428)),hAPP(hAPP(c_COMBB(U_6424,tc_fun(U_6424,U_6424),U_6425),c_Groups_Otimes__class_Otimes(U_6424)),U_6426))),U_6429))),U_6430)),U_6427)
| ~ class_Rings_Osemiring__0(U_6424) ),
inference(clausify,[status(thm)],[f_1974_2]) ).
fof(f_1975_1,plain,
! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_r_2)),V_A_2)
| ~ class_Rings_Osemiring__0(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__left__distrib]) ).
fof(f_1975_2,plain,
! [U_6435,U_6434,U_6433,U_6432,U_6431] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6431),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6432,U_6431),U_6433),U_6434)),U_6435) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6432,U_6431),hAPP(hAPP(c_COMBC(U_6432,U_6431,U_6431),hAPP(hAPP(c_COMBB(U_6431,tc_fun(U_6431,U_6431),U_6432),c_Groups_Otimes__class_Otimes(U_6431)),U_6433)),U_6435)),U_6434)
| ~ class_Rings_Osemiring__0(U_6431) ),
inference(variable_rename,[status(thm)],[f_1975_1]) ).
cnf(f_1975_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6431),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6432,U_6431),U_6433),U_6434)),U_6435) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6432,U_6431),hAPP(hAPP(c_COMBC(U_6432,U_6431,U_6431),hAPP(hAPP(c_COMBB(U_6431,tc_fun(U_6431,U_6431),U_6432),c_Groups_Otimes__class_Otimes(U_6431)),U_6433)),U_6435)),U_6434)
| ~ class_Rings_Osemiring__0(U_6431) ),
inference(clausify,[status(thm)],[f_1975_2]) ).
fof(f_1976_1,plain,
! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2)),V_f_2)),V_A_2)
| ~ class_Rings_Osemiring__0(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__right__distrib]) ).
fof(f_1976_2,plain,
! [U_6440,U_6439,U_6438,U_6437,U_6436] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6436),U_6437),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6438,U_6436),U_6439),U_6440)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6438,U_6436),hAPP(hAPP(c_COMBB(U_6436,U_6436,U_6438),hAPP(c_Groups_Otimes__class_Otimes(U_6436),U_6437)),U_6439)),U_6440)
| ~ class_Rings_Osemiring__0(U_6436) ),
inference(variable_rename,[status(thm)],[f_1976_1]) ).
cnf(f_1976_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6436),U_6437),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6438,U_6436),U_6439),U_6440)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6438,U_6436),hAPP(hAPP(c_COMBB(U_6436,U_6436,U_6438),hAPP(c_Groups_Otimes__class_Otimes(U_6436),U_6437)),U_6439)),U_6440)
| ~ class_Rings_Osemiring__0(U_6436) ),
inference(clausify,[status(thm)],[f_1976_2]) ).
fof(f_1977_1,plain,
! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2))
| ~ class_Groups_Oab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__subtractf]) ).
fof(f_1977_2,plain,
! [U_6445,U_6444,U_6443,U_6442,U_6441] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6442,U_6441),hAPP(hAPP(c_COMBS(U_6442,U_6441,U_6441),hAPP(hAPP(c_COMBB(U_6441,tc_fun(U_6441,U_6441),U_6442),c_Groups_Ominus__class_Ominus(U_6441)),U_6443)),U_6444)),U_6445) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6441),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6442,U_6441),U_6443),U_6445)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6442,U_6441),U_6444),U_6445))
| ~ class_Groups_Oab__group__add(U_6441) ),
inference(variable_rename,[status(thm)],[f_1977_1]) ).
cnf(f_1977_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6442,U_6441),hAPP(hAPP(c_COMBS(U_6442,U_6441,U_6441),hAPP(hAPP(c_COMBB(U_6441,tc_fun(U_6441,U_6441),U_6442),c_Groups_Ominus__class_Ominus(U_6441)),U_6443)),U_6444)),U_6445) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6441),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6442,U_6441),U_6443),U_6445)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6442,U_6441),U_6444),U_6445))
| ~ class_Groups_Oab__group__add(U_6441) ),
inference(clausify,[status(thm)],[f_1977_2]) ).
fof(f_1978_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2))
| ~ class_Groups_Oab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__negf]) ).
fof(f_1978_2,plain,
! [U_6449,U_6448,U_6447,U_6446] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6447,U_6446),hAPP(hAPP(c_COMBB(U_6446,U_6446,U_6447),c_Groups_Ouminus__class_Ouminus(U_6446)),U_6448)),U_6449) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6446),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6447,U_6446),U_6448),U_6449))
| ~ class_Groups_Oab__group__add(U_6446) ),
inference(variable_rename,[status(thm)],[f_1978_1]) ).
cnf(f_1978_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6447,U_6446),hAPP(hAPP(c_COMBB(U_6446,U_6446,U_6447),c_Groups_Ouminus__class_Ouminus(U_6446)),U_6448)),U_6449) = hAPP(c_Groups_Ouminus__class_Ouminus(U_6446),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6447,U_6446),U_6448),U_6449))
| ~ class_Groups_Oab__group__add(U_6446) ),
inference(clausify,[status(thm)],[f_1978_2]) ).
fof(f_1979_1,plain,
! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_r_2)),V_A_2)
| ~ class_Fields_Ofield(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__divide__distrib]) ).
fof(f_1979_2,plain,
! [U_6454,U_6453,U_6452,U_6451,U_6450] :
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6450),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6451,U_6450),U_6452),U_6453)),U_6454) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6451,U_6450),hAPP(hAPP(c_COMBC(U_6451,U_6450,U_6450),hAPP(hAPP(c_COMBB(U_6450,tc_fun(U_6450,U_6450),U_6451),c_Rings_Oinverse__class_Odivide(U_6450)),U_6452)),U_6454)),U_6453)
| ~ class_Fields_Ofield(U_6450) ),
inference(variable_rename,[status(thm)],[f_1979_1]) ).
cnf(f_1979_3,plain,
( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6450),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6451,U_6450),U_6452),U_6453)),U_6454) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6451,U_6450),hAPP(hAPP(c_COMBC(U_6451,U_6450,U_6450),hAPP(hAPP(c_COMBB(U_6450,tc_fun(U_6450,U_6450),U_6451),c_Rings_Oinverse__class_Odivide(U_6450)),U_6452)),U_6454)),U_6453)
| ~ class_Fields_Ofield(U_6450) ),
inference(clausify,[status(thm)],[f_1979_2]) ).
fof(f_1980_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)
| ~ class_Groups_Oordered__ab__group__add__abs(T_b) ),
inference(fof_nnf,[status(thm)],[fact_abs__setsum__abs]) ).
fof(f_1980_2,plain,
! [U_6458,U_6457,U_6456,U_6455] :
( hAPP(c_Groups_Oabs__class_Oabs(U_6455),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6456,U_6455),hAPP(hAPP(c_COMBB(U_6455,U_6455,U_6456),c_Groups_Oabs__class_Oabs(U_6455)),U_6457)),U_6458)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6456,U_6455),hAPP(hAPP(c_COMBB(U_6455,U_6455,U_6456),c_Groups_Oabs__class_Oabs(U_6455)),U_6457)),U_6458)
| ~ class_Groups_Oordered__ab__group__add__abs(U_6455) ),
inference(variable_rename,[status(thm)],[f_1980_1]) ).
cnf(f_1980_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_6455),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6456,U_6455),hAPP(hAPP(c_COMBB(U_6455,U_6455,U_6456),c_Groups_Oabs__class_Oabs(U_6455)),U_6457)),U_6458)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6456,U_6455),hAPP(hAPP(c_COMBB(U_6455,U_6455,U_6456),c_Groups_Oabs__class_Oabs(U_6455)),U_6457)),U_6458)
| ~ class_Groups_Oordered__ab__group__add__abs(U_6455) ),
inference(clausify,[status(thm)],[f_1980_2]) ).
fof(f_1981_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2))) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lessThan__subset__iff]) ).
fof(f_1981_2,plain,
! [U_6461,U_6460,U_6459] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6459,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6459),U_6460)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6459),U_6461)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6459),U_6460),U_6461)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6459),U_6460),U_6461))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6459,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6459),U_6460)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6459),U_6461))) ) )
| ~ class_Orderings_Olinorder(U_6459) ),
inference(variable_rename,[status(thm)],[f_1981_1]) ).
cnf(f_1981_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6459),U_6460),U_6461))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6459,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6459),U_6460)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6459),U_6461)))
| ~ class_Orderings_Olinorder(U_6459) ),
inference(clausify,[status(thm)],[f_1981_2]) ).
cnf(f_1981_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6459,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6459),U_6460)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6459),U_6461)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6459),U_6460),U_6461))
| ~ class_Orderings_Olinorder(U_6459) ),
inference(clausify,[status(thm)],[f_1981_2]) ).
fof(f_1982_1,plain,
! [V_na_2,V_m_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_na_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_na_2))) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lessThan__strict__subset__iff]) ).
fof(f_1982_2,plain,
! [U_6464,U_6463,U_6462] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6462,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6462),U_6463)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6462),U_6464)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6462),U_6463),U_6464)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6462),U_6463),U_6464))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6462,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6462),U_6463)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6462),U_6464))) ) )
| ~ class_Orderings_Olinorder(U_6462) ),
inference(variable_rename,[status(thm)],[f_1982_1]) ).
cnf(f_1982_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6462),U_6463),U_6464))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6462,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6462),U_6463)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6462),U_6464)))
| ~ class_Orderings_Olinorder(U_6462) ),
inference(clausify,[status(thm)],[f_1982_2]) ).
cnf(f_1982_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6462,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6462),U_6463)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6462),U_6464)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6462),U_6463),U_6464))
| ~ class_Orderings_Olinorder(U_6462) ),
inference(clausify,[status(thm)],[f_1982_2]) ).
fof(f_1983_1,plain,
! [V_na_2,V_d_2,V_a_2,T_b] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_b)),c_Nat_Osemiring__1__class_Oof__nat(T_b))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2))))
| ~ class_Rings_Ocomm__semiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_arith__series__general]) ).
fof(f_1983_2,plain,
! [U_6468,U_6467,U_6466,U_6465] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6465),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6465),c_Groups_Oone__class_Oone(U_6465)),c_Groups_Oone__class_Oone(U_6465))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6465),hAPP(hAPP(c_COMBB(U_6465,U_6465,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_6465),U_6466)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_6465,U_6465),hAPP(hAPP(c_COMBB(U_6465,tc_fun(U_6465,U_6465),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_6465)),c_Nat_Osemiring__1__class_Oof__nat(U_6465))),U_6467))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6468))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6465),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6465),U_6468)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6465),U_6466),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6465),U_6466),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6465),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6465),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6468),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_6467))))
| ~ class_Rings_Ocomm__semiring__1(U_6465) ),
inference(variable_rename,[status(thm)],[f_1983_1]) ).
cnf(f_1983_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6465),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6465),c_Groups_Oone__class_Oone(U_6465)),c_Groups_Oone__class_Oone(U_6465))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6465),hAPP(hAPP(c_COMBB(U_6465,U_6465,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_6465),U_6466)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_6465,U_6465),hAPP(hAPP(c_COMBB(U_6465,tc_fun(U_6465,U_6465),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_6465)),c_Nat_Osemiring__1__class_Oof__nat(U_6465))),U_6467))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6468))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6465),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6465),U_6468)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6465),U_6466),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6465),U_6466),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6465),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6465),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6468),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_6467))))
| ~ class_Rings_Ocomm__semiring__1(U_6465) ),
inference(clausify,[status(thm)],[f_1983_2]) ).
fof(f_1984_1,plain,
! [V_na_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_na_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_na_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_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_d_2)))),
inference(fof_nnf,[status(thm)],[fact_arith__series__nat]) ).
fof(f_1984_2,plain,
! [U_6471,U_6470,U_6469] : 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_6469)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_6470))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6471))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6471),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6469),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6469),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6471),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_6470)))),
inference(variable_rename,[status(thm)],[f_1984_1]) ).
cnf(f_1984_3,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_6469)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_6470))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6471))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6471),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6469),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6469),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6471),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_6470)))),
inference(clausify,[status(thm)],[f_1984_2]) ).
fof(f_1985_1,plain,
! [V_f_2,V_na_2,V_m_2,T_b] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_2)) = c_Groups_Ozero__class_Ozero(T_b)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_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_na_2)) ) )
| ~ class_Groups_Oab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__natinterval__difff]) ).
fof(f_1985_2,plain,
! [U_6475,U_6474,U_6473,U_6472] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6472),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_6472,U_6472),hAPP(hAPP(c_COMBB(U_6472,tc_fun(U_6472,U_6472),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_6472)),U_6475)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6472,tc_Nat_Onat),U_6475),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_6473,U_6474)) = c_Groups_Ozero__class_Ozero(U_6472)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6473),U_6474)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6472),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_6472,U_6472),hAPP(hAPP(c_COMBB(U_6472,tc_fun(U_6472,U_6472),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_6472)),U_6475)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6472,tc_Nat_Onat),U_6475),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_6473,U_6474)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6472),hAPP(U_6475,U_6473)),hAPP(U_6475,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6474),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6473),U_6474)) ) )
| ~ class_Groups_Oab__group__add(U_6472) ),
inference(variable_rename,[status(thm)],[f_1985_1]) ).
cnf(f_1985_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6472),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_6472,U_6472),hAPP(hAPP(c_COMBB(U_6472,tc_fun(U_6472,U_6472),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_6472)),U_6475)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6472,tc_Nat_Onat),U_6475),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_6473,U_6474)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6472),hAPP(U_6475,U_6473)),hAPP(U_6475,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6474),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6473),U_6474))
| ~ class_Groups_Oab__group__add(U_6472) ),
inference(clausify,[status(thm)],[f_1985_2]) ).
cnf(f_1985_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6472),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_6472,U_6472),hAPP(hAPP(c_COMBB(U_6472,tc_fun(U_6472,U_6472),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_6472)),U_6475)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6472,tc_Nat_Onat),U_6475),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_6473,U_6474)) = c_Groups_Ozero__class_Ozero(U_6472)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6473),U_6474))
| ~ class_Groups_Oab__group__add(U_6472) ),
inference(clausify,[status(thm)],[f_1985_2]) ).
fof(f_1986_1,plain,
! [V_na_2,T_b] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_na_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)),c_Groups_Oone__class_Oone(T_b)))
| ~ class_Rings_Ocomm__semiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_gauss__sum]) ).
fof(f_1986_2,plain,
! [U_6477,U_6476] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6476),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6476),c_Groups_Oone__class_Oone(U_6476)),c_Groups_Oone__class_Oone(U_6476))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6476),c_Nat_Osemiring__1__class_Oof__nat(U_6476)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_6477))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6476),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6476),U_6477)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6476),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6476),U_6477)),c_Groups_Oone__class_Oone(U_6476)))
| ~ class_Rings_Ocomm__semiring__1(U_6476) ),
inference(variable_rename,[status(thm)],[f_1986_1]) ).
cnf(f_1986_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6476),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6476),c_Groups_Oone__class_Oone(U_6476)),c_Groups_Oone__class_Oone(U_6476))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6476),c_Nat_Osemiring__1__class_Oof__nat(U_6476)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_6477))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6476),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6476),U_6477)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6476),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6476),U_6477)),c_Groups_Oone__class_Oone(U_6476)))
| ~ class_Rings_Ocomm__semiring__1(U_6476) ),
inference(clausify,[status(thm)],[f_1986_2]) ).
fof(f_1987_1,plain,
! [V_na_2,V_x_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_Power_Opower__class_Opower(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),V_na_2)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_x_2),c_Groups_Oone__class_Oone(T_b)))
| V_x_2 = c_Groups_Oone__class_Oone(T_b)
| ~ class_Fields_Ofield(T_b) ),
inference(fof_nnf,[status(thm)],[fact_geometric__sum]) ).
fof(f_1987_2,plain,
! [U_6480,U_6479,U_6478] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6478),hAPP(c_Power_Opower__class_Opower(U_6478),U_6479)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6480)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6478),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6478),hAPP(hAPP(c_Power_Opower__class_Opower(U_6478),U_6479),U_6480)),c_Groups_Oone__class_Oone(U_6478))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6478),U_6479),c_Groups_Oone__class_Oone(U_6478)))
| U_6479 = c_Groups_Oone__class_Oone(U_6478)
| ~ class_Fields_Ofield(U_6478) ),
inference(variable_rename,[status(thm)],[f_1987_1]) ).
cnf(f_1987_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6478),hAPP(c_Power_Opower__class_Opower(U_6478),U_6479)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6480)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6478),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6478),hAPP(hAPP(c_Power_Opower__class_Opower(U_6478),U_6479),U_6480)),c_Groups_Oone__class_Oone(U_6478))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6478),U_6479),c_Groups_Oone__class_Oone(U_6478)))
| U_6479 = c_Groups_Oone__class_Oone(U_6478)
| ~ class_Fields_Ofield(U_6478) ),
inference(clausify,[status(thm)],[f_1987_2]) ).
fof(f_1988_1,plain,
! [V_p_2,V_f_2,V_na_2,V_m_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),V_p_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_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_na_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__ub__add__nat]) ).
fof(f_1988_2,plain,
! [U_6485,U_6484,U_6483,U_6482,U_6481] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6481),U_6484),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6482,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6483),U_6485))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6481),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6481),U_6484),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6482,U_6483))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6481),U_6484),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6483),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6483),U_6485))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6482),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6483),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Groups_Ocomm__monoid__add(U_6481) ),
inference(variable_rename,[status(thm)],[f_1988_1]) ).
cnf(f_1988_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6481),U_6484),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6482,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6483),U_6485))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6481),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6481),U_6484),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6482,U_6483))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6481),U_6484),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6483),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6483),U_6485))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6482),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6483),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Groups_Ocomm__monoid__add(U_6481) ),
inference(clausify,[status(thm)],[f_1988_2]) ).
fof(f_1989_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_1989_2,plain,
! [U_6487,U_6486] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_6486),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6487)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_6486),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6487))
| hAPP(U_6486,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_1989_1]) ).
cnf(f_1989_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_6486),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6487)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_6486),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6487))
| hAPP(U_6486,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_1989_2]) ).
fof(f_1990_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_1990_2,plain,
! [U_6489,U_6488] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6488),hAPP(c_Nat_OSuc,U_6489)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6488,U_6489),
inference(variable_rename,[status(thm)],[f_1990_1]) ).
cnf(f_1990_3,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6488),hAPP(c_Nat_OSuc,U_6489)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6488,U_6489),
inference(clausify,[status(thm)],[f_1990_2]) ).
fof(f_1991_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( V_b_2 = V_d_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J]) ).
fof(f_1991_2,plain,
! [U_6494,U_6493,U_6492,U_6491,U_6490] :
( U_6492 = U_6494
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6490),U_6493),U_6494))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6490),U_6491),U_6492))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6490,U_6491),U_6492) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6490,U_6493),U_6494)
| ~ class_Orderings_Olinorder(U_6490) ),
inference(variable_rename,[status(thm)],[f_1991_1]) ).
cnf(f_1991_3,plain,
( U_6492 = U_6494
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6490),U_6493),U_6494))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6490),U_6491),U_6492))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6490,U_6491),U_6492) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6490,U_6493),U_6494)
| ~ class_Orderings_Olinorder(U_6490) ),
inference(clausify,[status(thm)],[f_1991_2]) ).
fof(f_1992_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( V_a_2 = V_c_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J]) ).
fof(f_1992_2,plain,
! [U_6499,U_6498,U_6497,U_6496,U_6495] :
( U_6496 = U_6498
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6495),U_6498),U_6499))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6495),U_6496),U_6497))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6495,U_6496),U_6497) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6495,U_6498),U_6499)
| ~ class_Orderings_Olinorder(U_6495) ),
inference(variable_rename,[status(thm)],[f_1992_1]) ).
cnf(f_1992_3,plain,
( U_6496 = U_6498
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6495),U_6498),U_6499))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6495),U_6496),U_6497))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6495,U_6496),U_6497) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6495,U_6498),U_6499)
| ~ class_Orderings_Olinorder(U_6495) ),
inference(clausify,[status(thm)],[f_1992_2]) ).
fof(f_1993_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_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_b,V_a_2),V_b_2) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__eq__iff]) ).
fof(f_1993_2,plain,
! [U_6504,U_6503,U_6502,U_6501,U_6500] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6500,U_6501),U_6502) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6500,U_6503),U_6504)
| U_6502 != U_6504
| U_6501 != U_6503 )
& ( ( U_6502 = U_6504
& U_6501 = U_6503 )
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6500,U_6501),U_6502) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6500,U_6503),U_6504) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6500),U_6503),U_6504))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6500),U_6501),U_6502))
| ~ class_Orderings_Olinorder(U_6500) ),
inference(variable_rename,[status(thm)],[f_1993_1]) ).
cnf(f_1993_3,plain,
( U_6501 = U_6503
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6500,U_6501),U_6502) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6500,U_6503),U_6504)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6500),U_6503),U_6504))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6500),U_6501),U_6502))
| ~ class_Orderings_Olinorder(U_6500) ),
inference(clausify,[status(thm)],[f_1993_2]) ).
cnf(f_1993_4,plain,
( U_6502 = U_6504
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6500,U_6501),U_6502) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6500,U_6503),U_6504)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6500),U_6503),U_6504))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6500),U_6501),U_6502))
| ~ class_Orderings_Olinorder(U_6500) ),
inference(clausify,[status(thm)],[f_1993_2]) ).
cnf(f_1993_5,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6500,U_6501),U_6502) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6500,U_6503),U_6504)
| U_6502 != U_6504
| U_6501 != U_6503
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6500),U_6503),U_6504))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6500),U_6501),U_6502))
| ~ class_Orderings_Olinorder(U_6500) ),
inference(clausify,[status(thm)],[f_1993_2]) ).
fof(f_1994_1,plain,
! [V_na_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_na_2) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_2),
inference(fof_nnf,[status(thm)],[fact_atLeast0LessThan]) ).
fof(f_1994_2,plain,
! [U_6505] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6505) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6505),
inference(variable_rename,[status(thm)],[f_1994_1]) ).
cnf(f_1994_3,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6505) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6505),
inference(clausify,[status(thm)],[f_1994_2]) ).
fof(f_1995_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2))) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastatMost__subset__iff]) ).
fof(f_1995_2,plain,
! [U_6510,U_6509,U_6508,U_6507,U_6506] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6506,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_6506,U_6507,U_6508)),c_SetInterval_Oord__class_OatLeastAtMost(U_6506,U_6509,U_6510)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6506),U_6508),U_6510))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6506),U_6509),U_6507)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6506),U_6507),U_6508)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6506),U_6508),U_6510))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6506),U_6509),U_6507)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6506),U_6507),U_6508))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6506,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_6506,U_6507,U_6508)),c_SetInterval_Oord__class_OatLeastAtMost(U_6506,U_6509,U_6510))) ) )
| ~ class_Orderings_Oorder(U_6506) ),
inference(variable_rename,[status(thm)],[f_1995_1]) ).
cnf(f_1995_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6506),U_6509),U_6507))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6506),U_6507),U_6508))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6506,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_6506,U_6507,U_6508)),c_SetInterval_Oord__class_OatLeastAtMost(U_6506,U_6509,U_6510)))
| ~ class_Orderings_Oorder(U_6506) ),
inference(clausify,[status(thm)],[f_1995_2]) ).
cnf(f_1995_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6506),U_6508),U_6510))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6506),U_6507),U_6508))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6506,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_6506,U_6507,U_6508)),c_SetInterval_Oord__class_OatLeastAtMost(U_6506,U_6509,U_6510)))
| ~ class_Orderings_Oorder(U_6506) ),
inference(clausify,[status(thm)],[f_1995_2]) ).
cnf(f_1995_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6506),U_6507),U_6508))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6506,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_6506,U_6507,U_6508)),c_SetInterval_Oord__class_OatLeastAtMost(U_6506,U_6509,U_6510)))
| ~ class_Orderings_Oorder(U_6506) ),
inference(clausify,[status(thm)],[f_1995_2]) ).
cnf(f_1995_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6506),U_6508),U_6510))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6506),U_6509),U_6507))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6506,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_6506,U_6507,U_6508)),c_SetInterval_Oord__class_OatLeastAtMost(U_6506,U_6509,U_6510)))
| ~ class_Orderings_Oorder(U_6506) ),
inference(clausify,[status(thm)],[f_1995_2]) ).
fof(f_1996_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__subset__iff]) ).
fof(f_1996_2,plain,
! [U_6515,U_6514,U_6513,U_6512,U_6511] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6511),U_6513),U_6515))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6511),U_6514),U_6512)) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6511),U_6513),U_6512))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6511,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6511,U_6512),U_6513)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6511,U_6514),U_6515)))
| ~ class_Orderings_Olinorder(U_6511) ),
inference(variable_rename,[status(thm)],[f_1996_1]) ).
cnf(f_1996_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6511),U_6514),U_6512))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6511),U_6513),U_6512))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6511,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6511,U_6512),U_6513)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6511,U_6514),U_6515)))
| ~ class_Orderings_Olinorder(U_6511) ),
inference(clausify,[status(thm)],[f_1996_2]) ).
cnf(f_1996_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6511),U_6513),U_6515))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6511),U_6513),U_6512))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6511,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6511,U_6512),U_6513)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6511,U_6514),U_6515)))
| ~ class_Orderings_Olinorder(U_6511) ),
inference(clausify,[status(thm)],[f_1996_2]) ).
fof(f_1997_1,plain,
! [V_na_2,V_m_2,V_f_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),hAPP(c_Nat_OSuc,V_na_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_na_2))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__Suc__ivl]) ).
fof(f_1997_2,plain,
! [U_6519,U_6518,U_6517,U_6516] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6516),U_6517),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6518)),hAPP(c_Nat_OSuc,U_6519))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6516),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6516,tc_Nat_Onat),U_6517),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6518),U_6519))
| ~ class_Groups_Ocomm__monoid__add(U_6516) ),
inference(variable_rename,[status(thm)],[f_1997_1]) ).
cnf(f_1997_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6516),U_6517),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6518)),hAPP(c_Nat_OSuc,U_6519))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6516),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6516,tc_Nat_Onat),U_6517),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6518),U_6519))
| ~ class_Groups_Ocomm__monoid__add(U_6516) ),
inference(clausify,[status(thm)],[f_1997_2]) ).
fof(f_1998_1,plain,
! [V_na_2,V_k_2,V_m_2,V_f_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_na_2))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__nat__ivl]) ).
fof(f_1998_2,plain,
! [U_6524,U_6523,U_6522,U_6521,U_6520] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6520),U_6521),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6522),U_6523)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6524),U_6523))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6520),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6520,tc_Nat_Onat),U_6521),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_6523))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6522),U_6524))
| ~ class_Groups_Ocomm__monoid__add(U_6520) ),
inference(variable_rename,[status(thm)],[f_1998_1]) ).
cnf(f_1998_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6520),U_6521),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6522),U_6523)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6524),U_6523))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6520),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6520,tc_Nat_Onat),U_6521),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_6523))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6522),U_6524))
| ~ class_Groups_Ocomm__monoid__add(U_6520) ),
inference(clausify,[status(thm)],[f_1998_2]) ).
fof(f_1999_1,plain,
! [V_m_2,V_na_2,V_i_2,T_b] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_na_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_na_2),V_m_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_na_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__diff]) ).
fof(f_1999_2,plain,
! [U_6528,U_6527,U_6526,U_6525] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6525,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6525,U_6526),U_6528)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6525,U_6526),U_6527)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6525,U_6527),U_6528)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6525),U_6526),U_6527))
| ~ class_Orderings_Olinorder(U_6525) ),
inference(variable_rename,[status(thm)],[f_1999_1]) ).
cnf(f_1999_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6525,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6525,U_6526),U_6528)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6525,U_6526),U_6527)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6525,U_6527),U_6528)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6525),U_6526),U_6527))
| ~ class_Orderings_Olinorder(U_6525) ),
inference(clausify,[status(thm)],[f_1999_2]) ).
fof(f_2000_1,plain,
! [V_na_2,V_m_2,V_f_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_na_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_2))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__Suc__ivl]) ).
fof(f_2000_2,plain,
! [U_6532,U_6531,U_6530,U_6529] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6529),U_6530),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6531),hAPP(c_Nat_OSuc,U_6532))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6529),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6529,tc_Nat_Onat),U_6530),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6531,U_6532))
| ~ class_Groups_Ocomm__monoid__add(U_6529) ),
inference(variable_rename,[status(thm)],[f_2000_1]) ).
cnf(f_2000_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6529),U_6530),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6531),hAPP(c_Nat_OSuc,U_6532))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6529),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6529,tc_Nat_Onat),U_6530),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6531,U_6532))
| ~ class_Groups_Ocomm__monoid__add(U_6529) ),
inference(clausify,[status(thm)],[f_2000_2]) ).
fof(f_2001_1,plain,
! [V_na_2,V_k_2,V_m_2,V_f_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),V_k_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_2))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__nat__ivl]) ).
fof(f_2001_2,plain,
! [U_6537,U_6536,U_6535,U_6534,U_6533] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6533),U_6534),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6535),U_6536),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6537),U_6536))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6533),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6533,tc_Nat_Onat),U_6534),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_6536))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6535,U_6537))
| ~ class_Groups_Ocomm__monoid__add(U_6533) ),
inference(variable_rename,[status(thm)],[f_2001_1]) ).
cnf(f_2001_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6533),U_6534),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6535),U_6536),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6537),U_6536))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6533),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6533,tc_Nat_Onat),U_6534),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_6536))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6535,U_6537))
| ~ class_Groups_Ocomm__monoid__add(U_6533) ),
inference(clausify,[status(thm)],[f_2001_2]) ).
fof(f_2002_1,plain,
! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2),
inference(fof_nnf,[status(thm)],[fact_int__setsum]) ).
fof(f_2002_2,plain,
! [U_6540,U_6539,U_6538] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6538,tc_Nat_Onat),U_6539),U_6540)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6538,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_6538),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6539)),U_6540),
inference(variable_rename,[status(thm)],[f_2002_1]) ).
cnf(f_2002_3,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6538,tc_Nat_Onat),U_6539),U_6540)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6538,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_6538),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6539)),U_6540),
inference(clausify,[status(thm)],[f_2002_2]) ).
fof(f_2003_1,plain,
! [V_f_2,V_p_2,V_na_2,V_m_2,T_b] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_na_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_na_2),V_p_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_p_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__add__nat__ivl]) ).
fof(f_2003_2,plain,
! [U_6545,U_6544,U_6543,U_6542,U_6541] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6541),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6541),U_6545),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6542),U_6543))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6541),U_6545),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6543),U_6544))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6541),U_6545),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6542),U_6544))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6543),U_6544))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6542),U_6543))
| ~ class_Groups_Ocomm__monoid__add(U_6541) ),
inference(variable_rename,[status(thm)],[f_2003_1]) ).
cnf(f_2003_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6541),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6541),U_6545),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6542),U_6543))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6541),U_6545),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6543),U_6544))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6541),U_6545),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6542),U_6544))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6543),U_6544))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6542),U_6543))
| ~ class_Groups_Ocomm__monoid__add(U_6541) ),
inference(clausify,[status(thm)],[f_2003_2]) ).
fof(f_2004_1,plain,
! [V_f_2,V_p_2,V_na_2,V_m_2,T_b] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_na_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_na_2),V_p_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_na_2),V_p_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
| ~ class_Groups_Oab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat__ivl]) ).
fof(f_2004_2,plain,
! [U_6550,U_6549,U_6548,U_6547,U_6546] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6546),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6546),U_6550),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6547),U_6549))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6546),U_6550),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6547),U_6548))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6546),U_6550),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6548),U_6549))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6548),U_6549))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6547),U_6548))
| ~ class_Groups_Oab__group__add(U_6546) ),
inference(variable_rename,[status(thm)],[f_2004_1]) ).
cnf(f_2004_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6546),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6546),U_6550),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6547),U_6549))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6546),U_6550),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6547),U_6548))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6546),U_6550),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6548),U_6549))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6548),U_6549))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6547),U_6548))
| ~ class_Groups_Oab__group__add(U_6546) ),
inference(clausify,[status(thm)],[f_2004_2]) ).
fof(f_2005_1,plain,
! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod2_I1_J]) ).
fof(f_2005_2,plain,
! [U_6553,U_6552,U_6551] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6551,tc_Nat_Onat),U_6552),U_6553) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6551,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_6551),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6552)),U_6553)),
inference(variable_rename,[status(thm)],[f_2005_1]) ).
cnf(f_2005_3,plain,
hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6551,tc_Nat_Onat),U_6552),U_6553) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6551,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_6551),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6552)),U_6553)),
inference(clausify,[status(thm)],[f_2005_2]) ).
fof(f_2006_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2))) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastatMost__psubset__iff]) ).
fof(f_2006_2,plain,
! [U_6558,U_6557,U_6556,U_6555,U_6554] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6554,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_6554,U_6555,U_6556)),c_SetInterval_Oord__class_OatLeastAtMost(U_6554,U_6557,U_6558)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6557),U_6558))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6554),U_6556),U_6558))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6554),U_6557),U_6555)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6556),U_6558))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6557),U_6555)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6555),U_6556)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6557),U_6558))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6554),U_6556),U_6558))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6554),U_6557),U_6555)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6556),U_6558))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6557),U_6555)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6555),U_6556)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6554,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_6554,U_6555,U_6556)),c_SetInterval_Oord__class_OatLeastAtMost(U_6554,U_6557,U_6558))) ) )
| ~ class_Orderings_Oorder(U_6554) ),
inference(variable_rename,[status(thm)],[f_2006_1]) ).
cnf(f_2006_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6557),U_6555))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6555),U_6556))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6554,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_6554,U_6555,U_6556)),c_SetInterval_Oord__class_OatLeastAtMost(U_6554,U_6557,U_6558)))
| ~ class_Orderings_Oorder(U_6554) ),
inference(clausify,[status(thm)],[f_2006_2]) ).
cnf(f_2006_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6556),U_6558))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6555),U_6556))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6554,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_6554,U_6555,U_6556)),c_SetInterval_Oord__class_OatLeastAtMost(U_6554,U_6557,U_6558)))
| ~ class_Orderings_Oorder(U_6554) ),
inference(clausify,[status(thm)],[f_2006_2]) ).
cnf(f_2006_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6554),U_6556),U_6558))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6554),U_6557),U_6555))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6555),U_6556))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6554,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_6554,U_6555,U_6556)),c_SetInterval_Oord__class_OatLeastAtMost(U_6554,U_6557,U_6558)))
| ~ class_Orderings_Oorder(U_6554) ),
inference(clausify,[status(thm)],[f_2006_2]) ).
cnf(f_2006_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6557),U_6558))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6554,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_6554,U_6555,U_6556)),c_SetInterval_Oord__class_OatLeastAtMost(U_6554,U_6557,U_6558)))
| ~ class_Orderings_Oorder(U_6554) ),
inference(clausify,[status(thm)],[f_2006_2]) ).
cnf(f_2006_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6555),U_6556))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6557),U_6558))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6554,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_6554,U_6555,U_6556)),c_SetInterval_Oord__class_OatLeastAtMost(U_6554,U_6557,U_6558)))
| ~ class_Orderings_Oorder(U_6554) ),
inference(clausify,[status(thm)],[f_2006_2]) ).
cnf(f_2006_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6554),U_6557),U_6555))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6556),U_6558))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6557),U_6555))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6557),U_6558))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6554,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_6554,U_6555,U_6556)),c_SetInterval_Oord__class_OatLeastAtMost(U_6554,U_6557,U_6558)))
| ~ class_Orderings_Oorder(U_6554) ),
inference(clausify,[status(thm)],[f_2006_2]) ).
cnf(f_2006_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6554),U_6556),U_6558))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6556),U_6558))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6557),U_6555))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6554),U_6557),U_6558))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_6554,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_6554,U_6555,U_6556)),c_SetInterval_Oord__class_OatLeastAtMost(U_6554,U_6557,U_6558)))
| ~ class_Orderings_Oorder(U_6554) ),
inference(clausify,[status(thm)],[f_2006_2]) ).
fof(f_2007_1,plain,
! [V_k_2,V_f_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
| hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(T_b)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0__upt]) ).
fof(f_2007_2,plain,
! [U_6561,U_6560,U_6559] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6559),U_6560),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6561)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6559),U_6560),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6561))
| hAPP(U_6560,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_6559)
| ~ class_Groups_Ocomm__monoid__add(U_6559) ),
inference(variable_rename,[status(thm)],[f_2007_1]) ).
cnf(f_2007_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6559),U_6560),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_6561)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6559),U_6560),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6561))
| hAPP(U_6560,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_6559)
| ~ class_Groups_Ocomm__monoid__add(U_6559) ),
inference(clausify,[status(thm)],[f_2007_2]) ).
fof(f_2008_1,plain,
! [V_f_2,V_na_2,V_m_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_na_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_2))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__head__upt__Suc]) ).
fof(f_2008_2,plain,
! [U_6565,U_6564,U_6563,U_6562] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6562),U_6565),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6563),U_6564)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6562),hAPP(U_6565,U_6563)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6562),U_6565),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6563)),U_6564)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6563),U_6564))
| ~ class_Groups_Ocomm__monoid__add(U_6562) ),
inference(variable_rename,[status(thm)],[f_2008_1]) ).
cnf(f_2008_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6562),U_6565),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6563),U_6564)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6562),hAPP(U_6565,U_6563)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6562),U_6565),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6563)),U_6564)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6563),U_6564))
| ~ class_Groups_Ocomm__monoid__add(U_6562) ),
inference(clausify,[status(thm)],[f_2008_2]) ).
fof(f_2009_1,plain,
! [V_f_2,V_na_2,V_m_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__head__Suc]) ).
fof(f_2009_2,plain,
! [U_6569,U_6568,U_6567,U_6566] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6566),U_6569),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6567,U_6568)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6566),hAPP(U_6569,U_6567)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6566),U_6569),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6567),U_6568)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6567),U_6568))
| ~ class_Groups_Ocomm__monoid__add(U_6566) ),
inference(variable_rename,[status(thm)],[f_2009_1]) ).
cnf(f_2009_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6566),U_6569),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6567,U_6568)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6566),hAPP(U_6569,U_6567)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6566),U_6569),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6567),U_6568)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6567),U_6568))
| ~ class_Groups_Ocomm__monoid__add(U_6566) ),
inference(clausify,[status(thm)],[f_2009_2]) ).
fof(f_2010_1,plain,
! [V_f_2,V_m_2,V_na_2,T_b] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_na_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_na_2))),hAPP(V_f_2,V_na_2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_na_2))) = c_Groups_Ozero__class_Ozero(T_b)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_na_2),V_m_2)) ) )
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__op__ivl__Suc]) ).
fof(f_2010_2,plain,
! [U_6573,U_6572,U_6571,U_6570] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6570),U_6573),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6572),hAPP(c_Nat_OSuc,U_6571))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6570),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6570),U_6573),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6572),U_6571))),hAPP(U_6573,U_6571))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6571),U_6572)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6570),U_6573),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6572),hAPP(c_Nat_OSuc,U_6571))) = c_Groups_Ozero__class_Ozero(U_6570)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6571),U_6572)) ) )
| ~ class_Groups_Ocomm__monoid__add(U_6570) ),
inference(variable_rename,[status(thm)],[f_2010_1]) ).
cnf(f_2010_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6570),U_6573),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6572),hAPP(c_Nat_OSuc,U_6571))) = c_Groups_Ozero__class_Ozero(U_6570)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6571),U_6572))
| ~ class_Groups_Ocomm__monoid__add(U_6570) ),
inference(clausify,[status(thm)],[f_2010_2]) ).
cnf(f_2010_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6570),U_6573),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6572),hAPP(c_Nat_OSuc,U_6571))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6570),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6570),U_6573),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6572),U_6571))),hAPP(U_6573,U_6571))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6571),U_6572))
| ~ class_Groups_Ocomm__monoid__add(U_6570) ),
inference(clausify,[status(thm)],[f_2010_2]) ).
fof(f_2011_1,plain,
! [V_f_2,V_m_2,V_na_2,T_b] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_na_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_na_2)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_na_2))) = c_Groups_Ozero__class_Ozero(T_b)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),V_m_2)) ) )
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__cl__ivl__Suc]) ).
fof(f_2011_2,plain,
! [U_6577,U_6576,U_6575,U_6574] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6574),U_6577),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6576,hAPP(c_Nat_OSuc,U_6575))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6574),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6574),U_6577),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6576,U_6575))),hAPP(U_6577,hAPP(c_Nat_OSuc,U_6575)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6575)),U_6576)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6574),U_6577),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6576,hAPP(c_Nat_OSuc,U_6575))) = c_Groups_Ozero__class_Ozero(U_6574)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6575)),U_6576)) ) )
| ~ class_Groups_Ocomm__monoid__add(U_6574) ),
inference(variable_rename,[status(thm)],[f_2011_1]) ).
cnf(f_2011_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6574),U_6577),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6576,hAPP(c_Nat_OSuc,U_6575))) = c_Groups_Ozero__class_Ozero(U_6574)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6575)),U_6576))
| ~ class_Groups_Ocomm__monoid__add(U_6574) ),
inference(clausify,[status(thm)],[f_2011_2]) ).
cnf(f_2011_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6574),U_6577),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6576,hAPP(c_Nat_OSuc,U_6575))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6574),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6574),U_6577),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6576,U_6575))),hAPP(U_6577,hAPP(c_Nat_OSuc,U_6575)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6575)),U_6576))
| ~ class_Groups_Ocomm__monoid__add(U_6574) ),
inference(clausify,[status(thm)],[f_2011_2]) ).
fof(f_2012_1,plain,
! [V_P_2,V_na_2] :
( ( ! [B_m] :
( hBOOL(hAPP(V_P_2,B_m))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_na_2)) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_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_na_2))) ) )
& ( ! [B_x] :
( hBOOL(hAPP(V_P_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_na_2))) )
| ? [B_m] :
( ~ hBOOL(hAPP(V_P_2,B_m))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_na_2)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_all__nat__less]) ).
fof(f_2012_2,plain,
! [U_6583,U_6582] :
( ( ! [U_6581] :
( hBOOL(hAPP(U_6583,U_6581))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6581),U_6582)) )
| ? [U_6580] :
( ~ hBOOL(hAPP(U_6583,U_6580))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6580),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6582))) ) )
& ( ! [U_6579] :
( hBOOL(hAPP(U_6583,U_6579))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6579),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6582))) )
| ? [U_6578] :
( ~ hBOOL(hAPP(U_6583,U_6578))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6578),U_6582)) ) ) ),
inference(variable_rename,[status(thm)],[f_2012_1]) ).
fof(f_2012_3,plain,
( ! [U_6587,U_6585] :
( ! [U_6581] :
( hBOOL(hAPP(U_6587,U_6581))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6581),U_6585)) )
| ? [U_6580] :
( ~ hBOOL(hAPP(U_6587,U_6580))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6580),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6585))) ) )
& ! [U_6586,U_6584] :
( ! [U_6579] :
( hBOOL(hAPP(U_6586,U_6579))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6579),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6584))) )
| ? [U_6578] :
( ~ hBOOL(hAPP(U_6586,U_6578))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6578),U_6584)) ) ) ),
inference(miniscope,[status(thm)],[f_2012_2]) ).
fof(f_2012_4,plain,
( ! [U_6587,U_6585] :
( ! [U_6581] :
( hBOOL(hAPP(U_6587,U_6581))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6581),U_6585)) )
| ? [U_6580] :
( ~ hBOOL(hAPP(U_6587,U_6580))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6580),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6585))) ) )
& ! [U_6586,U_6584] :
( ! [U_6579] :
( hBOOL(hAPP(U_6586,U_6579))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6579),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6584))) )
| ( ~ hBOOL(hAPP(U_6586,sK93(U_6586,U_6584)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK93(U_6586,U_6584)),U_6584)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_6578,sK93(U_6586,U_6584))],[f_2012_3]) ).
fof(f_2012_5,plain,
( ! [U_6587,U_6585] :
( ! [U_6581] :
( hBOOL(hAPP(U_6587,U_6581))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6581),U_6585)) )
| ( ~ hBOOL(hAPP(U_6587,sK94(U_6587,U_6585)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK94(U_6587,U_6585)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6585))) ) )
& ! [U_6586,U_6584] :
( ! [U_6579] :
( hBOOL(hAPP(U_6586,U_6579))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6579),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6584))) )
| ( ~ hBOOL(hAPP(U_6586,sK93(U_6586,U_6584)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK93(U_6586,U_6584)),U_6584)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_6580,sK94(U_6587,U_6585))],[f_2012_4]) ).
cnf(f_2012_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK93(U_6586,U_6584)),U_6584))
| hBOOL(hAPP(U_6586,U_6579))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6579),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6584))) ),
inference(clausify,[status(thm)],[f_2012_5]) ).
cnf(f_2012_7,plain,
( ~ hBOOL(hAPP(U_6586,sK93(U_6586,U_6584)))
| hBOOL(hAPP(U_6586,U_6579))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6579),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6584))) ),
inference(clausify,[status(thm)],[f_2012_5]) ).
cnf(f_2012_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK94(U_6587,U_6585)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6585)))
| hBOOL(hAPP(U_6587,U_6581))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6581),U_6585)) ),
inference(clausify,[status(thm)],[f_2012_5]) ).
cnf(f_2012_9,plain,
( ~ hBOOL(hAPP(U_6587,sK94(U_6587,U_6585)))
| hBOOL(hAPP(U_6587,U_6581))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6581),U_6585)) ),
inference(clausify,[status(thm)],[f_2012_5]) ).
fof(f_2013_1,plain,
! [V_P_2,V_na_2] :
( ( ? [B_m] :
( hBOOL(hAPP(V_P_2,B_m))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_na_2)) )
| ! [B_x] :
( ~ hBOOL(hAPP(V_P_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_na_2))) ) )
& ( ? [B_x] :
( hBOOL(hAPP(V_P_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_na_2))) )
| ! [B_m] :
( ~ hBOOL(hAPP(V_P_2,B_m))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_na_2)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_ex__nat__less]) ).
fof(f_2013_2,plain,
! [U_6593,U_6592] :
( ( ? [U_6591] :
( hBOOL(hAPP(U_6593,U_6591))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6591),U_6592)) )
| ! [U_6590] :
( ~ hBOOL(hAPP(U_6593,U_6590))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6590),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6592))) ) )
& ( ? [U_6589] :
( hBOOL(hAPP(U_6593,U_6589))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6589),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6592))) )
| ! [U_6588] :
( ~ hBOOL(hAPP(U_6593,U_6588))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6588),U_6592)) ) ) ),
inference(variable_rename,[status(thm)],[f_2013_1]) ).
fof(f_2013_3,plain,
( ! [U_6597,U_6595] :
( ? [U_6591] :
( hBOOL(hAPP(U_6597,U_6591))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6591),U_6595)) )
| ! [U_6590] :
( ~ hBOOL(hAPP(U_6597,U_6590))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6590),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6595))) ) )
& ! [U_6596,U_6594] :
( ? [U_6589] :
( hBOOL(hAPP(U_6596,U_6589))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6589),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6594))) )
| ! [U_6588] :
( ~ hBOOL(hAPP(U_6596,U_6588))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6588),U_6594)) ) ) ),
inference(miniscope,[status(thm)],[f_2013_2]) ).
fof(f_2013_4,plain,
( ! [U_6597,U_6595] :
( ? [U_6591] :
( hBOOL(hAPP(U_6597,U_6591))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6591),U_6595)) )
| ! [U_6590] :
( ~ hBOOL(hAPP(U_6597,U_6590))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6590),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6595))) ) )
& ! [U_6596,U_6594] :
( ( hBOOL(hAPP(U_6596,sK95(U_6596,U_6594)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK95(U_6596,U_6594)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6594))) )
| ! [U_6588] :
( ~ hBOOL(hAPP(U_6596,U_6588))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6588),U_6594)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_6589,sK95(U_6596,U_6594))],[f_2013_3]) ).
fof(f_2013_5,plain,
( ! [U_6597,U_6595] :
( ( hBOOL(hAPP(U_6597,sK96(U_6597,U_6595)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK96(U_6597,U_6595)),U_6595)) )
| ! [U_6590] :
( ~ hBOOL(hAPP(U_6597,U_6590))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6590),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6595))) ) )
& ! [U_6596,U_6594] :
( ( hBOOL(hAPP(U_6596,sK95(U_6596,U_6594)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK95(U_6596,U_6594)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6594))) )
| ! [U_6588] :
( ~ hBOOL(hAPP(U_6596,U_6588))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6588),U_6594)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_6591,sK96(U_6597,U_6595))],[f_2013_4]) ).
cnf(f_2013_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK95(U_6596,U_6594)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6594)))
| ~ hBOOL(hAPP(U_6596,U_6588))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6588),U_6594)) ),
inference(clausify,[status(thm)],[f_2013_5]) ).
cnf(f_2013_7,plain,
( hBOOL(hAPP(U_6596,sK95(U_6596,U_6594)))
| ~ hBOOL(hAPP(U_6596,U_6588))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6588),U_6594)) ),
inference(clausify,[status(thm)],[f_2013_5]) ).
cnf(f_2013_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK96(U_6597,U_6595)),U_6595))
| ~ hBOOL(hAPP(U_6597,U_6590))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6590),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6595))) ),
inference(clausify,[status(thm)],[f_2013_5]) ).
cnf(f_2013_9,plain,
( hBOOL(hAPP(U_6597,sK96(U_6597,U_6595)))
| ~ hBOOL(hAPP(U_6597,U_6590))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6590),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6595))) ),
inference(clausify,[status(thm)],[f_2013_5]) ).
fof(f_2014_1,plain,
! [V_P_2,V_na_2] :
( ( ! [B_m] :
( hBOOL(hAPP(V_P_2,B_m))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_na_2)) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_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_na_2))) ) )
& ( ! [B_x] :
( hBOOL(hAPP(V_P_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_na_2))) )
| ? [B_m] :
( ~ hBOOL(hAPP(V_P_2,B_m))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_na_2)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_all__nat__less__eq]) ).
fof(f_2014_2,plain,
! [U_6603,U_6602] :
( ( ! [U_6601] :
( hBOOL(hAPP(U_6603,U_6601))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6601),U_6602)) )
| ? [U_6600] :
( ~ hBOOL(hAPP(U_6603,U_6600))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6600),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6602))) ) )
& ( ! [U_6599] :
( hBOOL(hAPP(U_6603,U_6599))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6599),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6602))) )
| ? [U_6598] :
( ~ hBOOL(hAPP(U_6603,U_6598))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6598),U_6602)) ) ) ),
inference(variable_rename,[status(thm)],[f_2014_1]) ).
fof(f_2014_3,plain,
( ! [U_6607,U_6605] :
( ! [U_6601] :
( hBOOL(hAPP(U_6607,U_6601))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6601),U_6605)) )
| ? [U_6600] :
( ~ hBOOL(hAPP(U_6607,U_6600))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6600),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6605))) ) )
& ! [U_6606,U_6604] :
( ! [U_6599] :
( hBOOL(hAPP(U_6606,U_6599))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6599),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6604))) )
| ? [U_6598] :
( ~ hBOOL(hAPP(U_6606,U_6598))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6598),U_6604)) ) ) ),
inference(miniscope,[status(thm)],[f_2014_2]) ).
fof(f_2014_4,plain,
( ! [U_6607,U_6605] :
( ! [U_6601] :
( hBOOL(hAPP(U_6607,U_6601))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6601),U_6605)) )
| ? [U_6600] :
( ~ hBOOL(hAPP(U_6607,U_6600))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6600),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6605))) ) )
& ! [U_6606,U_6604] :
( ! [U_6599] :
( hBOOL(hAPP(U_6606,U_6599))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6599),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6604))) )
| ( ~ hBOOL(hAPP(U_6606,sK97(U_6606,U_6604)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK97(U_6606,U_6604)),U_6604)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_6598,sK97(U_6606,U_6604))],[f_2014_3]) ).
fof(f_2014_5,plain,
( ! [U_6607,U_6605] :
( ! [U_6601] :
( hBOOL(hAPP(U_6607,U_6601))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6601),U_6605)) )
| ( ~ hBOOL(hAPP(U_6607,sK98(U_6607,U_6605)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK98(U_6607,U_6605)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6605))) ) )
& ! [U_6606,U_6604] :
( ! [U_6599] :
( hBOOL(hAPP(U_6606,U_6599))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6599),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6604))) )
| ( ~ hBOOL(hAPP(U_6606,sK97(U_6606,U_6604)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK97(U_6606,U_6604)),U_6604)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_6600,sK98(U_6607,U_6605))],[f_2014_4]) ).
cnf(f_2014_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK97(U_6606,U_6604)),U_6604))
| hBOOL(hAPP(U_6606,U_6599))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6599),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6604))) ),
inference(clausify,[status(thm)],[f_2014_5]) ).
cnf(f_2014_7,plain,
( ~ hBOOL(hAPP(U_6606,sK97(U_6606,U_6604)))
| hBOOL(hAPP(U_6606,U_6599))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6599),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6604))) ),
inference(clausify,[status(thm)],[f_2014_5]) ).
cnf(f_2014_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK98(U_6607,U_6605)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6605)))
| hBOOL(hAPP(U_6607,U_6601))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6601),U_6605)) ),
inference(clausify,[status(thm)],[f_2014_5]) ).
cnf(f_2014_9,plain,
( ~ hBOOL(hAPP(U_6607,sK98(U_6607,U_6605)))
| hBOOL(hAPP(U_6607,U_6601))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6601),U_6605)) ),
inference(clausify,[status(thm)],[f_2014_5]) ).
fof(f_2015_1,plain,
! [V_P_2,V_na_2] :
( ( ? [B_m] :
( hBOOL(hAPP(V_P_2,B_m))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_na_2)) )
| ! [B_x] :
( ~ hBOOL(hAPP(V_P_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_na_2))) ) )
& ( ? [B_x] :
( hBOOL(hAPP(V_P_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_na_2))) )
| ! [B_m] :
( ~ hBOOL(hAPP(V_P_2,B_m))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_na_2)) ) ) ),
inference(fof_nnf,[status(thm)],[fact_ex__nat__less__eq]) ).
fof(f_2015_2,plain,
! [U_6613,U_6612] :
( ( ? [U_6611] :
( hBOOL(hAPP(U_6613,U_6611))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6611),U_6612)) )
| ! [U_6610] :
( ~ hBOOL(hAPP(U_6613,U_6610))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6610),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6612))) ) )
& ( ? [U_6609] :
( hBOOL(hAPP(U_6613,U_6609))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6609),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6612))) )
| ! [U_6608] :
( ~ hBOOL(hAPP(U_6613,U_6608))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6608),U_6612)) ) ) ),
inference(variable_rename,[status(thm)],[f_2015_1]) ).
fof(f_2015_3,plain,
( ! [U_6617,U_6615] :
( ? [U_6611] :
( hBOOL(hAPP(U_6617,U_6611))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6611),U_6615)) )
| ! [U_6610] :
( ~ hBOOL(hAPP(U_6617,U_6610))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6610),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6615))) ) )
& ! [U_6616,U_6614] :
( ? [U_6609] :
( hBOOL(hAPP(U_6616,U_6609))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6609),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6614))) )
| ! [U_6608] :
( ~ hBOOL(hAPP(U_6616,U_6608))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6608),U_6614)) ) ) ),
inference(miniscope,[status(thm)],[f_2015_2]) ).
fof(f_2015_4,plain,
( ! [U_6617,U_6615] :
( ? [U_6611] :
( hBOOL(hAPP(U_6617,U_6611))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6611),U_6615)) )
| ! [U_6610] :
( ~ hBOOL(hAPP(U_6617,U_6610))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6610),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6615))) ) )
& ! [U_6616,U_6614] :
( ( hBOOL(hAPP(U_6616,sK99(U_6616,U_6614)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK99(U_6616,U_6614)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6614))) )
| ! [U_6608] :
( ~ hBOOL(hAPP(U_6616,U_6608))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6608),U_6614)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_6609,sK99(U_6616,U_6614))],[f_2015_3]) ).
fof(f_2015_5,plain,
( ! [U_6617,U_6615] :
( ( hBOOL(hAPP(U_6617,sK100(U_6617,U_6615)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK100(U_6617,U_6615)),U_6615)) )
| ! [U_6610] :
( ~ hBOOL(hAPP(U_6617,U_6610))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6610),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6615))) ) )
& ! [U_6616,U_6614] :
( ( hBOOL(hAPP(U_6616,sK99(U_6616,U_6614)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK99(U_6616,U_6614)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6614))) )
| ! [U_6608] :
( ~ hBOOL(hAPP(U_6616,U_6608))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6608),U_6614)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_6611,sK100(U_6617,U_6615))],[f_2015_4]) ).
cnf(f_2015_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK99(U_6616,U_6614)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6614)))
| ~ hBOOL(hAPP(U_6616,U_6608))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6608),U_6614)) ),
inference(clausify,[status(thm)],[f_2015_5]) ).
cnf(f_2015_7,plain,
( hBOOL(hAPP(U_6616,sK99(U_6616,U_6614)))
| ~ hBOOL(hAPP(U_6616,U_6608))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6608),U_6614)) ),
inference(clausify,[status(thm)],[f_2015_5]) ).
cnf(f_2015_8,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK100(U_6617,U_6615)),U_6615))
| ~ hBOOL(hAPP(U_6617,U_6610))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6610),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6615))) ),
inference(clausify,[status(thm)],[f_2015_5]) ).
cnf(f_2015_9,plain,
( hBOOL(hAPP(U_6617,sK100(U_6617,U_6615)))
| ~ hBOOL(hAPP(U_6617,U_6610))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6610),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6615))) ),
inference(clausify,[status(thm)],[f_2015_5]) ).
fof(f_2016_1,plain,
! [V_na_2,V_P_2,V_Q_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_P_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),V_Q_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_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_P_2)),V_Q_2)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_na_2))
| ? [B_x] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Q_2,B_x)),hAPP(V_P_2,B_x))) ),
inference(fof_nnf,[status(thm)],[fact_sum__diff__distrib]) ).
fof(f_2016_2,plain,
! [U_6621,U_6620,U_6619] :
( 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_6620),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6621))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_6619),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6621))) = 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_6620)),U_6619)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6621))
| ? [U_6618] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_6619,U_6618)),hAPP(U_6620,U_6618))) ),
inference(variable_rename,[status(thm)],[f_2016_1]) ).
fof(f_2016_3,plain,
! [U_6621,U_6620,U_6619] :
( 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_6620),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6621))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_6619),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6621))) = 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_6620)),U_6619)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6621))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_6619,sK101(U_6621,U_6620,U_6619))),hAPP(U_6620,sK101(U_6621,U_6620,U_6619)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_6618,sK101(U_6621,U_6620,U_6619))],[f_2016_2]) ).
cnf(f_2016_4,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_6620),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6621))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_6619),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6621))) = 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_6620)),U_6619)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6621))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_6619,sK101(U_6621,U_6620,U_6619))),hAPP(U_6620,sK101(U_6621,U_6620,U_6619)))) ),
inference(clausify,[status(thm)],[f_2016_3]) ).
fof(f_2017_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_2017_2,plain,
! [U_6623,U_6622] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_6622),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6623),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6622,U_6623),
inference(variable_rename,[status(thm)],[f_2017_1]) ).
cnf(f_2017_3,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_6622),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6623),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6622,U_6623),
inference(clausify,[status(thm)],[f_2017_2]) ).
fof(f_2018_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_2018_2,plain,
! [U_6629,U_6628,U_6627] :
( ! [U_6626] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6629),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6626),U_6627)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6629),U_6626))
| ? [U_6625] :
( ? [U_6624] :
( U_6626 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6624),U_6625)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6624),U_6628)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6625),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6627))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6627)) ),
inference(variable_rename,[status(thm)],[f_2018_1]) ).
fof(f_2018_3,plain,
! [U_6629,U_6628,U_6627] :
( ! [U_6626] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6629),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6626),U_6627)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6629),U_6626))
| ( ? [U_6624] :
( U_6626 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6624),sK102(U_6629,U_6628,U_6627,U_6626))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6624),U_6628)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK102(U_6629,U_6628,U_6627,U_6626)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6627))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6627)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_6625,sK102(U_6629,U_6628,U_6627,U_6626))],[f_2018_2]) ).
fof(f_2018_4,plain,
! [U_6629,U_6628,U_6627] :
( ! [U_6626] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6629),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6626),U_6627)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6629),U_6626))
| ( U_6626 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK103(U_6629,U_6628,U_6627,U_6626)),sK102(U_6629,U_6628,U_6627,U_6626))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK103(U_6629,U_6628,U_6627,U_6626)),U_6628))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK102(U_6629,U_6628,U_6627,U_6626)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6627))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6627)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_6624,sK103(U_6629,U_6628,U_6627,U_6626))],[f_2018_3]) ).
cnf(f_2018_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK102(U_6629,U_6628,U_6627,U_6626)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6627)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6629),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6626),U_6627)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6629),U_6626))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6627)) ),
inference(clausify,[status(thm)],[f_2018_4]) ).
cnf(f_2018_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK103(U_6629,U_6628,U_6627,U_6626)),U_6628))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6629),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6626),U_6627)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6629),U_6626))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6627)) ),
inference(clausify,[status(thm)],[f_2018_4]) ).
cnf(f_2018_7,plain,
( U_6626 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK103(U_6629,U_6628,U_6627,U_6626)),sK102(U_6629,U_6628,U_6627,U_6626))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6629),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6626),U_6627)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6629),U_6626))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6627)) ),
inference(clausify,[status(thm)],[f_2018_4]) ).
fof(f_2019_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_2019_2,plain,
! [U_6635,U_6634,U_6633] :
( ! [U_6632] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6632),U_6633)),U_6635))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6632),U_6635))
| ? [U_6631] :
( ? [U_6630] :
( U_6632 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6630),U_6631)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6630),U_6634)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6631),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6633))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6633)) ),
inference(variable_rename,[status(thm)],[f_2019_1]) ).
fof(f_2019_3,plain,
! [U_6635,U_6634,U_6633] :
( ! [U_6632] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6632),U_6633)),U_6635))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6632),U_6635))
| ( ? [U_6630] :
( U_6632 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6630),sK104(U_6635,U_6634,U_6633,U_6632))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6630),U_6634)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK104(U_6635,U_6634,U_6633,U_6632)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6633))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6633)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_6631,sK104(U_6635,U_6634,U_6633,U_6632))],[f_2019_2]) ).
fof(f_2019_4,plain,
! [U_6635,U_6634,U_6633] :
( ! [U_6632] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6632),U_6633)),U_6635))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6632),U_6635))
| ( U_6632 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK105(U_6635,U_6634,U_6633,U_6632)),sK104(U_6635,U_6634,U_6633,U_6632))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK105(U_6635,U_6634,U_6633,U_6632)),U_6634))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK104(U_6635,U_6634,U_6633,U_6632)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6633))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6633)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_6630,sK105(U_6635,U_6634,U_6633,U_6632))],[f_2019_3]) ).
cnf(f_2019_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK104(U_6635,U_6634,U_6633,U_6632)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6633)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6632),U_6633)),U_6635))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6632),U_6635))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6633)) ),
inference(clausify,[status(thm)],[f_2019_4]) ).
cnf(f_2019_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK105(U_6635,U_6634,U_6633,U_6632)),U_6634))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6632),U_6633)),U_6635))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6632),U_6635))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6633)) ),
inference(clausify,[status(thm)],[f_2019_4]) ).
cnf(f_2019_7,plain,
( U_6632 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK105(U_6635,U_6634,U_6633,U_6632)),sK104(U_6635,U_6634,U_6633,U_6632))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6632),U_6633)),U_6635))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6632),U_6635))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6633)) ),
inference(clausify,[status(thm)],[f_2019_4]) ).
fof(f_2020_1,plain,
! [V_P_2,V_d_2] :
( ( ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
| ! [B_x] :
( ~ hBOOL(hAPP(V_P_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_P_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_P_2,B_x1)) ) )
| ? [B_x,B_k] :
( ( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(V_P_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_P_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_P_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_2020_2,plain,
! [U_6643,U_6642] :
( ( ( ? [U_6641] : hBOOL(hAPP(U_6643,U_6641))
| ! [U_6640] :
( ~ hBOOL(hAPP(U_6643,U_6640))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6640),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642))) ) )
& ( ? [U_6639] :
( hBOOL(hAPP(U_6643,U_6639))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6639),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642))) )
| ! [U_6638] : ~ hBOOL(hAPP(U_6643,U_6638)) ) )
| ? [U_6637,U_6636] :
( ( ~ hBOOL(hAPP(U_6643,U_6637))
& hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6636),U_6642)))) )
| ( ~ hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6636),U_6642))))
& hBOOL(hAPP(U_6643,U_6637)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6642)) ),
inference(variable_rename,[status(thm)],[f_2020_1]) ).
fof(f_2020_3,plain,
! [U_6643,U_6642] :
( ( ( ? [U_6641] : hBOOL(hAPP(U_6643,U_6641))
| ! [U_6640] :
( ~ hBOOL(hAPP(U_6643,U_6640))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6640),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642))) ) )
& ( ? [U_6639] :
( hBOOL(hAPP(U_6643,U_6639))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6639),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642))) )
| ! [U_6638] : ~ hBOOL(hAPP(U_6643,U_6638)) ) )
| ? [U_6647] :
( ? [U_6645] : hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6645),U_6642))))
& ~ hBOOL(hAPP(U_6643,U_6647)) )
| ? [U_6646] :
( ? [U_6644] : ~ hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6646),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6644),U_6642))))
& hBOOL(hAPP(U_6643,U_6646)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6642)) ),
inference(miniscope,[status(thm)],[f_2020_2]) ).
fof(f_2020_4,plain,
! [U_6643,U_6642] :
( ( ( ? [U_6641] : hBOOL(hAPP(U_6643,U_6641))
| ! [U_6640] :
( ~ hBOOL(hAPP(U_6643,U_6640))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6640),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642))) ) )
& ( ? [U_6639] :
( hBOOL(hAPP(U_6643,U_6639))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6639),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642))) )
| ! [U_6638] : ~ hBOOL(hAPP(U_6643,U_6638)) ) )
| ? [U_6647] :
( ? [U_6645] : hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6645),U_6642))))
& ~ hBOOL(hAPP(U_6643,U_6647)) )
| ( ? [U_6644] : ~ hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK106(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6644),U_6642))))
& hBOOL(hAPP(U_6643,sK106(U_6643,U_6642))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6642)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_6646,sK106(U_6643,U_6642))],[f_2020_3]) ).
fof(f_2020_5,plain,
! [U_6643,U_6642] :
( ( ( ? [U_6641] : hBOOL(hAPP(U_6643,U_6641))
| ! [U_6640] :
( ~ hBOOL(hAPP(U_6643,U_6640))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6640),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642))) ) )
& ( ? [U_6639] :
( hBOOL(hAPP(U_6643,U_6639))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6639),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642))) )
| ! [U_6638] : ~ hBOOL(hAPP(U_6643,U_6638)) ) )
| ? [U_6647] :
( ? [U_6645] : hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6645),U_6642))))
& ~ hBOOL(hAPP(U_6643,U_6647)) )
| ( ~ hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK106(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK107(U_6643,U_6642)),U_6642))))
& hBOOL(hAPP(U_6643,sK106(U_6643,U_6642))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6642)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_6644,sK107(U_6643,U_6642))],[f_2020_4]) ).
fof(f_2020_6,plain,
! [U_6643,U_6642] :
( ( ( ? [U_6641] : hBOOL(hAPP(U_6643,U_6641))
| ! [U_6640] :
( ~ hBOOL(hAPP(U_6643,U_6640))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6640),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642))) ) )
& ( ? [U_6639] :
( hBOOL(hAPP(U_6643,U_6639))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6639),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642))) )
| ! [U_6638] : ~ hBOOL(hAPP(U_6643,U_6638)) ) )
| ( ? [U_6645] : hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK108(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6645),U_6642))))
& ~ hBOOL(hAPP(U_6643,sK108(U_6643,U_6642))) )
| ( ~ hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK106(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK107(U_6643,U_6642)),U_6642))))
& hBOOL(hAPP(U_6643,sK106(U_6643,U_6642))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6642)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_6647,sK108(U_6643,U_6642))],[f_2020_5]) ).
fof(f_2020_7,plain,
! [U_6643,U_6642] :
( ( ( ? [U_6641] : hBOOL(hAPP(U_6643,U_6641))
| ! [U_6640] :
( ~ hBOOL(hAPP(U_6643,U_6640))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6640),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642))) ) )
& ( ? [U_6639] :
( hBOOL(hAPP(U_6643,U_6639))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6639),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642))) )
| ! [U_6638] : ~ hBOOL(hAPP(U_6643,U_6638)) ) )
| ( hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK108(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK109(U_6643,U_6642)),U_6642))))
& ~ hBOOL(hAPP(U_6643,sK108(U_6643,U_6642))) )
| ( ~ hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK106(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK107(U_6643,U_6642)),U_6642))))
& hBOOL(hAPP(U_6643,sK106(U_6643,U_6642))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6642)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_6645,sK109(U_6643,U_6642))],[f_2020_6]) ).
fof(f_2020_8,plain,
! [U_6643,U_6642] :
( ( ( ? [U_6641] : hBOOL(hAPP(U_6643,U_6641))
| ! [U_6640] :
( ~ hBOOL(hAPP(U_6643,U_6640))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6640),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642))) ) )
& ( ( hBOOL(hAPP(U_6643,sK110(U_6643,U_6642)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK110(U_6643,U_6642)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642))) )
| ! [U_6638] : ~ hBOOL(hAPP(U_6643,U_6638)) ) )
| ( hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK108(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK109(U_6643,U_6642)),U_6642))))
& ~ hBOOL(hAPP(U_6643,sK108(U_6643,U_6642))) )
| ( ~ hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK106(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK107(U_6643,U_6642)),U_6642))))
& hBOOL(hAPP(U_6643,sK106(U_6643,U_6642))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6642)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_6639,sK110(U_6643,U_6642))],[f_2020_7]) ).
fof(f_2020_9,plain,
! [U_6643,U_6642] :
( ( ( hBOOL(hAPP(U_6643,sK111(U_6643,U_6642)))
| ! [U_6640] :
( ~ hBOOL(hAPP(U_6643,U_6640))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6640),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642))) ) )
& ( ( hBOOL(hAPP(U_6643,sK110(U_6643,U_6642)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK110(U_6643,U_6642)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642))) )
| ! [U_6638] : ~ hBOOL(hAPP(U_6643,U_6638)) ) )
| ( hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK108(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK109(U_6643,U_6642)),U_6642))))
& ~ hBOOL(hAPP(U_6643,sK108(U_6643,U_6642))) )
| ( ~ hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK106(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK107(U_6643,U_6642)),U_6642))))
& hBOOL(hAPP(U_6643,sK106(U_6643,U_6642))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6642)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_6641,sK111(U_6643,U_6642))],[f_2020_8]) ).
cnf(f_2020_10,plain,
( ~ hBOOL(hAPP(U_6643,sK108(U_6643,U_6642)))
| hBOOL(hAPP(U_6643,sK106(U_6643,U_6642)))
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK110(U_6643,U_6642)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642)))
| ~ hBOOL(hAPP(U_6643,U_6638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6642)) ),
inference(clausify,[status(thm)],[f_2020_9]) ).
cnf(f_2020_11,plain,
( hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK108(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK109(U_6643,U_6642)),U_6642))))
| hBOOL(hAPP(U_6643,sK106(U_6643,U_6642)))
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK110(U_6643,U_6642)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642)))
| ~ hBOOL(hAPP(U_6643,U_6638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6642)) ),
inference(clausify,[status(thm)],[f_2020_9]) ).
cnf(f_2020_12,plain,
( ~ hBOOL(hAPP(U_6643,sK108(U_6643,U_6642)))
| hBOOL(hAPP(U_6643,sK106(U_6643,U_6642)))
| hBOOL(hAPP(U_6643,sK110(U_6643,U_6642)))
| ~ hBOOL(hAPP(U_6643,U_6638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6642)) ),
inference(clausify,[status(thm)],[f_2020_9]) ).
cnf(f_2020_13,plain,
( hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK108(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK109(U_6643,U_6642)),U_6642))))
| hBOOL(hAPP(U_6643,sK106(U_6643,U_6642)))
| hBOOL(hAPP(U_6643,sK110(U_6643,U_6642)))
| ~ hBOOL(hAPP(U_6643,U_6638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6642)) ),
inference(clausify,[status(thm)],[f_2020_9]) ).
cnf(f_2020_14,plain,
( ~ hBOOL(hAPP(U_6643,sK108(U_6643,U_6642)))
| ~ hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK106(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK107(U_6643,U_6642)),U_6642))))
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK110(U_6643,U_6642)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642)))
| ~ hBOOL(hAPP(U_6643,U_6638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6642)) ),
inference(clausify,[status(thm)],[f_2020_9]) ).
cnf(f_2020_15,plain,
( hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK108(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK109(U_6643,U_6642)),U_6642))))
| ~ hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK106(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK107(U_6643,U_6642)),U_6642))))
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK110(U_6643,U_6642)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642)))
| ~ hBOOL(hAPP(U_6643,U_6638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6642)) ),
inference(clausify,[status(thm)],[f_2020_9]) ).
cnf(f_2020_16,plain,
( ~ hBOOL(hAPP(U_6643,sK108(U_6643,U_6642)))
| ~ hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK106(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK107(U_6643,U_6642)),U_6642))))
| hBOOL(hAPP(U_6643,sK110(U_6643,U_6642)))
| ~ hBOOL(hAPP(U_6643,U_6638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6642)) ),
inference(clausify,[status(thm)],[f_2020_9]) ).
cnf(f_2020_17,plain,
( hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK108(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK109(U_6643,U_6642)),U_6642))))
| ~ hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK106(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK107(U_6643,U_6642)),U_6642))))
| hBOOL(hAPP(U_6643,sK110(U_6643,U_6642)))
| ~ hBOOL(hAPP(U_6643,U_6638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6642)) ),
inference(clausify,[status(thm)],[f_2020_9]) ).
cnf(f_2020_18,plain,
( ~ hBOOL(hAPP(U_6643,sK108(U_6643,U_6642)))
| hBOOL(hAPP(U_6643,sK106(U_6643,U_6642)))
| hBOOL(hAPP(U_6643,sK111(U_6643,U_6642)))
| ~ hBOOL(hAPP(U_6643,U_6640))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6640),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6642)) ),
inference(clausify,[status(thm)],[f_2020_9]) ).
cnf(f_2020_19,plain,
( hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK108(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK109(U_6643,U_6642)),U_6642))))
| hBOOL(hAPP(U_6643,sK106(U_6643,U_6642)))
| hBOOL(hAPP(U_6643,sK111(U_6643,U_6642)))
| ~ hBOOL(hAPP(U_6643,U_6640))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6640),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6642)) ),
inference(clausify,[status(thm)],[f_2020_9]) ).
cnf(f_2020_20,plain,
( ~ hBOOL(hAPP(U_6643,sK108(U_6643,U_6642)))
| ~ hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK106(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK107(U_6643,U_6642)),U_6642))))
| hBOOL(hAPP(U_6643,sK111(U_6643,U_6642)))
| ~ hBOOL(hAPP(U_6643,U_6640))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6640),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6642)) ),
inference(clausify,[status(thm)],[f_2020_9]) ).
cnf(f_2020_21,plain,
( hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK108(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK109(U_6643,U_6642)),U_6642))))
| ~ hBOOL(hAPP(U_6643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK106(U_6643,U_6642)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK107(U_6643,U_6642)),U_6642))))
| hBOOL(hAPP(U_6643,sK111(U_6643,U_6642)))
| ~ hBOOL(hAPP(U_6643,U_6640))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6640),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6642)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6642)) ),
inference(clausify,[status(thm)],[f_2020_9]) ).
fof(f_2021_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_2021_2,plain,
! [U_6653,U_6652,U_6651] :
( ! [U_6650] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6650),U_6651)),U_6653))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6650),U_6653))
| ? [U_6649] :
( ? [U_6648] :
( U_6650 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6648),U_6649)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6648),U_6652)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6649),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6651))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6651)) ),
inference(variable_rename,[status(thm)],[f_2021_1]) ).
fof(f_2021_3,plain,
! [U_6653,U_6652,U_6651] :
( ! [U_6650] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6650),U_6651)),U_6653))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6650),U_6653))
| ( ? [U_6648] :
( U_6650 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6648),sK112(U_6653,U_6652,U_6651,U_6650))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6648),U_6652)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK112(U_6653,U_6652,U_6651,U_6650)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6651))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6651)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_6649,sK112(U_6653,U_6652,U_6651,U_6650))],[f_2021_2]) ).
fof(f_2021_4,plain,
! [U_6653,U_6652,U_6651] :
( ! [U_6650] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6650),U_6651)),U_6653))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6650),U_6653))
| ( U_6650 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK113(U_6653,U_6652,U_6651,U_6650)),sK112(U_6653,U_6652,U_6651,U_6650))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK113(U_6653,U_6652,U_6651,U_6650)),U_6652))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK112(U_6653,U_6652,U_6651,U_6650)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6651))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6651)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_6648,sK113(U_6653,U_6652,U_6651,U_6650))],[f_2021_3]) ).
cnf(f_2021_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK112(U_6653,U_6652,U_6651,U_6650)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6651)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6650),U_6651)),U_6653))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6650),U_6653))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6651)) ),
inference(clausify,[status(thm)],[f_2021_4]) ).
cnf(f_2021_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK113(U_6653,U_6652,U_6651,U_6650)),U_6652))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6650),U_6651)),U_6653))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6650),U_6653))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6651)) ),
inference(clausify,[status(thm)],[f_2021_4]) ).
cnf(f_2021_7,plain,
( U_6650 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK113(U_6653,U_6652,U_6651,U_6650)),sK112(U_6653,U_6652,U_6651,U_6650))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6650),U_6651)),U_6653))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6650),U_6653))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6651)) ),
inference(clausify,[status(thm)],[f_2021_4]) ).
fof(f_2022_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_2022_2,plain,
! [U_6659,U_6658,U_6657] :
( ! [U_6656] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6656),U_6657)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6659),U_6656))
| ? [U_6655] :
( ? [U_6654] :
( U_6656 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6654),U_6655)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6654),U_6658)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6655),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6657))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6657)) ),
inference(variable_rename,[status(thm)],[f_2022_1]) ).
fof(f_2022_3,plain,
! [U_6659,U_6658,U_6657] :
( ! [U_6656] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6656),U_6657)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6659),U_6656))
| ( ? [U_6654] :
( U_6656 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6654),sK114(U_6659,U_6658,U_6657,U_6656))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6654),U_6658)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK114(U_6659,U_6658,U_6657,U_6656)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6657))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6657)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_6655,sK114(U_6659,U_6658,U_6657,U_6656))],[f_2022_2]) ).
fof(f_2022_4,plain,
! [U_6659,U_6658,U_6657] :
( ! [U_6656] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6656),U_6657)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6659),U_6656))
| ( U_6656 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK115(U_6659,U_6658,U_6657,U_6656)),sK114(U_6659,U_6658,U_6657,U_6656))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK115(U_6659,U_6658,U_6657,U_6656)),U_6658))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK114(U_6659,U_6658,U_6657,U_6656)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6657))) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6657)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_6654,sK115(U_6659,U_6658,U_6657,U_6656))],[f_2022_3]) ).
cnf(f_2022_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK114(U_6659,U_6658,U_6657,U_6656)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6657)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6656),U_6657)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6659),U_6656))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6657)) ),
inference(clausify,[status(thm)],[f_2022_4]) ).
cnf(f_2022_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK115(U_6659,U_6658,U_6657,U_6656)),U_6658))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6656),U_6657)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6659),U_6656))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6657)) ),
inference(clausify,[status(thm)],[f_2022_4]) ).
cnf(f_2022_7,plain,
( U_6656 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK115(U_6659,U_6658,U_6657,U_6656)),sK114(U_6659,U_6658,U_6657,U_6656))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6656),U_6657)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6659),U_6656))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6657)) ),
inference(clausify,[status(thm)],[f_2022_4]) ).
fof(f_2023_1,plain,
! [V_t_2,V_B_2,V_D_2,V_d_2] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
| ? [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_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2)) ),
inference(fof_nnf,[status(thm)],[fact_bset_I9_J]) ).
fof(f_2023_2,plain,
! [U_6666,U_6665,U_6664,U_6663] :
( ! [U_6662] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6663),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6662),U_6664)),U_6666)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6663),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6662),U_6666)))
| ? [U_6661] :
( ? [U_6660] :
( U_6662 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6660),U_6661)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6660),U_6665)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6661),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6664))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6663),U_6664)) ),
inference(variable_rename,[status(thm)],[f_2023_1]) ).
fof(f_2023_3,plain,
! [U_6666,U_6665,U_6664,U_6663] :
( ! [U_6662] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6663),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6662),U_6664)),U_6666)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6663),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6662),U_6666)))
| ( ? [U_6660] :
( U_6662 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6660),sK116(U_6666,U_6665,U_6664,U_6663,U_6662))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6660),U_6665)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK116(U_6666,U_6665,U_6664,U_6663,U_6662)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6664))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6663),U_6664)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_6661,sK116(U_6666,U_6665,U_6664,U_6663,U_6662))],[f_2023_2]) ).
fof(f_2023_4,plain,
! [U_6666,U_6665,U_6664,U_6663] :
( ! [U_6662] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6663),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6662),U_6664)),U_6666)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6663),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6662),U_6666)))
| ( U_6662 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK117(U_6666,U_6665,U_6664,U_6663,U_6662)),sK116(U_6666,U_6665,U_6664,U_6663,U_6662))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK117(U_6666,U_6665,U_6664,U_6663,U_6662)),U_6665))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK116(U_6666,U_6665,U_6664,U_6663,U_6662)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6664))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6663),U_6664)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_6660,sK117(U_6666,U_6665,U_6664,U_6663,U_6662))],[f_2023_3]) ).
cnf(f_2023_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK116(U_6666,U_6665,U_6664,U_6663,U_6662)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6664)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6663),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6662),U_6664)),U_6666)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6663),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6662),U_6666)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6663),U_6664)) ),
inference(clausify,[status(thm)],[f_2023_4]) ).
cnf(f_2023_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK117(U_6666,U_6665,U_6664,U_6663,U_6662)),U_6665))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6663),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6662),U_6664)),U_6666)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6663),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6662),U_6666)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6663),U_6664)) ),
inference(clausify,[status(thm)],[f_2023_4]) ).
cnf(f_2023_7,plain,
( U_6662 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK117(U_6666,U_6665,U_6664,U_6663,U_6662)),sK116(U_6666,U_6665,U_6664,U_6663,U_6662))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6663),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6662),U_6664)),U_6666)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6663),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6662),U_6666)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6663),U_6664)) ),
inference(clausify,[status(thm)],[f_2023_4]) ).
fof(f_2024_1,plain,
! [V_t_2,V_A_2,V_D_2,V_d_2] :
( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
| ? [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_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2)) ),
inference(fof_nnf,[status(thm)],[fact_aset_I9_J]) ).
fof(f_2024_2,plain,
! [U_6673,U_6672,U_6671,U_6670] :
( ! [U_6669] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6670),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6669),U_6671)),U_6673)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6670),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6669),U_6673)))
| ? [U_6668] :
( ? [U_6667] :
( U_6669 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6667),U_6668)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6667),U_6672)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6668),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6671))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6670),U_6671)) ),
inference(variable_rename,[status(thm)],[f_2024_1]) ).
fof(f_2024_3,plain,
! [U_6673,U_6672,U_6671,U_6670] :
( ! [U_6669] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6670),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6669),U_6671)),U_6673)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6670),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6669),U_6673)))
| ( ? [U_6667] :
( U_6669 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6667),sK118(U_6673,U_6672,U_6671,U_6670,U_6669))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6667),U_6672)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK118(U_6673,U_6672,U_6671,U_6670,U_6669)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6671))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6670),U_6671)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_6668,sK118(U_6673,U_6672,U_6671,U_6670,U_6669))],[f_2024_2]) ).
fof(f_2024_4,plain,
! [U_6673,U_6672,U_6671,U_6670] :
( ! [U_6669] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6670),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6669),U_6671)),U_6673)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6670),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6669),U_6673)))
| ( U_6669 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK119(U_6673,U_6672,U_6671,U_6670,U_6669)),sK118(U_6673,U_6672,U_6671,U_6670,U_6669))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK119(U_6673,U_6672,U_6671,U_6670,U_6669)),U_6672))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK118(U_6673,U_6672,U_6671,U_6670,U_6669)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6671))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6670),U_6671)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_6667,sK119(U_6673,U_6672,U_6671,U_6670,U_6669))],[f_2024_3]) ).
cnf(f_2024_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK118(U_6673,U_6672,U_6671,U_6670,U_6669)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6671)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6670),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6669),U_6671)),U_6673)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6670),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6669),U_6673)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6670),U_6671)) ),
inference(clausify,[status(thm)],[f_2024_4]) ).
cnf(f_2024_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK119(U_6673,U_6672,U_6671,U_6670,U_6669)),U_6672))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6670),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6669),U_6671)),U_6673)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6670),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6669),U_6673)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6670),U_6671)) ),
inference(clausify,[status(thm)],[f_2024_4]) ).
cnf(f_2024_7,plain,
( U_6669 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK119(U_6673,U_6672,U_6671,U_6670,U_6669)),sK118(U_6673,U_6672,U_6671,U_6670,U_6669))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6670),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6669),U_6671)),U_6673)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6670),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6669),U_6673)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6670),U_6671)) ),
inference(clausify,[status(thm)],[f_2024_4]) ).
fof(f_2025_1,plain,
! [V_t_2,V_B_2,V_D_2,V_d_2] :
( ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
| ? [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_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2)) ),
inference(fof_nnf,[status(thm)],[fact_bset_I10_J]) ).
fof(f_2025_2,plain,
! [U_6680,U_6679,U_6678,U_6677] :
( ! [U_6676] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6676),U_6678)),U_6680)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6676),U_6680)))
| ? [U_6675] :
( ? [U_6674] :
( U_6676 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6674),U_6675)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6674),U_6679)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6675),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6678))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6677),U_6678)) ),
inference(variable_rename,[status(thm)],[f_2025_1]) ).
fof(f_2025_3,plain,
! [U_6680,U_6679,U_6678,U_6677] :
( ! [U_6676] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6676),U_6678)),U_6680)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6676),U_6680)))
| ( ? [U_6674] :
( U_6676 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6674),sK120(U_6680,U_6679,U_6678,U_6677,U_6676))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6674),U_6679)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK120(U_6680,U_6679,U_6678,U_6677,U_6676)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6678))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6677),U_6678)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_6675,sK120(U_6680,U_6679,U_6678,U_6677,U_6676))],[f_2025_2]) ).
fof(f_2025_4,plain,
! [U_6680,U_6679,U_6678,U_6677] :
( ! [U_6676] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6676),U_6678)),U_6680)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6676),U_6680)))
| ( U_6676 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK121(U_6680,U_6679,U_6678,U_6677,U_6676)),sK120(U_6680,U_6679,U_6678,U_6677,U_6676))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK121(U_6680,U_6679,U_6678,U_6677,U_6676)),U_6679))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK120(U_6680,U_6679,U_6678,U_6677,U_6676)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6678))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6677),U_6678)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_6674,sK121(U_6680,U_6679,U_6678,U_6677,U_6676))],[f_2025_3]) ).
cnf(f_2025_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK120(U_6680,U_6679,U_6678,U_6677,U_6676)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6678)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6676),U_6678)),U_6680)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6676),U_6680)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6677),U_6678)) ),
inference(clausify,[status(thm)],[f_2025_4]) ).
cnf(f_2025_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK121(U_6680,U_6679,U_6678,U_6677,U_6676)),U_6679))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6676),U_6678)),U_6680)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6676),U_6680)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6677),U_6678)) ),
inference(clausify,[status(thm)],[f_2025_4]) ).
cnf(f_2025_7,plain,
( U_6676 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK121(U_6680,U_6679,U_6678,U_6677,U_6676)),sK120(U_6680,U_6679,U_6678,U_6677,U_6676))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6676),U_6678)),U_6680)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6677),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6676),U_6680)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6677),U_6678)) ),
inference(clausify,[status(thm)],[f_2025_4]) ).
fof(f_2026_1,plain,
! [V_t_2,V_A_2,V_D_2,V_d_2] :
( ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2)),V_t_2)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_t_2)))
| ? [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_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_D_2)) ),
inference(fof_nnf,[status(thm)],[fact_aset_I10_J]) ).
fof(f_2026_2,plain,
! [U_6687,U_6686,U_6685,U_6684] :
( ! [U_6683] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6684),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6683),U_6685)),U_6687)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6684),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6683),U_6687)))
| ? [U_6682] :
( ? [U_6681] :
( U_6683 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6681),U_6682)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6681),U_6686)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6682),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6685))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6684),U_6685)) ),
inference(variable_rename,[status(thm)],[f_2026_1]) ).
fof(f_2026_3,plain,
! [U_6687,U_6686,U_6685,U_6684] :
( ! [U_6683] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6684),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6683),U_6685)),U_6687)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6684),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6683),U_6687)))
| ( ? [U_6681] :
( U_6683 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6681),sK122(U_6687,U_6686,U_6685,U_6684,U_6683))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6681),U_6686)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK122(U_6687,U_6686,U_6685,U_6684,U_6683)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6685))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6684),U_6685)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_6682,sK122(U_6687,U_6686,U_6685,U_6684,U_6683))],[f_2026_2]) ).
fof(f_2026_4,plain,
! [U_6687,U_6686,U_6685,U_6684] :
( ! [U_6683] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6684),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6683),U_6685)),U_6687)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6684),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6683),U_6687)))
| ( U_6683 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK123(U_6687,U_6686,U_6685,U_6684,U_6683)),sK122(U_6687,U_6686,U_6685,U_6684,U_6683))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK123(U_6687,U_6686,U_6685,U_6684,U_6683)),U_6686))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK122(U_6687,U_6686,U_6685,U_6684,U_6683)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6685))) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6684),U_6685)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_6681,sK123(U_6687,U_6686,U_6685,U_6684,U_6683))],[f_2026_3]) ).
cnf(f_2026_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK122(U_6687,U_6686,U_6685,U_6684,U_6683)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_6685)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6684),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6683),U_6685)),U_6687)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6684),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6683),U_6687)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6684),U_6685)) ),
inference(clausify,[status(thm)],[f_2026_4]) ).
cnf(f_2026_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK123(U_6687,U_6686,U_6685,U_6684,U_6683)),U_6686))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6684),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6683),U_6685)),U_6687)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6684),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6683),U_6687)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6684),U_6685)) ),
inference(clausify,[status(thm)],[f_2026_4]) ).
cnf(f_2026_7,plain,
( U_6683 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK123(U_6687,U_6686,U_6685,U_6684,U_6683)),sK122(U_6687,U_6686,U_6685,U_6684,U_6683))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6684),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6683),U_6685)),U_6687)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6684),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6683),U_6687)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_6684),U_6685)) ),
inference(clausify,[status(thm)],[f_2026_4]) ).
fof(f_2027_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_2027_2,plain,
! [U_6688] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6688) = 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_6688)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6688)) ),
inference(variable_rename,[status(thm)],[f_2027_1]) ).
cnf(f_2027_3,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6688) = 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_6688)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6688)) ),
inference(clausify,[status(thm)],[f_2027_2]) ).
fof(f_2028_1,plain,
! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_image__mono]) ).
fof(f_2028_2,plain,
! [U_6693,U_6692,U_6691,U_6690,U_6689] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6692,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_6689,U_6692,U_6693),U_6690)),hAPP(c_Set_Oimage(U_6689,U_6692,U_6693),U_6691)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6689,tc_HOL_Obool)),U_6690),U_6691)) ),
inference(variable_rename,[status(thm)],[f_2028_1]) ).
cnf(f_2028_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6692,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_6689,U_6692,U_6693),U_6690)),hAPP(c_Set_Oimage(U_6689,U_6692,U_6693),U_6691)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6689,tc_HOL_Obool)),U_6690),U_6691)) ),
inference(clausify,[status(thm)],[f_2028_2]) ).
fof(f_2029_1,plain,
! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
| ! [B_AA] :
( V_B_2 != hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) ) )
& ( ? [B_AA] :
( V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_subset__image__iff]) ).
fof(f_2029_2,plain,
! [U_6700,U_6699,U_6698,U_6697,U_6696] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6696,tc_HOL_Obool)),U_6697),hAPP(c_Set_Oimage(U_6698,U_6696,U_6699),U_6700)))
| ! [U_6695] :
( U_6697 != hAPP(c_Set_Oimage(U_6698,U_6696,U_6699),U_6695)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6698,tc_HOL_Obool)),U_6695),U_6700)) ) )
& ( ? [U_6694] :
( U_6697 = hAPP(c_Set_Oimage(U_6698,U_6696,U_6699),U_6694)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6698,tc_HOL_Obool)),U_6694),U_6700)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6696,tc_HOL_Obool)),U_6697),hAPP(c_Set_Oimage(U_6698,U_6696,U_6699),U_6700))) ) ),
inference(variable_rename,[status(thm)],[f_2029_1]) ).
fof(f_2029_3,plain,
( ! [U_6710,U_6708,U_6706,U_6704,U_6702] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6702,tc_HOL_Obool)),U_6704),hAPP(c_Set_Oimage(U_6706,U_6702,U_6708),U_6710)))
| ! [U_6695] :
( U_6704 != hAPP(c_Set_Oimage(U_6706,U_6702,U_6708),U_6695)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6706,tc_HOL_Obool)),U_6695),U_6710)) ) )
& ! [U_6709,U_6707,U_6705,U_6703,U_6701] :
( ? [U_6694] :
( U_6703 = hAPP(c_Set_Oimage(U_6705,U_6701,U_6707),U_6694)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6705,tc_HOL_Obool)),U_6694),U_6709)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6701,tc_HOL_Obool)),U_6703),hAPP(c_Set_Oimage(U_6705,U_6701,U_6707),U_6709))) ) ),
inference(miniscope,[status(thm)],[f_2029_2]) ).
fof(f_2029_4,plain,
( ! [U_6710,U_6708,U_6706,U_6704,U_6702] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6702,tc_HOL_Obool)),U_6704),hAPP(c_Set_Oimage(U_6706,U_6702,U_6708),U_6710)))
| ! [U_6695] :
( U_6704 != hAPP(c_Set_Oimage(U_6706,U_6702,U_6708),U_6695)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6706,tc_HOL_Obool)),U_6695),U_6710)) ) )
& ! [U_6709,U_6707,U_6705,U_6703,U_6701] :
( ( U_6703 = hAPP(c_Set_Oimage(U_6705,U_6701,U_6707),sK124(U_6709,U_6707,U_6705,U_6703,U_6701))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6705,tc_HOL_Obool)),sK124(U_6709,U_6707,U_6705,U_6703,U_6701)),U_6709)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6701,tc_HOL_Obool)),U_6703),hAPP(c_Set_Oimage(U_6705,U_6701,U_6707),U_6709))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_6694,sK124(U_6709,U_6707,U_6705,U_6703,U_6701))],[f_2029_3]) ).
cnf(f_2029_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6705,tc_HOL_Obool)),sK124(U_6709,U_6707,U_6705,U_6703,U_6701)),U_6709))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6701,tc_HOL_Obool)),U_6703),hAPP(c_Set_Oimage(U_6705,U_6701,U_6707),U_6709))) ),
inference(clausify,[status(thm)],[f_2029_4]) ).
cnf(f_2029_6,plain,
( U_6703 = hAPP(c_Set_Oimage(U_6705,U_6701,U_6707),sK124(U_6709,U_6707,U_6705,U_6703,U_6701))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6701,tc_HOL_Obool)),U_6703),hAPP(c_Set_Oimage(U_6705,U_6701,U_6707),U_6709))) ),
inference(clausify,[status(thm)],[f_2029_4]) ).
cnf(f_2029_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6702,tc_HOL_Obool)),U_6704),hAPP(c_Set_Oimage(U_6706,U_6702,U_6708),U_6710)))
| U_6704 != hAPP(c_Set_Oimage(U_6706,U_6702,U_6708),U_6695)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6706,tc_HOL_Obool)),U_6695),U_6710)) ),
inference(clausify,[status(thm)],[f_2029_4]) ).
fof(f_2030_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_2030_2,plain,
! [U_6712,U_6711] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6711),U_6712))
| ~ 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_6711)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6712))) )
& ( 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_6711)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6712)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6711),U_6712)) ) ),
inference(variable_rename,[status(thm)],[f_2030_1]) ).
fof(f_2030_3,plain,
( ! [U_6716,U_6714] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6714),U_6716))
| ~ 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_6714)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6716))) )
& ! [U_6715,U_6713] :
( 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_6713)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6715)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6713),U_6715)) ) ),
inference(miniscope,[status(thm)],[f_2030_2]) ).
cnf(f_2030_4,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_6713)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6715)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6713),U_6715)) ),
inference(clausify,[status(thm)],[f_2030_3]) ).
cnf(f_2030_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6714),U_6716))
| ~ 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_6714)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6716))) ),
inference(clausify,[status(thm)],[f_2030_3]) ).
fof(f_2031_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_2031_2,plain,
! [U_6718,U_6717] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6717),U_6718))
| ~ 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_6717)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6718))) )
& ( 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_6717)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6718)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6717),U_6718)) ) ),
inference(variable_rename,[status(thm)],[f_2031_1]) ).
fof(f_2031_3,plain,
( ! [U_6722,U_6720] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6720),U_6722))
| ~ 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_6720)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6722))) )
& ! [U_6721,U_6719] :
( 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_6719)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6721)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6719),U_6721)) ) ),
inference(miniscope,[status(thm)],[f_2031_2]) ).
cnf(f_2031_4,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_6719)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6721)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6719),U_6721)) ),
inference(clausify,[status(thm)],[f_2031_3]) ).
cnf(f_2031_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6720),U_6722))
| ~ 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_6720)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6722))) ),
inference(clausify,[status(thm)],[f_2031_3]) ).
fof(f_2032_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_2032_2,plain,
! [U_6724,U_6723] :
( ( U_6723 = U_6724
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6723) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6724) )
& ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6723) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6724)
| U_6723 != U_6724 ) ),
inference(variable_rename,[status(thm)],[f_2032_1]) ).
fof(f_2032_3,plain,
( ! [U_6728,U_6726] :
( U_6726 = U_6728
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6726) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6728) )
& ! [U_6727,U_6725] :
( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6725) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6727)
| U_6725 != U_6727 ) ),
inference(miniscope,[status(thm)],[f_2032_2]) ).
cnf(f_2032_4,plain,
( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6725) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6727)
| U_6725 != U_6727 ),
inference(clausify,[status(thm)],[f_2032_3]) ).
cnf(f_2032_5,plain,
( U_6726 = U_6728
| hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6726) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6728) ),
inference(clausify,[status(thm)],[f_2032_3]) ).
fof(f_2033_1,plain,
! [V_A_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_d,T_b,hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_f_2),V_g_2)),V_A_2),
inference(fof_nnf,[status(thm)],[fact_image__image]) ).
fof(f_2033_2,plain,
! [U_6734,U_6733,U_6732,U_6731,U_6730,U_6729] : hAPP(c_Set_Oimage(U_6729,U_6730,U_6731),hAPP(c_Set_Oimage(U_6732,U_6729,U_6733),U_6734)) = hAPP(c_Set_Oimage(U_6732,U_6730,hAPP(hAPP(c_COMBB(U_6729,U_6730,U_6732),U_6731),U_6733)),U_6734),
inference(variable_rename,[status(thm)],[f_2033_1]) ).
cnf(f_2033_3,plain,
hAPP(c_Set_Oimage(U_6729,U_6730,U_6731),hAPP(c_Set_Oimage(U_6732,U_6729,U_6733),U_6734)) = hAPP(c_Set_Oimage(U_6732,U_6730,hAPP(hAPP(c_COMBB(U_6729,U_6730,U_6732),U_6731),U_6733)),U_6734),
inference(clausify,[status(thm)],[f_2033_2]) ).
fof(f_2034_1,plain,
! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I10_J]) ).
fof(f_2034_2,plain,
! [U_6740,U_6739,U_6738,U_6737,U_6736,U_6735] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6735,tc_fun(U_6736,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_6737,U_6735,U_6738),U_6739)),U_6740) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6737,tc_fun(U_6736,tc_HOL_Obool)),U_6739),hAPP(hAPP(c_COMBB(U_6735,tc_fun(U_6736,tc_HOL_Obool),U_6737),U_6740),U_6738)),
inference(variable_rename,[status(thm)],[f_2034_1]) ).
cnf(f_2034_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6735,tc_fun(U_6736,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_6737,U_6735,U_6738),U_6739)),U_6740) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6737,tc_fun(U_6736,tc_HOL_Obool)),U_6739),hAPP(hAPP(c_COMBB(U_6735,tc_fun(U_6736,tc_HOL_Obool),U_6737),U_6740),U_6738)),
inference(clausify,[status(thm)],[f_2034_2]) ).
fof(f_2035_1,plain,
! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I10_J]) ).
fof(f_2035_2,plain,
! [U_6746,U_6745,U_6744,U_6743,U_6742,U_6741] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6741,tc_fun(U_6742,tc_HOL_Obool)),U_6743),hAPP(hAPP(c_COMBB(U_6744,tc_fun(U_6742,tc_HOL_Obool),U_6741),U_6745),U_6746)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6744,tc_fun(U_6742,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_6741,U_6744,U_6746),U_6743)),U_6745),
inference(variable_rename,[status(thm)],[f_2035_1]) ).
cnf(f_2035_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6741,tc_fun(U_6742,tc_HOL_Obool)),U_6743),hAPP(hAPP(c_COMBB(U_6744,tc_fun(U_6742,tc_HOL_Obool),U_6741),U_6745),U_6746)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_6744,tc_fun(U_6742,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_6741,U_6744,U_6746),U_6743)),U_6745),
inference(clausify,[status(thm)],[f_2035_2]) ).
fof(f_2036_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_image__diff__subset]) ).
fof(f_2036_2,plain,
! [U_6751,U_6750,U_6749,U_6748,U_6747] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6747,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6747,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_6748,U_6747,U_6749),U_6750)),hAPP(c_Set_Oimage(U_6748,U_6747,U_6749),U_6751))),hAPP(c_Set_Oimage(U_6748,U_6747,U_6749),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6748,tc_HOL_Obool)),U_6750),U_6751)))),
inference(variable_rename,[status(thm)],[f_2036_1]) ).
cnf(f_2036_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6747,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6747,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_6748,U_6747,U_6749),U_6750)),hAPP(c_Set_Oimage(U_6748,U_6747,U_6749),U_6751))),hAPP(c_Set_Oimage(U_6748,U_6747,U_6749),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6748,tc_HOL_Obool)),U_6750),U_6751)))),
inference(clausify,[status(thm)],[f_2036_2]) ).
fof(f_2037_1,plain,
! [V_y_2,V_x_2,T_b] :
( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastAtMost]) ).
fof(f_2037_2,plain,
! [U_6754,U_6753,U_6752] :
( hAPP(c_Set_Oimage(U_6752,U_6752,c_Groups_Ouminus__class_Ouminus(U_6752)),c_SetInterval_Oord__class_OatLeastAtMost(U_6752,U_6753,U_6754)) = c_SetInterval_Oord__class_OatLeastAtMost(U_6752,hAPP(c_Groups_Ouminus__class_Ouminus(U_6752),U_6754),hAPP(c_Groups_Ouminus__class_Ouminus(U_6752),U_6753))
| ~ class_Groups_Oordered__ab__group__add(U_6752) ),
inference(variable_rename,[status(thm)],[f_2037_1]) ).
cnf(f_2037_3,plain,
( hAPP(c_Set_Oimage(U_6752,U_6752,c_Groups_Ouminus__class_Ouminus(U_6752)),c_SetInterval_Oord__class_OatLeastAtMost(U_6752,U_6753,U_6754)) = c_SetInterval_Oord__class_OatLeastAtMost(U_6752,hAPP(c_Groups_Ouminus__class_Ouminus(U_6752),U_6754),hAPP(c_Groups_Ouminus__class_Ouminus(U_6752),U_6753))
| ~ class_Groups_Oordered__ab__group__add(U_6752) ),
inference(clausify,[status(thm)],[f_2037_2]) ).
fof(f_2038_1,plain,
! [V_A_2,V_f_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_b)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I1_J]) ).
fof(f_2038_2,plain,
! [U_6757,U_6756,U_6755] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6755),U_6756),U_6757) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_6755),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6755,tc_Int_Oint),U_6756),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6757))
| ~ class_Groups_Ocomm__monoid__mult(U_6755)
| ~ class_Groups_Ocomm__monoid__add(U_6755) ),
inference(variable_rename,[status(thm)],[f_2038_1]) ).
cnf(f_2038_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6755),U_6756),U_6757) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_6755),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6755,tc_Int_Oint),U_6756),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6757))
| ~ class_Groups_Ocomm__monoid__mult(U_6755)
| ~ class_Groups_Ocomm__monoid__add(U_6755) ),
inference(clausify,[status(thm)],[f_2038_2]) ).
fof(f_2039_1,plain,
! [V_na_2,V_m_2] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_m_2,V_na_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_na_2)))
| ~ c_Nat__Transfer_Ois__nat(V_na_2)
| ~ c_Nat__Transfer_Ois__nat(V_m_2) ),
inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__functions]) ).
fof(f_2039_2,plain,
! [U_6759,U_6758] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6758,U_6759) = 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_6758),hAPP(c_Int_Onat,U_6759)))
| ~ c_Nat__Transfer_Ois__nat(U_6759)
| ~ c_Nat__Transfer_Ois__nat(U_6758) ),
inference(variable_rename,[status(thm)],[f_2039_1]) ).
cnf(f_2039_3,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6758,U_6759) = 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_6758),hAPP(c_Int_Onat,U_6759)))
| ~ c_Nat__Transfer_Ois__nat(U_6759)
| ~ c_Nat__Transfer_Ois__nat(U_6758) ),
inference(clausify,[status(thm)],[f_2039_2]) ).
fof(f_2040_1,plain,
! [V_P_2,V_na_2,V_m_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(V_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_na_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__head]) ).
fof(f_2040_2,plain,
! [U_6763,U_6762,U_6761,U_6760] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6760),U_6763),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6761,U_6762)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6760),hAPP(U_6763,U_6761)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6760),U_6763),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_6761,U_6762)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6761),U_6762))
| ~ class_Groups_Ocomm__monoid__add(U_6760) ),
inference(variable_rename,[status(thm)],[f_2040_1]) ).
cnf(f_2040_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6760),U_6763),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6761,U_6762)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6760),hAPP(U_6763,U_6761)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6760),U_6763),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_6761,U_6762)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6761),U_6762))
| ~ class_Groups_Ocomm__monoid__add(U_6760) ),
inference(clausify,[status(thm)],[f_2040_2]) ).
fof(f_2041_1,plain,
! [V_na_2,V_A_2,V_f_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) != hAPP(c_Nat_OSuc,V_na_2) ),
inference(fof_nnf,[status(thm)],[fact_setsum__SucD]) ).
fof(f_2041_2,plain,
! [U_6768,U_6767,U_6766,U_6765] :
( ? [U_6764] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_6766,U_6764)))
& hBOOL(hAPP(hAPP(c_member(U_6765),U_6764),U_6767)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6765,tc_Nat_Onat),U_6766),U_6767) != hAPP(c_Nat_OSuc,U_6768) ),
inference(variable_rename,[status(thm)],[f_2041_1]) ).
fof(f_2041_3,plain,
! [U_6768,U_6767,U_6766,U_6765] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_6766,sK125(U_6768,U_6767,U_6766,U_6765))))
& hBOOL(hAPP(hAPP(c_member(U_6765),sK125(U_6768,U_6767,U_6766,U_6765)),U_6767)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6765,tc_Nat_Onat),U_6766),U_6767) != hAPP(c_Nat_OSuc,U_6768) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_6764,sK125(U_6768,U_6767,U_6766,U_6765))],[f_2041_2]) ).
cnf(f_2041_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_6765),sK125(U_6768,U_6767,U_6766,U_6765)),U_6767))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6765,tc_Nat_Onat),U_6766),U_6767) != hAPP(c_Nat_OSuc,U_6768) ),
inference(clausify,[status(thm)],[f_2041_3]) ).
cnf(f_2041_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_6766,sK125(U_6768,U_6767,U_6766,U_6765))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6765,tc_Nat_Onat),U_6766),U_6767) != hAPP(c_Nat_OSuc,U_6768) ),
inference(clausify,[status(thm)],[f_2041_3]) ).
fof(f_2042_1,plain,
! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2))
| ? [B_x] :
( hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x)) )
| V_b_2 != V_d_2
| V_a_2 != V_c_2
| ~ class_Orderings_Oord(T_b)
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__ivl__cong]) ).
fof(f_2042_2,plain,
! [U_6777,U_6776,U_6775,U_6774,U_6773,U_6772,U_6771,U_6770] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6771,U_6770),U_6776),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6771,U_6772),U_6774)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6771,U_6770),U_6777),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6771,U_6773),U_6775))
| ? [U_6769] :
( hAPP(U_6776,U_6769) != hAPP(U_6777,U_6769)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6771),U_6769),U_6775))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6771),U_6773),U_6769)) )
| U_6774 != U_6775
| U_6772 != U_6773
| ~ class_Orderings_Oord(U_6771)
| ~ class_Groups_Ocomm__monoid__add(U_6770) ),
inference(variable_rename,[status(thm)],[f_2042_1]) ).
fof(f_2042_3,plain,
! [U_6777,U_6776,U_6775,U_6774,U_6773,U_6772,U_6771,U_6770] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6771,U_6770),U_6776),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6771,U_6772),U_6774)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6771,U_6770),U_6777),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6771,U_6773),U_6775))
| ( hAPP(U_6776,sK126(U_6777,U_6776,U_6775,U_6774,U_6773,U_6772,U_6771,U_6770)) != hAPP(U_6777,sK126(U_6777,U_6776,U_6775,U_6774,U_6773,U_6772,U_6771,U_6770))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6771),sK126(U_6777,U_6776,U_6775,U_6774,U_6773,U_6772,U_6771,U_6770)),U_6775))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6771),U_6773),sK126(U_6777,U_6776,U_6775,U_6774,U_6773,U_6772,U_6771,U_6770))) )
| U_6774 != U_6775
| U_6772 != U_6773
| ~ class_Orderings_Oord(U_6771)
| ~ class_Groups_Ocomm__monoid__add(U_6770) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_6769,sK126(U_6777,U_6776,U_6775,U_6774,U_6773,U_6772,U_6771,U_6770))],[f_2042_2]) ).
cnf(f_2042_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6771),U_6773),sK126(U_6777,U_6776,U_6775,U_6774,U_6773,U_6772,U_6771,U_6770)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6771,U_6770),U_6776),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6771,U_6772),U_6774)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6771,U_6770),U_6777),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6771,U_6773),U_6775))
| U_6774 != U_6775
| U_6772 != U_6773
| ~ class_Orderings_Oord(U_6771)
| ~ class_Groups_Ocomm__monoid__add(U_6770) ),
inference(clausify,[status(thm)],[f_2042_3]) ).
cnf(f_2042_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6771),sK126(U_6777,U_6776,U_6775,U_6774,U_6773,U_6772,U_6771,U_6770)),U_6775))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6771,U_6770),U_6776),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6771,U_6772),U_6774)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6771,U_6770),U_6777),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6771,U_6773),U_6775))
| U_6774 != U_6775
| U_6772 != U_6773
| ~ class_Orderings_Oord(U_6771)
| ~ class_Groups_Ocomm__monoid__add(U_6770) ),
inference(clausify,[status(thm)],[f_2042_3]) ).
cnf(f_2042_6,plain,
( hAPP(U_6776,sK126(U_6777,U_6776,U_6775,U_6774,U_6773,U_6772,U_6771,U_6770)) != hAPP(U_6777,sK126(U_6777,U_6776,U_6775,U_6774,U_6773,U_6772,U_6771,U_6770))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6771,U_6770),U_6776),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6771,U_6772),U_6774)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6771,U_6770),U_6777),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6771,U_6773),U_6775))
| U_6774 != U_6775
| U_6772 != U_6773
| ~ class_Orderings_Oord(U_6771)
| ~ class_Groups_Ocomm__monoid__add(U_6770) ),
inference(clausify,[status(thm)],[f_2042_3]) ).
fof(f_2043_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_2043_2,plain,
! [U_6779,U_6778] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6778,U_6779)) = 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_6779),U_6778)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[f_2043_1]) ).
cnf(f_2043_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6778,U_6779)) = 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_6779),U_6778)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(clausify,[status(thm)],[f_2043_2]) ).
fof(f_2044_1,plain,
! [V_x_2,T_b] :
( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThan]) ).
fof(f_2044_2,plain,
! [U_6781,U_6780] :
( hAPP(c_Set_Oimage(U_6780,U_6780,c_Groups_Ouminus__class_Ouminus(U_6780)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6780),U_6781)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_6780),hAPP(c_Groups_Ouminus__class_Ouminus(U_6780),U_6781))
| ~ class_Groups_Oordered__ab__group__add(U_6780) ),
inference(variable_rename,[status(thm)],[f_2044_1]) ).
cnf(f_2044_3,plain,
( hAPP(c_Set_Oimage(U_6780,U_6780,c_Groups_Ouminus__class_Ouminus(U_6780)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6780),U_6781)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_6780),hAPP(c_Groups_Ouminus__class_Ouminus(U_6780),U_6781))
| ~ class_Groups_Oordered__ab__group__add(U_6780) ),
inference(clausify,[status(thm)],[f_2044_2]) ).
fof(f_2045_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) != hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_greaterThan__eq__iff]) ).
fof(f_2045_2,plain,
! [U_6784,U_6783,U_6782] :
( ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6782),U_6783) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6782),U_6784)
| U_6783 != U_6784 )
& ( U_6783 = U_6784
| hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6782),U_6783) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6782),U_6784) ) )
| ~ class_Orderings_Olinorder(U_6782) ),
inference(variable_rename,[status(thm)],[f_2045_1]) ).
cnf(f_2045_3,plain,
( U_6783 = U_6784
| hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6782),U_6783) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6782),U_6784)
| ~ class_Orderings_Olinorder(U_6782) ),
inference(clausify,[status(thm)],[f_2045_2]) ).
cnf(f_2045_4,plain,
( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6782),U_6783) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6782),U_6784)
| U_6783 != U_6784
| ~ class_Orderings_Olinorder(U_6782) ),
inference(clausify,[status(thm)],[f_2045_2]) ).
fof(f_2046_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_2046_2,plain,
! [U_6786,U_6785] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6785),U_6786)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6785)),hAPP(c_Nat_OSuc,U_6786)),
inference(variable_rename,[status(thm)],[f_2046_1]) ).
cnf(f_2046_3,plain,
hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6785),U_6786)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6785)),hAPP(c_Nat_OSuc,U_6786)),
inference(clausify,[status(thm)],[f_2046_2]) ).
fof(f_2047_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_2047_2,plain,
! [U_6788,U_6787] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6787,U_6788)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6787),hAPP(c_Nat_OSuc,U_6788)),
inference(variable_rename,[status(thm)],[f_2047_1]) ).
cnf(f_2047_3,plain,
hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6787,U_6788)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6787),hAPP(c_Nat_OSuc,U_6788)),
inference(clausify,[status(thm)],[f_2047_2]) ).
fof(f_2048_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_2048_2,plain,
! [U_6791,U_6790,U_6789] : 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_6789)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6790),U_6791)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6790),U_6789)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6791),U_6789)),
inference(variable_rename,[status(thm)],[f_2048_1]) ).
cnf(f_2048_3,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_6789)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6790),U_6791)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6790),U_6789)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6791),U_6789)),
inference(clausify,[status(thm)],[f_2048_2]) ).
fof(f_2049_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_2049_2,plain,
! [U_6794,U_6793,U_6792] : 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_6792)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6793,U_6794)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6793),U_6792),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6794),U_6792)),
inference(variable_rename,[status(thm)],[f_2049_1]) ).
cnf(f_2049_3,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_6792)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6793,U_6794)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6793),U_6792),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6794),U_6792)),
inference(clausify,[status(thm)],[f_2049_2]) ).
fof(f_2050_1,plain,
! [V_A_2,T_b] : hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2),
inference(fof_nnf,[status(thm)],[fact_card__eq__setsum]) ).
fof(f_2050_2,plain,
! [U_6796,U_6795] : hAPP(c_Finite__Set_Ocard(U_6795),U_6796) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6795,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_6795),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_6796),
inference(variable_rename,[status(thm)],[f_2050_1]) ).
cnf(f_2050_3,plain,
hAPP(c_Finite__Set_Ocard(U_6795),U_6796) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6795,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_6795),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_6796),
inference(clausify,[status(thm)],[f_2050_2]) ).
fof(f_2051_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_2051_2,plain,
! [U_6798,U_6797] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6797),U_6798) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_6797,U_6798),
inference(variable_rename,[status(thm)],[f_2051_1]) ).
cnf(f_2051_3,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6797),U_6798) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_6797,U_6798),
inference(clausify,[status(thm)],[f_2051_2]) ).
fof(f_2052_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_2052_2,plain,
! [U_6799] : 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_6799)) = U_6799,
inference(variable_rename,[status(thm)],[f_2052_1]) ).
cnf(f_2052_3,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_6799)) = U_6799,
inference(clausify,[status(thm)],[f_2052_2]) ).
fof(f_2053_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2))) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_greaterThan__subset__iff]) ).
fof(f_2053_2,plain,
! [U_6802,U_6801,U_6800] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6800,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6800),U_6801)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6800),U_6802)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6800),U_6802),U_6801)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6800),U_6802),U_6801))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6800,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6800),U_6801)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6800),U_6802))) ) )
| ~ class_Orderings_Olinorder(U_6800) ),
inference(variable_rename,[status(thm)],[f_2053_1]) ).
cnf(f_2053_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6800),U_6802),U_6801))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6800,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6800),U_6801)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6800),U_6802)))
| ~ class_Orderings_Olinorder(U_6800) ),
inference(clausify,[status(thm)],[f_2053_2]) ).
cnf(f_2053_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6800,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6800),U_6801)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6800),U_6802)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6800),U_6802),U_6801))
| ~ class_Orderings_Olinorder(U_6800) ),
inference(clausify,[status(thm)],[f_2053_2]) ).
fof(f_2054_1,plain,
! [V_A_2,V_y_2,T_c,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))),V_y_2)
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__constant]) ).
fof(f_2054_2,plain,
! [U_6806,U_6805,U_6804,U_6803] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6804,U_6803),hAPP(c_COMBK(U_6803,U_6804),U_6805)),U_6806) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6803),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6803),hAPP(c_Finite__Set_Ocard(U_6804),U_6806))),U_6805)
| ~ class_Rings_Osemiring__1(U_6803) ),
inference(variable_rename,[status(thm)],[f_2054_1]) ).
cnf(f_2054_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_6804,U_6803),hAPP(c_COMBK(U_6803,U_6804),U_6805)),U_6806) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6803),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_6803),hAPP(c_Finite__Set_Ocard(U_6804),U_6806))),U_6805)
| ~ class_Rings_Osemiring__1(U_6803) ),
inference(clausify,[status(thm)],[f_2054_2]) ).
fof(f_2055_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_2055_2,plain,
! [U_6807] : 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_6807)) = hAPP(c_Int_Onat,U_6807),
inference(variable_rename,[status(thm)],[f_2055_1]) ).
cnf(f_2055_3,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_6807)) = hAPP(c_Int_Onat,U_6807),
inference(clausify,[status(thm)],[f_2055_2]) ).
fof(f_2056_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_2056_2,plain,
! [U_6809,U_6808] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_6808),U_6809)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6809),U_6808)),
inference(variable_rename,[status(thm)],[f_2056_1]) ).
cnf(f_2056_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_6808),U_6809)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6809),U_6808)),
inference(clausify,[status(thm)],[f_2056_2]) ).
fof(f_2057_1,plain,
! [V_na_2,V_m_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_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_na_2))),
inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I2_J]) ).
fof(f_2057_2,plain,
! [U_6811,U_6810] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6810,U_6811) = 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_6810),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6811))),
inference(variable_rename,[status(thm)],[f_2057_1]) ).
cnf(f_2057_3,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6810,U_6811) = 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_6810),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6811))),
inference(clausify,[status(thm)],[f_2057_2]) ).
fof(f_2058_1,plain,
! [V_y_2,V_x_2,T_b] :
( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastLessThan]) ).
fof(f_2058_2,plain,
! [U_6814,U_6813,U_6812] :
( hAPP(c_Set_Oimage(U_6812,U_6812,c_Groups_Ouminus__class_Ouminus(U_6812)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6812,U_6813),U_6814)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_6812,hAPP(c_Groups_Ouminus__class_Ouminus(U_6812),U_6814),hAPP(c_Groups_Ouminus__class_Ouminus(U_6812),U_6813))
| ~ class_Groups_Oordered__ab__group__add(U_6812) ),
inference(variable_rename,[status(thm)],[f_2058_1]) ).
cnf(f_2058_3,plain,
( hAPP(c_Set_Oimage(U_6812,U_6812,c_Groups_Ouminus__class_Ouminus(U_6812)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6812,U_6813),U_6814)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_6812,hAPP(c_Groups_Ouminus__class_Ouminus(U_6812),U_6814),hAPP(c_Groups_Ouminus__class_Ouminus(U_6812),U_6813))
| ~ class_Groups_Oordered__ab__group__add(U_6812) ),
inference(clausify,[status(thm)],[f_2058_2]) ).
fof(f_2059_1,plain,
! [V_y_2,V_x_2,T_b] :
( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanAtMost]) ).
fof(f_2059_2,plain,
! [U_6817,U_6816,U_6815] :
( hAPP(c_Set_Oimage(U_6815,U_6815,c_Groups_Ouminus__class_Ouminus(U_6815)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_6815,U_6816,U_6817)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6815,hAPP(c_Groups_Ouminus__class_Ouminus(U_6815),U_6817)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6815),U_6816))
| ~ class_Groups_Oordered__ab__group__add(U_6815) ),
inference(variable_rename,[status(thm)],[f_2059_1]) ).
cnf(f_2059_3,plain,
( hAPP(c_Set_Oimage(U_6815,U_6815,c_Groups_Ouminus__class_Ouminus(U_6815)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_6815,U_6816,U_6817)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6815,hAPP(c_Groups_Ouminus__class_Ouminus(U_6815),U_6817)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6815),U_6816))
| ~ class_Groups_Oordered__ab__group__add(U_6815) ),
inference(clausify,[status(thm)],[f_2059_2]) ).
fof(f_2060_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_2060_2,plain,
! [U_6819,U_6818] : 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_6818)),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_6819),U_6818))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_6818),U_6819),
inference(variable_rename,[status(thm)],[f_2060_1]) ).
cnf(f_2060_3,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_6818)),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_6819),U_6818))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_6818),U_6819),
inference(clausify,[status(thm)],[f_2060_2]) ).
fof(f_2061_1,plain,
! [V_x_2,T_b] :
( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__lessThan]) ).
fof(f_2061_2,plain,
! [U_6821,U_6820] :
( hAPP(c_Set_Oimage(U_6820,U_6820,c_Groups_Ouminus__class_Ouminus(U_6820)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6820),U_6821)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6820),hAPP(c_Groups_Ouminus__class_Ouminus(U_6820),U_6821))
| ~ class_Groups_Oordered__ab__group__add(U_6820) ),
inference(variable_rename,[status(thm)],[f_2061_1]) ).
cnf(f_2061_3,plain,
( hAPP(c_Set_Oimage(U_6820,U_6820,c_Groups_Ouminus__class_Ouminus(U_6820)),hAPP(c_SetInterval_Oord__class_OlessThan(U_6820),U_6821)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6820),hAPP(c_Groups_Ouminus__class_Ouminus(U_6820),U_6821))
| ~ class_Groups_Oordered__ab__group__add(U_6820) ),
inference(clausify,[status(thm)],[f_2061_2]) ).
fof(f_2062_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_2062_2,plain,
! [U_6823,U_6822] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_6822,U_6823)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6823),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6822),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[f_2062_1]) ).
cnf(f_2062_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_6822,U_6823)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6823),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6822),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(clausify,[status(thm)],[f_2062_2]) ).
fof(f_2063_1,plain,
! [V_f_2,V_A_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))
| ~ c_Nat__Transfer_Onat__set(V_A_2)
| ~ class_Groups_Ocomm__monoid__mult(T_b)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I1_J]) ).
fof(f_2063_2,plain,
! [U_6826,U_6825,U_6824] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_6824),U_6826),U_6825) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6824),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_6824,tc_Nat_Onat),U_6826),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6825))
| ~ c_Nat__Transfer_Onat__set(U_6825)
| ~ class_Groups_Ocomm__monoid__mult(U_6824)
| ~ class_Groups_Ocomm__monoid__add(U_6824) ),
inference(variable_rename,[status(thm)],[f_2063_1]) ).
cnf(f_2063_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_6824),U_6826),U_6825) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6824),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_6824,tc_Nat_Onat),U_6826),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6825))
| ~ c_Nat__Transfer_Onat__set(U_6825)
| ~ class_Groups_Ocomm__monoid__mult(U_6824)
| ~ class_Groups_Ocomm__monoid__add(U_6824) ),
inference(clausify,[status(thm)],[f_2063_2]) ).
fof(f_2064_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_2064_2,plain,
! [U_6828,U_6827] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_6827),U_6828))
| ~ 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_6827)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6828))) )
& ( 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_6827)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6828)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_6827),U_6828)) ) )
| ~ c_Nat__Transfer_Onat__set(U_6828)
| ~ c_Nat__Transfer_Onat__set(U_6827) ),
inference(variable_rename,[status(thm)],[f_2064_1]) ).
cnf(f_2064_3,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_6827)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6828)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_6827),U_6828))
| ~ c_Nat__Transfer_Onat__set(U_6828)
| ~ c_Nat__Transfer_Onat__set(U_6827) ),
inference(clausify,[status(thm)],[f_2064_2]) ).
cnf(f_2064_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_6827),U_6828))
| ~ 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_6827)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6828)))
| ~ c_Nat__Transfer_Onat__set(U_6828)
| ~ c_Nat__Transfer_Onat__set(U_6827) ),
inference(clausify,[status(thm)],[f_2064_2]) ).
fof(f_2065_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_2065_2,plain,
! [U_6830,U_6829] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_6829),U_6830))
| ~ 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_6829)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6830))) )
& ( 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_6829)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6830)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_6829),U_6830)) ) )
| ~ c_Nat__Transfer_Onat__set(U_6830)
| ~ c_Nat__Transfer_Onat__set(U_6829) ),
inference(variable_rename,[status(thm)],[f_2065_1]) ).
cnf(f_2065_3,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_6829)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6830)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_6829),U_6830))
| ~ c_Nat__Transfer_Onat__set(U_6830)
| ~ c_Nat__Transfer_Onat__set(U_6829) ),
inference(clausify,[status(thm)],[f_2065_2]) ).
cnf(f_2065_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_6829),U_6830))
| ~ 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_6829)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6830)))
| ~ c_Nat__Transfer_Onat__set(U_6830)
| ~ c_Nat__Transfer_Onat__set(U_6829) ),
inference(clausify,[status(thm)],[f_2065_2]) ).
fof(f_2066_1,plain,
! [V_na_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_na_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_na_2))),
inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I1_J]) ).
fof(f_2066_2,plain,
! [U_6831] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_6831) = 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_6831))),
inference(variable_rename,[status(thm)],[f_2066_1]) ).
cnf(f_2066_3,plain,
hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_6831) = 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_6831))),
inference(clausify,[status(thm)],[f_2066_2]) ).
fof(f_2067_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_2067_2,plain,
! [U_6832] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_6832)) = hAPP(c_Nat_OSuc,U_6832),
inference(variable_rename,[status(thm)],[f_2067_1]) ).
cnf(f_2067_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_6832)) = hAPP(c_Nat_OSuc,U_6832),
inference(clausify,[status(thm)],[f_2067_2]) ).
fof(f_2068_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) != hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atMost__eq__iff]) ).
fof(f_2068_2,plain,
! [U_6835,U_6834,U_6833] :
( ( ( hAPP(c_SetInterval_Oord__class_OatMost(U_6833),U_6834) = hAPP(c_SetInterval_Oord__class_OatMost(U_6833),U_6835)
| U_6834 != U_6835 )
& ( U_6834 = U_6835
| hAPP(c_SetInterval_Oord__class_OatMost(U_6833),U_6834) != hAPP(c_SetInterval_Oord__class_OatMost(U_6833),U_6835) ) )
| ~ class_Orderings_Olinorder(U_6833) ),
inference(variable_rename,[status(thm)],[f_2068_1]) ).
cnf(f_2068_3,plain,
( U_6834 = U_6835
| hAPP(c_SetInterval_Oord__class_OatMost(U_6833),U_6834) != hAPP(c_SetInterval_Oord__class_OatMost(U_6833),U_6835)
| ~ class_Orderings_Olinorder(U_6833) ),
inference(clausify,[status(thm)],[f_2068_2]) ).
cnf(f_2068_4,plain,
( hAPP(c_SetInterval_Oord__class_OatMost(U_6833),U_6834) = hAPP(c_SetInterval_Oord__class_OatMost(U_6833),U_6835)
| U_6834 != U_6835
| ~ class_Orderings_Olinorder(U_6833) ),
inference(clausify,[status(thm)],[f_2068_2]) ).
fof(f_2069_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_2069_2,plain,
! [U_6836] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6836)) = U_6836,
inference(variable_rename,[status(thm)],[f_2069_1]) ).
cnf(f_2069_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_6836)) = U_6836,
inference(clausify,[status(thm)],[f_2069_2]) ).
fof(f_2070_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_2070_2,plain,
! [U_6837] :
( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_6837) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6837))
| ~ c_Nat__Transfer_Onat__set(U_6837) ),
inference(variable_rename,[status(thm)],[f_2070_1]) ).
cnf(f_2070_3,plain,
( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_6837) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6837))
| ~ c_Nat__Transfer_Onat__set(U_6837) ),
inference(clausify,[status(thm)],[f_2070_2]) ).
fof(f_2071_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_2071_2,plain,
! [U_6839,U_6838] :
( ( ( U_6838 = U_6839
| hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6838) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6839) )
& ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6838) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6839)
| U_6838 != U_6839 ) )
| ~ c_Nat__Transfer_Onat__set(U_6839)
| ~ c_Nat__Transfer_Onat__set(U_6838) ),
inference(variable_rename,[status(thm)],[f_2071_1]) ).
cnf(f_2071_3,plain,
( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6838) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6839)
| U_6838 != U_6839
| ~ c_Nat__Transfer_Onat__set(U_6839)
| ~ c_Nat__Transfer_Onat__set(U_6838) ),
inference(clausify,[status(thm)],[f_2071_2]) ).
cnf(f_2071_4,plain,
( U_6838 = U_6839
| hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6838) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6839)
| ~ c_Nat__Transfer_Onat__set(U_6839)
| ~ c_Nat__Transfer_Onat__set(U_6838) ),
inference(clausify,[status(thm)],[f_2071_2]) ).
fof(f_2072_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_2072_2,plain,
! [U_6841,U_6840] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6840),U_6841)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6841),U_6840),
inference(variable_rename,[status(thm)],[f_2072_1]) ).
cnf(f_2072_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6840),U_6841)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6841),U_6840),
inference(clausify,[status(thm)],[f_2072_2]) ).
fof(f_2073_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_2073_2,plain,
! [U_6843,U_6842] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_6842,U_6843)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6843),U_6842),
inference(variable_rename,[status(thm)],[f_2073_1]) ).
cnf(f_2073_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_6842,U_6843)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6843),U_6842),
inference(clausify,[status(thm)],[f_2073_2]) ).
fof(f_2074_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_2074_2,plain,
! [U_6846] :
( ( c_Nat__Transfer_Onat__set(U_6846)
| ? [U_6845] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6845))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6845),U_6846)) ) )
& ( ! [U_6844] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6844))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6844),U_6846)) )
| ~ c_Nat__Transfer_Onat__set(U_6846) ) ),
inference(variable_rename,[status(thm)],[f_2074_1]) ).
fof(f_2074_3,plain,
( ! [U_6848] :
( c_Nat__Transfer_Onat__set(U_6848)
| ? [U_6845] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6845))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6845),U_6848)) ) )
& ! [U_6847] :
( ! [U_6844] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6844))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6844),U_6847)) )
| ~ c_Nat__Transfer_Onat__set(U_6847) ) ),
inference(miniscope,[status(thm)],[f_2074_2]) ).
fof(f_2074_4,plain,
( ! [U_6848] :
( c_Nat__Transfer_Onat__set(U_6848)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK127(U_6848)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK127(U_6848)),U_6848)) ) )
& ! [U_6847] :
( ! [U_6844] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6844))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6844),U_6847)) )
| ~ c_Nat__Transfer_Onat__set(U_6847) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_6845,sK127(U_6848))],[f_2074_3]) ).
cnf(f_2074_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6844))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6844),U_6847))
| ~ c_Nat__Transfer_Onat__set(U_6847) ),
inference(clausify,[status(thm)],[f_2074_4]) ).
cnf(f_2074_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK127(U_6848)),U_6848))
| c_Nat__Transfer_Onat__set(U_6848) ),
inference(clausify,[status(thm)],[f_2074_4]) ).
cnf(f_2074_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK127(U_6848)))
| c_Nat__Transfer_Onat__set(U_6848) ),
inference(clausify,[status(thm)],[f_2074_4]) ).
fof(f_2075_1,plain,
! [V_na_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_na_2) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_na_2),
inference(fof_nnf,[status(thm)],[fact_atLeast0AtMost]) ).
fof(f_2075_2,plain,
! [U_6849] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6849) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_6849),
inference(variable_rename,[status(thm)],[f_2075_1]) ).
cnf(f_2075_3,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_6849) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_6849),
inference(clausify,[status(thm)],[f_2075_2]) ).
fof(f_2076_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_2076_2,plain,
! [U_6850] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6850)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_6850),
inference(variable_rename,[status(thm)],[f_2076_1]) ).
cnf(f_2076_3,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6850)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_6850),
inference(clausify,[status(thm)],[f_2076_2]) ).
fof(f_2077_1,plain,
! [V_y_2,V_x_2,T_b] :
( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanLessThan]) ).
fof(f_2077_2,plain,
! [U_6853,U_6852,U_6851] :
( hAPP(c_Set_Oimage(U_6851,U_6851,c_Groups_Ouminus__class_Ouminus(U_6851)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_6851,U_6852,U_6853)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_6851,hAPP(c_Groups_Ouminus__class_Ouminus(U_6851),U_6853),hAPP(c_Groups_Ouminus__class_Ouminus(U_6851),U_6852))
| ~ class_Groups_Oordered__ab__group__add(U_6851) ),
inference(variable_rename,[status(thm)],[f_2077_1]) ).
cnf(f_2077_3,plain,
( hAPP(c_Set_Oimage(U_6851,U_6851,c_Groups_Ouminus__class_Ouminus(U_6851)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_6851,U_6852,U_6853)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_6851,hAPP(c_Groups_Ouminus__class_Ouminus(U_6851),U_6853),hAPP(c_Groups_Ouminus__class_Ouminus(U_6851),U_6852))
| ~ class_Groups_Oordered__ab__group__add(U_6851) ),
inference(clausify,[status(thm)],[f_2077_2]) ).
fof(f_2078_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_2078_2,plain,
! [U_6854] : 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_6854)),
inference(variable_rename,[status(thm)],[f_2078_1]) ).
cnf(f_2078_3,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_6854)),
inference(clausify,[status(thm)],[f_2078_2]) ).
fof(f_2079_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2))) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atMost__subset__iff]) ).
fof(f_2079_2,plain,
! [U_6857,U_6856,U_6855] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6855,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_6855),U_6856)),hAPP(c_SetInterval_Oord__class_OatMost(U_6855),U_6857)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6855),U_6856),U_6857)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6855),U_6856),U_6857))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6855,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_6855),U_6856)),hAPP(c_SetInterval_Oord__class_OatMost(U_6855),U_6857))) ) )
| ~ class_Orderings_Oorder(U_6855) ),
inference(variable_rename,[status(thm)],[f_2079_1]) ).
cnf(f_2079_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6855),U_6856),U_6857))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6855,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_6855),U_6856)),hAPP(c_SetInterval_Oord__class_OatMost(U_6855),U_6857)))
| ~ class_Orderings_Oorder(U_6855) ),
inference(clausify,[status(thm)],[f_2079_2]) ).
cnf(f_2079_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6855,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_6855),U_6856)),hAPP(c_SetInterval_Oord__class_OatMost(U_6855),U_6857)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6855),U_6856),U_6857))
| ~ class_Orderings_Oorder(U_6855) ),
inference(clausify,[status(thm)],[f_2079_2]) ).
fof(f_2080_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_2080_2,plain,
! [U_6859,U_6858] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6858,U_6859))
| ~ c_Nat__Transfer_Ois__nat(U_6858) ),
inference(variable_rename,[status(thm)],[f_2080_1]) ).
cnf(f_2080_3,plain,
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6858,U_6859))
| ~ c_Nat__Transfer_Ois__nat(U_6858) ),
inference(clausify,[status(thm)],[f_2080_2]) ).
fof(f_2081_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_2081_2,plain,
! [U_6861,U_6860] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6860,U_6861)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6861)),U_6860),
inference(variable_rename,[status(thm)],[f_2081_1]) ).
cnf(f_2081_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_6860,U_6861)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6861)),U_6860),
inference(clausify,[status(thm)],[f_2081_2]) ).
fof(f_2082_1,plain,
! [V_k_2,T_b] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Compl__atMost]) ).
fof(f_2082_2,plain,
! [U_6863,U_6862] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6862,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_6862),U_6863)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6862),U_6863)
| ~ class_Orderings_Olinorder(U_6862) ),
inference(variable_rename,[status(thm)],[f_2082_1]) ).
cnf(f_2082_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6862,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_6862),U_6863)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6862),U_6863)
| ~ class_Orderings_Olinorder(U_6862) ),
inference(clausify,[status(thm)],[f_2082_2]) ).
fof(f_2083_1,plain,
! [V_k_2,T_b] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Compl__greaterThan]) ).
fof(f_2083_2,plain,
! [U_6865,U_6864] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6864,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6864),U_6865)) = hAPP(c_SetInterval_Oord__class_OatMost(U_6864),U_6865)
| ~ class_Orderings_Olinorder(U_6864) ),
inference(variable_rename,[status(thm)],[f_2083_1]) ).
cnf(f_2083_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_6864,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_6864),U_6865)) = hAPP(c_SetInterval_Oord__class_OatMost(U_6864),U_6865)
| ~ class_Orderings_Olinorder(U_6864) ),
inference(clausify,[status(thm)],[f_2083_2]) ).
fof(f_2084_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_2084_2,plain,
! [U_6866] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_6866) = 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_6866)),
inference(variable_rename,[status(thm)],[f_2084_1]) ).
cnf(f_2084_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_6866) = 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_6866)),
inference(clausify,[status(thm)],[f_2084_2]) ).
fof(f_2085_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_2085_2,plain,
! [U_6868,U_6867] :
( U_6867 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6868),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6868),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_6867)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6867),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6868),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6868),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_6867))))) ),
inference(variable_rename,[status(thm)],[f_2085_1]) ).
cnf(f_2085_3,plain,
( U_6867 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6868),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6868),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_6867)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6867),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_6868),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6868),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_6867))))) ),
inference(clausify,[status(thm)],[f_2085_2]) ).
fof(f_2086_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_2086_2,plain,
! [U_6870,U_6869] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6869,U_6870))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6869)) ),
inference(variable_rename,[status(thm)],[f_2086_1]) ).
cnf(f_2086_3,plain,
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_6869,U_6870))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6869)) ),
inference(clausify,[status(thm)],[f_2086_2]) ).
fof(f_2087_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_2087_2,plain,
! [U_6872,U_6871] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6871),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6872) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_6871,U_6872),
inference(variable_rename,[status(thm)],[f_2087_1]) ).
cnf(f_2087_3,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6871),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_6872) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_6871,U_6872),
inference(clausify,[status(thm)],[f_2087_2]) ).
fof(f_2088_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_2088_2,plain,
! [U_6873] :
( 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_6873)) = U_6873
| ~ c_Nat__Transfer_Onat__set(U_6873) ),
inference(variable_rename,[status(thm)],[f_2088_1]) ).
cnf(f_2088_3,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_6873)) = U_6873
| ~ c_Nat__Transfer_Onat__set(U_6873) ),
inference(clausify,[status(thm)],[f_2088_2]) ).
fof(f_2089_1,plain,
! [V_na_2,V_f_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_na_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_na_2)))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__atMost__Suc]) ).
fof(f_2089_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_OatMost(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_OatMost(tc_Nat_Onat),U_6876))),hAPP(U_6875,hAPP(c_Nat_OSuc,U_6876)))
| ~ class_Groups_Ocomm__monoid__add(U_6874) ),
inference(variable_rename,[status(thm)],[f_2089_1]) ).
cnf(f_2089_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_6874),U_6875),hAPP(c_SetInterval_Oord__class_OatMost(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_OatMost(tc_Nat_Onat),U_6876))),hAPP(U_6875,hAPP(c_Nat_OSuc,U_6876)))
| ~ class_Groups_Ocomm__monoid__add(U_6874) ),
inference(clausify,[status(thm)],[f_2089_2]) ).
fof(f_2090_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_2090_2,plain,
! [U_6878,U_6877] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6877),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6878) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_6877,U_6878),
inference(variable_rename,[status(thm)],[f_2090_1]) ).
cnf(f_2090_3,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6877),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6878) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_6877,U_6878),
inference(clausify,[status(thm)],[f_2090_2]) ).
fof(f_2091_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_2091_2,plain,
! [U_6880,U_6879] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_6879,U_6880)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6880),U_6879)),
inference(variable_rename,[status(thm)],[f_2091_1]) ).
cnf(f_2091_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_6879,U_6880)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_6880),U_6879)),
inference(clausify,[status(thm)],[f_2091_2]) ).
fof(f_2092_1,plain,
! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_g_2),V_B_2)
| ? [B_x] :
( hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
| ~ c_Nat__Transfer_Onat__set(V_B_2)
| V_A_2 != V_B_2
| ~ class_Groups_Ocomm__monoid__mult(T_b)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod__cong_I1_J]) ).
fof(f_2092_2,plain,
! [U_6886,U_6885,U_6884,U_6883,U_6882] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_6882),U_6885),U_6883) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_6882),U_6886),U_6884)
| ? [U_6881] :
( hAPP(U_6885,U_6881) != hAPP(U_6886,U_6881)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6881)) )
| ~ c_Nat__Transfer_Onat__set(U_6884)
| U_6883 != U_6884
| ~ class_Groups_Ocomm__monoid__mult(U_6882)
| ~ class_Groups_Ocomm__monoid__add(U_6882) ),
inference(variable_rename,[status(thm)],[f_2092_1]) ).
fof(f_2092_3,plain,
! [U_6886,U_6885,U_6884,U_6883,U_6882] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_6882),U_6885),U_6883) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_6882),U_6886),U_6884)
| ( hAPP(U_6885,sK128(U_6886,U_6885,U_6884,U_6883,U_6882)) != hAPP(U_6886,sK128(U_6886,U_6885,U_6884,U_6883,U_6882))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK128(U_6886,U_6885,U_6884,U_6883,U_6882))) )
| ~ c_Nat__Transfer_Onat__set(U_6884)
| U_6883 != U_6884
| ~ class_Groups_Ocomm__monoid__mult(U_6882)
| ~ class_Groups_Ocomm__monoid__add(U_6882) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_6881,sK128(U_6886,U_6885,U_6884,U_6883,U_6882))],[f_2092_2]) ).
cnf(f_2092_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK128(U_6886,U_6885,U_6884,U_6883,U_6882)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_6882),U_6885),U_6883) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_6882),U_6886),U_6884)
| ~ c_Nat__Transfer_Onat__set(U_6884)
| U_6883 != U_6884
| ~ class_Groups_Ocomm__monoid__mult(U_6882)
| ~ class_Groups_Ocomm__monoid__add(U_6882) ),
inference(clausify,[status(thm)],[f_2092_3]) ).
cnf(f_2092_5,plain,
( hAPP(U_6885,sK128(U_6886,U_6885,U_6884,U_6883,U_6882)) != hAPP(U_6886,sK128(U_6886,U_6885,U_6884,U_6883,U_6882))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_6882),U_6885),U_6883) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_6882),U_6886),U_6884)
| ~ c_Nat__Transfer_Onat__set(U_6884)
| U_6883 != U_6884
| ~ class_Groups_Ocomm__monoid__mult(U_6882)
| ~ class_Groups_Ocomm__monoid__add(U_6882) ),
inference(clausify,[status(thm)],[f_2092_3]) ).
fof(f_2093_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I19_J]) ).
fof(f_2093_2,plain,
! [U_6890,U_6889,U_6888,U_6887] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6887,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_6887,U_6888,U_6889)),c_SetInterval_Oord__class_OatLeastAtMost(U_6887,U_6889,U_6890)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_6887,U_6888,U_6890)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6887),U_6889),U_6890))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6887),U_6888),U_6889))
| ~ class_Orderings_Olinorder(U_6887) ),
inference(variable_rename,[status(thm)],[f_2093_1]) ).
cnf(f_2093_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6887,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_6887,U_6888,U_6889)),c_SetInterval_Oord__class_OatLeastAtMost(U_6887,U_6889,U_6890)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_6887,U_6888,U_6890)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6887),U_6889),U_6890))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6887),U_6888),U_6889))
| ~ class_Orderings_Olinorder(U_6887) ),
inference(clausify,[status(thm)],[f_2093_2]) ).
fof(f_2094_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I18_J]) ).
fof(f_2094_2,plain,
! [U_6894,U_6893,U_6892,U_6891] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6891,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_6891,U_6892,U_6893)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_6891,U_6893,U_6894)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6891,U_6892),U_6894)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6891),U_6893),U_6894))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6891),U_6892),U_6893))
| ~ class_Orderings_Olinorder(U_6891) ),
inference(variable_rename,[status(thm)],[f_2094_1]) ).
cnf(f_2094_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6891,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_6891,U_6892,U_6893)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_6891,U_6893,U_6894)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_6891,U_6892),U_6894)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6891),U_6893),U_6894))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6891),U_6892),U_6893))
| ~ class_Orderings_Olinorder(U_6891) ),
inference(clausify,[status(thm)],[f_2094_2]) ).
fof(f_2095_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_d_2))
| ( ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_d_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_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_c_2),V_d_2))
& ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_d_2),V_b_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_c_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) ) )
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastatMost__psubset__iff]) ).
fof(f_2095_2,plain,
! [U_6898,U_6897,U_6896,U_6895] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6895,U_6896)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6897,U_6898)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6897),U_6898))
| ( ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6898),U_6896))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6896),U_6898)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6895),U_6897))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6897),U_6895)) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6896),U_6898))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6897),U_6895)) )
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6895),U_6896)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6897),U_6898))
& ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6898),U_6896))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6896),U_6898)) )
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6895),U_6897))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6897),U_6895)) ) )
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6896),U_6898))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6897),U_6895)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6895),U_6896)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6895,U_6896)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6897,U_6898))) ) ),
inference(variable_rename,[status(thm)],[f_2095_1]) ).
fof(f_2095_3,plain,
( ! [U_6906,U_6904,U_6902,U_6900] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6900,U_6902)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6904,U_6906)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6904),U_6906))
| ( ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6906),U_6902))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6902),U_6906)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6900),U_6904))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6904),U_6900)) ) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6902),U_6906))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6904),U_6900)) )
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6900),U_6902)) ) )
& ! [U_6905,U_6903,U_6901,U_6899] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903),U_6905))
& ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6905),U_6901))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6901),U_6905)) )
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6899),U_6903))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903),U_6899)) ) )
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6901),U_6905))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903),U_6899)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6899),U_6901)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6899,U_6901)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903,U_6905))) ) ),
inference(miniscope,[status(thm)],[f_2095_2]) ).
cnf(f_2095_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903),U_6899))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6899),U_6901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6899,U_6901)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903,U_6905))) ),
inference(clausify,[status(thm)],[f_2095_3]) ).
cnf(f_2095_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6901),U_6905))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6899),U_6901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6899,U_6901)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903,U_6905))) ),
inference(clausify,[status(thm)],[f_2095_3]) ).
cnf(f_2095_6,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6901),U_6905))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903),U_6899))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6899),U_6901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6899,U_6901)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903,U_6905))) ),
inference(clausify,[status(thm)],[f_2095_3]) ).
cnf(f_2095_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6905),U_6901))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903),U_6899))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6899),U_6901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6899,U_6901)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903,U_6905))) ),
inference(clausify,[status(thm)],[f_2095_3]) ).
cnf(f_2095_8,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6901),U_6905))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6899),U_6903))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6899),U_6901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6899,U_6901)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903,U_6905))) ),
inference(clausify,[status(thm)],[f_2095_3]) ).
cnf(f_2095_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6905),U_6901))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6899),U_6903))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6899),U_6901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6899,U_6901)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903,U_6905))) ),
inference(clausify,[status(thm)],[f_2095_3]) ).
cnf(f_2095_10,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903),U_6905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6899,U_6901)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6903,U_6905))) ),
inference(clausify,[status(thm)],[f_2095_3]) ).
cnf(f_2095_11,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6900),U_6902))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6904),U_6906))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6900,U_6902)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6904,U_6906))) ),
inference(clausify,[status(thm)],[f_2095_3]) ).
cnf(f_2095_12,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6900),U_6904))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6904),U_6900))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6902),U_6906))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6904),U_6900))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6904),U_6906))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6900,U_6902)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6904,U_6906))) ),
inference(clausify,[status(thm)],[f_2095_3]) ).
cnf(f_2095_13,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6906),U_6902))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6902),U_6906))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6902),U_6906))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6904),U_6900))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6904),U_6906))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6900,U_6902)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_6904,U_6906))) ),
inference(clausify,[status(thm)],[f_2095_3]) ).
fof(f_2096_1,plain,
! [V_P_2,V_a1_2,V_a0_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2))
| ? [B_i,B_j] :
( ~ hBOOL(hAPP(hAPP(V_P_2,B_i),B_j))
& ( hBOOL(hAPP(hAPP(V_P_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(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),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(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))) ),
inference(fof_nnf,[status(thm)],[fact_upto_Opinduct]) ).
fof(f_2096_2,plain,
! [U_6911,U_6910,U_6909] :
( hBOOL(hAPP(hAPP(U_6911,U_6909),U_6910))
| ? [U_6908,U_6907] :
( ~ hBOOL(hAPP(hAPP(U_6911,U_6908),U_6907))
& ( hBOOL(hAPP(hAPP(U_6911,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6908),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6907))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6908),U_6907)) )
& 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),U_6908),U_6907))) )
| ~ 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),U_6909),U_6910))) ),
inference(variable_rename,[status(thm)],[f_2096_1]) ).
fof(f_2096_3,plain,
! [U_6911,U_6910,U_6909] :
( hBOOL(hAPP(hAPP(U_6911,U_6909),U_6910))
| ? [U_6907] :
( ~ hBOOL(hAPP(hAPP(U_6911,sK129(U_6911,U_6910,U_6909)),U_6907))
& ( hBOOL(hAPP(hAPP(U_6911,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK129(U_6911,U_6910,U_6909)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_6907))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK129(U_6911,U_6910,U_6909)),U_6907)) )
& 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),sK129(U_6911,U_6910,U_6909)),U_6907))) )
| ~ 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),U_6909),U_6910))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_6908,sK129(U_6911,U_6910,U_6909))],[f_2096_2]) ).
fof(f_2096_4,plain,
! [U_6911,U_6910,U_6909] :
( hBOOL(hAPP(hAPP(U_6911,U_6909),U_6910))
| ( ~ hBOOL(hAPP(hAPP(U_6911,sK129(U_6911,U_6910,U_6909)),sK130(U_6911,U_6910,U_6909)))
& ( hBOOL(hAPP(hAPP(U_6911,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK129(U_6911,U_6910,U_6909)),c_Groups_Oone__class_Oone(tc_Int_Oint))),sK130(U_6911,U_6910,U_6909)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK129(U_6911,U_6910,U_6909)),sK130(U_6911,U_6910,U_6909))) )
& 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),sK129(U_6911,U_6910,U_6909)),sK130(U_6911,U_6910,U_6909)))) )
| ~ 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),U_6909),U_6910))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_6907,sK130(U_6911,U_6910,U_6909))],[f_2096_3]) ).
cnf(f_2096_5,plain,
( 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),sK129(U_6911,U_6910,U_6909)),sK130(U_6911,U_6910,U_6909))))
| hBOOL(hAPP(hAPP(U_6911,U_6909),U_6910))
| ~ 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),U_6909),U_6910))) ),
inference(clausify,[status(thm)],[f_2096_4]) ).
cnf(f_2096_6,plain,
( hBOOL(hAPP(hAPP(U_6911,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK129(U_6911,U_6910,U_6909)),c_Groups_Oone__class_Oone(tc_Int_Oint))),sK130(U_6911,U_6910,U_6909)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK129(U_6911,U_6910,U_6909)),sK130(U_6911,U_6910,U_6909)))
| hBOOL(hAPP(hAPP(U_6911,U_6909),U_6910))
| ~ 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),U_6909),U_6910))) ),
inference(clausify,[status(thm)],[f_2096_4]) ).
cnf(f_2096_7,plain,
( ~ hBOOL(hAPP(hAPP(U_6911,sK129(U_6911,U_6910,U_6909)),sK130(U_6911,U_6910,U_6909)))
| hBOOL(hAPP(hAPP(U_6911,U_6909),U_6910))
| ~ 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),U_6909),U_6910))) ),
inference(clausify,[status(thm)],[f_2096_4]) ).
fof(f_2097_1,plain,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(V_B_2,V_x_2))
| hBOOL(hAPP(V_A_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_sup1E]) ).
fof(f_2097_2,plain,
! [U_6915,U_6914,U_6913,U_6912] :
( hBOOL(hAPP(U_6914,U_6915))
| hBOOL(hAPP(U_6913,U_6915))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6912,tc_HOL_Obool)),U_6913),U_6914),U_6915)) ),
inference(variable_rename,[status(thm)],[f_2097_1]) ).
fof(f_2097_3,plain,
! [U_6915,U_6914,U_6913] :
( ! [U_6912] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6912,tc_HOL_Obool)),U_6913),U_6914),U_6915))
| hBOOL(hAPP(U_6914,U_6915))
| hBOOL(hAPP(U_6913,U_6915)) ),
inference(miniscope,[status(thm)],[f_2097_2]) ).
cnf(f_2097_4,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6912,tc_HOL_Obool)),U_6913),U_6914),U_6915))
| hBOOL(hAPP(U_6914,U_6915))
| hBOOL(hAPP(U_6913,U_6915)) ),
inference(clausify,[status(thm)],[f_2097_3]) ).
fof(f_2098_1,plain,
! [T_b,V_A_2,V_x_2,V_B_2] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
| ( ~ hBOOL(hAPP(V_A_2,V_x_2))
& ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_sup1CI]) ).
fof(f_2098_2,plain,
! [U_6919,U_6918,U_6917,U_6916] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6919,tc_HOL_Obool)),U_6918),U_6916),U_6917))
| ( ~ hBOOL(hAPP(U_6918,U_6917))
& ~ hBOOL(hAPP(U_6916,U_6917)) ) ),
inference(variable_rename,[status(thm)],[f_2098_1]) ).
cnf(f_2098_3,plain,
( ~ hBOOL(hAPP(U_6916,U_6917))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6919,tc_HOL_Obool)),U_6918),U_6916),U_6917)) ),
inference(clausify,[status(thm)],[f_2098_2]) ).
cnf(f_2098_4,plain,
( ~ hBOOL(hAPP(U_6918,U_6917))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6919,tc_HOL_Obool)),U_6918),U_6916),U_6917)) ),
inference(clausify,[status(thm)],[f_2098_2]) ).
fof(f_2099_1,plain,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_image__Un]) ).
fof(f_2099_2,plain,
! [U_6924,U_6923,U_6922,U_6921,U_6920] : hAPP(c_Set_Oimage(U_6920,U_6921,U_6922),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6920,tc_HOL_Obool)),U_6923),U_6924)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6921,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_6920,U_6921,U_6922),U_6923)),hAPP(c_Set_Oimage(U_6920,U_6921,U_6922),U_6924)),
inference(variable_rename,[status(thm)],[f_2099_1]) ).
cnf(f_2099_3,plain,
hAPP(c_Set_Oimage(U_6920,U_6921,U_6922),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6920,tc_HOL_Obool)),U_6923),U_6924)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6921,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_6920,U_6921,U_6922),U_6923)),hAPP(c_Set_Oimage(U_6920,U_6921,U_6922),U_6924)),
inference(clausify,[status(thm)],[f_2099_2]) ).
fof(f_2100_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Un__Diff]) ).
fof(f_2100_2,plain,
! [U_6928,U_6927,U_6926,U_6925] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6925,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6925,tc_HOL_Obool)),U_6926),U_6927)),U_6928) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6925,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6925,tc_HOL_Obool)),U_6926),U_6928)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6925,tc_HOL_Obool)),U_6927),U_6928)),
inference(variable_rename,[status(thm)],[f_2100_1]) ).
cnf(f_2100_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6925,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6925,tc_HOL_Obool)),U_6926),U_6927)),U_6928) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6925,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6925,tc_HOL_Obool)),U_6926),U_6928)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6925,tc_HOL_Obool)),U_6927),U_6928)),
inference(clausify,[status(thm)],[f_2100_2]) ).
fof(f_2101_1,plain,
! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2),
inference(fof_nnf,[status(thm)],[fact_Un__Diff__cancel2]) ).
fof(f_2101_2,plain,
! [U_6931,U_6930,U_6929] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6929,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6929,tc_HOL_Obool)),U_6930),U_6931)),U_6931) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6929,tc_HOL_Obool)),U_6930),U_6931),
inference(variable_rename,[status(thm)],[f_2101_1]) ).
cnf(f_2101_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6929,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6929,tc_HOL_Obool)),U_6930),U_6931)),U_6931) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6929,tc_HOL_Obool)),U_6930),U_6931),
inference(clausify,[status(thm)],[f_2101_2]) ).
fof(f_2102_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
inference(fof_nnf,[status(thm)],[fact_Un__Diff__cancel]) ).
fof(f_2102_2,plain,
! [U_6934,U_6933,U_6932] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6932,tc_HOL_Obool)),U_6933),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6932,tc_HOL_Obool)),U_6934),U_6933)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6932,tc_HOL_Obool)),U_6933),U_6934),
inference(variable_rename,[status(thm)],[f_2102_1]) ).
cnf(f_2102_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6932,tc_HOL_Obool)),U_6933),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6932,tc_HOL_Obool)),U_6934),U_6933)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6932,tc_HOL_Obool)),U_6933),U_6934),
inference(clausify,[status(thm)],[f_2102_2]) ).
fof(f_2103_1,plain,
! [T_b] :
( c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Lattices_Osemilattice__sup(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sup__max]) ).
fof(f_2103_2,plain,
! [U_6935] :
( c_Lattices_Osemilattice__sup__class_Osup(U_6935) = c_Orderings_Oord__class_Omax(U_6935)
| ~ class_Orderings_Olinorder(U_6935)
| ~ class_Lattices_Osemilattice__sup(U_6935) ),
inference(variable_rename,[status(thm)],[f_2103_1]) ).
cnf(f_2103_3,plain,
( c_Lattices_Osemilattice__sup__class_Osup(U_6935) = c_Orderings_Oord__class_Omax(U_6935)
| ~ class_Orderings_Olinorder(U_6935)
| ~ class_Lattices_Osemilattice__sup(U_6935) ),
inference(clausify,[status(thm)],[f_2103_2]) ).
fof(f_2104_1,plain,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Un__absorb]) ).
fof(f_2104_2,plain,
! [U_6937,U_6936] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6936,tc_HOL_Obool)),U_6937),U_6937) = U_6937,
inference(variable_rename,[status(thm)],[f_2104_1]) ).
cnf(f_2104_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6936,tc_HOL_Obool)),U_6937),U_6937) = U_6937,
inference(clausify,[status(thm)],[f_2104_2]) ).
fof(f_2105_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2),
inference(fof_nnf,[status(thm)],[fact_Un__commute]) ).
fof(f_2105_2,plain,
! [U_6940,U_6939,U_6938] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6938,tc_HOL_Obool)),U_6939),U_6940) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6938,tc_HOL_Obool)),U_6940),U_6939),
inference(variable_rename,[status(thm)],[f_2105_1]) ).
cnf(f_2105_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6938,tc_HOL_Obool)),U_6939),U_6940) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6938,tc_HOL_Obool)),U_6940),U_6939),
inference(clausify,[status(thm)],[f_2105_2]) ).
fof(f_2106_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
inference(fof_nnf,[status(thm)],[fact_Un__left__absorb]) ).
fof(f_2106_2,plain,
! [U_6943,U_6942,U_6941] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6941,tc_HOL_Obool)),U_6942),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6941,tc_HOL_Obool)),U_6942),U_6943)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6941,tc_HOL_Obool)),U_6942),U_6943),
inference(variable_rename,[status(thm)],[f_2106_1]) ).
cnf(f_2106_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6941,tc_HOL_Obool)),U_6942),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6941,tc_HOL_Obool)),U_6942),U_6943)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6941,tc_HOL_Obool)),U_6942),U_6943),
inference(clausify,[status(thm)],[f_2106_2]) ).
fof(f_2107_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Un__left__commute]) ).
fof(f_2107_2,plain,
! [U_6947,U_6946,U_6945,U_6944] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6944,tc_HOL_Obool)),U_6945),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6944,tc_HOL_Obool)),U_6946),U_6947)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6944,tc_HOL_Obool)),U_6946),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6944,tc_HOL_Obool)),U_6945),U_6947)),
inference(variable_rename,[status(thm)],[f_2107_1]) ).
cnf(f_2107_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6944,tc_HOL_Obool)),U_6945),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6944,tc_HOL_Obool)),U_6946),U_6947)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6944,tc_HOL_Obool)),U_6946),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6944,tc_HOL_Obool)),U_6945),U_6947)),
inference(clausify,[status(thm)],[f_2107_2]) ).
fof(f_2108_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Un__assoc]) ).
fof(f_2108_2,plain,
! [U_6951,U_6950,U_6949,U_6948] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6948,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6948,tc_HOL_Obool)),U_6949),U_6950)),U_6951) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6948,tc_HOL_Obool)),U_6949),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6948,tc_HOL_Obool)),U_6950),U_6951)),
inference(variable_rename,[status(thm)],[f_2108_1]) ).
cnf(f_2108_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6948,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6948,tc_HOL_Obool)),U_6949),U_6950)),U_6951) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6948,tc_HOL_Obool)),U_6949),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6948,tc_HOL_Obool)),U_6950),U_6951)),
inference(clausify,[status(thm)],[f_2108_2]) ).
fof(f_2109_1,plain,
! [V_P_2,V_B_2,V_A_2,T_b] :
( ( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
| ( ! [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
& ! [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) )
& ( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
| ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ! [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
inference(fof_nnf,[status(thm)],[fact_bex__Un]) ).
fof(f_2109_2,plain,
! [U_6961,U_6960,U_6959,U_6958] :
( ( ? [U_6957] :
( hBOOL(hAPP(U_6961,U_6957))
& hBOOL(hAPP(hAPP(c_member(U_6958),U_6957),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6958,tc_HOL_Obool)),U_6959),U_6960))) )
| ( ! [U_6956] :
( ~ hBOOL(hAPP(U_6961,U_6956))
| ~ hBOOL(hAPP(hAPP(c_member(U_6958),U_6956),U_6960)) )
& ! [U_6955] :
( ~ hBOOL(hAPP(U_6961,U_6955))
| ~ hBOOL(hAPP(hAPP(c_member(U_6958),U_6955),U_6959)) ) ) )
& ( ? [U_6954] :
( hBOOL(hAPP(U_6961,U_6954))
& hBOOL(hAPP(hAPP(c_member(U_6958),U_6954),U_6960)) )
| ? [U_6953] :
( hBOOL(hAPP(U_6961,U_6953))
& hBOOL(hAPP(hAPP(c_member(U_6958),U_6953),U_6959)) )
| ! [U_6952] :
( ~ hBOOL(hAPP(U_6961,U_6952))
| ~ hBOOL(hAPP(hAPP(c_member(U_6958),U_6952),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6958,tc_HOL_Obool)),U_6959),U_6960))) ) ) ),
inference(variable_rename,[status(thm)],[f_2109_1]) ).
fof(f_2109_3,plain,
( ! [U_6969,U_6967,U_6965,U_6963] :
( ? [U_6957] :
( hBOOL(hAPP(U_6969,U_6957))
& hBOOL(hAPP(hAPP(c_member(U_6963),U_6957),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6963,tc_HOL_Obool)),U_6965),U_6967))) )
| ( ! [U_6956] :
( ~ hBOOL(hAPP(U_6969,U_6956))
| ~ hBOOL(hAPP(hAPP(c_member(U_6963),U_6956),U_6967)) )
& ! [U_6955] :
( ~ hBOOL(hAPP(U_6969,U_6955))
| ~ hBOOL(hAPP(hAPP(c_member(U_6963),U_6955),U_6965)) ) ) )
& ! [U_6968,U_6966,U_6964,U_6962] :
( ? [U_6954] :
( hBOOL(hAPP(U_6968,U_6954))
& hBOOL(hAPP(hAPP(c_member(U_6962),U_6954),U_6966)) )
| ? [U_6953] :
( hBOOL(hAPP(U_6968,U_6953))
& hBOOL(hAPP(hAPP(c_member(U_6962),U_6953),U_6964)) )
| ! [U_6952] :
( ~ hBOOL(hAPP(U_6968,U_6952))
| ~ hBOOL(hAPP(hAPP(c_member(U_6962),U_6952),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6962,tc_HOL_Obool)),U_6964),U_6966))) ) ) ),
inference(miniscope,[status(thm)],[f_2109_2]) ).
fof(f_2109_4,plain,
( ! [U_6969,U_6967,U_6965,U_6963] :
( ? [U_6957] :
( hBOOL(hAPP(U_6969,U_6957))
& hBOOL(hAPP(hAPP(c_member(U_6963),U_6957),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6963,tc_HOL_Obool)),U_6965),U_6967))) )
| ( ! [U_6956] :
( ~ hBOOL(hAPP(U_6969,U_6956))
| ~ hBOOL(hAPP(hAPP(c_member(U_6963),U_6956),U_6967)) )
& ! [U_6955] :
( ~ hBOOL(hAPP(U_6969,U_6955))
| ~ hBOOL(hAPP(hAPP(c_member(U_6963),U_6955),U_6965)) ) ) )
& ! [U_6968,U_6966,U_6964,U_6962] :
( ? [U_6954] :
( hBOOL(hAPP(U_6968,U_6954))
& hBOOL(hAPP(hAPP(c_member(U_6962),U_6954),U_6966)) )
| ( hBOOL(hAPP(U_6968,sK131(U_6968,U_6966,U_6964,U_6962)))
& hBOOL(hAPP(hAPP(c_member(U_6962),sK131(U_6968,U_6966,U_6964,U_6962)),U_6964)) )
| ! [U_6952] :
( ~ hBOOL(hAPP(U_6968,U_6952))
| ~ hBOOL(hAPP(hAPP(c_member(U_6962),U_6952),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6962,tc_HOL_Obool)),U_6964),U_6966))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_6953,sK131(U_6968,U_6966,U_6964,U_6962))],[f_2109_3]) ).
fof(f_2109_5,plain,
( ! [U_6969,U_6967,U_6965,U_6963] :
( ? [U_6957] :
( hBOOL(hAPP(U_6969,U_6957))
& hBOOL(hAPP(hAPP(c_member(U_6963),U_6957),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6963,tc_HOL_Obool)),U_6965),U_6967))) )
| ( ! [U_6956] :
( ~ hBOOL(hAPP(U_6969,U_6956))
| ~ hBOOL(hAPP(hAPP(c_member(U_6963),U_6956),U_6967)) )
& ! [U_6955] :
( ~ hBOOL(hAPP(U_6969,U_6955))
| ~ hBOOL(hAPP(hAPP(c_member(U_6963),U_6955),U_6965)) ) ) )
& ! [U_6968,U_6966,U_6964,U_6962] :
( ( hBOOL(hAPP(U_6968,sK132(U_6968,U_6966,U_6964,U_6962)))
& hBOOL(hAPP(hAPP(c_member(U_6962),sK132(U_6968,U_6966,U_6964,U_6962)),U_6966)) )
| ( hBOOL(hAPP(U_6968,sK131(U_6968,U_6966,U_6964,U_6962)))
& hBOOL(hAPP(hAPP(c_member(U_6962),sK131(U_6968,U_6966,U_6964,U_6962)),U_6964)) )
| ! [U_6952] :
( ~ hBOOL(hAPP(U_6968,U_6952))
| ~ hBOOL(hAPP(hAPP(c_member(U_6962),U_6952),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6962,tc_HOL_Obool)),U_6964),U_6966))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_6954,sK132(U_6968,U_6966,U_6964,U_6962))],[f_2109_4]) ).
fof(f_2109_6,plain,
( ! [U_6969,U_6967,U_6965,U_6963] :
( ( hBOOL(hAPP(U_6969,sK133(U_6969,U_6967,U_6965,U_6963)))
& hBOOL(hAPP(hAPP(c_member(U_6963),sK133(U_6969,U_6967,U_6965,U_6963)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6963,tc_HOL_Obool)),U_6965),U_6967))) )
| ( ! [U_6956] :
( ~ hBOOL(hAPP(U_6969,U_6956))
| ~ hBOOL(hAPP(hAPP(c_member(U_6963),U_6956),U_6967)) )
& ! [U_6955] :
( ~ hBOOL(hAPP(U_6969,U_6955))
| ~ hBOOL(hAPP(hAPP(c_member(U_6963),U_6955),U_6965)) ) ) )
& ! [U_6968,U_6966,U_6964,U_6962] :
( ( hBOOL(hAPP(U_6968,sK132(U_6968,U_6966,U_6964,U_6962)))
& hBOOL(hAPP(hAPP(c_member(U_6962),sK132(U_6968,U_6966,U_6964,U_6962)),U_6966)) )
| ( hBOOL(hAPP(U_6968,sK131(U_6968,U_6966,U_6964,U_6962)))
& hBOOL(hAPP(hAPP(c_member(U_6962),sK131(U_6968,U_6966,U_6964,U_6962)),U_6964)) )
| ! [U_6952] :
( ~ hBOOL(hAPP(U_6968,U_6952))
| ~ hBOOL(hAPP(hAPP(c_member(U_6962),U_6952),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6962,tc_HOL_Obool)),U_6964),U_6966))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_6957,sK133(U_6969,U_6967,U_6965,U_6963))],[f_2109_5]) ).
cnf(f_2109_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_6962),sK132(U_6968,U_6966,U_6964,U_6962)),U_6966))
| hBOOL(hAPP(hAPP(c_member(U_6962),sK131(U_6968,U_6966,U_6964,U_6962)),U_6964))
| ~ hBOOL(hAPP(U_6968,U_6952))
| ~ hBOOL(hAPP(hAPP(c_member(U_6962),U_6952),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6962,tc_HOL_Obool)),U_6964),U_6966))) ),
inference(clausify,[status(thm)],[f_2109_6]) ).
cnf(f_2109_8,plain,
( hBOOL(hAPP(U_6968,sK132(U_6968,U_6966,U_6964,U_6962)))
| hBOOL(hAPP(hAPP(c_member(U_6962),sK131(U_6968,U_6966,U_6964,U_6962)),U_6964))
| ~ hBOOL(hAPP(U_6968,U_6952))
| ~ hBOOL(hAPP(hAPP(c_member(U_6962),U_6952),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6962,tc_HOL_Obool)),U_6964),U_6966))) ),
inference(clausify,[status(thm)],[f_2109_6]) ).
cnf(f_2109_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_6962),sK132(U_6968,U_6966,U_6964,U_6962)),U_6966))
| hBOOL(hAPP(U_6968,sK131(U_6968,U_6966,U_6964,U_6962)))
| ~ hBOOL(hAPP(U_6968,U_6952))
| ~ hBOOL(hAPP(hAPP(c_member(U_6962),U_6952),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6962,tc_HOL_Obool)),U_6964),U_6966))) ),
inference(clausify,[status(thm)],[f_2109_6]) ).
cnf(f_2109_10,plain,
( hBOOL(hAPP(U_6968,sK132(U_6968,U_6966,U_6964,U_6962)))
| hBOOL(hAPP(U_6968,sK131(U_6968,U_6966,U_6964,U_6962)))
| ~ hBOOL(hAPP(U_6968,U_6952))
| ~ hBOOL(hAPP(hAPP(c_member(U_6962),U_6952),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6962,tc_HOL_Obool)),U_6964),U_6966))) ),
inference(clausify,[status(thm)],[f_2109_6]) ).
cnf(f_2109_11,plain,
( hBOOL(hAPP(hAPP(c_member(U_6963),sK133(U_6969,U_6967,U_6965,U_6963)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6963,tc_HOL_Obool)),U_6965),U_6967)))
| ~ hBOOL(hAPP(U_6969,U_6955))
| ~ hBOOL(hAPP(hAPP(c_member(U_6963),U_6955),U_6965)) ),
inference(clausify,[status(thm)],[f_2109_6]) ).
cnf(f_2109_12,plain,
( hBOOL(hAPP(U_6969,sK133(U_6969,U_6967,U_6965,U_6963)))
| ~ hBOOL(hAPP(U_6969,U_6955))
| ~ hBOOL(hAPP(hAPP(c_member(U_6963),U_6955),U_6965)) ),
inference(clausify,[status(thm)],[f_2109_6]) ).
cnf(f_2109_13,plain,
( hBOOL(hAPP(hAPP(c_member(U_6963),sK133(U_6969,U_6967,U_6965,U_6963)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6963,tc_HOL_Obool)),U_6965),U_6967)))
| ~ hBOOL(hAPP(U_6969,U_6956))
| ~ hBOOL(hAPP(hAPP(c_member(U_6963),U_6956),U_6967)) ),
inference(clausify,[status(thm)],[f_2109_6]) ).
cnf(f_2109_14,plain,
( hBOOL(hAPP(U_6969,sK133(U_6969,U_6967,U_6965,U_6963)))
| ~ hBOOL(hAPP(U_6969,U_6956))
| ~ hBOOL(hAPP(hAPP(c_member(U_6963),U_6956),U_6967)) ),
inference(clausify,[status(thm)],[f_2109_6]) ).
fof(f_2110_1,plain,
! [V_P_2,V_B_2,V_A_2,T_b] :
( ( ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ( ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
& ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
inference(fof_nnf,[status(thm)],[fact_ball__Un]) ).
fof(f_2110_2,plain,
! [U_6979,U_6978,U_6977,U_6976] :
( ( ! [U_6975] :
( hBOOL(hAPP(U_6979,U_6975))
| ~ hBOOL(hAPP(hAPP(c_member(U_6976),U_6975),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6976,tc_HOL_Obool)),U_6977),U_6978))) )
| ? [U_6974] :
( ~ hBOOL(hAPP(U_6979,U_6974))
& hBOOL(hAPP(hAPP(c_member(U_6976),U_6974),U_6978)) )
| ? [U_6973] :
( ~ hBOOL(hAPP(U_6979,U_6973))
& hBOOL(hAPP(hAPP(c_member(U_6976),U_6973),U_6977)) ) )
& ( ( ! [U_6972] :
( hBOOL(hAPP(U_6979,U_6972))
| ~ hBOOL(hAPP(hAPP(c_member(U_6976),U_6972),U_6978)) )
& ! [U_6971] :
( hBOOL(hAPP(U_6979,U_6971))
| ~ hBOOL(hAPP(hAPP(c_member(U_6976),U_6971),U_6977)) ) )
| ? [U_6970] :
( ~ hBOOL(hAPP(U_6979,U_6970))
& hBOOL(hAPP(hAPP(c_member(U_6976),U_6970),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6976,tc_HOL_Obool)),U_6977),U_6978))) ) ) ),
inference(variable_rename,[status(thm)],[f_2110_1]) ).
fof(f_2110_3,plain,
( ! [U_6987,U_6985,U_6983,U_6981] :
( ! [U_6975] :
( hBOOL(hAPP(U_6987,U_6975))
| ~ hBOOL(hAPP(hAPP(c_member(U_6981),U_6975),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6981,tc_HOL_Obool)),U_6983),U_6985))) )
| ? [U_6974] :
( ~ hBOOL(hAPP(U_6987,U_6974))
& hBOOL(hAPP(hAPP(c_member(U_6981),U_6974),U_6985)) )
| ? [U_6973] :
( ~ hBOOL(hAPP(U_6987,U_6973))
& hBOOL(hAPP(hAPP(c_member(U_6981),U_6973),U_6983)) ) )
& ! [U_6986,U_6984,U_6982,U_6980] :
( ( ! [U_6972] :
( hBOOL(hAPP(U_6986,U_6972))
| ~ hBOOL(hAPP(hAPP(c_member(U_6980),U_6972),U_6984)) )
& ! [U_6971] :
( hBOOL(hAPP(U_6986,U_6971))
| ~ hBOOL(hAPP(hAPP(c_member(U_6980),U_6971),U_6982)) ) )
| ? [U_6970] :
( ~ hBOOL(hAPP(U_6986,U_6970))
& hBOOL(hAPP(hAPP(c_member(U_6980),U_6970),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6980,tc_HOL_Obool)),U_6982),U_6984))) ) ) ),
inference(miniscope,[status(thm)],[f_2110_2]) ).
fof(f_2110_4,plain,
( ! [U_6987,U_6985,U_6983,U_6981] :
( ! [U_6975] :
( hBOOL(hAPP(U_6987,U_6975))
| ~ hBOOL(hAPP(hAPP(c_member(U_6981),U_6975),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6981,tc_HOL_Obool)),U_6983),U_6985))) )
| ? [U_6974] :
( ~ hBOOL(hAPP(U_6987,U_6974))
& hBOOL(hAPP(hAPP(c_member(U_6981),U_6974),U_6985)) )
| ? [U_6973] :
( ~ hBOOL(hAPP(U_6987,U_6973))
& hBOOL(hAPP(hAPP(c_member(U_6981),U_6973),U_6983)) ) )
& ! [U_6986,U_6984,U_6982,U_6980] :
( ( ! [U_6972] :
( hBOOL(hAPP(U_6986,U_6972))
| ~ hBOOL(hAPP(hAPP(c_member(U_6980),U_6972),U_6984)) )
& ! [U_6971] :
( hBOOL(hAPP(U_6986,U_6971))
| ~ hBOOL(hAPP(hAPP(c_member(U_6980),U_6971),U_6982)) ) )
| ( ~ hBOOL(hAPP(U_6986,sK134(U_6986,U_6984,U_6982,U_6980)))
& hBOOL(hAPP(hAPP(c_member(U_6980),sK134(U_6986,U_6984,U_6982,U_6980)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6980,tc_HOL_Obool)),U_6982),U_6984))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_6970,sK134(U_6986,U_6984,U_6982,U_6980))],[f_2110_3]) ).
fof(f_2110_5,plain,
( ! [U_6987,U_6985,U_6983,U_6981] :
( ! [U_6975] :
( hBOOL(hAPP(U_6987,U_6975))
| ~ hBOOL(hAPP(hAPP(c_member(U_6981),U_6975),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6981,tc_HOL_Obool)),U_6983),U_6985))) )
| ? [U_6974] :
( ~ hBOOL(hAPP(U_6987,U_6974))
& hBOOL(hAPP(hAPP(c_member(U_6981),U_6974),U_6985)) )
| ( ~ hBOOL(hAPP(U_6987,sK135(U_6987,U_6985,U_6983,U_6981)))
& hBOOL(hAPP(hAPP(c_member(U_6981),sK135(U_6987,U_6985,U_6983,U_6981)),U_6983)) ) )
& ! [U_6986,U_6984,U_6982,U_6980] :
( ( ! [U_6972] :
( hBOOL(hAPP(U_6986,U_6972))
| ~ hBOOL(hAPP(hAPP(c_member(U_6980),U_6972),U_6984)) )
& ! [U_6971] :
( hBOOL(hAPP(U_6986,U_6971))
| ~ hBOOL(hAPP(hAPP(c_member(U_6980),U_6971),U_6982)) ) )
| ( ~ hBOOL(hAPP(U_6986,sK134(U_6986,U_6984,U_6982,U_6980)))
& hBOOL(hAPP(hAPP(c_member(U_6980),sK134(U_6986,U_6984,U_6982,U_6980)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6980,tc_HOL_Obool)),U_6982),U_6984))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_6973,sK135(U_6987,U_6985,U_6983,U_6981))],[f_2110_4]) ).
fof(f_2110_6,plain,
( ! [U_6987,U_6985,U_6983,U_6981] :
( ! [U_6975] :
( hBOOL(hAPP(U_6987,U_6975))
| ~ hBOOL(hAPP(hAPP(c_member(U_6981),U_6975),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6981,tc_HOL_Obool)),U_6983),U_6985))) )
| ( ~ hBOOL(hAPP(U_6987,sK136(U_6987,U_6985,U_6983,U_6981)))
& hBOOL(hAPP(hAPP(c_member(U_6981),sK136(U_6987,U_6985,U_6983,U_6981)),U_6985)) )
| ( ~ hBOOL(hAPP(U_6987,sK135(U_6987,U_6985,U_6983,U_6981)))
& hBOOL(hAPP(hAPP(c_member(U_6981),sK135(U_6987,U_6985,U_6983,U_6981)),U_6983)) ) )
& ! [U_6986,U_6984,U_6982,U_6980] :
( ( ! [U_6972] :
( hBOOL(hAPP(U_6986,U_6972))
| ~ hBOOL(hAPP(hAPP(c_member(U_6980),U_6972),U_6984)) )
& ! [U_6971] :
( hBOOL(hAPP(U_6986,U_6971))
| ~ hBOOL(hAPP(hAPP(c_member(U_6980),U_6971),U_6982)) ) )
| ( ~ hBOOL(hAPP(U_6986,sK134(U_6986,U_6984,U_6982,U_6980)))
& hBOOL(hAPP(hAPP(c_member(U_6980),sK134(U_6986,U_6984,U_6982,U_6980)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6980,tc_HOL_Obool)),U_6982),U_6984))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_6974,sK136(U_6987,U_6985,U_6983,U_6981))],[f_2110_5]) ).
cnf(f_2110_7,plain,
( hBOOL(hAPP(U_6986,U_6971))
| ~ hBOOL(hAPP(hAPP(c_member(U_6980),U_6971),U_6982))
| hBOOL(hAPP(hAPP(c_member(U_6980),sK134(U_6986,U_6984,U_6982,U_6980)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6980,tc_HOL_Obool)),U_6982),U_6984))) ),
inference(clausify,[status(thm)],[f_2110_6]) ).
cnf(f_2110_8,plain,
( hBOOL(hAPP(U_6986,U_6972))
| ~ hBOOL(hAPP(hAPP(c_member(U_6980),U_6972),U_6984))
| hBOOL(hAPP(hAPP(c_member(U_6980),sK134(U_6986,U_6984,U_6982,U_6980)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6980,tc_HOL_Obool)),U_6982),U_6984))) ),
inference(clausify,[status(thm)],[f_2110_6]) ).
cnf(f_2110_9,plain,
( hBOOL(hAPP(U_6986,U_6971))
| ~ hBOOL(hAPP(hAPP(c_member(U_6980),U_6971),U_6982))
| ~ hBOOL(hAPP(U_6986,sK134(U_6986,U_6984,U_6982,U_6980))) ),
inference(clausify,[status(thm)],[f_2110_6]) ).
cnf(f_2110_10,plain,
( hBOOL(hAPP(U_6986,U_6972))
| ~ hBOOL(hAPP(hAPP(c_member(U_6980),U_6972),U_6984))
| ~ hBOOL(hAPP(U_6986,sK134(U_6986,U_6984,U_6982,U_6980))) ),
inference(clausify,[status(thm)],[f_2110_6]) ).
cnf(f_2110_11,plain,
( hBOOL(hAPP(hAPP(c_member(U_6981),sK136(U_6987,U_6985,U_6983,U_6981)),U_6985))
| hBOOL(hAPP(hAPP(c_member(U_6981),sK135(U_6987,U_6985,U_6983,U_6981)),U_6983))
| hBOOL(hAPP(U_6987,U_6975))
| ~ hBOOL(hAPP(hAPP(c_member(U_6981),U_6975),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6981,tc_HOL_Obool)),U_6983),U_6985))) ),
inference(clausify,[status(thm)],[f_2110_6]) ).
cnf(f_2110_12,plain,
( ~ hBOOL(hAPP(U_6987,sK136(U_6987,U_6985,U_6983,U_6981)))
| hBOOL(hAPP(hAPP(c_member(U_6981),sK135(U_6987,U_6985,U_6983,U_6981)),U_6983))
| hBOOL(hAPP(U_6987,U_6975))
| ~ hBOOL(hAPP(hAPP(c_member(U_6981),U_6975),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6981,tc_HOL_Obool)),U_6983),U_6985))) ),
inference(clausify,[status(thm)],[f_2110_6]) ).
cnf(f_2110_13,plain,
( hBOOL(hAPP(hAPP(c_member(U_6981),sK136(U_6987,U_6985,U_6983,U_6981)),U_6985))
| ~ hBOOL(hAPP(U_6987,sK135(U_6987,U_6985,U_6983,U_6981)))
| hBOOL(hAPP(U_6987,U_6975))
| ~ hBOOL(hAPP(hAPP(c_member(U_6981),U_6975),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6981,tc_HOL_Obool)),U_6983),U_6985))) ),
inference(clausify,[status(thm)],[f_2110_6]) ).
cnf(f_2110_14,plain,
( ~ hBOOL(hAPP(U_6987,sK136(U_6987,U_6985,U_6983,U_6981)))
| ~ hBOOL(hAPP(U_6987,sK135(U_6987,U_6985,U_6983,U_6981)))
| hBOOL(hAPP(U_6987,U_6975))
| ~ hBOOL(hAPP(hAPP(c_member(U_6981),U_6975),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_6981,tc_HOL_Obool)),U_6983),U_6985))) ),
inference(clausify,[status(thm)],[f_2110_6]) ).
fof(f_2111_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_2111_2,plain,
! [U_6989,U_6988] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_6988),U_6989),U_6989) = U_6989
| ~ class_Lattices_Osemilattice__sup(U_6988) ),
inference(variable_rename,[status(thm)],[f_2111_1]) ).
cnf(f_2111_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_6988),U_6989),U_6989) = U_6989
| ~ class_Lattices_Osemilattice__sup(U_6988) ),
inference(clausify,[status(thm)],[f_2111_2]) ).
fof(f_2112_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_2112_2,plain,
! [U_6991,U_6990] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_6990),U_6991),U_6991) = U_6991
| ~ class_Lattices_Osemilattice__sup(U_6990) ),
inference(variable_rename,[status(thm)],[f_2112_1]) ).
cnf(f_2112_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_6990),U_6991),U_6991) = U_6991
| ~ class_Lattices_Osemilattice__sup(U_6990) ),
inference(clausify,[status(thm)],[f_2112_2]) ).
fof(f_2113_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_2113_2,plain,
! [U_6994,U_6993,U_6992] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_6992),U_6993),U_6994) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_6992),U_6994),U_6993)
| ~ class_Lattices_Osemilattice__sup(U_6992) ),
inference(variable_rename,[status(thm)],[f_2113_1]) ).
cnf(f_2113_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_6992),U_6993),U_6994) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_6992),U_6994),U_6993)
| ~ class_Lattices_Osemilattice__sup(U_6992) ),
inference(clausify,[status(thm)],[f_2113_2]) ).
fof(f_2114_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_2114_2,plain,
! [U_6997,U_6996,U_6995] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_6995),U_6996),U_6997) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_6995),U_6997),U_6996)
| ~ class_Lattices_Olattice(U_6995) ),
inference(variable_rename,[status(thm)],[f_2114_1]) ).
cnf(f_2114_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_6995),U_6996),U_6997) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_6995),U_6997),U_6996)
| ~ class_Lattices_Olattice(U_6995) ),
inference(clausify,[status(thm)],[f_2114_2]) ).
fof(f_2115_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_2115_2,plain,
! [U_7000,U_6999,U_6998] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_6998),U_6999),U_7000) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_6998),U_7000),U_6999)
| ~ class_Lattices_Osemilattice__sup(U_6998) ),
inference(variable_rename,[status(thm)],[f_2115_1]) ).
cnf(f_2115_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_6998),U_6999),U_7000) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_6998),U_7000),U_6999)
| ~ class_Lattices_Osemilattice__sup(U_6998) ),
inference(clausify,[status(thm)],[f_2115_2]) ).
fof(f_2116_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_2116_2,plain,
! [U_7003,U_7002,U_7001] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7001),U_7002),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7001),U_7002),U_7003)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7001),U_7002),U_7003)
| ~ class_Lattices_Osemilattice__sup(U_7001) ),
inference(variable_rename,[status(thm)],[f_2116_1]) ).
cnf(f_2116_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7001),U_7002),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7001),U_7002),U_7003)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7001),U_7002),U_7003)
| ~ class_Lattices_Osemilattice__sup(U_7001) ),
inference(clausify,[status(thm)],[f_2116_2]) ).
fof(f_2117_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_2117_2,plain,
! [U_7006,U_7005,U_7004] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7004),U_7005),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7004),U_7005),U_7006)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7004),U_7005),U_7006)
| ~ class_Lattices_Olattice(U_7004) ),
inference(variable_rename,[status(thm)],[f_2117_1]) ).
cnf(f_2117_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7004),U_7005),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7004),U_7005),U_7006)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7004),U_7005),U_7006)
| ~ class_Lattices_Olattice(U_7004) ),
inference(clausify,[status(thm)],[f_2117_2]) ).
fof(f_2118_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_2118_2,plain,
! [U_7009,U_7008,U_7007] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7007),U_7008),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7007),U_7008),U_7009)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7007),U_7008),U_7009)
| ~ class_Lattices_Osemilattice__sup(U_7007) ),
inference(variable_rename,[status(thm)],[f_2118_1]) ).
cnf(f_2118_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7007),U_7008),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7007),U_7008),U_7009)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7007),U_7008),U_7009)
| ~ class_Lattices_Osemilattice__sup(U_7007) ),
inference(clausify,[status(thm)],[f_2118_2]) ).
fof(f_2119_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_2119_2,plain,
! [U_7013,U_7012,U_7011,U_7010] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7010),U_7011),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7010),U_7012),U_7013)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7010),U_7012),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7010),U_7011),U_7013))
| ~ class_Lattices_Osemilattice__sup(U_7010) ),
inference(variable_rename,[status(thm)],[f_2119_1]) ).
cnf(f_2119_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7010),U_7011),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7010),U_7012),U_7013)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7010),U_7012),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7010),U_7011),U_7013))
| ~ class_Lattices_Osemilattice__sup(U_7010) ),
inference(clausify,[status(thm)],[f_2119_2]) ).
fof(f_2120_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_2120_2,plain,
! [U_7017,U_7016,U_7015,U_7014] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7014),U_7015),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7014),U_7016),U_7017)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7014),U_7016),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7014),U_7015),U_7017))
| ~ class_Lattices_Olattice(U_7014) ),
inference(variable_rename,[status(thm)],[f_2120_1]) ).
cnf(f_2120_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7014),U_7015),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7014),U_7016),U_7017)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7014),U_7016),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7014),U_7015),U_7017))
| ~ class_Lattices_Olattice(U_7014) ),
inference(clausify,[status(thm)],[f_2120_2]) ).
fof(f_2121_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_2121_2,plain,
! [U_7021,U_7020,U_7019,U_7018] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7018),U_7019),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7018),U_7020),U_7021)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7018),U_7020),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7018),U_7019),U_7021))
| ~ class_Lattices_Osemilattice__sup(U_7018) ),
inference(variable_rename,[status(thm)],[f_2121_1]) ).
cnf(f_2121_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7018),U_7019),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7018),U_7020),U_7021)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7018),U_7020),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7018),U_7019),U_7021))
| ~ class_Lattices_Osemilattice__sup(U_7018) ),
inference(clausify,[status(thm)],[f_2121_2]) ).
fof(f_2122_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_2122_2,plain,
! [U_7025,U_7024,U_7023,U_7022] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7022),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7022),U_7023),U_7024)),U_7025) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7022),U_7023),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7022),U_7024),U_7025))
| ~ class_Lattices_Osemilattice__sup(U_7022) ),
inference(variable_rename,[status(thm)],[f_2122_1]) ).
cnf(f_2122_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7022),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7022),U_7023),U_7024)),U_7025) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7022),U_7023),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7022),U_7024),U_7025))
| ~ class_Lattices_Osemilattice__sup(U_7022) ),
inference(clausify,[status(thm)],[f_2122_2]) ).
fof(f_2123_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_2123_2,plain,
! [U_7029,U_7028,U_7027,U_7026] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7026),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7026),U_7027),U_7028)),U_7029) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7026),U_7027),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7026),U_7028),U_7029))
| ~ class_Lattices_Olattice(U_7026) ),
inference(variable_rename,[status(thm)],[f_2123_1]) ).
cnf(f_2123_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7026),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7026),U_7027),U_7028)),U_7029) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7026),U_7027),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7026),U_7028),U_7029))
| ~ class_Lattices_Olattice(U_7026) ),
inference(clausify,[status(thm)],[f_2123_2]) ).
fof(f_2124_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_2124_2,plain,
! [U_7033,U_7032,U_7031,U_7030] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7030),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7030),U_7031),U_7032)),U_7033) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7030),U_7031),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7030),U_7032),U_7033))
| ~ class_Lattices_Osemilattice__sup(U_7030) ),
inference(variable_rename,[status(thm)],[f_2124_1]) ).
cnf(f_2124_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7030),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7030),U_7031),U_7032)),U_7033) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7030),U_7031),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7030),U_7032),U_7033))
| ~ class_Lattices_Osemilattice__sup(U_7030) ),
inference(clausify,[status(thm)],[f_2124_2]) ).
fof(f_2125_1,plain,
! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sup__apply]) ).
fof(f_2125_2,plain,
! [U_7038,U_7037,U_7036,U_7035,U_7034] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7035,U_7034)),U_7036),U_7037),U_7038) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7034),hAPP(U_7036,U_7038)),hAPP(U_7037,U_7038))
| ~ class_Lattices_Olattice(U_7034) ),
inference(variable_rename,[status(thm)],[f_2125_1]) ).
cnf(f_2125_3,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7035,U_7034)),U_7036),U_7037),U_7038) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7034),hAPP(U_7036,U_7038)),hAPP(U_7037,U_7038))
| ~ class_Lattices_Olattice(U_7034) ),
inference(clausify,[status(thm)],[f_2125_2]) ).
fof(f_2126_1,plain,
! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sup__fun__def]) ).
fof(f_2126_2,plain,
! [U_7043,U_7042,U_7041,U_7040,U_7039] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7040,U_7039)),U_7041),U_7042),U_7043) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7039),hAPP(U_7041,U_7043)),hAPP(U_7042,U_7043))
| ~ class_Lattices_Olattice(U_7039) ),
inference(variable_rename,[status(thm)],[f_2126_1]) ).
cnf(f_2126_3,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7040,U_7039)),U_7041),U_7042),U_7043) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7039),hAPP(U_7041,U_7043)),hAPP(U_7042,U_7043))
| ~ class_Lattices_Olattice(U_7039) ),
inference(clausify,[status(thm)],[f_2126_2]) ).
fof(f_2127_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_2127_2,plain,
! [U_7045,U_7044] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7044),U_7045),U_7045) = U_7045
| ~ class_Lattices_Olattice(U_7044) ),
inference(variable_rename,[status(thm)],[f_2127_1]) ).
cnf(f_2127_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7044),U_7045),U_7045) = U_7045
| ~ class_Lattices_Olattice(U_7044) ),
inference(clausify,[status(thm)],[f_2127_2]) ).
fof(f_2128_1,plain,
! [V_B_2,T_b,V_x_2,V_A_2] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
| ~ hBOOL(hAPP(V_A_2,V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_sup1I1]) ).
fof(f_2128_2,plain,
! [U_7049,U_7048,U_7047,U_7046] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7048,tc_HOL_Obool)),U_7046),U_7049),U_7047))
| ~ hBOOL(hAPP(U_7046,U_7047)) ),
inference(variable_rename,[status(thm)],[f_2128_1]) ).
cnf(f_2128_3,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7048,tc_HOL_Obool)),U_7046),U_7049),U_7047))
| ~ hBOOL(hAPP(U_7046,U_7047)) ),
inference(clausify,[status(thm)],[f_2128_2]) ).
fof(f_2129_1,plain,
! [V_A_2,T_b,V_x_2,V_B_2] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
| ~ hBOOL(hAPP(V_B_2,V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_sup1I2]) ).
fof(f_2129_2,plain,
! [U_7053,U_7052,U_7051,U_7050] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7052,tc_HOL_Obool)),U_7053),U_7050),U_7051))
| ~ hBOOL(hAPP(U_7050,U_7051)) ),
inference(variable_rename,[status(thm)],[f_2129_1]) ).
cnf(f_2129_3,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7052,tc_HOL_Obool)),U_7053),U_7050),U_7051))
| ~ hBOOL(hAPP(U_7050,U_7051)) ),
inference(clausify,[status(thm)],[f_2129_2]) ).
fof(f_2130_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_2130_2,plain,
! [U_7057,U_7056,U_7055,U_7054] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7054),U_7056),U_7057))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7054),U_7055),U_7057)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7054),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7054),U_7055),U_7056)),U_7057))
| ~ class_Lattices_Osemilattice__sup(U_7054) ),
inference(variable_rename,[status(thm)],[f_2130_1]) ).
cnf(f_2130_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7054),U_7055),U_7057))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7054),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7054),U_7055),U_7056)),U_7057))
| ~ class_Lattices_Osemilattice__sup(U_7054) ),
inference(clausify,[status(thm)],[f_2130_2]) ).
cnf(f_2130_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7054),U_7056),U_7057))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7054),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7054),U_7055),U_7056)),U_7057))
| ~ class_Lattices_Osemilattice__sup(U_7054) ),
inference(clausify,[status(thm)],[f_2130_2]) ).
fof(f_2131_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_2131_2,plain,
! [U_7062,U_7061,U_7060,U_7059,U_7058] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7058),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7058),U_7059),U_7061)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7058),U_7060),U_7062)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7058),U_7061),U_7062))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7058),U_7059),U_7060))
| ~ class_Lattices_Osemilattice__sup(U_7058) ),
inference(variable_rename,[status(thm)],[f_2131_1]) ).
cnf(f_2131_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7058),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7058),U_7059),U_7061)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7058),U_7060),U_7062)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7058),U_7061),U_7062))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7058),U_7059),U_7060))
| ~ class_Lattices_Osemilattice__sup(U_7058) ),
inference(clausify,[status(thm)],[f_2131_2]) ).
fof(f_2132_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_2132_2,plain,
! [U_7066,U_7065,U_7064,U_7063] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7063),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7063),U_7064),U_7066)),U_7065))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7063),U_7066),U_7065))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7063),U_7064),U_7065))
| ~ class_Lattices_Osemilattice__sup(U_7063) ),
inference(variable_rename,[status(thm)],[f_2132_1]) ).
cnf(f_2132_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7063),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7063),U_7064),U_7066)),U_7065))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7063),U_7066),U_7065))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7063),U_7064),U_7065))
| ~ class_Lattices_Osemilattice__sup(U_7063) ),
inference(clausify,[status(thm)],[f_2132_2]) ).
fof(f_2133_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_2133_2,plain,
! [U_7070,U_7069,U_7068,U_7067] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7067),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7067),U_7068),U_7070)),U_7069))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7067),U_7070),U_7069))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7067),U_7068),U_7069))
| ~ class_Lattices_Osemilattice__sup(U_7067) ),
inference(variable_rename,[status(thm)],[f_2133_1]) ).
cnf(f_2133_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7067),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7067),U_7068),U_7070)),U_7069))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7067),U_7070),U_7069))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7067),U_7068),U_7069))
| ~ class_Lattices_Osemilattice__sup(U_7067) ),
inference(clausify,[status(thm)],[f_2133_2]) ).
fof(f_2134_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_2134_2,plain,
! [U_7073,U_7072,U_7071] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7071),U_7073),U_7072) = U_7073
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7071),U_7072),U_7073))
| ~ class_Lattices_Osemilattice__sup(U_7071) ),
inference(variable_rename,[status(thm)],[f_2134_1]) ).
cnf(f_2134_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7071),U_7073),U_7072) = U_7073
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7071),U_7072),U_7073))
| ~ class_Lattices_Osemilattice__sup(U_7071) ),
inference(clausify,[status(thm)],[f_2134_2]) ).
fof(f_2135_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_2135_2,plain,
! [U_7076,U_7075,U_7074] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7074),U_7075),U_7076) = U_7076
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7074),U_7075),U_7076))
| ~ class_Lattices_Osemilattice__sup(U_7074) ),
inference(variable_rename,[status(thm)],[f_2135_1]) ).
cnf(f_2135_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7074),U_7075),U_7076) = U_7076
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7074),U_7075),U_7076))
| ~ class_Lattices_Osemilattice__sup(U_7074) ),
inference(clausify,[status(thm)],[f_2135_2]) ).
fof(f_2136_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_2136_2,plain,
! [U_7080,U_7079,U_7078,U_7077] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7077),U_7078),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7077),U_7080),U_7079)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7077),U_7078),U_7079))
| ~ class_Lattices_Osemilattice__sup(U_7077) ),
inference(variable_rename,[status(thm)],[f_2136_1]) ).
cnf(f_2136_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7077),U_7078),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7077),U_7080),U_7079)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7077),U_7078),U_7079))
| ~ class_Lattices_Osemilattice__sup(U_7077) ),
inference(clausify,[status(thm)],[f_2136_2]) ).
fof(f_2137_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_2137_2,plain,
! [U_7084,U_7083,U_7082,U_7081] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7081),U_7082),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7081),U_7083),U_7084)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7081),U_7082),U_7083))
| ~ class_Lattices_Osemilattice__sup(U_7081) ),
inference(variable_rename,[status(thm)],[f_2137_1]) ).
cnf(f_2137_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7081),U_7082),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7081),U_7083),U_7084)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7081),U_7082),U_7083))
| ~ class_Lattices_Osemilattice__sup(U_7081) ),
inference(clausify,[status(thm)],[f_2137_2]) ).
fof(f_2138_1,plain,
! [V_z_2,V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2)),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2)),V_z_2)) ) )
| ~ class_Lattices_Osemilattice__sup(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__sup__iff]) ).
fof(f_2138_2,plain,
! [U_7088,U_7087,U_7086,U_7085] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7085),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7085),U_7086),U_7087)),U_7088))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7085),U_7087),U_7088))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7085),U_7086),U_7088)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7085),U_7087),U_7088))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7085),U_7086),U_7088)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7085),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7085),U_7086),U_7087)),U_7088)) ) )
| ~ class_Lattices_Osemilattice__sup(U_7085) ),
inference(variable_rename,[status(thm)],[f_2138_1]) ).
cnf(f_2138_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7085),U_7086),U_7088))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7085),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7085),U_7086),U_7087)),U_7088))
| ~ class_Lattices_Osemilattice__sup(U_7085) ),
inference(clausify,[status(thm)],[f_2138_2]) ).
cnf(f_2138_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7085),U_7087),U_7088))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7085),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7085),U_7086),U_7087)),U_7088))
| ~ class_Lattices_Osemilattice__sup(U_7085) ),
inference(clausify,[status(thm)],[f_2138_2]) ).
cnf(f_2138_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7085),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7085),U_7086),U_7087)),U_7088))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7085),U_7087),U_7088))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7085),U_7086),U_7088))
| ~ class_Lattices_Osemilattice__sup(U_7085) ),
inference(clausify,[status(thm)],[f_2138_2]) ).
fof(f_2139_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) != V_y_2 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
| ~ class_Lattices_Osemilattice__sup(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__sup]) ).
fof(f_2139_2,plain,
! [U_7091,U_7090,U_7089] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7089),U_7090),U_7091))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7089),U_7090),U_7091) != U_7091 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7089),U_7090),U_7091) = U_7091
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7089),U_7090),U_7091)) ) )
| ~ class_Lattices_Osemilattice__sup(U_7089) ),
inference(variable_rename,[status(thm)],[f_2139_1]) ).
cnf(f_2139_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7089),U_7090),U_7091) = U_7091
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7089),U_7090),U_7091))
| ~ class_Lattices_Osemilattice__sup(U_7089) ),
inference(clausify,[status(thm)],[f_2139_2]) ).
cnf(f_2139_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7089),U_7090),U_7091))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7089),U_7090),U_7091) != U_7091
| ~ class_Lattices_Osemilattice__sup(U_7089) ),
inference(clausify,[status(thm)],[f_2139_2]) ).
fof(f_2140_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_2140_2,plain,
! [U_7094,U_7093,U_7092] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7092),U_7093),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7092),U_7094),U_7093)))
| ~ class_Lattices_Osemilattice__sup(U_7092) ),
inference(variable_rename,[status(thm)],[f_2140_1]) ).
cnf(f_2140_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7092),U_7093),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7092),U_7094),U_7093)))
| ~ class_Lattices_Osemilattice__sup(U_7092) ),
inference(clausify,[status(thm)],[f_2140_2]) ).
fof(f_2141_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_2141_2,plain,
! [U_7097,U_7096,U_7095] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7095),U_7096),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7095),U_7097),U_7096)))
| ~ class_Lattices_Olattice(U_7095) ),
inference(variable_rename,[status(thm)],[f_2141_1]) ).
cnf(f_2141_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7095),U_7096),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7095),U_7097),U_7096)))
| ~ class_Lattices_Olattice(U_7095) ),
inference(clausify,[status(thm)],[f_2141_2]) ).
fof(f_2142_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_2142_2,plain,
! [U_7100,U_7099,U_7098] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7098),U_7099),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7098),U_7099),U_7100)))
| ~ class_Lattices_Osemilattice__sup(U_7098) ),
inference(variable_rename,[status(thm)],[f_2142_1]) ).
cnf(f_2142_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7098),U_7099),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7098),U_7099),U_7100)))
| ~ class_Lattices_Osemilattice__sup(U_7098) ),
inference(clausify,[status(thm)],[f_2142_2]) ).
fof(f_2143_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_2143_2,plain,
! [U_7103,U_7102,U_7101] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7101),U_7102),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7101),U_7102),U_7103)))
| ~ class_Lattices_Olattice(U_7101) ),
inference(variable_rename,[status(thm)],[f_2143_1]) ).
cnf(f_2143_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7101),U_7102),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7101),U_7102),U_7103)))
| ~ class_Lattices_Olattice(U_7101) ),
inference(clausify,[status(thm)],[f_2143_2]) ).
fof(f_2144_1,plain,
! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),
inference(fof_nnf,[status(thm)],[fact_Un__upper1]) ).
fof(f_2144_2,plain,
! [U_7106,U_7105,U_7104] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7104,tc_HOL_Obool)),U_7105),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7104,tc_HOL_Obool)),U_7105),U_7106))),
inference(variable_rename,[status(thm)],[f_2144_1]) ).
cnf(f_2144_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7104,tc_HOL_Obool)),U_7105),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7104,tc_HOL_Obool)),U_7105),U_7106))),
inference(clausify,[status(thm)],[f_2144_2]) ).
fof(f_2145_1,plain,
! [V_A_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),
inference(fof_nnf,[status(thm)],[fact_Un__upper2]) ).
fof(f_2145_2,plain,
! [U_7109,U_7108,U_7107] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7107,tc_HOL_Obool)),U_7108),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7107,tc_HOL_Obool)),U_7109),U_7108))),
inference(variable_rename,[status(thm)],[f_2145_1]) ).
cnf(f_2145_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7107,tc_HOL_Obool)),U_7108),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7107,tc_HOL_Obool)),U_7109),U_7108))),
inference(clausify,[status(thm)],[f_2145_2]) ).
fof(f_2146_1,plain,
! [V_B_2,V_A_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != V_B_2 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_subset__Un__eq]) ).
fof(f_2146_2,plain,
! [U_7112,U_7111,U_7110] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7110,tc_HOL_Obool)),U_7111),U_7112))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7110,tc_HOL_Obool)),U_7111),U_7112) != U_7112 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7110,tc_HOL_Obool)),U_7111),U_7112) = U_7112
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7110,tc_HOL_Obool)),U_7111),U_7112)) ) ),
inference(variable_rename,[status(thm)],[f_2146_1]) ).
fof(f_2146_3,plain,
( ! [U_7118,U_7116,U_7114] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7114,tc_HOL_Obool)),U_7116),U_7118))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7114,tc_HOL_Obool)),U_7116),U_7118) != U_7118 )
& ! [U_7117,U_7115,U_7113] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7113,tc_HOL_Obool)),U_7115),U_7117) = U_7117
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7113,tc_HOL_Obool)),U_7115),U_7117)) ) ),
inference(miniscope,[status(thm)],[f_2146_2]) ).
cnf(f_2146_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7113,tc_HOL_Obool)),U_7115),U_7117) = U_7117
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7113,tc_HOL_Obool)),U_7115),U_7117)) ),
inference(clausify,[status(thm)],[f_2146_3]) ).
cnf(f_2146_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7114,tc_HOL_Obool)),U_7116),U_7118))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7114,tc_HOL_Obool)),U_7116),U_7118) != U_7118 ),
inference(clausify,[status(thm)],[f_2146_3]) ).
fof(f_2147_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Un__absorb1]) ).
fof(f_2147_2,plain,
! [U_7121,U_7120,U_7119] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7119,tc_HOL_Obool)),U_7120),U_7121) = U_7121
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7119,tc_HOL_Obool)),U_7120),U_7121)) ),
inference(variable_rename,[status(thm)],[f_2147_1]) ).
cnf(f_2147_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7119,tc_HOL_Obool)),U_7120),U_7121) = U_7121
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7119,tc_HOL_Obool)),U_7120),U_7121)) ),
inference(clausify,[status(thm)],[f_2147_2]) ).
fof(f_2148_1,plain,
! [V_A_2,V_B_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Un__absorb2]) ).
fof(f_2148_2,plain,
! [U_7124,U_7123,U_7122] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7122,tc_HOL_Obool)),U_7124),U_7123) = U_7124
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7122,tc_HOL_Obool)),U_7123),U_7124)) ),
inference(variable_rename,[status(thm)],[f_2148_1]) ).
cnf(f_2148_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7122,tc_HOL_Obool)),U_7124),U_7123) = U_7124
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7122,tc_HOL_Obool)),U_7123),U_7124)) ),
inference(clausify,[status(thm)],[f_2148_2]) ).
fof(f_2149_1,plain,
! [V_B_2,V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Un__least]) ).
fof(f_2149_2,plain,
! [U_7128,U_7127,U_7126,U_7125] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7125,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7125,tc_HOL_Obool)),U_7126),U_7128)),U_7127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7125,tc_HOL_Obool)),U_7128),U_7127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7125,tc_HOL_Obool)),U_7126),U_7127)) ),
inference(variable_rename,[status(thm)],[f_2149_1]) ).
cnf(f_2149_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7125,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7125,tc_HOL_Obool)),U_7126),U_7128)),U_7127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7125,tc_HOL_Obool)),U_7128),U_7127))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7125,tc_HOL_Obool)),U_7126),U_7127)) ),
inference(clausify,[status(thm)],[f_2149_2]) ).
fof(f_2150_1,plain,
! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Un__mono]) ).
fof(f_2150_2,plain,
! [U_7133,U_7132,U_7131,U_7130,U_7129] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7129,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7129,tc_HOL_Obool)),U_7130),U_7132)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7129,tc_HOL_Obool)),U_7131),U_7133)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7129,tc_HOL_Obool)),U_7132),U_7133))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7129,tc_HOL_Obool)),U_7130),U_7131)) ),
inference(variable_rename,[status(thm)],[f_2150_1]) ).
cnf(f_2150_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7129,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7129,tc_HOL_Obool)),U_7130),U_7132)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7129,tc_HOL_Obool)),U_7131),U_7133)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7129,tc_HOL_Obool)),U_7132),U_7133))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7129,tc_HOL_Obool)),U_7130),U_7131)) ),
inference(clausify,[status(thm)],[f_2150_2]) ).
fof(f_2151_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_mono__Un]) ).
fof(f_2151_2,plain,
! [U_7138,U_7137,U_7136,U_7135,U_7134] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7135,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7135,tc_HOL_Obool)),hAPP(U_7136,U_7137)),hAPP(U_7136,U_7138))),hAPP(U_7136,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7134,tc_HOL_Obool)),U_7137),U_7138))))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_7134,tc_HOL_Obool),tc_fun(U_7135,tc_HOL_Obool),U_7136) ),
inference(variable_rename,[status(thm)],[f_2151_1]) ).
cnf(f_2151_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7135,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7135,tc_HOL_Obool)),hAPP(U_7136,U_7137)),hAPP(U_7136,U_7138))),hAPP(U_7136,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7134,tc_HOL_Obool)),U_7137),U_7138))))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_7134,tc_HOL_Obool),tc_fun(U_7135,tc_HOL_Obool),U_7136) ),
inference(clausify,[status(thm)],[f_2151_2]) ).
fof(f_2152_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_2152_2,plain,
! [U_7142,U_7141,U_7140,U_7139] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7139),U_7140),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7139),U_7141),U_7142)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7139),U_7140),U_7141))
| ~ class_Lattices_Osemilattice__sup(U_7139) ),
inference(variable_rename,[status(thm)],[f_2152_1]) ).
cnf(f_2152_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7139),U_7140),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7139),U_7141),U_7142)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7139),U_7140),U_7141))
| ~ class_Lattices_Osemilattice__sup(U_7139) ),
inference(clausify,[status(thm)],[f_2152_2]) ).
fof(f_2153_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_2153_2,plain,
! [U_7146,U_7145,U_7144,U_7143] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7143),U_7144),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7143),U_7146),U_7145)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7143),U_7144),U_7145))
| ~ class_Lattices_Osemilattice__sup(U_7143) ),
inference(variable_rename,[status(thm)],[f_2153_1]) ).
cnf(f_2153_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7143),U_7144),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7143),U_7146),U_7145)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7143),U_7144),U_7145))
| ~ class_Lattices_Osemilattice__sup(U_7143) ),
inference(clausify,[status(thm)],[f_2153_2]) ).
fof(f_2154_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_2154_2,plain,
! [U_7148,U_7147] :
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7147),U_7148))
| ~ c_Nat__Transfer_Onat__set(U_7148)
| ~ c_Nat__Transfer_Onat__set(U_7147) ),
inference(variable_rename,[status(thm)],[f_2154_1]) ).
cnf(f_2154_3,plain,
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7147),U_7148))
| ~ c_Nat__Transfer_Onat__set(U_7148)
| ~ c_Nat__Transfer_Onat__set(U_7147) ),
inference(clausify,[status(thm)],[f_2154_2]) ).
fof(f_2155_1,plain,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I7_J]) ).
fof(f_2155_2,plain,
! [U_7153,U_7152,U_7151,U_7150,U_7149] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7149,tc_fun(U_7150,tc_HOL_Obool)),U_7151),hAPP(hAPP(c_COMBB(tc_fun(U_7150,tc_HOL_Obool),tc_fun(U_7150,tc_HOL_Obool),U_7149),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7150,tc_HOL_Obool)),U_7152)),U_7153)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7150,tc_HOL_Obool)),U_7152),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7149,tc_fun(U_7150,tc_HOL_Obool)),U_7151),U_7153)),
inference(variable_rename,[status(thm)],[f_2155_1]) ).
cnf(f_2155_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7149,tc_fun(U_7150,tc_HOL_Obool)),U_7151),hAPP(hAPP(c_COMBB(tc_fun(U_7150,tc_HOL_Obool),tc_fun(U_7150,tc_HOL_Obool),U_7149),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7150,tc_HOL_Obool)),U_7152)),U_7153)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7150,tc_HOL_Obool)),U_7152),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7149,tc_fun(U_7150,tc_HOL_Obool)),U_7151),U_7153)),
inference(clausify,[status(thm)],[f_2155_2]) ).
fof(f_2156_1,plain,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I6_J]) ).
fof(f_2156_2,plain,
! [U_7158,U_7157,U_7156,U_7155,U_7154] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7154,tc_fun(U_7155,tc_HOL_Obool)),U_7156),hAPP(hAPP(c_COMBC(U_7154,tc_fun(U_7155,tc_HOL_Obool),tc_fun(U_7155,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7155,tc_HOL_Obool),tc_fun(tc_fun(U_7155,tc_HOL_Obool),tc_fun(U_7155,tc_HOL_Obool)),U_7154),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7155,tc_HOL_Obool))),U_7157)),U_7158)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7155,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7154,tc_fun(U_7155,tc_HOL_Obool)),U_7156),U_7157)),U_7158),
inference(variable_rename,[status(thm)],[f_2156_1]) ).
cnf(f_2156_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7154,tc_fun(U_7155,tc_HOL_Obool)),U_7156),hAPP(hAPP(c_COMBC(U_7154,tc_fun(U_7155,tc_HOL_Obool),tc_fun(U_7155,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7155,tc_HOL_Obool),tc_fun(tc_fun(U_7155,tc_HOL_Obool),tc_fun(U_7155,tc_HOL_Obool)),U_7154),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7155,tc_HOL_Obool))),U_7157)),U_7158)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7155,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7154,tc_fun(U_7155,tc_HOL_Obool)),U_7156),U_7157)),U_7158),
inference(clausify,[status(thm)],[f_2156_2]) ).
fof(f_2157_1,plain,
! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I7_J]) ).
fof(f_2157_2,plain,
! [U_7163,U_7162,U_7161,U_7160,U_7159] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7159,tc_HOL_Obool)),U_7160),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7161,tc_fun(U_7159,tc_HOL_Obool)),U_7162),U_7163)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7161,tc_fun(U_7159,tc_HOL_Obool)),U_7162),hAPP(hAPP(c_COMBB(tc_fun(U_7159,tc_HOL_Obool),tc_fun(U_7159,tc_HOL_Obool),U_7161),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7159,tc_HOL_Obool)),U_7160)),U_7163)),
inference(variable_rename,[status(thm)],[f_2157_1]) ).
cnf(f_2157_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7159,tc_HOL_Obool)),U_7160),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7161,tc_fun(U_7159,tc_HOL_Obool)),U_7162),U_7163)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7161,tc_fun(U_7159,tc_HOL_Obool)),U_7162),hAPP(hAPP(c_COMBB(tc_fun(U_7159,tc_HOL_Obool),tc_fun(U_7159,tc_HOL_Obool),U_7161),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7159,tc_HOL_Obool)),U_7160)),U_7163)),
inference(clausify,[status(thm)],[f_2157_2]) ).
fof(f_2158_1,plain,
! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Un__INT__distrib]) ).
fof(f_2158_2,plain,
! [U_7168,U_7167,U_7166,U_7165,U_7164] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7164,tc_HOL_Obool)),U_7165),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7166,tc_fun(U_7164,tc_HOL_Obool)),U_7167),U_7168)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7166,tc_fun(U_7164,tc_HOL_Obool)),U_7167),hAPP(hAPP(c_COMBB(tc_fun(U_7164,tc_HOL_Obool),tc_fun(U_7164,tc_HOL_Obool),U_7166),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7164,tc_HOL_Obool)),U_7165)),U_7168)),
inference(variable_rename,[status(thm)],[f_2158_1]) ).
cnf(f_2158_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7164,tc_HOL_Obool)),U_7165),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7166,tc_fun(U_7164,tc_HOL_Obool)),U_7167),U_7168)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7166,tc_fun(U_7164,tc_HOL_Obool)),U_7167),hAPP(hAPP(c_COMBB(tc_fun(U_7164,tc_HOL_Obool),tc_fun(U_7164,tc_HOL_Obool),U_7166),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7164,tc_HOL_Obool)),U_7165)),U_7168)),
inference(clausify,[status(thm)],[f_2158_2]) ).
fof(f_2159_1,plain,
! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I6_J]) ).
fof(f_2159_2,plain,
! [U_7173,U_7172,U_7171,U_7170,U_7169] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7169,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7170,tc_fun(U_7169,tc_HOL_Obool)),U_7171),U_7172)),U_7173) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7170,tc_fun(U_7169,tc_HOL_Obool)),U_7171),hAPP(hAPP(c_COMBC(U_7170,tc_fun(U_7169,tc_HOL_Obool),tc_fun(U_7169,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7169,tc_HOL_Obool),tc_fun(tc_fun(U_7169,tc_HOL_Obool),tc_fun(U_7169,tc_HOL_Obool)),U_7170),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7169,tc_HOL_Obool))),U_7172)),U_7173)),
inference(variable_rename,[status(thm)],[f_2159_1]) ).
cnf(f_2159_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7169,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7170,tc_fun(U_7169,tc_HOL_Obool)),U_7171),U_7172)),U_7173) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7170,tc_fun(U_7169,tc_HOL_Obool)),U_7171),hAPP(hAPP(c_COMBC(U_7170,tc_fun(U_7169,tc_HOL_Obool),tc_fun(U_7169,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7169,tc_HOL_Obool),tc_fun(tc_fun(U_7169,tc_HOL_Obool),tc_fun(U_7169,tc_HOL_Obool)),U_7170),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7169,tc_HOL_Obool))),U_7172)),U_7173)),
inference(clausify,[status(thm)],[f_2159_2]) ).
fof(f_2160_1,plain,
! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))),
inference(fof_nnf,[status(thm)],[fact_Un__INT__distrib2]) ).
fof(f_2160_2,plain,
! [U_7180,U_7179,U_7178,U_7177,U_7176,U_7175,U_7174] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7174,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7175,tc_fun(U_7174,tc_HOL_Obool)),U_7176),U_7177)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7178,tc_fun(U_7174,tc_HOL_Obool)),U_7179),U_7180)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7175,tc_fun(U_7174,tc_HOL_Obool)),U_7176),hAPP(hAPP(c_COMBB(tc_fun(U_7178,tc_fun(U_7174,tc_HOL_Obool)),tc_fun(U_7174,tc_HOL_Obool),U_7175),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7178,tc_fun(U_7174,tc_HOL_Obool)),U_7179)),hAPP(hAPP(c_COMBC(U_7175,tc_fun(U_7178,tc_fun(U_7174,tc_HOL_Obool)),tc_fun(U_7178,tc_fun(U_7174,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_7174,tc_HOL_Obool),tc_fun(U_7174,tc_HOL_Obool)),tc_fun(tc_fun(U_7178,tc_fun(U_7174,tc_HOL_Obool)),tc_fun(U_7178,tc_fun(U_7174,tc_HOL_Obool))),U_7175),c_COMBB(tc_fun(U_7174,tc_HOL_Obool),tc_fun(U_7174,tc_HOL_Obool),U_7178)),hAPP(hAPP(c_COMBB(tc_fun(U_7174,tc_HOL_Obool),tc_fun(tc_fun(U_7174,tc_HOL_Obool),tc_fun(U_7174,tc_HOL_Obool)),U_7175),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7174,tc_HOL_Obool))),U_7177))),U_7180))),
inference(variable_rename,[status(thm)],[f_2160_1]) ).
cnf(f_2160_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7174,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7175,tc_fun(U_7174,tc_HOL_Obool)),U_7176),U_7177)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7178,tc_fun(U_7174,tc_HOL_Obool)),U_7179),U_7180)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7175,tc_fun(U_7174,tc_HOL_Obool)),U_7176),hAPP(hAPP(c_COMBB(tc_fun(U_7178,tc_fun(U_7174,tc_HOL_Obool)),tc_fun(U_7174,tc_HOL_Obool),U_7175),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7178,tc_fun(U_7174,tc_HOL_Obool)),U_7179)),hAPP(hAPP(c_COMBC(U_7175,tc_fun(U_7178,tc_fun(U_7174,tc_HOL_Obool)),tc_fun(U_7178,tc_fun(U_7174,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_7174,tc_HOL_Obool),tc_fun(U_7174,tc_HOL_Obool)),tc_fun(tc_fun(U_7178,tc_fun(U_7174,tc_HOL_Obool)),tc_fun(U_7178,tc_fun(U_7174,tc_HOL_Obool))),U_7175),c_COMBB(tc_fun(U_7174,tc_HOL_Obool),tc_fun(U_7174,tc_HOL_Obool),U_7178)),hAPP(hAPP(c_COMBB(tc_fun(U_7174,tc_HOL_Obool),tc_fun(tc_fun(U_7174,tc_HOL_Obool),tc_fun(U_7174,tc_HOL_Obool)),U_7175),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7174,tc_HOL_Obool))),U_7177))),U_7180))),
inference(clausify,[status(thm)],[f_2160_2]) ).
fof(f_2161_1,plain,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_A_2),V_B_2))))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
| ~ class_Lattices_Osemilattice__sup(T_b)
| ~ class_Lattices_Osemilattice__sup(T_c) ),
inference(fof_nnf,[status(thm)],[fact_mono__sup]) ).
fof(f_2161_2,plain,
! [U_7185,U_7184,U_7183,U_7182,U_7181] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7181),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7181),hAPP(U_7183,U_7184)),hAPP(U_7183,U_7185))),hAPP(U_7183,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7182),U_7184),U_7185))))
| ~ c_Orderings_Oorder__class_Omono(U_7182,U_7181,U_7183)
| ~ class_Lattices_Osemilattice__sup(U_7182)
| ~ class_Lattices_Osemilattice__sup(U_7181) ),
inference(variable_rename,[status(thm)],[f_2161_1]) ).
cnf(f_2161_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7181),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7181),hAPP(U_7183,U_7184)),hAPP(U_7183,U_7185))),hAPP(U_7183,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7182),U_7184),U_7185))))
| ~ c_Orderings_Oorder__class_Omono(U_7182,U_7181,U_7183)
| ~ class_Lattices_Osemilattice__sup(U_7182)
| ~ class_Lattices_Osemilattice__sup(U_7181) ),
inference(clausify,[status(thm)],[f_2161_2]) ).
fof(f_2162_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I17_J]) ).
fof(f_2162_2,plain,
! [U_7189,U_7188,U_7187,U_7186] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7186,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7186,U_7187),U_7188)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7186,U_7188),U_7189)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7186,U_7187),U_7189)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7186),U_7188),U_7189))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7186),U_7187),U_7188))
| ~ class_Orderings_Olinorder(U_7186) ),
inference(variable_rename,[status(thm)],[f_2162_1]) ).
cnf(f_2162_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7186,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7186,U_7187),U_7188)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7186,U_7188),U_7189)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7186,U_7187),U_7189)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7186),U_7188),U_7189))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7186),U_7187),U_7188))
| ~ class_Orderings_Olinorder(U_7186) ),
inference(clausify,[status(thm)],[f_2162_2]) ).
fof(f_2163_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Diff__partition]) ).
fof(f_2163_2,plain,
! [U_7192,U_7191,U_7190] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7190,tc_HOL_Obool)),U_7191),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7190,tc_HOL_Obool)),U_7192),U_7191)) = U_7192
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7190,tc_HOL_Obool)),U_7191),U_7192)) ),
inference(variable_rename,[status(thm)],[f_2163_1]) ).
cnf(f_2163_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7190,tc_HOL_Obool)),U_7191),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7190,tc_HOL_Obool)),U_7192),U_7191)) = U_7192
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7190,tc_HOL_Obool)),U_7191),U_7192)) ),
inference(clausify,[status(thm)],[f_2163_2]) ).
fof(f_2164_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Diff__subset__conv]) ).
fof(f_2164_2,plain,
! [U_7196,U_7195,U_7194,U_7193] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7193,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7193,tc_HOL_Obool)),U_7194),U_7195)),U_7196))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7193,tc_HOL_Obool)),U_7194),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7193,tc_HOL_Obool)),U_7195),U_7196))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7193,tc_HOL_Obool)),U_7194),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7193,tc_HOL_Obool)),U_7195),U_7196)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7193,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7193,tc_HOL_Obool)),U_7194),U_7195)),U_7196)) ) ),
inference(variable_rename,[status(thm)],[f_2164_1]) ).
fof(f_2164_3,plain,
( ! [U_7204,U_7202,U_7200,U_7198] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7198,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7198,tc_HOL_Obool)),U_7200),U_7202)),U_7204))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7198,tc_HOL_Obool)),U_7200),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7198,tc_HOL_Obool)),U_7202),U_7204))) )
& ! [U_7203,U_7201,U_7199,U_7197] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7197,tc_HOL_Obool)),U_7199),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7197,tc_HOL_Obool)),U_7201),U_7203)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7197,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7197,tc_HOL_Obool)),U_7199),U_7201)),U_7203)) ) ),
inference(miniscope,[status(thm)],[f_2164_2]) ).
cnf(f_2164_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7197,tc_HOL_Obool)),U_7199),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7197,tc_HOL_Obool)),U_7201),U_7203)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7197,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7197,tc_HOL_Obool)),U_7199),U_7201)),U_7203)) ),
inference(clausify,[status(thm)],[f_2164_3]) ).
cnf(f_2164_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7198,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7198,tc_HOL_Obool)),U_7200),U_7202)),U_7204))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7198,tc_HOL_Obool)),U_7200),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7198,tc_HOL_Obool)),U_7202),U_7204))) ),
inference(clausify,[status(thm)],[f_2164_3]) ).
fof(f_2165_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_2165_2,plain,
! [U_7206,U_7205] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7205),U_7206) = 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_7205)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7206))),
inference(variable_rename,[status(thm)],[f_2165_1]) ).
cnf(f_2165_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_7205),U_7206) = 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_7205)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_7206))),
inference(clausify,[status(thm)],[f_2165_2]) ).
fof(f_2166_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I20_J]) ).
fof(f_2166_2,plain,
! [U_7210,U_7209,U_7208,U_7207] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7207,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7207,U_7208,U_7209)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7207,U_7209,U_7210)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7207,U_7208,U_7210)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7207),U_7209),U_7210))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7207),U_7208),U_7209))
| ~ class_Orderings_Olinorder(U_7207) ),
inference(variable_rename,[status(thm)],[f_2166_1]) ).
cnf(f_2166_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7207,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7207,U_7208,U_7209)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7207,U_7209,U_7210)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_7207,U_7208,U_7210)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7207),U_7209),U_7210))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7207),U_7208),U_7209))
| ~ class_Orderings_Olinorder(U_7207) ),
inference(clausify,[status(thm)],[f_2166_2]) ).
fof(f_2167_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2),
inference(fof_nnf,[status(thm)],[fact_Compl__Diff__eq]) ).
fof(f_2167_2,plain,
! [U_7213,U_7212,U_7211] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7211,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7211,tc_HOL_Obool)),U_7212),U_7213)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7211,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7211,tc_HOL_Obool)),U_7212)),U_7213),
inference(variable_rename,[status(thm)],[f_2167_1]) ).
cnf(f_2167_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7211,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7211,tc_HOL_Obool)),U_7212),U_7213)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7211,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7211,tc_HOL_Obool)),U_7212)),U_7213),
inference(clausify,[status(thm)],[f_2167_2]) ).
fof(f_2168_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_2168_2,plain,
! [U_7215,U_7214] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7214),U_7215) = 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_7214)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7215)))
| ~ c_Nat__Transfer_Onat__set(U_7215)
| ~ c_Nat__Transfer_Onat__set(U_7214) ),
inference(variable_rename,[status(thm)],[f_2168_1]) ).
cnf(f_2168_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_7214),U_7215) = 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_7214)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7215)))
| ~ c_Nat__Transfer_Onat__set(U_7215)
| ~ c_Nat__Transfer_Onat__set(U_7214) ),
inference(clausify,[status(thm)],[f_2168_2]) ).
fof(f_2169_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_2169_2,plain,
! [U_7217,U_7216] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_7216,U_7217)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7217),hAPP(c_Nat_OSuc,U_7216)),
inference(variable_rename,[status(thm)],[f_2169_1]) ).
cnf(f_2169_3,plain,
hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_7216,U_7217)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7217),hAPP(c_Nat_OSuc,U_7216)),
inference(clausify,[status(thm)],[f_2169_2]) ).
fof(f_2170_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_2170_2,plain,
! [U_7219,U_7218] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7218)),U_7219) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_7218,U_7219),
inference(variable_rename,[status(thm)],[f_2170_1]) ).
cnf(f_2170_3,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_7218)),U_7219) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_7218,U_7219),
inference(clausify,[status(thm)],[f_2170_2]) ).
fof(f_2171_1,plain,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_A_2),V_B_2))))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Lattices_Osemilattice__sup(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Omono__sup]) ).
fof(f_2171_2,plain,
! [U_7224,U_7223,U_7222,U_7221,U_7220] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7220),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7220),hAPP(U_7222,U_7223)),hAPP(U_7222,U_7224))),hAPP(U_7222,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_7221),U_7223),U_7224))))
| ~ c_Orderings_Oorder__class_Omono(U_7221,U_7220,U_7222)
| ~ class_Orderings_Olinorder(U_7221)
| ~ class_Lattices_Osemilattice__sup(U_7220) ),
inference(variable_rename,[status(thm)],[f_2171_1]) ).
cnf(f_2171_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7220),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7220),hAPP(U_7222,U_7223)),hAPP(U_7222,U_7224))),hAPP(U_7222,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_7221),U_7223),U_7224))))
| ~ c_Orderings_Oorder__class_Omono(U_7221,U_7220,U_7222)
| ~ class_Orderings_Olinorder(U_7221)
| ~ class_Lattices_Osemilattice__sup(U_7220) ),
inference(clausify,[status(thm)],[f_2171_2]) ).
fof(f_2172_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I21_J]) ).
fof(f_2172_2,plain,
! [U_7228,U_7227,U_7226,U_7225] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7225,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7225,U_7226),U_7227)),c_SetInterval_Oord__class_OatLeastAtMost(U_7225,U_7227,U_7228)) = c_SetInterval_Oord__class_OatLeastAtMost(U_7225,U_7226,U_7228)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7225),U_7227),U_7228))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7225),U_7226),U_7227))
| ~ class_Orderings_Olinorder(U_7225) ),
inference(variable_rename,[status(thm)],[f_2172_1]) ).
cnf(f_2172_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7225,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7225,U_7226),U_7227)),c_SetInterval_Oord__class_OatLeastAtMost(U_7225,U_7227,U_7228)) = c_SetInterval_Oord__class_OatLeastAtMost(U_7225,U_7226,U_7228)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7225),U_7227),U_7228))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7225),U_7226),U_7227))
| ~ class_Orderings_Olinorder(U_7225) ),
inference(clausify,[status(thm)],[f_2172_2]) ).
fof(f_2173_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_2173_2,plain,
! [U_7231,U_7230,U_7229] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7229),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7230),U_7231)) = 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_7229),U_7230)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7230),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7230),U_7231)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7229),U_7230)) ),
inference(variable_rename,[status(thm)],[f_2173_1]) ).
cnf(f_2173_3,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7229),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7230),U_7231)) = 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_7229),U_7230)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7230),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7230),U_7231)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7229),U_7230)) ),
inference(clausify,[status(thm)],[f_2173_2]) ).
fof(f_2174_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I8_J]) ).
fof(f_2174_2,plain,
! [U_7234,U_7233,U_7232] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7232,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_7232),U_7233)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7232,U_7233),U_7234)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_7232),U_7234)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7232),U_7233),U_7234))
| ~ class_Orderings_Olinorder(U_7232) ),
inference(variable_rename,[status(thm)],[f_2174_1]) ).
cnf(f_2174_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7232,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_7232),U_7233)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7232,U_7233),U_7234)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_7232),U_7234)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7232),U_7233),U_7234))
| ~ class_Orderings_Olinorder(U_7232) ),
inference(clausify,[status(thm)],[f_2174_2]) ).
fof(f_2175_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I22_J]) ).
fof(f_2175_2,plain,
! [U_7238,U_7237,U_7236,U_7235] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7235,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7235,U_7236,U_7237)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7235,U_7237,U_7238)) = c_SetInterval_Oord__class_OatLeastAtMost(U_7235,U_7236,U_7238)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7235),U_7237),U_7238))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7235),U_7236),U_7237))
| ~ class_Orderings_Olinorder(U_7235) ),
inference(variable_rename,[status(thm)],[f_2175_1]) ).
cnf(f_2175_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7235,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7235,U_7236,U_7237)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7235,U_7237,U_7238)) = c_SetInterval_Oord__class_OatLeastAtMost(U_7235,U_7236,U_7238)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7235),U_7237),U_7238))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7235),U_7236),U_7237))
| ~ class_Orderings_Olinorder(U_7235) ),
inference(clausify,[status(thm)],[f_2175_2]) ).
fof(f_2176_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I9_J]) ).
fof(f_2176_2,plain,
! [U_7241,U_7240,U_7239] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7239,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_7239),U_7240)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7239,U_7240,U_7241)) = hAPP(c_SetInterval_Oord__class_OatMost(U_7239),U_7241)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7239),U_7240),U_7241))
| ~ class_Orderings_Olinorder(U_7239) ),
inference(variable_rename,[status(thm)],[f_2176_1]) ).
cnf(f_2176_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7239,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_7239),U_7240)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7239,U_7240,U_7241)) = hAPP(c_SetInterval_Oord__class_OatMost(U_7239),U_7241)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7239),U_7240),U_7241))
| ~ class_Orderings_Olinorder(U_7239) ),
inference(clausify,[status(thm)],[f_2176_2]) ).
fof(f_2177_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I11_J]) ).
fof(f_2177_2,plain,
! [U_7244,U_7243,U_7242] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7242,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7242,U_7243,U_7244)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7242),U_7244)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7242),U_7243)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7242),U_7243),U_7244))
| ~ class_Orderings_Olinorder(U_7242) ),
inference(variable_rename,[status(thm)],[f_2177_1]) ).
cnf(f_2177_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7242,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7242,U_7243,U_7244)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7242),U_7244)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7242),U_7243)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7242),U_7243),U_7244))
| ~ class_Orderings_Olinorder(U_7242) ),
inference(clausify,[status(thm)],[f_2177_2]) ).
fof(f_2178_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I15_J]) ).
fof(f_2178_2,plain,
! [U_7248,U_7247,U_7246,U_7245] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7245,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7245,U_7246,U_7247)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7245,U_7247),U_7248)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_7245,U_7246,U_7248)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7245),U_7247),U_7248))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7245),U_7246),U_7247))
| ~ class_Orderings_Olinorder(U_7245) ),
inference(variable_rename,[status(thm)],[f_2178_1]) ).
cnf(f_2178_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7245,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7245,U_7246,U_7247)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7245,U_7247),U_7248)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_7245,U_7246,U_7248)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7245),U_7247),U_7248))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7245),U_7246),U_7247))
| ~ class_Orderings_Olinorder(U_7245) ),
inference(clausify,[status(thm)],[f_2178_2]) ).
fof(f_2179_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I16_J]) ).
fof(f_2179_2,plain,
! [U_7252,U_7251,U_7250,U_7249] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7249,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7249,U_7250,U_7251)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7249,U_7251,U_7252)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_7249,U_7250,U_7252)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7249),U_7251),U_7252))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7249),U_7250),U_7251))
| ~ class_Orderings_Olinorder(U_7249) ),
inference(variable_rename,[status(thm)],[f_2179_1]) ).
cnf(f_2179_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7249,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_7249,U_7250,U_7251)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7249,U_7251,U_7252)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_7249,U_7250,U_7252)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7249),U_7251),U_7252))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7249),U_7250),U_7251))
| ~ class_Orderings_Olinorder(U_7249) ),
inference(clausify,[status(thm)],[f_2179_2]) ).
fof(f_2180_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I10_J]) ).
fof(f_2180_2,plain,
! [U_7255,U_7254,U_7253] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7253,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_7253),U_7254)),c_SetInterval_Oord__class_OatLeastAtMost(U_7253,U_7254,U_7255)) = hAPP(c_SetInterval_Oord__class_OatMost(U_7253),U_7255)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7253),U_7254),U_7255))
| ~ class_Orderings_Olinorder(U_7253) ),
inference(variable_rename,[status(thm)],[f_2180_1]) ).
cnf(f_2180_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7253,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_7253),U_7254)),c_SetInterval_Oord__class_OatLeastAtMost(U_7253,U_7254,U_7255)) = hAPP(c_SetInterval_Oord__class_OatMost(U_7253),U_7255)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7253),U_7254),U_7255))
| ~ class_Orderings_Olinorder(U_7253) ),
inference(clausify,[status(thm)],[f_2180_2]) ).
fof(f_2181_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I7_J]) ).
fof(f_2181_2,plain,
! [U_7258,U_7257,U_7256] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7256,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_7256),U_7257)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7256,U_7257,U_7258)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_7256),U_7258)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7256),U_7257),U_7258))
| ~ class_Orderings_Olinorder(U_7256) ),
inference(variable_rename,[status(thm)],[f_2181_1]) ).
cnf(f_2181_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7256,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_7256),U_7257)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7256,U_7257,U_7258)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_7256),U_7258)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7256),U_7257),U_7258))
| ~ class_Orderings_Olinorder(U_7256) ),
inference(clausify,[status(thm)],[f_2181_2]) ).
fof(f_2182_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_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_d_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastatMost__subset__iff]) ).
fof(f_2182_2,plain,
! [U_7262,U_7261,U_7260,U_7259] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7259,U_7260)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7261,U_7262)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7260),U_7262))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7261),U_7259)) )
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7259),U_7260)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7260),U_7262))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7261),U_7259)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7259),U_7260))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7259,U_7260)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7261,U_7262))) ) ),
inference(variable_rename,[status(thm)],[f_2182_1]) ).
fof(f_2182_3,plain,
( ! [U_7270,U_7268,U_7266,U_7264] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7264,U_7266)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7268,U_7270)))
| ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7266),U_7270))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7268),U_7264)) )
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7264),U_7266)) ) )
& ! [U_7269,U_7267,U_7265,U_7263] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7265),U_7269))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7267),U_7263)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7263),U_7265))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7263,U_7265)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7267,U_7269))) ) ),
inference(miniscope,[status(thm)],[f_2182_2]) ).
cnf(f_2182_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7267),U_7263))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7263),U_7265))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7263,U_7265)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7267,U_7269))) ),
inference(clausify,[status(thm)],[f_2182_3]) ).
cnf(f_2182_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7265),U_7269))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7263),U_7265))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7263,U_7265)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7267,U_7269))) ),
inference(clausify,[status(thm)],[f_2182_3]) ).
cnf(f_2182_6,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7264),U_7266))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7264,U_7266)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7268,U_7270))) ),
inference(clausify,[status(thm)],[f_2182_3]) ).
cnf(f_2182_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7266),U_7270))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7268),U_7264))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7264,U_7266)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7268,U_7270))) ),
inference(clausify,[status(thm)],[f_2182_3]) ).
fof(f_2183_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I12_J]) ).
fof(f_2183_2,plain,
! [U_7273,U_7272,U_7271] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7271,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7271,U_7272,U_7273)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7271),U_7273)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7271),U_7272)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7271),U_7272),U_7273))
| ~ class_Orderings_Olinorder(U_7271) ),
inference(variable_rename,[status(thm)],[f_2183_1]) ).
cnf(f_2183_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7271,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_7271,U_7272,U_7273)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7271),U_7273)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7271),U_7272)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7271),U_7272),U_7273))
| ~ class_Orderings_Olinorder(U_7271) ),
inference(clausify,[status(thm)],[f_2183_2]) ).
fof(f_2184_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I13_J]) ).
fof(f_2184_2,plain,
! [U_7276,U_7275,U_7274] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7274,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7274,U_7275,U_7276)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7274),U_7276)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_7274),U_7275)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7274),U_7275),U_7276))
| ~ class_Orderings_Olinorder(U_7274) ),
inference(variable_rename,[status(thm)],[f_2184_1]) ).
cnf(f_2184_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7274,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_7274,U_7275,U_7276)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_7274),U_7276)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_7274),U_7275)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7274),U_7275),U_7276))
| ~ class_Orderings_Olinorder(U_7274) ),
inference(clausify,[status(thm)],[f_2184_2]) ).
fof(f_2185_1,plain,
! [V_M_2,V_na_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_na_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_na_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_2185_2,plain,
! [U_7279,U_7278,U_7277] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7277,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7278)),U_7279) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7277,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7277,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_7278)),U_7279)),hAPP(U_7279,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(variable_rename,[status(thm)],[f_2185_1]) ).
cnf(f_2185_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7277,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7278)),U_7279) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7277,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7277,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_7278)),U_7279)),hAPP(U_7279,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(clausify,[status(thm)],[f_2185_2]) ).
fof(f_2186_1,plain,
! [V_B_2,V_X_2,V_f_2,T_c,T_b] :
( c_Orderings_Oorder__class_Omono(T_b,tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_f_2)),V_X_2))),V_B_2))
| ~ c_Orderings_Oorder__class_Omono(T_b,tc_fun(T_c,tc_HOL_Obool),V_f_2)
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_coinduct3__mono__lemma]) ).
fof(f_2186_2,plain,
! [U_7284,U_7283,U_7282,U_7281,U_7280] :
( c_Orderings_Oorder__class_Omono(U_7280,tc_fun(U_7281,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_7280,tc_fun(U_7281,tc_HOL_Obool),tc_fun(U_7281,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7281,tc_HOL_Obool),tc_fun(tc_fun(U_7281,tc_HOL_Obool),tc_fun(U_7281,tc_HOL_Obool)),U_7280),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7281,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7280,tc_fun(U_7281,tc_HOL_Obool),tc_fun(U_7281,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7281,tc_HOL_Obool),tc_fun(tc_fun(U_7281,tc_HOL_Obool),tc_fun(U_7281,tc_HOL_Obool)),U_7280),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7281,tc_HOL_Obool))),U_7282)),U_7283))),U_7284))
| ~ c_Orderings_Oorder__class_Omono(U_7280,tc_fun(U_7281,tc_HOL_Obool),U_7282)
| ~ class_Orderings_Oorder(U_7280) ),
inference(variable_rename,[status(thm)],[f_2186_1]) ).
cnf(f_2186_3,plain,
( c_Orderings_Oorder__class_Omono(U_7280,tc_fun(U_7281,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_7280,tc_fun(U_7281,tc_HOL_Obool),tc_fun(U_7281,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7281,tc_HOL_Obool),tc_fun(tc_fun(U_7281,tc_HOL_Obool),tc_fun(U_7281,tc_HOL_Obool)),U_7280),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7281,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_7280,tc_fun(U_7281,tc_HOL_Obool),tc_fun(U_7281,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7281,tc_HOL_Obool),tc_fun(tc_fun(U_7281,tc_HOL_Obool),tc_fun(U_7281,tc_HOL_Obool)),U_7280),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7281,tc_HOL_Obool))),U_7282)),U_7283))),U_7284))
| ~ c_Orderings_Oorder__class_Omono(U_7280,tc_fun(U_7281,tc_HOL_Obool),U_7282)
| ~ class_Orderings_Oorder(U_7280) ),
inference(clausify,[status(thm)],[f_2186_2]) ).
fof(f_2187_1,plain,
! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2,
inference(fof_nnf,[status(thm)],[fact_image__ident]) ).
fof(f_2187_2,plain,
! [U_7286,U_7285] : hAPP(c_Set_Oimage(U_7285,U_7285,c_COMBI(U_7285)),U_7286) = U_7286,
inference(variable_rename,[status(thm)],[f_2187_1]) ).
cnf(f_2187_3,plain,
hAPP(c_Set_Oimage(U_7285,U_7285,c_COMBI(U_7285)),U_7286) = U_7286,
inference(clausify,[status(thm)],[f_2187_2]) ).
fof(f_2188_1,plain,
! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_SUP1__iff]) ).
fof(f_2188_2,plain,
! [U_7293,U_7292,U_7291,U_7290,U_7289] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7289,tc_fun(U_7290,tc_HOL_Obool)),U_7291),U_7292),U_7293))
| ! [U_7288] :
( ~ hBOOL(hAPP(hAPP(U_7292,U_7288),U_7293))
| ~ hBOOL(hAPP(hAPP(c_member(U_7289),U_7288),U_7291)) ) )
& ( ? [U_7287] :
( hBOOL(hAPP(hAPP(U_7292,U_7287),U_7293))
& hBOOL(hAPP(hAPP(c_member(U_7289),U_7287),U_7291)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7289,tc_fun(U_7290,tc_HOL_Obool)),U_7291),U_7292),U_7293)) ) ),
inference(variable_rename,[status(thm)],[f_2188_1]) ).
fof(f_2188_3,plain,
( ! [U_7303,U_7301,U_7299,U_7297,U_7295] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7295,tc_fun(U_7297,tc_HOL_Obool)),U_7299),U_7301),U_7303))
| ! [U_7288] :
( ~ hBOOL(hAPP(hAPP(U_7301,U_7288),U_7303))
| ~ hBOOL(hAPP(hAPP(c_member(U_7295),U_7288),U_7299)) ) )
& ! [U_7302,U_7300,U_7298,U_7296,U_7294] :
( ? [U_7287] :
( hBOOL(hAPP(hAPP(U_7300,U_7287),U_7302))
& hBOOL(hAPP(hAPP(c_member(U_7294),U_7287),U_7298)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7294,tc_fun(U_7296,tc_HOL_Obool)),U_7298),U_7300),U_7302)) ) ),
inference(miniscope,[status(thm)],[f_2188_2]) ).
fof(f_2188_4,plain,
( ! [U_7303,U_7301,U_7299,U_7297,U_7295] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7295,tc_fun(U_7297,tc_HOL_Obool)),U_7299),U_7301),U_7303))
| ! [U_7288] :
( ~ hBOOL(hAPP(hAPP(U_7301,U_7288),U_7303))
| ~ hBOOL(hAPP(hAPP(c_member(U_7295),U_7288),U_7299)) ) )
& ! [U_7302,U_7300,U_7298,U_7296,U_7294] :
( ( hBOOL(hAPP(hAPP(U_7300,sK137(U_7302,U_7300,U_7298,U_7296,U_7294)),U_7302))
& hBOOL(hAPP(hAPP(c_member(U_7294),sK137(U_7302,U_7300,U_7298,U_7296,U_7294)),U_7298)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7294,tc_fun(U_7296,tc_HOL_Obool)),U_7298),U_7300),U_7302)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_7287,sK137(U_7302,U_7300,U_7298,U_7296,U_7294))],[f_2188_3]) ).
cnf(f_2188_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_7294),sK137(U_7302,U_7300,U_7298,U_7296,U_7294)),U_7298))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7294,tc_fun(U_7296,tc_HOL_Obool)),U_7298),U_7300),U_7302)) ),
inference(clausify,[status(thm)],[f_2188_4]) ).
cnf(f_2188_6,plain,
( hBOOL(hAPP(hAPP(U_7300,sK137(U_7302,U_7300,U_7298,U_7296,U_7294)),U_7302))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7294,tc_fun(U_7296,tc_HOL_Obool)),U_7298),U_7300),U_7302)) ),
inference(clausify,[status(thm)],[f_2188_4]) ).
cnf(f_2188_7,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7295,tc_fun(U_7297,tc_HOL_Obool)),U_7299),U_7301),U_7303))
| ~ hBOOL(hAPP(hAPP(U_7301,U_7288),U_7303))
| ~ hBOOL(hAPP(hAPP(c_member(U_7295),U_7288),U_7299)) ),
inference(clausify,[status(thm)],[f_2188_4]) ).
fof(f_2189_1,plain,
! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_SUPR__apply]) ).
fof(f_2189_2,plain,
! [U_7309,U_7308,U_7307,U_7306,U_7305,U_7304] :
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7305,tc_fun(U_7306,U_7304)),U_7307),U_7308),U_7309) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7305,U_7304),U_7307),hAPP(hAPP(c_COMBC(U_7305,U_7306,U_7304),U_7308),U_7309))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7304) ),
inference(variable_rename,[status(thm)],[f_2189_1]) ).
cnf(f_2189_3,plain,
( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7305,tc_fun(U_7306,U_7304)),U_7307),U_7308),U_7309) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7305,U_7304),U_7307),hAPP(hAPP(c_COMBC(U_7305,U_7306,U_7304),U_7308),U_7309))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7304) ),
inference(clausify,[status(thm)],[f_2189_2]) ).
fof(f_2190_1,plain,
! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_UN__UN__flatten]) ).
fof(f_2190_2,plain,
! [U_7315,U_7314,U_7313,U_7312,U_7311,U_7310] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7310,tc_fun(U_7311,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7312,tc_fun(U_7310,tc_HOL_Obool)),U_7313),U_7314)),U_7315) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7312,tc_fun(U_7311,tc_HOL_Obool)),U_7313),hAPP(hAPP(c_COMBC(U_7312,tc_fun(U_7310,tc_fun(U_7311,tc_HOL_Obool)),tc_fun(U_7311,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7310,tc_HOL_Obool),tc_fun(tc_fun(U_7310,tc_fun(U_7311,tc_HOL_Obool)),tc_fun(U_7311,tc_HOL_Obool)),U_7312),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7310,tc_fun(U_7311,tc_HOL_Obool))),U_7314)),U_7315)),
inference(variable_rename,[status(thm)],[f_2190_1]) ).
cnf(f_2190_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7310,tc_fun(U_7311,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7312,tc_fun(U_7310,tc_HOL_Obool)),U_7313),U_7314)),U_7315) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7312,tc_fun(U_7311,tc_HOL_Obool)),U_7313),hAPP(hAPP(c_COMBC(U_7312,tc_fun(U_7310,tc_fun(U_7311,tc_HOL_Obool)),tc_fun(U_7311,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7310,tc_HOL_Obool),tc_fun(tc_fun(U_7310,tc_fun(U_7311,tc_HOL_Obool)),tc_fun(U_7311,tc_HOL_Obool)),U_7312),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7310,tc_fun(U_7311,tc_HOL_Obool))),U_7314)),U_7315)),
inference(clausify,[status(thm)],[f_2190_2]) ).
fof(f_2191_1,plain,
! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I9_J]) ).
fof(f_2191_2,plain,
! [U_7321,U_7320,U_7319,U_7318,U_7317,U_7316] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7316,tc_fun(U_7317,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7318,tc_fun(U_7316,tc_HOL_Obool)),U_7319),U_7320)),U_7321) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7318,tc_fun(U_7317,tc_HOL_Obool)),U_7319),hAPP(hAPP(c_COMBC(U_7318,tc_fun(U_7316,tc_fun(U_7317,tc_HOL_Obool)),tc_fun(U_7317,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7316,tc_HOL_Obool),tc_fun(tc_fun(U_7316,tc_fun(U_7317,tc_HOL_Obool)),tc_fun(U_7317,tc_HOL_Obool)),U_7318),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7316,tc_fun(U_7317,tc_HOL_Obool))),U_7320)),U_7321)),
inference(variable_rename,[status(thm)],[f_2191_1]) ).
cnf(f_2191_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7316,tc_fun(U_7317,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7318,tc_fun(U_7316,tc_HOL_Obool)),U_7319),U_7320)),U_7321) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7318,tc_fun(U_7317,tc_HOL_Obool)),U_7319),hAPP(hAPP(c_COMBC(U_7318,tc_fun(U_7316,tc_fun(U_7317,tc_HOL_Obool)),tc_fun(U_7317,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7316,tc_HOL_Obool),tc_fun(tc_fun(U_7316,tc_fun(U_7317,tc_HOL_Obool)),tc_fun(U_7317,tc_HOL_Obool)),U_7318),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7316,tc_fun(U_7317,tc_HOL_Obool))),U_7320)),U_7321)),
inference(clausify,[status(thm)],[f_2191_2]) ).
fof(f_2192_1,plain,
! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I9_J]) ).
fof(f_2192_2,plain,
! [U_7327,U_7326,U_7325,U_7324,U_7323,U_7322] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7322,tc_fun(U_7323,tc_HOL_Obool)),U_7324),hAPP(hAPP(c_COMBC(U_7322,tc_fun(U_7325,tc_fun(U_7323,tc_HOL_Obool)),tc_fun(U_7323,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7325,tc_HOL_Obool),tc_fun(tc_fun(U_7325,tc_fun(U_7323,tc_HOL_Obool)),tc_fun(U_7323,tc_HOL_Obool)),U_7322),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7325,tc_fun(U_7323,tc_HOL_Obool))),U_7326)),U_7327)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7325,tc_fun(U_7323,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7322,tc_fun(U_7325,tc_HOL_Obool)),U_7324),U_7326)),U_7327),
inference(variable_rename,[status(thm)],[f_2192_1]) ).
cnf(f_2192_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7322,tc_fun(U_7323,tc_HOL_Obool)),U_7324),hAPP(hAPP(c_COMBC(U_7322,tc_fun(U_7325,tc_fun(U_7323,tc_HOL_Obool)),tc_fun(U_7323,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7325,tc_HOL_Obool),tc_fun(tc_fun(U_7325,tc_fun(U_7323,tc_HOL_Obool)),tc_fun(U_7323,tc_HOL_Obool)),U_7322),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7325,tc_fun(U_7323,tc_HOL_Obool))),U_7326)),U_7327)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7325,tc_fun(U_7323,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7322,tc_fun(U_7325,tc_HOL_Obool)),U_7324),U_7326)),U_7327),
inference(clausify,[status(thm)],[f_2192_2]) ).
fof(f_2193_1,plain,
! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2)))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_SUP__commute]) ).
fof(f_2193_2,plain,
! [U_7333,U_7332,U_7331,U_7330,U_7329,U_7328] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7329,U_7328),U_7330),hAPP(hAPP(c_COMBB(tc_fun(U_7331,U_7328),U_7328,U_7329),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7331,U_7328),U_7332)),U_7333)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7331,U_7328),U_7332),hAPP(hAPP(c_COMBB(tc_fun(U_7329,U_7328),U_7328,U_7331),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7329,U_7328),U_7330)),hAPP(c_COMBC(U_7329,U_7331,U_7328),U_7333)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7328) ),
inference(variable_rename,[status(thm)],[f_2193_1]) ).
cnf(f_2193_3,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7329,U_7328),U_7330),hAPP(hAPP(c_COMBB(tc_fun(U_7331,U_7328),U_7328,U_7329),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7331,U_7328),U_7332)),U_7333)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7331,U_7328),U_7332),hAPP(hAPP(c_COMBB(tc_fun(U_7329,U_7328),U_7328,U_7331),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7329,U_7328),U_7330)),hAPP(c_COMBC(U_7329,U_7331,U_7328),U_7333)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7328) ),
inference(clausify,[status(thm)],[f_2193_2]) ).
fof(f_2194_1,plain,
! [V_P_2,V_B_2,V_A_2,T_c,T_b] :
( ( ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
| ? [B_x] :
( ? [B_xa] :
( ~ hBOOL(hAPP(V_P_2,B_xa))
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x))) )
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( ! [B_xa] :
( hBOOL(hAPP(V_P_2,B_xa))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x))) )
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ),
inference(fof_nnf,[status(thm)],[fact_ball__UN]) ).
fof(f_2194_2,plain,
! [U_7344,U_7343,U_7342,U_7341,U_7340] :
( ( ! [U_7339] :
( hBOOL(hAPP(U_7344,U_7339))
| ~ hBOOL(hAPP(hAPP(c_member(U_7340),U_7339),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7341,tc_fun(U_7340,tc_HOL_Obool)),U_7342),U_7343))) )
| ? [U_7338] :
( ? [U_7337] :
( ~ hBOOL(hAPP(U_7344,U_7337))
& hBOOL(hAPP(hAPP(c_member(U_7340),U_7337),hAPP(U_7343,U_7338))) )
& hBOOL(hAPP(hAPP(c_member(U_7341),U_7338),U_7342)) ) )
& ( ! [U_7336] :
( ! [U_7335] :
( hBOOL(hAPP(U_7344,U_7335))
| ~ hBOOL(hAPP(hAPP(c_member(U_7340),U_7335),hAPP(U_7343,U_7336))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_7341),U_7336),U_7342)) )
| ? [U_7334] :
( ~ hBOOL(hAPP(U_7344,U_7334))
& hBOOL(hAPP(hAPP(c_member(U_7340),U_7334),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7341,tc_fun(U_7340,tc_HOL_Obool)),U_7342),U_7343))) ) ) ),
inference(variable_rename,[status(thm)],[f_2194_1]) ).
fof(f_2194_3,plain,
( ! [U_7354,U_7352,U_7350,U_7348,U_7346] :
( ! [U_7339] :
( hBOOL(hAPP(U_7354,U_7339))
| ~ hBOOL(hAPP(hAPP(c_member(U_7346),U_7339),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7348,tc_fun(U_7346,tc_HOL_Obool)),U_7350),U_7352))) )
| ? [U_7338] :
( ? [U_7337] :
( ~ hBOOL(hAPP(U_7354,U_7337))
& hBOOL(hAPP(hAPP(c_member(U_7346),U_7337),hAPP(U_7352,U_7338))) )
& hBOOL(hAPP(hAPP(c_member(U_7348),U_7338),U_7350)) ) )
& ! [U_7353,U_7351,U_7349,U_7347,U_7345] :
( ! [U_7336] :
( ! [U_7335] :
( hBOOL(hAPP(U_7353,U_7335))
| ~ hBOOL(hAPP(hAPP(c_member(U_7345),U_7335),hAPP(U_7351,U_7336))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_7347),U_7336),U_7349)) )
| ? [U_7334] :
( ~ hBOOL(hAPP(U_7353,U_7334))
& hBOOL(hAPP(hAPP(c_member(U_7345),U_7334),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7347,tc_fun(U_7345,tc_HOL_Obool)),U_7349),U_7351))) ) ) ),
inference(miniscope,[status(thm)],[f_2194_2]) ).
fof(f_2194_4,plain,
( ! [U_7354,U_7352,U_7350,U_7348,U_7346] :
( ! [U_7339] :
( hBOOL(hAPP(U_7354,U_7339))
| ~ hBOOL(hAPP(hAPP(c_member(U_7346),U_7339),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7348,tc_fun(U_7346,tc_HOL_Obool)),U_7350),U_7352))) )
| ? [U_7338] :
( ? [U_7337] :
( ~ hBOOL(hAPP(U_7354,U_7337))
& hBOOL(hAPP(hAPP(c_member(U_7346),U_7337),hAPP(U_7352,U_7338))) )
& hBOOL(hAPP(hAPP(c_member(U_7348),U_7338),U_7350)) ) )
& ! [U_7353,U_7351,U_7349,U_7347,U_7345] :
( ! [U_7336] :
( ! [U_7335] :
( hBOOL(hAPP(U_7353,U_7335))
| ~ hBOOL(hAPP(hAPP(c_member(U_7345),U_7335),hAPP(U_7351,U_7336))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_7347),U_7336),U_7349)) )
| ( ~ hBOOL(hAPP(U_7353,sK138(U_7353,U_7351,U_7349,U_7347,U_7345)))
& hBOOL(hAPP(hAPP(c_member(U_7345),sK138(U_7353,U_7351,U_7349,U_7347,U_7345)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7347,tc_fun(U_7345,tc_HOL_Obool)),U_7349),U_7351))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_7334,sK138(U_7353,U_7351,U_7349,U_7347,U_7345))],[f_2194_3]) ).
fof(f_2194_5,plain,
( ! [U_7354,U_7352,U_7350,U_7348,U_7346] :
( ! [U_7339] :
( hBOOL(hAPP(U_7354,U_7339))
| ~ hBOOL(hAPP(hAPP(c_member(U_7346),U_7339),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7348,tc_fun(U_7346,tc_HOL_Obool)),U_7350),U_7352))) )
| ( ? [U_7337] :
( ~ hBOOL(hAPP(U_7354,U_7337))
& hBOOL(hAPP(hAPP(c_member(U_7346),U_7337),hAPP(U_7352,sK139(U_7354,U_7352,U_7350,U_7348,U_7346)))) )
& hBOOL(hAPP(hAPP(c_member(U_7348),sK139(U_7354,U_7352,U_7350,U_7348,U_7346)),U_7350)) ) )
& ! [U_7353,U_7351,U_7349,U_7347,U_7345] :
( ! [U_7336] :
( ! [U_7335] :
( hBOOL(hAPP(U_7353,U_7335))
| ~ hBOOL(hAPP(hAPP(c_member(U_7345),U_7335),hAPP(U_7351,U_7336))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_7347),U_7336),U_7349)) )
| ( ~ hBOOL(hAPP(U_7353,sK138(U_7353,U_7351,U_7349,U_7347,U_7345)))
& hBOOL(hAPP(hAPP(c_member(U_7345),sK138(U_7353,U_7351,U_7349,U_7347,U_7345)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7347,tc_fun(U_7345,tc_HOL_Obool)),U_7349),U_7351))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_7338,sK139(U_7354,U_7352,U_7350,U_7348,U_7346))],[f_2194_4]) ).
fof(f_2194_6,plain,
( ! [U_7354,U_7352,U_7350,U_7348,U_7346] :
( ! [U_7339] :
( hBOOL(hAPP(U_7354,U_7339))
| ~ hBOOL(hAPP(hAPP(c_member(U_7346),U_7339),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7348,tc_fun(U_7346,tc_HOL_Obool)),U_7350),U_7352))) )
| ( ~ hBOOL(hAPP(U_7354,sK140(U_7354,U_7352,U_7350,U_7348,U_7346)))
& hBOOL(hAPP(hAPP(c_member(U_7346),sK140(U_7354,U_7352,U_7350,U_7348,U_7346)),hAPP(U_7352,sK139(U_7354,U_7352,U_7350,U_7348,U_7346))))
& hBOOL(hAPP(hAPP(c_member(U_7348),sK139(U_7354,U_7352,U_7350,U_7348,U_7346)),U_7350)) ) )
& ! [U_7353,U_7351,U_7349,U_7347,U_7345] :
( ! [U_7336] :
( ! [U_7335] :
( hBOOL(hAPP(U_7353,U_7335))
| ~ hBOOL(hAPP(hAPP(c_member(U_7345),U_7335),hAPP(U_7351,U_7336))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_7347),U_7336),U_7349)) )
| ( ~ hBOOL(hAPP(U_7353,sK138(U_7353,U_7351,U_7349,U_7347,U_7345)))
& hBOOL(hAPP(hAPP(c_member(U_7345),sK138(U_7353,U_7351,U_7349,U_7347,U_7345)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7347,tc_fun(U_7345,tc_HOL_Obool)),U_7349),U_7351))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_7337,sK140(U_7354,U_7352,U_7350,U_7348,U_7346))],[f_2194_5]) ).
cnf(f_2194_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_7345),sK138(U_7353,U_7351,U_7349,U_7347,U_7345)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7347,tc_fun(U_7345,tc_HOL_Obool)),U_7349),U_7351)))
| hBOOL(hAPP(U_7353,U_7335))
| ~ hBOOL(hAPP(hAPP(c_member(U_7345),U_7335),hAPP(U_7351,U_7336)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7347),U_7336),U_7349)) ),
inference(clausify,[status(thm)],[f_2194_6]) ).
cnf(f_2194_8,plain,
( ~ hBOOL(hAPP(U_7353,sK138(U_7353,U_7351,U_7349,U_7347,U_7345)))
| hBOOL(hAPP(U_7353,U_7335))
| ~ hBOOL(hAPP(hAPP(c_member(U_7345),U_7335),hAPP(U_7351,U_7336)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7347),U_7336),U_7349)) ),
inference(clausify,[status(thm)],[f_2194_6]) ).
cnf(f_2194_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_7348),sK139(U_7354,U_7352,U_7350,U_7348,U_7346)),U_7350))
| hBOOL(hAPP(U_7354,U_7339))
| ~ hBOOL(hAPP(hAPP(c_member(U_7346),U_7339),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7348,tc_fun(U_7346,tc_HOL_Obool)),U_7350),U_7352))) ),
inference(clausify,[status(thm)],[f_2194_6]) ).
cnf(f_2194_10,plain,
( hBOOL(hAPP(hAPP(c_member(U_7346),sK140(U_7354,U_7352,U_7350,U_7348,U_7346)),hAPP(U_7352,sK139(U_7354,U_7352,U_7350,U_7348,U_7346))))
| hBOOL(hAPP(U_7354,U_7339))
| ~ hBOOL(hAPP(hAPP(c_member(U_7346),U_7339),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7348,tc_fun(U_7346,tc_HOL_Obool)),U_7350),U_7352))) ),
inference(clausify,[status(thm)],[f_2194_6]) ).
cnf(f_2194_11,plain,
( ~ hBOOL(hAPP(U_7354,sK140(U_7354,U_7352,U_7350,U_7348,U_7346)))
| hBOOL(hAPP(U_7354,U_7339))
| ~ hBOOL(hAPP(hAPP(c_member(U_7346),U_7339),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7348,tc_fun(U_7346,tc_HOL_Obool)),U_7350),U_7352))) ),
inference(clausify,[status(thm)],[f_2194_6]) ).
fof(f_2195_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) != hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2) ) )
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeast__eq__iff]) ).
fof(f_2195_2,plain,
! [U_7357,U_7356,U_7355] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeast(U_7355),U_7356) = hAPP(c_SetInterval_Oord__class_OatLeast(U_7355),U_7357)
| U_7356 != U_7357 )
& ( U_7356 = U_7357
| hAPP(c_SetInterval_Oord__class_OatLeast(U_7355),U_7356) != hAPP(c_SetInterval_Oord__class_OatLeast(U_7355),U_7357) ) )
| ~ class_Orderings_Olinorder(U_7355) ),
inference(variable_rename,[status(thm)],[f_2195_1]) ).
cnf(f_2195_3,plain,
( U_7356 = U_7357
| hAPP(c_SetInterval_Oord__class_OatLeast(U_7355),U_7356) != hAPP(c_SetInterval_Oord__class_OatLeast(U_7355),U_7357)
| ~ class_Orderings_Olinorder(U_7355) ),
inference(clausify,[status(thm)],[f_2195_2]) ).
cnf(f_2195_4,plain,
( hAPP(c_SetInterval_Oord__class_OatLeast(U_7355),U_7356) = hAPP(c_SetInterval_Oord__class_OatLeast(U_7355),U_7357)
| U_7356 != U_7357
| ~ class_Orderings_Olinorder(U_7355) ),
inference(clausify,[status(thm)],[f_2195_2]) ).
fof(f_2196_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]) ).
cnf(f_2196_2,plain,
c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_2196_1]) ).
fof(f_2197_1,plain,
! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__subset__iff]) ).
fof(f_2197_2,plain,
! [U_7364,U_7363,U_7362,U_7361,U_7360] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7360,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7361,tc_fun(U_7360,tc_HOL_Obool)),U_7362),U_7363)),U_7364))
| ? [U_7359] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7360,tc_HOL_Obool)),hAPP(U_7363,U_7359)),U_7364))
& hBOOL(hAPP(hAPP(c_member(U_7361),U_7359),U_7362)) ) )
& ( ! [U_7358] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7360,tc_HOL_Obool)),hAPP(U_7363,U_7358)),U_7364))
| ~ hBOOL(hAPP(hAPP(c_member(U_7361),U_7358),U_7362)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7360,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7361,tc_fun(U_7360,tc_HOL_Obool)),U_7362),U_7363)),U_7364)) ) ),
inference(variable_rename,[status(thm)],[f_2197_1]) ).
fof(f_2197_3,plain,
( ! [U_7374,U_7372,U_7370,U_7368,U_7366] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7366,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7368,tc_fun(U_7366,tc_HOL_Obool)),U_7370),U_7372)),U_7374))
| ? [U_7359] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7366,tc_HOL_Obool)),hAPP(U_7372,U_7359)),U_7374))
& hBOOL(hAPP(hAPP(c_member(U_7368),U_7359),U_7370)) ) )
& ! [U_7373,U_7371,U_7369,U_7367,U_7365] :
( ! [U_7358] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7365,tc_HOL_Obool)),hAPP(U_7371,U_7358)),U_7373))
| ~ hBOOL(hAPP(hAPP(c_member(U_7367),U_7358),U_7369)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7365,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7367,tc_fun(U_7365,tc_HOL_Obool)),U_7369),U_7371)),U_7373)) ) ),
inference(miniscope,[status(thm)],[f_2197_2]) ).
fof(f_2197_4,plain,
( ! [U_7374,U_7372,U_7370,U_7368,U_7366] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7366,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7368,tc_fun(U_7366,tc_HOL_Obool)),U_7370),U_7372)),U_7374))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7366,tc_HOL_Obool)),hAPP(U_7372,sK141(U_7374,U_7372,U_7370,U_7368,U_7366))),U_7374))
& hBOOL(hAPP(hAPP(c_member(U_7368),sK141(U_7374,U_7372,U_7370,U_7368,U_7366)),U_7370)) ) )
& ! [U_7373,U_7371,U_7369,U_7367,U_7365] :
( ! [U_7358] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7365,tc_HOL_Obool)),hAPP(U_7371,U_7358)),U_7373))
| ~ hBOOL(hAPP(hAPP(c_member(U_7367),U_7358),U_7369)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7365,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7367,tc_fun(U_7365,tc_HOL_Obool)),U_7369),U_7371)),U_7373)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_7359,sK141(U_7374,U_7372,U_7370,U_7368,U_7366))],[f_2197_3]) ).
cnf(f_2197_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7365,tc_HOL_Obool)),hAPP(U_7371,U_7358)),U_7373))
| ~ hBOOL(hAPP(hAPP(c_member(U_7367),U_7358),U_7369))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7365,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7367,tc_fun(U_7365,tc_HOL_Obool)),U_7369),U_7371)),U_7373)) ),
inference(clausify,[status(thm)],[f_2197_4]) ).
cnf(f_2197_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_7368),sK141(U_7374,U_7372,U_7370,U_7368,U_7366)),U_7370))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7366,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7368,tc_fun(U_7366,tc_HOL_Obool)),U_7370),U_7372)),U_7374)) ),
inference(clausify,[status(thm)],[f_2197_4]) ).
cnf(f_2197_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7366,tc_HOL_Obool)),hAPP(U_7372,sK141(U_7374,U_7372,U_7370,U_7368,U_7366))),U_7374))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7366,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7368,tc_fun(U_7366,tc_HOL_Obool)),U_7370),U_7372)),U_7374)) ),
inference(clausify,[status(thm)],[f_2197_4]) ).
fof(f_2198_1,plain,
! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I10_J]) ).
fof(f_2198_2,plain,
! [U_7380,U_7379,U_7378,U_7377,U_7376,U_7375] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7375,tc_fun(U_7376,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7377,U_7375,U_7378),U_7379)),U_7380) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7377,tc_fun(U_7376,tc_HOL_Obool)),U_7379),hAPP(hAPP(c_COMBB(U_7375,tc_fun(U_7376,tc_HOL_Obool),U_7377),U_7380),U_7378)),
inference(variable_rename,[status(thm)],[f_2198_1]) ).
cnf(f_2198_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7375,tc_fun(U_7376,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7377,U_7375,U_7378),U_7379)),U_7380) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7377,tc_fun(U_7376,tc_HOL_Obool)),U_7379),hAPP(hAPP(c_COMBB(U_7375,tc_fun(U_7376,tc_HOL_Obool),U_7377),U_7380),U_7378)),
inference(clausify,[status(thm)],[f_2198_2]) ).
fof(f_2199_1,plain,
! [V_B_2,V_A_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Oimage(T_c,T_b,V_f_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_image__UN]) ).
fof(f_2199_2,plain,
! [U_7386,U_7385,U_7384,U_7383,U_7382,U_7381] : hAPP(c_Set_Oimage(U_7381,U_7382,U_7383),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7384,tc_fun(U_7381,tc_HOL_Obool)),U_7385),U_7386)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7384,tc_fun(U_7382,tc_HOL_Obool)),U_7385),hAPP(hAPP(c_COMBB(tc_fun(U_7381,tc_HOL_Obool),tc_fun(U_7382,tc_HOL_Obool),U_7384),c_Set_Oimage(U_7381,U_7382,U_7383)),U_7386)),
inference(variable_rename,[status(thm)],[f_2199_1]) ).
cnf(f_2199_3,plain,
hAPP(c_Set_Oimage(U_7381,U_7382,U_7383),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7384,tc_fun(U_7381,tc_HOL_Obool)),U_7385),U_7386)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7384,tc_fun(U_7382,tc_HOL_Obool)),U_7385),hAPP(hAPP(c_COMBB(tc_fun(U_7381,tc_HOL_Obool),tc_fun(U_7382,tc_HOL_Obool),U_7384),c_Set_Oimage(U_7381,U_7382,U_7383)),U_7386)),
inference(clausify,[status(thm)],[f_2199_2]) ).
fof(f_2200_1,plain,
! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I10_J]) ).
fof(f_2200_2,plain,
! [U_7392,U_7391,U_7390,U_7389,U_7388,U_7387] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7387,tc_fun(U_7388,tc_HOL_Obool)),U_7389),hAPP(hAPP(c_COMBB(U_7390,tc_fun(U_7388,tc_HOL_Obool),U_7387),U_7391),U_7392)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7390,tc_fun(U_7388,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7387,U_7390,U_7392),U_7389)),U_7391),
inference(variable_rename,[status(thm)],[f_2200_1]) ).
cnf(f_2200_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7387,tc_fun(U_7388,tc_HOL_Obool)),U_7389),hAPP(hAPP(c_COMBB(U_7390,tc_fun(U_7388,tc_HOL_Obool),U_7387),U_7391),U_7392)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7390,tc_fun(U_7388,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_7387,U_7390,U_7392),U_7389)),U_7391),
inference(clausify,[status(thm)],[f_2200_2]) ).
fof(f_2201_1,plain,
! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)),
inference(fof_nnf,[status(thm)],[fact_UN__Un]) ).
fof(f_2201_2,plain,
! [U_7397,U_7396,U_7395,U_7394,U_7393] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7393,tc_fun(U_7394,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7393,tc_HOL_Obool)),U_7395),U_7396)),U_7397) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7394,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7393,tc_fun(U_7394,tc_HOL_Obool)),U_7395),U_7397)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7393,tc_fun(U_7394,tc_HOL_Obool)),U_7396),U_7397)),
inference(variable_rename,[status(thm)],[f_2201_1]) ).
cnf(f_2201_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7393,tc_fun(U_7394,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7393,tc_HOL_Obool)),U_7395),U_7396)),U_7397) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7394,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7393,tc_fun(U_7394,tc_HOL_Obool)),U_7395),U_7397)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7393,tc_fun(U_7394,tc_HOL_Obool)),U_7396),U_7397)),
inference(clausify,[status(thm)],[f_2201_2]) ).
fof(f_2202_1,plain,
! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_UN__Un__distrib]) ).
fof(f_2202_2,plain,
! [U_7402,U_7401,U_7400,U_7399,U_7398] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7398,tc_fun(U_7399,tc_HOL_Obool)),U_7400),hAPP(hAPP(c_COMBS(U_7398,tc_fun(U_7399,tc_HOL_Obool),tc_fun(U_7399,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7399,tc_HOL_Obool),tc_fun(tc_fun(U_7399,tc_HOL_Obool),tc_fun(U_7399,tc_HOL_Obool)),U_7398),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7399,tc_HOL_Obool))),U_7401)),U_7402)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7399,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7398,tc_fun(U_7399,tc_HOL_Obool)),U_7400),U_7401)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7398,tc_fun(U_7399,tc_HOL_Obool)),U_7400),U_7402)),
inference(variable_rename,[status(thm)],[f_2202_1]) ).
cnf(f_2202_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7398,tc_fun(U_7399,tc_HOL_Obool)),U_7400),hAPP(hAPP(c_COMBS(U_7398,tc_fun(U_7399,tc_HOL_Obool),tc_fun(U_7399,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7399,tc_HOL_Obool),tc_fun(tc_fun(U_7399,tc_HOL_Obool),tc_fun(U_7399,tc_HOL_Obool)),U_7398),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7399,tc_HOL_Obool))),U_7401)),U_7402)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7399,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7398,tc_fun(U_7399,tc_HOL_Obool)),U_7400),U_7401)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7398,tc_fun(U_7399,tc_HOL_Obool)),U_7400),U_7402)),
inference(clausify,[status(thm)],[f_2202_2]) ).
fof(f_2203_1,plain,
! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I6_J]) ).
fof(f_2203_2,plain,
! [U_7407,U_7406,U_7405,U_7404,U_7403] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7403,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7404,tc_fun(U_7403,tc_HOL_Obool)),U_7405),U_7406)),U_7407) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7404,tc_fun(U_7403,tc_HOL_Obool)),U_7405),hAPP(hAPP(c_COMBC(U_7404,tc_fun(U_7403,tc_HOL_Obool),tc_fun(U_7403,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7403,tc_HOL_Obool),tc_fun(tc_fun(U_7403,tc_HOL_Obool),tc_fun(U_7403,tc_HOL_Obool)),U_7404),c_Groups_Ominus__class_Ominus(tc_fun(U_7403,tc_HOL_Obool))),U_7406)),U_7407)),
inference(variable_rename,[status(thm)],[f_2203_1]) ).
cnf(f_2203_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7403,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7404,tc_fun(U_7403,tc_HOL_Obool)),U_7405),U_7406)),U_7407) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7404,tc_fun(U_7403,tc_HOL_Obool)),U_7405),hAPP(hAPP(c_COMBC(U_7404,tc_fun(U_7403,tc_HOL_Obool),tc_fun(U_7403,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7403,tc_HOL_Obool),tc_fun(tc_fun(U_7403,tc_HOL_Obool),tc_fun(U_7403,tc_HOL_Obool)),U_7404),c_Groups_Ominus__class_Ominus(tc_fun(U_7403,tc_HOL_Obool))),U_7406)),U_7407)),
inference(clausify,[status(thm)],[f_2203_2]) ).
fof(f_2204_1,plain,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I6_J]) ).
fof(f_2204_2,plain,
! [U_7412,U_7411,U_7410,U_7409,U_7408] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7408,tc_fun(U_7409,tc_HOL_Obool)),U_7410),hAPP(hAPP(c_COMBC(U_7408,tc_fun(U_7409,tc_HOL_Obool),tc_fun(U_7409,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7409,tc_HOL_Obool),tc_fun(tc_fun(U_7409,tc_HOL_Obool),tc_fun(U_7409,tc_HOL_Obool)),U_7408),c_Groups_Ominus__class_Ominus(tc_fun(U_7409,tc_HOL_Obool))),U_7411)),U_7412)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7409,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7408,tc_fun(U_7409,tc_HOL_Obool)),U_7410),U_7411)),U_7412),
inference(variable_rename,[status(thm)],[f_2204_1]) ).
cnf(f_2204_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7408,tc_fun(U_7409,tc_HOL_Obool)),U_7410),hAPP(hAPP(c_COMBC(U_7408,tc_fun(U_7409,tc_HOL_Obool),tc_fun(U_7409,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7409,tc_HOL_Obool),tc_fun(tc_fun(U_7409,tc_HOL_Obool),tc_fun(U_7409,tc_HOL_Obool)),U_7408),c_Groups_Ominus__class_Ominus(tc_fun(U_7409,tc_HOL_Obool))),U_7411)),U_7412)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7409,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7408,tc_fun(U_7409,tc_HOL_Obool)),U_7410),U_7411)),U_7412),
inference(clausify,[status(thm)],[f_2204_2]) ).
fof(f_2205_1,plain,
! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I9_J]) ).
fof(f_2205_2,plain,
! [U_7418,U_7417,U_7416,U_7415,U_7414,U_7413] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7413,tc_fun(U_7414,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7415,tc_fun(U_7413,tc_HOL_Obool)),U_7416),U_7417)),U_7418) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7415,tc_fun(U_7414,tc_HOL_Obool)),U_7416),hAPP(hAPP(c_COMBC(U_7415,tc_fun(U_7413,tc_fun(U_7414,tc_HOL_Obool)),tc_fun(U_7414,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7413,tc_HOL_Obool),tc_fun(tc_fun(U_7413,tc_fun(U_7414,tc_HOL_Obool)),tc_fun(U_7414,tc_HOL_Obool)),U_7415),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7413,tc_fun(U_7414,tc_HOL_Obool))),U_7417)),U_7418)),
inference(variable_rename,[status(thm)],[f_2205_1]) ).
cnf(f_2205_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7413,tc_fun(U_7414,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7415,tc_fun(U_7413,tc_HOL_Obool)),U_7416),U_7417)),U_7418) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7415,tc_fun(U_7414,tc_HOL_Obool)),U_7416),hAPP(hAPP(c_COMBC(U_7415,tc_fun(U_7413,tc_fun(U_7414,tc_HOL_Obool)),tc_fun(U_7414,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7413,tc_HOL_Obool),tc_fun(tc_fun(U_7413,tc_fun(U_7414,tc_HOL_Obool)),tc_fun(U_7414,tc_HOL_Obool)),U_7415),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7413,tc_fun(U_7414,tc_HOL_Obool))),U_7417)),U_7418)),
inference(clausify,[status(thm)],[f_2205_2]) ).
fof(f_2206_1,plain,
! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I9_J]) ).
fof(f_2206_2,plain,
! [U_7424,U_7423,U_7422,U_7421,U_7420,U_7419] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7419,tc_fun(U_7420,tc_HOL_Obool)),U_7421),hAPP(hAPP(c_COMBC(U_7419,tc_fun(U_7422,tc_fun(U_7420,tc_HOL_Obool)),tc_fun(U_7420,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7422,tc_HOL_Obool),tc_fun(tc_fun(U_7422,tc_fun(U_7420,tc_HOL_Obool)),tc_fun(U_7420,tc_HOL_Obool)),U_7419),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7422,tc_fun(U_7420,tc_HOL_Obool))),U_7423)),U_7424)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7422,tc_fun(U_7420,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7419,tc_fun(U_7422,tc_HOL_Obool)),U_7421),U_7423)),U_7424),
inference(variable_rename,[status(thm)],[f_2206_1]) ).
cnf(f_2206_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7419,tc_fun(U_7420,tc_HOL_Obool)),U_7421),hAPP(hAPP(c_COMBC(U_7419,tc_fun(U_7422,tc_fun(U_7420,tc_HOL_Obool)),tc_fun(U_7420,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7422,tc_HOL_Obool),tc_fun(tc_fun(U_7422,tc_fun(U_7420,tc_HOL_Obool)),tc_fun(U_7420,tc_HOL_Obool)),U_7419),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7422,tc_fun(U_7420,tc_HOL_Obool))),U_7423)),U_7424)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7422,tc_fun(U_7420,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7419,tc_fun(U_7422,tc_HOL_Obool)),U_7421),U_7423)),U_7424),
inference(clausify,[status(thm)],[f_2206_2]) ).
fof(f_2207_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_2207_2,plain,
! [U_7425] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7425)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_7425),
inference(variable_rename,[status(thm)],[f_2207_1]) ).
cnf(f_2207_3,plain,
hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7425)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_7425),
inference(clausify,[status(thm)],[f_2207_2]) ).
fof(f_2208_1,plain,
! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_M_2)),V_u_2))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_M_2)),V_u_2)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_SUP__le__iff]) ).
fof(f_2208_2,plain,
! [U_7432,U_7431,U_7430,U_7429,U_7428] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7428),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7429,U_7428),U_7430),U_7431)),U_7432))
| ? [U_7427] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7428),hAPP(U_7431,U_7427)),U_7432))
& hBOOL(hAPP(hAPP(c_member(U_7429),U_7427),U_7430)) ) )
& ( ! [U_7426] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7428),hAPP(U_7431,U_7426)),U_7432))
| ~ hBOOL(hAPP(hAPP(c_member(U_7429),U_7426),U_7430)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7428),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7429,U_7428),U_7430),U_7431)),U_7432)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7428) ),
inference(variable_rename,[status(thm)],[f_2208_1]) ).
fof(f_2208_3,plain,
! [U_7432,U_7431,U_7430,U_7429,U_7428] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7428),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7429,U_7428),U_7430),U_7431)),U_7432))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7428),hAPP(U_7431,sK142(U_7432,U_7431,U_7430,U_7429,U_7428))),U_7432))
& hBOOL(hAPP(hAPP(c_member(U_7429),sK142(U_7432,U_7431,U_7430,U_7429,U_7428)),U_7430)) ) )
& ( ! [U_7426] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7428),hAPP(U_7431,U_7426)),U_7432))
| ~ hBOOL(hAPP(hAPP(c_member(U_7429),U_7426),U_7430)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7428),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7429,U_7428),U_7430),U_7431)),U_7432)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7428) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_7427,sK142(U_7432,U_7431,U_7430,U_7429,U_7428))],[f_2208_2]) ).
cnf(f_2208_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7428),hAPP(U_7431,U_7426)),U_7432))
| ~ hBOOL(hAPP(hAPP(c_member(U_7429),U_7426),U_7430))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7428),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7429,U_7428),U_7430),U_7431)),U_7432))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7428) ),
inference(clausify,[status(thm)],[f_2208_3]) ).
cnf(f_2208_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_7429),sK142(U_7432,U_7431,U_7430,U_7429,U_7428)),U_7430))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7428),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7429,U_7428),U_7430),U_7431)),U_7432))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7428) ),
inference(clausify,[status(thm)],[f_2208_3]) ).
cnf(f_2208_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7428),hAPP(U_7431,sK142(U_7432,U_7431,U_7430,U_7429,U_7428))),U_7432))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7428),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7429,U_7428),U_7430),U_7431)),U_7432))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7428) ),
inference(clausify,[status(thm)],[f_2208_3]) ).
fof(f_2209_1,plain,
! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_f_2)))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_f_2))) ) )
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__SUP__iff]) ).
fof(f_2209_2,plain,
! [U_7439,U_7438,U_7437,U_7436,U_7435] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7435),U_7436),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7437,U_7435),U_7438),U_7439)))
| ! [U_7434] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7435),U_7436),hAPP(U_7439,U_7434)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7437),U_7434),U_7438)) ) )
& ( ? [U_7433] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7435),U_7436),hAPP(U_7439,U_7433)))
& hBOOL(hAPP(hAPP(c_member(U_7437),U_7433),U_7438)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7435),U_7436),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7437,U_7435),U_7438),U_7439))) ) )
| ~ class_Orderings_Olinorder(U_7435)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7435) ),
inference(variable_rename,[status(thm)],[f_2209_1]) ).
fof(f_2209_3,plain,
! [U_7439,U_7438,U_7437,U_7436,U_7435] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7435),U_7436),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7437,U_7435),U_7438),U_7439)))
| ! [U_7434] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7435),U_7436),hAPP(U_7439,U_7434)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7437),U_7434),U_7438)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7435),U_7436),hAPP(U_7439,sK143(U_7439,U_7438,U_7437,U_7436,U_7435))))
& hBOOL(hAPP(hAPP(c_member(U_7437),sK143(U_7439,U_7438,U_7437,U_7436,U_7435)),U_7438)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7435),U_7436),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7437,U_7435),U_7438),U_7439))) ) )
| ~ class_Orderings_Olinorder(U_7435)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7435) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_7433,sK143(U_7439,U_7438,U_7437,U_7436,U_7435))],[f_2209_2]) ).
cnf(f_2209_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_7437),sK143(U_7439,U_7438,U_7437,U_7436,U_7435)),U_7438))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7435),U_7436),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7437,U_7435),U_7438),U_7439)))
| ~ class_Orderings_Olinorder(U_7435)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7435) ),
inference(clausify,[status(thm)],[f_2209_3]) ).
cnf(f_2209_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7435),U_7436),hAPP(U_7439,sK143(U_7439,U_7438,U_7437,U_7436,U_7435))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7435),U_7436),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7437,U_7435),U_7438),U_7439)))
| ~ class_Orderings_Olinorder(U_7435)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7435) ),
inference(clausify,[status(thm)],[f_2209_3]) ).
cnf(f_2209_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7435),U_7436),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7437,U_7435),U_7438),U_7439)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7435),U_7436),hAPP(U_7439,U_7434)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7437),U_7434),U_7438))
| ~ class_Orderings_Olinorder(U_7435)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7435) ),
inference(clausify,[status(thm)],[f_2209_3]) ).
fof(f_2210_1,plain,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I7_J]) ).
fof(f_2210_2,plain,
! [U_7444,U_7443,U_7442,U_7441,U_7440] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7440,tc_fun(U_7441,tc_HOL_Obool)),U_7442),hAPP(hAPP(c_COMBB(tc_fun(U_7441,tc_HOL_Obool),tc_fun(U_7441,tc_HOL_Obool),U_7440),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7441,tc_HOL_Obool)),U_7443)),U_7444)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7441,tc_HOL_Obool)),U_7443),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7440,tc_fun(U_7441,tc_HOL_Obool)),U_7442),U_7444)),
inference(variable_rename,[status(thm)],[f_2210_1]) ).
cnf(f_2210_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7440,tc_fun(U_7441,tc_HOL_Obool)),U_7442),hAPP(hAPP(c_COMBB(tc_fun(U_7441,tc_HOL_Obool),tc_fun(U_7441,tc_HOL_Obool),U_7440),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7441,tc_HOL_Obool)),U_7443)),U_7444)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7441,tc_HOL_Obool)),U_7443),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7440,tc_fun(U_7441,tc_HOL_Obool)),U_7442),U_7444)),
inference(clausify,[status(thm)],[f_2210_2]) ).
fof(f_2211_1,plain,
! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I7_J]) ).
fof(f_2211_2,plain,
! [U_7449,U_7448,U_7447,U_7446,U_7445] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7445,tc_HOL_Obool)),U_7446),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7447,tc_fun(U_7445,tc_HOL_Obool)),U_7448),U_7449)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7447,tc_fun(U_7445,tc_HOL_Obool)),U_7448),hAPP(hAPP(c_COMBB(tc_fun(U_7445,tc_HOL_Obool),tc_fun(U_7445,tc_HOL_Obool),U_7447),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7445,tc_HOL_Obool)),U_7446)),U_7449)),
inference(variable_rename,[status(thm)],[f_2211_1]) ).
cnf(f_2211_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7445,tc_HOL_Obool)),U_7446),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7447,tc_fun(U_7445,tc_HOL_Obool)),U_7448),U_7449)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7447,tc_fun(U_7445,tc_HOL_Obool)),U_7448),hAPP(hAPP(c_COMBB(tc_fun(U_7445,tc_HOL_Obool),tc_fun(U_7445,tc_HOL_Obool),U_7447),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7445,tc_HOL_Obool)),U_7446)),U_7449)),
inference(clausify,[status(thm)],[f_2211_2]) ).
fof(f_2212_1,plain,
! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Compl__UN]) ).
fof(f_2212_2,plain,
! [U_7453,U_7452,U_7451,U_7450] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7450,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7451,tc_fun(U_7450,tc_HOL_Obool)),U_7452),U_7453)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7451,tc_fun(U_7450,tc_HOL_Obool)),U_7452),hAPP(hAPP(c_COMBB(tc_fun(U_7450,tc_HOL_Obool),tc_fun(U_7450,tc_HOL_Obool),U_7451),c_Groups_Ouminus__class_Ouminus(tc_fun(U_7450,tc_HOL_Obool))),U_7453)),
inference(variable_rename,[status(thm)],[f_2212_1]) ).
cnf(f_2212_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7450,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7451,tc_fun(U_7450,tc_HOL_Obool)),U_7452),U_7453)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7451,tc_fun(U_7450,tc_HOL_Obool)),U_7452),hAPP(hAPP(c_COMBB(tc_fun(U_7450,tc_HOL_Obool),tc_fun(U_7450,tc_HOL_Obool),U_7451),c_Groups_Ouminus__class_Ouminus(tc_fun(U_7450,tc_HOL_Obool))),U_7453)),
inference(clausify,[status(thm)],[f_2212_2]) ).
fof(f_2213_1,plain,
! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Compl__INT]) ).
fof(f_2213_2,plain,
! [U_7457,U_7456,U_7455,U_7454] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7454,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7455,tc_fun(U_7454,tc_HOL_Obool)),U_7456),U_7457)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7455,tc_fun(U_7454,tc_HOL_Obool)),U_7456),hAPP(hAPP(c_COMBB(tc_fun(U_7454,tc_HOL_Obool),tc_fun(U_7454,tc_HOL_Obool),U_7455),c_Groups_Ouminus__class_Ouminus(tc_fun(U_7454,tc_HOL_Obool))),U_7457)),
inference(variable_rename,[status(thm)],[f_2213_1]) ).
cnf(f_2213_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7454,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7455,tc_fun(U_7454,tc_HOL_Obool)),U_7456),U_7457)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7455,tc_fun(U_7454,tc_HOL_Obool)),U_7456),hAPP(hAPP(c_COMBB(tc_fun(U_7454,tc_HOL_Obool),tc_fun(U_7454,tc_HOL_Obool),U_7455),c_Groups_Ouminus__class_Ouminus(tc_fun(U_7454,tc_HOL_Obool))),U_7457)),
inference(clausify,[status(thm)],[f_2213_2]) ).
fof(f_2214_1,plain,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_B_2),V_f_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_SUP__subset]) ).
fof(f_2214_2,plain,
! [U_7462,U_7461,U_7460,U_7459,U_7458] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7458),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7459,U_7458),U_7460),U_7462)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7459,U_7458),U_7461),U_7462)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7459,tc_HOL_Obool)),U_7460),U_7461))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7458) ),
inference(variable_rename,[status(thm)],[f_2214_1]) ).
cnf(f_2214_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7458),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7459,U_7458),U_7460),U_7462)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7459,U_7458),U_7461),U_7462)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7459,tc_HOL_Obool)),U_7460),U_7461))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7458) ),
inference(clausify,[status(thm)],[f_2214_2]) ).
fof(f_2215_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2))) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeast__subset__iff]) ).
fof(f_2215_2,plain,
! [U_7465,U_7464,U_7463] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7463,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7463),U_7464)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7463),U_7465)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7463),U_7465),U_7464)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7463),U_7465),U_7464))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7463,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7463),U_7464)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7463),U_7465))) ) )
| ~ class_Orderings_Oorder(U_7463) ),
inference(variable_rename,[status(thm)],[f_2215_1]) ).
cnf(f_2215_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7463),U_7465),U_7464))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7463,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7463),U_7464)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7463),U_7465)))
| ~ class_Orderings_Oorder(U_7463) ),
inference(clausify,[status(thm)],[f_2215_2]) ).
cnf(f_2215_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7463,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7463),U_7464)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7463),U_7465)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7463),U_7465),U_7464))
| ~ class_Orderings_Oorder(U_7463) ),
inference(clausify,[status(thm)],[f_2215_2]) ).
fof(f_2216_1,plain,
! [V_k_2,T_b] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Compl__lessThan]) ).
fof(f_2216_2,plain,
! [U_7467,U_7466] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7466,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_7466),U_7467)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_7466),U_7467)
| ~ class_Orderings_Olinorder(U_7466) ),
inference(variable_rename,[status(thm)],[f_2216_1]) ).
cnf(f_2216_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7466,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_7466),U_7467)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_7466),U_7467)
| ~ class_Orderings_Olinorder(U_7466) ),
inference(clausify,[status(thm)],[f_2216_2]) ).
fof(f_2217_1,plain,
! [V_k_2,T_b] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Compl__atLeast]) ).
fof(f_2217_2,plain,
! [U_7469,U_7468] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7468,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7468),U_7469)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_7468),U_7469)
| ~ class_Orderings_Olinorder(U_7468) ),
inference(variable_rename,[status(thm)],[f_2217_1]) ).
cnf(f_2217_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7468,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7468),U_7469)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_7468),U_7469)
| ~ class_Orderings_Olinorder(U_7468) ),
inference(clausify,[status(thm)],[f_2217_2]) ).
fof(f_2218_1,plain,
! [V_k_2,V_M_2,V_na_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_na_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool),tc_Nat_Onat),V_M_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_k_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_na_2),V_k_2))),V_M_2),
inference(fof_nnf,[status(thm)],[fact_UN__le__add__shift]) ).
fof(f_2218_2,plain,
! [U_7473,U_7472,U_7471,U_7470] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7470,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7471)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_7470,tc_HOL_Obool),tc_Nat_Onat),U_7472),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_7473))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7470,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7473,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7471),U_7473))),U_7472),
inference(variable_rename,[status(thm)],[f_2218_1]) ).
cnf(f_2218_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7470,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7471)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_7470,tc_HOL_Obool),tc_Nat_Onat),U_7472),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_7473))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_7470,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7473,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7471),U_7473))),U_7472),
inference(clausify,[status(thm)],[f_2218_2]) ).
fof(f_2219_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I14_J]) ).
fof(f_2219_2,plain,
! [U_7476,U_7475,U_7474] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7474,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7474,U_7475),U_7476)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7474),U_7476)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_7474),U_7475)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7474),U_7475),U_7476))
| ~ class_Orderings_Olinorder(U_7474) ),
inference(variable_rename,[status(thm)],[f_2219_1]) ).
cnf(f_2219_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7474,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7474,U_7475),U_7476)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7474),U_7476)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_7474),U_7475)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7474),U_7475),U_7476))
| ~ class_Orderings_Olinorder(U_7474) ),
inference(clausify,[status(thm)],[f_2219_2]) ).
fof(f_2220_1,plain,
! [V_x_2,T_b] :
( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__atMost]) ).
fof(f_2220_2,plain,
! [U_7478,U_7477] :
( hAPP(c_Set_Oimage(U_7477,U_7477,c_Groups_Ouminus__class_Ouminus(U_7477)),hAPP(c_SetInterval_Oord__class_OatMost(U_7477),U_7478)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_7477),hAPP(c_Groups_Ouminus__class_Ouminus(U_7477),U_7478))
| ~ class_Groups_Oordered__ab__group__add(U_7477) ),
inference(variable_rename,[status(thm)],[f_2220_1]) ).
cnf(f_2220_3,plain,
( hAPP(c_Set_Oimage(U_7477,U_7477,c_Groups_Ouminus__class_Ouminus(U_7477)),hAPP(c_SetInterval_Oord__class_OatMost(U_7477),U_7478)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_7477),hAPP(c_Groups_Ouminus__class_Ouminus(U_7477),U_7478))
| ~ class_Groups_Oordered__ab__group__add(U_7477) ),
inference(clausify,[status(thm)],[f_2220_2]) ).
fof(f_2221_1,plain,
! [V_x_2,T_b] :
( hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2))
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeast]) ).
fof(f_2221_2,plain,
! [U_7480,U_7479] :
( hAPP(c_Set_Oimage(U_7479,U_7479,c_Groups_Ouminus__class_Ouminus(U_7479)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7479),U_7480)) = hAPP(c_SetInterval_Oord__class_OatMost(U_7479),hAPP(c_Groups_Ouminus__class_Ouminus(U_7479),U_7480))
| ~ class_Groups_Oordered__ab__group__add(U_7479) ),
inference(variable_rename,[status(thm)],[f_2221_1]) ).
cnf(f_2221_3,plain,
( hAPP(c_Set_Oimage(U_7479,U_7479,c_Groups_Ouminus__class_Ouminus(U_7479)),hAPP(c_SetInterval_Oord__class_OatLeast(U_7479),U_7480)) = hAPP(c_SetInterval_Oord__class_OatMost(U_7479),hAPP(c_Groups_Ouminus__class_Ouminus(U_7479),U_7480))
| ~ class_Groups_Oordered__ab__group__add(U_7479) ),
inference(clausify,[status(thm)],[f_2221_2]) ).
fof(f_2222_1,plain,
! [V_na_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_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_na_2))),
inference(fof_nnf,[status(thm)],[fact_lessThan__Suc__eq__insert__0]) ).
fof(f_2222_2,plain,
! [U_7481] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7481)) = 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_7481))),
inference(variable_rename,[status(thm)],[f_2222_1]) ).
cnf(f_2222_3,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7481)) = 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_7481))),
inference(clausify,[status(thm)],[f_2222_2]) ).
fof(f_2223_1,plain,
! [V_f_2,V_A_2,V_B_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat]) ).
fof(f_2223_2,plain,
! [U_7485,U_7484,U_7483,U_7482] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7482,tc_Nat_Onat),U_7485),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7482,tc_HOL_Obool)),U_7484),U_7483)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7482,tc_Nat_Onat),U_7485),U_7484)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7482,tc_Nat_Onat),U_7485),U_7483))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7482,tc_HOL_Obool)),U_7483),U_7484))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7482),U_7483)) ),
inference(variable_rename,[status(thm)],[f_2223_1]) ).
cnf(f_2223_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7482,tc_Nat_Onat),U_7485),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7482,tc_HOL_Obool)),U_7484),U_7483)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7482,tc_Nat_Onat),U_7485),U_7484)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7482,tc_Nat_Onat),U_7485),U_7483))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7482,tc_HOL_Obool)),U_7483),U_7484))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7482),U_7483)) ),
inference(clausify,[status(thm)],[f_2223_2]) ).
fof(f_2224_1,plain,
! [V_X_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_coinduct]) ).
fof(f_2224_2,plain,
! [U_7488,U_7487,U_7486] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7486),U_7488),c_Inductive_Ocomplete__lattice__class_Ogfp(U_7486,U_7487)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7486),U_7488),hAPP(U_7487,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7486),U_7488),c_Inductive_Ocomplete__lattice__class_Ogfp(U_7486,U_7487)))))
| ~ c_Orderings_Oorder__class_Omono(U_7486,U_7486,U_7487)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7486) ),
inference(variable_rename,[status(thm)],[f_2224_1]) ).
cnf(f_2224_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7486),U_7488),c_Inductive_Ocomplete__lattice__class_Ogfp(U_7486,U_7487)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7486),U_7488),hAPP(U_7487,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7486),U_7488),c_Inductive_Ocomplete__lattice__class_Ogfp(U_7486,U_7487)))))
| ~ c_Orderings_Oorder__class_Omono(U_7486,U_7486,U_7487)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7486) ),
inference(clausify,[status(thm)],[f_2224_2]) ).
fof(f_2225_1,plain,
! [V_f_2,V_X_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_coinduct__lemma]) ).
fof(f_2225_2,plain,
! [U_7491,U_7490,U_7489] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7489),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7489),U_7490),c_Inductive_Ocomplete__lattice__class_Ogfp(U_7489,U_7491))),hAPP(U_7491,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7489),U_7490),c_Inductive_Ocomplete__lattice__class_Ogfp(U_7489,U_7491)))))
| ~ c_Orderings_Oorder__class_Omono(U_7489,U_7489,U_7491)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7489),U_7490),hAPP(U_7491,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7489),U_7490),c_Inductive_Ocomplete__lattice__class_Ogfp(U_7489,U_7491)))))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7489) ),
inference(variable_rename,[status(thm)],[f_2225_1]) ).
cnf(f_2225_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7489),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7489),U_7490),c_Inductive_Ocomplete__lattice__class_Ogfp(U_7489,U_7491))),hAPP(U_7491,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7489),U_7490),c_Inductive_Ocomplete__lattice__class_Ogfp(U_7489,U_7491)))))
| ~ c_Orderings_Oorder__class_Omono(U_7489,U_7489,U_7491)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7489),U_7490),hAPP(U_7491,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7489),U_7490),c_Inductive_Ocomplete__lattice__class_Ogfp(U_7489,U_7491)))))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7489) ),
inference(clausify,[status(thm)],[f_2225_2]) ).
fof(f_2226_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_2226_2,plain,
! [U_7493,U_7492] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7492),U_7493))),
inference(variable_rename,[status(thm)],[f_2226_1]) ).
cnf(f_2226_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7492),U_7493))),
inference(clausify,[status(thm)],[f_2226_2]) ).
fof(f_2227_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_2227_2,plain,
! [U_7495,U_7494] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7494,U_7495))),
inference(variable_rename,[status(thm)],[f_2227_1]) ).
cnf(f_2227_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_7494,U_7495))),
inference(clausify,[status(thm)],[f_2227_2]) ).
fof(f_2228_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_2228_2,plain,
! [U_7497,U_7496] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7496,U_7497))),
inference(variable_rename,[status(thm)],[f_2228_1]) ).
cnf(f_2228_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7496,U_7497))),
inference(clausify,[status(thm)],[f_2228_2]) ).
fof(f_2229_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_2229_2,plain,
! [U_7498] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_7498))),
inference(variable_rename,[status(thm)],[f_2229_1]) ).
cnf(f_2229_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_7498))),
inference(clausify,[status(thm)],[f_2229_2]) ).
fof(f_2230_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_2230_2,plain,
! [U_7499] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7499))),
inference(variable_rename,[status(thm)],[f_2230_1]) ).
cnf(f_2230_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7499))),
inference(clausify,[status(thm)],[f_2230_2]) ).
fof(f_2231_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_2231_2,plain,
! [U_7501,U_7500] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7500),U_7501))),
inference(variable_rename,[status(thm)],[f_2231_1]) ).
cnf(f_2231_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_7500),U_7501))),
inference(clausify,[status(thm)],[f_2231_2]) ).
fof(f_2232_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_2232_2,plain,
! [U_7503,U_7502] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_7502,U_7503))),
inference(variable_rename,[status(thm)],[f_2232_1]) ).
cnf(f_2232_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_7502,U_7503))),
inference(clausify,[status(thm)],[f_2232_2]) ).
fof(f_2233_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_2233_2,plain,
! [U_7505,U_7504] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7504,U_7505))),
inference(variable_rename,[status(thm)],[f_2233_1]) ).
cnf(f_2233_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_7504,U_7505))),
inference(clausify,[status(thm)],[f_2233_2]) ).
fof(f_2234_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_2234_2,plain,
! [U_7507,U_7506] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_7506,U_7507))),
inference(variable_rename,[status(thm)],[f_2234_1]) ).
cnf(f_2234_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_7506,U_7507))),
inference(clausify,[status(thm)],[f_2234_2]) ).
fof(f_2235_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_2235_2,plain,
! [U_7509,U_7508] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_7508,U_7509))),
inference(variable_rename,[status(thm)],[f_2235_1]) ).
cnf(f_2235_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_7508,U_7509))),
inference(clausify,[status(thm)],[f_2235_2]) ).
fof(f_2236_1,plain,
! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Un__insert__right]) ).
fof(f_2236_2,plain,
! [U_7513,U_7512,U_7511,U_7510] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7510,tc_HOL_Obool)),U_7511),hAPP(hAPP(c_Set_Oinsert(U_7510),U_7512),U_7513)) = hAPP(hAPP(c_Set_Oinsert(U_7510),U_7512),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7510,tc_HOL_Obool)),U_7511),U_7513)),
inference(variable_rename,[status(thm)],[f_2236_1]) ).
cnf(f_2236_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7510,tc_HOL_Obool)),U_7511),hAPP(hAPP(c_Set_Oinsert(U_7510),U_7512),U_7513)) = hAPP(hAPP(c_Set_Oinsert(U_7510),U_7512),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7510,tc_HOL_Obool)),U_7511),U_7513)),
inference(clausify,[status(thm)],[f_2236_2]) ).
fof(f_2237_1,plain,
! [V_C_2,V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Un__insert__left]) ).
fof(f_2237_2,plain,
! [U_7517,U_7516,U_7515,U_7514] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7514,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7514),U_7515),U_7516)),U_7517) = hAPP(hAPP(c_Set_Oinsert(U_7514),U_7515),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7514,tc_HOL_Obool)),U_7516),U_7517)),
inference(variable_rename,[status(thm)],[f_2237_1]) ).
cnf(f_2237_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7514,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7514),U_7515),U_7516)),U_7517) = hAPP(hAPP(c_Set_Oinsert(U_7514),U_7515),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7514,tc_HOL_Obool)),U_7516),U_7517)),
inference(clausify,[status(thm)],[f_2237_2]) ).
fof(f_2238_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_2238_2,plain,
! [U_7518] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7518))
| ~ 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_7518))) )
& ( 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_7518)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7518)) ) ),
inference(variable_rename,[status(thm)],[f_2238_1]) ).
fof(f_2238_3,plain,
( ! [U_7520] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7520))
| ~ 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_7520))) )
& ! [U_7519] :
( 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_7519)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7519)) ) ),
inference(miniscope,[status(thm)],[f_2238_2]) ).
cnf(f_2238_4,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_7519)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7519)) ),
inference(clausify,[status(thm)],[f_2238_3]) ).
cnf(f_2238_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7520))
| ~ 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_7520))) ),
inference(clausify,[status(thm)],[f_2238_3]) ).
fof(f_2239_1,plain,
! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_image__insert]) ).
fof(f_2239_2,plain,
! [U_7525,U_7524,U_7523,U_7522,U_7521] : hAPP(c_Set_Oimage(U_7521,U_7522,U_7523),hAPP(hAPP(c_Set_Oinsert(U_7521),U_7524),U_7525)) = hAPP(hAPP(c_Set_Oinsert(U_7522),hAPP(U_7523,U_7524)),hAPP(c_Set_Oimage(U_7521,U_7522,U_7523),U_7525)),
inference(variable_rename,[status(thm)],[f_2239_1]) ).
cnf(f_2239_3,plain,
hAPP(c_Set_Oimage(U_7521,U_7522,U_7523),hAPP(hAPP(c_Set_Oinsert(U_7521),U_7524),U_7525)) = hAPP(hAPP(c_Set_Oinsert(U_7522),hAPP(U_7523,U_7524)),hAPP(c_Set_Oimage(U_7521,U_7522,U_7523),U_7525)),
inference(clausify,[status(thm)],[f_2239_2]) ).
fof(f_2240_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_2240_2,plain,
! [U_7530] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7530))
| ! [U_7529] :
? [U_7528] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7528),U_7529))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7528),U_7530)) ) )
& ( ? [U_7527] :
! [U_7526] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7526),U_7527))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7526),U_7530)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7530)) ) ),
inference(variable_rename,[status(thm)],[f_2240_1]) ).
fof(f_2240_3,plain,
( ! [U_7532] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7532))
| ! [U_7529] :
? [U_7528] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7528),U_7529))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7528),U_7532)) ) )
& ! [U_7531] :
( ? [U_7527] :
! [U_7526] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7526),U_7527))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7526),U_7531)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7531)) ) ),
inference(miniscope,[status(thm)],[f_2240_2]) ).
fof(f_2240_4,plain,
( ! [U_7532] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7532))
| ! [U_7529] :
? [U_7528] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7528),U_7529))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7528),U_7532)) ) )
& ! [U_7531] :
( ! [U_7526] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7526),sK144(U_7531)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7526),U_7531)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7531)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_7527,sK144(U_7531))],[f_2240_3]) ).
fof(f_2240_5,plain,
( ! [U_7532] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7532))
| ! [U_7529] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK145(U_7532,U_7529)),U_7529))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK145(U_7532,U_7529)),U_7532)) ) )
& ! [U_7531] :
( ! [U_7526] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7526),sK144(U_7531)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7526),U_7531)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7531)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_7528,sK145(U_7532,U_7529))],[f_2240_4]) ).
cnf(f_2240_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7526),sK144(U_7531)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7526),U_7531))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7531)) ),
inference(clausify,[status(thm)],[f_2240_5]) ).
cnf(f_2240_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK145(U_7532,U_7529)),U_7532))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7532)) ),
inference(clausify,[status(thm)],[f_2240_5]) ).
cnf(f_2240_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK145(U_7532,U_7529)),U_7529))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7532)) ),
inference(clausify,[status(thm)],[f_2240_5]) ).
fof(f_2241_1,plain,
! [V_A_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2),
inference(fof_nnf,[status(thm)],[fact_insert__absorb2]) ).
fof(f_2241_2,plain,
! [U_7535,U_7534,U_7533] : hAPP(hAPP(c_Set_Oinsert(U_7533),U_7534),hAPP(hAPP(c_Set_Oinsert(U_7533),U_7534),U_7535)) = hAPP(hAPP(c_Set_Oinsert(U_7533),U_7534),U_7535),
inference(variable_rename,[status(thm)],[f_2241_1]) ).
cnf(f_2241_3,plain,
hAPP(hAPP(c_Set_Oinsert(U_7533),U_7534),hAPP(hAPP(c_Set_Oinsert(U_7533),U_7534),U_7535)) = hAPP(hAPP(c_Set_Oinsert(U_7533),U_7534),U_7535),
inference(clausify,[status(thm)],[f_2241_2]) ).
fof(f_2242_1,plain,
! [V_A_2,V_y_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_insert__commute]) ).
fof(f_2242_2,plain,
! [U_7539,U_7538,U_7537,U_7536] : hAPP(hAPP(c_Set_Oinsert(U_7536),U_7537),hAPP(hAPP(c_Set_Oinsert(U_7536),U_7538),U_7539)) = hAPP(hAPP(c_Set_Oinsert(U_7536),U_7538),hAPP(hAPP(c_Set_Oinsert(U_7536),U_7537),U_7539)),
inference(variable_rename,[status(thm)],[f_2242_1]) ).
cnf(f_2242_3,plain,
hAPP(hAPP(c_Set_Oinsert(U_7536),U_7537),hAPP(hAPP(c_Set_Oinsert(U_7536),U_7538),U_7539)) = hAPP(hAPP(c_Set_Oinsert(U_7536),U_7538),hAPP(hAPP(c_Set_Oinsert(U_7536),U_7537),U_7539)),
inference(clausify,[status(thm)],[f_2242_2]) ).
fof(f_2243_1,plain,
! [V_x_2,V_A_2,V_y_2,T_b] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
| ( ~ hBOOL(hAPP(V_A_2,V_x_2))
& V_y_2 != V_x_2 ) )
& ( hBOOL(hAPP(V_A_2,V_x_2))
| V_y_2 = V_x_2
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_insert__code]) ).
fof(f_2243_2,plain,
! [U_7543,U_7542,U_7541,U_7540] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7540),U_7541),U_7542),U_7543))
| ( ~ hBOOL(hAPP(U_7542,U_7543))
& U_7541 != U_7543 ) )
& ( hBOOL(hAPP(U_7542,U_7543))
| U_7541 = U_7543
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7540),U_7541),U_7542),U_7543)) ) ),
inference(variable_rename,[status(thm)],[f_2243_1]) ).
fof(f_2243_3,plain,
( ! [U_7551,U_7549,U_7547] :
( ! [U_7545] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7545),U_7547),U_7549),U_7551))
| ( ~ hBOOL(hAPP(U_7549,U_7551))
& U_7547 != U_7551 ) )
& ! [U_7550,U_7548,U_7546] :
( ! [U_7544] : ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7544),U_7546),U_7548),U_7550))
| hBOOL(hAPP(U_7548,U_7550))
| U_7546 = U_7550 ) ),
inference(miniscope,[status(thm)],[f_2243_2]) ).
cnf(f_2243_4,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7544),U_7546),U_7548),U_7550))
| hBOOL(hAPP(U_7548,U_7550))
| U_7546 = U_7550 ),
inference(clausify,[status(thm)],[f_2243_3]) ).
cnf(f_2243_5,plain,
( U_7547 != U_7551
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7545),U_7547),U_7549),U_7551)) ),
inference(clausify,[status(thm)],[f_2243_3]) ).
cnf(f_2243_6,plain,
( ~ hBOOL(hAPP(U_7549,U_7551))
| hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_7545),U_7547),U_7549),U_7551)) ),
inference(clausify,[status(thm)],[f_2243_3]) ).
fof(f_2244_1,plain,
! [V_a_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
inference(fof_nnf,[status(thm)],[fact_subset__insertI]) ).
fof(f_2244_2,plain,
! [U_7554,U_7553,U_7552] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7552,tc_HOL_Obool)),U_7553),hAPP(hAPP(c_Set_Oinsert(U_7552),U_7554),U_7553))),
inference(variable_rename,[status(thm)],[f_2244_1]) ).
cnf(f_2244_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7552,tc_HOL_Obool)),U_7553),hAPP(hAPP(c_Set_Oinsert(U_7552),U_7554),U_7553))),
inference(clausify,[status(thm)],[f_2244_2]) ).
fof(f_2245_1,plain,
! [V_b_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_subset__insertI2]) ).
fof(f_2245_2,plain,
! [U_7558,U_7557,U_7556,U_7555] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7555,tc_HOL_Obool)),U_7556),hAPP(hAPP(c_Set_Oinsert(U_7555),U_7558),U_7557)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7555,tc_HOL_Obool)),U_7556),U_7557)) ),
inference(variable_rename,[status(thm)],[f_2245_1]) ).
cnf(f_2245_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7555,tc_HOL_Obool)),U_7556),hAPP(hAPP(c_Set_Oinsert(U_7555),U_7558),U_7557)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7555,tc_HOL_Obool)),U_7556),U_7557)) ),
inference(clausify,[status(thm)],[f_2245_2]) ).
fof(f_2246_1,plain,
! [V_a_2,V_D_2,V_C_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__mono]) ).
fof(f_2246_2,plain,
! [U_7562,U_7561,U_7560,U_7559] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7559,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7559),U_7562),U_7560)),hAPP(hAPP(c_Set_Oinsert(U_7559),U_7562),U_7561)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7559,tc_HOL_Obool)),U_7560),U_7561)) ),
inference(variable_rename,[status(thm)],[f_2246_1]) ).
cnf(f_2246_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7559,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7559),U_7562),U_7560)),hAPP(hAPP(c_Set_Oinsert(U_7559),U_7562),U_7561)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7559,tc_HOL_Obool)),U_7560),U_7561)) ),
inference(clausify,[status(thm)],[f_2246_2]) ).
fof(f_2247_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_2247_2,plain,
! [U_7567] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7567))
| ! [U_7566] :
? [U_7565] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7565),U_7566))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7565),U_7567)) ) )
& ( ? [U_7564] :
! [U_7563] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7563),U_7564))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7563),U_7567)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7567)) ) ),
inference(variable_rename,[status(thm)],[f_2247_1]) ).
fof(f_2247_3,plain,
( ! [U_7569] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7569))
| ! [U_7566] :
? [U_7565] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7565),U_7566))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7565),U_7569)) ) )
& ! [U_7568] :
( ? [U_7564] :
! [U_7563] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7563),U_7564))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7563),U_7568)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7568)) ) ),
inference(miniscope,[status(thm)],[f_2247_2]) ).
fof(f_2247_4,plain,
( ! [U_7569] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7569))
| ! [U_7566] :
? [U_7565] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7565),U_7566))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7565),U_7569)) ) )
& ! [U_7568] :
( ! [U_7563] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7563),sK146(U_7568)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7563),U_7568)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7568)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_7564,sK146(U_7568))],[f_2247_3]) ).
fof(f_2247_5,plain,
( ! [U_7569] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7569))
| ! [U_7566] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK147(U_7569,U_7566)),U_7566))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK147(U_7569,U_7566)),U_7569)) ) )
& ! [U_7568] :
( ! [U_7563] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7563),sK146(U_7568)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7563),U_7568)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7568)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_7565,sK147(U_7569,U_7566))],[f_2247_4]) ).
cnf(f_2247_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7563),sK146(U_7568)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7563),U_7568))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7568)) ),
inference(clausify,[status(thm)],[f_2247_5]) ).
cnf(f_2247_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK147(U_7569,U_7566)),U_7569))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7569)) ),
inference(clausify,[status(thm)],[f_2247_5]) ).
cnf(f_2247_8,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK147(U_7569,U_7566)),U_7566))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_7569)) ),
inference(clausify,[status(thm)],[f_2247_5]) ).
fof(f_2248_1,plain,
! [V_B_2,V_a_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I5_J]) ).
fof(f_2248_2,plain,
! [U_7574,U_7573,U_7572,U_7571,U_7570] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7570,tc_fun(U_7571,tc_HOL_Obool)),U_7572),hAPP(hAPP(c_COMBB(tc_fun(U_7571,tc_HOL_Obool),tc_fun(U_7571,tc_HOL_Obool),U_7570),hAPP(c_Set_Oinsert(U_7571),U_7573)),U_7574)) = hAPP(hAPP(c_Set_Oinsert(U_7571),U_7573),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7570,tc_fun(U_7571,tc_HOL_Obool)),U_7572),U_7574)),
inference(variable_rename,[status(thm)],[f_2248_1]) ).
cnf(f_2248_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7570,tc_fun(U_7571,tc_HOL_Obool)),U_7572),hAPP(hAPP(c_COMBB(tc_fun(U_7571,tc_HOL_Obool),tc_fun(U_7571,tc_HOL_Obool),U_7570),hAPP(c_Set_Oinsert(U_7571),U_7573)),U_7574)) = hAPP(hAPP(c_Set_Oinsert(U_7571),U_7573),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7570,tc_fun(U_7571,tc_HOL_Obool)),U_7572),U_7574)),
inference(clausify,[status(thm)],[f_2248_2]) ).
fof(f_2249_1,plain,
! [V_B_2,V_C_2,T_c,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I5_J]) ).
fof(f_2249_2,plain,
! [U_7579,U_7578,U_7577,U_7576,U_7575] : hAPP(hAPP(c_Set_Oinsert(U_7575),U_7576),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7577,tc_fun(U_7575,tc_HOL_Obool)),U_7578),U_7579)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7577,tc_fun(U_7575,tc_HOL_Obool)),U_7578),hAPP(hAPP(c_COMBB(tc_fun(U_7575,tc_HOL_Obool),tc_fun(U_7575,tc_HOL_Obool),U_7577),hAPP(c_Set_Oinsert(U_7575),U_7576)),U_7579)),
inference(variable_rename,[status(thm)],[f_2249_1]) ).
cnf(f_2249_3,plain,
hAPP(hAPP(c_Set_Oinsert(U_7575),U_7576),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7577,tc_fun(U_7575,tc_HOL_Obool)),U_7578),U_7579)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7577,tc_fun(U_7575,tc_HOL_Obool)),U_7578),hAPP(hAPP(c_COMBB(tc_fun(U_7575,tc_HOL_Obool),tc_fun(U_7575,tc_HOL_Obool),U_7577),hAPP(c_Set_Oinsert(U_7575),U_7576)),U_7579)),
inference(clausify,[status(thm)],[f_2249_2]) ).
fof(f_2250_1,plain,
! [V_f_2,V_X_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,V_X_2)))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_gfp__upperbound]) ).
fof(f_2250_2,plain,
! [U_7582,U_7581,U_7580] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7580),U_7581),c_Inductive_Ocomplete__lattice__class_Ogfp(U_7580,U_7582)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7580),U_7581),hAPP(U_7582,U_7581)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7580) ),
inference(variable_rename,[status(thm)],[f_2250_1]) ).
cnf(f_2250_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7580),U_7581),c_Inductive_Ocomplete__lattice__class_Ogfp(U_7580,U_7582)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7580),U_7581),hAPP(U_7582,U_7581)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7580) ),
inference(clausify,[status(thm)],[f_2250_2]) ).
fof(f_2251_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_2251_2,plain,
! [U_7583] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_7583))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7583))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7583)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_7583)) ) )
| ~ c_Nat__Transfer_Onat__set(U_7583) ),
inference(variable_rename,[status(thm)],[f_2251_1]) ).
cnf(f_2251_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7583)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_7583))
| ~ c_Nat__Transfer_Onat__set(U_7583) ),
inference(clausify,[status(thm)],[f_2251_2]) ).
cnf(f_2251_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_7583))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_7583)))
| ~ c_Nat__Transfer_Onat__set(U_7583) ),
inference(clausify,[status(thm)],[f_2251_2]) ).
fof(f_2252_1,plain,
! [V_f_2,T_b] :
( c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2) = hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_gfp__unfold]) ).
fof(f_2252_2,plain,
! [U_7585,U_7584] :
( c_Inductive_Ocomplete__lattice__class_Ogfp(U_7584,U_7585) = hAPP(U_7585,c_Inductive_Ocomplete__lattice__class_Ogfp(U_7584,U_7585))
| ~ c_Orderings_Oorder__class_Omono(U_7584,U_7584,U_7585)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7584) ),
inference(variable_rename,[status(thm)],[f_2252_1]) ).
cnf(f_2252_3,plain,
( c_Inductive_Ocomplete__lattice__class_Ogfp(U_7584,U_7585) = hAPP(U_7585,c_Inductive_Ocomplete__lattice__class_Ogfp(U_7584,U_7585))
| ~ c_Orderings_Oorder__class_Omono(U_7584,U_7584,U_7585)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7584) ),
inference(clausify,[status(thm)],[f_2252_2]) ).
fof(f_2253_1,plain,
! [V_f_2,V_A_2,T_b] :
( V_A_2 = hAPP(V_f_2,V_A_2)
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| V_A_2 != c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_def__gfp__unfold]) ).
fof(f_2253_2,plain,
! [U_7588,U_7587,U_7586] :
( U_7587 = hAPP(U_7588,U_7587)
| ~ c_Orderings_Oorder__class_Omono(U_7586,U_7586,U_7588)
| U_7587 != c_Inductive_Ocomplete__lattice__class_Ogfp(U_7586,U_7588)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7586) ),
inference(variable_rename,[status(thm)],[f_2253_1]) ).
cnf(f_2253_3,plain,
( U_7587 = hAPP(U_7588,U_7587)
| ~ c_Orderings_Oorder__class_Omono(U_7586,U_7586,U_7588)
| U_7587 != c_Inductive_Ocomplete__lattice__class_Ogfp(U_7586,U_7588)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7586) ),
inference(clausify,[status(thm)],[f_2253_2]) ).
fof(f_2254_1,plain,
! [V_f_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__infinite]) ).
fof(f_2254_2,plain,
! [U_7592,U_7591,U_7590,U_7589] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7590,U_7589),U_7592),U_7591) = c_Groups_Ozero__class_Ozero(U_7589)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_7590),U_7591))
| ~ class_Groups_Ocomm__monoid__add(U_7589) ),
inference(variable_rename,[status(thm)],[f_2254_1]) ).
cnf(f_2254_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7590,U_7589),U_7592),U_7591) = c_Groups_Ozero__class_Ozero(U_7589)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_7590),U_7591))
| ~ class_Groups_Ocomm__monoid__add(U_7589) ),
inference(clausify,[status(thm)],[f_2254_2]) ).
fof(f_2255_1,plain,
! [V_g_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Oinfinite]) ).
fof(f_2255_2,plain,
! [U_7596,U_7595,U_7594,U_7593] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7594,U_7593),U_7596),U_7595) = c_Groups_Ozero__class_Ozero(U_7593)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_7594),U_7595))
| ~ class_Groups_Ocomm__monoid__add(U_7593) ),
inference(variable_rename,[status(thm)],[f_2255_1]) ).
cnf(f_2255_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7594,U_7593),U_7596),U_7595) = c_Groups_Ozero__class_Ozero(U_7593)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_7594),U_7595))
| ~ class_Groups_Ocomm__monoid__add(U_7593) ),
inference(clausify,[status(thm)],[f_2255_2]) ).
fof(f_2256_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_2256_2,plain,
! [U_7597] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7597)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_7597),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_7597)),
inference(variable_rename,[status(thm)],[f_2256_1]) ).
cnf(f_2256_3,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7597)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_7597),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_7597)),
inference(clausify,[status(thm)],[f_2256_2]) ).
fof(f_2257_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_2257_2,plain,
! [U_7598] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7598)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7598)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7598)),
inference(variable_rename,[status(thm)],[f_2257_1]) ).
cnf(f_2257_3,plain,
hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7598)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7598)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_7598)),
inference(clausify,[status(thm)],[f_2257_2]) ).
fof(f_2258_1,plain,
! [V_f_2,V_F_2,T_b] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) ) )
& ( ! [B_x] :
( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_F_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__eq__0__iff]) ).
fof(f_2258_2,plain,
! [U_7603,U_7602,U_7601] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7601,tc_Nat_Onat),U_7603),U_7602) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [U_7600] :
( hAPP(U_7603,U_7600) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_7601),U_7600),U_7602)) ) )
& ( ! [U_7599] :
( hAPP(U_7603,U_7599) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_7601),U_7599),U_7602)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7601,tc_Nat_Onat),U_7603),U_7602) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7601),U_7602)) ),
inference(variable_rename,[status(thm)],[f_2258_1]) ).
fof(f_2258_3,plain,
! [U_7603,U_7602,U_7601] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7601,tc_Nat_Onat),U_7603),U_7602) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hAPP(U_7603,sK148(U_7603,U_7602,U_7601)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_7601),sK148(U_7603,U_7602,U_7601)),U_7602)) ) )
& ( ! [U_7599] :
( hAPP(U_7603,U_7599) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_7601),U_7599),U_7602)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7601,tc_Nat_Onat),U_7603),U_7602) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7601),U_7602)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_7600,sK148(U_7603,U_7602,U_7601))],[f_2258_2]) ).
cnf(f_2258_4,plain,
( hAPP(U_7603,U_7599) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_7601),U_7599),U_7602))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7601,tc_Nat_Onat),U_7603),U_7602) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7601),U_7602)) ),
inference(clausify,[status(thm)],[f_2258_3]) ).
cnf(f_2258_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_7601),sK148(U_7603,U_7602,U_7601)),U_7602))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7601,tc_Nat_Onat),U_7603),U_7602) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7601),U_7602)) ),
inference(clausify,[status(thm)],[f_2258_3]) ).
cnf(f_2258_6,plain,
( hAPP(U_7603,sK148(U_7603,U_7602,U_7601)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7601,tc_Nat_Onat),U_7603),U_7602) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7601),U_7602)) ),
inference(clausify,[status(thm)],[f_2258_3]) ).
fof(f_2259_1,plain,
! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_UN__insert]) ).
fof(f_2259_2,plain,
! [U_7608,U_7607,U_7606,U_7605,U_7604] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7604,tc_fun(U_7605,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7604),U_7606),U_7607)),U_7608) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7605,tc_HOL_Obool)),hAPP(U_7608,U_7606)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7604,tc_fun(U_7605,tc_HOL_Obool)),U_7607),U_7608)),
inference(variable_rename,[status(thm)],[f_2259_1]) ).
cnf(f_2259_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7604,tc_fun(U_7605,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7604),U_7606),U_7607)),U_7608) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7605,tc_HOL_Obool)),hAPP(U_7608,U_7606)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7604,tc_fun(U_7605,tc_HOL_Obool)),U_7607),U_7608)),
inference(clausify,[status(thm)],[f_2259_2]) ).
fof(f_2260_1,plain,
! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Oplus__class_Oplus(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Odistrib]) ).
fof(f_2260_2,plain,
! [U_7613,U_7612,U_7611,U_7610,U_7609] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7610,U_7609),hAPP(hAPP(c_COMBS(U_7610,U_7609,U_7609),hAPP(hAPP(c_COMBB(U_7609,tc_fun(U_7609,U_7609),U_7610),c_Groups_Oplus__class_Oplus(U_7609)),U_7612)),U_7613)),U_7611) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7609),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7610,U_7609),U_7612),U_7611)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7610,U_7609),U_7613),U_7611))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7610),U_7611))
| ~ class_Groups_Ocomm__monoid__add(U_7609) ),
inference(variable_rename,[status(thm)],[f_2260_1]) ).
cnf(f_2260_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7610,U_7609),hAPP(hAPP(c_COMBS(U_7610,U_7609,U_7609),hAPP(hAPP(c_COMBB(U_7609,tc_fun(U_7609,U_7609),U_7610),c_Groups_Oplus__class_Oplus(U_7609)),U_7612)),U_7613)),U_7611) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7609),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7610,U_7609),U_7612),U_7611)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7610,U_7609),U_7613),U_7611))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7610),U_7611))
| ~ class_Groups_Ocomm__monoid__add(U_7609) ),
inference(clausify,[status(thm)],[f_2260_2]) ).
fof(f_2261_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_2261_2,plain,
! [U_7614] : 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_7614))),
inference(variable_rename,[status(thm)],[f_2261_1]) ).
cnf(f_2261_3,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_7614))),
inference(clausify,[status(thm)],[f_2261_2]) ).
fof(f_2262_1,plain,
! [V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_gfp__lemma3]) ).
fof(f_2262_2,plain,
! [U_7616,U_7615] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7615),hAPP(U_7616,c_Inductive_Ocomplete__lattice__class_Ogfp(U_7615,U_7616))),c_Inductive_Ocomplete__lattice__class_Ogfp(U_7615,U_7616)))
| ~ c_Orderings_Oorder__class_Omono(U_7615,U_7615,U_7616)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7615) ),
inference(variable_rename,[status(thm)],[f_2262_1]) ).
cnf(f_2262_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7615),hAPP(U_7616,c_Inductive_Ocomplete__lattice__class_Ogfp(U_7615,U_7616))),c_Inductive_Ocomplete__lattice__class_Ogfp(U_7615,U_7616)))
| ~ c_Orderings_Oorder__class_Omono(U_7615,U_7615,U_7616)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7615) ),
inference(clausify,[status(thm)],[f_2262_2]) ).
fof(f_2263_1,plain,
! [V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_gfp__lemma2]) ).
fof(f_2263_2,plain,
! [U_7618,U_7617] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7617),c_Inductive_Ocomplete__lattice__class_Ogfp(U_7617,U_7618)),hAPP(U_7618,c_Inductive_Ocomplete__lattice__class_Ogfp(U_7617,U_7618))))
| ~ c_Orderings_Oorder__class_Omono(U_7617,U_7617,U_7618)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7617) ),
inference(variable_rename,[status(thm)],[f_2263_1]) ).
cnf(f_2263_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7617),c_Inductive_Ocomplete__lattice__class_Ogfp(U_7617,U_7618)),hAPP(U_7618,c_Inductive_Ocomplete__lattice__class_Ogfp(U_7617,U_7618))))
| ~ c_Orderings_Oorder__class_Omono(U_7617,U_7617,U_7618)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7617) ),
inference(clausify,[status(thm)],[f_2263_2]) ).
fof(f_2264_1,plain,
! [V_na_2,V_m_2] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,hAPP(c_Nat_OSuc,V_na_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_na_2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_na_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_na_2))) ),
inference(fof_nnf,[status(thm)],[fact_atLeastAtMostSuc__conv]) ).
fof(f_2264_2,plain,
! [U_7620,U_7619] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7619,hAPP(c_Nat_OSuc,U_7620)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7620)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7619,U_7620))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7619),hAPP(c_Nat_OSuc,U_7620))) ),
inference(variable_rename,[status(thm)],[f_2264_1]) ).
cnf(f_2264_3,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7619,hAPP(c_Nat_OSuc,U_7620)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_7620)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_7619,U_7620))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7619),hAPP(c_Nat_OSuc,U_7620))) ),
inference(clausify,[status(thm)],[f_2264_2]) ).
fof(f_2265_1,plain,
! [V_f_2,V_A_2,T_b] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ! [B_x] :
( ? [B_xa] :
( hAPP(V_f_2,B_xa) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& B_x != B_xa
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
| hAPP(V_f_2,B_x) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ? [B_x] :
( ! [B_xa] :
( hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| B_x = B_xa
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
& hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__eq__Suc0__iff]) ).
fof(f_2265_2,plain,
! [U_7627,U_7626,U_7625] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7625,tc_Nat_Onat),U_7627),U_7626) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ! [U_7624] :
( ? [U_7623] :
( hAPP(U_7627,U_7623) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_7624 != U_7623
& hBOOL(hAPP(hAPP(c_member(U_7625),U_7623),U_7626)) )
| hAPP(U_7627,U_7624) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_7625),U_7624),U_7626)) ) )
& ( ? [U_7622] :
( ! [U_7621] :
( hAPP(U_7627,U_7621) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_7622 = U_7621
| ~ hBOOL(hAPP(hAPP(c_member(U_7625),U_7621),U_7626)) )
& hAPP(U_7627,U_7622) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(U_7625),U_7622),U_7626)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7625,tc_Nat_Onat),U_7627),U_7626) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7625),U_7626)) ),
inference(variable_rename,[status(thm)],[f_2265_1]) ).
fof(f_2265_3,plain,
! [U_7627,U_7626,U_7625] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7625,tc_Nat_Onat),U_7627),U_7626) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ! [U_7624] :
( ? [U_7623] :
( hAPP(U_7627,U_7623) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_7624 != U_7623
& hBOOL(hAPP(hAPP(c_member(U_7625),U_7623),U_7626)) )
| hAPP(U_7627,U_7624) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_7625),U_7624),U_7626)) ) )
& ( ( ! [U_7621] :
( hAPP(U_7627,U_7621) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK149(U_7627,U_7626,U_7625) = U_7621
| ~ hBOOL(hAPP(hAPP(c_member(U_7625),U_7621),U_7626)) )
& hAPP(U_7627,sK149(U_7627,U_7626,U_7625)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(U_7625),sK149(U_7627,U_7626,U_7625)),U_7626)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7625,tc_Nat_Onat),U_7627),U_7626) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7625),U_7626)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_7622,sK149(U_7627,U_7626,U_7625))],[f_2265_2]) ).
fof(f_2265_4,plain,
! [U_7627,U_7626,U_7625] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7625,tc_Nat_Onat),U_7627),U_7626) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ! [U_7624] :
( ( hAPP(U_7627,sK150(U_7627,U_7626,U_7625,U_7624)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_7624 != sK150(U_7627,U_7626,U_7625,U_7624)
& hBOOL(hAPP(hAPP(c_member(U_7625),sK150(U_7627,U_7626,U_7625,U_7624)),U_7626)) )
| hAPP(U_7627,U_7624) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_7625),U_7624),U_7626)) ) )
& ( ( ! [U_7621] :
( hAPP(U_7627,U_7621) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK149(U_7627,U_7626,U_7625) = U_7621
| ~ hBOOL(hAPP(hAPP(c_member(U_7625),U_7621),U_7626)) )
& hAPP(U_7627,sK149(U_7627,U_7626,U_7625)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(U_7625),sK149(U_7627,U_7626,U_7625)),U_7626)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7625,tc_Nat_Onat),U_7627),U_7626) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7625),U_7626)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_7623,sK150(U_7627,U_7626,U_7625,U_7624))],[f_2265_3]) ).
cnf(f_2265_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_7625),sK149(U_7627,U_7626,U_7625)),U_7626))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7625,tc_Nat_Onat),U_7627),U_7626) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7625),U_7626)) ),
inference(clausify,[status(thm)],[f_2265_4]) ).
cnf(f_2265_6,plain,
( hAPP(U_7627,sK149(U_7627,U_7626,U_7625)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7625,tc_Nat_Onat),U_7627),U_7626) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7625),U_7626)) ),
inference(clausify,[status(thm)],[f_2265_4]) ).
cnf(f_2265_7,plain,
( hAPP(U_7627,U_7621) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK149(U_7627,U_7626,U_7625) = U_7621
| ~ hBOOL(hAPP(hAPP(c_member(U_7625),U_7621),U_7626))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7625,tc_Nat_Onat),U_7627),U_7626) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7625),U_7626)) ),
inference(clausify,[status(thm)],[f_2265_4]) ).
cnf(f_2265_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_7625),sK150(U_7627,U_7626,U_7625,U_7624)),U_7626))
| hAPP(U_7627,U_7624) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_7625),U_7624),U_7626))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7625,tc_Nat_Onat),U_7627),U_7626) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7625),U_7626)) ),
inference(clausify,[status(thm)],[f_2265_4]) ).
cnf(f_2265_9,plain,
( U_7624 != sK150(U_7627,U_7626,U_7625,U_7624)
| hAPP(U_7627,U_7624) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_7625),U_7624),U_7626))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7625,tc_Nat_Onat),U_7627),U_7626) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7625),U_7626)) ),
inference(clausify,[status(thm)],[f_2265_4]) ).
cnf(f_2265_10,plain,
( hAPP(U_7627,sK150(U_7627,U_7626,U_7625,U_7624)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(U_7627,U_7624) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_7625),U_7624),U_7626))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7625,tc_Nat_Onat),U_7627),U_7626) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7625),U_7626)) ),
inference(clausify,[status(thm)],[f_2265_4]) ).
fof(f_2266_1,plain,
! [V_f_2,V_A_2,T_b] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ! [B_x] :
( ? [B_xa] :
( hAPP(V_f_2,B_xa) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& B_x != B_xa
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
| hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ? [B_x] :
( ! [B_xa] :
( hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| B_x = B_xa
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
& hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__eq__1__iff]) ).
fof(f_2266_2,plain,
! [U_7634,U_7633,U_7632] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7632,tc_Nat_Onat),U_7634),U_7633) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ! [U_7631] :
( ? [U_7630] :
( hAPP(U_7634,U_7630) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_7631 != U_7630
& hBOOL(hAPP(hAPP(c_member(U_7632),U_7630),U_7633)) )
| hAPP(U_7634,U_7631) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_7632),U_7631),U_7633)) ) )
& ( ? [U_7629] :
( ! [U_7628] :
( hAPP(U_7634,U_7628) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_7629 = U_7628
| ~ hBOOL(hAPP(hAPP(c_member(U_7632),U_7628),U_7633)) )
& hAPP(U_7634,U_7629) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_7632),U_7629),U_7633)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7632,tc_Nat_Onat),U_7634),U_7633) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7632),U_7633)) ),
inference(variable_rename,[status(thm)],[f_2266_1]) ).
fof(f_2266_3,plain,
! [U_7634,U_7633,U_7632] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7632,tc_Nat_Onat),U_7634),U_7633) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ! [U_7631] :
( ? [U_7630] :
( hAPP(U_7634,U_7630) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_7631 != U_7630
& hBOOL(hAPP(hAPP(c_member(U_7632),U_7630),U_7633)) )
| hAPP(U_7634,U_7631) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_7632),U_7631),U_7633)) ) )
& ( ( ! [U_7628] :
( hAPP(U_7634,U_7628) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK151(U_7634,U_7633,U_7632) = U_7628
| ~ hBOOL(hAPP(hAPP(c_member(U_7632),U_7628),U_7633)) )
& hAPP(U_7634,sK151(U_7634,U_7633,U_7632)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_7632),sK151(U_7634,U_7633,U_7632)),U_7633)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7632,tc_Nat_Onat),U_7634),U_7633) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7632),U_7633)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_7629,sK151(U_7634,U_7633,U_7632))],[f_2266_2]) ).
fof(f_2266_4,plain,
! [U_7634,U_7633,U_7632] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7632,tc_Nat_Onat),U_7634),U_7633) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ! [U_7631] :
( ( hAPP(U_7634,sK152(U_7634,U_7633,U_7632,U_7631)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_7631 != sK152(U_7634,U_7633,U_7632,U_7631)
& hBOOL(hAPP(hAPP(c_member(U_7632),sK152(U_7634,U_7633,U_7632,U_7631)),U_7633)) )
| hAPP(U_7634,U_7631) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_7632),U_7631),U_7633)) ) )
& ( ( ! [U_7628] :
( hAPP(U_7634,U_7628) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK151(U_7634,U_7633,U_7632) = U_7628
| ~ hBOOL(hAPP(hAPP(c_member(U_7632),U_7628),U_7633)) )
& hAPP(U_7634,sK151(U_7634,U_7633,U_7632)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_7632),sK151(U_7634,U_7633,U_7632)),U_7633)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7632,tc_Nat_Onat),U_7634),U_7633) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7632),U_7633)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_7630,sK152(U_7634,U_7633,U_7632,U_7631))],[f_2266_3]) ).
cnf(f_2266_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_7632),sK151(U_7634,U_7633,U_7632)),U_7633))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7632,tc_Nat_Onat),U_7634),U_7633) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7632),U_7633)) ),
inference(clausify,[status(thm)],[f_2266_4]) ).
cnf(f_2266_6,plain,
( hAPP(U_7634,sK151(U_7634,U_7633,U_7632)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7632,tc_Nat_Onat),U_7634),U_7633) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7632),U_7633)) ),
inference(clausify,[status(thm)],[f_2266_4]) ).
cnf(f_2266_7,plain,
( hAPP(U_7634,U_7628) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sK151(U_7634,U_7633,U_7632) = U_7628
| ~ hBOOL(hAPP(hAPP(c_member(U_7632),U_7628),U_7633))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7632,tc_Nat_Onat),U_7634),U_7633) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7632),U_7633)) ),
inference(clausify,[status(thm)],[f_2266_4]) ).
cnf(f_2266_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_7632),sK152(U_7634,U_7633,U_7632,U_7631)),U_7633))
| hAPP(U_7634,U_7631) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_7632),U_7631),U_7633))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7632,tc_Nat_Onat),U_7634),U_7633) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7632),U_7633)) ),
inference(clausify,[status(thm)],[f_2266_4]) ).
cnf(f_2266_9,plain,
( U_7631 != sK152(U_7634,U_7633,U_7632,U_7631)
| hAPP(U_7634,U_7631) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_7632),U_7631),U_7633))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7632,tc_Nat_Onat),U_7634),U_7633) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7632),U_7633)) ),
inference(clausify,[status(thm)],[f_2266_4]) ).
cnf(f_2266_10,plain,
( hAPP(U_7634,sK152(U_7634,U_7633,U_7632,U_7631)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(U_7634,U_7631) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_7632),U_7631),U_7633))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7632,tc_Nat_Onat),U_7634),U_7633) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7632),U_7633)) ),
inference(clausify,[status(thm)],[f_2266_4]) ).
fof(f_2267_1,plain,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Oab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff]) ).
fof(f_2267_2,plain,
! [U_7639,U_7638,U_7637,U_7636,U_7635] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7636,U_7635),U_7639),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7636,tc_HOL_Obool)),U_7637),U_7638)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7635),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7636,U_7635),U_7639),U_7637)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7636,U_7635),U_7639),U_7638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7636,tc_HOL_Obool)),U_7638),U_7637))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7636),U_7637))
| ~ class_Groups_Oab__group__add(U_7635) ),
inference(variable_rename,[status(thm)],[f_2267_1]) ).
cnf(f_2267_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7636,U_7635),U_7639),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7636,tc_HOL_Obool)),U_7637),U_7638)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7635),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7636,U_7635),U_7639),U_7637)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7636,U_7635),U_7639),U_7638))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7636,tc_HOL_Obool)),U_7638),U_7637))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7636),U_7637))
| ~ class_Groups_Oab__group__add(U_7635) ),
inference(clausify,[status(thm)],[f_2267_2]) ).
fof(f_2268_1,plain,
! [V_X_2,V_f_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),V_A_2))))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| V_A_2 != c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_def__coinduct]) ).
fof(f_2268_2,plain,
! [U_7643,U_7642,U_7641,U_7640] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7640),U_7643),U_7641))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7640),U_7643),hAPP(U_7642,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7640),U_7643),U_7641))))
| ~ c_Orderings_Oorder__class_Omono(U_7640,U_7640,U_7642)
| U_7641 != c_Inductive_Ocomplete__lattice__class_Ogfp(U_7640,U_7642)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7640) ),
inference(variable_rename,[status(thm)],[f_2268_1]) ).
cnf(f_2268_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7640),U_7643),U_7641))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7640),U_7643),hAPP(U_7642,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7640),U_7643),U_7641))))
| ~ c_Orderings_Oorder__class_Omono(U_7640,U_7640,U_7642)
| U_7641 != c_Inductive_Ocomplete__lattice__class_Ogfp(U_7640,U_7642)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7640) ),
inference(clausify,[status(thm)],[f_2268_2]) ).
fof(f_2269_1,plain,
! [V_A_2,T_c,V_I_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)))
| ! [B_x] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__INT]) ).
fof(f_2269_2,plain,
! [U_7648,U_7647,U_7646,U_7645] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7647),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7645,tc_fun(U_7647,tc_HOL_Obool)),U_7646),U_7648)))
| ! [U_7644] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7647),hAPP(U_7648,U_7644)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7645),U_7644),U_7646)) ) ),
inference(variable_rename,[status(thm)],[f_2269_1]) ).
cnf(f_2269_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7647),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7645,tc_fun(U_7647,tc_HOL_Obool)),U_7646),U_7648)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7647),hAPP(U_7648,U_7644)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7645),U_7644),U_7646)) ),
inference(clausify,[status(thm)],[f_2269_2]) ).
fof(f_2270_1,plain,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__psubset]) ).
fof(f_2270_2,plain,
! [U_7651,U_7650,U_7649] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7649,tc_HOL_Obool)),U_7651),U_7650))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7649),U_7651)),hAPP(c_Finite__Set_Ocard(U_7649),U_7650)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7649,tc_HOL_Obool)),U_7651),U_7650))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7649),U_7650)) ),
inference(variable_rename,[status(thm)],[f_2270_1]) ).
cnf(f_2270_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7649,tc_HOL_Obool)),U_7651),U_7650))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7649),U_7651)),hAPP(c_Finite__Set_Ocard(U_7649),U_7650)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7649,tc_HOL_Obool)),U_7651),U_7650))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7649),U_7650)) ),
inference(clausify,[status(thm)],[f_2270_2]) ).
fof(f_2271_1,plain,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_diff__card__le__card__Diff]) ).
fof(f_2271_2,plain,
! [U_7654,U_7653,U_7652] :
( 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_7652),U_7654)),hAPP(c_Finite__Set_Ocard(U_7652),U_7653))),hAPP(c_Finite__Set_Ocard(U_7652),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7652,tc_HOL_Obool)),U_7654),U_7653))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7652),U_7653)) ),
inference(variable_rename,[status(thm)],[f_2271_1]) ).
cnf(f_2271_3,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_7652),U_7654)),hAPP(c_Finite__Set_Ocard(U_7652),U_7653))),hAPP(c_Finite__Set_Ocard(U_7652),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7652,tc_HOL_Obool)),U_7654),U_7653))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7652),U_7653)) ),
inference(clausify,[status(thm)],[f_2271_2]) ).
fof(f_2272_1,plain,
! [V_A_2,V_B_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff__subset]) ).
fof(f_2272_2,plain,
! [U_7657,U_7656,U_7655] :
( hAPP(c_Finite__Set_Ocard(U_7655),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7655,tc_HOL_Obool)),U_7657),U_7656)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7655),U_7657)),hAPP(c_Finite__Set_Ocard(U_7655),U_7656))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7655,tc_HOL_Obool)),U_7656),U_7657))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7655),U_7656)) ),
inference(variable_rename,[status(thm)],[f_2272_1]) ).
cnf(f_2272_3,plain,
( hAPP(c_Finite__Set_Ocard(U_7655),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7655,tc_HOL_Obool)),U_7657),U_7656)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7655),U_7657)),hAPP(c_Finite__Set_Ocard(U_7655),U_7656))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7655,tc_HOL_Obool)),U_7656),U_7657))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7655),U_7656)) ),
inference(clausify,[status(thm)],[f_2272_2]) ).
fof(f_2273_1,plain,
! [V_a_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite_OinsertI]) ).
fof(f_2273_2,plain,
! [U_7660,U_7659,U_7658] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7658),hAPP(hAPP(c_Set_Oinsert(U_7658),U_7660),U_7659)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7658),U_7659)) ),
inference(variable_rename,[status(thm)],[f_2273_1]) ).
cnf(f_2273_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7658),hAPP(hAPP(c_Set_Oinsert(U_7658),U_7660),U_7659)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7658),U_7659)) ),
inference(clausify,[status(thm)],[f_2273_2]) ).
fof(f_2274_1,plain,
! [V_h_2,T_c,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__imageI]) ).
fof(f_2274_2,plain,
! [U_7664,U_7663,U_7662,U_7661] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7663),hAPP(c_Set_Oimage(U_7661,U_7663,U_7664),U_7662)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7661),U_7662)) ),
inference(variable_rename,[status(thm)],[f_2274_1]) ).
cnf(f_2274_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7663),hAPP(c_Set_Oimage(U_7661,U_7663,U_7664),U_7662)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7661),U_7662)) ),
inference(clausify,[status(thm)],[f_2274_2]) ).
fof(f_2275_1,plain,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__Diff]) ).
fof(f_2275_2,plain,
! [U_7667,U_7666,U_7665] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7665),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7665,tc_HOL_Obool)),U_7666),U_7667)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7665),U_7666)) ),
inference(variable_rename,[status(thm)],[f_2275_1]) ).
cnf(f_2275_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7665),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7665,tc_HOL_Obool)),U_7666),U_7667)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7665),U_7666)) ),
inference(clausify,[status(thm)],[f_2275_2]) ).
fof(f_2276_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Finite__Set_Ofinite(T_b) ),
inference(fof_nnf,[status(thm)],[fact_finite]) ).
fof(f_2276_2,plain,
! [U_7669,U_7668] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7668),U_7669))
| ~ class_Finite__Set_Ofinite(U_7668) ),
inference(variable_rename,[status(thm)],[f_2276_1]) ).
cnf(f_2276_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7668),U_7669))
| ~ class_Finite__Set_Ofinite(U_7668) ),
inference(clausify,[status(thm)],[f_2276_2]) ).
fof(f_2277_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Finite__Set_Ofinite(T_b) ),
inference(fof_nnf,[status(thm)],[fact_finite__code]) ).
fof(f_2277_2,plain,
! [U_7671,U_7670] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7670),U_7671))
| ~ class_Finite__Set_Ofinite(U_7670) ),
inference(variable_rename,[status(thm)],[f_2277_1]) ).
cnf(f_2277_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7670),U_7671))
| ~ class_Finite__Set_Ofinite(U_7670) ),
inference(clausify,[status(thm)],[f_2277_2]) ).
fof(f_2278_1,plain,
! [V_A_2,V_a_2,T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__insert]) ).
fof(f_2278_2,plain,
! [U_7674,U_7673,U_7672] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7672),hAPP(hAPP(c_Set_Oinsert(U_7672),U_7673),U_7674)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7672),U_7674)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7672),U_7674))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7672),hAPP(hAPP(c_Set_Oinsert(U_7672),U_7673),U_7674))) ) ),
inference(variable_rename,[status(thm)],[f_2278_1]) ).
fof(f_2278_3,plain,
( ! [U_7680,U_7678,U_7676] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7676),hAPP(hAPP(c_Set_Oinsert(U_7676),U_7678),U_7680)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7676),U_7680)) )
& ! [U_7679,U_7677,U_7675] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7675),U_7679))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7675),hAPP(hAPP(c_Set_Oinsert(U_7675),U_7677),U_7679))) ) ),
inference(miniscope,[status(thm)],[f_2278_2]) ).
cnf(f_2278_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7675),U_7679))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7675),hAPP(hAPP(c_Set_Oinsert(U_7675),U_7677),U_7679))) ),
inference(clausify,[status(thm)],[f_2278_3]) ).
cnf(f_2278_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7676),hAPP(hAPP(c_Set_Oinsert(U_7676),U_7678),U_7680)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7676),U_7680)) ),
inference(clausify,[status(thm)],[f_2278_3]) ).
fof(f_2279_1,plain,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_rev__finite__subset]) ).
fof(f_2279_2,plain,
! [U_7683,U_7682,U_7681] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7681),U_7683))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7681,tc_HOL_Obool)),U_7683),U_7682))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7681),U_7682)) ),
inference(variable_rename,[status(thm)],[f_2279_1]) ).
cnf(f_2279_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7681),U_7683))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7681,tc_HOL_Obool)),U_7683),U_7682))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7681),U_7682)) ),
inference(clausify,[status(thm)],[f_2279_2]) ).
fof(f_2280_1,plain,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__subset]) ).
fof(f_2280_2,plain,
! [U_7686,U_7685,U_7684] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7684),U_7685))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7684),U_7686))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7684,tc_HOL_Obool)),U_7685),U_7686)) ),
inference(variable_rename,[status(thm)],[f_2280_1]) ).
cnf(f_2280_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7684),U_7685))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7684),U_7686))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7684,tc_HOL_Obool)),U_7685),U_7686)) ),
inference(clausify,[status(thm)],[f_2280_2]) ).
fof(f_2281_1,plain,
! [V_G_2,V_F_2,T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Un]) ).
fof(f_2281_2,plain,
! [U_7689,U_7688,U_7687] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7687),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7687,tc_HOL_Obool)),U_7688),U_7689)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7687),U_7689))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7687),U_7688)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7687),U_7689))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_7687),U_7688)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7687),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7687,tc_HOL_Obool)),U_7688),U_7689))) ) ),
inference(variable_rename,[status(thm)],[f_2281_1]) ).
fof(f_2281_3,plain,
( ! [U_7695,U_7693,U_7691] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7691),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7691,tc_HOL_Obool)),U_7693),U_7695)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7691),U_7695))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7691),U_7693)) )
& ! [U_7694,U_7692,U_7690] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7690),U_7694))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_7690),U_7692)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7690),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7690,tc_HOL_Obool)),U_7692),U_7694))) ) ),
inference(miniscope,[status(thm)],[f_2281_2]) ).
cnf(f_2281_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7690),U_7692))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7690),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7690,tc_HOL_Obool)),U_7692),U_7694))) ),
inference(clausify,[status(thm)],[f_2281_3]) ).
cnf(f_2281_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7690),U_7694))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7690),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7690,tc_HOL_Obool)),U_7692),U_7694))) ),
inference(clausify,[status(thm)],[f_2281_3]) ).
cnf(f_2281_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7691),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7691,tc_HOL_Obool)),U_7693),U_7695)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7691),U_7695))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7691),U_7693)) ),
inference(clausify,[status(thm)],[f_2281_3]) ).
fof(f_2282_1,plain,
! [V_G_2,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__UnI]) ).
fof(f_2282_2,plain,
! [U_7698,U_7697,U_7696] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7696),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7696,tc_HOL_Obool)),U_7697),U_7698)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7696),U_7698))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7696),U_7697)) ),
inference(variable_rename,[status(thm)],[f_2282_1]) ).
cnf(f_2282_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7696),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7696,tc_HOL_Obool)),U_7697),U_7698)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7696),U_7698))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7696),U_7697)) ),
inference(clausify,[status(thm)],[f_2282_2]) ).
fof(f_2283_1,plain,
! [V_A_2,V_B_2,T_b] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__Diff2]) ).
fof(f_2283_2,plain,
! [U_7701,U_7700,U_7699] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7699,tc_HOL_Obool)),U_7701),U_7700)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7699),U_7701)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7699),U_7701))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7699,tc_HOL_Obool)),U_7701),U_7700))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7699),U_7700)) ),
inference(variable_rename,[status(thm)],[f_2283_1]) ).
cnf(f_2283_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7699),U_7701))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7699,tc_HOL_Obool)),U_7701),U_7700)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7699),U_7700)) ),
inference(clausify,[status(thm)],[f_2283_2]) ).
cnf(f_2283_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7699,tc_HOL_Obool)),U_7701),U_7700)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7699),U_7701))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7699),U_7700)) ),
inference(clausify,[status(thm)],[f_2283_2]) ).
fof(f_2284_1,plain,
! [V_B_2,T_c,V_A_2,T_b] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__UN]) ).
fof(f_2284_2,plain,
! [U_7707,U_7706,U_7705,U_7704] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7706),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7704,tc_fun(U_7706,tc_HOL_Obool)),U_7705),U_7707)))
| ? [U_7703] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7706),hAPP(U_7707,U_7703)))
& hBOOL(hAPP(hAPP(c_member(U_7704),U_7703),U_7705)) ) )
& ( ! [U_7702] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7706),hAPP(U_7707,U_7702)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7704),U_7702),U_7705)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7706),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7704,tc_fun(U_7706,tc_HOL_Obool)),U_7705),U_7707))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7704),U_7705)) ),
inference(variable_rename,[status(thm)],[f_2284_1]) ).
fof(f_2284_3,plain,
! [U_7707,U_7706,U_7705,U_7704] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7706),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7704,tc_fun(U_7706,tc_HOL_Obool)),U_7705),U_7707)))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7706),hAPP(U_7707,sK153(U_7707,U_7706,U_7705,U_7704))))
& hBOOL(hAPP(hAPP(c_member(U_7704),sK153(U_7707,U_7706,U_7705,U_7704)),U_7705)) ) )
& ( ! [U_7702] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7706),hAPP(U_7707,U_7702)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7704),U_7702),U_7705)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7706),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7704,tc_fun(U_7706,tc_HOL_Obool)),U_7705),U_7707))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7704),U_7705)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(U_7703,sK153(U_7707,U_7706,U_7705,U_7704))],[f_2284_2]) ).
cnf(f_2284_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7706),hAPP(U_7707,U_7702)))
| ~ hBOOL(hAPP(hAPP(c_member(U_7704),U_7702),U_7705))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7706),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7704,tc_fun(U_7706,tc_HOL_Obool)),U_7705),U_7707)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7704),U_7705)) ),
inference(clausify,[status(thm)],[f_2284_3]) ).
cnf(f_2284_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_7704),sK153(U_7707,U_7706,U_7705,U_7704)),U_7705))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_7706),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7704,tc_fun(U_7706,tc_HOL_Obool)),U_7705),U_7707)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7704),U_7705)) ),
inference(clausify,[status(thm)],[f_2284_3]) ).
cnf(f_2284_6,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7706),hAPP(U_7707,sK153(U_7707,U_7706,U_7705,U_7704))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_7706),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7704,tc_fun(U_7706,tc_HOL_Obool)),U_7705),U_7707)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7704),U_7705)) ),
inference(clausify,[status(thm)],[f_2284_3]) ).
fof(f_2285_1,plain,
! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__surj]) ).
fof(f_2285_2,plain,
! [U_7712,U_7711,U_7710,U_7709,U_7708] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7710),U_7711))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7710,tc_HOL_Obool)),U_7711),hAPP(c_Set_Oimage(U_7708,U_7710,U_7712),U_7709)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7708),U_7709)) ),
inference(variable_rename,[status(thm)],[f_2285_1]) ).
cnf(f_2285_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7710),U_7711))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7710,tc_HOL_Obool)),U_7711),hAPP(c_Set_Oimage(U_7708,U_7710,U_7712),U_7709)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7708),U_7709)) ),
inference(clausify,[status(thm)],[f_2285_2]) ).
fof(f_2286_1,plain,
! [V_B_2,V_a_2,V_A_2,T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Diff__insert]) ).
fof(f_2286_2,plain,
! [U_7716,U_7715,U_7714,U_7713] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7713),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7713,tc_HOL_Obool)),U_7714),hAPP(hAPP(c_Set_Oinsert(U_7713),U_7715),U_7716))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7713),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7713,tc_HOL_Obool)),U_7714),U_7716))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7713),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7713,tc_HOL_Obool)),U_7714),U_7716)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7713),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7713,tc_HOL_Obool)),U_7714),hAPP(hAPP(c_Set_Oinsert(U_7713),U_7715),U_7716)))) ) ),
inference(variable_rename,[status(thm)],[f_2286_1]) ).
fof(f_2286_3,plain,
( ! [U_7724,U_7722,U_7720,U_7718] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7718),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7718,tc_HOL_Obool)),U_7720),hAPP(hAPP(c_Set_Oinsert(U_7718),U_7722),U_7724))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7718),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7718,tc_HOL_Obool)),U_7720),U_7724))) )
& ! [U_7723,U_7721,U_7719,U_7717] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7717),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7717,tc_HOL_Obool)),U_7719),U_7723)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7717),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7717,tc_HOL_Obool)),U_7719),hAPP(hAPP(c_Set_Oinsert(U_7717),U_7721),U_7723)))) ) ),
inference(miniscope,[status(thm)],[f_2286_2]) ).
cnf(f_2286_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7717),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7717,tc_HOL_Obool)),U_7719),U_7723)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7717),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7717,tc_HOL_Obool)),U_7719),hAPP(hAPP(c_Set_Oinsert(U_7717),U_7721),U_7723)))) ),
inference(clausify,[status(thm)],[f_2286_3]) ).
cnf(f_2286_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7718),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7718,tc_HOL_Obool)),U_7720),hAPP(hAPP(c_Set_Oinsert(U_7718),U_7722),U_7724))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7718),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7718,tc_HOL_Obool)),U_7720),U_7724))) ),
inference(clausify,[status(thm)],[f_2286_3]) ).
fof(f_2287_1,plain,
! [V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__infinite]) ).
fof(f_2287_2,plain,
! [U_7726,U_7725] :
( hAPP(c_Finite__Set_Ocard(U_7725),U_7726) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_7725),U_7726)) ),
inference(variable_rename,[status(thm)],[f_2287_1]) ).
cnf(f_2287_3,plain,
( hAPP(c_Finite__Set_Ocard(U_7725),U_7726) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_7725),U_7726)) ),
inference(clausify,[status(thm)],[f_2287_2]) ).
fof(f_2288_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite]) ).
fof(f_2288_2,plain,
! [U_7728,U_7727] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7727),U_7728))
| ~ 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_7727),U_7728))) ),
inference(variable_rename,[status(thm)],[f_2288_1]) ).
cnf(f_2288_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7727),U_7728))
| ~ 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_7727),U_7728))) ),
inference(clausify,[status(thm)],[f_2288_2]) ).
fof(f_2289_1,plain,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__insert__le]) ).
fof(f_2289_2,plain,
! [U_7731,U_7730,U_7729] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7729),U_7730)),hAPP(c_Finite__Set_Ocard(U_7729),hAPP(hAPP(c_Set_Oinsert(U_7729),U_7731),U_7730))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7729),U_7730)) ),
inference(variable_rename,[status(thm)],[f_2289_1]) ).
cnf(f_2289_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7729),U_7730)),hAPP(c_Finite__Set_Ocard(U_7729),hAPP(hAPP(c_Set_Oinsert(U_7729),U_7731),U_7730))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7729),U_7730)) ),
inference(clausify,[status(thm)],[f_2289_2]) ).
fof(f_2290_1,plain,
! [V_A_2,V_B_2,T_b] :
( V_A_2 = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__seteq]) ).
fof(f_2290_2,plain,
! [U_7734,U_7733,U_7732] :
( U_7734 = U_7733
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7732),U_7733)),hAPP(c_Finite__Set_Ocard(U_7732),U_7734)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7732,tc_HOL_Obool)),U_7734),U_7733))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7732),U_7733)) ),
inference(variable_rename,[status(thm)],[f_2290_1]) ).
cnf(f_2290_3,plain,
( U_7734 = U_7733
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7732),U_7733)),hAPP(c_Finite__Set_Ocard(U_7732),U_7734)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7732,tc_HOL_Obool)),U_7734),U_7733))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7732),U_7733)) ),
inference(clausify,[status(thm)],[f_2290_2]) ).
fof(f_2291_1,plain,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__mono]) ).
fof(f_2291_2,plain,
! [U_7737,U_7736,U_7735] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7735),U_7737)),hAPP(c_Finite__Set_Ocard(U_7735),U_7736)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7735,tc_HOL_Obool)),U_7737),U_7736))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7735),U_7736)) ),
inference(variable_rename,[status(thm)],[f_2291_1]) ).
cnf(f_2291_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7735),U_7737)),hAPP(c_Finite__Set_Ocard(U_7735),U_7736)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7735,tc_HOL_Obool)),U_7737),U_7736))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7735),U_7736)) ),
inference(clausify,[status(thm)],[f_2291_2]) ).
fof(f_2292_1,plain,
! [V_f_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__image__le]) ).
fof(f_2292_2,plain,
! [U_7741,U_7740,U_7739,U_7738] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7740),hAPP(c_Set_Oimage(U_7738,U_7740,U_7741),U_7739))),hAPP(c_Finite__Set_Ocard(U_7738),U_7739)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7738),U_7739)) ),
inference(variable_rename,[status(thm)],[f_2292_1]) ).
cnf(f_2292_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7740),hAPP(c_Set_Oimage(U_7738,U_7740,U_7741),U_7739))),hAPP(c_Finite__Set_Ocard(U_7738),U_7739)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7738),U_7739)) ),
inference(clausify,[status(thm)],[f_2292_2]) ).
fof(f_2293_1,plain,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_psubset__card__mono]) ).
fof(f_2293_2,plain,
! [U_7744,U_7743,U_7742] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7742),U_7744)),hAPP(c_Finite__Set_Ocard(U_7742),U_7743)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7742,tc_HOL_Obool)),U_7744),U_7743))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7742),U_7743)) ),
inference(variable_rename,[status(thm)],[f_2293_1]) ).
cnf(f_2293_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7742),U_7744)),hAPP(c_Finite__Set_Ocard(U_7742),U_7743)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7742,tc_HOL_Obool)),U_7744),U_7743))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7742),U_7743)) ),
inference(clausify,[status(thm)],[f_2293_2]) ).
fof(f_2294_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_2294_2,plain,
! [U_7747,U_7746,U_7745] :
( ( ( ( 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_7745)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7747),U_7746)) = 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_7747),U_7746)) )
& ( 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_7745)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7747),U_7746)) = 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_7747),U_7746)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7745),U_7746)) )
& ( 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_7745)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7747),U_7746)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7747),U_7745)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7746),U_7745))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7745),U_7746)) ) ),
inference(variable_rename,[status(thm)],[f_2294_1]) ).
fof(f_2294_3,plain,
( ! [U_7753,U_7751,U_7749] :
( ( ( 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_7749)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7753),U_7751)) = 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_7753),U_7751)) )
& ( 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_7749)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7753),U_7751)) = 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_7753),U_7751)) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7749),U_7751)) )
& ! [U_7752,U_7750,U_7748] :
( 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_7748)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7752),U_7750)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7752),U_7748)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7750),U_7748))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7748),U_7750)) ) ),
inference(miniscope,[status(thm)],[f_2294_2]) ).
cnf(f_2294_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_Ominus__class_Ominus(tc_Nat_Onat)),U_7748)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7752),U_7750)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7752),U_7748)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7750),U_7748))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7748),U_7750)) ),
inference(clausify,[status(thm)],[f_2294_3]) ).
cnf(f_2294_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_7749)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7753),U_7751)) = 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_7753),U_7751))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7749),U_7751)) ),
inference(clausify,[status(thm)],[f_2294_3]) ).
cnf(f_2294_6,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_7749)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_7753),U_7751)) = 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_7753),U_7751))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7749),U_7751)) ),
inference(clausify,[status(thm)],[f_2294_3]) ).
fof(f_2295_1,plain,
! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ class_Groups_Oordered__ab__semigroup__add(T_c)
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__mono3]) ).
fof(f_2295_2,plain,
! [U_7759,U_7758,U_7757,U_7756,U_7755] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7755),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7756,U_7755),U_7759),U_7758)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7756,U_7755),U_7759),U_7757)))
| ? [U_7754] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7755),c_Groups_Ozero__class_Ozero(U_7755)),hAPP(U_7759,U_7754)))
& hBOOL(hAPP(hAPP(c_member(U_7756),U_7754),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7756,tc_HOL_Obool)),U_7757),U_7758))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7756,tc_HOL_Obool)),U_7758),U_7757))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7756),U_7757))
| ~ class_Groups_Oordered__ab__semigroup__add(U_7755)
| ~ class_Groups_Ocomm__monoid__add(U_7755) ),
inference(variable_rename,[status(thm)],[f_2295_1]) ).
fof(f_2295_3,plain,
! [U_7759,U_7758,U_7757,U_7756,U_7755] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7755),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7756,U_7755),U_7759),U_7758)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7756,U_7755),U_7759),U_7757)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7755),c_Groups_Ozero__class_Ozero(U_7755)),hAPP(U_7759,sK154(U_7759,U_7758,U_7757,U_7756,U_7755))))
& hBOOL(hAPP(hAPP(c_member(U_7756),sK154(U_7759,U_7758,U_7757,U_7756,U_7755)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7756,tc_HOL_Obool)),U_7757),U_7758))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7756,tc_HOL_Obool)),U_7758),U_7757))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7756),U_7757))
| ~ class_Groups_Oordered__ab__semigroup__add(U_7755)
| ~ class_Groups_Ocomm__monoid__add(U_7755) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(U_7754,sK154(U_7759,U_7758,U_7757,U_7756,U_7755))],[f_2295_2]) ).
cnf(f_2295_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_7756),sK154(U_7759,U_7758,U_7757,U_7756,U_7755)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7756,tc_HOL_Obool)),U_7757),U_7758)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7755),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7756,U_7755),U_7759),U_7758)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7756,U_7755),U_7759),U_7757)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7756,tc_HOL_Obool)),U_7758),U_7757))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7756),U_7757))
| ~ class_Groups_Oordered__ab__semigroup__add(U_7755)
| ~ class_Groups_Ocomm__monoid__add(U_7755) ),
inference(clausify,[status(thm)],[f_2295_3]) ).
cnf(f_2295_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7755),c_Groups_Ozero__class_Ozero(U_7755)),hAPP(U_7759,sK154(U_7759,U_7758,U_7757,U_7756,U_7755))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7755),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7756,U_7755),U_7759),U_7758)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7756,U_7755),U_7759),U_7757)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7756,tc_HOL_Obool)),U_7758),U_7757))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7756),U_7757))
| ~ class_Groups_Oordered__ab__semigroup__add(U_7755)
| ~ class_Groups_Ocomm__monoid__add(U_7755) ),
inference(clausify,[status(thm)],[f_2295_3]) ).
fof(f_2296_1,plain,
! [V_B_2,T_c,V_A_2,T_b] :
( ( hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) )
& ( hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_card__Plus__conv__if]) ).
fof(f_2296_2,plain,
! [U_7763,U_7762,U_7761,U_7760] :
( ( hAPP(c_Finite__Set_Ocard(tc_sum(U_7760,U_7762)),c_Sum__Type_OPlus(U_7760,U_7762,U_7761,U_7763)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7762),U_7763))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_7760),U_7761)) ) )
& ( hAPP(c_Finite__Set_Ocard(tc_sum(U_7760,U_7762)),c_Sum__Type_OPlus(U_7760,U_7762,U_7761,U_7763)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7760),U_7761)),hAPP(c_Finite__Set_Ocard(U_7762),U_7763))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7762),U_7763))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7760),U_7761)) ) ),
inference(variable_rename,[status(thm)],[f_2296_1]) ).
fof(f_2296_3,plain,
( ! [U_7771,U_7769,U_7767,U_7765] :
( hAPP(c_Finite__Set_Ocard(tc_sum(U_7765,U_7769)),c_Sum__Type_OPlus(U_7765,U_7769,U_7767,U_7771)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7769),U_7771))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_7765),U_7767)) ) )
& ! [U_7770,U_7768,U_7766,U_7764] :
( hAPP(c_Finite__Set_Ocard(tc_sum(U_7764,U_7768)),c_Sum__Type_OPlus(U_7764,U_7768,U_7766,U_7770)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7764),U_7766)),hAPP(c_Finite__Set_Ocard(U_7768),U_7770))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7768),U_7770))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7764),U_7766)) ) ),
inference(miniscope,[status(thm)],[f_2296_2]) ).
cnf(f_2296_4,plain,
( hAPP(c_Finite__Set_Ocard(tc_sum(U_7764,U_7768)),c_Sum__Type_OPlus(U_7764,U_7768,U_7766,U_7770)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_7764),U_7766)),hAPP(c_Finite__Set_Ocard(U_7768),U_7770))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7768),U_7770))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7764),U_7766)) ),
inference(clausify,[status(thm)],[f_2296_3]) ).
cnf(f_2296_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7765),U_7767))
| hAPP(c_Finite__Set_Ocard(tc_sum(U_7765,U_7769)),c_Sum__Type_OPlus(U_7765,U_7769,U_7767,U_7771)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_2296_3]) ).
cnf(f_2296_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7769),U_7771))
| hAPP(c_Finite__Set_Ocard(tc_sum(U_7765,U_7769)),c_Sum__Type_OPlus(U_7765,U_7769,U_7767,U_7771)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_2296_3]) ).
fof(f_2297_1,plain,
! [V_x_2,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card_Oinsert__remove]) ).
fof(f_2297_2,plain,
! [U_7774,U_7773,U_7772] :
( hAPP(c_Finite__Set_Ocard(U_7772),hAPP(hAPP(c_Set_Oinsert(U_7772),U_7774),U_7773)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_7772),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7772,tc_HOL_Obool)),U_7773),hAPP(hAPP(c_Set_Oinsert(U_7772),U_7774),c_Orderings_Obot__class_Obot(tc_fun(U_7772,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7772),U_7773)) ),
inference(variable_rename,[status(thm)],[f_2297_1]) ).
cnf(f_2297_3,plain,
( hAPP(c_Finite__Set_Ocard(U_7772),hAPP(hAPP(c_Set_Oinsert(U_7772),U_7774),U_7773)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_7772),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7772,tc_HOL_Obool)),U_7773),hAPP(hAPP(c_Set_Oinsert(U_7772),U_7774),c_Orderings_Obot__class_Obot(tc_fun(U_7772,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7772),U_7773)) ),
inference(clausify,[status(thm)],[f_2297_2]) ).
fof(f_2298_1,plain,
! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_finite_OemptyI]) ).
fof(f_2298_2,plain,
! [U_7775] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_7775),c_Orderings_Obot__class_Obot(tc_fun(U_7775,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_2298_1]) ).
cnf(f_2298_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(U_7775),c_Orderings_Obot__class_Obot(tc_fun(U_7775,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_2298_2]) ).
fof(f_2299_1,plain,
! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_empty__subsetI]) ).
fof(f_2299_2,plain,
! [U_7777,U_7776] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7776,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7776,tc_HOL_Obool))),U_7777)),
inference(variable_rename,[status(thm)],[f_2299_1]) ).
cnf(f_2299_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7776,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7776,tc_HOL_Obool))),U_7777)),
inference(clausify,[status(thm)],[f_2299_2]) ).
fof(f_2300_1,plain,
! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_finite_Oequations_I1_J]) ).
fof(f_2300_2,plain,
! [U_7778] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_7778),c_Orderings_Obot__class_Obot(tc_fun(U_7778,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_2300_1]) ).
cnf(f_2300_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(U_7778),c_Orderings_Obot__class_Obot(tc_fun(U_7778,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_2300_2]) ).
fof(f_2301_1,plain,
! [V_A_2,V_a_2,T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2),
inference(fof_nnf,[status(thm)],[fact_empty__not__insert]) ).
fof(f_2301_2,plain,
! [U_7781,U_7780,U_7779] : c_Orderings_Obot__class_Obot(tc_fun(U_7779,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_7779),U_7780),U_7781),
inference(variable_rename,[status(thm)],[f_2301_1]) ).
cnf(f_2301_3,plain,
c_Orderings_Obot__class_Obot(tc_fun(U_7779,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_7779),U_7780),U_7781),
inference(clausify,[status(thm)],[f_2301_2]) ).
fof(f_2302_1,plain,
! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_insert__not__empty]) ).
fof(f_2302_2,plain,
! [U_7784,U_7783,U_7782] : hAPP(hAPP(c_Set_Oinsert(U_7782),U_7783),U_7784) != c_Orderings_Obot__class_Obot(tc_fun(U_7782,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2302_1]) ).
cnf(f_2302_3,plain,
hAPP(hAPP(c_Set_Oinsert(U_7782),U_7783),U_7784) != c_Orderings_Obot__class_Obot(tc_fun(U_7782,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2302_2]) ).
fof(f_2303_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
| ( ( V_b_2 != V_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_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ),
inference(fof_nnf,[status(thm)],[fact_doubleton__eq__iff]) ).
fof(f_2303_2,plain,
! [U_7789,U_7788,U_7787,U_7786,U_7785] :
( ( hAPP(hAPP(c_Set_Oinsert(U_7785),U_7786),hAPP(hAPP(c_Set_Oinsert(U_7785),U_7787),c_Orderings_Obot__class_Obot(tc_fun(U_7785,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_7785),U_7788),hAPP(hAPP(c_Set_Oinsert(U_7785),U_7789),c_Orderings_Obot__class_Obot(tc_fun(U_7785,tc_HOL_Obool))))
| ( ( U_7787 != U_7788
| U_7786 != U_7789 )
& ( U_7787 != U_7789
| U_7786 != U_7788 ) ) )
& ( ( U_7787 = U_7788
& U_7786 = U_7789 )
| ( U_7787 = U_7789
& U_7786 = U_7788 )
| hAPP(hAPP(c_Set_Oinsert(U_7785),U_7786),hAPP(hAPP(c_Set_Oinsert(U_7785),U_7787),c_Orderings_Obot__class_Obot(tc_fun(U_7785,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_7785),U_7788),hAPP(hAPP(c_Set_Oinsert(U_7785),U_7789),c_Orderings_Obot__class_Obot(tc_fun(U_7785,tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[f_2303_1]) ).
fof(f_2303_3,plain,
( ! [U_7799,U_7797,U_7795,U_7793] :
( ! [U_7791] : hAPP(hAPP(c_Set_Oinsert(U_7791),U_7793),hAPP(hAPP(c_Set_Oinsert(U_7791),U_7795),c_Orderings_Obot__class_Obot(tc_fun(U_7791,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_7791),U_7797),hAPP(hAPP(c_Set_Oinsert(U_7791),U_7799),c_Orderings_Obot__class_Obot(tc_fun(U_7791,tc_HOL_Obool))))
| ( ( U_7795 != U_7797
| U_7793 != U_7799 )
& ( U_7795 != U_7799
| U_7793 != U_7797 ) ) )
& ! [U_7798,U_7796,U_7794,U_7792] :
( ! [U_7790] : hAPP(hAPP(c_Set_Oinsert(U_7790),U_7792),hAPP(hAPP(c_Set_Oinsert(U_7790),U_7794),c_Orderings_Obot__class_Obot(tc_fun(U_7790,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_7790),U_7796),hAPP(hAPP(c_Set_Oinsert(U_7790),U_7798),c_Orderings_Obot__class_Obot(tc_fun(U_7790,tc_HOL_Obool))))
| ( U_7794 = U_7796
& U_7792 = U_7798 )
| ( U_7794 = U_7798
& U_7792 = U_7796 ) ) ),
inference(miniscope,[status(thm)],[f_2303_2]) ).
cnf(f_2303_4,plain,
( U_7792 = U_7798
| U_7792 = U_7796
| hAPP(hAPP(c_Set_Oinsert(U_7790),U_7792),hAPP(hAPP(c_Set_Oinsert(U_7790),U_7794),c_Orderings_Obot__class_Obot(tc_fun(U_7790,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_7790),U_7796),hAPP(hAPP(c_Set_Oinsert(U_7790),U_7798),c_Orderings_Obot__class_Obot(tc_fun(U_7790,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_2303_3]) ).
cnf(f_2303_5,plain,
( U_7794 = U_7796
| U_7792 = U_7796
| hAPP(hAPP(c_Set_Oinsert(U_7790),U_7792),hAPP(hAPP(c_Set_Oinsert(U_7790),U_7794),c_Orderings_Obot__class_Obot(tc_fun(U_7790,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_7790),U_7796),hAPP(hAPP(c_Set_Oinsert(U_7790),U_7798),c_Orderings_Obot__class_Obot(tc_fun(U_7790,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_2303_3]) ).
cnf(f_2303_6,plain,
( U_7792 = U_7798
| U_7794 = U_7798
| hAPP(hAPP(c_Set_Oinsert(U_7790),U_7792),hAPP(hAPP(c_Set_Oinsert(U_7790),U_7794),c_Orderings_Obot__class_Obot(tc_fun(U_7790,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_7790),U_7796),hAPP(hAPP(c_Set_Oinsert(U_7790),U_7798),c_Orderings_Obot__class_Obot(tc_fun(U_7790,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_2303_3]) ).
cnf(f_2303_7,plain,
( U_7794 = U_7796
| U_7794 = U_7798
| hAPP(hAPP(c_Set_Oinsert(U_7790),U_7792),hAPP(hAPP(c_Set_Oinsert(U_7790),U_7794),c_Orderings_Obot__class_Obot(tc_fun(U_7790,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_7790),U_7796),hAPP(hAPP(c_Set_Oinsert(U_7790),U_7798),c_Orderings_Obot__class_Obot(tc_fun(U_7790,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_2303_3]) ).
cnf(f_2303_8,plain,
( U_7795 != U_7799
| U_7793 != U_7797
| hAPP(hAPP(c_Set_Oinsert(U_7791),U_7793),hAPP(hAPP(c_Set_Oinsert(U_7791),U_7795),c_Orderings_Obot__class_Obot(tc_fun(U_7791,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_7791),U_7797),hAPP(hAPP(c_Set_Oinsert(U_7791),U_7799),c_Orderings_Obot__class_Obot(tc_fun(U_7791,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_2303_3]) ).
cnf(f_2303_9,plain,
( U_7795 != U_7797
| U_7793 != U_7799
| hAPP(hAPP(c_Set_Oinsert(U_7791),U_7793),hAPP(hAPP(c_Set_Oinsert(U_7791),U_7795),c_Orderings_Obot__class_Obot(tc_fun(U_7791,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_7791),U_7797),hAPP(hAPP(c_Set_Oinsert(U_7791),U_7799),c_Orderings_Obot__class_Obot(tc_fun(U_7791,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_2303_3]) ).
fof(f_2304_1,plain,
! [V_b_2,V_a_2,T_b] :
( V_a_2 = V_b_2
| hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_singleton__inject]) ).
fof(f_2304_2,plain,
! [U_7802,U_7801,U_7800] :
( U_7801 = U_7802
| hAPP(hAPP(c_Set_Oinsert(U_7800),U_7801),c_Orderings_Obot__class_Obot(tc_fun(U_7800,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_7800),U_7802),c_Orderings_Obot__class_Obot(tc_fun(U_7800,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_2304_1]) ).
fof(f_2304_3,plain,
! [U_7802,U_7801] :
( ! [U_7800] : hAPP(hAPP(c_Set_Oinsert(U_7800),U_7801),c_Orderings_Obot__class_Obot(tc_fun(U_7800,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_7800),U_7802),c_Orderings_Obot__class_Obot(tc_fun(U_7800,tc_HOL_Obool)))
| U_7801 = U_7802 ),
inference(miniscope,[status(thm)],[f_2304_2]) ).
cnf(f_2304_4,plain,
( hAPP(hAPP(c_Set_Oinsert(U_7800),U_7801),c_Orderings_Obot__class_Obot(tc_fun(U_7800,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_7800),U_7802),c_Orderings_Obot__class_Obot(tc_fun(U_7800,tc_HOL_Obool)))
| U_7801 = U_7802 ),
inference(clausify,[status(thm)],[f_2304_3]) ).
fof(f_2305_1,plain,
! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Diff__cancel]) ).
fof(f_2305_2,plain,
! [U_7804,U_7803] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7803,tc_HOL_Obool)),U_7804),U_7804) = c_Orderings_Obot__class_Obot(tc_fun(U_7803,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2305_1]) ).
cnf(f_2305_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7803,tc_HOL_Obool)),U_7804),U_7804) = c_Orderings_Obot__class_Obot(tc_fun(U_7803,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2305_2]) ).
fof(f_2306_1,plain,
! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Diff__empty]) ).
fof(f_2306_2,plain,
! [U_7806,U_7805] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7805,tc_HOL_Obool)),U_7806),c_Orderings_Obot__class_Obot(tc_fun(U_7805,tc_HOL_Obool))) = U_7806,
inference(variable_rename,[status(thm)],[f_2306_1]) ).
cnf(f_2306_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7805,tc_HOL_Obool)),U_7806),c_Orderings_Obot__class_Obot(tc_fun(U_7805,tc_HOL_Obool))) = U_7806,
inference(clausify,[status(thm)],[f_2306_2]) ).
fof(f_2307_1,plain,
! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_empty__Diff]) ).
fof(f_2307_2,plain,
! [U_7808,U_7807] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7807,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7807,tc_HOL_Obool))),U_7808) = c_Orderings_Obot__class_Obot(tc_fun(U_7807,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2307_1]) ).
cnf(f_2307_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7807,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7807,tc_HOL_Obool))),U_7808) = c_Orderings_Obot__class_Obot(tc_fun(U_7807,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2307_2]) ).
fof(f_2308_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]) ).
cnf(f_2308_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(clausify,[status(thm)],[f_2308_1]) ).
fof(f_2309_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]) ).
cnf(f_2309_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(clausify,[status(thm)],[f_2309_1]) ).
fof(f_2310_1,plain,
! [V_A_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ),
inference(fof_nnf,[status(thm)],[fact_subset__empty]) ).
fof(f_2310_2,plain,
! [U_7810,U_7809] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7809,tc_HOL_Obool)),U_7810),c_Orderings_Obot__class_Obot(tc_fun(U_7809,tc_HOL_Obool))))
| U_7810 != c_Orderings_Obot__class_Obot(tc_fun(U_7809,tc_HOL_Obool)) )
& ( U_7810 = c_Orderings_Obot__class_Obot(tc_fun(U_7809,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7809,tc_HOL_Obool)),U_7810),c_Orderings_Obot__class_Obot(tc_fun(U_7809,tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[f_2310_1]) ).
fof(f_2310_3,plain,
( ! [U_7814,U_7812] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7812,tc_HOL_Obool)),U_7814),c_Orderings_Obot__class_Obot(tc_fun(U_7812,tc_HOL_Obool))))
| U_7814 != c_Orderings_Obot__class_Obot(tc_fun(U_7812,tc_HOL_Obool)) )
& ! [U_7813,U_7811] :
( U_7813 = c_Orderings_Obot__class_Obot(tc_fun(U_7811,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7811,tc_HOL_Obool)),U_7813),c_Orderings_Obot__class_Obot(tc_fun(U_7811,tc_HOL_Obool)))) ) ),
inference(miniscope,[status(thm)],[f_2310_2]) ).
cnf(f_2310_4,plain,
( U_7813 = c_Orderings_Obot__class_Obot(tc_fun(U_7811,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7811,tc_HOL_Obool)),U_7813),c_Orderings_Obot__class_Obot(tc_fun(U_7811,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_2310_3]) ).
cnf(f_2310_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7812,tc_HOL_Obool)),U_7814),c_Orderings_Obot__class_Obot(tc_fun(U_7812,tc_HOL_Obool))))
| U_7814 != c_Orderings_Obot__class_Obot(tc_fun(U_7812,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2310_3]) ).
fof(f_2311_1,plain,
! [V_A_2,V_f_2,T_b,T_c] :
( ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_image__is__empty]) ).
fof(f_2311_2,plain,
! [U_7818,U_7817,U_7816,U_7815] :
( ( hAPP(c_Set_Oimage(U_7815,U_7816,U_7817),U_7818) = c_Orderings_Obot__class_Obot(tc_fun(U_7816,tc_HOL_Obool))
| U_7818 != c_Orderings_Obot__class_Obot(tc_fun(U_7815,tc_HOL_Obool)) )
& ( U_7818 = c_Orderings_Obot__class_Obot(tc_fun(U_7815,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_7815,U_7816,U_7817),U_7818) != c_Orderings_Obot__class_Obot(tc_fun(U_7816,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2311_1]) ).
fof(f_2311_3,plain,
( ! [U_7826,U_7824,U_7822,U_7820] :
( hAPP(c_Set_Oimage(U_7820,U_7822,U_7824),U_7826) = c_Orderings_Obot__class_Obot(tc_fun(U_7822,tc_HOL_Obool))
| U_7826 != c_Orderings_Obot__class_Obot(tc_fun(U_7820,tc_HOL_Obool)) )
& ! [U_7825,U_7823,U_7821,U_7819] :
( U_7825 = c_Orderings_Obot__class_Obot(tc_fun(U_7819,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_7819,U_7821,U_7823),U_7825) != c_Orderings_Obot__class_Obot(tc_fun(U_7821,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2311_2]) ).
cnf(f_2311_4,plain,
( U_7825 = c_Orderings_Obot__class_Obot(tc_fun(U_7819,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_7819,U_7821,U_7823),U_7825) != c_Orderings_Obot__class_Obot(tc_fun(U_7821,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2311_3]) ).
cnf(f_2311_5,plain,
( hAPP(c_Set_Oimage(U_7820,U_7822,U_7824),U_7826) = c_Orderings_Obot__class_Obot(tc_fun(U_7822,tc_HOL_Obool))
| U_7826 != c_Orderings_Obot__class_Obot(tc_fun(U_7820,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2311_3]) ).
fof(f_2312_1,plain,
! [V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_image__empty]) ).
fof(f_2312_2,plain,
! [U_7829,U_7828,U_7827] : hAPP(c_Set_Oimage(U_7827,U_7828,U_7829),c_Orderings_Obot__class_Obot(tc_fun(U_7827,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_7828,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2312_1]) ).
cnf(f_2312_3,plain,
hAPP(c_Set_Oimage(U_7827,U_7828,U_7829),c_Orderings_Obot__class_Obot(tc_fun(U_7827,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_7828,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2312_2]) ).
fof(f_2313_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) ) ),
inference(fof_nnf,[status(thm)],[fact_empty__is__image]) ).
fof(f_2313_2,plain,
! [U_7833,U_7832,U_7831,U_7830] :
( ( c_Orderings_Obot__class_Obot(tc_fun(U_7830,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_7831,U_7830,U_7832),U_7833)
| U_7833 != c_Orderings_Obot__class_Obot(tc_fun(U_7831,tc_HOL_Obool)) )
& ( U_7833 = c_Orderings_Obot__class_Obot(tc_fun(U_7831,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(U_7830,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_7831,U_7830,U_7832),U_7833) ) ),
inference(variable_rename,[status(thm)],[f_2313_1]) ).
fof(f_2313_3,plain,
( ! [U_7841,U_7839,U_7837] :
( ! [U_7835] : c_Orderings_Obot__class_Obot(tc_fun(U_7835,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_7837,U_7835,U_7839),U_7841)
| U_7841 != c_Orderings_Obot__class_Obot(tc_fun(U_7837,tc_HOL_Obool)) )
& ! [U_7840,U_7838,U_7836] :
( ! [U_7834] : c_Orderings_Obot__class_Obot(tc_fun(U_7834,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_7836,U_7834,U_7838),U_7840)
| U_7840 = c_Orderings_Obot__class_Obot(tc_fun(U_7836,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2313_2]) ).
cnf(f_2313_4,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_7834,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_7836,U_7834,U_7838),U_7840)
| U_7840 = c_Orderings_Obot__class_Obot(tc_fun(U_7836,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2313_3]) ).
cnf(f_2313_5,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_7835,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_7837,U_7835,U_7839),U_7841)
| U_7841 != c_Orderings_Obot__class_Obot(tc_fun(U_7837,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2313_3]) ).
fof(f_2314_1,plain,
! [V_P_2,T_b,B_x] :
( hBOOL(hAPP(V_P_2,B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_ball__empty]) ).
fof(f_2314_2,plain,
! [U_7844,U_7843,U_7842] :
( hBOOL(hAPP(U_7844,U_7842))
| ~ hBOOL(hAPP(hAPP(c_member(U_7843),U_7842),c_Orderings_Obot__class_Obot(tc_fun(U_7843,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_2314_1]) ).
cnf(f_2314_3,plain,
( hBOOL(hAPP(U_7844,U_7842))
| ~ hBOOL(hAPP(hAPP(c_member(U_7843),U_7842),c_Orderings_Obot__class_Obot(tc_fun(U_7843,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_2314_2]) ).
fof(f_2315_1,plain,
! [V_x_2,T_c,T_b] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b)
| ~ class_Orderings_Obot(T_b) ),
inference(fof_nnf,[status(thm)],[fact_bot__apply]) ).
fof(f_2315_2,plain,
! [U_7847,U_7846,U_7845] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7846,U_7845)),U_7847) = c_Orderings_Obot__class_Obot(U_7845)
| ~ class_Orderings_Obot(U_7845) ),
inference(variable_rename,[status(thm)],[f_2315_1]) ).
cnf(f_2315_3,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7846,U_7845)),U_7847) = c_Orderings_Obot__class_Obot(U_7845)
| ~ class_Orderings_Obot(U_7845) ),
inference(clausify,[status(thm)],[f_2315_2]) ).
fof(f_2316_1,plain,
! [V_x_2,T_c,T_b] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b)
| ~ class_Orderings_Obot(T_b) ),
inference(fof_nnf,[status(thm)],[fact_bot__fun__def]) ).
fof(f_2316_2,plain,
! [U_7850,U_7849,U_7848] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7849,U_7848)),U_7850) = c_Orderings_Obot__class_Obot(U_7848)
| ~ class_Orderings_Obot(U_7848) ),
inference(variable_rename,[status(thm)],[f_2316_1]) ).
cnf(f_2316_3,plain,
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_7849,U_7848)),U_7850) = c_Orderings_Obot__class_Obot(U_7848)
| ~ class_Orderings_Obot(U_7848) ),
inference(clausify,[status(thm)],[f_2316_2]) ).
fof(f_2317_1,plain,
! [V_B_2,V_A_2,T_b] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_Un__empty]) ).
fof(f_2317_2,plain,
! [U_7853,U_7852,U_7851] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7851,tc_HOL_Obool)),U_7852),U_7853) = c_Orderings_Obot__class_Obot(tc_fun(U_7851,tc_HOL_Obool))
| U_7853 != c_Orderings_Obot__class_Obot(tc_fun(U_7851,tc_HOL_Obool))
| U_7852 != c_Orderings_Obot__class_Obot(tc_fun(U_7851,tc_HOL_Obool)) )
& ( ( U_7853 = c_Orderings_Obot__class_Obot(tc_fun(U_7851,tc_HOL_Obool))
& U_7852 = c_Orderings_Obot__class_Obot(tc_fun(U_7851,tc_HOL_Obool)) )
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7851,tc_HOL_Obool)),U_7852),U_7853) != c_Orderings_Obot__class_Obot(tc_fun(U_7851,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2317_1]) ).
fof(f_2317_3,plain,
( ! [U_7859,U_7857,U_7855] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7855,tc_HOL_Obool)),U_7857),U_7859) = c_Orderings_Obot__class_Obot(tc_fun(U_7855,tc_HOL_Obool))
| U_7859 != c_Orderings_Obot__class_Obot(tc_fun(U_7855,tc_HOL_Obool))
| U_7857 != c_Orderings_Obot__class_Obot(tc_fun(U_7855,tc_HOL_Obool)) )
& ! [U_7858,U_7856,U_7854] :
( ( U_7858 = c_Orderings_Obot__class_Obot(tc_fun(U_7854,tc_HOL_Obool))
& U_7856 = c_Orderings_Obot__class_Obot(tc_fun(U_7854,tc_HOL_Obool)) )
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7854,tc_HOL_Obool)),U_7856),U_7858) != c_Orderings_Obot__class_Obot(tc_fun(U_7854,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2317_2]) ).
cnf(f_2317_4,plain,
( U_7856 = c_Orderings_Obot__class_Obot(tc_fun(U_7854,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7854,tc_HOL_Obool)),U_7856),U_7858) != c_Orderings_Obot__class_Obot(tc_fun(U_7854,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2317_3]) ).
cnf(f_2317_5,plain,
( U_7858 = c_Orderings_Obot__class_Obot(tc_fun(U_7854,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7854,tc_HOL_Obool)),U_7856),U_7858) != c_Orderings_Obot__class_Obot(tc_fun(U_7854,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2317_3]) ).
cnf(f_2317_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7855,tc_HOL_Obool)),U_7857),U_7859) = c_Orderings_Obot__class_Obot(tc_fun(U_7855,tc_HOL_Obool))
| U_7859 != c_Orderings_Obot__class_Obot(tc_fun(U_7855,tc_HOL_Obool))
| U_7857 != c_Orderings_Obot__class_Obot(tc_fun(U_7855,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2317_3]) ).
fof(f_2318_1,plain,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Un__empty__right]) ).
fof(f_2318_2,plain,
! [U_7861,U_7860] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7860,tc_HOL_Obool)),U_7861),c_Orderings_Obot__class_Obot(tc_fun(U_7860,tc_HOL_Obool))) = U_7861,
inference(variable_rename,[status(thm)],[f_2318_1]) ).
cnf(f_2318_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7860,tc_HOL_Obool)),U_7861),c_Orderings_Obot__class_Obot(tc_fun(U_7860,tc_HOL_Obool))) = U_7861,
inference(clausify,[status(thm)],[f_2318_2]) ).
fof(f_2319_1,plain,
! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2,
inference(fof_nnf,[status(thm)],[fact_Un__empty__left]) ).
fof(f_2319_2,plain,
! [U_7863,U_7862] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7862,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7862,tc_HOL_Obool))),U_7863) = U_7863,
inference(variable_rename,[status(thm)],[f_2319_1]) ).
cnf(f_2319_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7862,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_7862,tc_HOL_Obool))),U_7863) = U_7863,
inference(clausify,[status(thm)],[f_2319_2]) ).
fof(f_2320_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]) ).
cnf(f_2320_2,plain,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_2320_1]) ).
fof(f_2321_1,plain,
! [V_A_2,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_not__psubset__empty]) ).
fof(f_2321_2,plain,
! [U_7865,U_7864] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7864,tc_HOL_Obool)),U_7865),c_Orderings_Obot__class_Obot(tc_fun(U_7864,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_2321_1]) ).
cnf(f_2321_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_7864,tc_HOL_Obool)),U_7865),c_Orderings_Obot__class_Obot(tc_fun(U_7864,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_2321_2]) ).
fof(f_2322_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_2322_2,plain,
! [U_7867,U_7866] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7866),c_Orderings_Obot__class_Obot(U_7866)),U_7867))
| ~ class_Orderings_Obot(U_7866) ),
inference(variable_rename,[status(thm)],[f_2322_1]) ).
cnf(f_2322_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7866),c_Orderings_Obot__class_Obot(U_7866)),U_7867))
| ~ class_Orderings_Obot(U_7866) ),
inference(clausify,[status(thm)],[f_2322_2]) ).
fof(f_2323_1,plain,
! [V_M_2,T_b,V_A_2,T_c] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_SUP__const]) ).
fof(f_2323_2,plain,
! [U_7871,U_7870,U_7869,U_7868] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7870,U_7868),U_7869),hAPP(c_COMBK(U_7868,U_7870),U_7871)) = U_7871
| U_7869 = c_Orderings_Obot__class_Obot(tc_fun(U_7870,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7868) ),
inference(variable_rename,[status(thm)],[f_2323_1]) ).
cnf(f_2323_3,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7870,U_7868),U_7869),hAPP(c_COMBK(U_7868,U_7870),U_7871)) = U_7871
| U_7869 = c_Orderings_Obot__class_Obot(tc_fun(U_7870,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7868) ),
inference(clausify,[status(thm)],[f_2323_2]) ).
fof(f_2324_1,plain,
! [V_B_2,V_A_2,T_c,T_b] :
( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
| ? [B_x] :
( hAPP(V_B_2,B_x) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ),
inference(fof_nnf,[status(thm)],[fact_UNION__empty__conv_I1_J]) ).
fof(f_2324_2,plain,
! [U_7877,U_7876,U_7875,U_7874] :
( ( c_Orderings_Obot__class_Obot(tc_fun(U_7874,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7875,tc_fun(U_7874,tc_HOL_Obool)),U_7876),U_7877)
| ? [U_7873] :
( hAPP(U_7877,U_7873) != c_Orderings_Obot__class_Obot(tc_fun(U_7874,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_7875),U_7873),U_7876)) ) )
& ( ! [U_7872] :
( hAPP(U_7877,U_7872) = c_Orderings_Obot__class_Obot(tc_fun(U_7874,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_7875),U_7872),U_7876)) )
| c_Orderings_Obot__class_Obot(tc_fun(U_7874,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7875,tc_fun(U_7874,tc_HOL_Obool)),U_7876),U_7877) ) ),
inference(variable_rename,[status(thm)],[f_2324_1]) ).
fof(f_2324_3,plain,
( ! [U_7885,U_7883,U_7881,U_7879] :
( c_Orderings_Obot__class_Obot(tc_fun(U_7879,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7881,tc_fun(U_7879,tc_HOL_Obool)),U_7883),U_7885)
| ? [U_7873] :
( hAPP(U_7885,U_7873) != c_Orderings_Obot__class_Obot(tc_fun(U_7879,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_7881),U_7873),U_7883)) ) )
& ! [U_7884,U_7882,U_7880,U_7878] :
( ! [U_7872] :
( hAPP(U_7884,U_7872) = c_Orderings_Obot__class_Obot(tc_fun(U_7878,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_7880),U_7872),U_7882)) )
| c_Orderings_Obot__class_Obot(tc_fun(U_7878,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7880,tc_fun(U_7878,tc_HOL_Obool)),U_7882),U_7884) ) ),
inference(miniscope,[status(thm)],[f_2324_2]) ).
fof(f_2324_4,plain,
( ! [U_7885,U_7883,U_7881,U_7879] :
( c_Orderings_Obot__class_Obot(tc_fun(U_7879,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7881,tc_fun(U_7879,tc_HOL_Obool)),U_7883),U_7885)
| ( hAPP(U_7885,sK155(U_7885,U_7883,U_7881,U_7879)) != c_Orderings_Obot__class_Obot(tc_fun(U_7879,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_7881),sK155(U_7885,U_7883,U_7881,U_7879)),U_7883)) ) )
& ! [U_7884,U_7882,U_7880,U_7878] :
( ! [U_7872] :
( hAPP(U_7884,U_7872) = c_Orderings_Obot__class_Obot(tc_fun(U_7878,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_7880),U_7872),U_7882)) )
| c_Orderings_Obot__class_Obot(tc_fun(U_7878,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7880,tc_fun(U_7878,tc_HOL_Obool)),U_7882),U_7884) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(U_7873,sK155(U_7885,U_7883,U_7881,U_7879))],[f_2324_3]) ).
cnf(f_2324_5,plain,
( hAPP(U_7884,U_7872) = c_Orderings_Obot__class_Obot(tc_fun(U_7878,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_7880),U_7872),U_7882))
| c_Orderings_Obot__class_Obot(tc_fun(U_7878,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7880,tc_fun(U_7878,tc_HOL_Obool)),U_7882),U_7884) ),
inference(clausify,[status(thm)],[f_2324_4]) ).
cnf(f_2324_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_7881),sK155(U_7885,U_7883,U_7881,U_7879)),U_7883))
| c_Orderings_Obot__class_Obot(tc_fun(U_7879,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7881,tc_fun(U_7879,tc_HOL_Obool)),U_7883),U_7885) ),
inference(clausify,[status(thm)],[f_2324_4]) ).
cnf(f_2324_7,plain,
( hAPP(U_7885,sK155(U_7885,U_7883,U_7881,U_7879)) != c_Orderings_Obot__class_Obot(tc_fun(U_7879,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(U_7879,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7881,tc_fun(U_7879,tc_HOL_Obool)),U_7883),U_7885) ),
inference(clausify,[status(thm)],[f_2324_4]) ).
fof(f_2325_1,plain,
! [V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_UN__empty2]) ).
fof(f_2325_2,plain,
! [U_7888,U_7887,U_7886] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7886,tc_fun(U_7887,tc_HOL_Obool)),U_7888),hAPP(c_COMBK(tc_fun(U_7887,tc_HOL_Obool),U_7886),c_Orderings_Obot__class_Obot(tc_fun(U_7887,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_7887,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2325_1]) ).
cnf(f_2325_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7886,tc_fun(U_7887,tc_HOL_Obool)),U_7888),hAPP(c_COMBK(tc_fun(U_7887,tc_HOL_Obool),U_7886),c_Orderings_Obot__class_Obot(tc_fun(U_7887,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_7887,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2325_2]) ).
fof(f_2326_1,plain,
! [V_c_2,T_c,T_b,V_A_2] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__constant]) ).
fof(f_2326_2,plain,
! [U_7892,U_7891,U_7890,U_7889] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7890,tc_fun(U_7891,tc_HOL_Obool)),U_7889),hAPP(c_COMBK(tc_fun(U_7891,tc_HOL_Obool),U_7890),U_7892)) = U_7892
| U_7889 = c_Orderings_Obot__class_Obot(tc_fun(U_7890,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7890,tc_fun(U_7891,tc_HOL_Obool)),U_7889),hAPP(c_COMBK(tc_fun(U_7891,tc_HOL_Obool),U_7890),U_7892)) = c_Orderings_Obot__class_Obot(tc_fun(U_7891,tc_HOL_Obool))
| U_7889 != c_Orderings_Obot__class_Obot(tc_fun(U_7890,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2326_1]) ).
fof(f_2326_3,plain,
( ! [U_7900,U_7898,U_7896,U_7894] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7896,tc_fun(U_7898,tc_HOL_Obool)),U_7894),hAPP(c_COMBK(tc_fun(U_7898,tc_HOL_Obool),U_7896),U_7900)) = U_7900
| U_7894 = c_Orderings_Obot__class_Obot(tc_fun(U_7896,tc_HOL_Obool)) )
& ! [U_7899,U_7897,U_7895,U_7893] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7895,tc_fun(U_7897,tc_HOL_Obool)),U_7893),hAPP(c_COMBK(tc_fun(U_7897,tc_HOL_Obool),U_7895),U_7899)) = c_Orderings_Obot__class_Obot(tc_fun(U_7897,tc_HOL_Obool))
| U_7893 != c_Orderings_Obot__class_Obot(tc_fun(U_7895,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2326_2]) ).
cnf(f_2326_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7895,tc_fun(U_7897,tc_HOL_Obool)),U_7893),hAPP(c_COMBK(tc_fun(U_7897,tc_HOL_Obool),U_7895),U_7899)) = c_Orderings_Obot__class_Obot(tc_fun(U_7897,tc_HOL_Obool))
| U_7893 != c_Orderings_Obot__class_Obot(tc_fun(U_7895,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2326_3]) ).
cnf(f_2326_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7896,tc_fun(U_7898,tc_HOL_Obool)),U_7894),hAPP(c_COMBK(tc_fun(U_7898,tc_HOL_Obool),U_7896),U_7900)) = U_7900
| U_7894 = c_Orderings_Obot__class_Obot(tc_fun(U_7896,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2326_3]) ).
fof(f_2327_1,plain,
! [V_B_2,V_A_2,T_b,T_c] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ? [B_x] :
( hAPP(V_B_2,B_x) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UNION__empty__conv_I2_J]) ).
fof(f_2327_2,plain,
! [U_7906,U_7905,U_7904,U_7903] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7903,tc_fun(U_7904,tc_HOL_Obool)),U_7905),U_7906) = c_Orderings_Obot__class_Obot(tc_fun(U_7904,tc_HOL_Obool))
| ? [U_7902] :
( hAPP(U_7906,U_7902) != c_Orderings_Obot__class_Obot(tc_fun(U_7904,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_7903),U_7902),U_7905)) ) )
& ( ! [U_7901] :
( hAPP(U_7906,U_7901) = c_Orderings_Obot__class_Obot(tc_fun(U_7904,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_7903),U_7901),U_7905)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7903,tc_fun(U_7904,tc_HOL_Obool)),U_7905),U_7906) != c_Orderings_Obot__class_Obot(tc_fun(U_7904,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2327_1]) ).
fof(f_2327_3,plain,
( ! [U_7914,U_7912,U_7910,U_7908] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7908,tc_fun(U_7910,tc_HOL_Obool)),U_7912),U_7914) = c_Orderings_Obot__class_Obot(tc_fun(U_7910,tc_HOL_Obool))
| ? [U_7902] :
( hAPP(U_7914,U_7902) != c_Orderings_Obot__class_Obot(tc_fun(U_7910,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_7908),U_7902),U_7912)) ) )
& ! [U_7913,U_7911,U_7909,U_7907] :
( ! [U_7901] :
( hAPP(U_7913,U_7901) = c_Orderings_Obot__class_Obot(tc_fun(U_7909,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_7907),U_7901),U_7911)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7907,tc_fun(U_7909,tc_HOL_Obool)),U_7911),U_7913) != c_Orderings_Obot__class_Obot(tc_fun(U_7909,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2327_2]) ).
fof(f_2327_4,plain,
( ! [U_7914,U_7912,U_7910,U_7908] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7908,tc_fun(U_7910,tc_HOL_Obool)),U_7912),U_7914) = c_Orderings_Obot__class_Obot(tc_fun(U_7910,tc_HOL_Obool))
| ( hAPP(U_7914,sK156(U_7914,U_7912,U_7910,U_7908)) != c_Orderings_Obot__class_Obot(tc_fun(U_7910,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_7908),sK156(U_7914,U_7912,U_7910,U_7908)),U_7912)) ) )
& ! [U_7913,U_7911,U_7909,U_7907] :
( ! [U_7901] :
( hAPP(U_7913,U_7901) = c_Orderings_Obot__class_Obot(tc_fun(U_7909,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_7907),U_7901),U_7911)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7907,tc_fun(U_7909,tc_HOL_Obool)),U_7911),U_7913) != c_Orderings_Obot__class_Obot(tc_fun(U_7909,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK156]),skolemize(U_7902,sK156(U_7914,U_7912,U_7910,U_7908))],[f_2327_3]) ).
cnf(f_2327_5,plain,
( hAPP(U_7913,U_7901) = c_Orderings_Obot__class_Obot(tc_fun(U_7909,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_7907),U_7901),U_7911))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7907,tc_fun(U_7909,tc_HOL_Obool)),U_7911),U_7913) != c_Orderings_Obot__class_Obot(tc_fun(U_7909,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2327_4]) ).
cnf(f_2327_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_7908),sK156(U_7914,U_7912,U_7910,U_7908)),U_7912))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7908,tc_fun(U_7910,tc_HOL_Obool)),U_7912),U_7914) = c_Orderings_Obot__class_Obot(tc_fun(U_7910,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2327_4]) ).
cnf(f_2327_7,plain,
( hAPP(U_7914,sK156(U_7914,U_7912,U_7910,U_7908)) != c_Orderings_Obot__class_Obot(tc_fun(U_7910,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_7908,tc_fun(U_7910,tc_HOL_Obool)),U_7912),U_7914) = c_Orderings_Obot__class_Obot(tc_fun(U_7910,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2327_4]) ).
fof(f_2328_1,plain,
! [V_M_2,T_b,V_A_2,T_c] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_INF__const]) ).
fof(f_2328_2,plain,
! [U_7918,U_7917,U_7916,U_7915] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7917,U_7915),U_7916),hAPP(c_COMBK(U_7915,U_7917),U_7918)) = U_7918
| U_7916 = c_Orderings_Obot__class_Obot(tc_fun(U_7917,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7915) ),
inference(variable_rename,[status(thm)],[f_2328_1]) ).
cnf(f_2328_3,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_7917,U_7915),U_7916),hAPP(c_COMBK(U_7915,U_7917),U_7918)) = U_7918
| U_7916 = c_Orderings_Obot__class_Obot(tc_fun(U_7917,tc_HOL_Obool))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_7915) ),
inference(clausify,[status(thm)],[f_2328_2]) ).
fof(f_2329_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_2329_2,plain,
! [U_7920,U_7919] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7919),c_Orderings_Obot__class_Obot(U_7919)),U_7920) = U_7920
| ~ class_Lattices_Obounded__lattice__bot(U_7919) ),
inference(variable_rename,[status(thm)],[f_2329_1]) ).
cnf(f_2329_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7919),c_Orderings_Obot__class_Obot(U_7919)),U_7920) = U_7920
| ~ class_Lattices_Obounded__lattice__bot(U_7919) ),
inference(clausify,[status(thm)],[f_2329_2]) ).
fof(f_2330_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_2330_2,plain,
! [U_7922,U_7921] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7921),U_7922),c_Orderings_Obot__class_Obot(U_7921)) = U_7922
| ~ class_Lattices_Obounded__lattice__bot(U_7921) ),
inference(variable_rename,[status(thm)],[f_2330_1]) ).
cnf(f_2330_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7921),U_7922),c_Orderings_Obot__class_Obot(U_7921)) = U_7922
| ~ class_Lattices_Obounded__lattice__bot(U_7921) ),
inference(clausify,[status(thm)],[f_2330_2]) ).
fof(f_2331_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
| V_y_2 != c_Orderings_Obot__class_Obot(T_b)
| V_x_2 != c_Orderings_Obot__class_Obot(T_b) )
& ( ( V_y_2 = c_Orderings_Obot__class_Obot(T_b)
& V_x_2 = c_Orderings_Obot__class_Obot(T_b) )
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) != c_Orderings_Obot__class_Obot(T_b) ) )
| ~ class_Lattices_Obounded__lattice__bot(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sup__eq__bot__iff]) ).
fof(f_2331_2,plain,
! [U_7925,U_7924,U_7923] :
( ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7923),U_7924),U_7925) = c_Orderings_Obot__class_Obot(U_7923)
| U_7925 != c_Orderings_Obot__class_Obot(U_7923)
| U_7924 != c_Orderings_Obot__class_Obot(U_7923) )
& ( ( U_7925 = c_Orderings_Obot__class_Obot(U_7923)
& U_7924 = c_Orderings_Obot__class_Obot(U_7923) )
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7923),U_7924),U_7925) != c_Orderings_Obot__class_Obot(U_7923) ) )
| ~ class_Lattices_Obounded__lattice__bot(U_7923) ),
inference(variable_rename,[status(thm)],[f_2331_1]) ).
cnf(f_2331_3,plain,
( U_7924 = c_Orderings_Obot__class_Obot(U_7923)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7923),U_7924),U_7925) != c_Orderings_Obot__class_Obot(U_7923)
| ~ class_Lattices_Obounded__lattice__bot(U_7923) ),
inference(clausify,[status(thm)],[f_2331_2]) ).
cnf(f_2331_4,plain,
( U_7925 = c_Orderings_Obot__class_Obot(U_7923)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7923),U_7924),U_7925) != c_Orderings_Obot__class_Obot(U_7923)
| ~ class_Lattices_Obounded__lattice__bot(U_7923) ),
inference(clausify,[status(thm)],[f_2331_2]) ).
cnf(f_2331_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_7923),U_7924),U_7925) = c_Orderings_Obot__class_Obot(U_7923)
| U_7925 != c_Orderings_Obot__class_Obot(U_7923)
| U_7924 != c_Orderings_Obot__class_Obot(U_7923)
| ~ class_Lattices_Obounded__lattice__bot(U_7923) ),
inference(clausify,[status(thm)],[f_2331_2]) ).
fof(f_2332_1,plain,
! [V_B_2,V_A_2,T_c,T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff]) ).
fof(f_2332_2,plain,
! [U_7929,U_7928,U_7927,U_7926] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7926,U_7927)),c_Sum__Type_OPlus(U_7926,U_7927,U_7928,U_7929)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7927),U_7929))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7926),U_7928)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7927),U_7929))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_7926),U_7928)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7926,U_7927)),c_Sum__Type_OPlus(U_7926,U_7927,U_7928,U_7929))) ) ),
inference(variable_rename,[status(thm)],[f_2332_1]) ).
fof(f_2332_3,plain,
( ! [U_7937,U_7935,U_7933,U_7931] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7931,U_7933)),c_Sum__Type_OPlus(U_7931,U_7933,U_7935,U_7937)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7933),U_7937))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7931),U_7935)) )
& ! [U_7936,U_7934,U_7932,U_7930] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7932),U_7936))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_7930),U_7934)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7930,U_7932)),c_Sum__Type_OPlus(U_7930,U_7932,U_7934,U_7936))) ) ),
inference(miniscope,[status(thm)],[f_2332_2]) ).
cnf(f_2332_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7930),U_7934))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7930,U_7932)),c_Sum__Type_OPlus(U_7930,U_7932,U_7934,U_7936))) ),
inference(clausify,[status(thm)],[f_2332_3]) ).
cnf(f_2332_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7932),U_7936))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7930,U_7932)),c_Sum__Type_OPlus(U_7930,U_7932,U_7934,U_7936))) ),
inference(clausify,[status(thm)],[f_2332_3]) ).
cnf(f_2332_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7931,U_7933)),c_Sum__Type_OPlus(U_7931,U_7933,U_7935,U_7937)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7933),U_7937))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7931),U_7935)) ),
inference(clausify,[status(thm)],[f_2332_3]) ).
fof(f_2333_1,plain,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__Plus]) ).
fof(f_2333_2,plain,
! [U_7941,U_7940,U_7939,U_7938] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7938,U_7940)),c_Sum__Type_OPlus(U_7938,U_7940,U_7939,U_7941)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7940),U_7941))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7938),U_7939)) ),
inference(variable_rename,[status(thm)],[f_2333_1]) ).
cnf(f_2333_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7938,U_7940)),c_Sum__Type_OPlus(U_7938,U_7940,U_7939,U_7941)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7940),U_7941))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_7938),U_7939)) ),
inference(clausify,[status(thm)],[f_2333_2]) ).
fof(f_2334_1,plain,
! [V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J]) ).
fof(f_2334_2,plain,
! [U_7945,U_7944,U_7943,U_7942] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7942),U_7944))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7942,U_7943)),c_Sum__Type_OPlus(U_7942,U_7943,U_7944,U_7945))) ),
inference(variable_rename,[status(thm)],[f_2334_1]) ).
cnf(f_2334_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7942),U_7944))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7942,U_7943)),c_Sum__Type_OPlus(U_7942,U_7943,U_7944,U_7945))) ),
inference(clausify,[status(thm)],[f_2334_2]) ).
fof(f_2335_1,plain,
! [V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J]) ).
fof(f_2335_2,plain,
! [U_7949,U_7948,U_7947,U_7946] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_7947),U_7949))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7946,U_7947)),c_Sum__Type_OPlus(U_7946,U_7947,U_7948,U_7949))) ),
inference(variable_rename,[status(thm)],[f_2335_1]) ).
fof(f_2335_3,plain,
! [U_7949,U_7948,U_7947] :
( ! [U_7946] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7946,U_7947)),c_Sum__Type_OPlus(U_7946,U_7947,U_7948,U_7949)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_7947),U_7949)) ),
inference(miniscope,[status(thm)],[f_2335_2]) ).
cnf(f_2335_4,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_7946,U_7947)),c_Sum__Type_OPlus(U_7946,U_7947,U_7948,U_7949)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_7947),U_7949)) ),
inference(clausify,[status(thm)],[f_2335_3]) ).
fof(f_2336_1,plain,
! [V_f_2,T_c,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__empty]) ).
fof(f_2336_2,plain,
! [U_7952,U_7951,U_7950] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7951,U_7950),U_7952),c_Orderings_Obot__class_Obot(tc_fun(U_7951,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_7950)
| ~ class_Groups_Ocomm__monoid__add(U_7950) ),
inference(variable_rename,[status(thm)],[f_2336_1]) ).
cnf(f_2336_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7951,U_7950),U_7952),c_Orderings_Obot__class_Obot(tc_fun(U_7951,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_7950)
| ~ class_Groups_Ocomm__monoid__add(U_7950) ),
inference(clausify,[status(thm)],[f_2336_2]) ).
fof(f_2337_1,plain,
! [V_g_2,T_c,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Oempty]) ).
fof(f_2337_2,plain,
! [U_7955,U_7954,U_7953] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7954,U_7953),U_7955),c_Orderings_Obot__class_Obot(tc_fun(U_7954,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_7953)
| ~ class_Groups_Ocomm__monoid__add(U_7953) ),
inference(variable_rename,[status(thm)],[f_2337_1]) ).
cnf(f_2337_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_7954,U_7953),U_7955),c_Orderings_Obot__class_Obot(tc_fun(U_7954,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_7953)
| ~ class_Groups_Ocomm__monoid__add(U_7953) ),
inference(clausify,[status(thm)],[f_2337_2]) ).
fof(f_2338_1,plain,
! [V_x_2,V_A_2,T_b] :
( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ),
inference(fof_nnf,[status(thm)],[fact_subset__singletonD]) ).
fof(f_2338_2,plain,
! [U_7958,U_7957,U_7956] :
( U_7957 = hAPP(hAPP(c_Set_Oinsert(U_7956),U_7958),c_Orderings_Obot__class_Obot(tc_fun(U_7956,tc_HOL_Obool)))
| U_7957 = c_Orderings_Obot__class_Obot(tc_fun(U_7956,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7956,tc_HOL_Obool)),U_7957),hAPP(hAPP(c_Set_Oinsert(U_7956),U_7958),c_Orderings_Obot__class_Obot(tc_fun(U_7956,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[f_2338_1]) ).
cnf(f_2338_3,plain,
( U_7957 = hAPP(hAPP(c_Set_Oinsert(U_7956),U_7958),c_Orderings_Obot__class_Obot(tc_fun(U_7956,tc_HOL_Obool)))
| U_7957 = c_Orderings_Obot__class_Obot(tc_fun(U_7956,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7956,tc_HOL_Obool)),U_7957),hAPP(hAPP(c_Set_Oinsert(U_7956),U_7958),c_Orderings_Obot__class_Obot(tc_fun(U_7956,tc_HOL_Obool))))) ),
inference(clausify,[status(thm)],[f_2338_2]) ).
fof(f_2339_1,plain,
! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_A_2),
inference(fof_nnf,[status(thm)],[fact_insert__is__Un]) ).
fof(f_2339_2,plain,
! [U_7961,U_7960,U_7959] : hAPP(hAPP(c_Set_Oinsert(U_7959),U_7960),U_7961) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7959,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7959),U_7960),c_Orderings_Obot__class_Obot(tc_fun(U_7959,tc_HOL_Obool)))),U_7961),
inference(variable_rename,[status(thm)],[f_2339_1]) ).
cnf(f_2339_3,plain,
hAPP(hAPP(c_Set_Oinsert(U_7959),U_7960),U_7961) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_7959,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_7959),U_7960),c_Orderings_Obot__class_Obot(tc_fun(U_7959,tc_HOL_Obool)))),U_7961),
inference(clausify,[status(thm)],[f_2339_2]) ).
fof(f_2340_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty__iff2]) ).
fof(f_2340_2,plain,
! [U_7964,U_7963,U_7962] :
( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_7962,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_7962,U_7963,U_7964)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7962),U_7963),U_7964)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7962),U_7963),U_7964))
| c_Orderings_Obot__class_Obot(tc_fun(U_7962,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_7962,U_7963,U_7964) ) )
| ~ class_Orderings_Oorder(U_7962) ),
inference(variable_rename,[status(thm)],[f_2340_1]) ).
cnf(f_2340_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7962),U_7963),U_7964))
| c_Orderings_Obot__class_Obot(tc_fun(U_7962,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_7962,U_7963,U_7964)
| ~ class_Orderings_Oorder(U_7962) ),
inference(clausify,[status(thm)],[f_2340_2]) ).
cnf(f_2340_4,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_7962,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_7962,U_7963,U_7964)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7962),U_7963),U_7964))
| ~ class_Orderings_Oorder(U_7962) ),
inference(clausify,[status(thm)],[f_2340_2]) ).
fof(f_2341_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
| c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty__iff]) ).
fof(f_2341_2,plain,
! [U_7967,U_7966,U_7965] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost(U_7965,U_7966,U_7967) = c_Orderings_Obot__class_Obot(tc_fun(U_7965,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7965),U_7966),U_7967)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7965),U_7966),U_7967))
| c_SetInterval_Oord__class_OatLeastAtMost(U_7965,U_7966,U_7967) != c_Orderings_Obot__class_Obot(tc_fun(U_7965,tc_HOL_Obool)) ) )
| ~ class_Orderings_Oorder(U_7965) ),
inference(variable_rename,[status(thm)],[f_2341_1]) ).
cnf(f_2341_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7965),U_7966),U_7967))
| c_SetInterval_Oord__class_OatLeastAtMost(U_7965,U_7966,U_7967) != c_Orderings_Obot__class_Obot(tc_fun(U_7965,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_7965) ),
inference(clausify,[status(thm)],[f_2341_2]) ).
cnf(f_2341_4,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(U_7965,U_7966,U_7967) = c_Orderings_Obot__class_Obot(tc_fun(U_7965,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7965),U_7966),U_7967))
| ~ class_Orderings_Oorder(U_7965) ),
inference(clausify,[status(thm)],[f_2341_2]) ).
fof(f_2342_1,plain,
! [V_a_2,V_b_2,T_b] :
( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty]) ).
fof(f_2342_2,plain,
! [U_7970,U_7969,U_7968] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_7968,U_7970,U_7969) = c_Orderings_Obot__class_Obot(tc_fun(U_7968,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7968),U_7969),U_7970))
| ~ class_Orderings_Oorder(U_7968) ),
inference(variable_rename,[status(thm)],[f_2342_1]) ).
cnf(f_2342_3,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(U_7968,U_7970,U_7969) = c_Orderings_Obot__class_Obot(tc_fun(U_7968,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7968),U_7969),U_7970))
| ~ class_Orderings_Oorder(U_7968) ),
inference(clausify,[status(thm)],[f_2342_2]) ).
fof(f_2343_1,plain,
! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_Diff__insert]) ).
fof(f_2343_2,plain,
! [U_7974,U_7973,U_7972,U_7971] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7971,tc_HOL_Obool)),U_7972),hAPP(hAPP(c_Set_Oinsert(U_7971),U_7973),U_7974)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7971,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7971,tc_HOL_Obool)),U_7972),U_7974)),hAPP(hAPP(c_Set_Oinsert(U_7971),U_7973),c_Orderings_Obot__class_Obot(tc_fun(U_7971,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_2343_1]) ).
cnf(f_2343_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7971,tc_HOL_Obool)),U_7972),hAPP(hAPP(c_Set_Oinsert(U_7971),U_7973),U_7974)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7971,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7971,tc_HOL_Obool)),U_7972),U_7974)),hAPP(hAPP(c_Set_Oinsert(U_7971),U_7973),c_Orderings_Obot__class_Obot(tc_fun(U_7971,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_2343_2]) ).
fof(f_2344_1,plain,
! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2),
inference(fof_nnf,[status(thm)],[fact_Diff__insert2]) ).
fof(f_2344_2,plain,
! [U_7978,U_7977,U_7976,U_7975] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7975,tc_HOL_Obool)),U_7976),hAPP(hAPP(c_Set_Oinsert(U_7975),U_7977),U_7978)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7975,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7975,tc_HOL_Obool)),U_7976),hAPP(hAPP(c_Set_Oinsert(U_7975),U_7977),c_Orderings_Obot__class_Obot(tc_fun(U_7975,tc_HOL_Obool))))),U_7978),
inference(variable_rename,[status(thm)],[f_2344_1]) ).
cnf(f_2344_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7975,tc_HOL_Obool)),U_7976),hAPP(hAPP(c_Set_Oinsert(U_7975),U_7977),U_7978)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7975,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7975,tc_HOL_Obool)),U_7976),hAPP(hAPP(c_Set_Oinsert(U_7975),U_7977),c_Orderings_Obot__class_Obot(tc_fun(U_7975,tc_HOL_Obool))))),U_7978),
inference(clausify,[status(thm)],[f_2344_2]) ).
fof(f_2345_1,plain,
! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2),
inference(fof_nnf,[status(thm)],[fact_insert__Diff__single]) ).
fof(f_2345_2,plain,
! [U_7981,U_7980,U_7979] : hAPP(hAPP(c_Set_Oinsert(U_7979),U_7980),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7979,tc_HOL_Obool)),U_7981),hAPP(hAPP(c_Set_Oinsert(U_7979),U_7980),c_Orderings_Obot__class_Obot(tc_fun(U_7979,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_7979),U_7980),U_7981),
inference(variable_rename,[status(thm)],[f_2345_1]) ).
cnf(f_2345_3,plain,
hAPP(hAPP(c_Set_Oinsert(U_7979),U_7980),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7979,tc_HOL_Obool)),U_7981),hAPP(hAPP(c_Set_Oinsert(U_7979),U_7980),c_Orderings_Obot__class_Obot(tc_fun(U_7979,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_7979),U_7980),U_7981),
inference(clausify,[status(thm)],[f_2345_2]) ).
fof(f_2346_1,plain,
! [V_a_2,V_b_2,T_b] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty]) ).
fof(f_2346_2,plain,
! [U_7984,U_7983,U_7982] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7982,U_7984),U_7983) = c_Orderings_Obot__class_Obot(tc_fun(U_7982,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7982),U_7983),U_7984))
| ~ class_Orderings_Oorder(U_7982) ),
inference(variable_rename,[status(thm)],[f_2346_1]) ).
cnf(f_2346_3,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7982,U_7984),U_7983) = c_Orderings_Obot__class_Obot(tc_fun(U_7982,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7982),U_7983),U_7984))
| ~ class_Orderings_Oorder(U_7982) ),
inference(clausify,[status(thm)],[f_2346_2]) ).
fof(f_2347_1,plain,
! [T_b] : hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_card_Oempty]) ).
fof(f_2347_2,plain,
! [U_7985] : hAPP(c_Finite__Set_Ocard(U_7985),c_Orderings_Obot__class_Obot(tc_fun(U_7985,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_2347_1]) ).
cnf(f_2347_3,plain,
hAPP(c_Finite__Set_Ocard(U_7985),c_Orderings_Obot__class_Obot(tc_fun(U_7985,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_2347_2]) ).
fof(f_2348_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty__iff]) ).
fof(f_2348_2,plain,
! [U_7988,U_7987,U_7986] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7986,U_7987),U_7988) = c_Orderings_Obot__class_Obot(tc_fun(U_7986,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7986),U_7987),U_7988)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7986),U_7987),U_7988))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7986,U_7987),U_7988) != c_Orderings_Obot__class_Obot(tc_fun(U_7986,tc_HOL_Obool)) ) )
| ~ class_Orderings_Oorder(U_7986) ),
inference(variable_rename,[status(thm)],[f_2348_1]) ).
cnf(f_2348_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7986),U_7987),U_7988))
| hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7986,U_7987),U_7988) != c_Orderings_Obot__class_Obot(tc_fun(U_7986,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_7986) ),
inference(clausify,[status(thm)],[f_2348_2]) ).
cnf(f_2348_4,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7986,U_7987),U_7988) = c_Orderings_Obot__class_Obot(tc_fun(U_7986,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7986),U_7987),U_7988))
| ~ class_Orderings_Oorder(U_7986) ),
inference(clausify,[status(thm)],[f_2348_2]) ).
fof(f_2349_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
| c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty__iff2]) ).
fof(f_2349_2,plain,
! [U_7991,U_7990,U_7989] :
( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_7989,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7989,U_7990),U_7991)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7989),U_7990),U_7991)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7989),U_7990),U_7991))
| c_Orderings_Obot__class_Obot(tc_fun(U_7989,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7989,U_7990),U_7991) ) )
| ~ class_Orderings_Oorder(U_7989) ),
inference(variable_rename,[status(thm)],[f_2349_1]) ).
cnf(f_2349_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7989),U_7990),U_7991))
| c_Orderings_Obot__class_Obot(tc_fun(U_7989,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7989,U_7990),U_7991)
| ~ class_Orderings_Oorder(U_7989) ),
inference(clausify,[status(thm)],[f_2349_2]) ).
cnf(f_2349_4,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_7989,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_7989,U_7990),U_7991)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7989),U_7990),U_7991))
| ~ class_Orderings_Oorder(U_7989) ),
inference(clausify,[status(thm)],[f_2349_2]) ).
fof(f_2350_1,plain,
! [V_b_2,V_a_2,T_b] :
( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
| V_a_2 != V_b_2
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton_H]) ).
fof(f_2350_2,plain,
! [U_7994,U_7993,U_7992] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_7992,U_7993,U_7994) = hAPP(hAPP(c_Set_Oinsert(U_7992),U_7993),c_Orderings_Obot__class_Obot(tc_fun(U_7992,tc_HOL_Obool)))
| U_7993 != U_7994
| ~ class_Orderings_Oorder(U_7992) ),
inference(variable_rename,[status(thm)],[f_2350_1]) ).
cnf(f_2350_3,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(U_7992,U_7993,U_7994) = hAPP(hAPP(c_Set_Oinsert(U_7992),U_7993),c_Orderings_Obot__class_Obot(tc_fun(U_7992,tc_HOL_Obool)))
| U_7993 != U_7994
| ~ class_Orderings_Oorder(U_7992) ),
inference(clausify,[status(thm)],[f_2350_2]) ).
fof(f_2351_1,plain,
! [V_c_2,V_b_2,V_a_2,T_b] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,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_b,V_a_2,V_b_2) != hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton__iff]) ).
fof(f_2351_2,plain,
! [U_7998,U_7997,U_7996,U_7995] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost(U_7995,U_7996,U_7997) = hAPP(hAPP(c_Set_Oinsert(U_7995),U_7998),c_Orderings_Obot__class_Obot(tc_fun(U_7995,tc_HOL_Obool)))
| U_7997 != U_7998
| U_7996 != U_7997 )
& ( ( U_7997 = U_7998
& U_7996 = U_7997 )
| c_SetInterval_Oord__class_OatLeastAtMost(U_7995,U_7996,U_7997) != hAPP(hAPP(c_Set_Oinsert(U_7995),U_7998),c_Orderings_Obot__class_Obot(tc_fun(U_7995,tc_HOL_Obool))) ) )
| ~ class_Orderings_Oorder(U_7995) ),
inference(variable_rename,[status(thm)],[f_2351_1]) ).
cnf(f_2351_3,plain,
( U_7996 = U_7997
| c_SetInterval_Oord__class_OatLeastAtMost(U_7995,U_7996,U_7997) != hAPP(hAPP(c_Set_Oinsert(U_7995),U_7998),c_Orderings_Obot__class_Obot(tc_fun(U_7995,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_7995) ),
inference(clausify,[status(thm)],[f_2351_2]) ).
cnf(f_2351_4,plain,
( U_7997 = U_7998
| c_SetInterval_Oord__class_OatLeastAtMost(U_7995,U_7996,U_7997) != hAPP(hAPP(c_Set_Oinsert(U_7995),U_7998),c_Orderings_Obot__class_Obot(tc_fun(U_7995,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_7995) ),
inference(clausify,[status(thm)],[f_2351_2]) ).
cnf(f_2351_5,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(U_7995,U_7996,U_7997) = hAPP(hAPP(c_Set_Oinsert(U_7995),U_7998),c_Orderings_Obot__class_Obot(tc_fun(U_7995,tc_HOL_Obool)))
| U_7997 != U_7998
| U_7996 != U_7997
| ~ class_Orderings_Oorder(U_7995) ),
inference(clausify,[status(thm)],[f_2351_2]) ).
fof(f_2352_1,plain,
! [V_a_2,T_b] :
( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton]) ).
fof(f_2352_2,plain,
! [U_8000,U_7999] :
( c_SetInterval_Oord__class_OatLeastAtMost(U_7999,U_8000,U_8000) = hAPP(hAPP(c_Set_Oinsert(U_7999),U_8000),c_Orderings_Obot__class_Obot(tc_fun(U_7999,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_7999) ),
inference(variable_rename,[status(thm)],[f_2352_1]) ).
cnf(f_2352_3,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(U_7999,U_8000,U_8000) = hAPP(hAPP(c_Set_Oinsert(U_7999),U_8000),c_Orderings_Obot__class_Obot(tc_fun(U_7999,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_7999) ),
inference(clausify,[status(thm)],[f_2352_2]) ).
fof(f_2353_1,plain,
! [V_A_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_subset__Compl__self__eq]) ).
fof(f_2353_2,plain,
! [U_8002,U_8001] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8001,tc_HOL_Obool)),U_8002),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8001,tc_HOL_Obool)),U_8002)))
| U_8002 != c_Orderings_Obot__class_Obot(tc_fun(U_8001,tc_HOL_Obool)) )
& ( U_8002 = c_Orderings_Obot__class_Obot(tc_fun(U_8001,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8001,tc_HOL_Obool)),U_8002),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8001,tc_HOL_Obool)),U_8002))) ) ),
inference(variable_rename,[status(thm)],[f_2353_1]) ).
fof(f_2353_3,plain,
( ! [U_8006,U_8004] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8004,tc_HOL_Obool)),U_8006),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8004,tc_HOL_Obool)),U_8006)))
| U_8006 != c_Orderings_Obot__class_Obot(tc_fun(U_8004,tc_HOL_Obool)) )
& ! [U_8005,U_8003] :
( U_8005 = c_Orderings_Obot__class_Obot(tc_fun(U_8003,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8003,tc_HOL_Obool)),U_8005),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8003,tc_HOL_Obool)),U_8005))) ) ),
inference(miniscope,[status(thm)],[f_2353_2]) ).
cnf(f_2353_4,plain,
( U_8005 = c_Orderings_Obot__class_Obot(tc_fun(U_8003,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8003,tc_HOL_Obool)),U_8005),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8003,tc_HOL_Obool)),U_8005))) ),
inference(clausify,[status(thm)],[f_2353_3]) ).
cnf(f_2353_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8004,tc_HOL_Obool)),U_8006),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8004,tc_HOL_Obool)),U_8006)))
| U_8006 != c_Orderings_Obot__class_Obot(tc_fun(U_8004,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2353_3]) ).
fof(f_2354_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_2354_2,plain,
! [U_8007] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_8007),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_2354_1]) ).
cnf(f_2354_3,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_8007),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_2354_2]) ).
fof(f_2355_1,plain,
! [V_k_2,V_l_2,T_b] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty]) ).
fof(f_2355_2,plain,
! [U_8010,U_8009,U_8008] :
( c_SetInterval_Oord__class_OgreaterThanAtMost(U_8008,U_8010,U_8009) = c_Orderings_Obot__class_Obot(tc_fun(U_8008,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8008),U_8009),U_8010))
| ~ class_Orderings_Oorder(U_8008) ),
inference(variable_rename,[status(thm)],[f_2355_1]) ).
cnf(f_2355_3,plain,
( c_SetInterval_Oord__class_OgreaterThanAtMost(U_8008,U_8010,U_8009) = c_Orderings_Obot__class_Obot(tc_fun(U_8008,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8008),U_8009),U_8010))
| ~ class_Orderings_Oorder(U_8008) ),
inference(clausify,[status(thm)],[f_2355_2]) ).
fof(f_2356_1,plain,
! [V_l_2,V_k_2,T_b] :
( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2))
| c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty__iff]) ).
fof(f_2356_2,plain,
! [U_8013,U_8012,U_8011] :
( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_8011,U_8012,U_8013) = c_Orderings_Obot__class_Obot(tc_fun(U_8011,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8011),U_8012),U_8013)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8011),U_8012),U_8013))
| c_SetInterval_Oord__class_OgreaterThanAtMost(U_8011,U_8012,U_8013) != c_Orderings_Obot__class_Obot(tc_fun(U_8011,tc_HOL_Obool)) ) )
| ~ class_Orderings_Oorder(U_8011) ),
inference(variable_rename,[status(thm)],[f_2356_1]) ).
cnf(f_2356_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8011),U_8012),U_8013))
| c_SetInterval_Oord__class_OgreaterThanAtMost(U_8011,U_8012,U_8013) != c_Orderings_Obot__class_Obot(tc_fun(U_8011,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_8011) ),
inference(clausify,[status(thm)],[f_2356_2]) ).
cnf(f_2356_4,plain,
( c_SetInterval_Oord__class_OgreaterThanAtMost(U_8011,U_8012,U_8013) = c_Orderings_Obot__class_Obot(tc_fun(U_8011,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8011),U_8012),U_8013))
| ~ class_Orderings_Oorder(U_8011) ),
inference(clausify,[status(thm)],[f_2356_2]) ).
fof(f_2357_1,plain,
! [V_l_2,V_k_2,T_b] :
( ( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2))
| c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) ) )
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty__iff2]) ).
fof(f_2357_2,plain,
! [U_8016,U_8015,U_8014] :
( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_8014,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_8014,U_8015,U_8016)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8014),U_8015),U_8016)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8014),U_8015),U_8016))
| c_Orderings_Obot__class_Obot(tc_fun(U_8014,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_8014,U_8015,U_8016) ) )
| ~ class_Orderings_Oorder(U_8014) ),
inference(variable_rename,[status(thm)],[f_2357_1]) ).
cnf(f_2357_3,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8014),U_8015),U_8016))
| c_Orderings_Obot__class_Obot(tc_fun(U_8014,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_8014,U_8015,U_8016)
| ~ class_Orderings_Oorder(U_8014) ),
inference(clausify,[status(thm)],[f_2357_2]) ).
cnf(f_2357_4,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_8014,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_8014,U_8015,U_8016)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8014),U_8015),U_8016))
| ~ class_Orderings_Oorder(U_8014) ),
inference(clausify,[status(thm)],[f_2357_2]) ).
fof(f_2358_1,plain,
! [V_k_2,V_l_2,T_b] :
( c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_greaterThanLessThan__empty]) ).
fof(f_2358_2,plain,
! [U_8019,U_8018,U_8017] :
( c_SetInterval_Oord__class_OgreaterThanLessThan(U_8017,U_8019,U_8018) = c_Orderings_Obot__class_Obot(tc_fun(U_8017,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8017),U_8018),U_8019))
| ~ class_Orderings_Oorder(U_8017) ),
inference(variable_rename,[status(thm)],[f_2358_1]) ).
cnf(f_2358_3,plain,
( c_SetInterval_Oord__class_OgreaterThanLessThan(U_8017,U_8019,U_8018) = c_Orderings_Obot__class_Obot(tc_fun(U_8017,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8017),U_8018),U_8019))
| ~ class_Orderings_Oorder(U_8017) ),
inference(clausify,[status(thm)],[f_2358_2]) ).
fof(f_2359_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]) ).
cnf(f_2359_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(clausify,[status(thm)],[f_2359_1]) ).
fof(f_2360_1,plain,
! [V_c_2,T_c,T_b,V_A_2] :
( ( hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_image__constant__conv]) ).
fof(f_2360_2,plain,
! [U_8023,U_8022,U_8021,U_8020] :
( ( hAPP(c_Set_Oimage(U_8021,U_8022,hAPP(c_COMBK(U_8022,U_8021),U_8023)),U_8020) = hAPP(hAPP(c_Set_Oinsert(U_8022),U_8023),c_Orderings_Obot__class_Obot(tc_fun(U_8022,tc_HOL_Obool)))
| U_8020 = c_Orderings_Obot__class_Obot(tc_fun(U_8021,tc_HOL_Obool)) )
& ( hAPP(c_Set_Oimage(U_8021,U_8022,hAPP(c_COMBK(U_8022,U_8021),U_8023)),U_8020) = c_Orderings_Obot__class_Obot(tc_fun(U_8022,tc_HOL_Obool))
| U_8020 != c_Orderings_Obot__class_Obot(tc_fun(U_8021,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2360_1]) ).
fof(f_2360_3,plain,
( ! [U_8031,U_8029,U_8027,U_8025] :
( hAPP(c_Set_Oimage(U_8027,U_8029,hAPP(c_COMBK(U_8029,U_8027),U_8031)),U_8025) = hAPP(hAPP(c_Set_Oinsert(U_8029),U_8031),c_Orderings_Obot__class_Obot(tc_fun(U_8029,tc_HOL_Obool)))
| U_8025 = c_Orderings_Obot__class_Obot(tc_fun(U_8027,tc_HOL_Obool)) )
& ! [U_8030,U_8028,U_8026,U_8024] :
( hAPP(c_Set_Oimage(U_8026,U_8028,hAPP(c_COMBK(U_8028,U_8026),U_8030)),U_8024) = c_Orderings_Obot__class_Obot(tc_fun(U_8028,tc_HOL_Obool))
| U_8024 != c_Orderings_Obot__class_Obot(tc_fun(U_8026,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2360_2]) ).
cnf(f_2360_4,plain,
( hAPP(c_Set_Oimage(U_8026,U_8028,hAPP(c_COMBK(U_8028,U_8026),U_8030)),U_8024) = c_Orderings_Obot__class_Obot(tc_fun(U_8028,tc_HOL_Obool))
| U_8024 != c_Orderings_Obot__class_Obot(tc_fun(U_8026,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2360_3]) ).
cnf(f_2360_5,plain,
( hAPP(c_Set_Oimage(U_8027,U_8029,hAPP(c_COMBK(U_8029,U_8027),U_8031)),U_8025) = hAPP(hAPP(c_Set_Oinsert(U_8029),U_8031),c_Orderings_Obot__class_Obot(tc_fun(U_8029,tc_HOL_Obool)))
| U_8025 = c_Orderings_Obot__class_Obot(tc_fun(U_8027,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2360_3]) ).
fof(f_2361_1,plain,
! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
( ( hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I1_J]) ).
fof(f_2361_2,plain,
! [U_8036,U_8035,U_8034,U_8033,U_8032] :
( ( hAPP(hAPP(c_Set_Oinsert(U_8034),U_8035),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8033,tc_fun(U_8034,tc_HOL_Obool)),U_8032),U_8036)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8033,tc_fun(U_8034,tc_HOL_Obool)),U_8032),hAPP(hAPP(c_COMBB(tc_fun(U_8034,tc_HOL_Obool),tc_fun(U_8034,tc_HOL_Obool),U_8033),hAPP(c_Set_Oinsert(U_8034),U_8035)),U_8036))
| U_8032 = c_Orderings_Obot__class_Obot(tc_fun(U_8033,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Set_Oinsert(U_8034),U_8035),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8033,tc_fun(U_8034,tc_HOL_Obool)),U_8032),U_8036)) = hAPP(hAPP(c_Set_Oinsert(U_8034),U_8035),c_Orderings_Obot__class_Obot(tc_fun(U_8034,tc_HOL_Obool)))
| U_8032 != c_Orderings_Obot__class_Obot(tc_fun(U_8033,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2361_1]) ).
fof(f_2361_3,plain,
( ! [U_8046,U_8044,U_8042,U_8040,U_8038] :
( hAPP(hAPP(c_Set_Oinsert(U_8042),U_8044),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8040,tc_fun(U_8042,tc_HOL_Obool)),U_8038),U_8046)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8040,tc_fun(U_8042,tc_HOL_Obool)),U_8038),hAPP(hAPP(c_COMBB(tc_fun(U_8042,tc_HOL_Obool),tc_fun(U_8042,tc_HOL_Obool),U_8040),hAPP(c_Set_Oinsert(U_8042),U_8044)),U_8046))
| U_8038 = c_Orderings_Obot__class_Obot(tc_fun(U_8040,tc_HOL_Obool)) )
& ! [U_8045,U_8043,U_8041,U_8039,U_8037] :
( hAPP(hAPP(c_Set_Oinsert(U_8041),U_8043),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8039,tc_fun(U_8041,tc_HOL_Obool)),U_8037),U_8045)) = hAPP(hAPP(c_Set_Oinsert(U_8041),U_8043),c_Orderings_Obot__class_Obot(tc_fun(U_8041,tc_HOL_Obool)))
| U_8037 != c_Orderings_Obot__class_Obot(tc_fun(U_8039,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2361_2]) ).
cnf(f_2361_4,plain,
( hAPP(hAPP(c_Set_Oinsert(U_8041),U_8043),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8039,tc_fun(U_8041,tc_HOL_Obool)),U_8037),U_8045)) = hAPP(hAPP(c_Set_Oinsert(U_8041),U_8043),c_Orderings_Obot__class_Obot(tc_fun(U_8041,tc_HOL_Obool)))
| U_8037 != c_Orderings_Obot__class_Obot(tc_fun(U_8039,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2361_3]) ).
cnf(f_2361_5,plain,
( hAPP(hAPP(c_Set_Oinsert(U_8042),U_8044),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8040,tc_fun(U_8042,tc_HOL_Obool)),U_8038),U_8046)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8040,tc_fun(U_8042,tc_HOL_Obool)),U_8038),hAPP(hAPP(c_COMBB(tc_fun(U_8042,tc_HOL_Obool),tc_fun(U_8042,tc_HOL_Obool),U_8040),hAPP(c_Set_Oinsert(U_8042),U_8044)),U_8046))
| U_8038 = c_Orderings_Obot__class_Obot(tc_fun(U_8040,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2361_3]) ).
fof(f_2362_1,plain,
! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_UN__singleton]) ).
fof(f_2362_2,plain,
! [U_8048,U_8047] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8047,tc_fun(U_8047,tc_HOL_Obool)),U_8048),hAPP(hAPP(c_COMBC(U_8047,tc_fun(U_8047,tc_HOL_Obool),tc_fun(U_8047,tc_HOL_Obool)),c_Set_Oinsert(U_8047)),c_Orderings_Obot__class_Obot(tc_fun(U_8047,tc_HOL_Obool)))) = U_8048,
inference(variable_rename,[status(thm)],[f_2362_1]) ).
cnf(f_2362_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8047,tc_fun(U_8047,tc_HOL_Obool)),U_8048),hAPP(hAPP(c_COMBC(U_8047,tc_fun(U_8047,tc_HOL_Obool),tc_fun(U_8047,tc_HOL_Obool)),c_Set_Oinsert(U_8047)),c_Orderings_Obot__class_Obot(tc_fun(U_8047,tc_HOL_Obool)))) = U_8048,
inference(clausify,[status(thm)],[f_2362_2]) ).
fof(f_2363_1,plain,
! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I1_J]) ).
fof(f_2363_2,plain,
! [U_8053,U_8052,U_8051,U_8050,U_8049] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8050,tc_fun(U_8051,tc_HOL_Obool)),U_8049),hAPP(hAPP(c_COMBB(tc_fun(U_8051,tc_HOL_Obool),tc_fun(U_8051,tc_HOL_Obool),U_8050),hAPP(c_Set_Oinsert(U_8051),U_8052)),U_8053)) = hAPP(hAPP(c_Set_Oinsert(U_8051),U_8052),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8050,tc_fun(U_8051,tc_HOL_Obool)),U_8049),U_8053))
| U_8049 = c_Orderings_Obot__class_Obot(tc_fun(U_8050,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8050,tc_fun(U_8051,tc_HOL_Obool)),U_8049),hAPP(hAPP(c_COMBB(tc_fun(U_8051,tc_HOL_Obool),tc_fun(U_8051,tc_HOL_Obool),U_8050),hAPP(c_Set_Oinsert(U_8051),U_8052)),U_8053)) = c_Orderings_Obot__class_Obot(tc_fun(U_8051,tc_HOL_Obool))
| U_8049 != c_Orderings_Obot__class_Obot(tc_fun(U_8050,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2363_1]) ).
fof(f_2363_3,plain,
( ! [U_8063,U_8061,U_8059,U_8057,U_8055] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8057,tc_fun(U_8059,tc_HOL_Obool)),U_8055),hAPP(hAPP(c_COMBB(tc_fun(U_8059,tc_HOL_Obool),tc_fun(U_8059,tc_HOL_Obool),U_8057),hAPP(c_Set_Oinsert(U_8059),U_8061)),U_8063)) = hAPP(hAPP(c_Set_Oinsert(U_8059),U_8061),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8057,tc_fun(U_8059,tc_HOL_Obool)),U_8055),U_8063))
| U_8055 = c_Orderings_Obot__class_Obot(tc_fun(U_8057,tc_HOL_Obool)) )
& ! [U_8062,U_8060,U_8058,U_8056,U_8054] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8056,tc_fun(U_8058,tc_HOL_Obool)),U_8054),hAPP(hAPP(c_COMBB(tc_fun(U_8058,tc_HOL_Obool),tc_fun(U_8058,tc_HOL_Obool),U_8056),hAPP(c_Set_Oinsert(U_8058),U_8060)),U_8062)) = c_Orderings_Obot__class_Obot(tc_fun(U_8058,tc_HOL_Obool))
| U_8054 != c_Orderings_Obot__class_Obot(tc_fun(U_8056,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2363_2]) ).
cnf(f_2363_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8056,tc_fun(U_8058,tc_HOL_Obool)),U_8054),hAPP(hAPP(c_COMBB(tc_fun(U_8058,tc_HOL_Obool),tc_fun(U_8058,tc_HOL_Obool),U_8056),hAPP(c_Set_Oinsert(U_8058),U_8060)),U_8062)) = c_Orderings_Obot__class_Obot(tc_fun(U_8058,tc_HOL_Obool))
| U_8054 != c_Orderings_Obot__class_Obot(tc_fun(U_8056,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2363_3]) ).
cnf(f_2363_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8057,tc_fun(U_8059,tc_HOL_Obool)),U_8055),hAPP(hAPP(c_COMBB(tc_fun(U_8059,tc_HOL_Obool),tc_fun(U_8059,tc_HOL_Obool),U_8057),hAPP(c_Set_Oinsert(U_8059),U_8061)),U_8063)) = hAPP(hAPP(c_Set_Oinsert(U_8059),U_8061),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8057,tc_fun(U_8059,tc_HOL_Obool)),U_8055),U_8063))
| U_8055 = c_Orderings_Obot__class_Obot(tc_fun(U_8057,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2363_3]) ).
fof(f_2364_1,plain,
! [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)) )
& ( ~ hBOOL(hAPP(hAPP(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)) != c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastatMost__empty__iff2]) ).
fof(f_2364_2,plain,
! [U_8065,U_8064] :
( ( 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),U_8064,U_8065)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8064),U_8065)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8064),U_8065))
| 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),U_8064,U_8065) ) ),
inference(variable_rename,[status(thm)],[f_2364_1]) ).
fof(f_2364_3,plain,
( ! [U_8069,U_8067] :
( 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),U_8067,U_8069)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8067),U_8069)) )
& ! [U_8068,U_8066] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8066),U_8068))
| 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),U_8066,U_8068) ) ),
inference(miniscope,[status(thm)],[f_2364_2]) ).
cnf(f_2364_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8066),U_8068))
| 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),U_8066,U_8068) ),
inference(clausify,[status(thm)],[f_2364_3]) ).
cnf(f_2364_5,plain,
( 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),U_8067,U_8069)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8067),U_8069)) ),
inference(clausify,[status(thm)],[f_2364_3]) ).
fof(f_2365_1,plain,
! [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)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastatMost__empty__iff]) ).
fof(f_2365_2,plain,
! [U_8071,U_8070] :
( ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8070,U_8071) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8070),U_8071)) )
& ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8070),U_8071))
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8070,U_8071) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2365_1]) ).
fof(f_2365_3,plain,
( ! [U_8075,U_8073] :
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8073,U_8075) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8073),U_8075)) )
& ! [U_8074,U_8072] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8072),U_8074))
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8072,U_8074) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2365_2]) ).
cnf(f_2365_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8072),U_8074))
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8072,U_8074) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2365_3]) ).
cnf(f_2365_5,plain,
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8073,U_8075) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8073),U_8075)) ),
inference(clausify,[status(thm)],[f_2365_3]) ).
fof(f_2366_1,plain,
! [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) = 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))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastatMost__empty]) ).
fof(f_2366_2,plain,
! [U_8077,U_8076] :
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8077,U_8076) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8077),U_8076))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8076),U_8077)) ),
inference(variable_rename,[status(thm)],[f_2366_1]) ).
cnf(f_2366_3,plain,
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8077,U_8076) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8077),U_8076))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8076),U_8077)) ),
inference(clausify,[status(thm)],[f_2366_2]) ).
fof(f_2367_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I2_J]) ).
fof(f_2367_2,plain,
! [U_8082,U_8081,U_8080,U_8079,U_8078] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8080,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8079,tc_fun(U_8080,tc_HOL_Obool)),U_8078),U_8081)),U_8082) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8079,tc_fun(U_8080,tc_HOL_Obool)),U_8078),hAPP(hAPP(c_COMBC(U_8079,tc_fun(U_8080,tc_HOL_Obool),tc_fun(U_8080,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8080,tc_HOL_Obool),tc_fun(tc_fun(U_8080,tc_HOL_Obool),tc_fun(U_8080,tc_HOL_Obool)),U_8079),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8080,tc_HOL_Obool))),U_8081)),U_8082))
| U_8078 = c_Orderings_Obot__class_Obot(tc_fun(U_8079,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8080,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8079,tc_fun(U_8080,tc_HOL_Obool)),U_8078),U_8081)),U_8082) = U_8082
| U_8078 != c_Orderings_Obot__class_Obot(tc_fun(U_8079,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2367_1]) ).
fof(f_2367_3,plain,
( ! [U_8092,U_8090,U_8088,U_8086,U_8084] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8088,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8086,tc_fun(U_8088,tc_HOL_Obool)),U_8084),U_8090)),U_8092) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8086,tc_fun(U_8088,tc_HOL_Obool)),U_8084),hAPP(hAPP(c_COMBC(U_8086,tc_fun(U_8088,tc_HOL_Obool),tc_fun(U_8088,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8088,tc_HOL_Obool),tc_fun(tc_fun(U_8088,tc_HOL_Obool),tc_fun(U_8088,tc_HOL_Obool)),U_8086),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8088,tc_HOL_Obool))),U_8090)),U_8092))
| U_8084 = c_Orderings_Obot__class_Obot(tc_fun(U_8086,tc_HOL_Obool)) )
& ! [U_8091,U_8089,U_8087,U_8085,U_8083] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8087,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8085,tc_fun(U_8087,tc_HOL_Obool)),U_8083),U_8089)),U_8091) = U_8091
| U_8083 != c_Orderings_Obot__class_Obot(tc_fun(U_8085,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2367_2]) ).
cnf(f_2367_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8087,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8085,tc_fun(U_8087,tc_HOL_Obool)),U_8083),U_8089)),U_8091) = U_8091
| U_8083 != c_Orderings_Obot__class_Obot(tc_fun(U_8085,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2367_3]) ).
cnf(f_2367_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8088,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8086,tc_fun(U_8088,tc_HOL_Obool)),U_8084),U_8090)),U_8092) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8086,tc_fun(U_8088,tc_HOL_Obool)),U_8084),hAPP(hAPP(c_COMBC(U_8086,tc_fun(U_8088,tc_HOL_Obool),tc_fun(U_8088,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8088,tc_HOL_Obool),tc_fun(tc_fun(U_8088,tc_HOL_Obool),tc_fun(U_8088,tc_HOL_Obool)),U_8086),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8088,tc_HOL_Obool))),U_8090)),U_8092))
| U_8084 = c_Orderings_Obot__class_Obot(tc_fun(U_8086,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2367_3]) ).
fof(f_2368_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I3_J]) ).
fof(f_2368_2,plain,
! [U_8097,U_8096,U_8095,U_8094,U_8093] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8095,tc_HOL_Obool)),U_8096),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8094,tc_fun(U_8095,tc_HOL_Obool)),U_8093),U_8097)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8094,tc_fun(U_8095,tc_HOL_Obool)),U_8093),hAPP(hAPP(c_COMBB(tc_fun(U_8095,tc_HOL_Obool),tc_fun(U_8095,tc_HOL_Obool),U_8094),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8095,tc_HOL_Obool)),U_8096)),U_8097))
| U_8093 = c_Orderings_Obot__class_Obot(tc_fun(U_8094,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8095,tc_HOL_Obool)),U_8096),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8094,tc_fun(U_8095,tc_HOL_Obool)),U_8093),U_8097)) = U_8096
| U_8093 != c_Orderings_Obot__class_Obot(tc_fun(U_8094,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2368_1]) ).
fof(f_2368_3,plain,
( ! [U_8107,U_8105,U_8103,U_8101,U_8099] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8103,tc_HOL_Obool)),U_8105),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8101,tc_fun(U_8103,tc_HOL_Obool)),U_8099),U_8107)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8101,tc_fun(U_8103,tc_HOL_Obool)),U_8099),hAPP(hAPP(c_COMBB(tc_fun(U_8103,tc_HOL_Obool),tc_fun(U_8103,tc_HOL_Obool),U_8101),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8103,tc_HOL_Obool)),U_8105)),U_8107))
| U_8099 = c_Orderings_Obot__class_Obot(tc_fun(U_8101,tc_HOL_Obool)) )
& ! [U_8106,U_8104,U_8102,U_8100,U_8098] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8102,tc_HOL_Obool)),U_8104),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8100,tc_fun(U_8102,tc_HOL_Obool)),U_8098),U_8106)) = U_8104
| U_8098 != c_Orderings_Obot__class_Obot(tc_fun(U_8100,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2368_2]) ).
cnf(f_2368_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8102,tc_HOL_Obool)),U_8104),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8100,tc_fun(U_8102,tc_HOL_Obool)),U_8098),U_8106)) = U_8104
| U_8098 != c_Orderings_Obot__class_Obot(tc_fun(U_8100,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2368_3]) ).
cnf(f_2368_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8103,tc_HOL_Obool)),U_8105),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8101,tc_fun(U_8103,tc_HOL_Obool)),U_8099),U_8107)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8101,tc_fun(U_8103,tc_HOL_Obool)),U_8099),hAPP(hAPP(c_COMBB(tc_fun(U_8103,tc_HOL_Obool),tc_fun(U_8103,tc_HOL_Obool),U_8101),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8103,tc_HOL_Obool)),U_8105)),U_8107))
| U_8099 = c_Orderings_Obot__class_Obot(tc_fun(U_8101,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2368_3]) ).
fof(f_2369_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I2_J]) ).
fof(f_2369_2,plain,
! [U_8112,U_8111,U_8110,U_8109,U_8108] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8109,tc_fun(U_8110,tc_HOL_Obool)),U_8108),hAPP(hAPP(c_COMBC(U_8109,tc_fun(U_8110,tc_HOL_Obool),tc_fun(U_8110,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8110,tc_HOL_Obool),tc_fun(tc_fun(U_8110,tc_HOL_Obool),tc_fun(U_8110,tc_HOL_Obool)),U_8109),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8110,tc_HOL_Obool))),U_8111)),U_8112)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8110,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8109,tc_fun(U_8110,tc_HOL_Obool)),U_8108),U_8111)),U_8112)
| U_8108 = c_Orderings_Obot__class_Obot(tc_fun(U_8109,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8109,tc_fun(U_8110,tc_HOL_Obool)),U_8108),hAPP(hAPP(c_COMBC(U_8109,tc_fun(U_8110,tc_HOL_Obool),tc_fun(U_8110,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8110,tc_HOL_Obool),tc_fun(tc_fun(U_8110,tc_HOL_Obool),tc_fun(U_8110,tc_HOL_Obool)),U_8109),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8110,tc_HOL_Obool))),U_8111)),U_8112)) = c_Orderings_Obot__class_Obot(tc_fun(U_8110,tc_HOL_Obool))
| U_8108 != c_Orderings_Obot__class_Obot(tc_fun(U_8109,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2369_1]) ).
fof(f_2369_3,plain,
( ! [U_8122,U_8120,U_8118,U_8116,U_8114] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8116,tc_fun(U_8118,tc_HOL_Obool)),U_8114),hAPP(hAPP(c_COMBC(U_8116,tc_fun(U_8118,tc_HOL_Obool),tc_fun(U_8118,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8118,tc_HOL_Obool),tc_fun(tc_fun(U_8118,tc_HOL_Obool),tc_fun(U_8118,tc_HOL_Obool)),U_8116),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8118,tc_HOL_Obool))),U_8120)),U_8122)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8118,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8116,tc_fun(U_8118,tc_HOL_Obool)),U_8114),U_8120)),U_8122)
| U_8114 = c_Orderings_Obot__class_Obot(tc_fun(U_8116,tc_HOL_Obool)) )
& ! [U_8121,U_8119,U_8117,U_8115,U_8113] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8115,tc_fun(U_8117,tc_HOL_Obool)),U_8113),hAPP(hAPP(c_COMBC(U_8115,tc_fun(U_8117,tc_HOL_Obool),tc_fun(U_8117,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8117,tc_HOL_Obool),tc_fun(tc_fun(U_8117,tc_HOL_Obool),tc_fun(U_8117,tc_HOL_Obool)),U_8115),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8117,tc_HOL_Obool))),U_8119)),U_8121)) = c_Orderings_Obot__class_Obot(tc_fun(U_8117,tc_HOL_Obool))
| U_8113 != c_Orderings_Obot__class_Obot(tc_fun(U_8115,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2369_2]) ).
cnf(f_2369_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8115,tc_fun(U_8117,tc_HOL_Obool)),U_8113),hAPP(hAPP(c_COMBC(U_8115,tc_fun(U_8117,tc_HOL_Obool),tc_fun(U_8117,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8117,tc_HOL_Obool),tc_fun(tc_fun(U_8117,tc_HOL_Obool),tc_fun(U_8117,tc_HOL_Obool)),U_8115),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8117,tc_HOL_Obool))),U_8119)),U_8121)) = c_Orderings_Obot__class_Obot(tc_fun(U_8117,tc_HOL_Obool))
| U_8113 != c_Orderings_Obot__class_Obot(tc_fun(U_8115,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2369_3]) ).
cnf(f_2369_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8116,tc_fun(U_8118,tc_HOL_Obool)),U_8114),hAPP(hAPP(c_COMBC(U_8116,tc_fun(U_8118,tc_HOL_Obool),tc_fun(U_8118,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8118,tc_HOL_Obool),tc_fun(tc_fun(U_8118,tc_HOL_Obool),tc_fun(U_8118,tc_HOL_Obool)),U_8116),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8118,tc_HOL_Obool))),U_8120)),U_8122)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8118,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8116,tc_fun(U_8118,tc_HOL_Obool)),U_8114),U_8120)),U_8122)
| U_8114 = c_Orderings_Obot__class_Obot(tc_fun(U_8116,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2369_3]) ).
fof(f_2370_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I3_J]) ).
fof(f_2370_2,plain,
! [U_8127,U_8126,U_8125,U_8124,U_8123] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8124,tc_fun(U_8125,tc_HOL_Obool)),U_8123),hAPP(hAPP(c_COMBB(tc_fun(U_8125,tc_HOL_Obool),tc_fun(U_8125,tc_HOL_Obool),U_8124),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8125,tc_HOL_Obool)),U_8126)),U_8127)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8125,tc_HOL_Obool)),U_8126),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8124,tc_fun(U_8125,tc_HOL_Obool)),U_8123),U_8127))
| U_8123 = c_Orderings_Obot__class_Obot(tc_fun(U_8124,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8124,tc_fun(U_8125,tc_HOL_Obool)),U_8123),hAPP(hAPP(c_COMBB(tc_fun(U_8125,tc_HOL_Obool),tc_fun(U_8125,tc_HOL_Obool),U_8124),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8125,tc_HOL_Obool)),U_8126)),U_8127)) = c_Orderings_Obot__class_Obot(tc_fun(U_8125,tc_HOL_Obool))
| U_8123 != c_Orderings_Obot__class_Obot(tc_fun(U_8124,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2370_1]) ).
fof(f_2370_3,plain,
( ! [U_8137,U_8135,U_8133,U_8131,U_8129] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8131,tc_fun(U_8133,tc_HOL_Obool)),U_8129),hAPP(hAPP(c_COMBB(tc_fun(U_8133,tc_HOL_Obool),tc_fun(U_8133,tc_HOL_Obool),U_8131),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8133,tc_HOL_Obool)),U_8135)),U_8137)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8133,tc_HOL_Obool)),U_8135),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8131,tc_fun(U_8133,tc_HOL_Obool)),U_8129),U_8137))
| U_8129 = c_Orderings_Obot__class_Obot(tc_fun(U_8131,tc_HOL_Obool)) )
& ! [U_8136,U_8134,U_8132,U_8130,U_8128] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8130,tc_fun(U_8132,tc_HOL_Obool)),U_8128),hAPP(hAPP(c_COMBB(tc_fun(U_8132,tc_HOL_Obool),tc_fun(U_8132,tc_HOL_Obool),U_8130),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8132,tc_HOL_Obool)),U_8134)),U_8136)) = c_Orderings_Obot__class_Obot(tc_fun(U_8132,tc_HOL_Obool))
| U_8128 != c_Orderings_Obot__class_Obot(tc_fun(U_8130,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2370_2]) ).
cnf(f_2370_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8130,tc_fun(U_8132,tc_HOL_Obool)),U_8128),hAPP(hAPP(c_COMBB(tc_fun(U_8132,tc_HOL_Obool),tc_fun(U_8132,tc_HOL_Obool),U_8130),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8132,tc_HOL_Obool)),U_8134)),U_8136)) = c_Orderings_Obot__class_Obot(tc_fun(U_8132,tc_HOL_Obool))
| U_8128 != c_Orderings_Obot__class_Obot(tc_fun(U_8130,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2370_3]) ).
cnf(f_2370_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8131,tc_fun(U_8133,tc_HOL_Obool)),U_8129),hAPP(hAPP(c_COMBB(tc_fun(U_8133,tc_HOL_Obool),tc_fun(U_8133,tc_HOL_Obool),U_8131),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8133,tc_HOL_Obool)),U_8135)),U_8137)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8133,tc_HOL_Obool)),U_8135),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8131,tc_fun(U_8133,tc_HOL_Obool)),U_8129),U_8137))
| U_8129 = c_Orderings_Obot__class_Obot(tc_fun(U_8131,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2370_3]) ).
fof(f_2371_1,plain,
! [V_A_2,T_b] :
( ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
& V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(T_b),V_A_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_card__eq__0__iff]) ).
fof(f_2371_2,plain,
! [U_8139,U_8138] :
( ( hAPP(c_Finite__Set_Ocard(U_8138),U_8139) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8138),U_8139))
& U_8139 != c_Orderings_Obot__class_Obot(tc_fun(U_8138,tc_HOL_Obool)) ) )
& ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8138),U_8139))
| U_8139 = c_Orderings_Obot__class_Obot(tc_fun(U_8138,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_8138),U_8139) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_2371_1]) ).
fof(f_2371_3,plain,
( ! [U_8143,U_8141] :
( hAPP(c_Finite__Set_Ocard(U_8141),U_8143) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8141),U_8143))
& U_8143 != c_Orderings_Obot__class_Obot(tc_fun(U_8141,tc_HOL_Obool)) ) )
& ! [U_8142,U_8140] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8140),U_8142))
| U_8142 = c_Orderings_Obot__class_Obot(tc_fun(U_8140,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_8140),U_8142) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_2371_2]) ).
cnf(f_2371_4,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8140),U_8142))
| U_8142 = c_Orderings_Obot__class_Obot(tc_fun(U_8140,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_8140),U_8142) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_2371_3]) ).
cnf(f_2371_5,plain,
( U_8143 != c_Orderings_Obot__class_Obot(tc_fun(U_8141,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_8141),U_8143) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_2371_3]) ).
cnf(f_2371_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8141),U_8143))
| hAPP(c_Finite__Set_Ocard(U_8141),U_8143) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_2371_3]) ).
fof(f_2372_1,plain,
! [V_k_2,T_b] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_single__Diff__lessThan]) ).
fof(f_2372_2,plain,
! [U_8145,U_8144] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8144,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8144),U_8145),c_Orderings_Obot__class_Obot(tc_fun(U_8144,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_8144),U_8145)) = hAPP(hAPP(c_Set_Oinsert(U_8144),U_8145),c_Orderings_Obot__class_Obot(tc_fun(U_8144,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_8144) ),
inference(variable_rename,[status(thm)],[f_2372_1]) ).
cnf(f_2372_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8144,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8144),U_8145),c_Orderings_Obot__class_Obot(tc_fun(U_8144,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_8144),U_8145)) = hAPP(hAPP(c_Set_Oinsert(U_8144),U_8145),c_Orderings_Obot__class_Obot(tc_fun(U_8144,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_8144) ),
inference(clausify,[status(thm)],[f_2372_2]) ).
fof(f_2373_1,plain,
! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Set_Oinsert(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_image__eq__UN]) ).
fof(f_2373_2,plain,
! [U_8149,U_8148,U_8147,U_8146] : hAPP(c_Set_Oimage(U_8146,U_8147,U_8148),U_8149) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8146,tc_fun(U_8147,tc_HOL_Obool)),U_8149),hAPP(hAPP(c_COMBC(U_8146,tc_fun(U_8147,tc_HOL_Obool),tc_fun(U_8147,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_8147,tc_fun(tc_fun(U_8147,tc_HOL_Obool),tc_fun(U_8147,tc_HOL_Obool)),U_8146),c_Set_Oinsert(U_8147)),U_8148)),c_Orderings_Obot__class_Obot(tc_fun(U_8147,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_2373_1]) ).
cnf(f_2373_3,plain,
hAPP(c_Set_Oimage(U_8146,U_8147,U_8148),U_8149) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8146,tc_fun(U_8147,tc_HOL_Obool)),U_8149),hAPP(hAPP(c_COMBC(U_8146,tc_fun(U_8147,tc_HOL_Obool),tc_fun(U_8147,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_8147,tc_fun(tc_fun(U_8147,tc_HOL_Obool),tc_fun(U_8147,tc_HOL_Obool)),U_8146),c_Set_Oinsert(U_8147)),U_8148)),c_Orderings_Obot__class_Obot(tc_fun(U_8147,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_2373_2]) ).
fof(f_2374_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_2374_2,plain,
! [U_8150] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_8150),hAPP(c_Nat_OSuc,U_8150)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8150),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_2374_1]) ).
cnf(f_2374_3,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_8150),hAPP(c_Nat_OSuc,U_8150)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8150),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_2374_2]) ).
fof(f_2375_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I4_J]) ).
fof(f_2375_2,plain,
! [U_8155,U_8154,U_8153,U_8152,U_8151] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8153,tc_HOL_Obool)),U_8154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8152,tc_fun(U_8153,tc_HOL_Obool)),U_8151),U_8155)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8152,tc_fun(U_8153,tc_HOL_Obool)),U_8151),hAPP(hAPP(c_COMBB(tc_fun(U_8153,tc_HOL_Obool),tc_fun(U_8153,tc_HOL_Obool),U_8152),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8153,tc_HOL_Obool)),U_8154)),U_8155))
| U_8151 = c_Orderings_Obot__class_Obot(tc_fun(U_8152,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8153,tc_HOL_Obool)),U_8154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8152,tc_fun(U_8153,tc_HOL_Obool)),U_8151),U_8155)) = U_8154
| U_8151 != c_Orderings_Obot__class_Obot(tc_fun(U_8152,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2375_1]) ).
fof(f_2375_3,plain,
( ! [U_8165,U_8163,U_8161,U_8159,U_8157] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8161,tc_HOL_Obool)),U_8163),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8159,tc_fun(U_8161,tc_HOL_Obool)),U_8157),U_8165)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8159,tc_fun(U_8161,tc_HOL_Obool)),U_8157),hAPP(hAPP(c_COMBB(tc_fun(U_8161,tc_HOL_Obool),tc_fun(U_8161,tc_HOL_Obool),U_8159),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8161,tc_HOL_Obool)),U_8163)),U_8165))
| U_8157 = c_Orderings_Obot__class_Obot(tc_fun(U_8159,tc_HOL_Obool)) )
& ! [U_8164,U_8162,U_8160,U_8158,U_8156] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8160,tc_HOL_Obool)),U_8162),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8158,tc_fun(U_8160,tc_HOL_Obool)),U_8156),U_8164)) = U_8162
| U_8156 != c_Orderings_Obot__class_Obot(tc_fun(U_8158,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2375_2]) ).
cnf(f_2375_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8160,tc_HOL_Obool)),U_8162),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8158,tc_fun(U_8160,tc_HOL_Obool)),U_8156),U_8164)) = U_8162
| U_8156 != c_Orderings_Obot__class_Obot(tc_fun(U_8158,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2375_3]) ).
cnf(f_2375_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8161,tc_HOL_Obool)),U_8163),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8159,tc_fun(U_8161,tc_HOL_Obool)),U_8157),U_8165)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8159,tc_fun(U_8161,tc_HOL_Obool)),U_8157),hAPP(hAPP(c_COMBB(tc_fun(U_8161,tc_HOL_Obool),tc_fun(U_8161,tc_HOL_Obool),U_8159),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8161,tc_HOL_Obool)),U_8163)),U_8165))
| U_8157 = c_Orderings_Obot__class_Obot(tc_fun(U_8159,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2375_3]) ).
fof(f_2376_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]) ).
cnf(f_2376_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(clausify,[status(thm)],[f_2376_1]) ).
fof(f_2377_1,plain,
! [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_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| V_a_2 != V_b_2 ),
inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastAtMost__singleton_H]) ).
fof(f_2377_2,plain,
! [U_8167,U_8166] :
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8166,U_8167) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8166),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| U_8166 != U_8167 ),
inference(variable_rename,[status(thm)],[f_2377_1]) ).
cnf(f_2377_3,plain,
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8166,U_8167) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8166),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| U_8166 != U_8167 ),
inference(clausify,[status(thm)],[f_2377_2]) ).
fof(f_2378_1,plain,
! [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))),
inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastAtMost__singleton]) ).
fof(f_2378_2,plain,
! [U_8168] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8168,U_8168) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8168),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_2378_1]) ).
cnf(f_2378_3,plain,
c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8168,U_8168) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8168),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_2378_2]) ).
fof(f_2379_1,plain,
! [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 )
& ( ( V_b_2 = V_c_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_c_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastAtMost__singleton__iff]) ).
fof(f_2379_2,plain,
! [U_8171,U_8170,U_8169] :
( ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8169,U_8170) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8171),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| U_8170 != U_8171
| U_8169 != U_8170 )
& ( ( U_8170 = U_8171
& U_8169 = U_8170 )
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8169,U_8170) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8171),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ),
inference(variable_rename,[status(thm)],[f_2379_1]) ).
fof(f_2379_3,plain,
( ! [U_8177,U_8175,U_8173] :
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8173,U_8175) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8177),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| U_8175 != U_8177
| U_8173 != U_8175 )
& ! [U_8176,U_8174,U_8172] :
( ( U_8174 = U_8176
& U_8172 = U_8174 )
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8172,U_8174) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8176),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ),
inference(miniscope,[status(thm)],[f_2379_2]) ).
cnf(f_2379_4,plain,
( U_8172 = U_8174
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8172,U_8174) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8176),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_2379_3]) ).
cnf(f_2379_5,plain,
( U_8174 = U_8176
| c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8172,U_8174) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8176),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_2379_3]) ).
cnf(f_2379_6,plain,
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8173,U_8175) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8177),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| U_8175 != U_8177
| U_8173 != U_8175 ),
inference(clausify,[status(thm)],[f_2379_3]) ).
fof(f_2380_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_2380_2,plain,
! [U_8178] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8178)) = 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_8178)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8178),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_2380_1]) ).
cnf(f_2380_3,plain,
hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8178)) = 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_8178)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8178),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_2380_2]) ).
fof(f_2381_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_2381_2,plain,
! [U_8179] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8179)) = 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_8179)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8179)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_2381_1]) ).
cnf(f_2381_3,plain,
hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8179)) = 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_8179)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_8179)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_2381_2]) ).
fof(f_2382_1,plain,
! [V_A_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
& V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_card__gt__0__iff]) ).
fof(f_2382_2,plain,
! [U_8181,U_8180] :
( ( 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_8180),U_8181)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8180),U_8181))
| U_8181 = c_Orderings_Obot__class_Obot(tc_fun(U_8180,tc_HOL_Obool)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8180),U_8181))
& U_8181 != c_Orderings_Obot__class_Obot(tc_fun(U_8180,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_8180),U_8181))) ) ),
inference(variable_rename,[status(thm)],[f_2382_1]) ).
fof(f_2382_3,plain,
( ! [U_8185,U_8183] :
( 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_8183),U_8185)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8183),U_8185))
| U_8185 = c_Orderings_Obot__class_Obot(tc_fun(U_8183,tc_HOL_Obool)) )
& ! [U_8184,U_8182] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8182),U_8184))
& U_8184 != c_Orderings_Obot__class_Obot(tc_fun(U_8182,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_8182),U_8184))) ) ),
inference(miniscope,[status(thm)],[f_2382_2]) ).
cnf(f_2382_4,plain,
( U_8184 != c_Orderings_Obot__class_Obot(tc_fun(U_8182,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_8182),U_8184))) ),
inference(clausify,[status(thm)],[f_2382_3]) ).
cnf(f_2382_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_8182),U_8184))
| ~ 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_8182),U_8184))) ),
inference(clausify,[status(thm)],[f_2382_3]) ).
cnf(f_2382_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_8183),U_8185)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8183),U_8185))
| U_8185 = c_Orderings_Obot__class_Obot(tc_fun(U_8183,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2382_3]) ).
fof(f_2383_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_2383_2,plain,
! [U_8187,U_8186] :
( ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8187,U_8186) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_8187),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8187),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_8186))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8186),U_8187)) )
& ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8187,U_8186) = 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_8186),U_8187)) ) ),
inference(variable_rename,[status(thm)],[f_2383_1]) ).
fof(f_2383_3,plain,
( ! [U_8191,U_8189] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8191,U_8189) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_8191),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8191),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_8189))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8189),U_8191)) )
& ! [U_8190,U_8188] :
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8190,U_8188) = 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_8188),U_8190)) ) ),
inference(miniscope,[status(thm)],[f_2383_2]) ).
cnf(f_2383_4,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8190,U_8188) = 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_8188),U_8190)) ),
inference(clausify,[status(thm)],[f_2383_3]) ).
cnf(f_2383_5,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_8191,U_8189) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_8191),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8191),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_8189))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_8189),U_8191)) ),
inference(clausify,[status(thm)],[f_2383_3]) ).
fof(f_2384_1,plain,
! [V_u_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I2_J]) ).
fof(f_2384_2,plain,
! [U_8193,U_8192] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8192,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8192),U_8193)),hAPP(hAPP(c_Set_Oinsert(U_8192),U_8193),c_Orderings_Obot__class_Obot(tc_fun(U_8192,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_8192),U_8193)
| ~ class_Orderings_Olinorder(U_8192) ),
inference(variable_rename,[status(thm)],[f_2384_1]) ).
cnf(f_2384_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8192,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_8192),U_8193)),hAPP(hAPP(c_Set_Oinsert(U_8192),U_8193),c_Orderings_Obot__class_Obot(tc_fun(U_8192,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_8192),U_8193)
| ~ class_Orderings_Olinorder(U_8192) ),
inference(clausify,[status(thm)],[f_2384_2]) ).
fof(f_2385_1,plain,
! [V_na_2,V_m_2] :
( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_na_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_na_2)) )
& ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_na_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_na_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_na_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_atLeastLessThanSuc]) ).
fof(f_2385_2,plain,
! [U_8195,U_8194] :
( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_8194),hAPP(c_Nat_OSuc,U_8195)) = 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_8194),U_8195)) )
& ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_8194),hAPP(c_Nat_OSuc,U_8195)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8195),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_8194),U_8195))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8194),U_8195)) ) ),
inference(variable_rename,[status(thm)],[f_2385_1]) ).
fof(f_2385_3,plain,
( ! [U_8199,U_8197] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_8197),hAPP(c_Nat_OSuc,U_8199)) = 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_8197),U_8199)) )
& ! [U_8198,U_8196] :
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_8196),hAPP(c_Nat_OSuc,U_8198)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8198),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_8196),U_8198))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8196),U_8198)) ) ),
inference(miniscope,[status(thm)],[f_2385_2]) ).
cnf(f_2385_4,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_8196),hAPP(c_Nat_OSuc,U_8198)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_8198),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_8196),U_8198))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_8196),U_8198)) ),
inference(clausify,[status(thm)],[f_2385_3]) ).
cnf(f_2385_5,plain,
( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_8197),hAPP(c_Nat_OSuc,U_8199)) = 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_8197),U_8199)) ),
inference(clausify,[status(thm)],[f_2385_3]) ).
fof(f_2386_1,plain,
! [V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I1_J]) ).
fof(f_2386_2,plain,
! [U_8201,U_8200] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8200,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8200),U_8201),c_Orderings_Obot__class_Obot(tc_fun(U_8200,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8200),U_8201)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_8200),U_8201)
| ~ class_Orderings_Olinorder(U_8200) ),
inference(variable_rename,[status(thm)],[f_2386_1]) ).
cnf(f_2386_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8200,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8200),U_8201),c_Orderings_Obot__class_Obot(tc_fun(U_8200,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8200),U_8201)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_8200),U_8201)
| ~ class_Orderings_Olinorder(U_8200) ),
inference(clausify,[status(thm)],[f_2386_2]) ).
fof(f_2387_1,plain,
! [V_B_2,T_c,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Plus]) ).
fof(f_2387_2,plain,
! [U_8205,U_8204,U_8203,U_8202] :
( hAPP(c_Finite__Set_Ocard(tc_sum(U_8202,U_8204)),c_Sum__Type_OPlus(U_8202,U_8204,U_8203,U_8205)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_8202),U_8203)),hAPP(c_Finite__Set_Ocard(U_8204),U_8205))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8204),U_8205))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8202),U_8203)) ),
inference(variable_rename,[status(thm)],[f_2387_1]) ).
cnf(f_2387_3,plain,
( hAPP(c_Finite__Set_Ocard(tc_sum(U_8202,U_8204)),c_Sum__Type_OPlus(U_8202,U_8204,U_8203,U_8205)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_8202),U_8203)),hAPP(c_Finite__Set_Ocard(U_8204),U_8205))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8204),U_8205))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8202),U_8203)) ),
inference(clausify,[status(thm)],[f_2387_2]) ).
fof(f_2388_1,plain,
! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Oinsert__remove]) ).
fof(f_2388_2,plain,
! [U_8210,U_8209,U_8208,U_8207,U_8206] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8207,U_8206),U_8209),hAPP(hAPP(c_Set_Oinsert(U_8207),U_8210),U_8208)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8206),hAPP(U_8209,U_8210)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8207,U_8206),U_8209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8207,tc_HOL_Obool)),U_8208),hAPP(hAPP(c_Set_Oinsert(U_8207),U_8210),c_Orderings_Obot__class_Obot(tc_fun(U_8207,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8207),U_8208))
| ~ class_Groups_Ocomm__monoid__add(U_8206) ),
inference(variable_rename,[status(thm)],[f_2388_1]) ).
cnf(f_2388_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8207,U_8206),U_8209),hAPP(hAPP(c_Set_Oinsert(U_8207),U_8210),U_8208)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8206),hAPP(U_8209,U_8210)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8207,U_8206),U_8209),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8207,tc_HOL_Obool)),U_8208),hAPP(hAPP(c_Set_Oinsert(U_8207),U_8210),c_Orderings_Obot__class_Obot(tc_fun(U_8207,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8207),U_8208))
| ~ class_Groups_Ocomm__monoid__add(U_8206) ),
inference(clausify,[status(thm)],[f_2388_2]) ).
fof(f_2389_1,plain,
! [V_x_2,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__insert]) ).
fof(f_2389_2,plain,
! [U_8213,U_8212,U_8211] :
( hAPP(c_Finite__Set_Ocard(U_8211),hAPP(hAPP(c_Set_Oinsert(U_8211),U_8213),U_8212)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_8211),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8211,tc_HOL_Obool)),U_8212),hAPP(hAPP(c_Set_Oinsert(U_8211),U_8213),c_Orderings_Obot__class_Obot(tc_fun(U_8211,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8211),U_8212)) ),
inference(variable_rename,[status(thm)],[f_2389_1]) ).
cnf(f_2389_3,plain,
( hAPP(c_Finite__Set_Ocard(U_8211),hAPP(hAPP(c_Set_Oinsert(U_8211),U_8213),U_8212)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_8211),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8211,tc_HOL_Obool)),U_8212),hAPP(hAPP(c_Set_Oinsert(U_8211),U_8213),c_Orderings_Obot__class_Obot(tc_fun(U_8211,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8211),U_8212)) ),
inference(clausify,[status(thm)],[f_2389_2]) ).
fof(f_2390_1,plain,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff1__le]) ).
fof(f_2390_2,plain,
! [U_8216,U_8215,U_8214] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_8214),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8214,tc_HOL_Obool)),U_8215),hAPP(hAPP(c_Set_Oinsert(U_8214),U_8216),c_Orderings_Obot__class_Obot(tc_fun(U_8214,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_8214),U_8215)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8214),U_8215)) ),
inference(variable_rename,[status(thm)],[f_2390_1]) ).
cnf(f_2390_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_8214),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8214,tc_HOL_Obool)),U_8215),hAPP(hAPP(c_Set_Oinsert(U_8214),U_8216),c_Orderings_Obot__class_Obot(tc_fun(U_8214,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_8214),U_8215)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8214),U_8215)) ),
inference(clausify,[status(thm)],[f_2390_2]) ).
fof(f_2391_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I6_J]) ).
fof(f_2391_2,plain,
! [U_8219,U_8218,U_8217] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8217,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8217,U_8218),U_8219)),hAPP(hAPP(c_Set_Oinsert(U_8217),U_8219),c_Orderings_Obot__class_Obot(tc_fun(U_8217,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_8217,U_8218,U_8219)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8217),U_8218),U_8219))
| ~ class_Orderings_Olinorder(U_8217) ),
inference(variable_rename,[status(thm)],[f_2391_1]) ).
cnf(f_2391_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8217,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8217,U_8218),U_8219)),hAPP(hAPP(c_Set_Oinsert(U_8217),U_8219),c_Orderings_Obot__class_Obot(tc_fun(U_8217,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_8217,U_8218,U_8219)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8217),U_8218),U_8219))
| ~ class_Orderings_Olinorder(U_8217) ),
inference(clausify,[status(thm)],[f_2391_2]) ).
fof(f_2392_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I5_J]) ).
fof(f_2392_2,plain,
! [U_8222,U_8221,U_8220] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8220,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8220),U_8221),c_Orderings_Obot__class_Obot(tc_fun(U_8220,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8220,U_8221,U_8222)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8220,U_8221,U_8222)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8220),U_8221),U_8222))
| ~ class_Orderings_Olinorder(U_8220) ),
inference(variable_rename,[status(thm)],[f_2392_1]) ).
cnf(f_2392_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8220,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8220),U_8221),c_Orderings_Obot__class_Obot(tc_fun(U_8220,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_8220,U_8221,U_8222)) = c_SetInterval_Oord__class_OatLeastAtMost(U_8220,U_8221,U_8222)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8220),U_8221),U_8222))
| ~ class_Orderings_Olinorder(U_8220) ),
inference(clausify,[status(thm)],[f_2392_2]) ).
fof(f_2393_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I3_J]) ).
fof(f_2393_2,plain,
! [U_8225,U_8224,U_8223] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8223,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8223),U_8224),c_Orderings_Obot__class_Obot(tc_fun(U_8223,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8223,U_8224,U_8225)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8223,U_8224),U_8225)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8223),U_8224),U_8225))
| ~ class_Orderings_Olinorder(U_8223) ),
inference(variable_rename,[status(thm)],[f_2393_1]) ).
cnf(f_2393_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8223,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8223),U_8224),c_Orderings_Obot__class_Obot(tc_fun(U_8223,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8223,U_8224,U_8225)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_8223,U_8224),U_8225)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8223),U_8224),U_8225))
| ~ class_Orderings_Olinorder(U_8223) ),
inference(clausify,[status(thm)],[f_2393_2]) ).
fof(f_2394_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I4_J]) ).
fof(f_2394_2,plain,
! [U_8228,U_8227,U_8226] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8226,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8226,U_8227,U_8228)),hAPP(hAPP(c_Set_Oinsert(U_8226),U_8228),c_Orderings_Obot__class_Obot(tc_fun(U_8226,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_8226,U_8227,U_8228)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8226),U_8227),U_8228))
| ~ class_Orderings_Olinorder(U_8226) ),
inference(variable_rename,[status(thm)],[f_2394_1]) ).
cnf(f_2394_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8226,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_8226,U_8227,U_8228)),hAPP(hAPP(c_Set_Oinsert(U_8226),U_8228),c_Orderings_Obot__class_Obot(tc_fun(U_8226,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_8226,U_8227,U_8228)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8226),U_8227),U_8228))
| ~ class_Orderings_Olinorder(U_8226) ),
inference(clausify,[status(thm)],[f_2394_2]) ).
fof(f_2395_1,plain,
! [V_X_2,T_b] : c_Set_Othe__elem(T_b,V_X_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),hAPP(c_fequal,V_X_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),
inference(fof_nnf,[status(thm)],[fact_the__elem__def]) ).
fof(f_2395_2,plain,
! [U_8230,U_8229] : c_Set_Othe__elem(U_8229,U_8230) = c_HOL_OThe(U_8229,hAPP(hAPP(c_COMBB(tc_fun(U_8229,tc_HOL_Obool),tc_HOL_Obool,U_8229),hAPP(c_fequal,U_8230)),hAPP(hAPP(c_COMBC(U_8229,tc_fun(U_8229,tc_HOL_Obool),tc_fun(U_8229,tc_HOL_Obool)),c_Set_Oinsert(U_8229)),c_Orderings_Obot__class_Obot(tc_fun(U_8229,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_2395_1]) ).
cnf(f_2395_3,plain,
c_Set_Othe__elem(U_8229,U_8230) = c_HOL_OThe(U_8229,hAPP(hAPP(c_COMBB(tc_fun(U_8229,tc_HOL_Obool),tc_HOL_Obool,U_8229),hAPP(c_fequal,U_8230)),hAPP(hAPP(c_COMBC(U_8229,tc_fun(U_8229,tc_HOL_Obool),tc_fun(U_8229,tc_HOL_Obool)),c_Set_Oinsert(U_8229)),c_Orderings_Obot__class_Obot(tc_fun(U_8229,tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_2395_2]) ).
fof(f_2396_1,plain,
! [V_k_2,V_l_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))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThanLessThan__empty]) ).
fof(f_2396_2,plain,
! [U_8232,U_8231] :
( 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)))),U_8232,U_8231) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8231),U_8232)) ),
inference(variable_rename,[status(thm)],[f_2396_1]) ).
cnf(f_2396_3,plain,
( 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)))),U_8232,U_8231) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8231),U_8232)) ),
inference(clausify,[status(thm)],[f_2396_2]) ).
fof(f_2397_1,plain,
! [V_x_2,T_b] : c_Set_Othe__elem(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2,
inference(fof_nnf,[status(thm)],[fact_the__elem__eq]) ).
fof(f_2397_2,plain,
! [U_8234,U_8233] : c_Set_Othe__elem(U_8233,hAPP(hAPP(c_Set_Oinsert(U_8233),U_8234),c_Orderings_Obot__class_Obot(tc_fun(U_8233,tc_HOL_Obool)))) = U_8234,
inference(variable_rename,[status(thm)],[f_2397_1]) ).
cnf(f_2397_3,plain,
c_Set_Othe__elem(U_8233,hAPP(hAPP(c_Set_Oinsert(U_8233),U_8234),c_Orderings_Obot__class_Obot(tc_fun(U_8233,tc_HOL_Obool)))) = U_8234,
inference(clausify,[status(thm)],[f_2397_2]) ).
fof(f_2398_1,plain,
! [V_B_2,V_A_2,T_c,T_b] :
( ( c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))
| V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
& V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
| c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_Plus__eq__empty__conv]) ).
fof(f_2398_2,plain,
! [U_8238,U_8237,U_8236,U_8235] :
( ( c_Sum__Type_OPlus(U_8235,U_8236,U_8237,U_8238) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_8235,U_8236),tc_HOL_Obool))
| U_8238 != c_Orderings_Obot__class_Obot(tc_fun(U_8236,tc_HOL_Obool))
| U_8237 != c_Orderings_Obot__class_Obot(tc_fun(U_8235,tc_HOL_Obool)) )
& ( ( U_8238 = c_Orderings_Obot__class_Obot(tc_fun(U_8236,tc_HOL_Obool))
& U_8237 = c_Orderings_Obot__class_Obot(tc_fun(U_8235,tc_HOL_Obool)) )
| c_Sum__Type_OPlus(U_8235,U_8236,U_8237,U_8238) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_8235,U_8236),tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2398_1]) ).
fof(f_2398_3,plain,
( ! [U_8246,U_8244,U_8242,U_8240] :
( c_Sum__Type_OPlus(U_8240,U_8242,U_8244,U_8246) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_8240,U_8242),tc_HOL_Obool))
| U_8246 != c_Orderings_Obot__class_Obot(tc_fun(U_8242,tc_HOL_Obool))
| U_8244 != c_Orderings_Obot__class_Obot(tc_fun(U_8240,tc_HOL_Obool)) )
& ! [U_8245,U_8243,U_8241,U_8239] :
( ( U_8245 = c_Orderings_Obot__class_Obot(tc_fun(U_8241,tc_HOL_Obool))
& U_8243 = c_Orderings_Obot__class_Obot(tc_fun(U_8239,tc_HOL_Obool)) )
| c_Sum__Type_OPlus(U_8239,U_8241,U_8243,U_8245) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_8239,U_8241),tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2398_2]) ).
cnf(f_2398_4,plain,
( U_8243 = c_Orderings_Obot__class_Obot(tc_fun(U_8239,tc_HOL_Obool))
| c_Sum__Type_OPlus(U_8239,U_8241,U_8243,U_8245) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_8239,U_8241),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2398_3]) ).
cnf(f_2398_5,plain,
( U_8245 = c_Orderings_Obot__class_Obot(tc_fun(U_8241,tc_HOL_Obool))
| c_Sum__Type_OPlus(U_8239,U_8241,U_8243,U_8245) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_8239,U_8241),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2398_3]) ).
cnf(f_2398_6,plain,
( c_Sum__Type_OPlus(U_8240,U_8242,U_8244,U_8246) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_8240,U_8242),tc_HOL_Obool))
| U_8246 != c_Orderings_Obot__class_Obot(tc_fun(U_8242,tc_HOL_Obool))
| U_8244 != c_Orderings_Obot__class_Obot(tc_fun(U_8240,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2398_3]) ).
fof(f_2399_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]) ).
cnf(f_2399_2,plain,
c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_2399_1]) ).
fof(f_2400_1,plain,
! [V_z_2] : hAPP(c_Int_Onat,V_z_2) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),
inference(fof_nnf,[status(thm)],[fact_nat__def]) ).
fof(f_2400_2,plain,
! [U_8247] : hAPP(c_Int_Onat,U_8247) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_8247)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),
inference(variable_rename,[status(thm)],[f_2400_1]) ).
cnf(f_2400_3,plain,
hAPP(c_Int_Onat,U_8247) = c_Set_Othe__elem(tc_Nat_Onat,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_8247)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),
inference(clausify,[status(thm)],[f_2400_2]) ).
fof(f_2401_1,plain,
! [V_x_2,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff__singleton]) ).
fof(f_2401_2,plain,
! [U_8250,U_8249,U_8248] :
( hAPP(c_Finite__Set_Ocard(U_8248),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8248,tc_HOL_Obool)),U_8249),hAPP(hAPP(c_Set_Oinsert(U_8248),U_8250),c_Orderings_Obot__class_Obot(tc_fun(U_8248,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_8248),U_8249)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_8248),U_8250),U_8249))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8248),U_8249)) ),
inference(variable_rename,[status(thm)],[f_2401_1]) ).
cnf(f_2401_3,plain,
( hAPP(c_Finite__Set_Ocard(U_8248),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8248,tc_HOL_Obool)),U_8249),hAPP(hAPP(c_Set_Oinsert(U_8248),U_8250),c_Orderings_Obot__class_Obot(tc_fun(U_8248,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_8248),U_8249)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_8248),U_8250),U_8249))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8248),U_8249)) ),
inference(clausify,[status(thm)],[f_2401_2]) ).
fof(f_2402_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
& ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff__singleton__if]) ).
fof(f_2402_2,plain,
! [U_8253,U_8252,U_8251] :
( ( ( hAPP(c_Finite__Set_Ocard(U_8251),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8251,tc_HOL_Obool)),U_8252),hAPP(hAPP(c_Set_Oinsert(U_8251),U_8253),c_Orderings_Obot__class_Obot(tc_fun(U_8251,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_8251),U_8252)
| hBOOL(hAPP(hAPP(c_member(U_8251),U_8253),U_8252)) )
& ( hAPP(c_Finite__Set_Ocard(U_8251),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8251,tc_HOL_Obool)),U_8252),hAPP(hAPP(c_Set_Oinsert(U_8251),U_8253),c_Orderings_Obot__class_Obot(tc_fun(U_8251,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_8251),U_8252)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_8251),U_8253),U_8252)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8251),U_8252)) ),
inference(variable_rename,[status(thm)],[f_2402_1]) ).
cnf(f_2402_3,plain,
( hAPP(c_Finite__Set_Ocard(U_8251),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8251,tc_HOL_Obool)),U_8252),hAPP(hAPP(c_Set_Oinsert(U_8251),U_8253),c_Orderings_Obot__class_Obot(tc_fun(U_8251,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_8251),U_8252)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(U_8251),U_8253),U_8252))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8251),U_8252)) ),
inference(clausify,[status(thm)],[f_2402_2]) ).
cnf(f_2402_4,plain,
( hAPP(c_Finite__Set_Ocard(U_8251),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8251,tc_HOL_Obool)),U_8252),hAPP(hAPP(c_Set_Oinsert(U_8251),U_8253),c_Orderings_Obot__class_Obot(tc_fun(U_8251,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_8251),U_8252)
| hBOOL(hAPP(hAPP(c_member(U_8251),U_8253),U_8252))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8251),U_8252)) ),
inference(clausify,[status(thm)],[f_2402_2]) ).
fof(f_2403_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( ( ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Oinsert__remove]) ).
fof(f_2403_2,plain,
! [U_8258,U_8257,U_8256,U_8255,U_8254] :
( ( ( hAPP(U_8256,hAPP(hAPP(c_Set_Oinsert(U_8254),U_8258),U_8257)) = hAPP(hAPP(U_8255,U_8258),hAPP(U_8256,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8254,tc_HOL_Obool)),U_8257),hAPP(hAPP(c_Set_Oinsert(U_8254),U_8258),c_Orderings_Obot__class_Obot(tc_fun(U_8254,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8254,tc_HOL_Obool)),U_8257),hAPP(hAPP(c_Set_Oinsert(U_8254),U_8258),c_Orderings_Obot__class_Obot(tc_fun(U_8254,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8254,tc_HOL_Obool)) )
& ( hAPP(U_8256,hAPP(hAPP(c_Set_Oinsert(U_8254),U_8258),U_8257)) = U_8258
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8254,tc_HOL_Obool)),U_8257),hAPP(hAPP(c_Set_Oinsert(U_8254),U_8258),c_Orderings_Obot__class_Obot(tc_fun(U_8254,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8254,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8254),U_8257))
| ~ c_Finite__Set_Ofolding__one(U_8254,U_8255,U_8256) ),
inference(variable_rename,[status(thm)],[f_2403_1]) ).
cnf(f_2403_3,plain,
( hAPP(U_8256,hAPP(hAPP(c_Set_Oinsert(U_8254),U_8258),U_8257)) = U_8258
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8254,tc_HOL_Obool)),U_8257),hAPP(hAPP(c_Set_Oinsert(U_8254),U_8258),c_Orderings_Obot__class_Obot(tc_fun(U_8254,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8254,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8254),U_8257))
| ~ c_Finite__Set_Ofolding__one(U_8254,U_8255,U_8256) ),
inference(clausify,[status(thm)],[f_2403_2]) ).
cnf(f_2403_4,plain,
( hAPP(U_8256,hAPP(hAPP(c_Set_Oinsert(U_8254),U_8258),U_8257)) = hAPP(hAPP(U_8255,U_8258),hAPP(U_8256,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8254,tc_HOL_Obool)),U_8257),hAPP(hAPP(c_Set_Oinsert(U_8254),U_8258),c_Orderings_Obot__class_Obot(tc_fun(U_8254,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8254,tc_HOL_Obool)),U_8257),hAPP(hAPP(c_Set_Oinsert(U_8254),U_8258),c_Orderings_Obot__class_Obot(tc_fun(U_8254,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8254,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8254),U_8257))
| ~ c_Finite__Set_Ofolding__one(U_8254,U_8255,U_8256) ),
inference(clausify,[status(thm)],[f_2403_2]) ).
fof(f_2404_1,plain,
! [V_c_2,T_b,V_B_2,V_A_2] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
| ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_equalityCE]) ).
fof(f_2404_2,plain,
! [U_8262,U_8261,U_8260,U_8259] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_8261),U_8262),U_8260))
& ~ hBOOL(hAPP(hAPP(c_member(U_8261),U_8262),U_8259)) )
| ( hBOOL(hAPP(hAPP(c_member(U_8261),U_8262),U_8260))
& hBOOL(hAPP(hAPP(c_member(U_8261),U_8262),U_8259)) )
| U_8259 != U_8260 ),
inference(variable_rename,[status(thm)],[f_2404_1]) ).
cnf(f_2404_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8261),U_8262),U_8259))
| hBOOL(hAPP(hAPP(c_member(U_8261),U_8262),U_8259))
| U_8259 != U_8260 ),
inference(clausify,[status(thm)],[f_2404_2]) ).
cnf(f_2404_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8261),U_8262),U_8260))
| hBOOL(hAPP(hAPP(c_member(U_8261),U_8262),U_8259))
| U_8259 != U_8260 ),
inference(clausify,[status(thm)],[f_2404_2]) ).
cnf(f_2404_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8261),U_8262),U_8259))
| hBOOL(hAPP(hAPP(c_member(U_8261),U_8262),U_8260))
| U_8259 != U_8260 ),
inference(clausify,[status(thm)],[f_2404_2]) ).
cnf(f_2404_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8261),U_8262),U_8260))
| hBOOL(hAPP(hAPP(c_member(U_8261),U_8262),U_8260))
| U_8259 != U_8260 ),
inference(clausify,[status(thm)],[f_2404_2]) ).
fof(f_2405_1,plain,
! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ),
inference(fof_nnf,[status(thm)],[fact_INF2__E]) ).
fof(f_2405_2,plain,
! [U_8270,U_8269,U_8268,U_8267,U_8266,U_8265,U_8264,U_8263] :
( ~ hBOOL(hAPP(hAPP(c_member(U_8263),U_8270),U_8266))
| hBOOL(hAPP(hAPP(hAPP(U_8267,U_8270),U_8268),U_8269))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8263,tc_fun(U_8264,tc_fun(U_8265,tc_HOL_Obool))),U_8266),U_8267),U_8268),U_8269)) ),
inference(variable_rename,[status(thm)],[f_2405_1]) ).
cnf(f_2405_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8263),U_8270),U_8266))
| hBOOL(hAPP(hAPP(hAPP(U_8267,U_8270),U_8268),U_8269))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8263,tc_fun(U_8264,tc_fun(U_8265,tc_HOL_Obool))),U_8266),U_8267),U_8268),U_8269)) ),
inference(clausify,[status(thm)],[f_2405_2]) ).
fof(f_2406_1,plain,
! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ),
inference(fof_nnf,[status(thm)],[fact_INF2__D]) ).
fof(f_2406_2,plain,
! [U_8278,U_8277,U_8276,U_8275,U_8274,U_8273,U_8272,U_8271] :
( hBOOL(hAPP(hAPP(hAPP(U_8275,U_8278),U_8276),U_8277))
| ~ hBOOL(hAPP(hAPP(c_member(U_8271),U_8278),U_8274))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8271,tc_fun(U_8272,tc_fun(U_8273,tc_HOL_Obool))),U_8274),U_8275),U_8276),U_8277)) ),
inference(variable_rename,[status(thm)],[f_2406_1]) ).
cnf(f_2406_3,plain,
( hBOOL(hAPP(hAPP(hAPP(U_8275,U_8278),U_8276),U_8277))
| ~ hBOOL(hAPP(hAPP(c_member(U_8271),U_8278),U_8274))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8271,tc_fun(U_8272,tc_fun(U_8273,tc_HOL_Obool))),U_8274),U_8275),U_8276),U_8277)) ),
inference(clausify,[status(thm)],[f_2406_2]) ).
fof(f_2407_1,plain,
! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_SUP2__I]) ).
fof(f_2407_2,plain,
! [U_8286,U_8285,U_8284,U_8283,U_8282,U_8281,U_8280,U_8279] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8279,tc_fun(U_8285,tc_fun(U_8286,tc_HOL_Obool))),U_8281),U_8282),U_8283),U_8284))
| ~ hBOOL(hAPP(hAPP(hAPP(U_8282,U_8280),U_8283),U_8284))
| ~ hBOOL(hAPP(hAPP(c_member(U_8279),U_8280),U_8281)) ),
inference(variable_rename,[status(thm)],[f_2407_1]) ).
cnf(f_2407_3,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8279,tc_fun(U_8285,tc_fun(U_8286,tc_HOL_Obool))),U_8281),U_8282),U_8283),U_8284))
| ~ hBOOL(hAPP(hAPP(hAPP(U_8282,U_8280),U_8283),U_8284))
| ~ hBOOL(hAPP(hAPP(c_member(U_8279),U_8280),U_8281)) ),
inference(clausify,[status(thm)],[f_2407_2]) ).
fof(f_2408_1,plain,
! [V_a_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_emptyE]) ).
fof(f_2408_2,plain,
! [U_8288,U_8287] : ~ hBOOL(hAPP(hAPP(c_member(U_8287),U_8288),c_Orderings_Obot__class_Obot(tc_fun(U_8287,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_2408_1]) ).
cnf(f_2408_3,plain,
~ hBOOL(hAPP(hAPP(c_member(U_8287),U_8288),c_Orderings_Obot__class_Obot(tc_fun(U_8287,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_2408_2]) ).
fof(f_2409_1,plain,
! [V_A_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| V_a_2 = V_b_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_insertE]) ).
fof(f_2409_2,plain,
! [U_8292,U_8291,U_8290,U_8289] :
( hBOOL(hAPP(hAPP(c_member(U_8289),U_8290),U_8292))
| U_8290 = U_8291
| ~ hBOOL(hAPP(hAPP(c_member(U_8289),U_8290),hAPP(hAPP(c_Set_Oinsert(U_8289),U_8291),U_8292))) ),
inference(variable_rename,[status(thm)],[f_2409_1]) ).
cnf(f_2409_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8289),U_8290),U_8292))
| U_8290 = U_8291
| ~ hBOOL(hAPP(hAPP(c_member(U_8289),U_8290),hAPP(hAPP(c_Set_Oinsert(U_8289),U_8291),U_8292))) ),
inference(clausify,[status(thm)],[f_2409_2]) ).
fof(f_2410_1,plain,
! [V_b_2,V_B_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2)))
| ( V_a_2 != V_b_2
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_insertCI]) ).
fof(f_2410_2,plain,
! [U_8296,U_8295,U_8294,U_8293] :
( hBOOL(hAPP(hAPP(c_member(U_8293),U_8294),hAPP(hAPP(c_Set_Oinsert(U_8293),U_8296),U_8295)))
| ( U_8294 != U_8296
& ~ hBOOL(hAPP(hAPP(c_member(U_8293),U_8294),U_8295)) ) ),
inference(variable_rename,[status(thm)],[f_2410_1]) ).
cnf(f_2410_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8293),U_8294),U_8295))
| hBOOL(hAPP(hAPP(c_member(U_8293),U_8294),hAPP(hAPP(c_Set_Oinsert(U_8293),U_8296),U_8295))) ),
inference(clausify,[status(thm)],[f_2410_2]) ).
cnf(f_2410_4,plain,
( U_8294 != U_8296
| hBOOL(hAPP(hAPP(c_member(U_8293),U_8294),hAPP(hAPP(c_Set_Oinsert(U_8293),U_8296),U_8295))) ),
inference(clausify,[status(thm)],[f_2410_2]) ).
fof(f_2411_1,plain,
! [V_c_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_subsetD]) ).
fof(f_2411_2,plain,
! [U_8300,U_8299,U_8298,U_8297] :
( hBOOL(hAPP(hAPP(c_member(U_8297),U_8300),U_8299))
| ~ hBOOL(hAPP(hAPP(c_member(U_8297),U_8300),U_8298))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8297,tc_HOL_Obool)),U_8298),U_8299)) ),
inference(variable_rename,[status(thm)],[f_2411_1]) ).
cnf(f_2411_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8297),U_8300),U_8299))
| ~ hBOOL(hAPP(hAPP(c_member(U_8297),U_8300),U_8298))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8297,tc_HOL_Obool)),U_8298),U_8299)) ),
inference(clausify,[status(thm)],[f_2411_2]) ).
fof(f_2412_1,plain,
! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| V_b_2 != hAPP(V_f_2,V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_image__eqI]) ).
fof(f_2412_2,plain,
! [U_8306,U_8305,U_8304,U_8303,U_8302,U_8301] :
( hBOOL(hAPP(hAPP(c_member(U_8306),U_8301),hAPP(c_Set_Oimage(U_8304,U_8306,U_8302),U_8305)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8304),U_8303),U_8305))
| U_8301 != hAPP(U_8302,U_8303) ),
inference(variable_rename,[status(thm)],[f_2412_1]) ).
cnf(f_2412_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8306),U_8301),hAPP(c_Set_Oimage(U_8304,U_8306,U_8302),U_8305)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8304),U_8303),U_8305))
| U_8301 != hAPP(U_8302,U_8303) ),
inference(clausify,[status(thm)],[f_2412_2]) ).
fof(f_2413_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_UnE]) ).
fof(f_2413_2,plain,
! [U_8310,U_8309,U_8308,U_8307] :
( hBOOL(hAPP(hAPP(c_member(U_8307),U_8308),U_8310))
| hBOOL(hAPP(hAPP(c_member(U_8307),U_8308),U_8309))
| ~ hBOOL(hAPP(hAPP(c_member(U_8307),U_8308),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8307,tc_HOL_Obool)),U_8309),U_8310))) ),
inference(variable_rename,[status(thm)],[f_2413_1]) ).
cnf(f_2413_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8307),U_8308),U_8310))
| hBOOL(hAPP(hAPP(c_member(U_8307),U_8308),U_8309))
| ~ hBOOL(hAPP(hAPP(c_member(U_8307),U_8308),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8307,tc_HOL_Obool)),U_8309),U_8310))) ),
inference(clausify,[status(thm)],[f_2413_2]) ).
fof(f_2414_1,plain,
! [V_A_2,V_B_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_UnCI]) ).
fof(f_2414_2,plain,
! [U_8314,U_8313,U_8312,U_8311] :
( hBOOL(hAPP(hAPP(c_member(U_8311),U_8312),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8311,tc_HOL_Obool)),U_8314),U_8313)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_8311),U_8312),U_8314))
& ~ hBOOL(hAPP(hAPP(c_member(U_8311),U_8312),U_8313)) ) ),
inference(variable_rename,[status(thm)],[f_2414_1]) ).
cnf(f_2414_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8311),U_8312),U_8313))
| hBOOL(hAPP(hAPP(c_member(U_8311),U_8312),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8311,tc_HOL_Obool)),U_8314),U_8313))) ),
inference(clausify,[status(thm)],[f_2414_2]) ).
cnf(f_2414_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8311),U_8312),U_8314))
| hBOOL(hAPP(hAPP(c_member(U_8311),U_8312),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8311,tc_HOL_Obool)),U_8314),U_8313))) ),
inference(clausify,[status(thm)],[f_2414_2]) ).
fof(f_2415_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_DiffI]) ).
fof(f_2415_2,plain,
! [U_8318,U_8317,U_8316,U_8315] :
( hBOOL(hAPP(hAPP(c_member(U_8315),U_8316),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8315,tc_HOL_Obool)),U_8317),U_8318)))
| hBOOL(hAPP(hAPP(c_member(U_8315),U_8316),U_8318))
| ~ hBOOL(hAPP(hAPP(c_member(U_8315),U_8316),U_8317)) ),
inference(variable_rename,[status(thm)],[f_2415_1]) ).
cnf(f_2415_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8315),U_8316),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8315,tc_HOL_Obool)),U_8317),U_8318)))
| hBOOL(hAPP(hAPP(c_member(U_8315),U_8316),U_8318))
| ~ hBOOL(hAPP(hAPP(c_member(U_8315),U_8316),U_8317)) ),
inference(clausify,[status(thm)],[f_2415_2]) ).
fof(f_2416_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_DiffE]) ).
fof(f_2416_2,plain,
! [U_8322,U_8321,U_8320,U_8319] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_8319),U_8320),U_8322))
& hBOOL(hAPP(hAPP(c_member(U_8319),U_8320),U_8321)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8319),U_8320),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8319,tc_HOL_Obool)),U_8321),U_8322))) ),
inference(variable_rename,[status(thm)],[f_2416_1]) ).
cnf(f_2416_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8319),U_8320),U_8321))
| ~ hBOOL(hAPP(hAPP(c_member(U_8319),U_8320),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8319,tc_HOL_Obool)),U_8321),U_8322))) ),
inference(clausify,[status(thm)],[f_2416_2]) ).
cnf(f_2416_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8319),U_8320),U_8322))
| ~ hBOOL(hAPP(hAPP(c_member(U_8319),U_8320),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8319,tc_HOL_Obool)),U_8321),U_8322))) ),
inference(clausify,[status(thm)],[f_2416_2]) ).
fof(f_2417_1,plain,
! [V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
| hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_ComplI]) ).
fof(f_2417_2,plain,
! [U_8325,U_8324,U_8323] :
( hBOOL(hAPP(hAPP(c_member(U_8323),U_8324),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8323,tc_HOL_Obool)),U_8325)))
| hBOOL(hAPP(hAPP(c_member(U_8323),U_8324),U_8325)) ),
inference(variable_rename,[status(thm)],[f_2417_1]) ).
cnf(f_2417_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8323),U_8324),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8323,tc_HOL_Obool)),U_8325)))
| hBOOL(hAPP(hAPP(c_member(U_8323),U_8324),U_8325)) ),
inference(clausify,[status(thm)],[f_2417_2]) ).
fof(f_2418_1,plain,
! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_UN__I]) ).
fof(f_2418_2,plain,
! [U_8331,U_8330,U_8329,U_8328,U_8327,U_8326] :
( hBOOL(hAPP(hAPP(c_member(U_8329),U_8330),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8326,tc_fun(U_8329,tc_HOL_Obool)),U_8328),U_8331)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8329),U_8330),hAPP(U_8331,U_8327)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8326),U_8327),U_8328)) ),
inference(variable_rename,[status(thm)],[f_2418_1]) ).
cnf(f_2418_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8329),U_8330),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8326,tc_fun(U_8329,tc_HOL_Obool)),U_8328),U_8331)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8329),U_8330),hAPP(U_8331,U_8327)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8326),U_8327),U_8328)) ),
inference(clausify,[status(thm)],[f_2418_2]) ).
fof(f_2419_1,plain,
! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_SUP1__I]) ).
fof(f_2419_2,plain,
! [U_8337,U_8336,U_8335,U_8334,U_8333,U_8332] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8332,tc_fun(U_8337,tc_HOL_Obool)),U_8334),U_8335),U_8336))
| ~ hBOOL(hAPP(hAPP(U_8335,U_8333),U_8336))
| ~ hBOOL(hAPP(hAPP(c_member(U_8332),U_8333),U_8334)) ),
inference(variable_rename,[status(thm)],[f_2419_1]) ).
cnf(f_2419_3,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8332,tc_fun(U_8337,tc_HOL_Obool)),U_8334),U_8335),U_8336))
| ~ hBOOL(hAPP(hAPP(U_8335,U_8333),U_8336))
| ~ hBOOL(hAPP(hAPP(c_member(U_8332),U_8333),U_8334)) ),
inference(clausify,[status(thm)],[f_2419_2]) ).
fof(f_2420_1,plain,
! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_INF1__D]) ).
fof(f_2420_2,plain,
! [U_8343,U_8342,U_8341,U_8340,U_8339,U_8338] :
( hBOOL(hAPP(hAPP(U_8341,U_8343),U_8342))
| ~ hBOOL(hAPP(hAPP(c_member(U_8338),U_8343),U_8340))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8338,tc_fun(U_8339,tc_HOL_Obool)),U_8340),U_8341),U_8342)) ),
inference(variable_rename,[status(thm)],[f_2420_1]) ).
cnf(f_2420_3,plain,
( hBOOL(hAPP(hAPP(U_8341,U_8343),U_8342))
| ~ hBOOL(hAPP(hAPP(c_member(U_8338),U_8343),U_8340))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8338,tc_fun(U_8339,tc_HOL_Obool)),U_8340),U_8341),U_8342)) ),
inference(clausify,[status(thm)],[f_2420_2]) ).
fof(f_2421_1,plain,
! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_INF1__E]) ).
fof(f_2421_2,plain,
! [U_8349,U_8348,U_8347,U_8346,U_8345,U_8344] :
( ~ hBOOL(hAPP(hAPP(c_member(U_8344),U_8349),U_8346))
| hBOOL(hAPP(hAPP(U_8347,U_8349),U_8348))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8344,tc_fun(U_8345,tc_HOL_Obool)),U_8346),U_8347),U_8348)) ),
inference(variable_rename,[status(thm)],[f_2421_1]) ).
cnf(f_2421_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8344),U_8349),U_8346))
| hBOOL(hAPP(hAPP(U_8347,U_8349),U_8348))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8344,tc_fun(U_8345,tc_HOL_Obool)),U_8346),U_8347),U_8348)) ),
inference(clausify,[status(thm)],[f_2421_2]) ).
fof(f_2422_1,plain,
! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_INT__D]) ).
fof(f_2422_2,plain,
! [U_8355,U_8354,U_8353,U_8352,U_8351,U_8350] :
( hBOOL(hAPP(hAPP(c_member(U_8350),U_8351),hAPP(U_8354,U_8355)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8352),U_8355),U_8353))
| ~ hBOOL(hAPP(hAPP(c_member(U_8350),U_8351),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8352,tc_fun(U_8350,tc_HOL_Obool)),U_8353),U_8354))) ),
inference(variable_rename,[status(thm)],[f_2422_1]) ).
cnf(f_2422_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8350),U_8351),hAPP(U_8354,U_8355)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8352),U_8355),U_8353))
| ~ hBOOL(hAPP(hAPP(c_member(U_8350),U_8351),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8352,tc_fun(U_8350,tc_HOL_Obool)),U_8353),U_8354))) ),
inference(clausify,[status(thm)],[f_2422_2]) ).
fof(f_2423_1,plain,
! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_INT__E]) ).
fof(f_2423_2,plain,
! [U_8361,U_8360,U_8359,U_8358,U_8357,U_8356] :
( ~ hBOOL(hAPP(hAPP(c_member(U_8358),U_8361),U_8359))
| hBOOL(hAPP(hAPP(c_member(U_8356),U_8357),hAPP(U_8360,U_8361)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8356),U_8357),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8358,tc_fun(U_8356,tc_HOL_Obool)),U_8359),U_8360))) ),
inference(variable_rename,[status(thm)],[f_2423_1]) ).
cnf(f_2423_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8358),U_8361),U_8359))
| hBOOL(hAPP(hAPP(c_member(U_8356),U_8357),hAPP(U_8360,U_8361)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8356),U_8357),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8358,tc_fun(U_8356,tc_HOL_Obool)),U_8359),U_8360))) ),
inference(clausify,[status(thm)],[f_2423_2]) ).
fof(f_2424_1,plain,
! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2))) ),
inference(fof_nnf,[status(thm)],[fact_mem__splitI]) ).
fof(f_2424_2,plain,
! [U_8368,U_8367,U_8366,U_8365,U_8364,U_8363,U_8362] :
( hBOOL(hAPP(hAPP(c_member(U_8362),U_8363),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8367,U_8368,tc_fun(U_8362,tc_HOL_Obool)),U_8364),hAPP(hAPP(c_Product__Type_OPair(U_8367,U_8368),U_8365),U_8366))))
| ~ hBOOL(hAPP(hAPP(c_member(U_8362),U_8363),hAPP(hAPP(U_8364,U_8365),U_8366))) ),
inference(variable_rename,[status(thm)],[f_2424_1]) ).
cnf(f_2424_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8362),U_8363),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_8367,U_8368,tc_fun(U_8362,tc_HOL_Obool)),U_8364),hAPP(hAPP(c_Product__Type_OPair(U_8367,U_8368),U_8365),U_8366))))
| ~ hBOOL(hAPP(hAPP(c_member(U_8362),U_8363),hAPP(hAPP(U_8364,U_8365),U_8366))) ),
inference(clausify,[status(thm)],[f_2424_2]) ).
fof(f_2425_1,plain,
! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_d),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_pair__imageI]) ).
fof(f_2425_2,plain,
! [U_8375,U_8374,U_8373,U_8372,U_8371,U_8370,U_8369] :
( hBOOL(hAPP(hAPP(c_member(U_8374),hAPP(hAPP(U_8375,U_8371),U_8372)),hAPP(c_Set_Oimage(tc_prod(U_8369,U_8370),U_8374,hAPP(c_Product__Type_Oprod_Oprod__case(U_8369,U_8370,U_8374),U_8375)),U_8373)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8369,U_8370)),hAPP(hAPP(c_Product__Type_OPair(U_8369,U_8370),U_8371),U_8372)),U_8373)) ),
inference(variable_rename,[status(thm)],[f_2425_1]) ).
cnf(f_2425_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8374),hAPP(hAPP(U_8375,U_8371),U_8372)),hAPP(c_Set_Oimage(tc_prod(U_8369,U_8370),U_8374,hAPP(c_Product__Type_Oprod_Oprod__case(U_8369,U_8370,U_8374),U_8375)),U_8373)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8369,U_8370)),hAPP(hAPP(c_Product__Type_OPair(U_8369,U_8370),U_8371),U_8372)),U_8373)) ),
inference(clausify,[status(thm)],[f_2425_2]) ).
fof(f_2426_1,plain,
! [V_A_2,T_b] :
( ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_all__not__in__conv]) ).
fof(f_2426_2,plain,
! [U_8379,U_8378] :
( ( ! [U_8377] : ~ hBOOL(hAPP(hAPP(c_member(U_8378),U_8377),U_8379))
| U_8379 != c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool)) )
& ( U_8379 = c_Orderings_Obot__class_Obot(tc_fun(U_8378,tc_HOL_Obool))
| ? [U_8376] : hBOOL(hAPP(hAPP(c_member(U_8378),U_8376),U_8379)) ) ),
inference(variable_rename,[status(thm)],[f_2426_1]) ).
fof(f_2426_3,plain,
( ! [U_8383,U_8381] :
( ! [U_8377] : ~ hBOOL(hAPP(hAPP(c_member(U_8381),U_8377),U_8383))
| U_8383 != c_Orderings_Obot__class_Obot(tc_fun(U_8381,tc_HOL_Obool)) )
& ! [U_8382,U_8380] :
( U_8382 = c_Orderings_Obot__class_Obot(tc_fun(U_8380,tc_HOL_Obool))
| ? [U_8376] : hBOOL(hAPP(hAPP(c_member(U_8380),U_8376),U_8382)) ) ),
inference(miniscope,[status(thm)],[f_2426_2]) ).
fof(f_2426_4,plain,
( ! [U_8383,U_8381] :
( ! [U_8377] : ~ hBOOL(hAPP(hAPP(c_member(U_8381),U_8377),U_8383))
| U_8383 != c_Orderings_Obot__class_Obot(tc_fun(U_8381,tc_HOL_Obool)) )
& ! [U_8382,U_8380] :
( U_8382 = c_Orderings_Obot__class_Obot(tc_fun(U_8380,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8380),sK157(U_8382,U_8380)),U_8382)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK157]),skolemize(U_8376,sK157(U_8382,U_8380))],[f_2426_3]) ).
cnf(f_2426_5,plain,
( U_8382 = c_Orderings_Obot__class_Obot(tc_fun(U_8380,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8380),sK157(U_8382,U_8380)),U_8382)) ),
inference(clausify,[status(thm)],[f_2426_4]) ).
cnf(f_2426_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8381),U_8377),U_8383))
| U_8383 != c_Orderings_Obot__class_Obot(tc_fun(U_8381,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2426_4]) ).
fof(f_2427_1,plain,
! [V_A_2,T_b] :
( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_ex__in__conv]) ).
fof(f_2427_2,plain,
! [U_8387,U_8386] :
( ( ? [U_8385] : hBOOL(hAPP(hAPP(c_member(U_8386),U_8385),U_8387))
| U_8387 = c_Orderings_Obot__class_Obot(tc_fun(U_8386,tc_HOL_Obool)) )
& ( U_8387 != c_Orderings_Obot__class_Obot(tc_fun(U_8386,tc_HOL_Obool))
| ! [U_8384] : ~ hBOOL(hAPP(hAPP(c_member(U_8386),U_8384),U_8387)) ) ),
inference(variable_rename,[status(thm)],[f_2427_1]) ).
fof(f_2427_3,plain,
( ! [U_8391,U_8389] :
( ? [U_8385] : hBOOL(hAPP(hAPP(c_member(U_8389),U_8385),U_8391))
| U_8391 = c_Orderings_Obot__class_Obot(tc_fun(U_8389,tc_HOL_Obool)) )
& ! [U_8390,U_8388] :
( U_8390 != c_Orderings_Obot__class_Obot(tc_fun(U_8388,tc_HOL_Obool))
| ! [U_8384] : ~ hBOOL(hAPP(hAPP(c_member(U_8388),U_8384),U_8390)) ) ),
inference(miniscope,[status(thm)],[f_2427_2]) ).
fof(f_2427_4,plain,
( ! [U_8391,U_8389] :
( hBOOL(hAPP(hAPP(c_member(U_8389),sK158(U_8391,U_8389)),U_8391))
| U_8391 = c_Orderings_Obot__class_Obot(tc_fun(U_8389,tc_HOL_Obool)) )
& ! [U_8390,U_8388] :
( U_8390 != c_Orderings_Obot__class_Obot(tc_fun(U_8388,tc_HOL_Obool))
| ! [U_8384] : ~ hBOOL(hAPP(hAPP(c_member(U_8388),U_8384),U_8390)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK158]),skolemize(U_8385,sK158(U_8391,U_8389))],[f_2427_3]) ).
cnf(f_2427_5,plain,
( U_8390 != c_Orderings_Obot__class_Obot(tc_fun(U_8388,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_8388),U_8384),U_8390)) ),
inference(clausify,[status(thm)],[f_2427_4]) ).
cnf(f_2427_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8389),sK158(U_8391,U_8389)),U_8391))
| U_8391 = c_Orderings_Obot__class_Obot(tc_fun(U_8389,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2427_4]) ).
fof(f_2428_1,plain,
! [V_c_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_empty__iff]) ).
fof(f_2428_2,plain,
! [U_8393,U_8392] : ~ hBOOL(hAPP(hAPP(c_member(U_8392),U_8393),c_Orderings_Obot__class_Obot(tc_fun(U_8392,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_2428_1]) ).
cnf(f_2428_3,plain,
~ hBOOL(hAPP(hAPP(c_member(U_8392),U_8393),c_Orderings_Obot__class_Obot(tc_fun(U_8392,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_2428_2]) ).
fof(f_2429_1,plain,
! [V_a_2,T_b,V_A_2] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_equals0D]) ).
fof(f_2429_2,plain,
! [U_8396,U_8395,U_8394] :
( ~ hBOOL(hAPP(hAPP(c_member(U_8395),U_8396),U_8394))
| U_8394 != c_Orderings_Obot__class_Obot(tc_fun(U_8395,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_2429_1]) ).
cnf(f_2429_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8395),U_8396),U_8394))
| U_8394 != c_Orderings_Obot__class_Obot(tc_fun(U_8395,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2429_2]) ).
fof(f_2430_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Diff__iff]) ).
fof(f_2430_2,plain,
! [U_8400,U_8399,U_8398,U_8397] :
( ( hBOOL(hAPP(hAPP(c_member(U_8397),U_8398),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8397,tc_HOL_Obool)),U_8399),U_8400)))
| hBOOL(hAPP(hAPP(c_member(U_8397),U_8398),U_8400))
| ~ hBOOL(hAPP(hAPP(c_member(U_8397),U_8398),U_8399)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(U_8397),U_8398),U_8400))
& hBOOL(hAPP(hAPP(c_member(U_8397),U_8398),U_8399)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8397),U_8398),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8397,tc_HOL_Obool)),U_8399),U_8400))) ) ),
inference(variable_rename,[status(thm)],[f_2430_1]) ).
fof(f_2430_3,plain,
( ! [U_8408,U_8406,U_8404,U_8402] :
( hBOOL(hAPP(hAPP(c_member(U_8402),U_8404),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8402,tc_HOL_Obool)),U_8406),U_8408)))
| hBOOL(hAPP(hAPP(c_member(U_8402),U_8404),U_8408))
| ~ hBOOL(hAPP(hAPP(c_member(U_8402),U_8404),U_8406)) )
& ! [U_8407,U_8405,U_8403,U_8401] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_8401),U_8403),U_8407))
& hBOOL(hAPP(hAPP(c_member(U_8401),U_8403),U_8405)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8401),U_8403),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8401,tc_HOL_Obool)),U_8405),U_8407))) ) ),
inference(miniscope,[status(thm)],[f_2430_2]) ).
cnf(f_2430_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8401),U_8403),U_8405))
| ~ hBOOL(hAPP(hAPP(c_member(U_8401),U_8403),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8401,tc_HOL_Obool)),U_8405),U_8407))) ),
inference(clausify,[status(thm)],[f_2430_3]) ).
cnf(f_2430_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8401),U_8403),U_8407))
| ~ hBOOL(hAPP(hAPP(c_member(U_8401),U_8403),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8401,tc_HOL_Obool)),U_8405),U_8407))) ),
inference(clausify,[status(thm)],[f_2430_3]) ).
cnf(f_2430_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8402),U_8404),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8402,tc_HOL_Obool)),U_8406),U_8408)))
| hBOOL(hAPP(hAPP(c_member(U_8402),U_8404),U_8408))
| ~ hBOOL(hAPP(hAPP(c_member(U_8402),U_8404),U_8406)) ),
inference(clausify,[status(thm)],[f_2430_3]) ).
fof(f_2431_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_DiffD1]) ).
fof(f_2431_2,plain,
! [U_8412,U_8411,U_8410,U_8409] :
( hBOOL(hAPP(hAPP(c_member(U_8409),U_8410),U_8411))
| ~ hBOOL(hAPP(hAPP(c_member(U_8409),U_8410),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8409,tc_HOL_Obool)),U_8411),U_8412))) ),
inference(variable_rename,[status(thm)],[f_2431_1]) ).
cnf(f_2431_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8409),U_8410),U_8411))
| ~ hBOOL(hAPP(hAPP(c_member(U_8409),U_8410),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8409,tc_HOL_Obool)),U_8411),U_8412))) ),
inference(clausify,[status(thm)],[f_2431_2]) ).
fof(f_2432_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_DiffD2]) ).
fof(f_2432_2,plain,
! [U_8416,U_8415,U_8414,U_8413] :
( ~ hBOOL(hAPP(hAPP(c_member(U_8413),U_8414),U_8416))
| ~ hBOOL(hAPP(hAPP(c_member(U_8413),U_8414),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8413,tc_HOL_Obool)),U_8415),U_8416))) ),
inference(variable_rename,[status(thm)],[f_2432_1]) ).
cnf(f_2432_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8413),U_8414),U_8416))
| ~ hBOOL(hAPP(hAPP(c_member(U_8413),U_8414),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8413,tc_HOL_Obool)),U_8415),U_8416))) ),
inference(clausify,[status(thm)],[f_2432_2]) ).
fof(f_2433_1,plain,
! [V_A_2,V_a_2,T_b] :
( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__absorb]) ).
fof(f_2433_2,plain,
! [U_8419,U_8418,U_8417] :
( hAPP(hAPP(c_Set_Oinsert(U_8417),U_8418),U_8419) = U_8419
| ~ hBOOL(hAPP(hAPP(c_member(U_8417),U_8418),U_8419)) ),
inference(variable_rename,[status(thm)],[f_2433_1]) ).
cnf(f_2433_3,plain,
( hAPP(hAPP(c_Set_Oinsert(U_8417),U_8418),U_8419) = U_8419
| ~ hBOOL(hAPP(hAPP(c_member(U_8417),U_8418),U_8419)) ),
inference(clausify,[status(thm)],[f_2433_2]) ).
fof(f_2434_1,plain,
! [V_b_2,V_B_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_insertI2]) ).
fof(f_2434_2,plain,
! [U_8423,U_8422,U_8421,U_8420] :
( hBOOL(hAPP(hAPP(c_member(U_8420),U_8421),hAPP(hAPP(c_Set_Oinsert(U_8420),U_8423),U_8422)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8420),U_8421),U_8422)) ),
inference(variable_rename,[status(thm)],[f_2434_1]) ).
cnf(f_2434_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8420),U_8421),hAPP(hAPP(c_Set_Oinsert(U_8420),U_8423),U_8422)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8420),U_8421),U_8422)) ),
inference(clausify,[status(thm)],[f_2434_2]) ).
fof(f_2435_1,plain,
! [V_B_2,V_A_2,V_x_2,T_b] :
( ( ( hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)
| V_A_2 != V_B_2 )
& ( V_A_2 = V_B_2
| hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) != hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2) ) )
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__ident]) ).
fof(f_2435_2,plain,
! [U_8427,U_8426,U_8425,U_8424] :
( ( ( hAPP(hAPP(c_Set_Oinsert(U_8424),U_8425),U_8426) = hAPP(hAPP(c_Set_Oinsert(U_8424),U_8425),U_8427)
| U_8426 != U_8427 )
& ( U_8426 = U_8427
| hAPP(hAPP(c_Set_Oinsert(U_8424),U_8425),U_8426) != hAPP(hAPP(c_Set_Oinsert(U_8424),U_8425),U_8427) ) )
| hBOOL(hAPP(hAPP(c_member(U_8424),U_8425),U_8427))
| hBOOL(hAPP(hAPP(c_member(U_8424),U_8425),U_8426)) ),
inference(variable_rename,[status(thm)],[f_2435_1]) ).
cnf(f_2435_3,plain,
( U_8426 = U_8427
| hAPP(hAPP(c_Set_Oinsert(U_8424),U_8425),U_8426) != hAPP(hAPP(c_Set_Oinsert(U_8424),U_8425),U_8427)
| hBOOL(hAPP(hAPP(c_member(U_8424),U_8425),U_8427))
| hBOOL(hAPP(hAPP(c_member(U_8424),U_8425),U_8426)) ),
inference(clausify,[status(thm)],[f_2435_2]) ).
cnf(f_2435_4,plain,
( hAPP(hAPP(c_Set_Oinsert(U_8424),U_8425),U_8426) = hAPP(hAPP(c_Set_Oinsert(U_8424),U_8425),U_8427)
| U_8426 != U_8427
| hBOOL(hAPP(hAPP(c_member(U_8424),U_8425),U_8427))
| hBOOL(hAPP(hAPP(c_member(U_8424),U_8425),U_8426)) ),
inference(clausify,[status(thm)],[f_2435_2]) ).
fof(f_2436_1,plain,
! [V_A_2,V_b_2,V_a_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
| ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
& V_a_2 != V_b_2 ) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| V_a_2 = V_b_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_insert__iff]) ).
fof(f_2436_2,plain,
! [U_8431,U_8430,U_8429,U_8428] :
( ( hBOOL(hAPP(hAPP(c_member(U_8428),U_8429),hAPP(hAPP(c_Set_Oinsert(U_8428),U_8430),U_8431)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_8428),U_8429),U_8431))
& U_8429 != U_8430 ) )
& ( hBOOL(hAPP(hAPP(c_member(U_8428),U_8429),U_8431))
| U_8429 = U_8430
| ~ hBOOL(hAPP(hAPP(c_member(U_8428),U_8429),hAPP(hAPP(c_Set_Oinsert(U_8428),U_8430),U_8431))) ) ),
inference(variable_rename,[status(thm)],[f_2436_1]) ).
fof(f_2436_3,plain,
( ! [U_8439,U_8437,U_8435,U_8433] :
( hBOOL(hAPP(hAPP(c_member(U_8433),U_8435),hAPP(hAPP(c_Set_Oinsert(U_8433),U_8437),U_8439)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_8433),U_8435),U_8439))
& U_8435 != U_8437 ) )
& ! [U_8438,U_8436,U_8434,U_8432] :
( hBOOL(hAPP(hAPP(c_member(U_8432),U_8434),U_8438))
| U_8434 = U_8436
| ~ hBOOL(hAPP(hAPP(c_member(U_8432),U_8434),hAPP(hAPP(c_Set_Oinsert(U_8432),U_8436),U_8438))) ) ),
inference(miniscope,[status(thm)],[f_2436_2]) ).
cnf(f_2436_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8432),U_8434),U_8438))
| U_8434 = U_8436
| ~ hBOOL(hAPP(hAPP(c_member(U_8432),U_8434),hAPP(hAPP(c_Set_Oinsert(U_8432),U_8436),U_8438))) ),
inference(clausify,[status(thm)],[f_2436_3]) ).
cnf(f_2436_5,plain,
( U_8435 != U_8437
| hBOOL(hAPP(hAPP(c_member(U_8433),U_8435),hAPP(hAPP(c_Set_Oinsert(U_8433),U_8437),U_8439))) ),
inference(clausify,[status(thm)],[f_2436_3]) ).
cnf(f_2436_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8433),U_8435),U_8439))
| hBOOL(hAPP(hAPP(c_member(U_8433),U_8435),hAPP(hAPP(c_Set_Oinsert(U_8433),U_8437),U_8439))) ),
inference(clausify,[status(thm)],[f_2436_3]) ).
fof(f_2437_1,plain,
! [V_B_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
inference(fof_nnf,[status(thm)],[fact_insertI1]) ).
fof(f_2437_2,plain,
! [U_8442,U_8441,U_8440] : hBOOL(hAPP(hAPP(c_member(U_8440),U_8441),hAPP(hAPP(c_Set_Oinsert(U_8440),U_8441),U_8442))),
inference(variable_rename,[status(thm)],[f_2437_1]) ).
cnf(f_2437_3,plain,
hBOOL(hAPP(hAPP(c_member(U_8440),U_8441),hAPP(hAPP(c_Set_Oinsert(U_8440),U_8441),U_8442))),
inference(clausify,[status(thm)],[f_2437_2]) ).
fof(f_2438_1,plain,
! [V_A_2,V_c_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_ComplE]) ).
fof(f_2438_2,plain,
! [U_8445,U_8444,U_8443] :
( ~ hBOOL(hAPP(hAPP(c_member(U_8443),U_8444),U_8445))
| ~ hBOOL(hAPP(hAPP(c_member(U_8443),U_8444),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8443,tc_HOL_Obool)),U_8445))) ),
inference(variable_rename,[status(thm)],[f_2438_1]) ).
cnf(f_2438_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8443),U_8444),U_8445))
| ~ hBOOL(hAPP(hAPP(c_member(U_8443),U_8444),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8443,tc_HOL_Obool)),U_8445))) ),
inference(clausify,[status(thm)],[f_2438_2]) ).
fof(f_2439_1,plain,
! [V_A_2,V_c_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_ComplD]) ).
fof(f_2439_2,plain,
! [U_8448,U_8447,U_8446] :
( ~ hBOOL(hAPP(hAPP(c_member(U_8446),U_8447),U_8448))
| ~ hBOOL(hAPP(hAPP(c_member(U_8446),U_8447),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8446,tc_HOL_Obool)),U_8448))) ),
inference(variable_rename,[status(thm)],[f_2439_1]) ).
cnf(f_2439_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8446),U_8447),U_8448))
| ~ hBOOL(hAPP(hAPP(c_member(U_8446),U_8447),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8446,tc_HOL_Obool)),U_8448))) ),
inference(clausify,[status(thm)],[f_2439_2]) ).
fof(f_2440_1,plain,
! [V_A_2,V_c_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
| hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Compl__iff]) ).
fof(f_2440_2,plain,
! [U_8451,U_8450,U_8449] :
( ( hBOOL(hAPP(hAPP(c_member(U_8449),U_8450),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8449,tc_HOL_Obool)),U_8451)))
| hBOOL(hAPP(hAPP(c_member(U_8449),U_8450),U_8451)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(U_8449),U_8450),U_8451))
| ~ hBOOL(hAPP(hAPP(c_member(U_8449),U_8450),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8449,tc_HOL_Obool)),U_8451))) ) ),
inference(variable_rename,[status(thm)],[f_2440_1]) ).
fof(f_2440_3,plain,
( ! [U_8457,U_8455,U_8453] :
( hBOOL(hAPP(hAPP(c_member(U_8453),U_8455),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8453,tc_HOL_Obool)),U_8457)))
| hBOOL(hAPP(hAPP(c_member(U_8453),U_8455),U_8457)) )
& ! [U_8456,U_8454,U_8452] :
( ~ hBOOL(hAPP(hAPP(c_member(U_8452),U_8454),U_8456))
| ~ hBOOL(hAPP(hAPP(c_member(U_8452),U_8454),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8452,tc_HOL_Obool)),U_8456))) ) ),
inference(miniscope,[status(thm)],[f_2440_2]) ).
cnf(f_2440_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8452),U_8454),U_8456))
| ~ hBOOL(hAPP(hAPP(c_member(U_8452),U_8454),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8452,tc_HOL_Obool)),U_8456))) ),
inference(clausify,[status(thm)],[f_2440_3]) ).
cnf(f_2440_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_8453),U_8455),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8453,tc_HOL_Obool)),U_8457)))
| hBOOL(hAPP(hAPP(c_member(U_8453),U_8455),U_8457)) ),
inference(clausify,[status(thm)],[f_2440_3]) ).
fof(f_2441_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_2441_2,plain,
! [U_8459,U_8458] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8458),U_8459))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8458)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8459))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8458)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8459)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8458),U_8459)) ) ),
inference(variable_rename,[status(thm)],[f_2441_1]) ).
fof(f_2441_3,plain,
( ! [U_8463,U_8461] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8461),U_8463))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8461)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8463))) )
& ! [U_8462,U_8460] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8460)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8462)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8460),U_8462)) ) ),
inference(miniscope,[status(thm)],[f_2441_2]) ).
cnf(f_2441_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8460)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8462)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8460),U_8462)) ),
inference(clausify,[status(thm)],[f_2441_3]) ).
cnf(f_2441_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_8461),U_8463))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_8461)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8463))) ),
inference(clausify,[status(thm)],[f_2441_3]) ).
fof(f_2442_1,plain,
! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
| V_b_2 != hAPP(V_f_2,V_x_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_rev__image__eqI]) ).
fof(f_2442_2,plain,
! [U_8469,U_8468,U_8467,U_8466,U_8465,U_8464] :
( hBOOL(hAPP(hAPP(c_member(U_8469),U_8467),hAPP(c_Set_Oimage(U_8464,U_8469,U_8468),U_8466)))
| U_8467 != hAPP(U_8468,U_8465)
| ~ hBOOL(hAPP(hAPP(c_member(U_8464),U_8465),U_8466)) ),
inference(variable_rename,[status(thm)],[f_2442_1]) ).
cnf(f_2442_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8469),U_8467),hAPP(c_Set_Oimage(U_8464,U_8469,U_8468),U_8466)))
| U_8467 != hAPP(U_8468,U_8465)
| ~ hBOOL(hAPP(hAPP(c_member(U_8464),U_8465),U_8466)) ),
inference(clausify,[status(thm)],[f_2442_2]) ).
fof(f_2443_1,plain,
! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_imageI]) ).
fof(f_2443_2,plain,
! [U_8474,U_8473,U_8472,U_8471,U_8470] :
( hBOOL(hAPP(hAPP(c_member(U_8473),hAPP(U_8474,U_8471)),hAPP(c_Set_Oimage(U_8470,U_8473,U_8474),U_8472)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8470),U_8471),U_8472)) ),
inference(variable_rename,[status(thm)],[f_2443_1]) ).
cnf(f_2443_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8473),hAPP(U_8474,U_8471)),hAPP(c_Set_Oimage(U_8470,U_8473,U_8474),U_8472)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8470),U_8471),U_8472)) ),
inference(clausify,[status(thm)],[f_2443_2]) ).
fof(f_2444_1,plain,
! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
| ! [B_x] :
( V_z_2 != hAPP(V_f_2,B_x)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ? [B_x] :
( V_z_2 = hAPP(V_f_2,B_x)
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_image__iff]) ).
fof(f_2444_2,plain,
! [U_8481,U_8480,U_8479,U_8478,U_8477] :
( ( hBOOL(hAPP(hAPP(c_member(U_8477),U_8478),hAPP(c_Set_Oimage(U_8479,U_8477,U_8480),U_8481)))
| ! [U_8476] :
( U_8478 != hAPP(U_8480,U_8476)
| ~ hBOOL(hAPP(hAPP(c_member(U_8479),U_8476),U_8481)) ) )
& ( ? [U_8475] :
( U_8478 = hAPP(U_8480,U_8475)
& hBOOL(hAPP(hAPP(c_member(U_8479),U_8475),U_8481)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8477),U_8478),hAPP(c_Set_Oimage(U_8479,U_8477,U_8480),U_8481))) ) ),
inference(variable_rename,[status(thm)],[f_2444_1]) ).
fof(f_2444_3,plain,
( ! [U_8491,U_8489,U_8487,U_8485] :
( ! [U_8483] : hBOOL(hAPP(hAPP(c_member(U_8483),U_8485),hAPP(c_Set_Oimage(U_8487,U_8483,U_8489),U_8491)))
| ! [U_8476] :
( U_8485 != hAPP(U_8489,U_8476)
| ~ hBOOL(hAPP(hAPP(c_member(U_8487),U_8476),U_8491)) ) )
& ! [U_8490,U_8488,U_8486,U_8484] :
( ! [U_8482] : ~ hBOOL(hAPP(hAPP(c_member(U_8482),U_8484),hAPP(c_Set_Oimage(U_8486,U_8482,U_8488),U_8490)))
| ? [U_8475] :
( U_8484 = hAPP(U_8488,U_8475)
& hBOOL(hAPP(hAPP(c_member(U_8486),U_8475),U_8490)) ) ) ),
inference(miniscope,[status(thm)],[f_2444_2]) ).
fof(f_2444_4,plain,
( ! [U_8491,U_8489,U_8487,U_8485] :
( ! [U_8483] : hBOOL(hAPP(hAPP(c_member(U_8483),U_8485),hAPP(c_Set_Oimage(U_8487,U_8483,U_8489),U_8491)))
| ! [U_8476] :
( U_8485 != hAPP(U_8489,U_8476)
| ~ hBOOL(hAPP(hAPP(c_member(U_8487),U_8476),U_8491)) ) )
& ! [U_8490,U_8488,U_8486,U_8484] :
( ! [U_8482] : ~ hBOOL(hAPP(hAPP(c_member(U_8482),U_8484),hAPP(c_Set_Oimage(U_8486,U_8482,U_8488),U_8490)))
| ( U_8484 = hAPP(U_8488,sK159(U_8490,U_8488,U_8486,U_8484))
& hBOOL(hAPP(hAPP(c_member(U_8486),sK159(U_8490,U_8488,U_8486,U_8484)),U_8490)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK159]),skolemize(U_8475,sK159(U_8490,U_8488,U_8486,U_8484))],[f_2444_3]) ).
cnf(f_2444_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_8486),sK159(U_8490,U_8488,U_8486,U_8484)),U_8490))
| ~ hBOOL(hAPP(hAPP(c_member(U_8482),U_8484),hAPP(c_Set_Oimage(U_8486,U_8482,U_8488),U_8490))) ),
inference(clausify,[status(thm)],[f_2444_4]) ).
cnf(f_2444_6,plain,
( U_8484 = hAPP(U_8488,sK159(U_8490,U_8488,U_8486,U_8484))
| ~ hBOOL(hAPP(hAPP(c_member(U_8482),U_8484),hAPP(c_Set_Oimage(U_8486,U_8482,U_8488),U_8490))) ),
inference(clausify,[status(thm)],[f_2444_4]) ).
cnf(f_2444_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_8483),U_8485),hAPP(c_Set_Oimage(U_8487,U_8483,U_8489),U_8491)))
| U_8485 != hAPP(U_8489,U_8476)
| ~ hBOOL(hAPP(hAPP(c_member(U_8487),U_8476),U_8491)) ),
inference(clausify,[status(thm)],[f_2444_4]) ).
fof(f_2445_1,plain,
! [V_A_2,V_x_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(V_A_2,V_x_2)) )
& ( hBOOL(hAPP(V_A_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_mem__def]) ).
fof(f_2445_2,plain,
! [U_8494,U_8493,U_8492] :
( ( hBOOL(hAPP(hAPP(c_member(U_8492),U_8493),U_8494))
| ~ hBOOL(hAPP(U_8494,U_8493)) )
& ( hBOOL(hAPP(U_8494,U_8493))
| ~ hBOOL(hAPP(hAPP(c_member(U_8492),U_8493),U_8494)) ) ),
inference(variable_rename,[status(thm)],[f_2445_1]) ).
fof(f_2445_3,plain,
( ! [U_8500,U_8498] :
( ! [U_8496] : hBOOL(hAPP(hAPP(c_member(U_8496),U_8498),U_8500))
| ~ hBOOL(hAPP(U_8500,U_8498)) )
& ! [U_8499,U_8497] :
( ! [U_8495] : ~ hBOOL(hAPP(hAPP(c_member(U_8495),U_8497),U_8499))
| hBOOL(hAPP(U_8499,U_8497)) ) ),
inference(miniscope,[status(thm)],[f_2445_2]) ).
cnf(f_2445_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8495),U_8497),U_8499))
| hBOOL(hAPP(U_8499,U_8497)) ),
inference(clausify,[status(thm)],[f_2445_3]) ).
cnf(f_2445_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_8496),U_8498),U_8500))
| ~ hBOOL(hAPP(U_8500,U_8498)) ),
inference(clausify,[status(thm)],[f_2445_3]) ).
fof(f_2446_1,plain,
! [V_y_2,V_x_2] :
( ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_Int_ORep__Integ,V_x_2) != hAPP(c_Int_ORep__Integ,V_y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Rep__Integ__inject]) ).
fof(f_2446_2,plain,
! [U_8502,U_8501] :
( ( hAPP(c_Int_ORep__Integ,U_8501) = hAPP(c_Int_ORep__Integ,U_8502)
| U_8501 != U_8502 )
& ( U_8501 = U_8502
| hAPP(c_Int_ORep__Integ,U_8501) != hAPP(c_Int_ORep__Integ,U_8502) ) ),
inference(variable_rename,[status(thm)],[f_2446_1]) ).
fof(f_2446_3,plain,
( ! [U_8506,U_8504] :
( hAPP(c_Int_ORep__Integ,U_8504) = hAPP(c_Int_ORep__Integ,U_8506)
| U_8504 != U_8506 )
& ! [U_8505,U_8503] :
( U_8503 = U_8505
| hAPP(c_Int_ORep__Integ,U_8503) != hAPP(c_Int_ORep__Integ,U_8505) ) ),
inference(miniscope,[status(thm)],[f_2446_2]) ).
cnf(f_2446_4,plain,
( U_8503 = U_8505
| hAPP(c_Int_ORep__Integ,U_8503) != hAPP(c_Int_ORep__Integ,U_8505) ),
inference(clausify,[status(thm)],[f_2446_3]) ).
cnf(f_2446_5,plain,
( hAPP(c_Int_ORep__Integ,U_8504) = hAPP(c_Int_ORep__Integ,U_8506)
| U_8504 != U_8506 ),
inference(clausify,[status(thm)],[f_2446_3]) ).
fof(f_2447_1,plain,
! [V_x_2,T_b,V_B_2,V_A_2] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
| V_A_2 != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_eqset__imp__iff]) ).
fof(f_2447_2,plain,
! [U_8510,U_8509,U_8508,U_8507] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_8509),U_8510),U_8507))
| ~ hBOOL(hAPP(hAPP(c_member(U_8509),U_8510),U_8508)) )
& ( hBOOL(hAPP(hAPP(c_member(U_8509),U_8510),U_8508))
| ~ hBOOL(hAPP(hAPP(c_member(U_8509),U_8510),U_8507)) ) )
| U_8507 != U_8508 ),
inference(variable_rename,[status(thm)],[f_2447_1]) ).
cnf(f_2447_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8509),U_8510),U_8508))
| ~ hBOOL(hAPP(hAPP(c_member(U_8509),U_8510),U_8507))
| U_8507 != U_8508 ),
inference(clausify,[status(thm)],[f_2447_2]) ).
cnf(f_2447_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8509),U_8510),U_8507))
| ~ hBOOL(hAPP(hAPP(c_member(U_8509),U_8510),U_8508))
| U_8507 != U_8508 ),
inference(clausify,[status(thm)],[f_2447_2]) ).
fof(f_2448_1,plain,
! [V_A_2,T_b,V_y_2,V_x_2] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
| V_x_2 != V_y_2 ),
inference(fof_nnf,[status(thm)],[fact_eqelem__imp__iff]) ).
fof(f_2448_2,plain,
! [U_8514,U_8513,U_8512,U_8511] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_8513),U_8511),U_8514))
| ~ hBOOL(hAPP(hAPP(c_member(U_8513),U_8512),U_8514)) )
& ( hBOOL(hAPP(hAPP(c_member(U_8513),U_8512),U_8514))
| ~ hBOOL(hAPP(hAPP(c_member(U_8513),U_8511),U_8514)) ) )
| U_8511 != U_8512 ),
inference(variable_rename,[status(thm)],[f_2448_1]) ).
cnf(f_2448_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8513),U_8512),U_8514))
| ~ hBOOL(hAPP(hAPP(c_member(U_8513),U_8511),U_8514))
| U_8511 != U_8512 ),
inference(clausify,[status(thm)],[f_2448_2]) ).
cnf(f_2448_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8513),U_8511),U_8514))
| ~ hBOOL(hAPP(hAPP(c_member(U_8513),U_8512),U_8514))
| U_8511 != U_8512 ),
inference(clausify,[status(thm)],[f_2448_2]) ).
fof(f_2449_1,plain,
! [V_A_2,T_b,V_b_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
| V_a_2 != V_b_2 ),
inference(fof_nnf,[status(thm)],[fact_eq__mem__trans]) ).
fof(f_2449_2,plain,
! [U_8518,U_8517,U_8516,U_8515] :
( hBOOL(hAPP(hAPP(c_member(U_8517),U_8515),U_8518))
| ~ hBOOL(hAPP(hAPP(c_member(U_8517),U_8516),U_8518))
| U_8515 != U_8516 ),
inference(variable_rename,[status(thm)],[f_2449_1]) ).
cnf(f_2449_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8517),U_8515),U_8518))
| ~ hBOOL(hAPP(hAPP(c_member(U_8517),U_8516),U_8518))
| U_8515 != U_8516 ),
inference(clausify,[status(thm)],[f_2449_2]) ).
fof(f_2450_1,plain,
! [V_S_2,V_R_2,T_b] :
( ( hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)
| V_R_2 != V_S_2 )
& ( V_R_2 = V_S_2
| hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2) != hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2) ) ),
inference(fof_nnf,[status(thm)],[fact_pred__equals__eq]) ).
fof(f_2450_2,plain,
! [U_8521,U_8520,U_8519] :
( ( hAPP(hAPP(c_COMBC(U_8519,tc_fun(U_8519,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8519)),U_8520) = hAPP(hAPP(c_COMBC(U_8519,tc_fun(U_8519,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8519)),U_8521)
| U_8520 != U_8521 )
& ( U_8520 = U_8521
| hAPP(hAPP(c_COMBC(U_8519,tc_fun(U_8519,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8519)),U_8520) != hAPP(hAPP(c_COMBC(U_8519,tc_fun(U_8519,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8519)),U_8521) ) ),
inference(variable_rename,[status(thm)],[f_2450_1]) ).
fof(f_2450_3,plain,
( ! [U_8527,U_8525] :
( ! [U_8523] : hAPP(hAPP(c_COMBC(U_8523,tc_fun(U_8523,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8523)),U_8525) = hAPP(hAPP(c_COMBC(U_8523,tc_fun(U_8523,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8523)),U_8527)
| U_8525 != U_8527 )
& ! [U_8526,U_8524] :
( ! [U_8522] : hAPP(hAPP(c_COMBC(U_8522,tc_fun(U_8522,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8522)),U_8524) != hAPP(hAPP(c_COMBC(U_8522,tc_fun(U_8522,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8522)),U_8526)
| U_8524 = U_8526 ) ),
inference(miniscope,[status(thm)],[f_2450_2]) ).
cnf(f_2450_4,plain,
( hAPP(hAPP(c_COMBC(U_8522,tc_fun(U_8522,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8522)),U_8524) != hAPP(hAPP(c_COMBC(U_8522,tc_fun(U_8522,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8522)),U_8526)
| U_8524 = U_8526 ),
inference(clausify,[status(thm)],[f_2450_3]) ).
cnf(f_2450_5,plain,
( hAPP(hAPP(c_COMBC(U_8523,tc_fun(U_8523,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8523)),U_8525) = hAPP(hAPP(c_COMBC(U_8523,tc_fun(U_8523,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8523)),U_8527)
| U_8525 != U_8527 ),
inference(clausify,[status(thm)],[f_2450_3]) ).
fof(f_2451_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__mem]) ).
fof(f_2451_2,plain,
! [U_8530,U_8529,U_8528] :
( ( hBOOL(hAPP(hAPP(c_member(U_8528),U_8529),hAPP(c_fequal,U_8530)))
| U_8529 != U_8530 )
& ( U_8529 = U_8530
| ~ hBOOL(hAPP(hAPP(c_member(U_8528),U_8529),hAPP(c_fequal,U_8530))) ) ),
inference(variable_rename,[status(thm)],[f_2451_1]) ).
fof(f_2451_3,plain,
( ! [U_8536,U_8534] :
( ! [U_8532] : hBOOL(hAPP(hAPP(c_member(U_8532),U_8534),hAPP(c_fequal,U_8536)))
| U_8534 != U_8536 )
& ! [U_8535,U_8533] :
( ! [U_8531] : ~ hBOOL(hAPP(hAPP(c_member(U_8531),U_8533),hAPP(c_fequal,U_8535)))
| U_8533 = U_8535 ) ),
inference(miniscope,[status(thm)],[f_2451_2]) ).
cnf(f_2451_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8531),U_8533),hAPP(c_fequal,U_8535)))
| U_8533 = U_8535 ),
inference(clausify,[status(thm)],[f_2451_3]) ).
cnf(f_2451_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_8532),U_8534),hAPP(c_fequal,U_8536)))
| U_8534 != U_8536 ),
inference(clausify,[status(thm)],[f_2451_3]) ).
fof(f_2452_1,plain,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_in__mono]) ).
fof(f_2452_2,plain,
! [U_8540,U_8539,U_8538,U_8537] :
( hBOOL(hAPP(hAPP(c_member(U_8537),U_8540),U_8539))
| ~ hBOOL(hAPP(hAPP(c_member(U_8537),U_8540),U_8538))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8537,tc_HOL_Obool)),U_8538),U_8539)) ),
inference(variable_rename,[status(thm)],[f_2452_1]) ).
cnf(f_2452_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8537),U_8540),U_8539))
| ~ hBOOL(hAPP(hAPP(c_member(U_8537),U_8540),U_8538))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8537,tc_HOL_Obool)),U_8538),U_8539)) ),
inference(clausify,[status(thm)],[f_2452_2]) ).
fof(f_2453_1,plain,
! [V_B_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_set__rev__mp]) ).
fof(f_2453_2,plain,
! [U_8544,U_8543,U_8542,U_8541] :
( hBOOL(hAPP(hAPP(c_member(U_8541),U_8542),U_8544))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8541,tc_HOL_Obool)),U_8543),U_8544))
| ~ hBOOL(hAPP(hAPP(c_member(U_8541),U_8542),U_8543)) ),
inference(variable_rename,[status(thm)],[f_2453_1]) ).
cnf(f_2453_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8541),U_8542),U_8544))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8541,tc_HOL_Obool)),U_8543),U_8544))
| ~ hBOOL(hAPP(hAPP(c_member(U_8541),U_8542),U_8543)) ),
inference(clausify,[status(thm)],[f_2453_2]) ).
fof(f_2454_1,plain,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_set__mp]) ).
fof(f_2454_2,plain,
! [U_8548,U_8547,U_8546,U_8545] :
( hBOOL(hAPP(hAPP(c_member(U_8545),U_8548),U_8547))
| ~ hBOOL(hAPP(hAPP(c_member(U_8545),U_8548),U_8546))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8545,tc_HOL_Obool)),U_8546),U_8547)) ),
inference(variable_rename,[status(thm)],[f_2454_1]) ).
cnf(f_2454_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8545),U_8548),U_8547))
| ~ hBOOL(hAPP(hAPP(c_member(U_8545),U_8548),U_8546))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8545,tc_HOL_Obool)),U_8546),U_8547)) ),
inference(clausify,[status(thm)],[f_2454_2]) ).
fof(f_2455_1,plain,
! [V_f_2,V_X_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,V_X_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2)) ),
inference(fof_nnf,[status(thm)],[fact_weak__coinduct]) ).
fof(f_2455_2,plain,
! [U_8552,U_8551,U_8550,U_8549] :
( hBOOL(hAPP(hAPP(c_member(U_8549),U_8550),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_8549,tc_HOL_Obool),U_8552)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8549,tc_HOL_Obool)),U_8551),hAPP(U_8552,U_8551)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8549),U_8550),U_8551)) ),
inference(variable_rename,[status(thm)],[f_2455_1]) ).
cnf(f_2455_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8549),U_8550),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_8549,tc_HOL_Obool),U_8552)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8549,tc_HOL_Obool)),U_8551),hAPP(U_8552,U_8551)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8549),U_8550),U_8551)) ),
inference(clausify,[status(thm)],[f_2455_2]) ).
fof(f_2456_1,plain,
! [V_A_2,V_B_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_UnI2]) ).
fof(f_2456_2,plain,
! [U_8556,U_8555,U_8554,U_8553] :
( hBOOL(hAPP(hAPP(c_member(U_8553),U_8554),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8553,tc_HOL_Obool)),U_8556),U_8555)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8553),U_8554),U_8555)) ),
inference(variable_rename,[status(thm)],[f_2456_1]) ).
cnf(f_2456_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8553),U_8554),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8553,tc_HOL_Obool)),U_8556),U_8555)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8553),U_8554),U_8555)) ),
inference(clausify,[status(thm)],[f_2456_2]) ).
fof(f_2457_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_UnI1]) ).
fof(f_2457_2,plain,
! [U_8560,U_8559,U_8558,U_8557] :
( hBOOL(hAPP(hAPP(c_member(U_8557),U_8558),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8557,tc_HOL_Obool)),U_8559),U_8560)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8557),U_8558),U_8559)) ),
inference(variable_rename,[status(thm)],[f_2457_1]) ).
cnf(f_2457_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8557),U_8558),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8557,tc_HOL_Obool)),U_8559),U_8560)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8557),U_8558),U_8559)) ),
inference(clausify,[status(thm)],[f_2457_2]) ).
fof(f_2458_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Un__iff]) ).
fof(f_2458_2,plain,
! [U_8564,U_8563,U_8562,U_8561] :
( ( hBOOL(hAPP(hAPP(c_member(U_8561),U_8562),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8561,tc_HOL_Obool)),U_8563),U_8564)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_8561),U_8562),U_8564))
& ~ hBOOL(hAPP(hAPP(c_member(U_8561),U_8562),U_8563)) ) )
& ( hBOOL(hAPP(hAPP(c_member(U_8561),U_8562),U_8564))
| hBOOL(hAPP(hAPP(c_member(U_8561),U_8562),U_8563))
| ~ hBOOL(hAPP(hAPP(c_member(U_8561),U_8562),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8561,tc_HOL_Obool)),U_8563),U_8564))) ) ),
inference(variable_rename,[status(thm)],[f_2458_1]) ).
fof(f_2458_3,plain,
( ! [U_8572,U_8570,U_8568,U_8566] :
( hBOOL(hAPP(hAPP(c_member(U_8566),U_8568),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8566,tc_HOL_Obool)),U_8570),U_8572)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_8566),U_8568),U_8572))
& ~ hBOOL(hAPP(hAPP(c_member(U_8566),U_8568),U_8570)) ) )
& ! [U_8571,U_8569,U_8567,U_8565] :
( hBOOL(hAPP(hAPP(c_member(U_8565),U_8567),U_8571))
| hBOOL(hAPP(hAPP(c_member(U_8565),U_8567),U_8569))
| ~ hBOOL(hAPP(hAPP(c_member(U_8565),U_8567),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8565,tc_HOL_Obool)),U_8569),U_8571))) ) ),
inference(miniscope,[status(thm)],[f_2458_2]) ).
cnf(f_2458_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8565),U_8567),U_8571))
| hBOOL(hAPP(hAPP(c_member(U_8565),U_8567),U_8569))
| ~ hBOOL(hAPP(hAPP(c_member(U_8565),U_8567),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8565,tc_HOL_Obool)),U_8569),U_8571))) ),
inference(clausify,[status(thm)],[f_2458_3]) ).
cnf(f_2458_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8566),U_8568),U_8570))
| hBOOL(hAPP(hAPP(c_member(U_8566),U_8568),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8566,tc_HOL_Obool)),U_8570),U_8572))) ),
inference(clausify,[status(thm)],[f_2458_3]) ).
cnf(f_2458_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8566),U_8568),U_8572))
| hBOOL(hAPP(hAPP(c_member(U_8566),U_8568),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8566,tc_HOL_Obool)),U_8570),U_8572))) ),
inference(clausify,[status(thm)],[f_2458_3]) ).
fof(f_2459_1,plain,
! [V_c_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_psubsetD]) ).
fof(f_2459_2,plain,
! [U_8576,U_8575,U_8574,U_8573] :
( hBOOL(hAPP(hAPP(c_member(U_8573),U_8576),U_8575))
| ~ hBOOL(hAPP(hAPP(c_member(U_8573),U_8576),U_8574))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8573,tc_HOL_Obool)),U_8574),U_8575)) ),
inference(variable_rename,[status(thm)],[f_2459_1]) ).
cnf(f_2459_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8573),U_8576),U_8575))
| ~ hBOOL(hAPP(hAPP(c_member(U_8573),U_8576),U_8574))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8573,tc_HOL_Obool)),U_8574),U_8575)) ),
inference(clausify,[status(thm)],[f_2459_2]) ).
fof(f_2460_1,plain,
! [V_x_2,T_b] :
( ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_bot__empty__eq]) ).
fof(f_2460_2,plain,
! [U_8578,U_8577] :
( ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8577,tc_HOL_Obool)),U_8578))
| ~ hBOOL(hAPP(hAPP(c_member(U_8577),U_8578),c_Orderings_Obot__class_Obot(tc_fun(U_8577,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(hAPP(c_member(U_8577),U_8578),c_Orderings_Obot__class_Obot(tc_fun(U_8577,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8577,tc_HOL_Obool)),U_8578)) ) ),
inference(variable_rename,[status(thm)],[f_2460_1]) ).
fof(f_2460_3,plain,
( ! [U_8582,U_8580] :
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8580,tc_HOL_Obool)),U_8582))
| ~ hBOOL(hAPP(hAPP(c_member(U_8580),U_8582),c_Orderings_Obot__class_Obot(tc_fun(U_8580,tc_HOL_Obool)))) )
& ! [U_8581,U_8579] :
( hBOOL(hAPP(hAPP(c_member(U_8579),U_8581),c_Orderings_Obot__class_Obot(tc_fun(U_8579,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8579,tc_HOL_Obool)),U_8581)) ) ),
inference(miniscope,[status(thm)],[f_2460_2]) ).
cnf(f_2460_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8579),U_8581),c_Orderings_Obot__class_Obot(tc_fun(U_8579,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8579,tc_HOL_Obool)),U_8581)) ),
inference(clausify,[status(thm)],[f_2460_3]) ).
cnf(f_2460_5,plain,
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8580,tc_HOL_Obool)),U_8582))
| ~ hBOOL(hAPP(hAPP(c_member(U_8580),U_8582),c_Orderings_Obot__class_Obot(tc_fun(U_8580,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_2460_3]) ).
fof(f_2461_1,plain,
! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_b,V_less__eq_2,V_l_2,V_u_2)))
| ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) )
& ( ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
& hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_b,V_less__eq_2,V_l_2,V_u_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OatLeastAtMost__iff]) ).
fof(f_2461_2,plain,
! [U_8587,U_8586,U_8585,U_8584,U_8583] :
( ( hBOOL(hAPP(hAPP(c_member(U_8583),U_8584),c_SetInterval_Oord_OatLeastAtMost(U_8583,U_8585,U_8586,U_8587)))
| ~ hBOOL(hAPP(hAPP(U_8585,U_8584),U_8587))
| ~ hBOOL(hAPP(hAPP(U_8585,U_8586),U_8584)) )
& ( ( hBOOL(hAPP(hAPP(U_8585,U_8584),U_8587))
& hBOOL(hAPP(hAPP(U_8585,U_8586),U_8584)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8583),U_8584),c_SetInterval_Oord_OatLeastAtMost(U_8583,U_8585,U_8586,U_8587))) ) ),
inference(variable_rename,[status(thm)],[f_2461_1]) ).
fof(f_2461_3,plain,
( ! [U_8597,U_8595,U_8593,U_8591] :
( ! [U_8589] : hBOOL(hAPP(hAPP(c_member(U_8589),U_8591),c_SetInterval_Oord_OatLeastAtMost(U_8589,U_8593,U_8595,U_8597)))
| ~ hBOOL(hAPP(hAPP(U_8593,U_8591),U_8597))
| ~ hBOOL(hAPP(hAPP(U_8593,U_8595),U_8591)) )
& ! [U_8596,U_8594,U_8592,U_8590] :
( ! [U_8588] : ~ hBOOL(hAPP(hAPP(c_member(U_8588),U_8590),c_SetInterval_Oord_OatLeastAtMost(U_8588,U_8592,U_8594,U_8596)))
| ( hBOOL(hAPP(hAPP(U_8592,U_8590),U_8596))
& hBOOL(hAPP(hAPP(U_8592,U_8594),U_8590)) ) ) ),
inference(miniscope,[status(thm)],[f_2461_2]) ).
cnf(f_2461_4,plain,
( hBOOL(hAPP(hAPP(U_8592,U_8594),U_8590))
| ~ hBOOL(hAPP(hAPP(c_member(U_8588),U_8590),c_SetInterval_Oord_OatLeastAtMost(U_8588,U_8592,U_8594,U_8596))) ),
inference(clausify,[status(thm)],[f_2461_3]) ).
cnf(f_2461_5,plain,
( hBOOL(hAPP(hAPP(U_8592,U_8590),U_8596))
| ~ hBOOL(hAPP(hAPP(c_member(U_8588),U_8590),c_SetInterval_Oord_OatLeastAtMost(U_8588,U_8592,U_8594,U_8596))) ),
inference(clausify,[status(thm)],[f_2461_3]) ).
cnf(f_2461_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8589),U_8591),c_SetInterval_Oord_OatLeastAtMost(U_8589,U_8593,U_8595,U_8597)))
| ~ hBOOL(hAPP(hAPP(U_8593,U_8591),U_8597))
| ~ hBOOL(hAPP(hAPP(U_8593,U_8595),U_8591)) ),
inference(clausify,[status(thm)],[f_2461_3]) ).
fof(f_2462_1,plain,
! [V_S_2,V_R_2,T_c,T_b] :
( ( hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)
| V_R_2 != V_S_2 )
& ( V_R_2 = V_S_2
| hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2) != hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2) ) ),
inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2]) ).
fof(f_2462_2,plain,
! [U_8601,U_8600,U_8599,U_8598] :
( ( hAPP(hAPP(c_COMBC(U_8598,tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_fun(U_8599,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8599,tc_fun(tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_fun(U_8599,tc_HOL_Obool)),U_8598),c_COMBC(U_8599,tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8599,tc_prod(U_8598,U_8599)),tc_fun(U_8599,tc_fun(tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_HOL_Obool)),U_8598),hAPP(c_COMBB(tc_prod(U_8598,U_8599),tc_fun(tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_HOL_Obool),U_8599),c_member(tc_prod(U_8598,U_8599)))),c_Product__Type_OPair(U_8598,U_8599)))),U_8600) = hAPP(hAPP(c_COMBC(U_8598,tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_fun(U_8599,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8599,tc_fun(tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_fun(U_8599,tc_HOL_Obool)),U_8598),c_COMBC(U_8599,tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8599,tc_prod(U_8598,U_8599)),tc_fun(U_8599,tc_fun(tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_HOL_Obool)),U_8598),hAPP(c_COMBB(tc_prod(U_8598,U_8599),tc_fun(tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_HOL_Obool),U_8599),c_member(tc_prod(U_8598,U_8599)))),c_Product__Type_OPair(U_8598,U_8599)))),U_8601)
| U_8600 != U_8601 )
& ( U_8600 = U_8601
| hAPP(hAPP(c_COMBC(U_8598,tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_fun(U_8599,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8599,tc_fun(tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_fun(U_8599,tc_HOL_Obool)),U_8598),c_COMBC(U_8599,tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8599,tc_prod(U_8598,U_8599)),tc_fun(U_8599,tc_fun(tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_HOL_Obool)),U_8598),hAPP(c_COMBB(tc_prod(U_8598,U_8599),tc_fun(tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_HOL_Obool),U_8599),c_member(tc_prod(U_8598,U_8599)))),c_Product__Type_OPair(U_8598,U_8599)))),U_8600) != hAPP(hAPP(c_COMBC(U_8598,tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_fun(U_8599,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8599,tc_fun(tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_fun(U_8599,tc_HOL_Obool)),U_8598),c_COMBC(U_8599,tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8599,tc_prod(U_8598,U_8599)),tc_fun(U_8599,tc_fun(tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_HOL_Obool)),U_8598),hAPP(c_COMBB(tc_prod(U_8598,U_8599),tc_fun(tc_fun(tc_prod(U_8598,U_8599),tc_HOL_Obool),tc_HOL_Obool),U_8599),c_member(tc_prod(U_8598,U_8599)))),c_Product__Type_OPair(U_8598,U_8599)))),U_8601) ) ),
inference(variable_rename,[status(thm)],[f_2462_1]) ).
fof(f_2462_3,plain,
( ! [U_8609,U_8607] :
( ! [U_8605,U_8603] : hAPP(hAPP(c_COMBC(U_8603,tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_fun(U_8605,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8605,tc_fun(tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_fun(U_8605,tc_HOL_Obool)),U_8603),c_COMBC(U_8605,tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8605,tc_prod(U_8603,U_8605)),tc_fun(U_8605,tc_fun(tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_HOL_Obool)),U_8603),hAPP(c_COMBB(tc_prod(U_8603,U_8605),tc_fun(tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_HOL_Obool),U_8605),c_member(tc_prod(U_8603,U_8605)))),c_Product__Type_OPair(U_8603,U_8605)))),U_8607) = hAPP(hAPP(c_COMBC(U_8603,tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_fun(U_8605,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8605,tc_fun(tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_fun(U_8605,tc_HOL_Obool)),U_8603),c_COMBC(U_8605,tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8605,tc_prod(U_8603,U_8605)),tc_fun(U_8605,tc_fun(tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_HOL_Obool)),U_8603),hAPP(c_COMBB(tc_prod(U_8603,U_8605),tc_fun(tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_HOL_Obool),U_8605),c_member(tc_prod(U_8603,U_8605)))),c_Product__Type_OPair(U_8603,U_8605)))),U_8609)
| U_8607 != U_8609 )
& ! [U_8608,U_8606] :
( ! [U_8604,U_8602] : hAPP(hAPP(c_COMBC(U_8602,tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_fun(U_8604,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8604,tc_fun(tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_fun(U_8604,tc_HOL_Obool)),U_8602),c_COMBC(U_8604,tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8604,tc_prod(U_8602,U_8604)),tc_fun(U_8604,tc_fun(tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_HOL_Obool)),U_8602),hAPP(c_COMBB(tc_prod(U_8602,U_8604),tc_fun(tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_HOL_Obool),U_8604),c_member(tc_prod(U_8602,U_8604)))),c_Product__Type_OPair(U_8602,U_8604)))),U_8606) != hAPP(hAPP(c_COMBC(U_8602,tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_fun(U_8604,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8604,tc_fun(tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_fun(U_8604,tc_HOL_Obool)),U_8602),c_COMBC(U_8604,tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8604,tc_prod(U_8602,U_8604)),tc_fun(U_8604,tc_fun(tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_HOL_Obool)),U_8602),hAPP(c_COMBB(tc_prod(U_8602,U_8604),tc_fun(tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_HOL_Obool),U_8604),c_member(tc_prod(U_8602,U_8604)))),c_Product__Type_OPair(U_8602,U_8604)))),U_8608)
| U_8606 = U_8608 ) ),
inference(miniscope,[status(thm)],[f_2462_2]) ).
cnf(f_2462_4,plain,
( hAPP(hAPP(c_COMBC(U_8602,tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_fun(U_8604,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8604,tc_fun(tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_fun(U_8604,tc_HOL_Obool)),U_8602),c_COMBC(U_8604,tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8604,tc_prod(U_8602,U_8604)),tc_fun(U_8604,tc_fun(tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_HOL_Obool)),U_8602),hAPP(c_COMBB(tc_prod(U_8602,U_8604),tc_fun(tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_HOL_Obool),U_8604),c_member(tc_prod(U_8602,U_8604)))),c_Product__Type_OPair(U_8602,U_8604)))),U_8606) != hAPP(hAPP(c_COMBC(U_8602,tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_fun(U_8604,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8604,tc_fun(tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_fun(U_8604,tc_HOL_Obool)),U_8602),c_COMBC(U_8604,tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8604,tc_prod(U_8602,U_8604)),tc_fun(U_8604,tc_fun(tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_HOL_Obool)),U_8602),hAPP(c_COMBB(tc_prod(U_8602,U_8604),tc_fun(tc_fun(tc_prod(U_8602,U_8604),tc_HOL_Obool),tc_HOL_Obool),U_8604),c_member(tc_prod(U_8602,U_8604)))),c_Product__Type_OPair(U_8602,U_8604)))),U_8608)
| U_8606 = U_8608 ),
inference(clausify,[status(thm)],[f_2462_3]) ).
cnf(f_2462_5,plain,
( hAPP(hAPP(c_COMBC(U_8603,tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_fun(U_8605,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8605,tc_fun(tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_fun(U_8605,tc_HOL_Obool)),U_8603),c_COMBC(U_8605,tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8605,tc_prod(U_8603,U_8605)),tc_fun(U_8605,tc_fun(tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_HOL_Obool)),U_8603),hAPP(c_COMBB(tc_prod(U_8603,U_8605),tc_fun(tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_HOL_Obool),U_8605),c_member(tc_prod(U_8603,U_8605)))),c_Product__Type_OPair(U_8603,U_8605)))),U_8607) = hAPP(hAPP(c_COMBC(U_8603,tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_fun(U_8605,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8605,tc_fun(tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_fun(U_8605,tc_HOL_Obool)),U_8603),c_COMBC(U_8605,tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8605,tc_prod(U_8603,U_8605)),tc_fun(U_8605,tc_fun(tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_HOL_Obool)),U_8603),hAPP(c_COMBB(tc_prod(U_8603,U_8605),tc_fun(tc_fun(tc_prod(U_8603,U_8605),tc_HOL_Obool),tc_HOL_Obool),U_8605),c_member(tc_prod(U_8603,U_8605)))),c_Product__Type_OPair(U_8603,U_8605)))),U_8609)
| U_8607 != U_8609 ),
inference(clausify,[status(thm)],[f_2462_3]) ).
fof(f_2463_1,plain,
! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_sup__Un__eq2]) ).
fof(f_2463_2,plain,
! [U_8615,U_8614,U_8613,U_8612,U_8611,U_8610] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8610,tc_fun(U_8611,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8610,tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_fun(U_8611,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8611,tc_fun(tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_fun(U_8611,tc_HOL_Obool)),U_8610),c_COMBC(U_8611,tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8611,tc_prod(U_8610,U_8611)),tc_fun(U_8611,tc_fun(tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_HOL_Obool)),U_8610),hAPP(c_COMBB(tc_prod(U_8610,U_8611),tc_fun(tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_HOL_Obool),U_8611),c_member(tc_prod(U_8610,U_8611)))),c_Product__Type_OPair(U_8610,U_8611)))),U_8612)),hAPP(hAPP(c_COMBC(U_8610,tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_fun(U_8611,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8611,tc_fun(tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_fun(U_8611,tc_HOL_Obool)),U_8610),c_COMBC(U_8611,tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8611,tc_prod(U_8610,U_8611)),tc_fun(U_8611,tc_fun(tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_HOL_Obool)),U_8610),hAPP(c_COMBB(tc_prod(U_8610,U_8611),tc_fun(tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_HOL_Obool),U_8611),c_member(tc_prod(U_8610,U_8611)))),c_Product__Type_OPair(U_8610,U_8611)))),U_8613)),U_8614),U_8615))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8610,U_8611)),hAPP(hAPP(c_Product__Type_OPair(U_8610,U_8611),U_8614),U_8615)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool)),U_8612),U_8613))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8610,U_8611)),hAPP(hAPP(c_Product__Type_OPair(U_8610,U_8611),U_8614),U_8615)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool)),U_8612),U_8613)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8610,tc_fun(U_8611,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8610,tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_fun(U_8611,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8611,tc_fun(tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_fun(U_8611,tc_HOL_Obool)),U_8610),c_COMBC(U_8611,tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8611,tc_prod(U_8610,U_8611)),tc_fun(U_8611,tc_fun(tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_HOL_Obool)),U_8610),hAPP(c_COMBB(tc_prod(U_8610,U_8611),tc_fun(tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_HOL_Obool),U_8611),c_member(tc_prod(U_8610,U_8611)))),c_Product__Type_OPair(U_8610,U_8611)))),U_8612)),hAPP(hAPP(c_COMBC(U_8610,tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_fun(U_8611,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8611,tc_fun(tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_fun(U_8611,tc_HOL_Obool)),U_8610),c_COMBC(U_8611,tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8611,tc_prod(U_8610,U_8611)),tc_fun(U_8611,tc_fun(tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_HOL_Obool)),U_8610),hAPP(c_COMBB(tc_prod(U_8610,U_8611),tc_fun(tc_fun(tc_prod(U_8610,U_8611),tc_HOL_Obool),tc_HOL_Obool),U_8611),c_member(tc_prod(U_8610,U_8611)))),c_Product__Type_OPair(U_8610,U_8611)))),U_8613)),U_8614),U_8615)) ) ),
inference(variable_rename,[status(thm)],[f_2463_1]) ).
fof(f_2463_3,plain,
( ! [U_8627,U_8625,U_8623,U_8621,U_8619,U_8617] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8617,tc_fun(U_8619,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8617,tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_fun(U_8619,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8619,tc_fun(tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_fun(U_8619,tc_HOL_Obool)),U_8617),c_COMBC(U_8619,tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8619,tc_prod(U_8617,U_8619)),tc_fun(U_8619,tc_fun(tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_HOL_Obool)),U_8617),hAPP(c_COMBB(tc_prod(U_8617,U_8619),tc_fun(tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_HOL_Obool),U_8619),c_member(tc_prod(U_8617,U_8619)))),c_Product__Type_OPair(U_8617,U_8619)))),U_8621)),hAPP(hAPP(c_COMBC(U_8617,tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_fun(U_8619,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8619,tc_fun(tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_fun(U_8619,tc_HOL_Obool)),U_8617),c_COMBC(U_8619,tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8619,tc_prod(U_8617,U_8619)),tc_fun(U_8619,tc_fun(tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_HOL_Obool)),U_8617),hAPP(c_COMBB(tc_prod(U_8617,U_8619),tc_fun(tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_HOL_Obool),U_8619),c_member(tc_prod(U_8617,U_8619)))),c_Product__Type_OPair(U_8617,U_8619)))),U_8623)),U_8625),U_8627))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8617,U_8619)),hAPP(hAPP(c_Product__Type_OPair(U_8617,U_8619),U_8625),U_8627)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool)),U_8621),U_8623))) )
& ! [U_8626,U_8624,U_8622,U_8620,U_8618,U_8616] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8616,U_8618)),hAPP(hAPP(c_Product__Type_OPair(U_8616,U_8618),U_8624),U_8626)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool)),U_8620),U_8622)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8616,tc_fun(U_8618,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8616,tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_fun(U_8618,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8618,tc_fun(tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_fun(U_8618,tc_HOL_Obool)),U_8616),c_COMBC(U_8618,tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8618,tc_prod(U_8616,U_8618)),tc_fun(U_8618,tc_fun(tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_HOL_Obool)),U_8616),hAPP(c_COMBB(tc_prod(U_8616,U_8618),tc_fun(tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_HOL_Obool),U_8618),c_member(tc_prod(U_8616,U_8618)))),c_Product__Type_OPair(U_8616,U_8618)))),U_8620)),hAPP(hAPP(c_COMBC(U_8616,tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_fun(U_8618,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8618,tc_fun(tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_fun(U_8618,tc_HOL_Obool)),U_8616),c_COMBC(U_8618,tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8618,tc_prod(U_8616,U_8618)),tc_fun(U_8618,tc_fun(tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_HOL_Obool)),U_8616),hAPP(c_COMBB(tc_prod(U_8616,U_8618),tc_fun(tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_HOL_Obool),U_8618),c_member(tc_prod(U_8616,U_8618)))),c_Product__Type_OPair(U_8616,U_8618)))),U_8622)),U_8624),U_8626)) ) ),
inference(miniscope,[status(thm)],[f_2463_2]) ).
cnf(f_2463_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8616,U_8618)),hAPP(hAPP(c_Product__Type_OPair(U_8616,U_8618),U_8624),U_8626)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool)),U_8620),U_8622)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8616,tc_fun(U_8618,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8616,tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_fun(U_8618,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8618,tc_fun(tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_fun(U_8618,tc_HOL_Obool)),U_8616),c_COMBC(U_8618,tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8618,tc_prod(U_8616,U_8618)),tc_fun(U_8618,tc_fun(tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_HOL_Obool)),U_8616),hAPP(c_COMBB(tc_prod(U_8616,U_8618),tc_fun(tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_HOL_Obool),U_8618),c_member(tc_prod(U_8616,U_8618)))),c_Product__Type_OPair(U_8616,U_8618)))),U_8620)),hAPP(hAPP(c_COMBC(U_8616,tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_fun(U_8618,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8618,tc_fun(tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_fun(U_8618,tc_HOL_Obool)),U_8616),c_COMBC(U_8618,tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8618,tc_prod(U_8616,U_8618)),tc_fun(U_8618,tc_fun(tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_HOL_Obool)),U_8616),hAPP(c_COMBB(tc_prod(U_8616,U_8618),tc_fun(tc_fun(tc_prod(U_8616,U_8618),tc_HOL_Obool),tc_HOL_Obool),U_8618),c_member(tc_prod(U_8616,U_8618)))),c_Product__Type_OPair(U_8616,U_8618)))),U_8622)),U_8624),U_8626)) ),
inference(clausify,[status(thm)],[f_2463_3]) ).
cnf(f_2463_5,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8617,tc_fun(U_8619,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8617,tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_fun(U_8619,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8619,tc_fun(tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_fun(U_8619,tc_HOL_Obool)),U_8617),c_COMBC(U_8619,tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8619,tc_prod(U_8617,U_8619)),tc_fun(U_8619,tc_fun(tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_HOL_Obool)),U_8617),hAPP(c_COMBB(tc_prod(U_8617,U_8619),tc_fun(tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_HOL_Obool),U_8619),c_member(tc_prod(U_8617,U_8619)))),c_Product__Type_OPair(U_8617,U_8619)))),U_8621)),hAPP(hAPP(c_COMBC(U_8617,tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_fun(U_8619,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8619,tc_fun(tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_fun(U_8619,tc_HOL_Obool)),U_8617),c_COMBC(U_8619,tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8619,tc_prod(U_8617,U_8619)),tc_fun(U_8619,tc_fun(tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_HOL_Obool)),U_8617),hAPP(c_COMBB(tc_prod(U_8617,U_8619),tc_fun(tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool),tc_HOL_Obool),U_8619),c_member(tc_prod(U_8617,U_8619)))),c_Product__Type_OPair(U_8617,U_8619)))),U_8623)),U_8625),U_8627))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8617,U_8619)),hAPP(hAPP(c_Product__Type_OPair(U_8617,U_8619),U_8625),U_8627)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8617,U_8619),tc_HOL_Obool)),U_8621),U_8623))) ),
inference(clausify,[status(thm)],[f_2463_3]) ).
fof(f_2464_1,plain,
! [V_y_2,V_x_2,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_bot__empty__eq2]) ).
fof(f_2464_2,plain,
! [U_8631,U_8630,U_8629,U_8628] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8628,tc_fun(U_8629,tc_HOL_Obool))),U_8630),U_8631))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8628,U_8629)),hAPP(hAPP(c_Product__Type_OPair(U_8628,U_8629),U_8630),U_8631)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_8628,U_8629),tc_HOL_Obool)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8628,U_8629)),hAPP(hAPP(c_Product__Type_OPair(U_8628,U_8629),U_8630),U_8631)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_8628,U_8629),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8628,tc_fun(U_8629,tc_HOL_Obool))),U_8630),U_8631)) ) ),
inference(variable_rename,[status(thm)],[f_2464_1]) ).
fof(f_2464_3,plain,
( ! [U_8639,U_8637,U_8635,U_8633] :
( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8633,tc_fun(U_8635,tc_HOL_Obool))),U_8637),U_8639))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8633,U_8635)),hAPP(hAPP(c_Product__Type_OPair(U_8633,U_8635),U_8637),U_8639)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_8633,U_8635),tc_HOL_Obool)))) )
& ! [U_8638,U_8636,U_8634,U_8632] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8632,U_8634)),hAPP(hAPP(c_Product__Type_OPair(U_8632,U_8634),U_8636),U_8638)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_8632,U_8634),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8632,tc_fun(U_8634,tc_HOL_Obool))),U_8636),U_8638)) ) ),
inference(miniscope,[status(thm)],[f_2464_2]) ).
cnf(f_2464_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8632,U_8634)),hAPP(hAPP(c_Product__Type_OPair(U_8632,U_8634),U_8636),U_8638)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_8632,U_8634),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8632,tc_fun(U_8634,tc_HOL_Obool))),U_8636),U_8638)) ),
inference(clausify,[status(thm)],[f_2464_3]) ).
cnf(f_2464_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_8633,tc_fun(U_8635,tc_HOL_Obool))),U_8637),U_8639))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8633,U_8635)),hAPP(hAPP(c_Product__Type_OPair(U_8633,U_8635),U_8637),U_8639)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_8633,U_8635),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_2464_3]) ).
fof(f_2465_1,plain,
! [V_S_2,V_R_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_pred__subset__eq]) ).
fof(f_2465_2,plain,
! [U_8642,U_8641,U_8640] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8640,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8640,tc_fun(U_8640,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8640)),U_8641)),hAPP(hAPP(c_COMBC(U_8640,tc_fun(U_8640,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8640)),U_8642)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8640,tc_HOL_Obool)),U_8641),U_8642)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8640,tc_HOL_Obool)),U_8641),U_8642))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8640,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8640,tc_fun(U_8640,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8640)),U_8641)),hAPP(hAPP(c_COMBC(U_8640,tc_fun(U_8640,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8640)),U_8642))) ) ),
inference(variable_rename,[status(thm)],[f_2465_1]) ).
fof(f_2465_3,plain,
( ! [U_8648,U_8646,U_8644] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8644,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8644,tc_fun(U_8644,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8644)),U_8646)),hAPP(hAPP(c_COMBC(U_8644,tc_fun(U_8644,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8644)),U_8648)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8644,tc_HOL_Obool)),U_8646),U_8648)) )
& ! [U_8647,U_8645,U_8643] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8643,tc_HOL_Obool)),U_8645),U_8647))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8643,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8643,tc_fun(U_8643,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8643)),U_8645)),hAPP(hAPP(c_COMBC(U_8643,tc_fun(U_8643,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8643)),U_8647))) ) ),
inference(miniscope,[status(thm)],[f_2465_2]) ).
cnf(f_2465_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8643,tc_HOL_Obool)),U_8645),U_8647))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8643,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8643,tc_fun(U_8643,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8643)),U_8645)),hAPP(hAPP(c_COMBC(U_8643,tc_fun(U_8643,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8643)),U_8647))) ),
inference(clausify,[status(thm)],[f_2465_3]) ).
cnf(f_2465_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8644,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8644,tc_fun(U_8644,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8644)),U_8646)),hAPP(hAPP(c_COMBC(U_8644,tc_fun(U_8644,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8644)),U_8648)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8644,tc_HOL_Obool)),U_8646),U_8648)) ),
inference(clausify,[status(thm)],[f_2465_3]) ).
fof(f_2466_1,plain,
! [V_x_2,V_S_2,V_R_2,T_b] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_sup__Un__eq]) ).
fof(f_2466_2,plain,
! [U_8652,U_8651,U_8650,U_8649] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8649,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8649,tc_fun(U_8649,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8649)),U_8650)),hAPP(hAPP(c_COMBC(U_8649,tc_fun(U_8649,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8649)),U_8651)),U_8652))
| ~ hBOOL(hAPP(hAPP(c_member(U_8649),U_8652),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8649,tc_HOL_Obool)),U_8650),U_8651))) )
& ( hBOOL(hAPP(hAPP(c_member(U_8649),U_8652),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8649,tc_HOL_Obool)),U_8650),U_8651)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8649,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8649,tc_fun(U_8649,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8649)),U_8650)),hAPP(hAPP(c_COMBC(U_8649,tc_fun(U_8649,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8649)),U_8651)),U_8652)) ) ),
inference(variable_rename,[status(thm)],[f_2466_1]) ).
fof(f_2466_3,plain,
( ! [U_8660,U_8658,U_8656,U_8654] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8654,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8654,tc_fun(U_8654,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8654)),U_8656)),hAPP(hAPP(c_COMBC(U_8654,tc_fun(U_8654,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8654)),U_8658)),U_8660))
| ~ hBOOL(hAPP(hAPP(c_member(U_8654),U_8660),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8654,tc_HOL_Obool)),U_8656),U_8658))) )
& ! [U_8659,U_8657,U_8655,U_8653] :
( hBOOL(hAPP(hAPP(c_member(U_8653),U_8659),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8653,tc_HOL_Obool)),U_8655),U_8657)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8653,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8653,tc_fun(U_8653,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8653)),U_8655)),hAPP(hAPP(c_COMBC(U_8653,tc_fun(U_8653,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8653)),U_8657)),U_8659)) ) ),
inference(miniscope,[status(thm)],[f_2466_2]) ).
cnf(f_2466_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8653),U_8659),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8653,tc_HOL_Obool)),U_8655),U_8657)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8653,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8653,tc_fun(U_8653,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8653)),U_8655)),hAPP(hAPP(c_COMBC(U_8653,tc_fun(U_8653,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8653)),U_8657)),U_8659)) ),
inference(clausify,[status(thm)],[f_2466_3]) ).
cnf(f_2466_5,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8654,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8654,tc_fun(U_8654,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8654)),U_8656)),hAPP(hAPP(c_COMBC(U_8654,tc_fun(U_8654,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8654)),U_8658)),U_8660))
| ~ hBOOL(hAPP(hAPP(c_member(U_8654),U_8660),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8654,tc_HOL_Obool)),U_8656),U_8658))) ),
inference(clausify,[status(thm)],[f_2466_3]) ).
fof(f_2467_1,plain,
! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_UN__iff]) ).
fof(f_2467_2,plain,
! [U_8667,U_8666,U_8665,U_8664,U_8663] :
( ( hBOOL(hAPP(hAPP(c_member(U_8663),U_8664),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8665,tc_fun(U_8663,tc_HOL_Obool)),U_8666),U_8667)))
| ! [U_8662] :
( ~ hBOOL(hAPP(hAPP(c_member(U_8663),U_8664),hAPP(U_8667,U_8662)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8665),U_8662),U_8666)) ) )
& ( ? [U_8661] :
( hBOOL(hAPP(hAPP(c_member(U_8663),U_8664),hAPP(U_8667,U_8661)))
& hBOOL(hAPP(hAPP(c_member(U_8665),U_8661),U_8666)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8663),U_8664),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8665,tc_fun(U_8663,tc_HOL_Obool)),U_8666),U_8667))) ) ),
inference(variable_rename,[status(thm)],[f_2467_1]) ).
fof(f_2467_3,plain,
( ! [U_8677,U_8675,U_8673,U_8671,U_8669] :
( hBOOL(hAPP(hAPP(c_member(U_8669),U_8671),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8673,tc_fun(U_8669,tc_HOL_Obool)),U_8675),U_8677)))
| ! [U_8662] :
( ~ hBOOL(hAPP(hAPP(c_member(U_8669),U_8671),hAPP(U_8677,U_8662)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8673),U_8662),U_8675)) ) )
& ! [U_8676,U_8674,U_8672,U_8670,U_8668] :
( ? [U_8661] :
( hBOOL(hAPP(hAPP(c_member(U_8668),U_8670),hAPP(U_8676,U_8661)))
& hBOOL(hAPP(hAPP(c_member(U_8672),U_8661),U_8674)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8668),U_8670),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8672,tc_fun(U_8668,tc_HOL_Obool)),U_8674),U_8676))) ) ),
inference(miniscope,[status(thm)],[f_2467_2]) ).
fof(f_2467_4,plain,
( ! [U_8677,U_8675,U_8673,U_8671,U_8669] :
( hBOOL(hAPP(hAPP(c_member(U_8669),U_8671),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8673,tc_fun(U_8669,tc_HOL_Obool)),U_8675),U_8677)))
| ! [U_8662] :
( ~ hBOOL(hAPP(hAPP(c_member(U_8669),U_8671),hAPP(U_8677,U_8662)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8673),U_8662),U_8675)) ) )
& ! [U_8676,U_8674,U_8672,U_8670,U_8668] :
( ( hBOOL(hAPP(hAPP(c_member(U_8668),U_8670),hAPP(U_8676,sK160(U_8676,U_8674,U_8672,U_8670,U_8668))))
& hBOOL(hAPP(hAPP(c_member(U_8672),sK160(U_8676,U_8674,U_8672,U_8670,U_8668)),U_8674)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8668),U_8670),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8672,tc_fun(U_8668,tc_HOL_Obool)),U_8674),U_8676))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK160]),skolemize(U_8661,sK160(U_8676,U_8674,U_8672,U_8670,U_8668))],[f_2467_3]) ).
cnf(f_2467_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_8672),sK160(U_8676,U_8674,U_8672,U_8670,U_8668)),U_8674))
| ~ hBOOL(hAPP(hAPP(c_member(U_8668),U_8670),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8672,tc_fun(U_8668,tc_HOL_Obool)),U_8674),U_8676))) ),
inference(clausify,[status(thm)],[f_2467_4]) ).
cnf(f_2467_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8668),U_8670),hAPP(U_8676,sK160(U_8676,U_8674,U_8672,U_8670,U_8668))))
| ~ hBOOL(hAPP(hAPP(c_member(U_8668),U_8670),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8672,tc_fun(U_8668,tc_HOL_Obool)),U_8674),U_8676))) ),
inference(clausify,[status(thm)],[f_2467_4]) ).
cnf(f_2467_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_8669),U_8671),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8673,tc_fun(U_8669,tc_HOL_Obool)),U_8675),U_8677)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8669),U_8671),hAPP(U_8677,U_8662)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8673),U_8662),U_8675)) ),
inference(clausify,[status(thm)],[f_2467_4]) ).
fof(f_2468_1,plain,
! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__iff]) ).
fof(f_2468_2,plain,
! [U_8684,U_8683,U_8682,U_8681,U_8680] :
( ( hBOOL(hAPP(hAPP(c_member(U_8680),U_8681),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8682,tc_fun(U_8680,tc_HOL_Obool)),U_8683),U_8684)))
| ? [U_8679] :
( ~ hBOOL(hAPP(hAPP(c_member(U_8680),U_8681),hAPP(U_8684,U_8679)))
& hBOOL(hAPP(hAPP(c_member(U_8682),U_8679),U_8683)) ) )
& ( ! [U_8678] :
( hBOOL(hAPP(hAPP(c_member(U_8680),U_8681),hAPP(U_8684,U_8678)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8682),U_8678),U_8683)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8680),U_8681),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8682,tc_fun(U_8680,tc_HOL_Obool)),U_8683),U_8684))) ) ),
inference(variable_rename,[status(thm)],[f_2468_1]) ).
fof(f_2468_3,plain,
( ! [U_8694,U_8692,U_8690,U_8688,U_8686] :
( hBOOL(hAPP(hAPP(c_member(U_8686),U_8688),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8690,tc_fun(U_8686,tc_HOL_Obool)),U_8692),U_8694)))
| ? [U_8679] :
( ~ hBOOL(hAPP(hAPP(c_member(U_8686),U_8688),hAPP(U_8694,U_8679)))
& hBOOL(hAPP(hAPP(c_member(U_8690),U_8679),U_8692)) ) )
& ! [U_8693,U_8691,U_8689,U_8687,U_8685] :
( ! [U_8678] :
( hBOOL(hAPP(hAPP(c_member(U_8685),U_8687),hAPP(U_8693,U_8678)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8689),U_8678),U_8691)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8685),U_8687),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8689,tc_fun(U_8685,tc_HOL_Obool)),U_8691),U_8693))) ) ),
inference(miniscope,[status(thm)],[f_2468_2]) ).
fof(f_2468_4,plain,
( ! [U_8694,U_8692,U_8690,U_8688,U_8686] :
( hBOOL(hAPP(hAPP(c_member(U_8686),U_8688),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8690,tc_fun(U_8686,tc_HOL_Obool)),U_8692),U_8694)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_8686),U_8688),hAPP(U_8694,sK161(U_8694,U_8692,U_8690,U_8688,U_8686))))
& hBOOL(hAPP(hAPP(c_member(U_8690),sK161(U_8694,U_8692,U_8690,U_8688,U_8686)),U_8692)) ) )
& ! [U_8693,U_8691,U_8689,U_8687,U_8685] :
( ! [U_8678] :
( hBOOL(hAPP(hAPP(c_member(U_8685),U_8687),hAPP(U_8693,U_8678)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8689),U_8678),U_8691)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8685),U_8687),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8689,tc_fun(U_8685,tc_HOL_Obool)),U_8691),U_8693))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK161]),skolemize(U_8679,sK161(U_8694,U_8692,U_8690,U_8688,U_8686))],[f_2468_3]) ).
cnf(f_2468_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_8685),U_8687),hAPP(U_8693,U_8678)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8689),U_8678),U_8691))
| ~ hBOOL(hAPP(hAPP(c_member(U_8685),U_8687),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8689,tc_fun(U_8685,tc_HOL_Obool)),U_8691),U_8693))) ),
inference(clausify,[status(thm)],[f_2468_4]) ).
cnf(f_2468_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8690),sK161(U_8694,U_8692,U_8690,U_8688,U_8686)),U_8692))
| hBOOL(hAPP(hAPP(c_member(U_8686),U_8688),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8690,tc_fun(U_8686,tc_HOL_Obool)),U_8692),U_8694))) ),
inference(clausify,[status(thm)],[f_2468_4]) ).
cnf(f_2468_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8686),U_8688),hAPP(U_8694,sK161(U_8694,U_8692,U_8690,U_8688,U_8686))))
| hBOOL(hAPP(hAPP(c_member(U_8686),U_8688),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8690,tc_fun(U_8686,tc_HOL_Obool)),U_8692),U_8694))) ),
inference(clausify,[status(thm)],[f_2468_4]) ).
fof(f_2469_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Oinsert]) ).
fof(f_2469_2,plain,
! [U_8699,U_8698,U_8697,U_8696,U_8695] :
( hAPP(U_8697,hAPP(hAPP(c_Set_Oinsert(U_8695),U_8699),U_8698)) = hAPP(hAPP(U_8696,U_8699),hAPP(U_8697,U_8698))
| U_8698 = c_Orderings_Obot__class_Obot(tc_fun(U_8695,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8695),U_8699),U_8698))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8695),U_8698))
| ~ c_Finite__Set_Ofolding__one(U_8695,U_8696,U_8697) ),
inference(variable_rename,[status(thm)],[f_2469_1]) ).
cnf(f_2469_3,plain,
( hAPP(U_8697,hAPP(hAPP(c_Set_Oinsert(U_8695),U_8699),U_8698)) = hAPP(hAPP(U_8696,U_8699),hAPP(U_8697,U_8698))
| U_8698 = c_Orderings_Obot__class_Obot(tc_fun(U_8695,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_8695),U_8699),U_8698))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8695),U_8698))
| ~ c_Finite__Set_Ofolding__one(U_8695,U_8696,U_8697) ),
inference(clausify,[status(thm)],[f_2469_2]) ).
fof(f_2470_1,plain,
! [V_a_2,V_b_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
| V_b_2 != V_a_2 )
& ( V_b_2 = V_a_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ) ),
inference(fof_nnf,[status(thm)],[fact_singleton__iff]) ).
fof(f_2470_2,plain,
! [U_8702,U_8701,U_8700] :
( ( hBOOL(hAPP(hAPP(c_member(U_8700),U_8701),hAPP(hAPP(c_Set_Oinsert(U_8700),U_8702),c_Orderings_Obot__class_Obot(tc_fun(U_8700,tc_HOL_Obool)))))
| U_8701 != U_8702 )
& ( U_8701 = U_8702
| ~ hBOOL(hAPP(hAPP(c_member(U_8700),U_8701),hAPP(hAPP(c_Set_Oinsert(U_8700),U_8702),c_Orderings_Obot__class_Obot(tc_fun(U_8700,tc_HOL_Obool))))) ) ),
inference(variable_rename,[status(thm)],[f_2470_1]) ).
fof(f_2470_3,plain,
( ! [U_8708,U_8706] :
( ! [U_8704] : hBOOL(hAPP(hAPP(c_member(U_8704),U_8706),hAPP(hAPP(c_Set_Oinsert(U_8704),U_8708),c_Orderings_Obot__class_Obot(tc_fun(U_8704,tc_HOL_Obool)))))
| U_8706 != U_8708 )
& ! [U_8707,U_8705] :
( ! [U_8703] : ~ hBOOL(hAPP(hAPP(c_member(U_8703),U_8705),hAPP(hAPP(c_Set_Oinsert(U_8703),U_8707),c_Orderings_Obot__class_Obot(tc_fun(U_8703,tc_HOL_Obool)))))
| U_8705 = U_8707 ) ),
inference(miniscope,[status(thm)],[f_2470_2]) ).
cnf(f_2470_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8703),U_8705),hAPP(hAPP(c_Set_Oinsert(U_8703),U_8707),c_Orderings_Obot__class_Obot(tc_fun(U_8703,tc_HOL_Obool)))))
| U_8705 = U_8707 ),
inference(clausify,[status(thm)],[f_2470_3]) ).
cnf(f_2470_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_8704),U_8706),hAPP(hAPP(c_Set_Oinsert(U_8704),U_8708),c_Orderings_Obot__class_Obot(tc_fun(U_8704,tc_HOL_Obool)))))
| U_8706 != U_8708 ),
inference(clausify,[status(thm)],[f_2470_3]) ).
fof(f_2471_1,plain,
! [V_a_2,V_b_2,T_b] :
( V_b_2 = V_a_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ),
inference(fof_nnf,[status(thm)],[fact_singletonE]) ).
fof(f_2471_2,plain,
! [U_8711,U_8710,U_8709] :
( U_8710 = U_8711
| ~ hBOOL(hAPP(hAPP(c_member(U_8709),U_8710),hAPP(hAPP(c_Set_Oinsert(U_8709),U_8711),c_Orderings_Obot__class_Obot(tc_fun(U_8709,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[f_2471_1]) ).
fof(f_2471_3,plain,
! [U_8711,U_8710] :
( ! [U_8709] : ~ hBOOL(hAPP(hAPP(c_member(U_8709),U_8710),hAPP(hAPP(c_Set_Oinsert(U_8709),U_8711),c_Orderings_Obot__class_Obot(tc_fun(U_8709,tc_HOL_Obool)))))
| U_8710 = U_8711 ),
inference(miniscope,[status(thm)],[f_2471_2]) ).
cnf(f_2471_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8709),U_8710),hAPP(hAPP(c_Set_Oinsert(U_8709),U_8711),c_Orderings_Obot__class_Obot(tc_fun(U_8709,tc_HOL_Obool)))))
| U_8710 = U_8711 ),
inference(clausify,[status(thm)],[f_2471_3]) ).
fof(f_2472_1,plain,
! [V_B_2,V_A_2,V_x_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_insert__subset]) ).
fof(f_2472_2,plain,
! [U_8715,U_8714,U_8713,U_8712] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8712,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8712),U_8713),U_8714)),U_8715))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8712,tc_HOL_Obool)),U_8714),U_8715))
| ~ hBOOL(hAPP(hAPP(c_member(U_8712),U_8713),U_8715)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8712,tc_HOL_Obool)),U_8714),U_8715))
& hBOOL(hAPP(hAPP(c_member(U_8712),U_8713),U_8715)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8712,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8712),U_8713),U_8714)),U_8715)) ) ),
inference(variable_rename,[status(thm)],[f_2472_1]) ).
fof(f_2472_3,plain,
( ! [U_8723,U_8721,U_8719,U_8717] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8717,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8717),U_8719),U_8721)),U_8723))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8717,tc_HOL_Obool)),U_8721),U_8723))
| ~ hBOOL(hAPP(hAPP(c_member(U_8717),U_8719),U_8723)) )
& ! [U_8722,U_8720,U_8718,U_8716] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8716,tc_HOL_Obool)),U_8720),U_8722))
& hBOOL(hAPP(hAPP(c_member(U_8716),U_8718),U_8722)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8716,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8716),U_8718),U_8720)),U_8722)) ) ),
inference(miniscope,[status(thm)],[f_2472_2]) ).
cnf(f_2472_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8716),U_8718),U_8722))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8716,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8716),U_8718),U_8720)),U_8722)) ),
inference(clausify,[status(thm)],[f_2472_3]) ).
cnf(f_2472_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8716,tc_HOL_Obool)),U_8720),U_8722))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8716,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8716),U_8718),U_8720)),U_8722)) ),
inference(clausify,[status(thm)],[f_2472_3]) ).
cnf(f_2472_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8717,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8717),U_8719),U_8721)),U_8723))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8717,tc_HOL_Obool)),U_8721),U_8723))
| ~ hBOOL(hAPP(hAPP(c_member(U_8717),U_8719),U_8723)) ),
inference(clausify,[status(thm)],[f_2472_3]) ).
fof(f_2473_1,plain,
! [V_B_2,V_A_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) )
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_subset__insert]) ).
fof(f_2473_2,plain,
! [U_8727,U_8726,U_8725,U_8724] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8724,tc_HOL_Obool)),U_8726),hAPP(hAPP(c_Set_Oinsert(U_8724),U_8725),U_8727)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8724,tc_HOL_Obool)),U_8726),U_8727)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8724,tc_HOL_Obool)),U_8726),U_8727))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8724,tc_HOL_Obool)),U_8726),hAPP(hAPP(c_Set_Oinsert(U_8724),U_8725),U_8727))) ) )
| hBOOL(hAPP(hAPP(c_member(U_8724),U_8725),U_8726)) ),
inference(variable_rename,[status(thm)],[f_2473_1]) ).
cnf(f_2473_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8724,tc_HOL_Obool)),U_8726),U_8727))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8724,tc_HOL_Obool)),U_8726),hAPP(hAPP(c_Set_Oinsert(U_8724),U_8725),U_8727)))
| hBOOL(hAPP(hAPP(c_member(U_8724),U_8725),U_8726)) ),
inference(clausify,[status(thm)],[f_2473_2]) ).
cnf(f_2473_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8724,tc_HOL_Obool)),U_8726),hAPP(hAPP(c_Set_Oinsert(U_8724),U_8725),U_8727)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8724,tc_HOL_Obool)),U_8726),U_8727))
| hBOOL(hAPP(hAPP(c_member(U_8724),U_8725),U_8726)) ),
inference(clausify,[status(thm)],[f_2473_2]) ).
fof(f_2474_1,plain,
! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
( hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__image]) ).
fof(f_2474_2,plain,
! [U_8732,U_8731,U_8730,U_8729,U_8728] :
( hAPP(hAPP(c_Set_Oinsert(U_8731),hAPP(U_8732,U_8729)),hAPP(c_Set_Oimage(U_8728,U_8731,U_8732),U_8730)) = hAPP(c_Set_Oimage(U_8728,U_8731,U_8732),U_8730)
| ~ hBOOL(hAPP(hAPP(c_member(U_8728),U_8729),U_8730)) ),
inference(variable_rename,[status(thm)],[f_2474_1]) ).
cnf(f_2474_3,plain,
( hAPP(hAPP(c_Set_Oinsert(U_8731),hAPP(U_8732,U_8729)),hAPP(c_Set_Oimage(U_8728,U_8731,U_8732),U_8730)) = hAPP(c_Set_Oimage(U_8728,U_8731,U_8732),U_8730)
| ~ hBOOL(hAPP(hAPP(c_member(U_8728),U_8729),U_8730)) ),
inference(clausify,[status(thm)],[f_2474_2]) ).
fof(f_2475_1,plain,
! [V_f_2,V_g_2,T_c,V_X_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_g_2,V_a_2)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_c,tc_HOL_Obool),V_f_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_X_2)),hAPP(V_f_2,hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_X_2))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2)) ),
inference(fof_nnf,[status(thm)],[fact_weak__coinduct__image]) ).
fof(f_2475_2,plain,
! [U_8738,U_8737,U_8736,U_8735,U_8734,U_8733] :
( hBOOL(hAPP(hAPP(c_member(U_8736),hAPP(U_8737,U_8734)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_8736,tc_HOL_Obool),U_8738)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8736,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8733,U_8736,U_8737),U_8735)),hAPP(U_8738,hAPP(c_Set_Oimage(U_8733,U_8736,U_8737),U_8735))))
| ~ hBOOL(hAPP(hAPP(c_member(U_8733),U_8734),U_8735)) ),
inference(variable_rename,[status(thm)],[f_2475_1]) ).
cnf(f_2475_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8736),hAPP(U_8737,U_8734)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_8736,tc_HOL_Obool),U_8738)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8736,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8733,U_8736,U_8737),U_8735)),hAPP(U_8738,hAPP(c_Set_Oimage(U_8733,U_8736,U_8737),U_8735))))
| ~ hBOOL(hAPP(hAPP(c_member(U_8733),U_8734),U_8735)) ),
inference(clausify,[status(thm)],[f_2475_2]) ).
fof(f_2476_1,plain,
! [V_A_2,V_B_2,V_x_2,T_b] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_insert__Diff__if]) ).
fof(f_2476_2,plain,
! [U_8742,U_8741,U_8740,U_8739] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8739,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8739),U_8740),U_8742)),U_8741) = hAPP(hAPP(c_Set_Oinsert(U_8739),U_8740),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8739,tc_HOL_Obool)),U_8742),U_8741))
| hBOOL(hAPP(hAPP(c_member(U_8739),U_8740),U_8741)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8739,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8739),U_8740),U_8742)),U_8741) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8739,tc_HOL_Obool)),U_8742),U_8741)
| ~ hBOOL(hAPP(hAPP(c_member(U_8739),U_8740),U_8741)) ) ),
inference(variable_rename,[status(thm)],[f_2476_1]) ).
fof(f_2476_3,plain,
( ! [U_8750,U_8748,U_8746,U_8744] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8744,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8744),U_8746),U_8750)),U_8748) = hAPP(hAPP(c_Set_Oinsert(U_8744),U_8746),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8744,tc_HOL_Obool)),U_8750),U_8748))
| hBOOL(hAPP(hAPP(c_member(U_8744),U_8746),U_8748)) )
& ! [U_8749,U_8747,U_8745,U_8743] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8743,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8743),U_8745),U_8749)),U_8747) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8743,tc_HOL_Obool)),U_8749),U_8747)
| ~ hBOOL(hAPP(hAPP(c_member(U_8743),U_8745),U_8747)) ) ),
inference(miniscope,[status(thm)],[f_2476_2]) ).
cnf(f_2476_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8743,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8743),U_8745),U_8749)),U_8747) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8743,tc_HOL_Obool)),U_8749),U_8747)
| ~ hBOOL(hAPP(hAPP(c_member(U_8743),U_8745),U_8747)) ),
inference(clausify,[status(thm)],[f_2476_3]) ).
cnf(f_2476_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8744,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8744),U_8746),U_8750)),U_8748) = hAPP(hAPP(c_Set_Oinsert(U_8744),U_8746),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8744,tc_HOL_Obool)),U_8750),U_8748))
| hBOOL(hAPP(hAPP(c_member(U_8744),U_8746),U_8748)) ),
inference(clausify,[status(thm)],[f_2476_3]) ).
fof(f_2477_1,plain,
! [V_A_2,V_B_2,V_x_2,T_b] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__Diff1]) ).
fof(f_2477_2,plain,
! [U_8754,U_8753,U_8752,U_8751] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8751,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8751),U_8752),U_8754)),U_8753) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8751,tc_HOL_Obool)),U_8754),U_8753)
| ~ hBOOL(hAPP(hAPP(c_member(U_8751),U_8752),U_8753)) ),
inference(variable_rename,[status(thm)],[f_2477_1]) ).
cnf(f_2477_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8751,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8751),U_8752),U_8754)),U_8753) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8751,tc_HOL_Obool)),U_8754),U_8753)
| ~ hBOOL(hAPP(hAPP(c_member(U_8751),U_8752),U_8753)) ),
inference(clausify,[status(thm)],[f_2477_2]) ).
fof(f_2478_1,plain,
! [V_k_2,V_i_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2))) ) )
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lessThan__iff]) ).
fof(f_2478_2,plain,
! [U_8757,U_8756,U_8755] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_8755),U_8756),hAPP(c_SetInterval_Oord__class_OlessThan(U_8755),U_8757)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8755),U_8756),U_8757)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8755),U_8756),U_8757))
| ~ hBOOL(hAPP(hAPP(c_member(U_8755),U_8756),hAPP(c_SetInterval_Oord__class_OlessThan(U_8755),U_8757))) ) )
| ~ class_Orderings_Oord(U_8755) ),
inference(variable_rename,[status(thm)],[f_2478_1]) ).
cnf(f_2478_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8755),U_8756),U_8757))
| ~ hBOOL(hAPP(hAPP(c_member(U_8755),U_8756),hAPP(c_SetInterval_Oord__class_OlessThan(U_8755),U_8757)))
| ~ class_Orderings_Oord(U_8755) ),
inference(clausify,[status(thm)],[f_2478_2]) ).
cnf(f_2478_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8755),U_8756),hAPP(c_SetInterval_Oord__class_OlessThan(U_8755),U_8757)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8755),U_8756),U_8757))
| ~ class_Orderings_Oord(U_8755) ),
inference(clausify,[status(thm)],[f_2478_2]) ).
fof(f_2479_1,plain,
! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_b,V_less_2,V_l_2,V_u_2)))
| ~ hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) )
& ( ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
& hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_b,V_less_2,V_l_2,V_u_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanLessThan__iff]) ).
fof(f_2479_2,plain,
! [U_8762,U_8761,U_8760,U_8759,U_8758] :
( ( hBOOL(hAPP(hAPP(c_member(U_8758),U_8759),c_SetInterval_Oord_OgreaterThanLessThan(U_8758,U_8760,U_8761,U_8762)))
| ~ hBOOL(hAPP(hAPP(U_8760,U_8759),U_8762))
| ~ hBOOL(hAPP(hAPP(U_8760,U_8761),U_8759)) )
& ( ( hBOOL(hAPP(hAPP(U_8760,U_8759),U_8762))
& hBOOL(hAPP(hAPP(U_8760,U_8761),U_8759)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8758),U_8759),c_SetInterval_Oord_OgreaterThanLessThan(U_8758,U_8760,U_8761,U_8762))) ) ),
inference(variable_rename,[status(thm)],[f_2479_1]) ).
fof(f_2479_3,plain,
( ! [U_8772,U_8770,U_8768,U_8766] :
( ! [U_8764] : hBOOL(hAPP(hAPP(c_member(U_8764),U_8766),c_SetInterval_Oord_OgreaterThanLessThan(U_8764,U_8768,U_8770,U_8772)))
| ~ hBOOL(hAPP(hAPP(U_8768,U_8766),U_8772))
| ~ hBOOL(hAPP(hAPP(U_8768,U_8770),U_8766)) )
& ! [U_8771,U_8769,U_8767,U_8765] :
( ! [U_8763] : ~ hBOOL(hAPP(hAPP(c_member(U_8763),U_8765),c_SetInterval_Oord_OgreaterThanLessThan(U_8763,U_8767,U_8769,U_8771)))
| ( hBOOL(hAPP(hAPP(U_8767,U_8765),U_8771))
& hBOOL(hAPP(hAPP(U_8767,U_8769),U_8765)) ) ) ),
inference(miniscope,[status(thm)],[f_2479_2]) ).
cnf(f_2479_4,plain,
( hBOOL(hAPP(hAPP(U_8767,U_8769),U_8765))
| ~ hBOOL(hAPP(hAPP(c_member(U_8763),U_8765),c_SetInterval_Oord_OgreaterThanLessThan(U_8763,U_8767,U_8769,U_8771))) ),
inference(clausify,[status(thm)],[f_2479_3]) ).
cnf(f_2479_5,plain,
( hBOOL(hAPP(hAPP(U_8767,U_8765),U_8771))
| ~ hBOOL(hAPP(hAPP(c_member(U_8763),U_8765),c_SetInterval_Oord_OgreaterThanLessThan(U_8763,U_8767,U_8769,U_8771))) ),
inference(clausify,[status(thm)],[f_2479_3]) ).
cnf(f_2479_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_8764),U_8766),c_SetInterval_Oord_OgreaterThanLessThan(U_8764,U_8768,U_8770,U_8772)))
| ~ hBOOL(hAPP(hAPP(U_8768,U_8766),U_8772))
| ~ hBOOL(hAPP(hAPP(U_8768,U_8770),U_8766)) ),
inference(clausify,[status(thm)],[f_2479_3]) ).
fof(f_2480_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_2480_2,plain,
! [U_8774,U_8773] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8773),U_8774))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_8773)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8774))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_8773)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8774)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8773),U_8774)) ) )
| ~ c_Nat__Transfer_Onat__set(U_8774)
| ~ c_Nat__Transfer_Ois__nat(U_8773) ),
inference(variable_rename,[status(thm)],[f_2480_1]) ).
cnf(f_2480_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_8773)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8774)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8773),U_8774))
| ~ c_Nat__Transfer_Onat__set(U_8774)
| ~ c_Nat__Transfer_Ois__nat(U_8773) ),
inference(clausify,[status(thm)],[f_2480_2]) ).
cnf(f_2480_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8773),U_8774))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_8773)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8774)))
| ~ c_Nat__Transfer_Onat__set(U_8774)
| ~ c_Nat__Transfer_Ois__nat(U_8773) ),
inference(clausify,[status(thm)],[f_2480_2]) ).
fof(f_2481_1,plain,
! [V_k_2,V_i_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2))) ) )
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atMost__iff]) ).
fof(f_2481_2,plain,
! [U_8777,U_8776,U_8775] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_8775),U_8776),hAPP(c_SetInterval_Oord__class_OatMost(U_8775),U_8777)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8775),U_8776),U_8777)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8775),U_8776),U_8777))
| ~ hBOOL(hAPP(hAPP(c_member(U_8775),U_8776),hAPP(c_SetInterval_Oord__class_OatMost(U_8775),U_8777))) ) )
| ~ class_Orderings_Oord(U_8775) ),
inference(variable_rename,[status(thm)],[f_2481_1]) ).
cnf(f_2481_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8775),U_8776),U_8777))
| ~ hBOOL(hAPP(hAPP(c_member(U_8775),U_8776),hAPP(c_SetInterval_Oord__class_OatMost(U_8775),U_8777)))
| ~ class_Orderings_Oord(U_8775) ),
inference(clausify,[status(thm)],[f_2481_2]) ).
cnf(f_2481_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8775),U_8776),hAPP(c_SetInterval_Oord__class_OatMost(U_8775),U_8777)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8775),U_8776),U_8777))
| ~ class_Orderings_Oord(U_8775) ),
inference(clausify,[status(thm)],[f_2481_2]) ).
fof(f_2482_1,plain,
! [V_k_2,V_i_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2))) ) )
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atLeast__iff]) ).
fof(f_2482_2,plain,
! [U_8780,U_8779,U_8778] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_8778),U_8779),hAPP(c_SetInterval_Oord__class_OatLeast(U_8778),U_8780)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8778),U_8780),U_8779)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8778),U_8780),U_8779))
| ~ hBOOL(hAPP(hAPP(c_member(U_8778),U_8779),hAPP(c_SetInterval_Oord__class_OatLeast(U_8778),U_8780))) ) )
| ~ class_Orderings_Oord(U_8778) ),
inference(variable_rename,[status(thm)],[f_2482_1]) ).
cnf(f_2482_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8778),U_8780),U_8779))
| ~ hBOOL(hAPP(hAPP(c_member(U_8778),U_8779),hAPP(c_SetInterval_Oord__class_OatLeast(U_8778),U_8780)))
| ~ class_Orderings_Oord(U_8778) ),
inference(clausify,[status(thm)],[f_2482_2]) ).
cnf(f_2482_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8778),U_8779),hAPP(c_SetInterval_Oord__class_OatLeast(U_8778),U_8780)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8778),U_8780),U_8779))
| ~ class_Orderings_Oord(U_8778) ),
inference(clausify,[status(thm)],[f_2482_2]) ).
fof(f_2483_1,plain,
! [V_k_2,V_i_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2))) ) )
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_greaterThan__iff]) ).
fof(f_2483_2,plain,
! [U_8783,U_8782,U_8781] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_8781),U_8782),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8781),U_8783)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8781),U_8783),U_8782)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8781),U_8783),U_8782))
| ~ hBOOL(hAPP(hAPP(c_member(U_8781),U_8782),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8781),U_8783))) ) )
| ~ class_Orderings_Oord(U_8781) ),
inference(variable_rename,[status(thm)],[f_2483_1]) ).
cnf(f_2483_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8781),U_8783),U_8782))
| ~ hBOOL(hAPP(hAPP(c_member(U_8781),U_8782),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8781),U_8783)))
| ~ class_Orderings_Oord(U_8781) ),
inference(clausify,[status(thm)],[f_2483_2]) ).
cnf(f_2483_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8781),U_8782),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_8781),U_8783)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8781),U_8783),U_8782))
| ~ class_Orderings_Oord(U_8781) ),
inference(clausify,[status(thm)],[f_2483_2]) ).
fof(f_2484_1,plain,
! [V_X_2,V_a_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_gfp__fun__UnI2]) ).
fof(f_2484_2,plain,
! [U_8787,U_8786,U_8785,U_8784] :
( hBOOL(hAPP(hAPP(c_member(U_8784),U_8786),hAPP(U_8785,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8784,tc_HOL_Obool)),U_8787),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_8784,tc_HOL_Obool),U_8785)))))
| ~ hBOOL(hAPP(hAPP(c_member(U_8784),U_8786),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_8784,tc_HOL_Obool),U_8785)))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_8784,tc_HOL_Obool),tc_fun(U_8784,tc_HOL_Obool),U_8785) ),
inference(variable_rename,[status(thm)],[f_2484_1]) ).
cnf(f_2484_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8784),U_8786),hAPP(U_8785,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8784,tc_HOL_Obool)),U_8787),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_8784,tc_HOL_Obool),U_8785)))))
| ~ hBOOL(hAPP(hAPP(c_member(U_8784),U_8786),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_8784,tc_HOL_Obool),U_8785)))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_8784,tc_HOL_Obool),tc_fun(U_8784,tc_HOL_Obool),U_8785) ),
inference(clausify,[status(thm)],[f_2484_2]) ).
fof(f_2485_1,plain,
! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_M_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_le__SUPI]) ).
fof(f_2485_2,plain,
! [U_8792,U_8791,U_8790,U_8789,U_8788] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8788),hAPP(U_8792,U_8790)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8789,U_8788),U_8791),U_8792)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8789),U_8790),U_8791))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_8788) ),
inference(variable_rename,[status(thm)],[f_2485_1]) ).
cnf(f_2485_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8788),hAPP(U_8792,U_8790)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8789,U_8788),U_8791),U_8792)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8789),U_8790),U_8791))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_8788) ),
inference(clausify,[status(thm)],[f_2485_2]) ).
fof(f_2486_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_2486_2,plain,
! [U_8794,U_8793] :
( c_Nat__Transfer_Ois__nat(U_8794)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8794),U_8793))
| ~ c_Nat__Transfer_Onat__set(U_8793) ),
inference(variable_rename,[status(thm)],[f_2486_1]) ).
cnf(f_2486_3,plain,
( c_Nat__Transfer_Ois__nat(U_8794)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8794),U_8793))
| ~ c_Nat__Transfer_Onat__set(U_8793) ),
inference(clausify,[status(thm)],[f_2486_2]) ).
fof(f_2487_1,plain,
! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_INF__leI]) ).
fof(f_2487_2,plain,
! [U_8799,U_8798,U_8797,U_8796,U_8795] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8795),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8796,U_8795),U_8798),U_8799)),hAPP(U_8799,U_8797)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8796),U_8797),U_8798))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_8795) ),
inference(variable_rename,[status(thm)],[f_2487_1]) ).
cnf(f_2487_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8795),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8796,U_8795),U_8798),U_8799)),hAPP(U_8799,U_8797)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8796),U_8797),U_8798))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_8795) ),
inference(clausify,[status(thm)],[f_2487_2]) ).
fof(f_2488_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( ( ( hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(V_F_2,V_A_2) = V_x_2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Oremove]) ).
fof(f_2488_2,plain,
! [U_8804,U_8803,U_8802,U_8801,U_8800] :
( ( ( hAPP(U_8802,U_8803) = hAPP(hAPP(U_8801,U_8804),hAPP(U_8802,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8800,tc_HOL_Obool)),U_8803),hAPP(hAPP(c_Set_Oinsert(U_8800),U_8804),c_Orderings_Obot__class_Obot(tc_fun(U_8800,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8800,tc_HOL_Obool)),U_8803),hAPP(hAPP(c_Set_Oinsert(U_8800),U_8804),c_Orderings_Obot__class_Obot(tc_fun(U_8800,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8800,tc_HOL_Obool)) )
& ( hAPP(U_8802,U_8803) = U_8804
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8800,tc_HOL_Obool)),U_8803),hAPP(hAPP(c_Set_Oinsert(U_8800),U_8804),c_Orderings_Obot__class_Obot(tc_fun(U_8800,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8800,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_8800),U_8804),U_8803))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8800),U_8803))
| ~ c_Finite__Set_Ofolding__one(U_8800,U_8801,U_8802) ),
inference(variable_rename,[status(thm)],[f_2488_1]) ).
cnf(f_2488_3,plain,
( hAPP(U_8802,U_8803) = U_8804
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8800,tc_HOL_Obool)),U_8803),hAPP(hAPP(c_Set_Oinsert(U_8800),U_8804),c_Orderings_Obot__class_Obot(tc_fun(U_8800,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_8800,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_8800),U_8804),U_8803))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8800),U_8803))
| ~ c_Finite__Set_Ofolding__one(U_8800,U_8801,U_8802) ),
inference(clausify,[status(thm)],[f_2488_2]) ).
cnf(f_2488_4,plain,
( hAPP(U_8802,U_8803) = hAPP(hAPP(U_8801,U_8804),hAPP(U_8802,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8800,tc_HOL_Obool)),U_8803),hAPP(hAPP(c_Set_Oinsert(U_8800),U_8804),c_Orderings_Obot__class_Obot(tc_fun(U_8800,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8800,tc_HOL_Obool)),U_8803),hAPP(hAPP(c_Set_Oinsert(U_8800),U_8804),c_Orderings_Obot__class_Obot(tc_fun(U_8800,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_8800,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_8800),U_8804),U_8803))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8800),U_8803))
| ~ c_Finite__Set_Ofolding__one(U_8800,U_8801,U_8802) ),
inference(clausify,[status(thm)],[f_2488_2]) ).
fof(f_2489_1,plain,
! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_UN__insert__distrib]) ).
fof(f_2489_2,plain,
! [U_8810,U_8809,U_8808,U_8807,U_8806,U_8805] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8805,tc_fun(U_8808,tc_HOL_Obool)),U_8807),hAPP(hAPP(c_COMBB(tc_fun(U_8808,tc_HOL_Obool),tc_fun(U_8808,tc_HOL_Obool),U_8805),hAPP(c_Set_Oinsert(U_8808),U_8809)),U_8810)) = hAPP(hAPP(c_Set_Oinsert(U_8808),U_8809),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8805,tc_fun(U_8808,tc_HOL_Obool)),U_8807),U_8810))
| ~ hBOOL(hAPP(hAPP(c_member(U_8805),U_8806),U_8807)) ),
inference(variable_rename,[status(thm)],[f_2489_1]) ).
cnf(f_2489_3,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8805,tc_fun(U_8808,tc_HOL_Obool)),U_8807),hAPP(hAPP(c_COMBB(tc_fun(U_8808,tc_HOL_Obool),tc_fun(U_8808,tc_HOL_Obool),U_8805),hAPP(c_Set_Oinsert(U_8808),U_8809)),U_8810)) = hAPP(hAPP(c_Set_Oinsert(U_8808),U_8809),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8805,tc_fun(U_8808,tc_HOL_Obool)),U_8807),U_8810))
| ~ hBOOL(hAPP(hAPP(c_member(U_8805),U_8806),U_8807)) ),
inference(clausify,[status(thm)],[f_2489_2]) ).
fof(f_2490_1,plain,
! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_UN__upper]) ).
fof(f_2490_2,plain,
! [U_8815,U_8814,U_8813,U_8812,U_8811] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8814,tc_HOL_Obool)),hAPP(U_8815,U_8812)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8811,tc_fun(U_8814,tc_HOL_Obool)),U_8813),U_8815)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8811),U_8812),U_8813)) ),
inference(variable_rename,[status(thm)],[f_2490_1]) ).
cnf(f_2490_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8814,tc_HOL_Obool)),hAPP(U_8815,U_8812)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8811,tc_fun(U_8814,tc_HOL_Obool)),U_8813),U_8815)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8811),U_8812),U_8813)) ),
inference(clausify,[status(thm)],[f_2490_2]) ).
fof(f_2491_1,plain,
! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) ),
inference(fof_nnf,[status(thm)],[fact_UN__absorb]) ).
fof(f_2491_2,plain,
! [U_8820,U_8819,U_8818,U_8817,U_8816] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8819,tc_HOL_Obool)),hAPP(U_8820,U_8817)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8816,tc_fun(U_8819,tc_HOL_Obool)),U_8818),U_8820)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8816,tc_fun(U_8819,tc_HOL_Obool)),U_8818),U_8820)
| ~ hBOOL(hAPP(hAPP(c_member(U_8816),U_8817),U_8818)) ),
inference(variable_rename,[status(thm)],[f_2491_1]) ).
cnf(f_2491_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8819,tc_HOL_Obool)),hAPP(U_8820,U_8817)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8816,tc_fun(U_8819,tc_HOL_Obool)),U_8818),U_8820)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_8816,tc_fun(U_8819,tc_HOL_Obool)),U_8818),U_8820)
| ~ hBOOL(hAPP(hAPP(c_member(U_8816),U_8817),U_8818)) ),
inference(clausify,[status(thm)],[f_2491_2]) ).
fof(f_2492_1,plain,
! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_INT__insert__distrib]) ).
fof(f_2492_2,plain,
! [U_8826,U_8825,U_8824,U_8823,U_8822,U_8821] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8821,tc_fun(U_8824,tc_HOL_Obool)),U_8823),hAPP(hAPP(c_COMBB(tc_fun(U_8824,tc_HOL_Obool),tc_fun(U_8824,tc_HOL_Obool),U_8821),hAPP(c_Set_Oinsert(U_8824),U_8825)),U_8826)) = hAPP(hAPP(c_Set_Oinsert(U_8824),U_8825),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8821,tc_fun(U_8824,tc_HOL_Obool)),U_8823),U_8826))
| ~ hBOOL(hAPP(hAPP(c_member(U_8821),U_8822),U_8823)) ),
inference(variable_rename,[status(thm)],[f_2492_1]) ).
cnf(f_2492_3,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8821,tc_fun(U_8824,tc_HOL_Obool)),U_8823),hAPP(hAPP(c_COMBB(tc_fun(U_8824,tc_HOL_Obool),tc_fun(U_8824,tc_HOL_Obool),U_8821),hAPP(c_Set_Oinsert(U_8824),U_8825)),U_8826)) = hAPP(hAPP(c_Set_Oinsert(U_8824),U_8825),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8821,tc_fun(U_8824,tc_HOL_Obool)),U_8823),U_8826))
| ~ hBOOL(hAPP(hAPP(c_member(U_8821),U_8822),U_8823)) ),
inference(clausify,[status(thm)],[f_2492_2]) ).
fof(f_2493_1,plain,
! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_INT__lower]) ).
fof(f_2493_2,plain,
! [U_8831,U_8830,U_8829,U_8828,U_8827] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8830,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8827,tc_fun(U_8830,tc_HOL_Obool)),U_8829),U_8831)),hAPP(U_8831,U_8828)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8827),U_8828),U_8829)) ),
inference(variable_rename,[status(thm)],[f_2493_1]) ).
cnf(f_2493_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8830,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_8827,tc_fun(U_8830,tc_HOL_Obool)),U_8829),U_8831)),hAPP(U_8831,U_8828)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8827),U_8828),U_8829)) ),
inference(clausify,[status(thm)],[f_2493_2]) ).
fof(f_2494_1,plain,
! [V_S_2,V_R_2,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2]) ).
fof(f_2494_2,plain,
! [U_8835,U_8834,U_8833,U_8832] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8832,tc_fun(U_8833,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8832,tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_fun(U_8833,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8833,tc_fun(tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_fun(U_8833,tc_HOL_Obool)),U_8832),c_COMBC(U_8833,tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8833,tc_prod(U_8832,U_8833)),tc_fun(U_8833,tc_fun(tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_HOL_Obool)),U_8832),hAPP(c_COMBB(tc_prod(U_8832,U_8833),tc_fun(tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_HOL_Obool),U_8833),c_member(tc_prod(U_8832,U_8833)))),c_Product__Type_OPair(U_8832,U_8833)))),U_8834)),hAPP(hAPP(c_COMBC(U_8832,tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_fun(U_8833,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8833,tc_fun(tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_fun(U_8833,tc_HOL_Obool)),U_8832),c_COMBC(U_8833,tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8833,tc_prod(U_8832,U_8833)),tc_fun(U_8833,tc_fun(tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_HOL_Obool)),U_8832),hAPP(c_COMBB(tc_prod(U_8832,U_8833),tc_fun(tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_HOL_Obool),U_8833),c_member(tc_prod(U_8832,U_8833)))),c_Product__Type_OPair(U_8832,U_8833)))),U_8835)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool)),U_8834),U_8835)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool)),U_8834),U_8835))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8832,tc_fun(U_8833,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8832,tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_fun(U_8833,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8833,tc_fun(tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_fun(U_8833,tc_HOL_Obool)),U_8832),c_COMBC(U_8833,tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8833,tc_prod(U_8832,U_8833)),tc_fun(U_8833,tc_fun(tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_HOL_Obool)),U_8832),hAPP(c_COMBB(tc_prod(U_8832,U_8833),tc_fun(tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_HOL_Obool),U_8833),c_member(tc_prod(U_8832,U_8833)))),c_Product__Type_OPair(U_8832,U_8833)))),U_8834)),hAPP(hAPP(c_COMBC(U_8832,tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_fun(U_8833,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8833,tc_fun(tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_fun(U_8833,tc_HOL_Obool)),U_8832),c_COMBC(U_8833,tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8833,tc_prod(U_8832,U_8833)),tc_fun(U_8833,tc_fun(tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_HOL_Obool)),U_8832),hAPP(c_COMBB(tc_prod(U_8832,U_8833),tc_fun(tc_fun(tc_prod(U_8832,U_8833),tc_HOL_Obool),tc_HOL_Obool),U_8833),c_member(tc_prod(U_8832,U_8833)))),c_Product__Type_OPair(U_8832,U_8833)))),U_8835))) ) ),
inference(variable_rename,[status(thm)],[f_2494_1]) ).
fof(f_2494_3,plain,
( ! [U_8843,U_8841,U_8839,U_8837] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8837,tc_fun(U_8839,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8837,tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_fun(U_8839,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8839,tc_fun(tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_fun(U_8839,tc_HOL_Obool)),U_8837),c_COMBC(U_8839,tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8839,tc_prod(U_8837,U_8839)),tc_fun(U_8839,tc_fun(tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_HOL_Obool)),U_8837),hAPP(c_COMBB(tc_prod(U_8837,U_8839),tc_fun(tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_HOL_Obool),U_8839),c_member(tc_prod(U_8837,U_8839)))),c_Product__Type_OPair(U_8837,U_8839)))),U_8841)),hAPP(hAPP(c_COMBC(U_8837,tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_fun(U_8839,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8839,tc_fun(tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_fun(U_8839,tc_HOL_Obool)),U_8837),c_COMBC(U_8839,tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8839,tc_prod(U_8837,U_8839)),tc_fun(U_8839,tc_fun(tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_HOL_Obool)),U_8837),hAPP(c_COMBB(tc_prod(U_8837,U_8839),tc_fun(tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_HOL_Obool),U_8839),c_member(tc_prod(U_8837,U_8839)))),c_Product__Type_OPair(U_8837,U_8839)))),U_8843)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool)),U_8841),U_8843)) )
& ! [U_8842,U_8840,U_8838,U_8836] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool)),U_8840),U_8842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8836,tc_fun(U_8838,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8836,tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_fun(U_8838,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8838,tc_fun(tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_fun(U_8838,tc_HOL_Obool)),U_8836),c_COMBC(U_8838,tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8838,tc_prod(U_8836,U_8838)),tc_fun(U_8838,tc_fun(tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_HOL_Obool)),U_8836),hAPP(c_COMBB(tc_prod(U_8836,U_8838),tc_fun(tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_HOL_Obool),U_8838),c_member(tc_prod(U_8836,U_8838)))),c_Product__Type_OPair(U_8836,U_8838)))),U_8840)),hAPP(hAPP(c_COMBC(U_8836,tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_fun(U_8838,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8838,tc_fun(tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_fun(U_8838,tc_HOL_Obool)),U_8836),c_COMBC(U_8838,tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8838,tc_prod(U_8836,U_8838)),tc_fun(U_8838,tc_fun(tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_HOL_Obool)),U_8836),hAPP(c_COMBB(tc_prod(U_8836,U_8838),tc_fun(tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_HOL_Obool),U_8838),c_member(tc_prod(U_8836,U_8838)))),c_Product__Type_OPair(U_8836,U_8838)))),U_8842))) ) ),
inference(miniscope,[status(thm)],[f_2494_2]) ).
cnf(f_2494_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool)),U_8840),U_8842))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8836,tc_fun(U_8838,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8836,tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_fun(U_8838,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8838,tc_fun(tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_fun(U_8838,tc_HOL_Obool)),U_8836),c_COMBC(U_8838,tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8838,tc_prod(U_8836,U_8838)),tc_fun(U_8838,tc_fun(tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_HOL_Obool)),U_8836),hAPP(c_COMBB(tc_prod(U_8836,U_8838),tc_fun(tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_HOL_Obool),U_8838),c_member(tc_prod(U_8836,U_8838)))),c_Product__Type_OPair(U_8836,U_8838)))),U_8840)),hAPP(hAPP(c_COMBC(U_8836,tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_fun(U_8838,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8838,tc_fun(tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_fun(U_8838,tc_HOL_Obool)),U_8836),c_COMBC(U_8838,tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8838,tc_prod(U_8836,U_8838)),tc_fun(U_8838,tc_fun(tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_HOL_Obool)),U_8836),hAPP(c_COMBB(tc_prod(U_8836,U_8838),tc_fun(tc_fun(tc_prod(U_8836,U_8838),tc_HOL_Obool),tc_HOL_Obool),U_8838),c_member(tc_prod(U_8836,U_8838)))),c_Product__Type_OPair(U_8836,U_8838)))),U_8842))) ),
inference(clausify,[status(thm)],[f_2494_3]) ).
cnf(f_2494_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8837,tc_fun(U_8839,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8837,tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_fun(U_8839,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8839,tc_fun(tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_fun(U_8839,tc_HOL_Obool)),U_8837),c_COMBC(U_8839,tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8839,tc_prod(U_8837,U_8839)),tc_fun(U_8839,tc_fun(tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_HOL_Obool)),U_8837),hAPP(c_COMBB(tc_prod(U_8837,U_8839),tc_fun(tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_HOL_Obool),U_8839),c_member(tc_prod(U_8837,U_8839)))),c_Product__Type_OPair(U_8837,U_8839)))),U_8841)),hAPP(hAPP(c_COMBC(U_8837,tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_fun(U_8839,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8839,tc_fun(tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_fun(U_8839,tc_HOL_Obool)),U_8837),c_COMBC(U_8839,tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8839,tc_prod(U_8837,U_8839)),tc_fun(U_8839,tc_fun(tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_HOL_Obool)),U_8837),hAPP(c_COMBB(tc_prod(U_8837,U_8839),tc_fun(tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool),tc_HOL_Obool),U_8839),c_member(tc_prod(U_8837,U_8839)))),c_Product__Type_OPair(U_8837,U_8839)))),U_8843)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8837,U_8839),tc_HOL_Obool)),U_8841),U_8843)) ),
inference(clausify,[status(thm)],[f_2494_3]) ).
fof(f_2495_1,plain,
! [V_A_2,V_x_2,T_b] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_A_2
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Diff__insert__absorb]) ).
fof(f_2495_2,plain,
! [U_8846,U_8845,U_8844] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8844,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8844),U_8845),U_8846)),hAPP(hAPP(c_Set_Oinsert(U_8844),U_8845),c_Orderings_Obot__class_Obot(tc_fun(U_8844,tc_HOL_Obool)))) = U_8846
| hBOOL(hAPP(hAPP(c_member(U_8844),U_8845),U_8846)) ),
inference(variable_rename,[status(thm)],[f_2495_1]) ).
cnf(f_2495_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8844,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8844),U_8845),U_8846)),hAPP(hAPP(c_Set_Oinsert(U_8844),U_8845),c_Orderings_Obot__class_Obot(tc_fun(U_8844,tc_HOL_Obool)))) = U_8846
| hBOOL(hAPP(hAPP(c_member(U_8844),U_8845),U_8846)) ),
inference(clausify,[status(thm)],[f_2495_2]) ).
fof(f_2496_1,plain,
! [V_A_2,V_a_2,T_b] :
( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = V_A_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__Diff]) ).
fof(f_2496_2,plain,
! [U_8849,U_8848,U_8847] :
( hAPP(hAPP(c_Set_Oinsert(U_8847),U_8848),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8847,tc_HOL_Obool)),U_8849),hAPP(hAPP(c_Set_Oinsert(U_8847),U_8848),c_Orderings_Obot__class_Obot(tc_fun(U_8847,tc_HOL_Obool))))) = U_8849
| ~ hBOOL(hAPP(hAPP(c_member(U_8847),U_8848),U_8849)) ),
inference(variable_rename,[status(thm)],[f_2496_1]) ).
cnf(f_2496_3,plain,
( hAPP(hAPP(c_Set_Oinsert(U_8847),U_8848),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8847,tc_HOL_Obool)),U_8849),hAPP(hAPP(c_Set_Oinsert(U_8847),U_8848),c_Orderings_Obot__class_Obot(tc_fun(U_8847,tc_HOL_Obool))))) = U_8849
| ~ hBOOL(hAPP(hAPP(c_member(U_8847),U_8848),U_8849)) ),
inference(clausify,[status(thm)],[f_2496_2]) ).
fof(f_2497_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_2497_2,plain,
! [U_8851,U_8850] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8851))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8851),U_8850))
| ~ c_Nat__Transfer_Onat__set(U_8850) ),
inference(variable_rename,[status(thm)],[f_2497_1]) ).
cnf(f_2497_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8851))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8851),U_8850))
| ~ c_Nat__Transfer_Onat__set(U_8850) ),
inference(clausify,[status(thm)],[f_2497_2]) ).
fof(f_2498_1,plain,
! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__delta_H]) ).
fof(f_2498_2,plain,
! [U_8856,U_8855,U_8854,U_8853,U_8852] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8853,U_8852),hAPP(hAPP(c_COMBC(U_8853,U_8852,U_8852),hAPP(hAPP(c_COMBS(U_8853,U_8852,tc_fun(U_8852,U_8852)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_8852,tc_fun(U_8852,U_8852)),U_8853),c_If(U_8852)),hAPP(c_fequal,U_8855))),U_8856)),c_Groups_Ozero__class_Ozero(U_8852))),U_8854) = c_Groups_Ozero__class_Ozero(U_8852)
| hBOOL(hAPP(hAPP(c_member(U_8853),U_8855),U_8854)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8853,U_8852),hAPP(hAPP(c_COMBC(U_8853,U_8852,U_8852),hAPP(hAPP(c_COMBS(U_8853,U_8852,tc_fun(U_8852,U_8852)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_8852,tc_fun(U_8852,U_8852)),U_8853),c_If(U_8852)),hAPP(c_fequal,U_8855))),U_8856)),c_Groups_Ozero__class_Ozero(U_8852))),U_8854) = hAPP(U_8856,U_8855)
| ~ hBOOL(hAPP(hAPP(c_member(U_8853),U_8855),U_8854)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8853),U_8854))
| ~ class_Groups_Ocomm__monoid__add(U_8852) ),
inference(variable_rename,[status(thm)],[f_2498_1]) ).
cnf(f_2498_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8853,U_8852),hAPP(hAPP(c_COMBC(U_8853,U_8852,U_8852),hAPP(hAPP(c_COMBS(U_8853,U_8852,tc_fun(U_8852,U_8852)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_8852,tc_fun(U_8852,U_8852)),U_8853),c_If(U_8852)),hAPP(c_fequal,U_8855))),U_8856)),c_Groups_Ozero__class_Ozero(U_8852))),U_8854) = hAPP(U_8856,U_8855)
| ~ hBOOL(hAPP(hAPP(c_member(U_8853),U_8855),U_8854))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8853),U_8854))
| ~ class_Groups_Ocomm__monoid__add(U_8852) ),
inference(clausify,[status(thm)],[f_2498_2]) ).
cnf(f_2498_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8853,U_8852),hAPP(hAPP(c_COMBC(U_8853,U_8852,U_8852),hAPP(hAPP(c_COMBS(U_8853,U_8852,tc_fun(U_8852,U_8852)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_8852,tc_fun(U_8852,U_8852)),U_8853),c_If(U_8852)),hAPP(c_fequal,U_8855))),U_8856)),c_Groups_Ozero__class_Ozero(U_8852))),U_8854) = c_Groups_Ozero__class_Ozero(U_8852)
| hBOOL(hAPP(hAPP(c_member(U_8853),U_8855),U_8854))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8853),U_8854))
| ~ class_Groups_Ocomm__monoid__add(U_8852) ),
inference(clausify,[status(thm)],[f_2498_2]) ).
fof(f_2499_1,plain,
! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__delta]) ).
fof(f_2499_2,plain,
! [U_8861,U_8860,U_8859,U_8858,U_8857] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8858,U_8857),hAPP(hAPP(c_COMBC(U_8858,U_8857,U_8857),hAPP(hAPP(c_COMBS(U_8858,U_8857,tc_fun(U_8857,U_8857)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_8857,tc_fun(U_8857,U_8857)),U_8858),c_If(U_8857)),hAPP(hAPP(c_COMBC(U_8858,U_8858,tc_HOL_Obool),c_fequal),U_8860))),U_8861)),c_Groups_Ozero__class_Ozero(U_8857))),U_8859) = c_Groups_Ozero__class_Ozero(U_8857)
| hBOOL(hAPP(hAPP(c_member(U_8858),U_8860),U_8859)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8858,U_8857),hAPP(hAPP(c_COMBC(U_8858,U_8857,U_8857),hAPP(hAPP(c_COMBS(U_8858,U_8857,tc_fun(U_8857,U_8857)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_8857,tc_fun(U_8857,U_8857)),U_8858),c_If(U_8857)),hAPP(hAPP(c_COMBC(U_8858,U_8858,tc_HOL_Obool),c_fequal),U_8860))),U_8861)),c_Groups_Ozero__class_Ozero(U_8857))),U_8859) = hAPP(U_8861,U_8860)
| ~ hBOOL(hAPP(hAPP(c_member(U_8858),U_8860),U_8859)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8858),U_8859))
| ~ class_Groups_Ocomm__monoid__add(U_8857) ),
inference(variable_rename,[status(thm)],[f_2499_1]) ).
cnf(f_2499_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8858,U_8857),hAPP(hAPP(c_COMBC(U_8858,U_8857,U_8857),hAPP(hAPP(c_COMBS(U_8858,U_8857,tc_fun(U_8857,U_8857)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_8857,tc_fun(U_8857,U_8857)),U_8858),c_If(U_8857)),hAPP(hAPP(c_COMBC(U_8858,U_8858,tc_HOL_Obool),c_fequal),U_8860))),U_8861)),c_Groups_Ozero__class_Ozero(U_8857))),U_8859) = hAPP(U_8861,U_8860)
| ~ hBOOL(hAPP(hAPP(c_member(U_8858),U_8860),U_8859))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8858),U_8859))
| ~ class_Groups_Ocomm__monoid__add(U_8857) ),
inference(clausify,[status(thm)],[f_2499_2]) ).
cnf(f_2499_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8858,U_8857),hAPP(hAPP(c_COMBC(U_8858,U_8857,U_8857),hAPP(hAPP(c_COMBS(U_8858,U_8857,tc_fun(U_8857,U_8857)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_8857,tc_fun(U_8857,U_8857)),U_8858),c_If(U_8857)),hAPP(hAPP(c_COMBC(U_8858,U_8858,tc_HOL_Obool),c_fequal),U_8860))),U_8861)),c_Groups_Ozero__class_Ozero(U_8857))),U_8859) = c_Groups_Ozero__class_Ozero(U_8857)
| hBOOL(hAPP(hAPP(c_member(U_8858),U_8860),U_8859))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8858),U_8859))
| ~ class_Groups_Ocomm__monoid__add(U_8857) ),
inference(clausify,[status(thm)],[f_2499_2]) ).
fof(f_2500_1,plain,
! [V_X_2,V_a_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_coinduct__set]) ).
fof(f_2500_2,plain,
! [U_8865,U_8864,U_8863,U_8862] :
( hBOOL(hAPP(hAPP(c_member(U_8862),U_8864),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_8862,tc_HOL_Obool),U_8863)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8862,tc_HOL_Obool)),U_8865),hAPP(U_8863,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8862,tc_HOL_Obool)),U_8865),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_8862,tc_HOL_Obool),U_8863)))))
| ~ hBOOL(hAPP(hAPP(c_member(U_8862),U_8864),U_8865))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_8862,tc_HOL_Obool),tc_fun(U_8862,tc_HOL_Obool),U_8863) ),
inference(variable_rename,[status(thm)],[f_2500_1]) ).
cnf(f_2500_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8862),U_8864),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_8862,tc_HOL_Obool),U_8863)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8862,tc_HOL_Obool)),U_8865),hAPP(U_8863,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8862,tc_HOL_Obool)),U_8865),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_8862,tc_HOL_Obool),U_8863)))))
| ~ hBOOL(hAPP(hAPP(c_member(U_8862),U_8864),U_8865))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_8862,tc_HOL_Obool),tc_fun(U_8862,tc_HOL_Obool),U_8863) ),
inference(clausify,[status(thm)],[f_2500_2]) ).
fof(f_2501_1,plain,
! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_A_2))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
| V_A_2 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_def__coinduct__set]) ).
fof(f_2501_2,plain,
! [U_8870,U_8869,U_8868,U_8867,U_8866] :
( hBOOL(hAPP(hAPP(c_member(U_8867),U_8869),U_8866))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8867,tc_HOL_Obool)),U_8870),hAPP(U_8868,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8867,tc_HOL_Obool)),U_8870),U_8866))))
| ~ hBOOL(hAPP(hAPP(c_member(U_8867),U_8869),U_8870))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_8867,tc_HOL_Obool),tc_fun(U_8867,tc_HOL_Obool),U_8868)
| U_8866 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_8867,tc_HOL_Obool),U_8868) ),
inference(variable_rename,[status(thm)],[f_2501_1]) ).
cnf(f_2501_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_8867),U_8869),U_8866))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8867,tc_HOL_Obool)),U_8870),hAPP(U_8868,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8867,tc_HOL_Obool)),U_8870),U_8866))))
| ~ hBOOL(hAPP(hAPP(c_member(U_8867),U_8869),U_8870))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_8867,tc_HOL_Obool),tc_fun(U_8867,tc_HOL_Obool),U_8868)
| U_8866 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_8867,tc_HOL_Obool),U_8868) ),
inference(clausify,[status(thm)],[f_2501_2]) ).
fof(f_2502_1,plain,
! [V_c_2,T_c,V_A_2,V_x_2,T_b] :
( hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_image__constant]) ).
fof(f_2502_2,plain,
! [U_8875,U_8874,U_8873,U_8872,U_8871] :
( hAPP(c_Set_Oimage(U_8871,U_8874,hAPP(c_COMBK(U_8874,U_8871),U_8875)),U_8873) = hAPP(hAPP(c_Set_Oinsert(U_8874),U_8875),c_Orderings_Obot__class_Obot(tc_fun(U_8874,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8871),U_8872),U_8873)) ),
inference(variable_rename,[status(thm)],[f_2502_1]) ).
cnf(f_2502_3,plain,
( hAPP(c_Set_Oimage(U_8871,U_8874,hAPP(c_COMBK(U_8874,U_8871),U_8875)),U_8873) = hAPP(hAPP(c_Set_Oinsert(U_8874),U_8875),c_Orderings_Obot__class_Obot(tc_fun(U_8874,tc_HOL_Obool)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8871),U_8872),U_8873)) ),
inference(clausify,[status(thm)],[f_2502_2]) ).
fof(f_2503_1,plain,
! [V_x_2,V_F_2,V_f_2,T_b] :
( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
| ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Osingleton]) ).
fof(f_2503_2,plain,
! [U_8879,U_8878,U_8877,U_8876] :
( hAPP(U_8878,hAPP(hAPP(c_Set_Oinsert(U_8876),U_8879),c_Orderings_Obot__class_Obot(tc_fun(U_8876,tc_HOL_Obool)))) = U_8879
| ~ c_Finite__Set_Ofolding__one(U_8876,U_8877,U_8878) ),
inference(variable_rename,[status(thm)],[f_2503_1]) ).
cnf(f_2503_3,plain,
( hAPP(U_8878,hAPP(hAPP(c_Set_Oinsert(U_8876),U_8879),c_Orderings_Obot__class_Obot(tc_fun(U_8876,tc_HOL_Obool)))) = U_8879
| ~ c_Finite__Set_Ofolding__one(U_8876,U_8877,U_8878) ),
inference(clausify,[status(thm)],[f_2503_2]) ).
fof(f_2504_1,plain,
! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Oinsert]) ).
fof(f_2504_2,plain,
! [U_8884,U_8883,U_8882,U_8881,U_8880] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8881,U_8880),U_8884),hAPP(hAPP(c_Set_Oinsert(U_8881),U_8883),U_8882)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8880),hAPP(U_8884,U_8883)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8881,U_8880),U_8884),U_8882))
| hBOOL(hAPP(hAPP(c_member(U_8881),U_8883),U_8882))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8881),U_8882))
| ~ class_Groups_Ocomm__monoid__add(U_8880) ),
inference(variable_rename,[status(thm)],[f_2504_1]) ).
cnf(f_2504_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8881,U_8880),U_8884),hAPP(hAPP(c_Set_Oinsert(U_8881),U_8883),U_8882)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8880),hAPP(U_8884,U_8883)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8881,U_8880),U_8884),U_8882))
| hBOOL(hAPP(hAPP(c_member(U_8881),U_8883),U_8882))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8881),U_8882))
| ~ class_Groups_Ocomm__monoid__add(U_8880) ),
inference(clausify,[status(thm)],[f_2504_2]) ).
fof(f_2505_1,plain,
! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_F_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__insert]) ).
fof(f_2505_2,plain,
! [U_8889,U_8888,U_8887,U_8886,U_8885] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8886,U_8885),U_8889),hAPP(hAPP(c_Set_Oinsert(U_8886),U_8888),U_8887)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8885),hAPP(U_8889,U_8888)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8886,U_8885),U_8889),U_8887))
| hBOOL(hAPP(hAPP(c_member(U_8886),U_8888),U_8887))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8886),U_8887))
| ~ class_Groups_Ocomm__monoid__add(U_8885) ),
inference(variable_rename,[status(thm)],[f_2505_1]) ).
cnf(f_2505_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8886,U_8885),U_8889),hAPP(hAPP(c_Set_Oinsert(U_8886),U_8888),U_8887)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8885),hAPP(U_8889,U_8888)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8886,U_8885),U_8889),U_8887))
| hBOOL(hAPP(hAPP(c_member(U_8886),U_8888),U_8887))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8886),U_8887))
| ~ class_Groups_Ocomm__monoid__add(U_8885) ),
inference(clausify,[status(thm)],[f_2505_2]) ).
fof(f_2506_1,plain,
! [V_B_2,V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_diff__single__insert]) ).
fof(f_2506_2,plain,
! [U_8893,U_8892,U_8891,U_8890] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8890,tc_HOL_Obool)),U_8891),hAPP(hAPP(c_Set_Oinsert(U_8890),U_8892),U_8893)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8890),U_8892),U_8891))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8890,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8890,tc_HOL_Obool)),U_8891),hAPP(hAPP(c_Set_Oinsert(U_8890),U_8892),c_Orderings_Obot__class_Obot(tc_fun(U_8890,tc_HOL_Obool))))),U_8893)) ),
inference(variable_rename,[status(thm)],[f_2506_1]) ).
cnf(f_2506_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8890,tc_HOL_Obool)),U_8891),hAPP(hAPP(c_Set_Oinsert(U_8890),U_8892),U_8893)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8890),U_8892),U_8891))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8890,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8890,tc_HOL_Obool)),U_8891),hAPP(hAPP(c_Set_Oinsert(U_8890),U_8892),c_Orderings_Obot__class_Obot(tc_fun(U_8890,tc_HOL_Obool))))),U_8893)) ),
inference(clausify,[status(thm)],[f_2506_2]) ).
fof(f_2507_1,plain,
! [V_B_2,V_x_2,V_A_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_subset__insert__iff]) ).
fof(f_2507_2,plain,
! [U_8897,U_8896,U_8895,U_8894] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8894,tc_HOL_Obool)),U_8895),hAPP(hAPP(c_Set_Oinsert(U_8894),U_8896),U_8897)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8894,tc_HOL_Obool)),U_8895),U_8897))
& ~ hBOOL(hAPP(hAPP(c_member(U_8894),U_8896),U_8895)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8894,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8894,tc_HOL_Obool)),U_8895),hAPP(hAPP(c_Set_Oinsert(U_8894),U_8896),c_Orderings_Obot__class_Obot(tc_fun(U_8894,tc_HOL_Obool))))),U_8897))
& hBOOL(hAPP(hAPP(c_member(U_8894),U_8896),U_8895)) ) )
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8894,tc_HOL_Obool)),U_8895),U_8897))
| hBOOL(hAPP(hAPP(c_member(U_8894),U_8896),U_8895)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8894,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8894,tc_HOL_Obool)),U_8895),hAPP(hAPP(c_Set_Oinsert(U_8894),U_8896),c_Orderings_Obot__class_Obot(tc_fun(U_8894,tc_HOL_Obool))))),U_8897))
| ~ hBOOL(hAPP(hAPP(c_member(U_8894),U_8896),U_8895)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8894,tc_HOL_Obool)),U_8895),hAPP(hAPP(c_Set_Oinsert(U_8894),U_8896),U_8897))) ) ),
inference(variable_rename,[status(thm)],[f_2507_1]) ).
fof(f_2507_3,plain,
( ! [U_8905,U_8903,U_8901,U_8899] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8899,tc_HOL_Obool)),U_8901),hAPP(hAPP(c_Set_Oinsert(U_8899),U_8903),U_8905)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8899,tc_HOL_Obool)),U_8901),U_8905))
& ~ hBOOL(hAPP(hAPP(c_member(U_8899),U_8903),U_8901)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8899,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8899,tc_HOL_Obool)),U_8901),hAPP(hAPP(c_Set_Oinsert(U_8899),U_8903),c_Orderings_Obot__class_Obot(tc_fun(U_8899,tc_HOL_Obool))))),U_8905))
& hBOOL(hAPP(hAPP(c_member(U_8899),U_8903),U_8901)) ) )
& ! [U_8904,U_8902,U_8900,U_8898] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8898,tc_HOL_Obool)),U_8900),U_8904))
| hBOOL(hAPP(hAPP(c_member(U_8898),U_8902),U_8900)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8898,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8898,tc_HOL_Obool)),U_8900),hAPP(hAPP(c_Set_Oinsert(U_8898),U_8902),c_Orderings_Obot__class_Obot(tc_fun(U_8898,tc_HOL_Obool))))),U_8904))
| ~ hBOOL(hAPP(hAPP(c_member(U_8898),U_8902),U_8900)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8898,tc_HOL_Obool)),U_8900),hAPP(hAPP(c_Set_Oinsert(U_8898),U_8902),U_8904))) ) ),
inference(miniscope,[status(thm)],[f_2507_2]) ).
cnf(f_2507_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8898,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8898,tc_HOL_Obool)),U_8900),hAPP(hAPP(c_Set_Oinsert(U_8898),U_8902),c_Orderings_Obot__class_Obot(tc_fun(U_8898,tc_HOL_Obool))))),U_8904))
| ~ hBOOL(hAPP(hAPP(c_member(U_8898),U_8902),U_8900))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8898,tc_HOL_Obool)),U_8900),hAPP(hAPP(c_Set_Oinsert(U_8898),U_8902),U_8904))) ),
inference(clausify,[status(thm)],[f_2507_3]) ).
cnf(f_2507_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8898,tc_HOL_Obool)),U_8900),U_8904))
| hBOOL(hAPP(hAPP(c_member(U_8898),U_8902),U_8900))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8898,tc_HOL_Obool)),U_8900),hAPP(hAPP(c_Set_Oinsert(U_8898),U_8902),U_8904))) ),
inference(clausify,[status(thm)],[f_2507_3]) ).
cnf(f_2507_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8899),U_8903),U_8901))
| hBOOL(hAPP(hAPP(c_member(U_8899),U_8903),U_8901))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8899,tc_HOL_Obool)),U_8901),hAPP(hAPP(c_Set_Oinsert(U_8899),U_8903),U_8905))) ),
inference(clausify,[status(thm)],[f_2507_3]) ).
cnf(f_2507_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8899,tc_HOL_Obool)),U_8901),U_8905))
| hBOOL(hAPP(hAPP(c_member(U_8899),U_8903),U_8901))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8899,tc_HOL_Obool)),U_8901),hAPP(hAPP(c_Set_Oinsert(U_8899),U_8903),U_8905))) ),
inference(clausify,[status(thm)],[f_2507_3]) ).
cnf(f_2507_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8899),U_8903),U_8901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8899,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8899,tc_HOL_Obool)),U_8901),hAPP(hAPP(c_Set_Oinsert(U_8899),U_8903),c_Orderings_Obot__class_Obot(tc_fun(U_8899,tc_HOL_Obool))))),U_8905))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8899,tc_HOL_Obool)),U_8901),hAPP(hAPP(c_Set_Oinsert(U_8899),U_8903),U_8905))) ),
inference(clausify,[status(thm)],[f_2507_3]) ).
cnf(f_2507_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8899,tc_HOL_Obool)),U_8901),U_8905))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8899,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8899,tc_HOL_Obool)),U_8901),hAPP(hAPP(c_Set_Oinsert(U_8899),U_8903),c_Orderings_Obot__class_Obot(tc_fun(U_8899,tc_HOL_Obool))))),U_8905))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8899,tc_HOL_Obool)),U_8901),hAPP(hAPP(c_Set_Oinsert(U_8899),U_8903),U_8905))) ),
inference(clausify,[status(thm)],[f_2507_3]) ).
fof(f_2508_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
& ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__insert__if]) ).
fof(f_2508_2,plain,
! [U_8908,U_8907,U_8906] :
( ( ( hAPP(c_Finite__Set_Ocard(U_8906),hAPP(hAPP(c_Set_Oinsert(U_8906),U_8908),U_8907)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_8906),U_8907))
| hBOOL(hAPP(hAPP(c_member(U_8906),U_8908),U_8907)) )
& ( hAPP(c_Finite__Set_Ocard(U_8906),hAPP(hAPP(c_Set_Oinsert(U_8906),U_8908),U_8907)) = hAPP(c_Finite__Set_Ocard(U_8906),U_8907)
| ~ hBOOL(hAPP(hAPP(c_member(U_8906),U_8908),U_8907)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8906),U_8907)) ),
inference(variable_rename,[status(thm)],[f_2508_1]) ).
cnf(f_2508_3,plain,
( hAPP(c_Finite__Set_Ocard(U_8906),hAPP(hAPP(c_Set_Oinsert(U_8906),U_8908),U_8907)) = hAPP(c_Finite__Set_Ocard(U_8906),U_8907)
| ~ hBOOL(hAPP(hAPP(c_member(U_8906),U_8908),U_8907))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8906),U_8907)) ),
inference(clausify,[status(thm)],[f_2508_2]) ).
cnf(f_2508_4,plain,
( hAPP(c_Finite__Set_Ocard(U_8906),hAPP(hAPP(c_Set_Oinsert(U_8906),U_8908),U_8907)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_8906),U_8907))
| hBOOL(hAPP(hAPP(c_member(U_8906),U_8908),U_8907))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8906),U_8907)) ),
inference(clausify,[status(thm)],[f_2508_2]) ).
fof(f_2509_1,plain,
! [V_x_2,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__insert__disjoint]) ).
fof(f_2509_2,plain,
! [U_8911,U_8910,U_8909] :
( hAPP(c_Finite__Set_Ocard(U_8909),hAPP(hAPP(c_Set_Oinsert(U_8909),U_8911),U_8910)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_8909),U_8910))
| hBOOL(hAPP(hAPP(c_member(U_8909),U_8911),U_8910))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8909),U_8910)) ),
inference(variable_rename,[status(thm)],[f_2509_1]) ).
cnf(f_2509_3,plain,
( hAPP(c_Finite__Set_Ocard(U_8909),hAPP(hAPP(c_Set_Oinsert(U_8909),U_8911),U_8910)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_8909),U_8910))
| hBOOL(hAPP(hAPP(c_member(U_8909),U_8911),U_8910))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8909),U_8910)) ),
inference(clausify,[status(thm)],[f_2509_2]) ).
fof(f_2510_1,plain,
! [V_x_2,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card_Oinsert]) ).
fof(f_2510_2,plain,
! [U_8914,U_8913,U_8912] :
( hAPP(c_Finite__Set_Ocard(U_8912),hAPP(hAPP(c_Set_Oinsert(U_8912),U_8914),U_8913)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_8912),U_8913))
| hBOOL(hAPP(hAPP(c_member(U_8912),U_8914),U_8913))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8912),U_8913)) ),
inference(variable_rename,[status(thm)],[f_2510_1]) ).
cnf(f_2510_3,plain,
( hAPP(c_Finite__Set_Ocard(U_8912),hAPP(hAPP(c_Set_Oinsert(U_8912),U_8914),U_8913)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_8912),U_8913))
| hBOOL(hAPP(hAPP(c_member(U_8912),U_8914),U_8913))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8912),U_8913)) ),
inference(clausify,[status(thm)],[f_2510_2]) ).
fof(f_2511_1,plain,
! [V_B_2,V_x_2,V_A_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
& ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) )
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_psubset__insert__iff]) ).
fof(f_2511_2,plain,
! [U_8918,U_8917,U_8916,U_8915] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8915,tc_HOL_Obool)),U_8916),hAPP(hAPP(c_Set_Oinsert(U_8915),U_8917),U_8918)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8915,tc_HOL_Obool)),U_8916),U_8918))
& ~ hBOOL(hAPP(hAPP(c_member(U_8915),U_8917),U_8916)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8915,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8915,tc_HOL_Obool)),U_8916),hAPP(hAPP(c_Set_Oinsert(U_8915),U_8917),c_Orderings_Obot__class_Obot(tc_fun(U_8915,tc_HOL_Obool))))),U_8918))
& hBOOL(hAPP(hAPP(c_member(U_8915),U_8917),U_8916)) ) )
& ~ hBOOL(hAPP(hAPP(c_member(U_8915),U_8917),U_8918)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8915,tc_HOL_Obool)),U_8916),U_8918))
& hBOOL(hAPP(hAPP(c_member(U_8915),U_8917),U_8918)) ) )
& ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8915,tc_HOL_Obool)),U_8916),U_8918))
| hBOOL(hAPP(hAPP(c_member(U_8915),U_8917),U_8916)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8915,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8915,tc_HOL_Obool)),U_8916),hAPP(hAPP(c_Set_Oinsert(U_8915),U_8917),c_Orderings_Obot__class_Obot(tc_fun(U_8915,tc_HOL_Obool))))),U_8918))
| ~ hBOOL(hAPP(hAPP(c_member(U_8915),U_8917),U_8916)) ) )
| hBOOL(hAPP(hAPP(c_member(U_8915),U_8917),U_8918)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8915,tc_HOL_Obool)),U_8916),U_8918))
| ~ hBOOL(hAPP(hAPP(c_member(U_8915),U_8917),U_8918)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8915,tc_HOL_Obool)),U_8916),hAPP(hAPP(c_Set_Oinsert(U_8915),U_8917),U_8918))) ) ),
inference(variable_rename,[status(thm)],[f_2511_1]) ).
fof(f_2511_3,plain,
( ! [U_8926,U_8924,U_8922,U_8920] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),U_8922),hAPP(hAPP(c_Set_Oinsert(U_8920),U_8924),U_8926)))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8920,tc_HOL_Obool)),U_8922),U_8926))
& ~ hBOOL(hAPP(hAPP(c_member(U_8920),U_8924),U_8922)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8920,tc_HOL_Obool)),U_8922),hAPP(hAPP(c_Set_Oinsert(U_8920),U_8924),c_Orderings_Obot__class_Obot(tc_fun(U_8920,tc_HOL_Obool))))),U_8926))
& hBOOL(hAPP(hAPP(c_member(U_8920),U_8924),U_8922)) ) )
& ~ hBOOL(hAPP(hAPP(c_member(U_8920),U_8924),U_8926)) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),U_8922),U_8926))
& hBOOL(hAPP(hAPP(c_member(U_8920),U_8924),U_8926)) ) )
& ! [U_8925,U_8923,U_8921,U_8919] :
( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8919,tc_HOL_Obool)),U_8921),U_8925))
| hBOOL(hAPP(hAPP(c_member(U_8919),U_8923),U_8921)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8919,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8919,tc_HOL_Obool)),U_8921),hAPP(hAPP(c_Set_Oinsert(U_8919),U_8923),c_Orderings_Obot__class_Obot(tc_fun(U_8919,tc_HOL_Obool))))),U_8925))
| ~ hBOOL(hAPP(hAPP(c_member(U_8919),U_8923),U_8921)) ) )
| hBOOL(hAPP(hAPP(c_member(U_8919),U_8923),U_8925)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8919,tc_HOL_Obool)),U_8921),U_8925))
| ~ hBOOL(hAPP(hAPP(c_member(U_8919),U_8923),U_8925)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8919,tc_HOL_Obool)),U_8921),hAPP(hAPP(c_Set_Oinsert(U_8919),U_8923),U_8925))) ) ),
inference(miniscope,[status(thm)],[f_2511_2]) ).
cnf(f_2511_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8919,tc_HOL_Obool)),U_8921),U_8925))
| ~ hBOOL(hAPP(hAPP(c_member(U_8919),U_8923),U_8925))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8919,tc_HOL_Obool)),U_8921),hAPP(hAPP(c_Set_Oinsert(U_8919),U_8923),U_8925))) ),
inference(clausify,[status(thm)],[f_2511_3]) ).
cnf(f_2511_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8919,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8919,tc_HOL_Obool)),U_8921),hAPP(hAPP(c_Set_Oinsert(U_8919),U_8923),c_Orderings_Obot__class_Obot(tc_fun(U_8919,tc_HOL_Obool))))),U_8925))
| ~ hBOOL(hAPP(hAPP(c_member(U_8919),U_8923),U_8921))
| hBOOL(hAPP(hAPP(c_member(U_8919),U_8923),U_8925))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8919,tc_HOL_Obool)),U_8921),hAPP(hAPP(c_Set_Oinsert(U_8919),U_8923),U_8925))) ),
inference(clausify,[status(thm)],[f_2511_3]) ).
cnf(f_2511_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8919,tc_HOL_Obool)),U_8921),U_8925))
| hBOOL(hAPP(hAPP(c_member(U_8919),U_8923),U_8921))
| hBOOL(hAPP(hAPP(c_member(U_8919),U_8923),U_8925))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8919,tc_HOL_Obool)),U_8921),hAPP(hAPP(c_Set_Oinsert(U_8919),U_8923),U_8925))) ),
inference(clausify,[status(thm)],[f_2511_3]) ).
cnf(f_2511_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8920),U_8924),U_8926))
| hBOOL(hAPP(hAPP(c_member(U_8920),U_8924),U_8926))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),U_8922),hAPP(hAPP(c_Set_Oinsert(U_8920),U_8924),U_8926))) ),
inference(clausify,[status(thm)],[f_2511_3]) ).
cnf(f_2511_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8920),U_8924),U_8922))
| hBOOL(hAPP(hAPP(c_member(U_8920),U_8924),U_8922))
| hBOOL(hAPP(hAPP(c_member(U_8920),U_8924),U_8926))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),U_8922),hAPP(hAPP(c_Set_Oinsert(U_8920),U_8924),U_8926))) ),
inference(clausify,[status(thm)],[f_2511_3]) ).
cnf(f_2511_9,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8920,tc_HOL_Obool)),U_8922),U_8926))
| hBOOL(hAPP(hAPP(c_member(U_8920),U_8924),U_8922))
| hBOOL(hAPP(hAPP(c_member(U_8920),U_8924),U_8926))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),U_8922),hAPP(hAPP(c_Set_Oinsert(U_8920),U_8924),U_8926))) ),
inference(clausify,[status(thm)],[f_2511_3]) ).
cnf(f_2511_10,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8920),U_8924),U_8922))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8920,tc_HOL_Obool)),U_8922),hAPP(hAPP(c_Set_Oinsert(U_8920),U_8924),c_Orderings_Obot__class_Obot(tc_fun(U_8920,tc_HOL_Obool))))),U_8926))
| hBOOL(hAPP(hAPP(c_member(U_8920),U_8924),U_8926))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),U_8922),hAPP(hAPP(c_Set_Oinsert(U_8920),U_8924),U_8926))) ),
inference(clausify,[status(thm)],[f_2511_3]) ).
cnf(f_2511_11,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8920,tc_HOL_Obool)),U_8922),U_8926))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8920,tc_HOL_Obool)),U_8922),hAPP(hAPP(c_Set_Oinsert(U_8920),U_8924),c_Orderings_Obot__class_Obot(tc_fun(U_8920,tc_HOL_Obool))))),U_8926))
| hBOOL(hAPP(hAPP(c_member(U_8920),U_8924),U_8926))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),U_8922),hAPP(hAPP(c_Set_Oinsert(U_8920),U_8924),U_8926))) ),
inference(clausify,[status(thm)],[f_2511_3]) ).
cnf(f_2511_12,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8920),U_8924),U_8926))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),U_8922),U_8926))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),U_8922),hAPP(hAPP(c_Set_Oinsert(U_8920),U_8924),U_8926))) ),
inference(clausify,[status(thm)],[f_2511_3]) ).
cnf(f_2511_13,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8920),U_8924),U_8922))
| hBOOL(hAPP(hAPP(c_member(U_8920),U_8924),U_8922))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),U_8922),U_8926))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),U_8922),hAPP(hAPP(c_Set_Oinsert(U_8920),U_8924),U_8926))) ),
inference(clausify,[status(thm)],[f_2511_3]) ).
cnf(f_2511_14,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8920,tc_HOL_Obool)),U_8922),U_8926))
| hBOOL(hAPP(hAPP(c_member(U_8920),U_8924),U_8922))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),U_8922),U_8926))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),U_8922),hAPP(hAPP(c_Set_Oinsert(U_8920),U_8924),U_8926))) ),
inference(clausify,[status(thm)],[f_2511_3]) ).
cnf(f_2511_15,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_8920),U_8924),U_8922))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8920,tc_HOL_Obool)),U_8922),hAPP(hAPP(c_Set_Oinsert(U_8920),U_8924),c_Orderings_Obot__class_Obot(tc_fun(U_8920,tc_HOL_Obool))))),U_8926))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),U_8922),U_8926))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),U_8922),hAPP(hAPP(c_Set_Oinsert(U_8920),U_8924),U_8926))) ),
inference(clausify,[status(thm)],[f_2511_3]) ).
cnf(f_2511_16,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8920,tc_HOL_Obool)),U_8922),U_8926))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8920,tc_HOL_Obool)),U_8922),hAPP(hAPP(c_Set_Oinsert(U_8920),U_8924),c_Orderings_Obot__class_Obot(tc_fun(U_8920,tc_HOL_Obool))))),U_8926))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),U_8922),U_8926))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_8920,tc_HOL_Obool)),U_8922),hAPP(hAPP(c_Set_Oinsert(U_8920),U_8924),U_8926))) ),
inference(clausify,[status(thm)],[f_2511_3]) ).
fof(f_2512_1,plain,
! [V_f_2,V_A_2,V_a_2,T_b] :
( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff1__nat]) ).
fof(f_2512_2,plain,
! [U_8930,U_8929,U_8928,U_8927] :
( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8927,tc_Nat_Onat),U_8930),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8927,tc_HOL_Obool)),U_8929),hAPP(hAPP(c_Set_Oinsert(U_8927),U_8928),c_Orderings_Obot__class_Obot(tc_fun(U_8927,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8927,tc_Nat_Onat),U_8930),U_8929)
| hBOOL(hAPP(hAPP(c_member(U_8927),U_8928),U_8929)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8927,tc_Nat_Onat),U_8930),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8927,tc_HOL_Obool)),U_8929),hAPP(hAPP(c_Set_Oinsert(U_8927),U_8928),c_Orderings_Obot__class_Obot(tc_fun(U_8927,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8927,tc_Nat_Onat),U_8930),U_8929)),hAPP(U_8930,U_8928))
| ~ hBOOL(hAPP(hAPP(c_member(U_8927),U_8928),U_8929)) ) ),
inference(variable_rename,[status(thm)],[f_2512_1]) ).
fof(f_2512_3,plain,
( ! [U_8938,U_8936,U_8934,U_8932] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8932,tc_Nat_Onat),U_8938),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8932,tc_HOL_Obool)),U_8936),hAPP(hAPP(c_Set_Oinsert(U_8932),U_8934),c_Orderings_Obot__class_Obot(tc_fun(U_8932,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8932,tc_Nat_Onat),U_8938),U_8936)
| hBOOL(hAPP(hAPP(c_member(U_8932),U_8934),U_8936)) )
& ! [U_8937,U_8935,U_8933,U_8931] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8931,tc_Nat_Onat),U_8937),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8931,tc_HOL_Obool)),U_8935),hAPP(hAPP(c_Set_Oinsert(U_8931),U_8933),c_Orderings_Obot__class_Obot(tc_fun(U_8931,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8931,tc_Nat_Onat),U_8937),U_8935)),hAPP(U_8937,U_8933))
| ~ hBOOL(hAPP(hAPP(c_member(U_8931),U_8933),U_8935)) ) ),
inference(miniscope,[status(thm)],[f_2512_2]) ).
cnf(f_2512_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8931,tc_Nat_Onat),U_8937),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8931,tc_HOL_Obool)),U_8935),hAPP(hAPP(c_Set_Oinsert(U_8931),U_8933),c_Orderings_Obot__class_Obot(tc_fun(U_8931,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8931,tc_Nat_Onat),U_8937),U_8935)),hAPP(U_8937,U_8933))
| ~ hBOOL(hAPP(hAPP(c_member(U_8931),U_8933),U_8935)) ),
inference(clausify,[status(thm)],[f_2512_3]) ).
cnf(f_2512_5,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8932,tc_Nat_Onat),U_8938),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8932,tc_HOL_Obool)),U_8936),hAPP(hAPP(c_Set_Oinsert(U_8932),U_8934),c_Orderings_Obot__class_Obot(tc_fun(U_8932,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8932,tc_Nat_Onat),U_8938),U_8936)
| hBOOL(hAPP(hAPP(c_member(U_8932),U_8934),U_8936)) ),
inference(clausify,[status(thm)],[f_2512_3]) ).
fof(f_2513_1,plain,
! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff1_H]) ).
fof(f_2513_2,plain,
! [U_8943,U_8942,U_8941,U_8940,U_8939] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8940,U_8939),U_8943),U_8941) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8939),hAPP(U_8943,U_8942)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8940,U_8939),U_8943),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8940,tc_HOL_Obool)),U_8941),hAPP(hAPP(c_Set_Oinsert(U_8940),U_8942),c_Orderings_Obot__class_Obot(tc_fun(U_8940,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_8940),U_8942),U_8941))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8940),U_8941))
| ~ class_Groups_Ocomm__monoid__add(U_8939) ),
inference(variable_rename,[status(thm)],[f_2513_1]) ).
cnf(f_2513_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8940,U_8939),U_8943),U_8941) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8939),hAPP(U_8943,U_8942)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8940,U_8939),U_8943),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8940,tc_HOL_Obool)),U_8941),hAPP(hAPP(c_Set_Oinsert(U_8940),U_8942),c_Orderings_Obot__class_Obot(tc_fun(U_8940,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_8940),U_8942),U_8941))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8940),U_8941))
| ~ class_Groups_Ocomm__monoid__add(U_8939) ),
inference(clausify,[status(thm)],[f_2513_2]) ).
fof(f_2514_1,plain,
! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Oremove]) ).
fof(f_2514_2,plain,
! [U_8948,U_8947,U_8946,U_8945,U_8944] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8945,U_8944),U_8948),U_8946) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8944),hAPP(U_8948,U_8947)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8945,U_8944),U_8948),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8945,tc_HOL_Obool)),U_8946),hAPP(hAPP(c_Set_Oinsert(U_8945),U_8947),c_Orderings_Obot__class_Obot(tc_fun(U_8945,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_8945),U_8947),U_8946))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8945),U_8946))
| ~ class_Groups_Ocomm__monoid__add(U_8944) ),
inference(variable_rename,[status(thm)],[f_2514_1]) ).
cnf(f_2514_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8945,U_8944),U_8948),U_8946) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_8944),hAPP(U_8948,U_8947)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8945,U_8944),U_8948),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8945,tc_HOL_Obool)),U_8946),hAPP(hAPP(c_Set_Oinsert(U_8945),U_8947),c_Orderings_Obot__class_Obot(tc_fun(U_8945,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_8945),U_8947),U_8946))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8945),U_8946))
| ~ class_Groups_Ocomm__monoid__add(U_8944) ),
inference(clausify,[status(thm)],[f_2514_2]) ).
fof(f_2515_1,plain,
! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Rings_Oring(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff1__ring]) ).
fof(f_2515_2,plain,
! [U_8953,U_8952,U_8951,U_8950,U_8949] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8950,U_8949),U_8953),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8950,tc_HOL_Obool)),U_8951),hAPP(hAPP(c_Set_Oinsert(U_8950),U_8952),c_Orderings_Obot__class_Obot(tc_fun(U_8950,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8949),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8950,U_8949),U_8953),U_8951)),hAPP(U_8953,U_8952))
| ~ hBOOL(hAPP(hAPP(c_member(U_8950),U_8952),U_8951))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8950),U_8951))
| ~ class_Rings_Oring(U_8949) ),
inference(variable_rename,[status(thm)],[f_2515_1]) ).
cnf(f_2515_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8950,U_8949),U_8953),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8950,tc_HOL_Obool)),U_8951),hAPP(hAPP(c_Set_Oinsert(U_8950),U_8952),c_Orderings_Obot__class_Obot(tc_fun(U_8950,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8949),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8950,U_8949),U_8953),U_8951)),hAPP(U_8953,U_8952))
| ~ hBOOL(hAPP(hAPP(c_member(U_8950),U_8952),U_8951))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8950),U_8951))
| ~ class_Rings_Oring(U_8949) ),
inference(clausify,[status(thm)],[f_2515_2]) ).
fof(f_2516_1,plain,
! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Oab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__diff1]) ).
fof(f_2516_2,plain,
! [U_8958,U_8957,U_8956,U_8955,U_8954] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8955,U_8954),U_8958),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8955,tc_HOL_Obool)),U_8956),hAPP(hAPP(c_Set_Oinsert(U_8955),U_8957),c_Orderings_Obot__class_Obot(tc_fun(U_8955,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8955,U_8954),U_8958),U_8956)
| hBOOL(hAPP(hAPP(c_member(U_8955),U_8957),U_8956)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8955,U_8954),U_8958),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8955,tc_HOL_Obool)),U_8956),hAPP(hAPP(c_Set_Oinsert(U_8955),U_8957),c_Orderings_Obot__class_Obot(tc_fun(U_8955,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8954),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8955,U_8954),U_8958),U_8956)),hAPP(U_8958,U_8957))
| ~ hBOOL(hAPP(hAPP(c_member(U_8955),U_8957),U_8956)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8955),U_8956))
| ~ class_Groups_Oab__group__add(U_8954) ),
inference(variable_rename,[status(thm)],[f_2516_1]) ).
cnf(f_2516_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8955,U_8954),U_8958),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8955,tc_HOL_Obool)),U_8956),hAPP(hAPP(c_Set_Oinsert(U_8955),U_8957),c_Orderings_Obot__class_Obot(tc_fun(U_8955,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_8954),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8955,U_8954),U_8958),U_8956)),hAPP(U_8958,U_8957))
| ~ hBOOL(hAPP(hAPP(c_member(U_8955),U_8957),U_8956))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8955),U_8956))
| ~ class_Groups_Oab__group__add(U_8954) ),
inference(clausify,[status(thm)],[f_2516_2]) ).
cnf(f_2516_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8955,U_8954),U_8958),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8955,tc_HOL_Obool)),U_8956),hAPP(hAPP(c_Set_Oinsert(U_8955),U_8957),c_Orderings_Obot__class_Obot(tc_fun(U_8955,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8955,U_8954),U_8958),U_8956)
| hBOOL(hAPP(hAPP(c_member(U_8955),U_8957),U_8956))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8955),U_8956))
| ~ class_Groups_Oab__group__add(U_8954) ),
inference(clausify,[status(thm)],[f_2516_2]) ).
fof(f_2517_1,plain,
! [V_x_2,V_A_2,T_b] :
( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Suc__Diff1]) ).
fof(f_2517_2,plain,
! [U_8961,U_8960,U_8959] :
( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_8959),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8959,tc_HOL_Obool)),U_8960),hAPP(hAPP(c_Set_Oinsert(U_8959),U_8961),c_Orderings_Obot__class_Obot(tc_fun(U_8959,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_8959),U_8960)
| ~ hBOOL(hAPP(hAPP(c_member(U_8959),U_8961),U_8960))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8959),U_8960)) ),
inference(variable_rename,[status(thm)],[f_2517_1]) ).
cnf(f_2517_3,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_8959),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8959,tc_HOL_Obool)),U_8960),hAPP(hAPP(c_Set_Oinsert(U_8959),U_8961),c_Orderings_Obot__class_Obot(tc_fun(U_8959,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_8959),U_8960)
| ~ hBOOL(hAPP(hAPP(c_member(U_8959),U_8961),U_8960))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8959),U_8960)) ),
inference(clausify,[status(thm)],[f_2517_2]) ).
fof(f_2518_1,plain,
! [V_y_2,V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff2__less]) ).
fof(f_2518_2,plain,
! [U_8965,U_8964,U_8963,U_8962] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_8962),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8962,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8962,tc_HOL_Obool)),U_8963),hAPP(hAPP(c_Set_Oinsert(U_8962),U_8964),c_Orderings_Obot__class_Obot(tc_fun(U_8962,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_8962),U_8965),c_Orderings_Obot__class_Obot(tc_fun(U_8962,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_8962),U_8963)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8962),U_8965),U_8963))
| ~ hBOOL(hAPP(hAPP(c_member(U_8962),U_8964),U_8963))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8962),U_8963)) ),
inference(variable_rename,[status(thm)],[f_2518_1]) ).
cnf(f_2518_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_8962),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8962,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8962,tc_HOL_Obool)),U_8963),hAPP(hAPP(c_Set_Oinsert(U_8962),U_8964),c_Orderings_Obot__class_Obot(tc_fun(U_8962,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_8962),U_8965),c_Orderings_Obot__class_Obot(tc_fun(U_8962,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_8962),U_8963)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8962),U_8965),U_8963))
| ~ hBOOL(hAPP(hAPP(c_member(U_8962),U_8964),U_8963))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8962),U_8963)) ),
inference(clausify,[status(thm)],[f_2518_2]) ).
fof(f_2519_1,plain,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff1__less]) ).
fof(f_2519_2,plain,
! [U_8968,U_8967,U_8966] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_8966),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8966,tc_HOL_Obool)),U_8967),hAPP(hAPP(c_Set_Oinsert(U_8966),U_8968),c_Orderings_Obot__class_Obot(tc_fun(U_8966,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_8966),U_8967)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8966),U_8968),U_8967))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8966),U_8967)) ),
inference(variable_rename,[status(thm)],[f_2519_1]) ).
cnf(f_2519_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_8966),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8966,tc_HOL_Obool)),U_8967),hAPP(hAPP(c_Set_Oinsert(U_8966),U_8968),c_Orderings_Obot__class_Obot(tc_fun(U_8966,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_8966),U_8967)))
| ~ hBOOL(hAPP(hAPP(c_member(U_8966),U_8968),U_8967))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8966),U_8967)) ),
inference(clausify,[status(thm)],[f_2519_2]) ).
fof(f_2520_1,plain,
! [V_B_2,V_a_2,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff__insert]) ).
fof(f_2520_2,plain,
! [U_8972,U_8971,U_8970,U_8969] :
( hAPP(c_Finite__Set_Ocard(U_8969),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8969,tc_HOL_Obool)),U_8970),hAPP(hAPP(c_Set_Oinsert(U_8969),U_8971),U_8972))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_8969),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8969,tc_HOL_Obool)),U_8970),U_8972))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| hBOOL(hAPP(hAPP(c_member(U_8969),U_8971),U_8972))
| ~ hBOOL(hAPP(hAPP(c_member(U_8969),U_8971),U_8970))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8969),U_8970)) ),
inference(variable_rename,[status(thm)],[f_2520_1]) ).
cnf(f_2520_3,plain,
( hAPP(c_Finite__Set_Ocard(U_8969),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8969,tc_HOL_Obool)),U_8970),hAPP(hAPP(c_Set_Oinsert(U_8969),U_8971),U_8972))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_8969),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8969,tc_HOL_Obool)),U_8970),U_8972))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| hBOOL(hAPP(hAPP(c_member(U_8969),U_8971),U_8972))
| ~ hBOOL(hAPP(hAPP(c_member(U_8969),U_8971),U_8970))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8969),U_8970)) ),
inference(clausify,[status(thm)],[f_2520_2]) ).
fof(f_2521_1,plain,
! [V_x_2,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card_Oremove]) ).
fof(f_2521_2,plain,
! [U_8975,U_8974,U_8973] :
( hAPP(c_Finite__Set_Ocard(U_8973),U_8974) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_8973),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8973,tc_HOL_Obool)),U_8974),hAPP(hAPP(c_Set_Oinsert(U_8973),U_8975),c_Orderings_Obot__class_Obot(tc_fun(U_8973,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_8973),U_8975),U_8974))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8973),U_8974)) ),
inference(variable_rename,[status(thm)],[f_2521_1]) ).
cnf(f_2521_3,plain,
( hAPP(c_Finite__Set_Ocard(U_8973),U_8974) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_8973),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8973,tc_HOL_Obool)),U_8974),hAPP(hAPP(c_Set_Oinsert(U_8973),U_8975),c_Orderings_Obot__class_Obot(tc_fun(U_8973,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_8973),U_8975),U_8974))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_8973),U_8974)) ),
inference(clausify,[status(thm)],[f_2521_2]) ).
fof(f_2522_1,plain,
! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_R_2)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_R_2))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_in__rel__def]) ).
fof(f_2522_2,plain,
! [U_8980,U_8979,U_8978,U_8977,U_8976] :
( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_8976,U_8977,U_8978),U_8979),U_8980))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8976,U_8977)),hAPP(hAPP(c_Product__Type_OPair(U_8976,U_8977),U_8979),U_8980)),U_8978)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8976,U_8977)),hAPP(hAPP(c_Product__Type_OPair(U_8976,U_8977),U_8979),U_8980)),U_8978))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_8976,U_8977,U_8978),U_8979),U_8980)) ) ),
inference(variable_rename,[status(thm)],[f_2522_1]) ).
fof(f_2522_3,plain,
( ! [U_8990,U_8988,U_8986,U_8984,U_8982] :
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_8982,U_8984,U_8986),U_8988),U_8990))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8982,U_8984)),hAPP(hAPP(c_Product__Type_OPair(U_8982,U_8984),U_8988),U_8990)),U_8986)) )
& ! [U_8989,U_8987,U_8985,U_8983,U_8981] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8981,U_8983)),hAPP(hAPP(c_Product__Type_OPair(U_8981,U_8983),U_8987),U_8989)),U_8985))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_8981,U_8983,U_8985),U_8987),U_8989)) ) ),
inference(miniscope,[status(thm)],[f_2522_2]) ).
cnf(f_2522_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8981,U_8983)),hAPP(hAPP(c_Product__Type_OPair(U_8981,U_8983),U_8987),U_8989)),U_8985))
| ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_8981,U_8983,U_8985),U_8987),U_8989)) ),
inference(clausify,[status(thm)],[f_2522_3]) ).
cnf(f_2522_5,plain,
( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_8982,U_8984,U_8986),U_8988),U_8990))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8982,U_8984)),hAPP(hAPP(c_Product__Type_OPair(U_8982,U_8984),U_8988),U_8990)),U_8986)) ),
inference(clausify,[status(thm)],[f_2522_3]) ).
fof(f_2523_1,plain,
! [V_f_2,V_A_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2))
| ? [B_x] :
( ~ c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod2_I1_J]) ).
fof(f_2523_2,plain,
! [U_8994,U_8993,U_8992] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8992,tc_Int_Oint),U_8994),U_8993) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8992,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_8992),c_Int_Onat),U_8994)),U_8993))
| ? [U_8991] :
( ~ c_Nat__Transfer_Ois__nat(hAPP(U_8994,U_8991))
& hBOOL(hAPP(hAPP(c_member(U_8992),U_8991),U_8993)) ) ),
inference(variable_rename,[status(thm)],[f_2523_1]) ).
fof(f_2523_3,plain,
! [U_8994,U_8993,U_8992] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8992,tc_Int_Oint),U_8994),U_8993) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8992,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_8992),c_Int_Onat),U_8994)),U_8993))
| ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_8994,sK162(U_8994,U_8993,U_8992)))
& hBOOL(hAPP(hAPP(c_member(U_8992),sK162(U_8994,U_8993,U_8992)),U_8993)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK162]),skolemize(U_8991,sK162(U_8994,U_8993,U_8992))],[f_2523_2]) ).
cnf(f_2523_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_8992),sK162(U_8994,U_8993,U_8992)),U_8993))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8992,tc_Int_Oint),U_8994),U_8993) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8992,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_8992),c_Int_Onat),U_8994)),U_8993)) ),
inference(clausify,[status(thm)],[f_2523_3]) ).
cnf(f_2523_5,plain,
( ~ c_Nat__Transfer_Ois__nat(hAPP(U_8994,sK162(U_8994,U_8993,U_8992)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8992,tc_Int_Oint),U_8994),U_8993) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_8992,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_8992),c_Int_Onat),U_8994)),U_8993)) ),
inference(clausify,[status(thm)],[f_2523_3]) ).
fof(f_2524_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_2524_2,plain,
! [U_9000,U_8999,U_8998] :
( ! [U_8997] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8999),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8997),U_8998)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8999),U_8997))
| ? [U_8996] :
( ? [U_8995] :
( U_8997 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8995),U_8996)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8995),U_9000)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8996),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8998))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8999),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9000))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8998)) ),
inference(variable_rename,[status(thm)],[f_2524_1]) ).
fof(f_2524_3,plain,
! [U_9000,U_8999,U_8998] :
( ! [U_8997] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8999),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8997),U_8998)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8999),U_8997))
| ( ? [U_8995] :
( U_8997 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_8995),sK163(U_9000,U_8999,U_8998,U_8997))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_8995),U_9000)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK163(U_9000,U_8999,U_8998,U_8997)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8998))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8999),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9000))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8998)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK163]),skolemize(U_8996,sK163(U_9000,U_8999,U_8998,U_8997))],[f_2524_2]) ).
fof(f_2524_4,plain,
! [U_9000,U_8999,U_8998] :
( ! [U_8997] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8999),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8997),U_8998)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8999),U_8997))
| ( U_8997 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK164(U_9000,U_8999,U_8998,U_8997)),sK163(U_9000,U_8999,U_8998,U_8997))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK164(U_9000,U_8999,U_8998,U_8997)),U_9000))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK163(U_9000,U_8999,U_8998,U_8997)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8998))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8999),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9000))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8998)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK164]),skolemize(U_8995,sK164(U_9000,U_8999,U_8998,U_8997))],[f_2524_3]) ).
cnf(f_2524_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK163(U_9000,U_8999,U_8998,U_8997)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_8998)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8999),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8997),U_8998)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8999),U_8997))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8999),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9000))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8998)) ),
inference(clausify,[status(thm)],[f_2524_4]) ).
cnf(f_2524_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK164(U_9000,U_8999,U_8998,U_8997)),U_9000))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8999),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8997),U_8998)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8999),U_8997))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8999),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9000))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8998)) ),
inference(clausify,[status(thm)],[f_2524_4]) ).
cnf(f_2524_7,plain,
( U_8997 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK164(U_9000,U_8999,U_8998,U_8997)),sK163(U_9000,U_8999,U_8998,U_8997))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8999),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8997),U_8998)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_8999),U_8997))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_8999),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9000))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_8998)) ),
inference(clausify,[status(thm)],[f_2524_4]) ).
fof(f_2525_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_2525_2,plain,
! [U_9006,U_9005,U_9004] :
( ! [U_9003] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9003),U_9004)),U_9005))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9003),U_9005))
| ? [U_9002] :
( ? [U_9001] :
( U_9003 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9001),U_9002)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9001),U_9006)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9002),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9004))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9005),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9006))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9004)) ),
inference(variable_rename,[status(thm)],[f_2525_1]) ).
fof(f_2525_3,plain,
! [U_9006,U_9005,U_9004] :
( ! [U_9003] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9003),U_9004)),U_9005))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9003),U_9005))
| ( ? [U_9001] :
( U_9003 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9001),sK165(U_9006,U_9005,U_9004,U_9003))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9001),U_9006)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK165(U_9006,U_9005,U_9004,U_9003)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9004))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9005),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9006))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9004)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK165]),skolemize(U_9002,sK165(U_9006,U_9005,U_9004,U_9003))],[f_2525_2]) ).
fof(f_2525_4,plain,
! [U_9006,U_9005,U_9004] :
( ! [U_9003] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9003),U_9004)),U_9005))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9003),U_9005))
| ( U_9003 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK166(U_9006,U_9005,U_9004,U_9003)),sK165(U_9006,U_9005,U_9004,U_9003))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK166(U_9006,U_9005,U_9004,U_9003)),U_9006))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK165(U_9006,U_9005,U_9004,U_9003)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9004))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9005),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9006))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9004)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK166]),skolemize(U_9001,sK166(U_9006,U_9005,U_9004,U_9003))],[f_2525_3]) ).
cnf(f_2525_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK165(U_9006,U_9005,U_9004,U_9003)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9004)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9003),U_9004)),U_9005))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9003),U_9005))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9005),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9006))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9004)) ),
inference(clausify,[status(thm)],[f_2525_4]) ).
cnf(f_2525_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK166(U_9006,U_9005,U_9004,U_9003)),U_9006))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9003),U_9004)),U_9005))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9003),U_9005))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9005),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9006))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9004)) ),
inference(clausify,[status(thm)],[f_2525_4]) ).
cnf(f_2525_7,plain,
( U_9003 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK166(U_9006,U_9005,U_9004,U_9003)),sK165(U_9006,U_9005,U_9004,U_9003))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9003),U_9004)),U_9005))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_9003),U_9005))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9005),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9006))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9004)) ),
inference(clausify,[status(thm)],[f_2525_4]) ).
fof(f_2526_1,plain,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
| hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_sup2E]) ).
fof(f_2526_2,plain,
! [U_9012,U_9011,U_9010,U_9009,U_9008,U_9007] :
( hBOOL(hAPP(hAPP(U_9010,U_9011),U_9012))
| hBOOL(hAPP(hAPP(U_9009,U_9011),U_9012))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9007,tc_fun(U_9008,tc_HOL_Obool))),U_9009),U_9010),U_9011),U_9012)) ),
inference(variable_rename,[status(thm)],[f_2526_1]) ).
fof(f_2526_3,plain,
! [U_9012,U_9011,U_9010,U_9009] :
( ! [U_9008,U_9007] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9007,tc_fun(U_9008,tc_HOL_Obool))),U_9009),U_9010),U_9011),U_9012))
| hBOOL(hAPP(hAPP(U_9010,U_9011),U_9012))
| hBOOL(hAPP(hAPP(U_9009,U_9011),U_9012)) ),
inference(miniscope,[status(thm)],[f_2526_2]) ).
cnf(f_2526_4,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9007,tc_fun(U_9008,tc_HOL_Obool))),U_9009),U_9010),U_9011),U_9012))
| hBOOL(hAPP(hAPP(U_9010,U_9011),U_9012))
| hBOOL(hAPP(hAPP(U_9009,U_9011),U_9012)) ),
inference(clausify,[status(thm)],[f_2526_3]) ).
fof(f_2527_1,plain,
! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
| ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
& ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_sup2CI]) ).
fof(f_2527_2,plain,
! [U_9018,U_9017,U_9016,U_9015,U_9014,U_9013] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9017,tc_fun(U_9018,tc_HOL_Obool))),U_9016),U_9013),U_9014),U_9015))
| ( ~ hBOOL(hAPP(hAPP(U_9016,U_9014),U_9015))
& ~ hBOOL(hAPP(hAPP(U_9013,U_9014),U_9015)) ) ),
inference(variable_rename,[status(thm)],[f_2527_1]) ).
cnf(f_2527_3,plain,
( ~ hBOOL(hAPP(hAPP(U_9013,U_9014),U_9015))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9017,tc_fun(U_9018,tc_HOL_Obool))),U_9016),U_9013),U_9014),U_9015)) ),
inference(clausify,[status(thm)],[f_2527_2]) ).
cnf(f_2527_4,plain,
( ~ hBOOL(hAPP(hAPP(U_9016,U_9014),U_9015))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9017,tc_fun(U_9018,tc_HOL_Obool))),U_9016),U_9013),U_9014),U_9015)) ),
inference(clausify,[status(thm)],[f_2527_2]) ).
fof(f_2528_1,plain,
! [V_y_2,V_x_2,T_c,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)),
inference(fof_nnf,[status(thm)],[fact_bot2E]) ).
fof(f_2528_2,plain,
! [U_9022,U_9021,U_9020,U_9019] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9019,tc_fun(U_9020,tc_HOL_Obool))),U_9021),U_9022)),
inference(variable_rename,[status(thm)],[f_2528_1]) ).
cnf(f_2528_3,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9019,tc_fun(U_9020,tc_HOL_Obool))),U_9021),U_9022)),
inference(clausify,[status(thm)],[f_2528_2]) ).
fof(f_2529_1,plain,
! [V_B_2,T_b,V_A_2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_less__by__empty]) ).
fof(f_2529_2,plain,
! [U_9025,U_9024,U_9023] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9024,U_9024),tc_HOL_Obool)),U_9023),U_9025))
| U_9023 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9024,U_9024),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_2529_1]) ).
cnf(f_2529_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9024,U_9024),tc_HOL_Obool)),U_9023),U_9025))
| U_9023 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9024,U_9024),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2529_2]) ).
fof(f_2530_1,plain,
! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_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_b),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_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_SUP2__iff]) ).
fof(f_2530_2,plain,
! [U_9034,U_9033,U_9032,U_9031,U_9030,U_9029,U_9028] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9028,tc_fun(U_9029,tc_fun(U_9030,tc_HOL_Obool))),U_9031),U_9032),U_9033),U_9034))
| ! [U_9027] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_9032,U_9027),U_9033),U_9034))
| ~ hBOOL(hAPP(hAPP(c_member(U_9028),U_9027),U_9031)) ) )
& ( ? [U_9026] :
( hBOOL(hAPP(hAPP(hAPP(U_9032,U_9026),U_9033),U_9034))
& hBOOL(hAPP(hAPP(c_member(U_9028),U_9026),U_9031)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9028,tc_fun(U_9029,tc_fun(U_9030,tc_HOL_Obool))),U_9031),U_9032),U_9033),U_9034)) ) ),
inference(variable_rename,[status(thm)],[f_2530_1]) ).
fof(f_2530_3,plain,
( ! [U_9048,U_9046,U_9044,U_9042,U_9040,U_9038,U_9036] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9036,tc_fun(U_9038,tc_fun(U_9040,tc_HOL_Obool))),U_9042),U_9044),U_9046),U_9048))
| ! [U_9027] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_9044,U_9027),U_9046),U_9048))
| ~ hBOOL(hAPP(hAPP(c_member(U_9036),U_9027),U_9042)) ) )
& ! [U_9047,U_9045,U_9043,U_9041,U_9039,U_9037,U_9035] :
( ? [U_9026] :
( hBOOL(hAPP(hAPP(hAPP(U_9043,U_9026),U_9045),U_9047))
& hBOOL(hAPP(hAPP(c_member(U_9035),U_9026),U_9041)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9035,tc_fun(U_9037,tc_fun(U_9039,tc_HOL_Obool))),U_9041),U_9043),U_9045),U_9047)) ) ),
inference(miniscope,[status(thm)],[f_2530_2]) ).
fof(f_2530_4,plain,
( ! [U_9048,U_9046,U_9044,U_9042,U_9040,U_9038,U_9036] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9036,tc_fun(U_9038,tc_fun(U_9040,tc_HOL_Obool))),U_9042),U_9044),U_9046),U_9048))
| ! [U_9027] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_9044,U_9027),U_9046),U_9048))
| ~ hBOOL(hAPP(hAPP(c_member(U_9036),U_9027),U_9042)) ) )
& ! [U_9047,U_9045,U_9043,U_9041,U_9039,U_9037,U_9035] :
( ( hBOOL(hAPP(hAPP(hAPP(U_9043,sK167(U_9047,U_9045,U_9043,U_9041,U_9039,U_9037,U_9035)),U_9045),U_9047))
& hBOOL(hAPP(hAPP(c_member(U_9035),sK167(U_9047,U_9045,U_9043,U_9041,U_9039,U_9037,U_9035)),U_9041)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9035,tc_fun(U_9037,tc_fun(U_9039,tc_HOL_Obool))),U_9041),U_9043),U_9045),U_9047)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK167]),skolemize(U_9026,sK167(U_9047,U_9045,U_9043,U_9041,U_9039,U_9037,U_9035))],[f_2530_3]) ).
cnf(f_2530_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9035),sK167(U_9047,U_9045,U_9043,U_9041,U_9039,U_9037,U_9035)),U_9041))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9035,tc_fun(U_9037,tc_fun(U_9039,tc_HOL_Obool))),U_9041),U_9043),U_9045),U_9047)) ),
inference(clausify,[status(thm)],[f_2530_4]) ).
cnf(f_2530_6,plain,
( hBOOL(hAPP(hAPP(hAPP(U_9043,sK167(U_9047,U_9045,U_9043,U_9041,U_9039,U_9037,U_9035)),U_9045),U_9047))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9035,tc_fun(U_9037,tc_fun(U_9039,tc_HOL_Obool))),U_9041),U_9043),U_9045),U_9047)) ),
inference(clausify,[status(thm)],[f_2530_4]) ).
cnf(f_2530_7,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_9036,tc_fun(U_9038,tc_fun(U_9040,tc_HOL_Obool))),U_9042),U_9044),U_9046),U_9048))
| ~ hBOOL(hAPP(hAPP(hAPP(U_9044,U_9027),U_9046),U_9048))
| ~ hBOOL(hAPP(hAPP(c_member(U_9036),U_9027),U_9042)) ),
inference(clausify,[status(thm)],[f_2530_4]) ).
fof(f_2531_1,plain,
! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_sup2I1]) ).
fof(f_2531_2,plain,
! [U_9054,U_9053,U_9052,U_9051,U_9050,U_9049] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9052,tc_fun(U_9053,tc_HOL_Obool))),U_9049),U_9054),U_9050),U_9051))
| ~ hBOOL(hAPP(hAPP(U_9049,U_9050),U_9051)) ),
inference(variable_rename,[status(thm)],[f_2531_1]) ).
cnf(f_2531_3,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9052,tc_fun(U_9053,tc_HOL_Obool))),U_9049),U_9054),U_9050),U_9051))
| ~ hBOOL(hAPP(hAPP(U_9049,U_9050),U_9051)) ),
inference(clausify,[status(thm)],[f_2531_2]) ).
fof(f_2532_1,plain,
! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_sup2I2]) ).
fof(f_2532_2,plain,
! [U_9060,U_9059,U_9058,U_9057,U_9056,U_9055] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9058,tc_fun(U_9059,tc_HOL_Obool))),U_9060),U_9055),U_9056),U_9057))
| ~ hBOOL(hAPP(hAPP(U_9055,U_9056),U_9057)) ),
inference(variable_rename,[status(thm)],[f_2532_1]) ).
cnf(f_2532_3,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9058,tc_fun(U_9059,tc_HOL_Obool))),U_9060),U_9055),U_9056),U_9057))
| ~ hBOOL(hAPP(hAPP(U_9055,U_9056),U_9057)) ),
inference(clausify,[status(thm)],[f_2532_2]) ).
fof(f_2533_1,plain,
! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_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_b),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_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_INF2__iff]) ).
fof(f_2533_2,plain,
! [U_9069,U_9068,U_9067,U_9066,U_9065,U_9064,U_9063] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9063,tc_fun(U_9064,tc_fun(U_9065,tc_HOL_Obool))),U_9066),U_9067),U_9068),U_9069))
| ? [U_9062] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_9067,U_9062),U_9068),U_9069))
& hBOOL(hAPP(hAPP(c_member(U_9063),U_9062),U_9066)) ) )
& ( ! [U_9061] :
( hBOOL(hAPP(hAPP(hAPP(U_9067,U_9061),U_9068),U_9069))
| ~ hBOOL(hAPP(hAPP(c_member(U_9063),U_9061),U_9066)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9063,tc_fun(U_9064,tc_fun(U_9065,tc_HOL_Obool))),U_9066),U_9067),U_9068),U_9069)) ) ),
inference(variable_rename,[status(thm)],[f_2533_1]) ).
fof(f_2533_3,plain,
( ! [U_9083,U_9081,U_9079,U_9077,U_9075,U_9073,U_9071] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9071,tc_fun(U_9073,tc_fun(U_9075,tc_HOL_Obool))),U_9077),U_9079),U_9081),U_9083))
| ? [U_9062] :
( ~ hBOOL(hAPP(hAPP(hAPP(U_9079,U_9062),U_9081),U_9083))
& hBOOL(hAPP(hAPP(c_member(U_9071),U_9062),U_9077)) ) )
& ! [U_9082,U_9080,U_9078,U_9076,U_9074,U_9072,U_9070] :
( ! [U_9061] :
( hBOOL(hAPP(hAPP(hAPP(U_9078,U_9061),U_9080),U_9082))
| ~ hBOOL(hAPP(hAPP(c_member(U_9070),U_9061),U_9076)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9070,tc_fun(U_9072,tc_fun(U_9074,tc_HOL_Obool))),U_9076),U_9078),U_9080),U_9082)) ) ),
inference(miniscope,[status(thm)],[f_2533_2]) ).
fof(f_2533_4,plain,
( ! [U_9083,U_9081,U_9079,U_9077,U_9075,U_9073,U_9071] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9071,tc_fun(U_9073,tc_fun(U_9075,tc_HOL_Obool))),U_9077),U_9079),U_9081),U_9083))
| ( ~ hBOOL(hAPP(hAPP(hAPP(U_9079,sK168(U_9083,U_9081,U_9079,U_9077,U_9075,U_9073,U_9071)),U_9081),U_9083))
& hBOOL(hAPP(hAPP(c_member(U_9071),sK168(U_9083,U_9081,U_9079,U_9077,U_9075,U_9073,U_9071)),U_9077)) ) )
& ! [U_9082,U_9080,U_9078,U_9076,U_9074,U_9072,U_9070] :
( ! [U_9061] :
( hBOOL(hAPP(hAPP(hAPP(U_9078,U_9061),U_9080),U_9082))
| ~ hBOOL(hAPP(hAPP(c_member(U_9070),U_9061),U_9076)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9070,tc_fun(U_9072,tc_fun(U_9074,tc_HOL_Obool))),U_9076),U_9078),U_9080),U_9082)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK168]),skolemize(U_9062,sK168(U_9083,U_9081,U_9079,U_9077,U_9075,U_9073,U_9071))],[f_2533_3]) ).
cnf(f_2533_5,plain,
( hBOOL(hAPP(hAPP(hAPP(U_9078,U_9061),U_9080),U_9082))
| ~ hBOOL(hAPP(hAPP(c_member(U_9070),U_9061),U_9076))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9070,tc_fun(U_9072,tc_fun(U_9074,tc_HOL_Obool))),U_9076),U_9078),U_9080),U_9082)) ),
inference(clausify,[status(thm)],[f_2533_4]) ).
cnf(f_2533_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9071),sK168(U_9083,U_9081,U_9079,U_9077,U_9075,U_9073,U_9071)),U_9077))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9071,tc_fun(U_9073,tc_fun(U_9075,tc_HOL_Obool))),U_9077),U_9079),U_9081),U_9083)) ),
inference(clausify,[status(thm)],[f_2533_4]) ).
cnf(f_2533_7,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(U_9079,sK168(U_9083,U_9081,U_9079,U_9077,U_9075,U_9073,U_9071)),U_9081),U_9083))
| hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_9071,tc_fun(U_9073,tc_fun(U_9075,tc_HOL_Obool))),U_9077),U_9079),U_9081),U_9083)) ),
inference(clausify,[status(thm)],[f_2533_4]) ).
fof(f_2534_1,plain,
! [V_r_2,T_b] :
( ( c_Nitpick_Orefl_H(T_b,V_r_2)
| ? [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
& ( ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
| ~ c_Nitpick_Orefl_H(T_b,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Orefl_H__def]) ).
fof(f_2534_2,plain,
! [U_9087,U_9086] :
( ( c_Nitpick_Orefl_H(U_9086,U_9087)
| ? [U_9085] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9086,U_9086)),hAPP(hAPP(c_Product__Type_OPair(U_9086,U_9086),U_9085),U_9085)),U_9087)) )
& ( ! [U_9084] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_9086,U_9086)),hAPP(hAPP(c_Product__Type_OPair(U_9086,U_9086),U_9084),U_9084)),U_9087))
| ~ c_Nitpick_Orefl_H(U_9086,U_9087) ) ),
inference(variable_rename,[status(thm)],[f_2534_1]) ).
fof(f_2534_3,plain,
( ! [U_9091,U_9089] :
( c_Nitpick_Orefl_H(U_9089,U_9091)
| ? [U_9085] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9089,U_9089)),hAPP(hAPP(c_Product__Type_OPair(U_9089,U_9089),U_9085),U_9085)),U_9091)) )
& ! [U_9090,U_9088] :
( ! [U_9084] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_9088,U_9088)),hAPP(hAPP(c_Product__Type_OPair(U_9088,U_9088),U_9084),U_9084)),U_9090))
| ~ c_Nitpick_Orefl_H(U_9088,U_9090) ) ),
inference(miniscope,[status(thm)],[f_2534_2]) ).
fof(f_2534_4,plain,
( ! [U_9091,U_9089] :
( c_Nitpick_Orefl_H(U_9089,U_9091)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9089,U_9089)),hAPP(hAPP(c_Product__Type_OPair(U_9089,U_9089),sK169(U_9091,U_9089)),sK169(U_9091,U_9089))),U_9091)) )
& ! [U_9090,U_9088] :
( ! [U_9084] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_9088,U_9088)),hAPP(hAPP(c_Product__Type_OPair(U_9088,U_9088),U_9084),U_9084)),U_9090))
| ~ c_Nitpick_Orefl_H(U_9088,U_9090) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK169]),skolemize(U_9085,sK169(U_9091,U_9089))],[f_2534_3]) ).
cnf(f_2534_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9088,U_9088)),hAPP(hAPP(c_Product__Type_OPair(U_9088,U_9088),U_9084),U_9084)),U_9090))
| ~ c_Nitpick_Orefl_H(U_9088,U_9090) ),
inference(clausify,[status(thm)],[f_2534_4]) ).
cnf(f_2534_6,plain,
( c_Nitpick_Orefl_H(U_9089,U_9091)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9089,U_9089)),hAPP(hAPP(c_Product__Type_OPair(U_9089,U_9089),sK169(U_9091,U_9089)),sK169(U_9091,U_9089))),U_9091)) ),
inference(clausify,[status(thm)],[f_2534_4]) ).
fof(f_2535_1,plain,
! [V_k_2,V_i_2] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThan__iff]) ).
fof(f_2535_2,plain,
! [U_9093,U_9092] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9092),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9093)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9092),U_9093))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9093),U_9092)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9092),U_9093))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9093),U_9092)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9092),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9093))) ) ),
inference(variable_rename,[status(thm)],[f_2535_1]) ).
fof(f_2535_3,plain,
( ! [U_9097,U_9095] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9095),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9097)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9095),U_9097))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9097),U_9095)) )
& ! [U_9096,U_9094] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9094),U_9096))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9096),U_9094)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9094),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9096))) ) ),
inference(miniscope,[status(thm)],[f_2535_2]) ).
cnf(f_2535_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9096),U_9094))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9094),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9096))) ),
inference(clausify,[status(thm)],[f_2535_3]) ).
cnf(f_2535_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9094),U_9096))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9094),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9096))) ),
inference(clausify,[status(thm)],[f_2535_3]) ).
cnf(f_2535_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9095),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9097)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9095),U_9097))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9097),U_9095)) ),
inference(clausify,[status(thm)],[f_2535_3]) ).
fof(f_2536_1,plain,
! [V_k_2,V_i_2] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_OlessThan__iff]) ).
fof(f_2536_2,plain,
! [U_9099,U_9098] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9098),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9099)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9099),U_9098))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9098),U_9099)) )
& ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9099),U_9098))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9098),U_9099)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9098),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9099))) ) ),
inference(variable_rename,[status(thm)],[f_2536_1]) ).
fof(f_2536_3,plain,
( ! [U_9103,U_9101] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9101),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9103)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9103),U_9101))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9101),U_9103)) )
& ! [U_9102,U_9100] :
( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9102),U_9100))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9100),U_9102)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9100),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9102))) ) ),
inference(miniscope,[status(thm)],[f_2536_2]) ).
cnf(f_2536_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9100),U_9102))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9100),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9102))) ),
inference(clausify,[status(thm)],[f_2536_3]) ).
cnf(f_2536_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9102),U_9100))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9100),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9102))) ),
inference(clausify,[status(thm)],[f_2536_3]) ).
cnf(f_2536_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9101),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),U_9103)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9103),U_9101))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9101),U_9103)) ),
inference(clausify,[status(thm)],[f_2536_3]) ).
fof(f_2537_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_2537_2,plain,
! [U_9108,U_9107,U_9106] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9107),U_9106) = U_9107
| ? [U_9105] :
( ? [U_9104] :
( U_9107 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9104),U_9105)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9104),U_9108)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9105),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9106))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9107),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9108))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9106)) ),
inference(variable_rename,[status(thm)],[f_2537_1]) ).
fof(f_2537_3,plain,
! [U_9108,U_9107,U_9106] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9107),U_9106) = U_9107
| ( ? [U_9104] :
( U_9107 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9104),sK170(U_9108,U_9107,U_9106))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9104),U_9108)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK170(U_9108,U_9107,U_9106)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9106))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9107),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9108))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9106)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK170]),skolemize(U_9105,sK170(U_9108,U_9107,U_9106))],[f_2537_2]) ).
fof(f_2537_4,plain,
! [U_9108,U_9107,U_9106] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9107),U_9106) = U_9107
| ( U_9107 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK171(U_9108,U_9107,U_9106)),sK170(U_9108,U_9107,U_9106))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK171(U_9108,U_9107,U_9106)),U_9108))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK170(U_9108,U_9107,U_9106)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9106))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9107),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9108))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9106)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK171]),skolemize(U_9104,sK171(U_9108,U_9107,U_9106))],[f_2537_3]) ).
cnf(f_2537_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK170(U_9108,U_9107,U_9106)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9106)))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9107),U_9106) = U_9107
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9107),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9108))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9106)) ),
inference(clausify,[status(thm)],[f_2537_4]) ).
cnf(f_2537_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK171(U_9108,U_9107,U_9106)),U_9108))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9107),U_9106) = U_9107
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9107),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9108))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9106)) ),
inference(clausify,[status(thm)],[f_2537_4]) ).
cnf(f_2537_7,plain,
( U_9107 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK171(U_9108,U_9107,U_9106)),sK170(U_9108,U_9107,U_9106))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9107),U_9106) = U_9107
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9107),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9108))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9106)) ),
inference(clausify,[status(thm)],[f_2537_4]) ).
fof(f_2538_1,plain,
! [V_k_2,V_less_2,V_i_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
| ~ hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) )
& ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OlessThan__iff]) ).
fof(f_2538_2,plain,
! [U_9112,U_9111,U_9110,U_9109] :
( ( hBOOL(hAPP(hAPP(c_member(U_9109),U_9110),c_SetInterval_Oord_OlessThan(U_9109,U_9111,U_9112)))
| ~ hBOOL(hAPP(hAPP(U_9111,U_9110),U_9112)) )
& ( hBOOL(hAPP(hAPP(U_9111,U_9110),U_9112))
| ~ hBOOL(hAPP(hAPP(c_member(U_9109),U_9110),c_SetInterval_Oord_OlessThan(U_9109,U_9111,U_9112))) ) ),
inference(variable_rename,[status(thm)],[f_2538_1]) ).
fof(f_2538_3,plain,
( ! [U_9120,U_9118,U_9116] :
( ! [U_9114] : hBOOL(hAPP(hAPP(c_member(U_9114),U_9116),c_SetInterval_Oord_OlessThan(U_9114,U_9118,U_9120)))
| ~ hBOOL(hAPP(hAPP(U_9118,U_9116),U_9120)) )
& ! [U_9119,U_9117,U_9115] :
( ! [U_9113] : ~ hBOOL(hAPP(hAPP(c_member(U_9113),U_9115),c_SetInterval_Oord_OlessThan(U_9113,U_9117,U_9119)))
| hBOOL(hAPP(hAPP(U_9117,U_9115),U_9119)) ) ),
inference(miniscope,[status(thm)],[f_2538_2]) ).
cnf(f_2538_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_9113),U_9115),c_SetInterval_Oord_OlessThan(U_9113,U_9117,U_9119)))
| hBOOL(hAPP(hAPP(U_9117,U_9115),U_9119)) ),
inference(clausify,[status(thm)],[f_2538_3]) ).
cnf(f_2538_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9114),U_9116),c_SetInterval_Oord_OlessThan(U_9114,U_9118,U_9120)))
| ~ hBOOL(hAPP(hAPP(U_9118,U_9116),U_9120)) ),
inference(clausify,[status(thm)],[f_2538_3]) ).
fof(f_2539_1,plain,
! [V_k_2,V_less_2,V_i_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
| ~ hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) )
& ( hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThan__iff]) ).
fof(f_2539_2,plain,
! [U_9124,U_9123,U_9122,U_9121] :
( ( hBOOL(hAPP(hAPP(c_member(U_9121),U_9122),c_SetInterval_Oord_OgreaterThan(U_9121,U_9123,U_9124)))
| ~ hBOOL(hAPP(hAPP(U_9123,U_9124),U_9122)) )
& ( hBOOL(hAPP(hAPP(U_9123,U_9124),U_9122))
| ~ hBOOL(hAPP(hAPP(c_member(U_9121),U_9122),c_SetInterval_Oord_OgreaterThan(U_9121,U_9123,U_9124))) ) ),
inference(variable_rename,[status(thm)],[f_2539_1]) ).
fof(f_2539_3,plain,
( ! [U_9132,U_9130,U_9128] :
( ! [U_9126] : hBOOL(hAPP(hAPP(c_member(U_9126),U_9128),c_SetInterval_Oord_OgreaterThan(U_9126,U_9130,U_9132)))
| ~ hBOOL(hAPP(hAPP(U_9130,U_9132),U_9128)) )
& ! [U_9131,U_9129,U_9127] :
( ! [U_9125] : ~ hBOOL(hAPP(hAPP(c_member(U_9125),U_9127),c_SetInterval_Oord_OgreaterThan(U_9125,U_9129,U_9131)))
| hBOOL(hAPP(hAPP(U_9129,U_9131),U_9127)) ) ),
inference(miniscope,[status(thm)],[f_2539_2]) ).
cnf(f_2539_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_9125),U_9127),c_SetInterval_Oord_OgreaterThan(U_9125,U_9129,U_9131)))
| hBOOL(hAPP(hAPP(U_9129,U_9131),U_9127)) ),
inference(clausify,[status(thm)],[f_2539_3]) ).
cnf(f_2539_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9126),U_9128),c_SetInterval_Oord_OgreaterThan(U_9126,U_9130,U_9132)))
| ~ hBOOL(hAPP(hAPP(U_9130,U_9132),U_9128)) ),
inference(clausify,[status(thm)],[f_2539_3]) ).
fof(f_2540_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_2540_2,plain,
! [U_9138,U_9137,U_9136] :
( ! [U_9135] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9135),U_9136) != U_9137
| U_9135 = U_9137
| ? [U_9134] :
( ? [U_9133] :
( U_9135 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9133),U_9134)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9133),U_9138)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9134),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9136))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9137),U_9138))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9136)) ),
inference(variable_rename,[status(thm)],[f_2540_1]) ).
fof(f_2540_3,plain,
! [U_9138,U_9137,U_9136] :
( ! [U_9135] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9135),U_9136) != U_9137
| U_9135 = U_9137
| ( ? [U_9133] :
( U_9135 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9133),sK172(U_9138,U_9137,U_9136,U_9135))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9133),U_9138)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK172(U_9138,U_9137,U_9136,U_9135)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9136))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9137),U_9138))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9136)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK172]),skolemize(U_9134,sK172(U_9138,U_9137,U_9136,U_9135))],[f_2540_2]) ).
fof(f_2540_4,plain,
! [U_9138,U_9137,U_9136] :
( ! [U_9135] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9135),U_9136) != U_9137
| U_9135 = U_9137
| ( U_9135 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK173(U_9138,U_9137,U_9136,U_9135)),sK172(U_9138,U_9137,U_9136,U_9135))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK173(U_9138,U_9137,U_9136,U_9135)),U_9138))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK172(U_9138,U_9137,U_9136,U_9135)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9136))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9137),U_9138))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9136)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK173]),skolemize(U_9133,sK173(U_9138,U_9137,U_9136,U_9135))],[f_2540_3]) ).
cnf(f_2540_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK172(U_9138,U_9137,U_9136,U_9135)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9136)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9135),U_9136) != U_9137
| U_9135 = U_9137
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9137),U_9138))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9136)) ),
inference(clausify,[status(thm)],[f_2540_4]) ).
cnf(f_2540_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK173(U_9138,U_9137,U_9136,U_9135)),U_9138))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9135),U_9136) != U_9137
| U_9135 = U_9137
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9137),U_9138))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9136)) ),
inference(clausify,[status(thm)],[f_2540_4]) ).
cnf(f_2540_7,plain,
( U_9135 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK173(U_9138,U_9137,U_9136,U_9135)),sK172(U_9138,U_9137,U_9136,U_9135))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9135),U_9136) != U_9137
| U_9135 = U_9137
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9137),U_9138))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9136)) ),
inference(clausify,[status(thm)],[f_2540_4]) ).
fof(f_2541_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_2541_2,plain,
! [U_9144,U_9143,U_9142] :
( ! [U_9141] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9141),U_9142) != U_9143
| U_9141 = U_9143
| ? [U_9140] :
( ? [U_9139] :
( U_9141 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9139),U_9140)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9139),U_9144)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9140),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9142))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9143),U_9144))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9142)) ),
inference(variable_rename,[status(thm)],[f_2541_1]) ).
fof(f_2541_3,plain,
! [U_9144,U_9143,U_9142] :
( ! [U_9141] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9141),U_9142) != U_9143
| U_9141 = U_9143
| ( ? [U_9139] :
( U_9141 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9139),sK174(U_9144,U_9143,U_9142,U_9141))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9139),U_9144)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK174(U_9144,U_9143,U_9142,U_9141)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9142))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9143),U_9144))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9142)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK174]),skolemize(U_9140,sK174(U_9144,U_9143,U_9142,U_9141))],[f_2541_2]) ).
fof(f_2541_4,plain,
! [U_9144,U_9143,U_9142] :
( ! [U_9141] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9141),U_9142) != U_9143
| U_9141 = U_9143
| ( U_9141 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK175(U_9144,U_9143,U_9142,U_9141)),sK174(U_9144,U_9143,U_9142,U_9141))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK175(U_9144,U_9143,U_9142,U_9141)),U_9144))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK174(U_9144,U_9143,U_9142,U_9141)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9142))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9143),U_9144))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9142)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK175]),skolemize(U_9139,sK175(U_9144,U_9143,U_9142,U_9141))],[f_2541_3]) ).
cnf(f_2541_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK174(U_9144,U_9143,U_9142,U_9141)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9142)))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9141),U_9142) != U_9143
| U_9141 = U_9143
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9143),U_9144))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9142)) ),
inference(clausify,[status(thm)],[f_2541_4]) ).
cnf(f_2541_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK175(U_9144,U_9143,U_9142,U_9141)),U_9144))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9141),U_9142) != U_9143
| U_9141 = U_9143
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9143),U_9144))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9142)) ),
inference(clausify,[status(thm)],[f_2541_4]) ).
cnf(f_2541_7,plain,
( U_9141 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK175(U_9144,U_9143,U_9142,U_9141)),sK174(U_9144,U_9143,U_9142,U_9141))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9141),U_9142) != U_9143
| U_9141 = U_9143
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9143),U_9144))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9142)) ),
inference(clausify,[status(thm)],[f_2541_4]) ).
fof(f_2542_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_2542_2,plain,
! [U_9150,U_9149,U_9148] :
( ! [U_9147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9149),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9147),U_9148)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9149),U_9147))
| ? [U_9146] :
( ? [U_9145] :
( U_9147 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9145),U_9146)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9145),U_9150)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9146),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9148))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9149),U_9150))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9148)) ),
inference(variable_rename,[status(thm)],[f_2542_1]) ).
fof(f_2542_3,plain,
! [U_9150,U_9149,U_9148] :
( ! [U_9147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9149),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9147),U_9148)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9149),U_9147))
| ( ? [U_9145] :
( U_9147 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9145),sK176(U_9150,U_9149,U_9148,U_9147))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9145),U_9150)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK176(U_9150,U_9149,U_9148,U_9147)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9148))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9149),U_9150))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9148)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK176]),skolemize(U_9146,sK176(U_9150,U_9149,U_9148,U_9147))],[f_2542_2]) ).
fof(f_2542_4,plain,
! [U_9150,U_9149,U_9148] :
( ! [U_9147] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9149),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9147),U_9148)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9149),U_9147))
| ( U_9147 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK177(U_9150,U_9149,U_9148,U_9147)),sK176(U_9150,U_9149,U_9148,U_9147))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK177(U_9150,U_9149,U_9148,U_9147)),U_9150))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK176(U_9150,U_9149,U_9148,U_9147)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9148))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9149),U_9150))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9148)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK177]),skolemize(U_9145,sK177(U_9150,U_9149,U_9148,U_9147))],[f_2542_3]) ).
cnf(f_2542_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK176(U_9150,U_9149,U_9148,U_9147)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9148)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9149),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9147),U_9148)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9149),U_9147))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9149),U_9150))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9148)) ),
inference(clausify,[status(thm)],[f_2542_4]) ).
cnf(f_2542_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK177(U_9150,U_9149,U_9148,U_9147)),U_9150))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9149),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9147),U_9148)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9149),U_9147))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9149),U_9150))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9148)) ),
inference(clausify,[status(thm)],[f_2542_4]) ).
cnf(f_2542_7,plain,
( U_9147 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK177(U_9150,U_9149,U_9148,U_9147)),sK176(U_9150,U_9149,U_9148,U_9147))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9149),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9147),U_9148)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9149),U_9147))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9149),U_9150))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9148)) ),
inference(clausify,[status(thm)],[f_2542_4]) ).
fof(f_2543_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_2543_2,plain,
! [U_9156,U_9155,U_9154] :
( ! [U_9153] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9153),U_9154)),U_9155))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9153),U_9155))
| ? [U_9152] :
( ? [U_9151] :
( U_9153 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9151),U_9152)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9151),U_9156)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9152),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9154))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9155),U_9156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9154)) ),
inference(variable_rename,[status(thm)],[f_2543_1]) ).
fof(f_2543_3,plain,
! [U_9156,U_9155,U_9154] :
( ! [U_9153] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9153),U_9154)),U_9155))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9153),U_9155))
| ( ? [U_9151] :
( U_9153 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9151),sK178(U_9156,U_9155,U_9154,U_9153))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9151),U_9156)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK178(U_9156,U_9155,U_9154,U_9153)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9154))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9155),U_9156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9154)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK178]),skolemize(U_9152,sK178(U_9156,U_9155,U_9154,U_9153))],[f_2543_2]) ).
fof(f_2543_4,plain,
! [U_9156,U_9155,U_9154] :
( ! [U_9153] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9153),U_9154)),U_9155))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9153),U_9155))
| ( U_9153 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK179(U_9156,U_9155,U_9154,U_9153)),sK178(U_9156,U_9155,U_9154,U_9153))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK179(U_9156,U_9155,U_9154,U_9153)),U_9156))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK178(U_9156,U_9155,U_9154,U_9153)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9154))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9155),U_9156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9154)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK179]),skolemize(U_9151,sK179(U_9156,U_9155,U_9154,U_9153))],[f_2543_3]) ).
cnf(f_2543_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK178(U_9156,U_9155,U_9154,U_9153)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9154)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9153),U_9154)),U_9155))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9153),U_9155))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9155),U_9156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9154)) ),
inference(clausify,[status(thm)],[f_2543_4]) ).
cnf(f_2543_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK179(U_9156,U_9155,U_9154,U_9153)),U_9156))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9153),U_9154)),U_9155))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9153),U_9155))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9155),U_9156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9154)) ),
inference(clausify,[status(thm)],[f_2543_4]) ).
cnf(f_2543_7,plain,
( U_9153 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK179(U_9156,U_9155,U_9154,U_9153)),sK178(U_9156,U_9155,U_9154,U_9153))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9153),U_9154)),U_9155))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_9153),U_9155))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9155),U_9156))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9154)) ),
inference(clausify,[status(thm)],[f_2543_4]) ).
fof(f_2544_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_2544_2,plain,
! [U_9161,U_9160,U_9159] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9160),U_9159) = U_9160
| ? [U_9158] :
( ? [U_9157] :
( U_9160 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9157),U_9158)
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9157),U_9161)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9158),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9159))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9160),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9161))
| ~ 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_2544_1]) ).
fof(f_2544_3,plain,
! [U_9161,U_9160,U_9159] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9160),U_9159) = U_9160
| ( ? [U_9157] :
( U_9160 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_9157),sK180(U_9161,U_9160,U_9159))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_9157),U_9161)) )
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK180(U_9161,U_9160,U_9159)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9159))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9160),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9161))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9159)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK180]),skolemize(U_9158,sK180(U_9161,U_9160,U_9159))],[f_2544_2]) ).
fof(f_2544_4,plain,
! [U_9161,U_9160,U_9159] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9160),U_9159) = U_9160
| ( U_9160 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK181(U_9161,U_9160,U_9159)),sK180(U_9161,U_9160,U_9159))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK181(U_9161,U_9160,U_9159)),U_9161))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK180(U_9161,U_9160,U_9159)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9159))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9160),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9161))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_9159)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK181]),skolemize(U_9157,sK181(U_9161,U_9160,U_9159))],[f_2544_3]) ).
cnf(f_2544_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK180(U_9161,U_9160,U_9159)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_9159)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9160),U_9159) = U_9160
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9160),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9161))
| ~ 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_2544_4]) ).
cnf(f_2544_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK181(U_9161,U_9160,U_9159)),U_9161))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9160),U_9159) = U_9160
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9160),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9161))
| ~ 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_2544_4]) ).
cnf(f_2544_7,plain,
( U_9160 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK181(U_9161,U_9160,U_9159)),sK180(U_9161,U_9160,U_9159))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9160),U_9159) = U_9160
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_9160),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_9161))
| ~ 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_2544_4]) ).
fof(f_2545_1,plain,
! [V_f_2,V_y_2,V_x_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_in__measure]) ).
fof(f_2545_2,plain,
! [U_9165,U_9164,U_9163,U_9162] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9162,U_9162)),hAPP(hAPP(c_Product__Type_OPair(U_9162,U_9162),U_9163),U_9164)),hAPP(c_Wellfounded_Omeasure(U_9162),U_9165)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_9165,U_9163)),hAPP(U_9165,U_9164))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_9165,U_9163)),hAPP(U_9165,U_9164)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9162,U_9162)),hAPP(hAPP(c_Product__Type_OPair(U_9162,U_9162),U_9163),U_9164)),hAPP(c_Wellfounded_Omeasure(U_9162),U_9165))) ) ),
inference(variable_rename,[status(thm)],[f_2545_1]) ).
fof(f_2545_3,plain,
( ! [U_9173,U_9171,U_9169] :
( ! [U_9167] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_9167,U_9167)),hAPP(hAPP(c_Product__Type_OPair(U_9167,U_9167),U_9169),U_9171)),hAPP(c_Wellfounded_Omeasure(U_9167),U_9173)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_9173,U_9169)),hAPP(U_9173,U_9171))) )
& ! [U_9172,U_9170,U_9168] :
( ! [U_9166] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9166,U_9166)),hAPP(hAPP(c_Product__Type_OPair(U_9166,U_9166),U_9168),U_9170)),hAPP(c_Wellfounded_Omeasure(U_9166),U_9172)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_9172,U_9168)),hAPP(U_9172,U_9170))) ) ),
inference(miniscope,[status(thm)],[f_2545_2]) ).
cnf(f_2545_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9166,U_9166)),hAPP(hAPP(c_Product__Type_OPair(U_9166,U_9166),U_9168),U_9170)),hAPP(c_Wellfounded_Omeasure(U_9166),U_9172)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_9172,U_9168)),hAPP(U_9172,U_9170))) ),
inference(clausify,[status(thm)],[f_2545_3]) ).
cnf(f_2545_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9167,U_9167)),hAPP(hAPP(c_Product__Type_OPair(U_9167,U_9167),U_9169),U_9171)),hAPP(c_Wellfounded_Omeasure(U_9167),U_9173)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_9173,U_9169)),hAPP(U_9173,U_9171))) ),
inference(clausify,[status(thm)],[f_2545_3]) ).
fof(f_2546_1,plain,
! [V_k_2,V_i_2] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_OatLeast__iff]) ).
fof(f_2546_2,plain,
! [U_9175,U_9174] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9174),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9175)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9175),U_9174)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9175),U_9174))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9174),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9175))) ) ),
inference(variable_rename,[status(thm)],[f_2546_1]) ).
fof(f_2546_3,plain,
( ! [U_9179,U_9177] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9177),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9179)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9179),U_9177)) )
& ! [U_9178,U_9176] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9178),U_9176))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9176),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9178))) ) ),
inference(miniscope,[status(thm)],[f_2546_2]) ).
cnf(f_2546_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9178),U_9176))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9176),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9178))) ),
inference(clausify,[status(thm)],[f_2546_3]) ).
cnf(f_2546_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9177),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9179)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9179),U_9177)) ),
inference(clausify,[status(thm)],[f_2546_3]) ).
fof(f_2547_1,plain,
! [V_k_2,V_i_2] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_OatMost__iff]) ).
fof(f_2547_2,plain,
! [U_9181,U_9180] :
( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9180),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9181)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9180),U_9181)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9180),U_9181))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9180),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9181))) ) ),
inference(variable_rename,[status(thm)],[f_2547_1]) ).
fof(f_2547_3,plain,
( ! [U_9185,U_9183] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9183),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9185)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9183),U_9185)) )
& ! [U_9184,U_9182] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9182),U_9184))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9182),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9184))) ) ),
inference(miniscope,[status(thm)],[f_2547_2]) ).
cnf(f_2547_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9182),U_9184))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9182),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9184))) ),
inference(clausify,[status(thm)],[f_2547_3]) ).
cnf(f_2547_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9183),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9185)))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9183),U_9185)) ),
inference(clausify,[status(thm)],[f_2547_3]) ).
fof(f_2548_1,plain,
! [V_k_2,V_less__eq_2,V_i_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
| ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) )
& ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OatMost__iff]) ).
fof(f_2548_2,plain,
! [U_9189,U_9188,U_9187,U_9186] :
( ( hBOOL(hAPP(hAPP(c_member(U_9186),U_9187),c_SetInterval_Oord_OatMost(U_9186,U_9188,U_9189)))
| ~ hBOOL(hAPP(hAPP(U_9188,U_9187),U_9189)) )
& ( hBOOL(hAPP(hAPP(U_9188,U_9187),U_9189))
| ~ hBOOL(hAPP(hAPP(c_member(U_9186),U_9187),c_SetInterval_Oord_OatMost(U_9186,U_9188,U_9189))) ) ),
inference(variable_rename,[status(thm)],[f_2548_1]) ).
fof(f_2548_3,plain,
( ! [U_9197,U_9195,U_9193] :
( ! [U_9191] : hBOOL(hAPP(hAPP(c_member(U_9191),U_9193),c_SetInterval_Oord_OatMost(U_9191,U_9195,U_9197)))
| ~ hBOOL(hAPP(hAPP(U_9195,U_9193),U_9197)) )
& ! [U_9196,U_9194,U_9192] :
( ! [U_9190] : ~ hBOOL(hAPP(hAPP(c_member(U_9190),U_9192),c_SetInterval_Oord_OatMost(U_9190,U_9194,U_9196)))
| hBOOL(hAPP(hAPP(U_9194,U_9192),U_9196)) ) ),
inference(miniscope,[status(thm)],[f_2548_2]) ).
cnf(f_2548_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_9190),U_9192),c_SetInterval_Oord_OatMost(U_9190,U_9194,U_9196)))
| hBOOL(hAPP(hAPP(U_9194,U_9192),U_9196)) ),
inference(clausify,[status(thm)],[f_2548_3]) ).
cnf(f_2548_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9191),U_9193),c_SetInterval_Oord_OatMost(U_9191,U_9195,U_9197)))
| ~ hBOOL(hAPP(hAPP(U_9195,U_9193),U_9197)) ),
inference(clausify,[status(thm)],[f_2548_3]) ).
fof(f_2549_1,plain,
! [V_k_2,V_less__eq_2,V_i_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
| ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) )
& ( hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OatLeast__iff]) ).
fof(f_2549_2,plain,
! [U_9201,U_9200,U_9199,U_9198] :
( ( hBOOL(hAPP(hAPP(c_member(U_9198),U_9199),c_SetInterval_Oord_OatLeast(U_9198,U_9200,U_9201)))
| ~ hBOOL(hAPP(hAPP(U_9200,U_9201),U_9199)) )
& ( hBOOL(hAPP(hAPP(U_9200,U_9201),U_9199))
| ~ hBOOL(hAPP(hAPP(c_member(U_9198),U_9199),c_SetInterval_Oord_OatLeast(U_9198,U_9200,U_9201))) ) ),
inference(variable_rename,[status(thm)],[f_2549_1]) ).
fof(f_2549_3,plain,
( ! [U_9209,U_9207,U_9205] :
( ! [U_9203] : hBOOL(hAPP(hAPP(c_member(U_9203),U_9205),c_SetInterval_Oord_OatLeast(U_9203,U_9207,U_9209)))
| ~ hBOOL(hAPP(hAPP(U_9207,U_9209),U_9205)) )
& ! [U_9208,U_9206,U_9204] :
( ! [U_9202] : ~ hBOOL(hAPP(hAPP(c_member(U_9202),U_9204),c_SetInterval_Oord_OatLeast(U_9202,U_9206,U_9208)))
| hBOOL(hAPP(hAPP(U_9206,U_9208),U_9204)) ) ),
inference(miniscope,[status(thm)],[f_2549_2]) ).
cnf(f_2549_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_9202),U_9204),c_SetInterval_Oord_OatLeast(U_9202,U_9206,U_9208)))
| hBOOL(hAPP(hAPP(U_9206,U_9208),U_9204)) ),
inference(clausify,[status(thm)],[f_2549_3]) ).
cnf(f_2549_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9203),U_9205),c_SetInterval_Oord_OatLeast(U_9203,U_9207,U_9209)))
| ~ hBOOL(hAPP(hAPP(U_9207,U_9209),U_9205)) ),
inference(clausify,[status(thm)],[f_2549_3]) ).
fof(f_2550_1,plain,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(V_F_2,V_A_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oremove]) ).
fof(f_2550_2,plain,
! [U_9217,U_9216,U_9215,U_9214,U_9213,U_9212,U_9211,U_9210] :
( hAPP(U_9215,U_9216) = hAPP(hAPP(U_9212,hAPP(U_9214,U_9217)),hAPP(U_9215,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9211,tc_HOL_Obool)),U_9216),hAPP(hAPP(c_Set_Oinsert(U_9211),U_9217),c_Orderings_Obot__class_Obot(tc_fun(U_9211,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_9211),U_9217),U_9216))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9211),U_9216))
| ~ c_Finite__Set_Ofolding__image__simple(U_9210,U_9211,U_9212,U_9213,U_9214,U_9215) ),
inference(variable_rename,[status(thm)],[f_2550_1]) ).
fof(f_2550_3,plain,
! [U_9217,U_9216,U_9215,U_9214,U_9213,U_9212,U_9211] :
( ! [U_9210] : ~ c_Finite__Set_Ofolding__image__simple(U_9210,U_9211,U_9212,U_9213,U_9214,U_9215)
| hAPP(U_9215,U_9216) = hAPP(hAPP(U_9212,hAPP(U_9214,U_9217)),hAPP(U_9215,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9211,tc_HOL_Obool)),U_9216),hAPP(hAPP(c_Set_Oinsert(U_9211),U_9217),c_Orderings_Obot__class_Obot(tc_fun(U_9211,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_9211),U_9217),U_9216))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9211),U_9216)) ),
inference(miniscope,[status(thm)],[f_2550_2]) ).
cnf(f_2550_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_9210,U_9211,U_9212,U_9213,U_9214,U_9215)
| hAPP(U_9215,U_9216) = hAPP(hAPP(U_9212,hAPP(U_9214,U_9217)),hAPP(U_9215,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9211,tc_HOL_Obool)),U_9216),hAPP(hAPP(c_Set_Oinsert(U_9211),U_9217),c_Orderings_Obot__class_Obot(tc_fun(U_9211,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_9211),U_9217),U_9216))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9211),U_9216)) ),
inference(clausify,[status(thm)],[f_2550_3]) ).
fof(f_2551_1,plain,
! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
( c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2))
| ~ c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_y_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Ointros_I2_J]) ).
fof(f_2551_2,plain,
! [U_9224,U_9223,U_9222,U_9221,U_9220,U_9219,U_9218] :
( c_Nitpick_Ofold__graph_H(U_9218,U_9221,U_9222,U_9223,U_9220,hAPP(hAPP(U_9222,U_9219),U_9224))
| ~ c_Nitpick_Ofold__graph_H(U_9218,U_9221,U_9222,U_9223,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9218,tc_HOL_Obool)),U_9220),hAPP(hAPP(c_Set_Oinsert(U_9218),U_9219),c_Orderings_Obot__class_Obot(tc_fun(U_9218,tc_HOL_Obool)))),U_9224)
| ~ hBOOL(hAPP(hAPP(c_member(U_9218),U_9219),U_9220)) ),
inference(variable_rename,[status(thm)],[f_2551_1]) ).
cnf(f_2551_3,plain,
( c_Nitpick_Ofold__graph_H(U_9218,U_9221,U_9222,U_9223,U_9220,hAPP(hAPP(U_9222,U_9219),U_9224))
| ~ c_Nitpick_Ofold__graph_H(U_9218,U_9221,U_9222,U_9223,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9218,tc_HOL_Obool)),U_9220),hAPP(hAPP(c_Set_Oinsert(U_9218),U_9219),c_Orderings_Obot__class_Obot(tc_fun(U_9218,tc_HOL_Obool)))),U_9224)
| ~ hBOOL(hAPP(hAPP(c_member(U_9218),U_9219),U_9220)) ),
inference(clausify,[status(thm)],[f_2551_2]) ).
fof(f_2552_1,plain,
! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)))
| ? [B_b] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ class_Groups_Oordered__comm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__mono2]) ).
fof(f_2552_2,plain,
! [U_9230,U_9229,U_9228,U_9227,U_9226] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9226),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9227,U_9226),U_9230),U_9229)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9227,U_9226),U_9230),U_9228)))
| ? [U_9225] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9226),c_Groups_Ozero__class_Ozero(U_9226)),hAPP(U_9230,U_9225)))
& hBOOL(hAPP(hAPP(c_member(U_9227),U_9225),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9227,tc_HOL_Obool)),U_9228),U_9229))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9227,tc_HOL_Obool)),U_9229),U_9228))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9227),U_9228))
| ~ class_Groups_Oordered__comm__monoid__add(U_9226) ),
inference(variable_rename,[status(thm)],[f_2552_1]) ).
fof(f_2552_3,plain,
! [U_9230,U_9229,U_9228,U_9227,U_9226] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9226),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9227,U_9226),U_9230),U_9229)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9227,U_9226),U_9230),U_9228)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9226),c_Groups_Ozero__class_Ozero(U_9226)),hAPP(U_9230,sK182(U_9230,U_9229,U_9228,U_9227,U_9226))))
& hBOOL(hAPP(hAPP(c_member(U_9227),sK182(U_9230,U_9229,U_9228,U_9227,U_9226)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9227,tc_HOL_Obool)),U_9228),U_9229))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9227,tc_HOL_Obool)),U_9229),U_9228))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9227),U_9228))
| ~ class_Groups_Oordered__comm__monoid__add(U_9226) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK182]),skolemize(U_9225,sK182(U_9230,U_9229,U_9228,U_9227,U_9226))],[f_2552_2]) ).
cnf(f_2552_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_9227),sK182(U_9230,U_9229,U_9228,U_9227,U_9226)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9227,tc_HOL_Obool)),U_9228),U_9229)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9226),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9227,U_9226),U_9230),U_9229)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9227,U_9226),U_9230),U_9228)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9227,tc_HOL_Obool)),U_9229),U_9228))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9227),U_9228))
| ~ class_Groups_Oordered__comm__monoid__add(U_9226) ),
inference(clausify,[status(thm)],[f_2552_3]) ).
cnf(f_2552_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9226),c_Groups_Ozero__class_Ozero(U_9226)),hAPP(U_9230,sK182(U_9230,U_9229,U_9228,U_9227,U_9226))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9226),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9227,U_9226),U_9230),U_9229)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9227,U_9226),U_9230),U_9228)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9227,tc_HOL_Obool)),U_9229),U_9228))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9227),U_9228))
| ~ class_Groups_Oordered__comm__monoid__add(U_9226) ),
inference(clausify,[status(thm)],[f_2552_3]) ).
fof(f_2553_1,plain,
! [V_b_2,V_A_2,T_b] :
( ( c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) )
& ( c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ) ),
inference(fof_nnf,[status(thm)],[fact_flat__lub__def]) ).
fof(f_2553_2,plain,
! [U_9233,U_9232,U_9231] :
( ( c_Partial__Function_Oflat__lub(U_9231,U_9233,U_9232) = c_HOL_OThe(U_9231,hAPP(hAPP(c_COMBC(U_9231,tc_fun(U_9231,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9231)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9231,tc_HOL_Obool)),U_9232),hAPP(hAPP(c_Set_Oinsert(U_9231),U_9233),c_Orderings_Obot__class_Obot(tc_fun(U_9231,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9231,tc_HOL_Obool)),U_9232),hAPP(hAPP(c_Set_Oinsert(U_9231),U_9233),c_Orderings_Obot__class_Obot(tc_fun(U_9231,tc_HOL_Obool))))) )
& ( c_Partial__Function_Oflat__lub(U_9231,U_9233,U_9232) = U_9233
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9231,tc_HOL_Obool)),U_9232),hAPP(hAPP(c_Set_Oinsert(U_9231),U_9233),c_Orderings_Obot__class_Obot(tc_fun(U_9231,tc_HOL_Obool))))) ) ),
inference(variable_rename,[status(thm)],[f_2553_1]) ).
fof(f_2553_3,plain,
( ! [U_9239,U_9237,U_9235] :
( c_Partial__Function_Oflat__lub(U_9235,U_9239,U_9237) = c_HOL_OThe(U_9235,hAPP(hAPP(c_COMBC(U_9235,tc_fun(U_9235,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9235)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9235,tc_HOL_Obool)),U_9237),hAPP(hAPP(c_Set_Oinsert(U_9235),U_9239),c_Orderings_Obot__class_Obot(tc_fun(U_9235,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9235,tc_HOL_Obool)),U_9237),hAPP(hAPP(c_Set_Oinsert(U_9235),U_9239),c_Orderings_Obot__class_Obot(tc_fun(U_9235,tc_HOL_Obool))))) )
& ! [U_9238,U_9236,U_9234] :
( c_Partial__Function_Oflat__lub(U_9234,U_9238,U_9236) = U_9238
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9234,tc_HOL_Obool)),U_9236),hAPP(hAPP(c_Set_Oinsert(U_9234),U_9238),c_Orderings_Obot__class_Obot(tc_fun(U_9234,tc_HOL_Obool))))) ) ),
inference(miniscope,[status(thm)],[f_2553_2]) ).
cnf(f_2553_4,plain,
( c_Partial__Function_Oflat__lub(U_9234,U_9238,U_9236) = U_9238
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9234,tc_HOL_Obool)),U_9236),hAPP(hAPP(c_Set_Oinsert(U_9234),U_9238),c_Orderings_Obot__class_Obot(tc_fun(U_9234,tc_HOL_Obool))))) ),
inference(clausify,[status(thm)],[f_2553_3]) ).
cnf(f_2553_5,plain,
( c_Partial__Function_Oflat__lub(U_9235,U_9239,U_9237) = c_HOL_OThe(U_9235,hAPP(hAPP(c_COMBC(U_9235,tc_fun(U_9235,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9235)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9235,tc_HOL_Obool)),U_9237),hAPP(hAPP(c_Set_Oinsert(U_9235),U_9239),c_Orderings_Obot__class_Obot(tc_fun(U_9235,tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9235,tc_HOL_Obool)),U_9237),hAPP(hAPP(c_Set_Oinsert(U_9235),U_9239),c_Orderings_Obot__class_Obot(tc_fun(U_9235,tc_HOL_Obool))))) ),
inference(clausify,[status(thm)],[f_2553_3]) ).
fof(f_2554_1,plain,
! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2
| ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oempty]) ).
fof(f_2554_2,plain,
! [U_9245,U_9244,U_9243,U_9242,U_9241,U_9240] :
( hAPP(U_9245,c_Orderings_Obot__class_Obot(tc_fun(U_9241,tc_HOL_Obool))) = U_9243
| ~ c_Finite__Set_Ofolding__image__simple(U_9240,U_9241,U_9242,U_9243,U_9244,U_9245) ),
inference(variable_rename,[status(thm)],[f_2554_1]) ).
fof(f_2554_3,plain,
! [U_9245,U_9244,U_9243,U_9242,U_9241] :
( ! [U_9240] : ~ c_Finite__Set_Ofolding__image__simple(U_9240,U_9241,U_9242,U_9243,U_9244,U_9245)
| hAPP(U_9245,c_Orderings_Obot__class_Obot(tc_fun(U_9241,tc_HOL_Obool))) = U_9243 ),
inference(miniscope,[status(thm)],[f_2554_2]) ).
cnf(f_2554_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_9240,U_9241,U_9242,U_9243,U_9244,U_9245)
| hAPP(U_9245,c_Orderings_Obot__class_Obot(tc_fun(U_9241,tc_HOL_Obool))) = U_9243 ),
inference(clausify,[status(thm)],[f_2554_3]) ).
fof(f_2555_1,plain,
! [V_z_2,V_f_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_z_2),
inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Ointros_I1_J]) ).
fof(f_2555_2,plain,
! [U_9249,U_9248,U_9247,U_9246] : c_Nitpick_Ofold__graph_H(U_9246,U_9247,U_9248,U_9249,c_Orderings_Obot__class_Obot(tc_fun(U_9246,tc_HOL_Obool)),U_9249),
inference(variable_rename,[status(thm)],[f_2555_1]) ).
cnf(f_2555_3,plain,
c_Nitpick_Ofold__graph_H(U_9246,U_9247,U_9248,U_9249,c_Orderings_Obot__class_Obot(tc_fun(U_9246,tc_HOL_Obool)),U_9249),
inference(clausify,[status(thm)],[f_2555_2]) ).
fof(f_2556_1,plain,
! [V_a2_2,V_a1_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),
inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Oequations_I1_J]) ).
fof(f_2556_2,plain,
! [U_9253,U_9252,U_9251,U_9250] : c_Nitpick_Ofold__graph_H(U_9250,U_9251,U_9252,U_9253,c_Orderings_Obot__class_Obot(tc_fun(U_9250,tc_HOL_Obool)),U_9253),
inference(variable_rename,[status(thm)],[f_2556_1]) ).
cnf(f_2556_3,plain,
c_Nitpick_Ofold__graph_H(U_9250,U_9251,U_9252,U_9253,c_Orderings_Obot__class_Obot(tc_fun(U_9250,tc_HOL_Obool)),U_9253),
inference(clausify,[status(thm)],[f_2556_2]) ).
fof(f_2557_1,plain,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2))
| hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oinsert]) ).
fof(f_2557_2,plain,
! [U_9261,U_9260,U_9259,U_9258,U_9257,U_9256,U_9255,U_9254] :
( hAPP(U_9259,hAPP(hAPP(c_Set_Oinsert(U_9255),U_9261),U_9260)) = hAPP(hAPP(U_9256,hAPP(U_9258,U_9261)),hAPP(U_9259,U_9260))
| hBOOL(hAPP(hAPP(c_member(U_9255),U_9261),U_9260))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9255),U_9260))
| ~ c_Finite__Set_Ofolding__image__simple(U_9254,U_9255,U_9256,U_9257,U_9258,U_9259) ),
inference(variable_rename,[status(thm)],[f_2557_1]) ).
fof(f_2557_3,plain,
! [U_9261,U_9260,U_9259,U_9258,U_9257,U_9256,U_9255] :
( ! [U_9254] : ~ c_Finite__Set_Ofolding__image__simple(U_9254,U_9255,U_9256,U_9257,U_9258,U_9259)
| hAPP(U_9259,hAPP(hAPP(c_Set_Oinsert(U_9255),U_9261),U_9260)) = hAPP(hAPP(U_9256,hAPP(U_9258,U_9261)),hAPP(U_9259,U_9260))
| hBOOL(hAPP(hAPP(c_member(U_9255),U_9261),U_9260))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9255),U_9260)) ),
inference(miniscope,[status(thm)],[f_2557_2]) ).
cnf(f_2557_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_9254,U_9255,U_9256,U_9257,U_9258,U_9259)
| hAPP(U_9259,hAPP(hAPP(c_Set_Oinsert(U_9255),U_9261),U_9260)) = hAPP(hAPP(U_9256,hAPP(U_9258,U_9261)),hAPP(U_9259,U_9260))
| hBOOL(hAPP(hAPP(c_member(U_9255),U_9261),U_9260))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9255),U_9260)) ),
inference(clausify,[status(thm)],[f_2557_3]) ).
fof(f_2558_1,plain,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oinsert__remove]) ).
fof(f_2558_2,plain,
! [U_9269,U_9268,U_9267,U_9266,U_9265,U_9264,U_9263,U_9262] :
( hAPP(U_9267,hAPP(hAPP(c_Set_Oinsert(U_9263),U_9269),U_9268)) = hAPP(hAPP(U_9264,hAPP(U_9266,U_9269)),hAPP(U_9267,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9263,tc_HOL_Obool)),U_9268),hAPP(hAPP(c_Set_Oinsert(U_9263),U_9269),c_Orderings_Obot__class_Obot(tc_fun(U_9263,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9263),U_9268))
| ~ c_Finite__Set_Ofolding__image__simple(U_9262,U_9263,U_9264,U_9265,U_9266,U_9267) ),
inference(variable_rename,[status(thm)],[f_2558_1]) ).
fof(f_2558_3,plain,
! [U_9269,U_9268,U_9267,U_9266,U_9265,U_9264,U_9263] :
( ! [U_9262] : ~ c_Finite__Set_Ofolding__image__simple(U_9262,U_9263,U_9264,U_9265,U_9266,U_9267)
| hAPP(U_9267,hAPP(hAPP(c_Set_Oinsert(U_9263),U_9269),U_9268)) = hAPP(hAPP(U_9264,hAPP(U_9266,U_9269)),hAPP(U_9267,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9263,tc_HOL_Obool)),U_9268),hAPP(hAPP(c_Set_Oinsert(U_9263),U_9269),c_Orderings_Obot__class_Obot(tc_fun(U_9263,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9263),U_9268)) ),
inference(miniscope,[status(thm)],[f_2558_2]) ).
cnf(f_2558_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_9262,U_9263,U_9264,U_9265,U_9266,U_9267)
| hAPP(U_9267,hAPP(hAPP(c_Set_Oinsert(U_9263),U_9269),U_9268)) = hAPP(hAPP(U_9264,hAPP(U_9266,U_9269)),hAPP(U_9267,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9263,tc_HOL_Obool)),U_9268),hAPP(hAPP(c_Set_Oinsert(U_9263),U_9269),c_Orderings_Obot__class_Obot(tc_fun(U_9263,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9263),U_9268)) ),
inference(clausify,[status(thm)],[f_2558_3]) ).
fof(f_2559_1,plain,
! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ),
inference(fof_nnf,[status(thm)],[fact_mlex__leq]) ).
fof(f_2559_2,plain,
! [U_9274,U_9273,U_9272,U_9271,U_9270] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9273,U_9273)),hAPP(hAPP(c_Product__Type_OPair(U_9273,U_9273),U_9271),U_9272)),c_Wellfounded_Omlex__prod(U_9273,U_9270,U_9274)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9273,U_9273)),hAPP(hAPP(c_Product__Type_OPair(U_9273,U_9273),U_9271),U_9272)),U_9274))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_9270,U_9271)),hAPP(U_9270,U_9272))) ),
inference(variable_rename,[status(thm)],[f_2559_1]) ).
cnf(f_2559_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9273,U_9273)),hAPP(hAPP(c_Product__Type_OPair(U_9273,U_9273),U_9271),U_9272)),c_Wellfounded_Omlex__prod(U_9273,U_9270,U_9274)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9273,U_9273)),hAPP(hAPP(c_Product__Type_OPair(U_9273,U_9273),U_9271),U_9272)),U_9274))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_9270,U_9271)),hAPP(U_9270,U_9272))) ),
inference(clausify,[status(thm)],[f_2559_2]) ).
fof(f_2560_1,plain,
! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ),
inference(fof_nnf,[status(thm)],[fact_mlex__less]) ).
fof(f_2560_2,plain,
! [U_9279,U_9278,U_9277,U_9276,U_9275] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9278,U_9278)),hAPP(hAPP(c_Product__Type_OPair(U_9278,U_9278),U_9276),U_9277)),c_Wellfounded_Omlex__prod(U_9278,U_9275,U_9279)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_9275,U_9276)),hAPP(U_9275,U_9277))) ),
inference(variable_rename,[status(thm)],[f_2560_1]) ).
cnf(f_2560_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9278,U_9278)),hAPP(hAPP(c_Product__Type_OPair(U_9278,U_9278),U_9276),U_9277)),c_Wellfounded_Omlex__prod(U_9278,U_9275,U_9279)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_9275,U_9276)),hAPP(U_9275,U_9277))) ),
inference(clausify,[status(thm)],[f_2560_2]) ).
fof(f_2561_1,plain,
! [V_S_2,V_f_2,T_b,T_c] :
( c_Orderings_Oord__class_OLeast(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2))) = hAPP(V_f_2,c_Orderings_Oord__class_OLeast(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))
| ! [B_x] :
( ? [B_xa] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa))
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_S_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
| ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
| ~ class_Orderings_Oorder(T_b)
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_Least__mono]) ).
fof(f_2561_2,plain,
! [U_9285,U_9284,U_9283,U_9282] :
( c_Orderings_Oord__class_OLeast(U_9282,hAPP(hAPP(c_COMBC(U_9282,tc_fun(U_9282,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9282)),hAPP(c_Set_Oimage(U_9283,U_9282,U_9284),U_9285))) = hAPP(U_9284,c_Orderings_Oord__class_OLeast(U_9283,hAPP(hAPP(c_COMBC(U_9283,tc_fun(U_9283,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9283)),U_9285)))
| ! [U_9281] :
( ? [U_9280] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9283),U_9281),U_9280))
& hBOOL(hAPP(hAPP(c_member(U_9283),U_9280),U_9285)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9283),U_9281),U_9285)) )
| ~ c_Orderings_Oorder__class_Omono(U_9283,U_9282,U_9284)
| ~ class_Orderings_Oorder(U_9283)
| ~ class_Orderings_Oorder(U_9282) ),
inference(variable_rename,[status(thm)],[f_2561_1]) ).
fof(f_2561_3,plain,
! [U_9285,U_9284,U_9283,U_9282] :
( c_Orderings_Oord__class_OLeast(U_9282,hAPP(hAPP(c_COMBC(U_9282,tc_fun(U_9282,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9282)),hAPP(c_Set_Oimage(U_9283,U_9282,U_9284),U_9285))) = hAPP(U_9284,c_Orderings_Oord__class_OLeast(U_9283,hAPP(hAPP(c_COMBC(U_9283,tc_fun(U_9283,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9283)),U_9285)))
| ! [U_9281] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9283),U_9281),sK183(U_9285,U_9284,U_9283,U_9282,U_9281)))
& hBOOL(hAPP(hAPP(c_member(U_9283),sK183(U_9285,U_9284,U_9283,U_9282,U_9281)),U_9285)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9283),U_9281),U_9285)) )
| ~ c_Orderings_Oorder__class_Omono(U_9283,U_9282,U_9284)
| ~ class_Orderings_Oorder(U_9283)
| ~ class_Orderings_Oorder(U_9282) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK183]),skolemize(U_9280,sK183(U_9285,U_9284,U_9283,U_9282,U_9281))],[f_2561_2]) ).
cnf(f_2561_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_9283),sK183(U_9285,U_9284,U_9283,U_9282,U_9281)),U_9285))
| ~ hBOOL(hAPP(hAPP(c_member(U_9283),U_9281),U_9285))
| c_Orderings_Oord__class_OLeast(U_9282,hAPP(hAPP(c_COMBC(U_9282,tc_fun(U_9282,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9282)),hAPP(c_Set_Oimage(U_9283,U_9282,U_9284),U_9285))) = hAPP(U_9284,c_Orderings_Oord__class_OLeast(U_9283,hAPP(hAPP(c_COMBC(U_9283,tc_fun(U_9283,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9283)),U_9285)))
| ~ c_Orderings_Oorder__class_Omono(U_9283,U_9282,U_9284)
| ~ class_Orderings_Oorder(U_9283)
| ~ class_Orderings_Oorder(U_9282) ),
inference(clausify,[status(thm)],[f_2561_3]) ).
cnf(f_2561_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9283),U_9281),sK183(U_9285,U_9284,U_9283,U_9282,U_9281)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9283),U_9281),U_9285))
| c_Orderings_Oord__class_OLeast(U_9282,hAPP(hAPP(c_COMBC(U_9282,tc_fun(U_9282,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9282)),hAPP(c_Set_Oimage(U_9283,U_9282,U_9284),U_9285))) = hAPP(U_9284,c_Orderings_Oord__class_OLeast(U_9283,hAPP(hAPP(c_COMBC(U_9283,tc_fun(U_9283,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9283)),U_9285)))
| ~ c_Orderings_Oorder__class_Omono(U_9283,U_9282,U_9284)
| ~ class_Orderings_Oorder(U_9283)
| ~ class_Orderings_Oorder(U_9282) ),
inference(clausify,[status(thm)],[f_2561_3]) ).
fof(f_2562_1,plain,
! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),V_A_2)))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
| V_A_2 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_def__coinduct3]) ).
fof(f_2562_2,plain,
! [U_9290,U_9289,U_9288,U_9287,U_9286] :
( hBOOL(hAPP(hAPP(c_member(U_9287),U_9289),U_9286))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9287,tc_HOL_Obool)),U_9290),hAPP(U_9288,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_9287,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_9287,tc_HOL_Obool),tc_fun(U_9287,tc_HOL_Obool),tc_fun(U_9287,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9287,tc_HOL_Obool),tc_fun(tc_fun(U_9287,tc_HOL_Obool),tc_fun(U_9287,tc_HOL_Obool)),tc_fun(U_9287,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9287,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_9287,tc_HOL_Obool),tc_fun(U_9287,tc_HOL_Obool),tc_fun(U_9287,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9287,tc_HOL_Obool),tc_fun(tc_fun(U_9287,tc_HOL_Obool),tc_fun(U_9287,tc_HOL_Obool)),tc_fun(U_9287,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9287,tc_HOL_Obool))),U_9288)),U_9290))),U_9286)))))
| ~ hBOOL(hAPP(hAPP(c_member(U_9287),U_9289),U_9290))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_9287,tc_HOL_Obool),tc_fun(U_9287,tc_HOL_Obool),U_9288)
| U_9286 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_9287,tc_HOL_Obool),U_9288) ),
inference(variable_rename,[status(thm)],[f_2562_1]) ).
cnf(f_2562_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9287),U_9289),U_9286))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9287,tc_HOL_Obool)),U_9290),hAPP(U_9288,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_9287,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_9287,tc_HOL_Obool),tc_fun(U_9287,tc_HOL_Obool),tc_fun(U_9287,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9287,tc_HOL_Obool),tc_fun(tc_fun(U_9287,tc_HOL_Obool),tc_fun(U_9287,tc_HOL_Obool)),tc_fun(U_9287,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9287,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_9287,tc_HOL_Obool),tc_fun(U_9287,tc_HOL_Obool),tc_fun(U_9287,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9287,tc_HOL_Obool),tc_fun(tc_fun(U_9287,tc_HOL_Obool),tc_fun(U_9287,tc_HOL_Obool)),tc_fun(U_9287,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9287,tc_HOL_Obool))),U_9288)),U_9290))),U_9286)))))
| ~ hBOOL(hAPP(hAPP(c_member(U_9287),U_9289),U_9290))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_9287,tc_HOL_Obool),tc_fun(U_9287,tc_HOL_Obool),U_9288)
| U_9286 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_9287,tc_HOL_Obool),U_9288) ),
inference(clausify,[status(thm)],[f_2562_2]) ).
fof(f_2563_1,plain,
! [V_t_2,T_b] :
( c_Inductive_Ocomplete__lattice__class_Olfp(T_b,hAPP(c_COMBK(T_b,T_b),V_t_2)) = V_t_2
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lfp__const]) ).
fof(f_2563_2,plain,
! [U_9292,U_9291] :
( c_Inductive_Ocomplete__lattice__class_Olfp(U_9291,hAPP(c_COMBK(U_9291,U_9291),U_9292)) = U_9292
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9291) ),
inference(variable_rename,[status(thm)],[f_2563_1]) ).
cnf(f_2563_3,plain,
( c_Inductive_Ocomplete__lattice__class_Olfp(U_9291,hAPP(c_COMBK(U_9291,U_9291),U_9292)) = U_9292
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9291) ),
inference(clausify,[status(thm)],[f_2563_2]) ).
fof(f_2564_1,plain,
! [V_P_2,T_b] :
( hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2)))
| ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1))
| ~ class_Orderings_Owellorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_LeastI__ex]) ).
fof(f_2564_2,plain,
! [U_9295,U_9294] :
( hBOOL(hAPP(U_9295,c_Orderings_Oord__class_OLeast(U_9294,U_9295)))
| ! [U_9293] : ~ hBOOL(hAPP(U_9295,U_9293))
| ~ class_Orderings_Owellorder(U_9294) ),
inference(variable_rename,[status(thm)],[f_2564_1]) ).
cnf(f_2564_3,plain,
( hBOOL(hAPP(U_9295,c_Orderings_Oord__class_OLeast(U_9294,U_9295)))
| ~ hBOOL(hAPP(U_9295,U_9293))
| ~ class_Orderings_Owellorder(U_9294) ),
inference(clausify,[status(thm)],[f_2564_2]) ).
fof(f_2565_1,plain,
! [V_k_2,V_P_2,T_b] :
( hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2)))
| ~ hBOOL(hAPP(V_P_2,V_k_2))
| ~ class_Orderings_Owellorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_LeastI]) ).
fof(f_2565_2,plain,
! [U_9298,U_9297,U_9296] :
( hBOOL(hAPP(U_9297,c_Orderings_Oord__class_OLeast(U_9296,U_9297)))
| ~ hBOOL(hAPP(U_9297,U_9298))
| ~ class_Orderings_Owellorder(U_9296) ),
inference(variable_rename,[status(thm)],[f_2565_1]) ).
cnf(f_2565_3,plain,
( hBOOL(hAPP(U_9297,c_Orderings_Oord__class_OLeast(U_9296,U_9297)))
| ~ hBOOL(hAPP(U_9297,U_9298))
| ~ class_Orderings_Owellorder(U_9296) ),
inference(clausify,[status(thm)],[f_2565_2]) ).
fof(f_2566_1,plain,
! [V_A_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_A_2)),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lfp__lowerbound]) ).
fof(f_2566_2,plain,
! [U_9301,U_9300,U_9299] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9299),c_Inductive_Ocomplete__lattice__class_Olfp(U_9299,U_9300)),U_9301))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9299),hAPP(U_9300,U_9301)),U_9301))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9299) ),
inference(variable_rename,[status(thm)],[f_2566_1]) ).
cnf(f_2566_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9299),c_Inductive_Ocomplete__lattice__class_Olfp(U_9299,U_9300)),U_9301))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9299),hAPP(U_9300,U_9301)),U_9301))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9299) ),
inference(clausify,[status(thm)],[f_2566_2]) ).
fof(f_2567_1,plain,
! [V_f_2,T_b] :
( c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2) = hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lfp__unfold]) ).
fof(f_2567_2,plain,
! [U_9303,U_9302] :
( c_Inductive_Ocomplete__lattice__class_Olfp(U_9302,U_9303) = hAPP(U_9303,c_Inductive_Ocomplete__lattice__class_Olfp(U_9302,U_9303))
| ~ c_Orderings_Oorder__class_Omono(U_9302,U_9302,U_9303)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9302) ),
inference(variable_rename,[status(thm)],[f_2567_1]) ).
cnf(f_2567_3,plain,
( c_Inductive_Ocomplete__lattice__class_Olfp(U_9302,U_9303) = hAPP(U_9303,c_Inductive_Ocomplete__lattice__class_Olfp(U_9302,U_9303))
| ~ c_Orderings_Oorder__class_Omono(U_9302,U_9302,U_9303)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9302) ),
inference(clausify,[status(thm)],[f_2567_2]) ).
fof(f_2568_1,plain,
! [V_f_2,V_h_2,T_b] :
( V_h_2 = hAPP(V_f_2,V_h_2)
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| V_h_2 != c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_def__lfp__unfold]) ).
fof(f_2568_2,plain,
! [U_9306,U_9305,U_9304] :
( U_9305 = hAPP(U_9306,U_9305)
| ~ c_Orderings_Oorder__class_Omono(U_9304,U_9304,U_9306)
| U_9305 != c_Inductive_Ocomplete__lattice__class_Olfp(U_9304,U_9306)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9304) ),
inference(variable_rename,[status(thm)],[f_2568_1]) ).
cnf(f_2568_3,plain,
( U_9305 = hAPP(U_9306,U_9305)
| ~ c_Orderings_Oorder__class_Omono(U_9304,U_9304,U_9306)
| U_9305 != c_Inductive_Ocomplete__lattice__class_Olfp(U_9304,U_9306)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9304) ),
inference(clausify,[status(thm)],[f_2568_2]) ).
fof(f_2569_1,plain,
! [V_k_2,V_P_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Orderings_Oord__class_OLeast(T_b,V_P_2)),V_k_2))
| ~ hBOOL(hAPP(V_P_2,V_k_2))
| ~ class_Orderings_Owellorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Least__le]) ).
fof(f_2569_2,plain,
! [U_9309,U_9308,U_9307] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9307),c_Orderings_Oord__class_OLeast(U_9307,U_9308)),U_9309))
| ~ hBOOL(hAPP(U_9308,U_9309))
| ~ class_Orderings_Owellorder(U_9307) ),
inference(variable_rename,[status(thm)],[f_2569_1]) ).
cnf(f_2569_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9307),c_Orderings_Oord__class_OLeast(U_9307,U_9308)),U_9309))
| ~ hBOOL(hAPP(U_9308,U_9309))
| ~ class_Orderings_Owellorder(U_9307) ),
inference(clausify,[status(thm)],[f_2569_2]) ).
fof(f_2570_1,plain,
! [V_P_2,V_k_2,T_b] :
( ~ hBOOL(hAPP(V_P_2,V_k_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),c_Orderings_Oord__class_OLeast(T_b,V_P_2)))
| ~ class_Orderings_Owellorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_not__less__Least]) ).
fof(f_2570_2,plain,
! [U_9312,U_9311,U_9310] :
( ~ hBOOL(hAPP(U_9312,U_9311))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9310),U_9311),c_Orderings_Oord__class_OLeast(U_9310,U_9312)))
| ~ class_Orderings_Owellorder(U_9310) ),
inference(variable_rename,[status(thm)],[f_2570_1]) ).
cnf(f_2570_3,plain,
( ~ hBOOL(hAPP(U_9312,U_9311))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9310),U_9311),c_Orderings_Oord__class_OLeast(U_9310,U_9312)))
| ~ class_Orderings_Owellorder(U_9310) ),
inference(clausify,[status(thm)],[f_2570_2]) ).
fof(f_2571_1,plain,
! [V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2))),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lfp__lemma2]) ).
fof(f_2571_2,plain,
! [U_9314,U_9313] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9313),hAPP(U_9314,c_Inductive_Ocomplete__lattice__class_Olfp(U_9313,U_9314))),c_Inductive_Ocomplete__lattice__class_Olfp(U_9313,U_9314)))
| ~ c_Orderings_Oorder__class_Omono(U_9313,U_9313,U_9314)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9313) ),
inference(variable_rename,[status(thm)],[f_2571_1]) ).
cnf(f_2571_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9313),hAPP(U_9314,c_Inductive_Ocomplete__lattice__class_Olfp(U_9313,U_9314))),c_Inductive_Ocomplete__lattice__class_Olfp(U_9313,U_9314)))
| ~ c_Orderings_Oorder__class_Omono(U_9313,U_9313,U_9314)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9313) ),
inference(clausify,[status(thm)],[f_2571_2]) ).
fof(f_2572_1,plain,
! [V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2))))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lfp__lemma3]) ).
fof(f_2572_2,plain,
! [U_9316,U_9315] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9315),c_Inductive_Ocomplete__lattice__class_Olfp(U_9315,U_9316)),hAPP(U_9316,c_Inductive_Ocomplete__lattice__class_Olfp(U_9315,U_9316))))
| ~ c_Orderings_Oorder__class_Omono(U_9315,U_9315,U_9316)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9315) ),
inference(variable_rename,[status(thm)],[f_2572_1]) ).
cnf(f_2572_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9315),c_Inductive_Ocomplete__lattice__class_Olfp(U_9315,U_9316)),hAPP(U_9316,c_Inductive_Ocomplete__lattice__class_Olfp(U_9315,U_9316))))
| ~ c_Orderings_Oorder__class_Omono(U_9315,U_9315,U_9316)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_9315) ),
inference(clausify,[status(thm)],[f_2572_2]) ).
fof(f_2573_1,plain,
! [V_na_2,V_P_2] :
( c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_OSuc)))
| hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(V_P_2,V_na_2)) ),
inference(fof_nnf,[status(thm)],[fact_Least__Suc]) ).
fof(f_2573_2,plain,
! [U_9318,U_9317] :
( c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_9317) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),U_9317),c_Nat_OSuc)))
| hBOOL(hAPP(U_9317,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(U_9317,U_9318)) ),
inference(variable_rename,[status(thm)],[f_2573_1]) ).
cnf(f_2573_3,plain,
( c_Orderings_Oord__class_OLeast(tc_Nat_Onat,U_9317) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),U_9317),c_Nat_OSuc)))
| hBOOL(hAPP(U_9317,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(U_9317,U_9318)) ),
inference(clausify,[status(thm)],[f_2573_2]) ).
fof(f_2574_1,plain,
! [V_f_2,V_X_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))))))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))))) ),
inference(fof_nnf,[status(thm)],[fact_coinduct3__lemma]) ).
fof(f_2574_2,plain,
! [U_9321,U_9320,U_9319] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9319,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_9319,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9319,tc_HOL_Obool),tc_fun(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),tc_fun(U_9319,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9319,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9319,tc_HOL_Obool),tc_fun(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),tc_fun(U_9319,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9319,tc_HOL_Obool))),U_9321)),U_9320))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_9319,tc_HOL_Obool),U_9321)))),hAPP(U_9321,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_9319,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9319,tc_HOL_Obool),tc_fun(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),tc_fun(U_9319,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9319,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9319,tc_HOL_Obool),tc_fun(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),tc_fun(U_9319,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9319,tc_HOL_Obool))),U_9321)),U_9320))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_9319,tc_HOL_Obool),U_9321))))))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool),U_9321)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9319,tc_HOL_Obool)),U_9320),hAPP(U_9321,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_9319,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9319,tc_HOL_Obool),tc_fun(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),tc_fun(U_9319,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9319,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9319,tc_HOL_Obool),tc_fun(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),tc_fun(U_9319,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9319,tc_HOL_Obool))),U_9321)),U_9320))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_9319,tc_HOL_Obool),U_9321)))))) ),
inference(variable_rename,[status(thm)],[f_2574_1]) ).
cnf(f_2574_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9319,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_9319,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9319,tc_HOL_Obool),tc_fun(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),tc_fun(U_9319,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9319,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9319,tc_HOL_Obool),tc_fun(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),tc_fun(U_9319,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9319,tc_HOL_Obool))),U_9321)),U_9320))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_9319,tc_HOL_Obool),U_9321)))),hAPP(U_9321,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_9319,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9319,tc_HOL_Obool),tc_fun(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),tc_fun(U_9319,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9319,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9319,tc_HOL_Obool),tc_fun(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),tc_fun(U_9319,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9319,tc_HOL_Obool))),U_9321)),U_9320))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_9319,tc_HOL_Obool),U_9321))))))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool),U_9321)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9319,tc_HOL_Obool)),U_9320),hAPP(U_9321,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_9319,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9319,tc_HOL_Obool),tc_fun(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),tc_fun(U_9319,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9319,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9319,tc_HOL_Obool),tc_fun(tc_fun(U_9319,tc_HOL_Obool),tc_fun(U_9319,tc_HOL_Obool)),tc_fun(U_9319,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9319,tc_HOL_Obool))),U_9321)),U_9320))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_9319,tc_HOL_Obool),U_9321)))))) ),
inference(clausify,[status(thm)],[f_2574_2]) ).
fof(f_2575_1,plain,
! [V_X_2,V_a_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_coinduct3]) ).
fof(f_2575_2,plain,
! [U_9325,U_9324,U_9323,U_9322] :
( hBOOL(hAPP(hAPP(c_member(U_9322),U_9324),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_9322,tc_HOL_Obool),U_9323)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9322,tc_HOL_Obool)),U_9325),hAPP(U_9323,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_9322,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_9322,tc_HOL_Obool),tc_fun(U_9322,tc_HOL_Obool),tc_fun(U_9322,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9322,tc_HOL_Obool),tc_fun(tc_fun(U_9322,tc_HOL_Obool),tc_fun(U_9322,tc_HOL_Obool)),tc_fun(U_9322,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9322,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_9322,tc_HOL_Obool),tc_fun(U_9322,tc_HOL_Obool),tc_fun(U_9322,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9322,tc_HOL_Obool),tc_fun(tc_fun(U_9322,tc_HOL_Obool),tc_fun(U_9322,tc_HOL_Obool)),tc_fun(U_9322,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9322,tc_HOL_Obool))),U_9323)),U_9325))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_9322,tc_HOL_Obool),U_9323))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_9322),U_9324),U_9325))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_9322,tc_HOL_Obool),tc_fun(U_9322,tc_HOL_Obool),U_9323) ),
inference(variable_rename,[status(thm)],[f_2575_1]) ).
cnf(f_2575_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9322),U_9324),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_9322,tc_HOL_Obool),U_9323)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9322,tc_HOL_Obool)),U_9325),hAPP(U_9323,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_9322,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_9322,tc_HOL_Obool),tc_fun(U_9322,tc_HOL_Obool),tc_fun(U_9322,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9322,tc_HOL_Obool),tc_fun(tc_fun(U_9322,tc_HOL_Obool),tc_fun(U_9322,tc_HOL_Obool)),tc_fun(U_9322,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9322,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_9322,tc_HOL_Obool),tc_fun(U_9322,tc_HOL_Obool),tc_fun(U_9322,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9322,tc_HOL_Obool),tc_fun(tc_fun(U_9322,tc_HOL_Obool),tc_fun(U_9322,tc_HOL_Obool)),tc_fun(U_9322,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9322,tc_HOL_Obool))),U_9323)),U_9325))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_9322,tc_HOL_Obool),U_9323))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_9322),U_9324),U_9325))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_9322,tc_HOL_Obool),tc_fun(U_9322,tc_HOL_Obool),U_9323) ),
inference(clausify,[status(thm)],[f_2575_2]) ).
fof(f_2576_1,plain,
! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_K_2)))
| ? [B_i] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2)) )
| ~ class_Rings_Osemiring__1(T_c)
| ~ class_Groups_Oordered__ab__semigroup__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__bounded]) ).
fof(f_2576_2,plain,
! [U_9331,U_9330,U_9329,U_9328,U_9327] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9327),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9328,U_9327),U_9330),U_9329)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9327),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9327),hAPP(c_Finite__Set_Ocard(U_9328),U_9329))),U_9331)))
| ? [U_9326] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9327),hAPP(U_9330,U_9326)),U_9331))
& hBOOL(hAPP(hAPP(c_member(U_9328),U_9326),U_9329)) )
| ~ class_Rings_Osemiring__1(U_9327)
| ~ class_Groups_Oordered__ab__semigroup__add(U_9327) ),
inference(variable_rename,[status(thm)],[f_2576_1]) ).
fof(f_2576_3,plain,
! [U_9331,U_9330,U_9329,U_9328,U_9327] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9327),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9328,U_9327),U_9330),U_9329)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9327),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9327),hAPP(c_Finite__Set_Ocard(U_9328),U_9329))),U_9331)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9327),hAPP(U_9330,sK184(U_9331,U_9330,U_9329,U_9328,U_9327))),U_9331))
& hBOOL(hAPP(hAPP(c_member(U_9328),sK184(U_9331,U_9330,U_9329,U_9328,U_9327)),U_9329)) )
| ~ class_Rings_Osemiring__1(U_9327)
| ~ class_Groups_Oordered__ab__semigroup__add(U_9327) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK184]),skolemize(U_9326,sK184(U_9331,U_9330,U_9329,U_9328,U_9327))],[f_2576_2]) ).
cnf(f_2576_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_9328),sK184(U_9331,U_9330,U_9329,U_9328,U_9327)),U_9329))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9327),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9328,U_9327),U_9330),U_9329)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9327),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9327),hAPP(c_Finite__Set_Ocard(U_9328),U_9329))),U_9331)))
| ~ class_Rings_Osemiring__1(U_9327)
| ~ class_Groups_Oordered__ab__semigroup__add(U_9327) ),
inference(clausify,[status(thm)],[f_2576_3]) ).
cnf(f_2576_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9327),hAPP(U_9330,sK184(U_9331,U_9330,U_9329,U_9328,U_9327))),U_9331))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9327),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9328,U_9327),U_9330),U_9329)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9327),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9327),hAPP(c_Finite__Set_Ocard(U_9328),U_9329))),U_9331)))
| ~ class_Rings_Osemiring__1(U_9327)
| ~ class_Groups_Oordered__ab__semigroup__add(U_9327) ),
inference(clausify,[status(thm)],[f_2576_3]) ).
fof(f_2577_1,plain,
! [V_k_2,V_A_2,T_b] :
( ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
| ! [B_b,B_B] :
( ( B_B != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Finite__Set_Ocard(T_b),B_B) != V_k_2
| hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
| V_A_2 != hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) ) )
& ( ? [B_b,B_B] :
( ( B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
& ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
& V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B) )
| hAPP(c_Finite__Set_Ocard(T_b),V_A_2) != hAPP(c_Nat_OSuc,V_k_2) ) ),
inference(fof_nnf,[status(thm)],[fact_card__Suc__eq]) ).
fof(f_2577_2,plain,
! [U_9338,U_9337,U_9336] :
( ( hAPP(c_Finite__Set_Ocard(U_9336),U_9337) = hAPP(c_Nat_OSuc,U_9338)
| ! [U_9335,U_9334] :
( ( U_9334 != c_Orderings_Obot__class_Obot(tc_fun(U_9336,tc_HOL_Obool))
& U_9338 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Finite__Set_Ocard(U_9336),U_9334) != U_9338
| hBOOL(hAPP(hAPP(c_member(U_9336),U_9335),U_9334))
| U_9337 != hAPP(hAPP(c_Set_Oinsert(U_9336),U_9335),U_9334) ) )
& ( ? [U_9333,U_9332] :
( ( U_9332 = c_Orderings_Obot__class_Obot(tc_fun(U_9336,tc_HOL_Obool))
| U_9338 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hAPP(c_Finite__Set_Ocard(U_9336),U_9332) = U_9338
& ~ hBOOL(hAPP(hAPP(c_member(U_9336),U_9333),U_9332))
& U_9337 = hAPP(hAPP(c_Set_Oinsert(U_9336),U_9333),U_9332) )
| hAPP(c_Finite__Set_Ocard(U_9336),U_9337) != hAPP(c_Nat_OSuc,U_9338) ) ),
inference(variable_rename,[status(thm)],[f_2577_1]) ).
fof(f_2577_3,plain,
( ! [U_9344,U_9342,U_9340] :
( hAPP(c_Finite__Set_Ocard(U_9340),U_9342) = hAPP(c_Nat_OSuc,U_9344)
| ! [U_9335,U_9334] :
( ( U_9334 != c_Orderings_Obot__class_Obot(tc_fun(U_9340,tc_HOL_Obool))
& U_9344 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Finite__Set_Ocard(U_9340),U_9334) != U_9344
| hBOOL(hAPP(hAPP(c_member(U_9340),U_9335),U_9334))
| U_9342 != hAPP(hAPP(c_Set_Oinsert(U_9340),U_9335),U_9334) ) )
& ! [U_9343,U_9341,U_9339] :
( ? [U_9333,U_9332] :
( ( U_9332 = c_Orderings_Obot__class_Obot(tc_fun(U_9339,tc_HOL_Obool))
| U_9343 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hAPP(c_Finite__Set_Ocard(U_9339),U_9332) = U_9343
& ~ hBOOL(hAPP(hAPP(c_member(U_9339),U_9333),U_9332))
& U_9341 = hAPP(hAPP(c_Set_Oinsert(U_9339),U_9333),U_9332) )
| hAPP(c_Finite__Set_Ocard(U_9339),U_9341) != hAPP(c_Nat_OSuc,U_9343) ) ),
inference(miniscope,[status(thm)],[f_2577_2]) ).
fof(f_2577_4,plain,
( ! [U_9344,U_9342,U_9340] :
( hAPP(c_Finite__Set_Ocard(U_9340),U_9342) = hAPP(c_Nat_OSuc,U_9344)
| ! [U_9335,U_9334] :
( ( U_9334 != c_Orderings_Obot__class_Obot(tc_fun(U_9340,tc_HOL_Obool))
& U_9344 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Finite__Set_Ocard(U_9340),U_9334) != U_9344
| hBOOL(hAPP(hAPP(c_member(U_9340),U_9335),U_9334))
| U_9342 != hAPP(hAPP(c_Set_Oinsert(U_9340),U_9335),U_9334) ) )
& ! [U_9343,U_9341,U_9339] :
( ? [U_9332] :
( ( U_9332 = c_Orderings_Obot__class_Obot(tc_fun(U_9339,tc_HOL_Obool))
| U_9343 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hAPP(c_Finite__Set_Ocard(U_9339),U_9332) = U_9343
& ~ hBOOL(hAPP(hAPP(c_member(U_9339),sK185(U_9343,U_9341,U_9339)),U_9332))
& U_9341 = hAPP(hAPP(c_Set_Oinsert(U_9339),sK185(U_9343,U_9341,U_9339)),U_9332) )
| hAPP(c_Finite__Set_Ocard(U_9339),U_9341) != hAPP(c_Nat_OSuc,U_9343) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK185]),skolemize(U_9333,sK185(U_9343,U_9341,U_9339))],[f_2577_3]) ).
fof(f_2577_5,plain,
( ! [U_9344,U_9342,U_9340] :
( hAPP(c_Finite__Set_Ocard(U_9340),U_9342) = hAPP(c_Nat_OSuc,U_9344)
| ! [U_9335,U_9334] :
( ( U_9334 != c_Orderings_Obot__class_Obot(tc_fun(U_9340,tc_HOL_Obool))
& U_9344 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| hAPP(c_Finite__Set_Ocard(U_9340),U_9334) != U_9344
| hBOOL(hAPP(hAPP(c_member(U_9340),U_9335),U_9334))
| U_9342 != hAPP(hAPP(c_Set_Oinsert(U_9340),U_9335),U_9334) ) )
& ! [U_9343,U_9341,U_9339] :
( ( ( sK186(U_9343,U_9341,U_9339) = c_Orderings_Obot__class_Obot(tc_fun(U_9339,tc_HOL_Obool))
| U_9343 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& hAPP(c_Finite__Set_Ocard(U_9339),sK186(U_9343,U_9341,U_9339)) = U_9343
& ~ hBOOL(hAPP(hAPP(c_member(U_9339),sK185(U_9343,U_9341,U_9339)),sK186(U_9343,U_9341,U_9339)))
& U_9341 = hAPP(hAPP(c_Set_Oinsert(U_9339),sK185(U_9343,U_9341,U_9339)),sK186(U_9343,U_9341,U_9339)) )
| hAPP(c_Finite__Set_Ocard(U_9339),U_9341) != hAPP(c_Nat_OSuc,U_9343) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK186]),skolemize(U_9332,sK186(U_9343,U_9341,U_9339))],[f_2577_4]) ).
cnf(f_2577_6,plain,
( U_9341 = hAPP(hAPP(c_Set_Oinsert(U_9339),sK185(U_9343,U_9341,U_9339)),sK186(U_9343,U_9341,U_9339))
| hAPP(c_Finite__Set_Ocard(U_9339),U_9341) != hAPP(c_Nat_OSuc,U_9343) ),
inference(clausify,[status(thm)],[f_2577_5]) ).
cnf(f_2577_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_9339),sK185(U_9343,U_9341,U_9339)),sK186(U_9343,U_9341,U_9339)))
| hAPP(c_Finite__Set_Ocard(U_9339),U_9341) != hAPP(c_Nat_OSuc,U_9343) ),
inference(clausify,[status(thm)],[f_2577_5]) ).
cnf(f_2577_8,plain,
( hAPP(c_Finite__Set_Ocard(U_9339),sK186(U_9343,U_9341,U_9339)) = U_9343
| hAPP(c_Finite__Set_Ocard(U_9339),U_9341) != hAPP(c_Nat_OSuc,U_9343) ),
inference(clausify,[status(thm)],[f_2577_5]) ).
cnf(f_2577_9,plain,
( sK186(U_9343,U_9341,U_9339) = c_Orderings_Obot__class_Obot(tc_fun(U_9339,tc_HOL_Obool))
| U_9343 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Finite__Set_Ocard(U_9339),U_9341) != hAPP(c_Nat_OSuc,U_9343) ),
inference(clausify,[status(thm)],[f_2577_5]) ).
cnf(f_2577_10,plain,
( U_9344 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Finite__Set_Ocard(U_9340),U_9334) != U_9344
| hBOOL(hAPP(hAPP(c_member(U_9340),U_9335),U_9334))
| U_9342 != hAPP(hAPP(c_Set_Oinsert(U_9340),U_9335),U_9334)
| hAPP(c_Finite__Set_Ocard(U_9340),U_9342) = hAPP(c_Nat_OSuc,U_9344) ),
inference(clausify,[status(thm)],[f_2577_5]) ).
cnf(f_2577_11,plain,
( U_9334 != c_Orderings_Obot__class_Obot(tc_fun(U_9340,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_9340),U_9334) != U_9344
| hBOOL(hAPP(hAPP(c_member(U_9340),U_9335),U_9334))
| U_9342 != hAPP(hAPP(c_Set_Oinsert(U_9340),U_9335),U_9334)
| hAPP(c_Finite__Set_Ocard(U_9340),U_9342) = hAPP(c_Nat_OSuc,U_9344) ),
inference(clausify,[status(thm)],[f_2577_5]) ).
fof(f_2578_1,plain,
! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
| ~ hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) )
& ( ( hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2))
& hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OatLeastLessThan__iff]) ).
fof(f_2578_2,plain,
! [U_9350,U_9349,U_9348,U_9347,U_9346,U_9345] :
( ( hBOOL(hAPP(hAPP(c_member(U_9345),U_9346),c_SetInterval_Oord_OatLeastLessThan(U_9345,U_9347,U_9348,U_9349,U_9350)))
| ~ hBOOL(hAPP(hAPP(U_9348,U_9346),U_9350))
| ~ hBOOL(hAPP(hAPP(U_9347,U_9349),U_9346)) )
& ( ( hBOOL(hAPP(hAPP(U_9348,U_9346),U_9350))
& hBOOL(hAPP(hAPP(U_9347,U_9349),U_9346)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9345),U_9346),c_SetInterval_Oord_OatLeastLessThan(U_9345,U_9347,U_9348,U_9349,U_9350))) ) ),
inference(variable_rename,[status(thm)],[f_2578_1]) ).
fof(f_2578_3,plain,
( ! [U_9362,U_9360,U_9358,U_9356,U_9354] :
( ! [U_9352] : hBOOL(hAPP(hAPP(c_member(U_9352),U_9354),c_SetInterval_Oord_OatLeastLessThan(U_9352,U_9356,U_9358,U_9360,U_9362)))
| ~ hBOOL(hAPP(hAPP(U_9358,U_9354),U_9362))
| ~ hBOOL(hAPP(hAPP(U_9356,U_9360),U_9354)) )
& ! [U_9361,U_9359,U_9357,U_9355,U_9353] :
( ! [U_9351] : ~ hBOOL(hAPP(hAPP(c_member(U_9351),U_9353),c_SetInterval_Oord_OatLeastLessThan(U_9351,U_9355,U_9357,U_9359,U_9361)))
| ( hBOOL(hAPP(hAPP(U_9357,U_9353),U_9361))
& hBOOL(hAPP(hAPP(U_9355,U_9359),U_9353)) ) ) ),
inference(miniscope,[status(thm)],[f_2578_2]) ).
cnf(f_2578_4,plain,
( hBOOL(hAPP(hAPP(U_9355,U_9359),U_9353))
| ~ hBOOL(hAPP(hAPP(c_member(U_9351),U_9353),c_SetInterval_Oord_OatLeastLessThan(U_9351,U_9355,U_9357,U_9359,U_9361))) ),
inference(clausify,[status(thm)],[f_2578_3]) ).
cnf(f_2578_5,plain,
( hBOOL(hAPP(hAPP(U_9357,U_9353),U_9361))
| ~ hBOOL(hAPP(hAPP(c_member(U_9351),U_9353),c_SetInterval_Oord_OatLeastLessThan(U_9351,U_9355,U_9357,U_9359,U_9361))) ),
inference(clausify,[status(thm)],[f_2578_3]) ).
cnf(f_2578_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9352),U_9354),c_SetInterval_Oord_OatLeastLessThan(U_9352,U_9356,U_9358,U_9360,U_9362)))
| ~ hBOOL(hAPP(hAPP(U_9358,U_9354),U_9362))
| ~ hBOOL(hAPP(hAPP(U_9356,U_9360),U_9354)) ),
inference(clausify,[status(thm)],[f_2578_3]) ).
fof(f_2579_1,plain,
! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
| ~ hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
| ~ hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) )
& ( ( hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2))
& hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanAtMost__iff]) ).
fof(f_2579_2,plain,
! [U_9368,U_9367,U_9366,U_9365,U_9364,U_9363] :
( ( hBOOL(hAPP(hAPP(c_member(U_9363),U_9364),c_SetInterval_Oord_OgreaterThanAtMost(U_9363,U_9365,U_9366,U_9367,U_9368)))
| ~ hBOOL(hAPP(hAPP(U_9365,U_9364),U_9368))
| ~ hBOOL(hAPP(hAPP(U_9366,U_9367),U_9364)) )
& ( ( hBOOL(hAPP(hAPP(U_9365,U_9364),U_9368))
& hBOOL(hAPP(hAPP(U_9366,U_9367),U_9364)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9363),U_9364),c_SetInterval_Oord_OgreaterThanAtMost(U_9363,U_9365,U_9366,U_9367,U_9368))) ) ),
inference(variable_rename,[status(thm)],[f_2579_1]) ).
fof(f_2579_3,plain,
( ! [U_9380,U_9378,U_9376,U_9374,U_9372] :
( ! [U_9370] : hBOOL(hAPP(hAPP(c_member(U_9370),U_9372),c_SetInterval_Oord_OgreaterThanAtMost(U_9370,U_9374,U_9376,U_9378,U_9380)))
| ~ hBOOL(hAPP(hAPP(U_9374,U_9372),U_9380))
| ~ hBOOL(hAPP(hAPP(U_9376,U_9378),U_9372)) )
& ! [U_9379,U_9377,U_9375,U_9373,U_9371] :
( ! [U_9369] : ~ hBOOL(hAPP(hAPP(c_member(U_9369),U_9371),c_SetInterval_Oord_OgreaterThanAtMost(U_9369,U_9373,U_9375,U_9377,U_9379)))
| ( hBOOL(hAPP(hAPP(U_9373,U_9371),U_9379))
& hBOOL(hAPP(hAPP(U_9375,U_9377),U_9371)) ) ) ),
inference(miniscope,[status(thm)],[f_2579_2]) ).
cnf(f_2579_4,plain,
( hBOOL(hAPP(hAPP(U_9375,U_9377),U_9371))
| ~ hBOOL(hAPP(hAPP(c_member(U_9369),U_9371),c_SetInterval_Oord_OgreaterThanAtMost(U_9369,U_9373,U_9375,U_9377,U_9379))) ),
inference(clausify,[status(thm)],[f_2579_3]) ).
cnf(f_2579_5,plain,
( hBOOL(hAPP(hAPP(U_9373,U_9371),U_9379))
| ~ hBOOL(hAPP(hAPP(c_member(U_9369),U_9371),c_SetInterval_Oord_OgreaterThanAtMost(U_9369,U_9373,U_9375,U_9377,U_9379))) ),
inference(clausify,[status(thm)],[f_2579_3]) ).
cnf(f_2579_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9370),U_9372),c_SetInterval_Oord_OgreaterThanAtMost(U_9370,U_9374,U_9376,U_9378,U_9380)))
| ~ hBOOL(hAPP(hAPP(U_9374,U_9372),U_9380))
| ~ hBOOL(hAPP(hAPP(U_9376,U_9378),U_9372)) ),
inference(clausify,[status(thm)],[f_2579_3]) ).
fof(f_2580_1,plain,
! [V_k_2,V_l_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)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty]) ).
fof(f_2580_2,plain,
! [U_9382,U_9381] :
( 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)))),U_9382,U_9381) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9381),U_9382)) ),
inference(variable_rename,[status(thm)],[f_2580_1]) ).
cnf(f_2580_3,plain,
( 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)))),U_9382,U_9381) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9381),U_9382)) ),
inference(clausify,[status(thm)],[f_2580_2]) ).
fof(f_2581_1,plain,
! [V_a_2,V_b_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)) ),
inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastLessThan__empty]) ).
fof(f_2581_2,plain,
! [U_9384,U_9383] :
( 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)))),U_9384,U_9383) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9383),U_9384)) ),
inference(variable_rename,[status(thm)],[f_2581_1]) ).
cnf(f_2581_3,plain,
( 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)))),U_9384,U_9383) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9383),U_9384)) ),
inference(clausify,[status(thm)],[f_2581_2]) ).
fof(f_2582_1,plain,
! [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)) ) )
& ( 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))
| 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty__iff]) ).
fof(f_2582_2,plain,
! [U_9386,U_9385] :
( ( 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)))),U_9385,U_9386) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9386),U_9385))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9385),U_9386)) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9386),U_9385))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9385),U_9386))
| 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)))),U_9385,U_9386) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2582_1]) ).
fof(f_2582_3,plain,
( ! [U_9390,U_9388] :
( 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)))),U_9388,U_9390) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9390),U_9388))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9388),U_9390)) ) )
& ! [U_9389,U_9387] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9389),U_9387))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9387),U_9389))
| 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)))),U_9387,U_9389) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2582_2]) ).
cnf(f_2582_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9389),U_9387))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9387),U_9389))
| 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)))),U_9387,U_9389) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2582_3]) ).
cnf(f_2582_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9388),U_9390))
| 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)))),U_9388,U_9390) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2582_3]) ).
cnf(f_2582_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9390),U_9388))
| 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)))),U_9388,U_9390) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2582_3]) ).
fof(f_2583_1,plain,
! [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)) ) )
& ( 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))
| 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)) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastLessThan__empty__iff]) ).
fof(f_2583_2,plain,
! [U_9392,U_9391] :
( ( 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)))),U_9391,U_9392) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9392),U_9391))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9391),U_9392)) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9392),U_9391))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9391),U_9392))
| 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)))),U_9391,U_9392) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2583_1]) ).
fof(f_2583_3,plain,
( ! [U_9396,U_9394] :
( 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)))),U_9394,U_9396) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9396),U_9394))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9394),U_9396)) ) )
& ! [U_9395,U_9393] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9395),U_9393))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9393),U_9395))
| 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)))),U_9393,U_9395) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2583_2]) ).
cnf(f_2583_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9395),U_9393))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9393),U_9395))
| 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)))),U_9393,U_9395) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2583_3]) ).
cnf(f_2583_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9394),U_9396))
| 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)))),U_9394,U_9396) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2583_3]) ).
cnf(f_2583_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9396),U_9394))
| 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)))),U_9394,U_9396) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2583_3]) ).
fof(f_2584_1,plain,
! [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)) ) )
& ( 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))
| 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) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty__iff2]) ).
fof(f_2584_2,plain,
! [U_9398,U_9397] :
( ( 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)))),U_9397,U_9398)
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9398),U_9397))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9397),U_9398)) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9398),U_9397))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9397),U_9398))
| 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)))),U_9397,U_9398) ) ),
inference(variable_rename,[status(thm)],[f_2584_1]) ).
fof(f_2584_3,plain,
( ! [U_9402,U_9400] :
( 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)))),U_9400,U_9402)
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9402),U_9400))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9400),U_9402)) ) )
& ! [U_9401,U_9399] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9401),U_9399))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9399),U_9401))
| 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)))),U_9399,U_9401) ) ),
inference(miniscope,[status(thm)],[f_2584_2]) ).
cnf(f_2584_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9401),U_9399))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9399),U_9401))
| 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)))),U_9399,U_9401) ),
inference(clausify,[status(thm)],[f_2584_3]) ).
cnf(f_2584_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9400),U_9402))
| 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)))),U_9400,U_9402) ),
inference(clausify,[status(thm)],[f_2584_3]) ).
cnf(f_2584_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9402),U_9400))
| 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)))),U_9400,U_9402) ),
inference(clausify,[status(thm)],[f_2584_3]) ).
fof(f_2585_1,plain,
! [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)) ) )
& ( 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))
| 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) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastLessThan__empty__iff2]) ).
fof(f_2585_2,plain,
! [U_9404,U_9403] :
( ( 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)))),U_9403,U_9404)
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9404),U_9403))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9403),U_9404)) ) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9404),U_9403))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9403),U_9404))
| 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)))),U_9403,U_9404) ) ),
inference(variable_rename,[status(thm)],[f_2585_1]) ).
fof(f_2585_3,plain,
( ! [U_9408,U_9406] :
( 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)))),U_9406,U_9408)
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9408),U_9406))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9406),U_9408)) ) )
& ! [U_9407,U_9405] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9407),U_9405))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9405),U_9407))
| 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)))),U_9405,U_9407) ) ),
inference(miniscope,[status(thm)],[f_2585_2]) ).
cnf(f_2585_4,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9407),U_9405))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9405),U_9407))
| 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)))),U_9405,U_9407) ),
inference(clausify,[status(thm)],[f_2585_3]) ).
cnf(f_2585_5,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9406),U_9408))
| 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)))),U_9406,U_9408) ),
inference(clausify,[status(thm)],[f_2585_3]) ).
cnf(f_2585_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9408),U_9406))
| 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)))),U_9406,U_9408) ),
inference(clausify,[status(thm)],[f_2585_3]) ).
fof(f_2586_1,plain,
! [V_w_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Nats__number__of]) ).
fof(f_2586_2,plain,
! [U_9410,U_9409] :
( hBOOL(hAPP(hAPP(c_member(U_9409),hAPP(c_Int_Onumber__class_Onumber__of(U_9409),U_9410)),c_Nat_Osemiring__1__class_ONats(U_9409)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_9410))
| ~ class_Int_Onumber__ring(U_9409) ),
inference(variable_rename,[status(thm)],[f_2586_1]) ).
cnf(f_2586_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9409),hAPP(c_Int_Onumber__class_Onumber__of(U_9409),U_9410)),c_Nat_Osemiring__1__class_ONats(U_9409)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_9410))
| ~ class_Int_Onumber__ring(U_9409) ),
inference(clausify,[status(thm)],[f_2586_2]) ).
fof(f_2587_1,plain,
! [V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_b))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Rings_Olinordered__idom(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0]) ).
fof(f_2587_2,plain,
! [U_9412,U_9411] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9411),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9411),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9411),c_Groups_Oone__class_Oone(U_9411)),U_9412)),U_9412)),c_Groups_Ozero__class_Ozero(U_9411)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9411),U_9412),c_Groups_Ozero__class_Ozero(U_9411))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9411),U_9412),c_Groups_Ozero__class_Ozero(U_9411)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9411),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9411),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9411),c_Groups_Oone__class_Oone(U_9411)),U_9412)),U_9412)),c_Groups_Ozero__class_Ozero(U_9411))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9411),U_9412),c_Int_Oring__1__class_OInts(U_9411)))
| ~ class_Rings_Olinordered__idom(U_9411) ),
inference(variable_rename,[status(thm)],[f_2587_1]) ).
cnf(f_2587_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9411),U_9412),c_Groups_Ozero__class_Ozero(U_9411)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9411),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9411),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9411),c_Groups_Oone__class_Oone(U_9411)),U_9412)),U_9412)),c_Groups_Ozero__class_Ozero(U_9411)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9411),U_9412),c_Int_Oring__1__class_OInts(U_9411)))
| ~ class_Rings_Olinordered__idom(U_9411) ),
inference(clausify,[status(thm)],[f_2587_2]) ).
cnf(f_2587_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9411),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9411),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9411),c_Groups_Oone__class_Oone(U_9411)),U_9412)),U_9412)),c_Groups_Ozero__class_Ozero(U_9411)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_9411),U_9412),c_Groups_Ozero__class_Ozero(U_9411)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9411),U_9412),c_Int_Oring__1__class_OInts(U_9411)))
| ~ class_Rings_Olinordered__idom(U_9411) ),
inference(clausify,[status(thm)],[f_2587_2]) ).
fof(f_2588_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oremove]) ).
fof(f_2588_2,plain,
! [U_9415,U_9414,U_9413] :
( ( ( c_Big__Operators_Olattice__class_OSup__fin(U_9413,U_9414) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9413),U_9415),c_Big__Operators_Olattice__class_OSup__fin(U_9413,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9413,tc_HOL_Obool)),U_9414),hAPP(hAPP(c_Set_Oinsert(U_9413),U_9415),c_Orderings_Obot__class_Obot(tc_fun(U_9413,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9413,tc_HOL_Obool)),U_9414),hAPP(hAPP(c_Set_Oinsert(U_9413),U_9415),c_Orderings_Obot__class_Obot(tc_fun(U_9413,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9413,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OSup__fin(U_9413,U_9414) = U_9415
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9413,tc_HOL_Obool)),U_9414),hAPP(hAPP(c_Set_Oinsert(U_9413),U_9415),c_Orderings_Obot__class_Obot(tc_fun(U_9413,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9413,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9413),U_9415),U_9414))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9413),U_9414))
| ~ class_Lattices_Olattice(U_9413) ),
inference(variable_rename,[status(thm)],[f_2588_1]) ).
cnf(f_2588_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_9413,U_9414) = U_9415
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9413,tc_HOL_Obool)),U_9414),hAPP(hAPP(c_Set_Oinsert(U_9413),U_9415),c_Orderings_Obot__class_Obot(tc_fun(U_9413,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9413,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9413),U_9415),U_9414))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9413),U_9414))
| ~ class_Lattices_Olattice(U_9413) ),
inference(clausify,[status(thm)],[f_2588_2]) ).
cnf(f_2588_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_9413,U_9414) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9413),U_9415),c_Big__Operators_Olattice__class_OSup__fin(U_9413,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9413,tc_HOL_Obool)),U_9414),hAPP(hAPP(c_Set_Oinsert(U_9413),U_9415),c_Orderings_Obot__class_Obot(tc_fun(U_9413,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9413,tc_HOL_Obool)),U_9414),hAPP(hAPP(c_Set_Oinsert(U_9413),U_9415),c_Orderings_Obot__class_Obot(tc_fun(U_9413,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9413,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9413),U_9415),U_9414))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9413),U_9414))
| ~ class_Lattices_Olattice(U_9413) ),
inference(clausify,[status(thm)],[f_2588_2]) ).
fof(f_2589_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oremove]) ).
fof(f_2589_2,plain,
! [U_9418,U_9417,U_9416] :
( ( ( c_Big__Operators_Olinorder__class_OMax(U_9416,U_9417) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9416),U_9418),c_Big__Operators_Olinorder__class_OMax(U_9416,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9416,tc_HOL_Obool)),U_9417),hAPP(hAPP(c_Set_Oinsert(U_9416),U_9418),c_Orderings_Obot__class_Obot(tc_fun(U_9416,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9416,tc_HOL_Obool)),U_9417),hAPP(hAPP(c_Set_Oinsert(U_9416),U_9418),c_Orderings_Obot__class_Obot(tc_fun(U_9416,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9416,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMax(U_9416,U_9417) = U_9418
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9416,tc_HOL_Obool)),U_9417),hAPP(hAPP(c_Set_Oinsert(U_9416),U_9418),c_Orderings_Obot__class_Obot(tc_fun(U_9416,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9416,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9416),U_9418),U_9417))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9416),U_9417))
| ~ class_Orderings_Olinorder(U_9416) ),
inference(variable_rename,[status(thm)],[f_2589_1]) ).
cnf(f_2589_3,plain,
( c_Big__Operators_Olinorder__class_OMax(U_9416,U_9417) = U_9418
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9416,tc_HOL_Obool)),U_9417),hAPP(hAPP(c_Set_Oinsert(U_9416),U_9418),c_Orderings_Obot__class_Obot(tc_fun(U_9416,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9416,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9416),U_9418),U_9417))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9416),U_9417))
| ~ class_Orderings_Olinorder(U_9416) ),
inference(clausify,[status(thm)],[f_2589_2]) ).
cnf(f_2589_4,plain,
( c_Big__Operators_Olinorder__class_OMax(U_9416,U_9417) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9416),U_9418),c_Big__Operators_Olinorder__class_OMax(U_9416,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9416,tc_HOL_Obool)),U_9417),hAPP(hAPP(c_Set_Oinsert(U_9416),U_9418),c_Orderings_Obot__class_Obot(tc_fun(U_9416,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9416,tc_HOL_Obool)),U_9417),hAPP(hAPP(c_Set_Oinsert(U_9416),U_9418),c_Orderings_Obot__class_Obot(tc_fun(U_9416,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9416,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9416),U_9418),U_9417))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9416),U_9417))
| ~ class_Orderings_Olinorder(U_9416) ),
inference(clausify,[status(thm)],[f_2589_2]) ).
fof(f_2590_1,plain,
! [V_x_2,T_b] :
( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Osingleton]) ).
fof(f_2590_2,plain,
! [U_9420,U_9419] :
( c_Big__Operators_Olinorder__class_OMax(U_9419,hAPP(hAPP(c_Set_Oinsert(U_9419),U_9420),c_Orderings_Obot__class_Obot(tc_fun(U_9419,tc_HOL_Obool)))) = U_9420
| ~ class_Orderings_Olinorder(U_9419) ),
inference(variable_rename,[status(thm)],[f_2590_1]) ).
cnf(f_2590_3,plain,
( c_Big__Operators_Olinorder__class_OMax(U_9419,hAPP(hAPP(c_Set_Oinsert(U_9419),U_9420),c_Orderings_Obot__class_Obot(tc_fun(U_9419,tc_HOL_Obool)))) = U_9420
| ~ class_Orderings_Olinorder(U_9419) ),
inference(clausify,[status(thm)],[f_2590_2]) ).
fof(f_2591_1,plain,
! [V_x_2,T_b] :
( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osingleton]) ).
fof(f_2591_2,plain,
! [U_9422,U_9421] :
( c_Big__Operators_Olattice__class_OSup__fin(U_9421,hAPP(hAPP(c_Set_Oinsert(U_9421),U_9422),c_Orderings_Obot__class_Obot(tc_fun(U_9421,tc_HOL_Obool)))) = U_9422
| ~ class_Lattices_Olattice(U_9421) ),
inference(variable_rename,[status(thm)],[f_2591_1]) ).
cnf(f_2591_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_9421,hAPP(hAPP(c_Set_Oinsert(U_9421),U_9422),c_Orderings_Obot__class_Obot(tc_fun(U_9421,tc_HOL_Obool)))) = U_9422
| ~ class_Lattices_Olattice(U_9421) ),
inference(clausify,[status(thm)],[f_2591_2]) ).
fof(f_2592_1,plain,
! [T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__0]) ).
fof(f_2592_2,plain,
! [U_9423] :
( hBOOL(hAPP(hAPP(c_member(U_9423),c_Groups_Ozero__class_Ozero(U_9423)),c_Int_Oring__1__class_OInts(U_9423)))
| ~ class_Rings_Oring__1(U_9423) ),
inference(variable_rename,[status(thm)],[f_2592_1]) ).
cnf(f_2592_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9423),c_Groups_Ozero__class_Ozero(U_9423)),c_Int_Oring__1__class_OInts(U_9423)))
| ~ class_Rings_Oring__1(U_9423) ),
inference(clausify,[status(thm)],[f_2592_2]) ).
fof(f_2593_1,plain,
! [V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__add]) ).
fof(f_2593_2,plain,
! [U_9426,U_9425,U_9424] :
( hBOOL(hAPP(hAPP(c_member(U_9424),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9424),U_9425),U_9426)),c_Int_Oring__1__class_OInts(U_9424)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9424),U_9426),c_Int_Oring__1__class_OInts(U_9424)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9424),U_9425),c_Int_Oring__1__class_OInts(U_9424)))
| ~ class_Rings_Oring__1(U_9424) ),
inference(variable_rename,[status(thm)],[f_2593_1]) ).
cnf(f_2593_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9424),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9424),U_9425),U_9426)),c_Int_Oring__1__class_OInts(U_9424)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9424),U_9426),c_Int_Oring__1__class_OInts(U_9424)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9424),U_9425),c_Int_Oring__1__class_OInts(U_9424)))
| ~ class_Rings_Oring__1(U_9424) ),
inference(clausify,[status(thm)],[f_2593_2]) ).
fof(f_2594_1,plain,
! [V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__mult]) ).
fof(f_2594_2,plain,
! [U_9429,U_9428,U_9427] :
( hBOOL(hAPP(hAPP(c_member(U_9427),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9427),U_9428),U_9429)),c_Int_Oring__1__class_OInts(U_9427)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9427),U_9429),c_Int_Oring__1__class_OInts(U_9427)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9427),U_9428),c_Int_Oring__1__class_OInts(U_9427)))
| ~ class_Rings_Oring__1(U_9427) ),
inference(variable_rename,[status(thm)],[f_2594_1]) ).
cnf(f_2594_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9427),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9427),U_9428),U_9429)),c_Int_Oring__1__class_OInts(U_9427)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9427),U_9429),c_Int_Oring__1__class_OInts(U_9427)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9427),U_9428),c_Int_Oring__1__class_OInts(U_9427)))
| ~ class_Rings_Oring__1(U_9427) ),
inference(clausify,[status(thm)],[f_2594_2]) ).
fof(f_2595_1,plain,
! [V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__diff]) ).
fof(f_2595_2,plain,
! [U_9432,U_9431,U_9430] :
( hBOOL(hAPP(hAPP(c_member(U_9430),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9430),U_9431),U_9432)),c_Int_Oring__1__class_OInts(U_9430)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9430),U_9432),c_Int_Oring__1__class_OInts(U_9430)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9430),U_9431),c_Int_Oring__1__class_OInts(U_9430)))
| ~ class_Rings_Oring__1(U_9430) ),
inference(variable_rename,[status(thm)],[f_2595_1]) ).
cnf(f_2595_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9430),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_9430),U_9431),U_9432)),c_Int_Oring__1__class_OInts(U_9430)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9430),U_9432),c_Int_Oring__1__class_OInts(U_9430)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9430),U_9431),c_Int_Oring__1__class_OInts(U_9430)))
| ~ class_Rings_Oring__1(U_9430) ),
inference(clausify,[status(thm)],[f_2595_2]) ).
fof(f_2596_1,plain,
! [V_w_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Int_Onumber__ring(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__number__of]) ).
fof(f_2596_2,plain,
! [U_9434,U_9433] :
( hBOOL(hAPP(hAPP(c_member(U_9433),hAPP(c_Int_Onumber__class_Onumber__of(U_9433),U_9434)),c_Int_Oring__1__class_OInts(U_9433)))
| ~ class_Int_Onumber__ring(U_9433) ),
inference(variable_rename,[status(thm)],[f_2596_1]) ).
cnf(f_2596_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9433),hAPP(c_Int_Onumber__class_Onumber__of(U_9433),U_9434)),c_Int_Oring__1__class_OInts(U_9433)))
| ~ class_Int_Onumber__ring(U_9433) ),
inference(clausify,[status(thm)],[f_2596_2]) ).
fof(f_2597_1,plain,
! [T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__1]) ).
fof(f_2597_2,plain,
! [U_9435] :
( hBOOL(hAPP(hAPP(c_member(U_9435),c_Groups_Oone__class_Oone(U_9435)),c_Int_Oring__1__class_OInts(U_9435)))
| ~ class_Rings_Oring__1(U_9435) ),
inference(variable_rename,[status(thm)],[f_2597_1]) ).
cnf(f_2597_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9435),c_Groups_Oone__class_Oone(U_9435)),c_Int_Oring__1__class_OInts(U_9435)))
| ~ class_Rings_Oring__1(U_9435) ),
inference(clausify,[status(thm)],[f_2597_2]) ).
fof(f_2598_1,plain,
! [V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Int_Oring__1__class_OInts(T_b)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__minus]) ).
fof(f_2598_2,plain,
! [U_9437,U_9436] :
( hBOOL(hAPP(hAPP(c_member(U_9436),hAPP(c_Groups_Ouminus__class_Ouminus(U_9436),U_9437)),c_Int_Oring__1__class_OInts(U_9436)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9436),U_9437),c_Int_Oring__1__class_OInts(U_9436)))
| ~ class_Rings_Oring__1(U_9436) ),
inference(variable_rename,[status(thm)],[f_2598_1]) ).
cnf(f_2598_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9436),hAPP(c_Groups_Ouminus__class_Ouminus(U_9436),U_9437)),c_Int_Oring__1__class_OInts(U_9436)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9436),U_9437),c_Int_Oring__1__class_OInts(U_9436)))
| ~ class_Rings_Oring__1(U_9436) ),
inference(clausify,[status(thm)],[f_2598_2]) ).
fof(f_2599_1,plain,
! [V_na_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_na_2)),c_Int_Oring__1__class_OInts(T_b)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__power]) ).
fof(f_2599_2,plain,
! [U_9440,U_9439,U_9438] :
( hBOOL(hAPP(hAPP(c_member(U_9438),hAPP(hAPP(c_Power_Opower__class_Opower(U_9438),U_9439),U_9440)),c_Int_Oring__1__class_OInts(U_9438)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9438),U_9439),c_Int_Oring__1__class_OInts(U_9438)))
| ~ class_Rings_Oring__1(U_9438) ),
inference(variable_rename,[status(thm)],[f_2599_1]) ).
cnf(f_2599_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9438),hAPP(hAPP(c_Power_Opower__class_Opower(U_9438),U_9439),U_9440)),c_Int_Oring__1__class_OInts(U_9438)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9438),U_9439),c_Int_Oring__1__class_OInts(U_9438)))
| ~ class_Rings_Oring__1(U_9438) ),
inference(clausify,[status(thm)],[f_2599_2]) ).
fof(f_2600_1,plain,
! [V_na_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__of__nat]) ).
fof(f_2600_2,plain,
! [U_9442,U_9441] :
( hBOOL(hAPP(hAPP(c_member(U_9441),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9441),U_9442)),c_Int_Oring__1__class_OInts(U_9441)))
| ~ class_Rings_Oring__1(U_9441) ),
inference(variable_rename,[status(thm)],[f_2600_1]) ).
cnf(f_2600_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9441),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9441),U_9442)),c_Int_Oring__1__class_OInts(U_9441)))
| ~ class_Rings_Oring__1(U_9441) ),
inference(clausify,[status(thm)],[f_2600_2]) ).
fof(f_2601_1,plain,
! [V_z_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__of__int]) ).
fof(f_2601_2,plain,
! [U_9444,U_9443] :
( hBOOL(hAPP(hAPP(c_member(U_9443),hAPP(c_Int_Oring__1__class_Oof__int(U_9443),U_9444)),c_Int_Oring__1__class_OInts(U_9443)))
| ~ class_Rings_Oring__1(U_9443) ),
inference(variable_rename,[status(thm)],[f_2601_1]) ).
cnf(f_2601_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9443),hAPP(c_Int_Oring__1__class_Oof__int(U_9443),U_9444)),c_Int_Oring__1__class_OInts(U_9443)))
| ~ class_Rings_Oring__1(U_9443) ),
inference(clausify,[status(thm)],[f_2601_2]) ).
fof(f_2602_1,plain,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max__ge]) ).
fof(f_2602_2,plain,
! [U_9447,U_9446,U_9445] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9445),U_9447),c_Big__Operators_Olinorder__class_OMax(U_9445,U_9446)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9445),U_9447),U_9446))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9445),U_9446))
| ~ class_Orderings_Olinorder(U_9445) ),
inference(variable_rename,[status(thm)],[f_2602_1]) ).
cnf(f_2602_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9445),U_9447),c_Big__Operators_Olinorder__class_OMax(U_9445,U_9446)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9445),U_9447),U_9446))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9445),U_9446))
| ~ class_Orderings_Olinorder(U_9445) ),
inference(clausify,[status(thm)],[f_2602_2]) ).
fof(f_2603_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max__in]) ).
fof(f_2603_2,plain,
! [U_9449,U_9448] :
( hBOOL(hAPP(hAPP(c_member(U_9448),c_Big__Operators_Olinorder__class_OMax(U_9448,U_9449)),U_9449))
| U_9449 = c_Orderings_Obot__class_Obot(tc_fun(U_9448,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9448),U_9449))
| ~ class_Orderings_Olinorder(U_9448) ),
inference(variable_rename,[status(thm)],[f_2603_1]) ).
cnf(f_2603_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9448),c_Big__Operators_Olinorder__class_OMax(U_9448,U_9449)),U_9449))
| U_9449 = c_Orderings_Obot__class_Obot(tc_fun(U_9448,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9448),U_9449))
| ~ class_Orderings_Olinorder(U_9448) ),
inference(clausify,[status(thm)],[f_2603_2]) ).
fof(f_2604_1,plain,
! [V_x_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oin__idem]) ).
fof(f_2604_2,plain,
! [U_9452,U_9451,U_9450] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9450),U_9452),c_Big__Operators_Olattice__class_OSup__fin(U_9450,U_9451)) = c_Big__Operators_Olattice__class_OSup__fin(U_9450,U_9451)
| ~ hBOOL(hAPP(hAPP(c_member(U_9450),U_9452),U_9451))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9450),U_9451))
| ~ class_Lattices_Olattice(U_9450) ),
inference(variable_rename,[status(thm)],[f_2604_1]) ).
cnf(f_2604_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9450),U_9452),c_Big__Operators_Olattice__class_OSup__fin(U_9450,U_9451)) = c_Big__Operators_Olattice__class_OSup__fin(U_9450,U_9451)
| ~ hBOOL(hAPP(hAPP(c_member(U_9450),U_9452),U_9451))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9450),U_9451))
| ~ class_Lattices_Olattice(U_9450) ),
inference(clausify,[status(thm)],[f_2604_2]) ).
fof(f_2605_1,plain,
! [V_x_2,V_A_2,T_b] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oin__idem]) ).
fof(f_2605_2,plain,
! [U_9455,U_9454,U_9453] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9453),U_9455),c_Big__Operators_Olinorder__class_OMax(U_9453,U_9454)) = c_Big__Operators_Olinorder__class_OMax(U_9453,U_9454)
| ~ hBOOL(hAPP(hAPP(c_member(U_9453),U_9455),U_9454))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9453),U_9454))
| ~ class_Orderings_Olinorder(U_9453) ),
inference(variable_rename,[status(thm)],[f_2605_1]) ).
cnf(f_2605_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9453),U_9455),c_Big__Operators_Olinorder__class_OMax(U_9453,U_9454)) = c_Big__Operators_Olinorder__class_OMax(U_9453,U_9454)
| ~ hBOOL(hAPP(hAPP(c_member(U_9453),U_9455),U_9454))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9453),U_9454))
| ~ class_Orderings_Olinorder(U_9453) ),
inference(clausify,[status(thm)],[f_2605_2]) ).
fof(f_2606_1,plain,
! [T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b)))
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Nats__0]) ).
fof(f_2606_2,plain,
! [U_9456] :
( hBOOL(hAPP(hAPP(c_member(U_9456),c_Groups_Ozero__class_Ozero(U_9456)),c_Nat_Osemiring__1__class_ONats(U_9456)))
| ~ class_Rings_Osemiring__1(U_9456) ),
inference(variable_rename,[status(thm)],[f_2606_1]) ).
cnf(f_2606_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9456),c_Groups_Ozero__class_Ozero(U_9456)),c_Nat_Osemiring__1__class_ONats(U_9456)))
| ~ class_Rings_Osemiring__1(U_9456) ),
inference(clausify,[status(thm)],[f_2606_2]) ).
fof(f_2607_1,plain,
! [V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Nats__add]) ).
fof(f_2607_2,plain,
! [U_9459,U_9458,U_9457] :
( hBOOL(hAPP(hAPP(c_member(U_9457),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9457),U_9458),U_9459)),c_Nat_Osemiring__1__class_ONats(U_9457)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9457),U_9459),c_Nat_Osemiring__1__class_ONats(U_9457)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9457),U_9458),c_Nat_Osemiring__1__class_ONats(U_9457)))
| ~ class_Rings_Osemiring__1(U_9457) ),
inference(variable_rename,[status(thm)],[f_2607_1]) ).
cnf(f_2607_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9457),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9457),U_9458),U_9459)),c_Nat_Osemiring__1__class_ONats(U_9457)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9457),U_9459),c_Nat_Osemiring__1__class_ONats(U_9457)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9457),U_9458),c_Nat_Osemiring__1__class_ONats(U_9457)))
| ~ class_Rings_Osemiring__1(U_9457) ),
inference(clausify,[status(thm)],[f_2607_2]) ).
fof(f_2608_1,plain,
! [V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Nats__mult]) ).
fof(f_2608_2,plain,
! [U_9462,U_9461,U_9460] :
( hBOOL(hAPP(hAPP(c_member(U_9460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9460),U_9461),U_9462)),c_Nat_Osemiring__1__class_ONats(U_9460)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9460),U_9462),c_Nat_Osemiring__1__class_ONats(U_9460)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9460),U_9461),c_Nat_Osemiring__1__class_ONats(U_9460)))
| ~ class_Rings_Osemiring__1(U_9460) ),
inference(variable_rename,[status(thm)],[f_2608_1]) ).
cnf(f_2608_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9460),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9460),U_9461),U_9462)),c_Nat_Osemiring__1__class_ONats(U_9460)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9460),U_9462),c_Nat_Osemiring__1__class_ONats(U_9460)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9460),U_9461),c_Nat_Osemiring__1__class_ONats(U_9460)))
| ~ class_Rings_Osemiring__1(U_9460) ),
inference(clausify,[status(thm)],[f_2608_2]) ).
fof(f_2609_1,plain,
! [T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b)))
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Nats__1]) ).
fof(f_2609_2,plain,
! [U_9463] :
( hBOOL(hAPP(hAPP(c_member(U_9463),c_Groups_Oone__class_Oone(U_9463)),c_Nat_Osemiring__1__class_ONats(U_9463)))
| ~ class_Rings_Osemiring__1(U_9463) ),
inference(variable_rename,[status(thm)],[f_2609_1]) ).
cnf(f_2609_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9463),c_Groups_Oone__class_Oone(U_9463)),c_Nat_Osemiring__1__class_ONats(U_9463)))
| ~ class_Rings_Osemiring__1(U_9463) ),
inference(clausify,[status(thm)],[f_2609_2]) ).
fof(f_2610_1,plain,
! [V_na_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_na_2)),c_Nat_Osemiring__1__class_ONats(T_b)))
| ~ class_Rings_Osemiring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__in__Nats]) ).
fof(f_2610_2,plain,
! [U_9465,U_9464] :
( hBOOL(hAPP(hAPP(c_member(U_9464),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9464),U_9465)),c_Nat_Osemiring__1__class_ONats(U_9464)))
| ~ class_Rings_Osemiring__1(U_9464) ),
inference(variable_rename,[status(thm)],[f_2610_1]) ).
cnf(f_2610_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9464),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9464),U_9465)),c_Nat_Osemiring__1__class_ONats(U_9464)))
| ~ class_Rings_Osemiring__1(U_9464) ),
inference(clausify,[status(thm)],[f_2610_2]) ).
fof(f_2611_1,plain,
! [V_a_2,T_b] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_b) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Int_Oring__char__0(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__double__eq__0__iff]) ).
fof(f_2611_2,plain,
! [U_9467,U_9466] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9466),U_9467),U_9467) = c_Groups_Ozero__class_Ozero(U_9466)
| U_9467 != c_Groups_Ozero__class_Ozero(U_9466) )
& ( U_9467 = c_Groups_Ozero__class_Ozero(U_9466)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9466),U_9467),U_9467) != c_Groups_Ozero__class_Ozero(U_9466) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9466),U_9467),c_Int_Oring__1__class_OInts(U_9466)))
| ~ class_Int_Oring__char__0(U_9466) ),
inference(variable_rename,[status(thm)],[f_2611_1]) ).
cnf(f_2611_3,plain,
( U_9467 = c_Groups_Ozero__class_Ozero(U_9466)
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9466),U_9467),U_9467) != c_Groups_Ozero__class_Ozero(U_9466)
| ~ hBOOL(hAPP(hAPP(c_member(U_9466),U_9467),c_Int_Oring__1__class_OInts(U_9466)))
| ~ class_Int_Oring__char__0(U_9466) ),
inference(clausify,[status(thm)],[f_2611_2]) ).
cnf(f_2611_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9466),U_9467),U_9467) = c_Groups_Ozero__class_Ozero(U_9466)
| U_9467 != c_Groups_Ozero__class_Ozero(U_9466)
| ~ hBOOL(hAPP(hAPP(c_member(U_9466),U_9467),c_Int_Oring__1__class_OInts(U_9466)))
| ~ class_Int_Oring__char__0(U_9466) ),
inference(clausify,[status(thm)],[f_2611_2]) ).
fof(f_2612_1,plain,
! [V_N_2,V_M_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| V_M_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max__mono]) ).
fof(f_2612_2,plain,
! [U_9470,U_9469,U_9468] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9468),c_Big__Operators_Olinorder__class_OMax(U_9468,U_9469)),c_Big__Operators_Olinorder__class_OMax(U_9468,U_9470)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9468),U_9470))
| U_9469 = c_Orderings_Obot__class_Obot(tc_fun(U_9468,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9468,tc_HOL_Obool)),U_9469),U_9470))
| ~ class_Orderings_Olinorder(U_9468) ),
inference(variable_rename,[status(thm)],[f_2612_1]) ).
cnf(f_2612_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9468),c_Big__Operators_Olinorder__class_OMax(U_9468,U_9469)),c_Big__Operators_Olinorder__class_OMax(U_9468,U_9470)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9468),U_9470))
| U_9469 = c_Orderings_Obot__class_Obot(tc_fun(U_9468,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9468,tc_HOL_Obool)),U_9469),U_9470))
| ~ class_Orderings_Olinorder(U_9468) ),
inference(clausify,[status(thm)],[f_2612_2]) ).
fof(f_2613_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__idem]) ).
fof(f_2613_2,plain,
! [U_9473,U_9472,U_9471] :
( c_Big__Operators_Olattice__class_OSup__fin(U_9471,hAPP(hAPP(c_Set_Oinsert(U_9471),U_9473),U_9472)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9471),U_9473),c_Big__Operators_Olattice__class_OSup__fin(U_9471,U_9472))
| U_9472 = c_Orderings_Obot__class_Obot(tc_fun(U_9471,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9471),U_9472))
| ~ class_Lattices_Olattice(U_9471) ),
inference(variable_rename,[status(thm)],[f_2613_1]) ).
cnf(f_2613_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_9471,hAPP(hAPP(c_Set_Oinsert(U_9471),U_9473),U_9472)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9471),U_9473),c_Big__Operators_Olattice__class_OSup__fin(U_9471,U_9472))
| U_9472 = c_Orderings_Obot__class_Obot(tc_fun(U_9471,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9471),U_9472))
| ~ class_Lattices_Olattice(U_9471) ),
inference(clausify,[status(thm)],[f_2613_2]) ).
fof(f_2614_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osubset__idem]) ).
fof(f_2614_2,plain,
! [U_9476,U_9475,U_9474] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9474),c_Big__Operators_Olattice__class_OSup__fin(U_9474,U_9476)),c_Big__Operators_Olattice__class_OSup__fin(U_9474,U_9475)) = c_Big__Operators_Olattice__class_OSup__fin(U_9474,U_9475)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9474,tc_HOL_Obool)),U_9476),U_9475))
| U_9476 = c_Orderings_Obot__class_Obot(tc_fun(U_9474,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9474),U_9475))
| ~ class_Lattices_Olattice(U_9474) ),
inference(variable_rename,[status(thm)],[f_2614_1]) ).
cnf(f_2614_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9474),c_Big__Operators_Olattice__class_OSup__fin(U_9474,U_9476)),c_Big__Operators_Olattice__class_OSup__fin(U_9474,U_9475)) = c_Big__Operators_Olattice__class_OSup__fin(U_9474,U_9475)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9474,tc_HOL_Obool)),U_9476),U_9475))
| U_9476 = c_Orderings_Obot__class_Obot(tc_fun(U_9474,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9474),U_9475))
| ~ class_Lattices_Olattice(U_9474) ),
inference(clausify,[status(thm)],[f_2614_2]) ).
fof(f_2615_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max__insert]) ).
fof(f_2615_2,plain,
! [U_9479,U_9478,U_9477] :
( c_Big__Operators_Olinorder__class_OMax(U_9477,hAPP(hAPP(c_Set_Oinsert(U_9477),U_9479),U_9478)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9477),U_9479),c_Big__Operators_Olinorder__class_OMax(U_9477,U_9478))
| U_9478 = c_Orderings_Obot__class_Obot(tc_fun(U_9477,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9477),U_9478))
| ~ class_Orderings_Olinorder(U_9477) ),
inference(variable_rename,[status(thm)],[f_2615_1]) ).
cnf(f_2615_3,plain,
( c_Big__Operators_Olinorder__class_OMax(U_9477,hAPP(hAPP(c_Set_Oinsert(U_9477),U_9479),U_9478)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9477),U_9479),c_Big__Operators_Olinorder__class_OMax(U_9477,U_9478))
| U_9478 = c_Orderings_Obot__class_Obot(tc_fun(U_9477,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9477),U_9478))
| ~ class_Orderings_Olinorder(U_9477) ),
inference(clausify,[status(thm)],[f_2615_2]) ).
fof(f_2616_1,plain,
! [V_B_2,V_A_2,T_b] :
( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__idem]) ).
fof(f_2616_2,plain,
! [U_9482,U_9481,U_9480] :
( c_Big__Operators_Olattice__class_OSup__fin(U_9480,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9480,tc_HOL_Obool)),U_9481),U_9482)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9480),c_Big__Operators_Olattice__class_OSup__fin(U_9480,U_9481)),c_Big__Operators_Olattice__class_OSup__fin(U_9480,U_9482))
| U_9482 = c_Orderings_Obot__class_Obot(tc_fun(U_9480,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9480),U_9482))
| U_9481 = c_Orderings_Obot__class_Obot(tc_fun(U_9480,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9480),U_9481))
| ~ class_Lattices_Olattice(U_9480) ),
inference(variable_rename,[status(thm)],[f_2616_1]) ).
cnf(f_2616_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_9480,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9480,tc_HOL_Obool)),U_9481),U_9482)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9480),c_Big__Operators_Olattice__class_OSup__fin(U_9480,U_9481)),c_Big__Operators_Olattice__class_OSup__fin(U_9480,U_9482))
| U_9482 = c_Orderings_Obot__class_Obot(tc_fun(U_9480,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9480),U_9482))
| U_9481 = c_Orderings_Obot__class_Obot(tc_fun(U_9480,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9480),U_9481))
| ~ class_Lattices_Olattice(U_9480) ),
inference(clausify,[status(thm)],[f_2616_2]) ).
fof(f_2617_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Osubset__idem]) ).
fof(f_2617_2,plain,
! [U_9485,U_9484,U_9483] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9483),c_Big__Operators_Olinorder__class_OMax(U_9483,U_9485)),c_Big__Operators_Olinorder__class_OMax(U_9483,U_9484)) = c_Big__Operators_Olinorder__class_OMax(U_9483,U_9484)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9483,tc_HOL_Obool)),U_9485),U_9484))
| U_9485 = c_Orderings_Obot__class_Obot(tc_fun(U_9483,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9483),U_9484))
| ~ class_Orderings_Olinorder(U_9483) ),
inference(variable_rename,[status(thm)],[f_2617_1]) ).
cnf(f_2617_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9483),c_Big__Operators_Olinorder__class_OMax(U_9483,U_9485)),c_Big__Operators_Olinorder__class_OMax(U_9483,U_9484)) = c_Big__Operators_Olinorder__class_OMax(U_9483,U_9484)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9483,tc_HOL_Obool)),U_9485),U_9484))
| U_9485 = c_Orderings_Obot__class_Obot(tc_fun(U_9483,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9483),U_9484))
| ~ class_Orderings_Olinorder(U_9483) ),
inference(clausify,[status(thm)],[f_2617_2]) ).
fof(f_2618_1,plain,
! [V_B_2,V_A_2,T_b] :
( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max__Un]) ).
fof(f_2618_2,plain,
! [U_9488,U_9487,U_9486] :
( c_Big__Operators_Olinorder__class_OMax(U_9486,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9486,tc_HOL_Obool)),U_9487),U_9488)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9486),c_Big__Operators_Olinorder__class_OMax(U_9486,U_9487)),c_Big__Operators_Olinorder__class_OMax(U_9486,U_9488))
| U_9488 = c_Orderings_Obot__class_Obot(tc_fun(U_9486,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9486),U_9488))
| U_9487 = c_Orderings_Obot__class_Obot(tc_fun(U_9486,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9486),U_9487))
| ~ class_Orderings_Olinorder(U_9486) ),
inference(variable_rename,[status(thm)],[f_2618_1]) ).
cnf(f_2618_3,plain,
( c_Big__Operators_Olinorder__class_OMax(U_9486,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9486,tc_HOL_Obool)),U_9487),U_9488)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9486),c_Big__Operators_Olinorder__class_OMax(U_9486,U_9487)),c_Big__Operators_Olinorder__class_OMax(U_9486,U_9488))
| U_9488 = c_Orderings_Obot__class_Obot(tc_fun(U_9486,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9486),U_9488))
| U_9487 = c_Orderings_Obot__class_Obot(tc_fun(U_9486,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9486),U_9487))
| ~ class_Orderings_Olinorder(U_9486) ),
inference(clausify,[status(thm)],[f_2618_2]) ).
fof(f_2619_1,plain,
! [V_a_2,T_b] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_b)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
| ~ class_Int_Oring__char__0(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero]) ).
fof(f_2619_2,plain,
! [U_9490,U_9489] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9489),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9489),c_Groups_Oone__class_Oone(U_9489)),U_9490)),U_9490) != c_Groups_Ozero__class_Ozero(U_9489)
| ~ hBOOL(hAPP(hAPP(c_member(U_9489),U_9490),c_Int_Oring__1__class_OInts(U_9489)))
| ~ class_Int_Oring__char__0(U_9489) ),
inference(variable_rename,[status(thm)],[f_2619_1]) ).
cnf(f_2619_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9489),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_9489),c_Groups_Oone__class_Oone(U_9489)),U_9490)),U_9490) != c_Groups_Ozero__class_Ozero(U_9489)
| ~ hBOOL(hAPP(hAPP(c_member(U_9489),U_9490),c_Int_Oring__1__class_OInts(U_9489)))
| ~ class_Int_Oring__char__0(U_9489) ),
inference(clausify,[status(thm)],[f_2619_2]) ).
fof(f_2620_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert]) ).
fof(f_2620_2,plain,
! [U_9493,U_9492,U_9491] :
( c_Big__Operators_Olattice__class_OSup__fin(U_9491,hAPP(hAPP(c_Set_Oinsert(U_9491),U_9493),U_9492)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9491),U_9493),c_Big__Operators_Olattice__class_OSup__fin(U_9491,U_9492))
| U_9492 = c_Orderings_Obot__class_Obot(tc_fun(U_9491,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_9491),U_9493),U_9492))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9491),U_9492))
| ~ class_Lattices_Olattice(U_9491) ),
inference(variable_rename,[status(thm)],[f_2620_1]) ).
cnf(f_2620_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_9491,hAPP(hAPP(c_Set_Oinsert(U_9491),U_9493),U_9492)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9491),U_9493),c_Big__Operators_Olattice__class_OSup__fin(U_9491,U_9492))
| U_9492 = c_Orderings_Obot__class_Obot(tc_fun(U_9491,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_9491),U_9493),U_9492))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9491),U_9492))
| ~ class_Lattices_Olattice(U_9491) ),
inference(clausify,[status(thm)],[f_2620_2]) ).
fof(f_2621_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oinsert]) ).
fof(f_2621_2,plain,
! [U_9496,U_9495,U_9494] :
( c_Big__Operators_Olinorder__class_OMax(U_9494,hAPP(hAPP(c_Set_Oinsert(U_9494),U_9496),U_9495)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9494),U_9496),c_Big__Operators_Olinorder__class_OMax(U_9494,U_9495))
| U_9495 = c_Orderings_Obot__class_Obot(tc_fun(U_9494,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_9494),U_9496),U_9495))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9494),U_9495))
| ~ class_Orderings_Olinorder(U_9494) ),
inference(variable_rename,[status(thm)],[f_2621_1]) ).
cnf(f_2621_3,plain,
( c_Big__Operators_Olinorder__class_OMax(U_9494,hAPP(hAPP(c_Set_Oinsert(U_9494),U_9496),U_9495)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9494),U_9496),c_Big__Operators_Olinorder__class_OMax(U_9494,U_9495))
| U_9495 = c_Orderings_Obot__class_Obot(tc_fun(U_9494,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_9494),U_9496),U_9495))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9494),U_9495))
| ~ class_Orderings_Olinorder(U_9494) ),
inference(clausify,[status(thm)],[f_2621_2]) ).
fof(f_2622_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__remove]) ).
fof(f_2622_2,plain,
! [U_9499,U_9498,U_9497] :
( ( ( c_Big__Operators_Olattice__class_OSup__fin(U_9497,hAPP(hAPP(c_Set_Oinsert(U_9497),U_9499),U_9498)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9497),U_9499),c_Big__Operators_Olattice__class_OSup__fin(U_9497,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9497,tc_HOL_Obool)),U_9498),hAPP(hAPP(c_Set_Oinsert(U_9497),U_9499),c_Orderings_Obot__class_Obot(tc_fun(U_9497,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9497,tc_HOL_Obool)),U_9498),hAPP(hAPP(c_Set_Oinsert(U_9497),U_9499),c_Orderings_Obot__class_Obot(tc_fun(U_9497,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9497,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OSup__fin(U_9497,hAPP(hAPP(c_Set_Oinsert(U_9497),U_9499),U_9498)) = U_9499
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9497,tc_HOL_Obool)),U_9498),hAPP(hAPP(c_Set_Oinsert(U_9497),U_9499),c_Orderings_Obot__class_Obot(tc_fun(U_9497,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9497,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9497),U_9498))
| ~ class_Lattices_Olattice(U_9497) ),
inference(variable_rename,[status(thm)],[f_2622_1]) ).
cnf(f_2622_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_9497,hAPP(hAPP(c_Set_Oinsert(U_9497),U_9499),U_9498)) = U_9499
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9497,tc_HOL_Obool)),U_9498),hAPP(hAPP(c_Set_Oinsert(U_9497),U_9499),c_Orderings_Obot__class_Obot(tc_fun(U_9497,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9497,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9497),U_9498))
| ~ class_Lattices_Olattice(U_9497) ),
inference(clausify,[status(thm)],[f_2622_2]) ).
cnf(f_2622_4,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_9497,hAPP(hAPP(c_Set_Oinsert(U_9497),U_9499),U_9498)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9497),U_9499),c_Big__Operators_Olattice__class_OSup__fin(U_9497,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9497,tc_HOL_Obool)),U_9498),hAPP(hAPP(c_Set_Oinsert(U_9497),U_9499),c_Orderings_Obot__class_Obot(tc_fun(U_9497,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9497,tc_HOL_Obool)),U_9498),hAPP(hAPP(c_Set_Oinsert(U_9497),U_9499),c_Orderings_Obot__class_Obot(tc_fun(U_9497,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9497,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9497),U_9498))
| ~ class_Lattices_Olattice(U_9497) ),
inference(clausify,[status(thm)],[f_2622_2]) ).
fof(f_2623_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oinsert__remove]) ).
fof(f_2623_2,plain,
! [U_9502,U_9501,U_9500] :
( ( ( c_Big__Operators_Olinorder__class_OMax(U_9500,hAPP(hAPP(c_Set_Oinsert(U_9500),U_9502),U_9501)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9500),U_9502),c_Big__Operators_Olinorder__class_OMax(U_9500,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9500,tc_HOL_Obool)),U_9501),hAPP(hAPP(c_Set_Oinsert(U_9500),U_9502),c_Orderings_Obot__class_Obot(tc_fun(U_9500,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9500,tc_HOL_Obool)),U_9501),hAPP(hAPP(c_Set_Oinsert(U_9500),U_9502),c_Orderings_Obot__class_Obot(tc_fun(U_9500,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9500,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMax(U_9500,hAPP(hAPP(c_Set_Oinsert(U_9500),U_9502),U_9501)) = U_9502
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9500,tc_HOL_Obool)),U_9501),hAPP(hAPP(c_Set_Oinsert(U_9500),U_9502),c_Orderings_Obot__class_Obot(tc_fun(U_9500,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9500,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9500),U_9501))
| ~ class_Orderings_Olinorder(U_9500) ),
inference(variable_rename,[status(thm)],[f_2623_1]) ).
cnf(f_2623_3,plain,
( c_Big__Operators_Olinorder__class_OMax(U_9500,hAPP(hAPP(c_Set_Oinsert(U_9500),U_9502),U_9501)) = U_9502
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9500,tc_HOL_Obool)),U_9501),hAPP(hAPP(c_Set_Oinsert(U_9500),U_9502),c_Orderings_Obot__class_Obot(tc_fun(U_9500,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9500,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9500),U_9501))
| ~ class_Orderings_Olinorder(U_9500) ),
inference(clausify,[status(thm)],[f_2623_2]) ).
cnf(f_2623_4,plain,
( c_Big__Operators_Olinorder__class_OMax(U_9500,hAPP(hAPP(c_Set_Oinsert(U_9500),U_9502),U_9501)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9500),U_9502),c_Big__Operators_Olinorder__class_OMax(U_9500,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9500,tc_HOL_Obool)),U_9501),hAPP(hAPP(c_Set_Oinsert(U_9500),U_9502),c_Orderings_Obot__class_Obot(tc_fun(U_9500,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9500,tc_HOL_Obool)),U_9501),hAPP(hAPP(c_Set_Oinsert(U_9500),U_9502),c_Orderings_Obot__class_Obot(tc_fun(U_9500,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9500,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9500),U_9501))
| ~ class_Orderings_Olinorder(U_9500) ),
inference(clausify,[status(thm)],[f_2623_2]) ).
fof(f_2624_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2))
| ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oclosed]) ).
fof(f_2624_2,plain,
! [U_9506,U_9505] :
( hBOOL(hAPP(hAPP(c_member(U_9505),c_Big__Operators_Olinorder__class_OMax(U_9505,U_9506)),U_9506))
| ? [U_9504,U_9503] : ~ hBOOL(hAPP(hAPP(c_member(U_9505),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9505),U_9504),U_9503)),hAPP(hAPP(c_Set_Oinsert(U_9505),U_9504),hAPP(hAPP(c_Set_Oinsert(U_9505),U_9503),c_Orderings_Obot__class_Obot(tc_fun(U_9505,tc_HOL_Obool))))))
| U_9506 = c_Orderings_Obot__class_Obot(tc_fun(U_9505,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9505),U_9506))
| ~ class_Orderings_Olinorder(U_9505) ),
inference(variable_rename,[status(thm)],[f_2624_1]) ).
fof(f_2624_3,plain,
! [U_9506,U_9505] :
( hBOOL(hAPP(hAPP(c_member(U_9505),c_Big__Operators_Olinorder__class_OMax(U_9505,U_9506)),U_9506))
| ? [U_9503] : ~ hBOOL(hAPP(hAPP(c_member(U_9505),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9505),sK187(U_9506,U_9505)),U_9503)),hAPP(hAPP(c_Set_Oinsert(U_9505),sK187(U_9506,U_9505)),hAPP(hAPP(c_Set_Oinsert(U_9505),U_9503),c_Orderings_Obot__class_Obot(tc_fun(U_9505,tc_HOL_Obool))))))
| U_9506 = c_Orderings_Obot__class_Obot(tc_fun(U_9505,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9505),U_9506))
| ~ class_Orderings_Olinorder(U_9505) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK187]),skolemize(U_9504,sK187(U_9506,U_9505))],[f_2624_2]) ).
fof(f_2624_4,plain,
! [U_9506,U_9505] :
( hBOOL(hAPP(hAPP(c_member(U_9505),c_Big__Operators_Olinorder__class_OMax(U_9505,U_9506)),U_9506))
| ~ hBOOL(hAPP(hAPP(c_member(U_9505),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9505),sK187(U_9506,U_9505)),sK188(U_9506,U_9505))),hAPP(hAPP(c_Set_Oinsert(U_9505),sK187(U_9506,U_9505)),hAPP(hAPP(c_Set_Oinsert(U_9505),sK188(U_9506,U_9505)),c_Orderings_Obot__class_Obot(tc_fun(U_9505,tc_HOL_Obool))))))
| U_9506 = c_Orderings_Obot__class_Obot(tc_fun(U_9505,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9505),U_9506))
| ~ class_Orderings_Olinorder(U_9505) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK188]),skolemize(U_9503,sK188(U_9506,U_9505))],[f_2624_3]) ).
cnf(f_2624_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9505),c_Big__Operators_Olinorder__class_OMax(U_9505,U_9506)),U_9506))
| ~ hBOOL(hAPP(hAPP(c_member(U_9505),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9505),sK187(U_9506,U_9505)),sK188(U_9506,U_9505))),hAPP(hAPP(c_Set_Oinsert(U_9505),sK187(U_9506,U_9505)),hAPP(hAPP(c_Set_Oinsert(U_9505),sK188(U_9506,U_9505)),c_Orderings_Obot__class_Obot(tc_fun(U_9505,tc_HOL_Obool))))))
| U_9506 = c_Orderings_Obot__class_Obot(tc_fun(U_9505,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9505),U_9506))
| ~ class_Orderings_Olinorder(U_9505) ),
inference(clausify,[status(thm)],[f_2624_4]) ).
fof(f_2625_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2))
| ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oclosed]) ).
fof(f_2625_2,plain,
! [U_9510,U_9509] :
( hBOOL(hAPP(hAPP(c_member(U_9509),c_Big__Operators_Olattice__class_OSup__fin(U_9509,U_9510)),U_9510))
| ? [U_9508,U_9507] : ~ hBOOL(hAPP(hAPP(c_member(U_9509),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9509),U_9508),U_9507)),hAPP(hAPP(c_Set_Oinsert(U_9509),U_9508),hAPP(hAPP(c_Set_Oinsert(U_9509),U_9507),c_Orderings_Obot__class_Obot(tc_fun(U_9509,tc_HOL_Obool))))))
| U_9510 = c_Orderings_Obot__class_Obot(tc_fun(U_9509,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9509),U_9510))
| ~ class_Lattices_Olattice(U_9509) ),
inference(variable_rename,[status(thm)],[f_2625_1]) ).
fof(f_2625_3,plain,
! [U_9510,U_9509] :
( hBOOL(hAPP(hAPP(c_member(U_9509),c_Big__Operators_Olattice__class_OSup__fin(U_9509,U_9510)),U_9510))
| ? [U_9507] : ~ hBOOL(hAPP(hAPP(c_member(U_9509),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9509),sK189(U_9510,U_9509)),U_9507)),hAPP(hAPP(c_Set_Oinsert(U_9509),sK189(U_9510,U_9509)),hAPP(hAPP(c_Set_Oinsert(U_9509),U_9507),c_Orderings_Obot__class_Obot(tc_fun(U_9509,tc_HOL_Obool))))))
| U_9510 = c_Orderings_Obot__class_Obot(tc_fun(U_9509,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9509),U_9510))
| ~ class_Lattices_Olattice(U_9509) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK189]),skolemize(U_9508,sK189(U_9510,U_9509))],[f_2625_2]) ).
fof(f_2625_4,plain,
! [U_9510,U_9509] :
( hBOOL(hAPP(hAPP(c_member(U_9509),c_Big__Operators_Olattice__class_OSup__fin(U_9509,U_9510)),U_9510))
| ~ hBOOL(hAPP(hAPP(c_member(U_9509),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9509),sK189(U_9510,U_9509)),sK190(U_9510,U_9509))),hAPP(hAPP(c_Set_Oinsert(U_9509),sK189(U_9510,U_9509)),hAPP(hAPP(c_Set_Oinsert(U_9509),sK190(U_9510,U_9509)),c_Orderings_Obot__class_Obot(tc_fun(U_9509,tc_HOL_Obool))))))
| U_9510 = c_Orderings_Obot__class_Obot(tc_fun(U_9509,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9509),U_9510))
| ~ class_Lattices_Olattice(U_9509) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK190]),skolemize(U_9507,sK190(U_9510,U_9509))],[f_2625_3]) ).
cnf(f_2625_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9509),c_Big__Operators_Olattice__class_OSup__fin(U_9509,U_9510)),U_9510))
| ~ hBOOL(hAPP(hAPP(c_member(U_9509),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9509),sK189(U_9510,U_9509)),sK190(U_9510,U_9509))),hAPP(hAPP(c_Set_Oinsert(U_9509),sK189(U_9510,U_9509)),hAPP(hAPP(c_Set_Oinsert(U_9509),sK190(U_9510,U_9509)),c_Orderings_Obot__class_Obot(tc_fun(U_9509,tc_HOL_Obool))))))
| U_9510 = c_Orderings_Obot__class_Obot(tc_fun(U_9509,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9509),U_9510))
| ~ class_Lattices_Olattice(U_9509) ),
inference(clausify,[status(thm)],[f_2625_4]) ).
fof(f_2626_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oremove]) ).
fof(f_2626_2,plain,
! [U_9513,U_9512,U_9511] :
( ( ( c_Big__Operators_Olinorder__class_OMin(U_9511,U_9512) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9511),U_9513),c_Big__Operators_Olinorder__class_OMin(U_9511,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9511,tc_HOL_Obool)),U_9512),hAPP(hAPP(c_Set_Oinsert(U_9511),U_9513),c_Orderings_Obot__class_Obot(tc_fun(U_9511,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9511,tc_HOL_Obool)),U_9512),hAPP(hAPP(c_Set_Oinsert(U_9511),U_9513),c_Orderings_Obot__class_Obot(tc_fun(U_9511,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9511,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMin(U_9511,U_9512) = U_9513
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9511,tc_HOL_Obool)),U_9512),hAPP(hAPP(c_Set_Oinsert(U_9511),U_9513),c_Orderings_Obot__class_Obot(tc_fun(U_9511,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9511,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9511),U_9513),U_9512))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9511),U_9512))
| ~ class_Orderings_Olinorder(U_9511) ),
inference(variable_rename,[status(thm)],[f_2626_1]) ).
cnf(f_2626_3,plain,
( c_Big__Operators_Olinorder__class_OMin(U_9511,U_9512) = U_9513
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9511,tc_HOL_Obool)),U_9512),hAPP(hAPP(c_Set_Oinsert(U_9511),U_9513),c_Orderings_Obot__class_Obot(tc_fun(U_9511,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9511,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9511),U_9513),U_9512))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9511),U_9512))
| ~ class_Orderings_Olinorder(U_9511) ),
inference(clausify,[status(thm)],[f_2626_2]) ).
cnf(f_2626_4,plain,
( c_Big__Operators_Olinorder__class_OMin(U_9511,U_9512) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9511),U_9513),c_Big__Operators_Olinorder__class_OMin(U_9511,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9511,tc_HOL_Obool)),U_9512),hAPP(hAPP(c_Set_Oinsert(U_9511),U_9513),c_Orderings_Obot__class_Obot(tc_fun(U_9511,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9511,tc_HOL_Obool)),U_9512),hAPP(hAPP(c_Set_Oinsert(U_9511),U_9513),c_Orderings_Obot__class_Obot(tc_fun(U_9511,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9511,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9511),U_9513),U_9512))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9511),U_9512))
| ~ class_Orderings_Olinorder(U_9511) ),
inference(clausify,[status(thm)],[f_2626_2]) ).
fof(f_2627_1,plain,
! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
( ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))
| ( ! [B_x,B_y] :
( ~ c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),B_y)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
| hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) != hAPP(hAPP(V_a3_2,B_x),B_y) )
& ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) != V_a4_2
| V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
& ( ? [B_x,B_y] :
( c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),B_y)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
& hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) )
| ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2
& V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
| ~ c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Oequations_I2_J]) ).
fof(f_2627_2,plain,
! [U_9524,U_9523,U_9522,U_9521,U_9520,U_9519,U_9518] :
( ( c_Nitpick_Ofold__graph_H(U_9518,U_9519,U_9520,U_9521,U_9522,hAPP(hAPP(U_9520,U_9523),U_9524))
| ( ! [U_9517,U_9516] :
( ~ c_Nitpick_Ofold__graph_H(U_9518,U_9519,U_9520,U_9521,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9518,tc_HOL_Obool)),U_9522),hAPP(hAPP(c_Set_Oinsert(U_9518),U_9517),c_Orderings_Obot__class_Obot(tc_fun(U_9518,tc_HOL_Obool)))),U_9516)
| ~ hBOOL(hAPP(hAPP(c_member(U_9518),U_9517),U_9522))
| hAPP(hAPP(U_9520,U_9523),U_9524) != hAPP(hAPP(U_9520,U_9517),U_9516) )
& ( hAPP(hAPP(U_9520,U_9523),U_9524) != U_9521
| U_9522 != c_Orderings_Obot__class_Obot(tc_fun(U_9518,tc_HOL_Obool)) ) ) )
& ( ? [U_9515,U_9514] :
( c_Nitpick_Ofold__graph_H(U_9518,U_9519,U_9520,U_9521,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9518,tc_HOL_Obool)),U_9522),hAPP(hAPP(c_Set_Oinsert(U_9518),U_9515),c_Orderings_Obot__class_Obot(tc_fun(U_9518,tc_HOL_Obool)))),U_9514)
& hBOOL(hAPP(hAPP(c_member(U_9518),U_9515),U_9522))
& hAPP(hAPP(U_9520,U_9523),U_9524) = hAPP(hAPP(U_9520,U_9515),U_9514) )
| ( hAPP(hAPP(U_9520,U_9523),U_9524) = U_9521
& U_9522 = c_Orderings_Obot__class_Obot(tc_fun(U_9518,tc_HOL_Obool)) )
| ~ c_Nitpick_Ofold__graph_H(U_9518,U_9519,U_9520,U_9521,U_9522,hAPP(hAPP(U_9520,U_9523),U_9524)) ) ),
inference(variable_rename,[status(thm)],[f_2627_1]) ).
fof(f_2627_3,plain,
( ! [U_9538,U_9536,U_9534,U_9532,U_9530,U_9528,U_9526] :
( c_Nitpick_Ofold__graph_H(U_9526,U_9528,U_9530,U_9532,U_9534,hAPP(hAPP(U_9530,U_9536),U_9538))
| ( ! [U_9517] :
( ! [U_9516] :
( ~ c_Nitpick_Ofold__graph_H(U_9526,U_9528,U_9530,U_9532,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9526,tc_HOL_Obool)),U_9534),hAPP(hAPP(c_Set_Oinsert(U_9526),U_9517),c_Orderings_Obot__class_Obot(tc_fun(U_9526,tc_HOL_Obool)))),U_9516)
| hAPP(hAPP(U_9530,U_9536),U_9538) != hAPP(hAPP(U_9530,U_9517),U_9516) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9526),U_9517),U_9534)) )
& ( hAPP(hAPP(U_9530,U_9536),U_9538) != U_9532
| U_9534 != c_Orderings_Obot__class_Obot(tc_fun(U_9526,tc_HOL_Obool)) ) ) )
& ! [U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525] :
( ? [U_9515] :
( ? [U_9514] :
( c_Nitpick_Ofold__graph_H(U_9525,U_9527,U_9529,U_9531,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9525,tc_HOL_Obool)),U_9533),hAPP(hAPP(c_Set_Oinsert(U_9525),U_9515),c_Orderings_Obot__class_Obot(tc_fun(U_9525,tc_HOL_Obool)))),U_9514)
& hAPP(hAPP(U_9529,U_9535),U_9537) = hAPP(hAPP(U_9529,U_9515),U_9514) )
& hBOOL(hAPP(hAPP(c_member(U_9525),U_9515),U_9533)) )
| ( hAPP(hAPP(U_9529,U_9535),U_9537) = U_9531
& U_9533 = c_Orderings_Obot__class_Obot(tc_fun(U_9525,tc_HOL_Obool)) )
| ~ c_Nitpick_Ofold__graph_H(U_9525,U_9527,U_9529,U_9531,U_9533,hAPP(hAPP(U_9529,U_9535),U_9537)) ) ),
inference(miniscope,[status(thm)],[f_2627_2]) ).
fof(f_2627_4,plain,
( ! [U_9538,U_9536,U_9534,U_9532,U_9530,U_9528,U_9526] :
( c_Nitpick_Ofold__graph_H(U_9526,U_9528,U_9530,U_9532,U_9534,hAPP(hAPP(U_9530,U_9536),U_9538))
| ( ! [U_9517] :
( ! [U_9516] :
( ~ c_Nitpick_Ofold__graph_H(U_9526,U_9528,U_9530,U_9532,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9526,tc_HOL_Obool)),U_9534),hAPP(hAPP(c_Set_Oinsert(U_9526),U_9517),c_Orderings_Obot__class_Obot(tc_fun(U_9526,tc_HOL_Obool)))),U_9516)
| hAPP(hAPP(U_9530,U_9536),U_9538) != hAPP(hAPP(U_9530,U_9517),U_9516) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9526),U_9517),U_9534)) )
& ( hAPP(hAPP(U_9530,U_9536),U_9538) != U_9532
| U_9534 != c_Orderings_Obot__class_Obot(tc_fun(U_9526,tc_HOL_Obool)) ) ) )
& ! [U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525] :
( ( ? [U_9514] :
( c_Nitpick_Ofold__graph_H(U_9525,U_9527,U_9529,U_9531,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9525,tc_HOL_Obool)),U_9533),hAPP(hAPP(c_Set_Oinsert(U_9525),sK191(U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525)),c_Orderings_Obot__class_Obot(tc_fun(U_9525,tc_HOL_Obool)))),U_9514)
& hAPP(hAPP(U_9529,U_9535),U_9537) = hAPP(hAPP(U_9529,sK191(U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525)),U_9514) )
& hBOOL(hAPP(hAPP(c_member(U_9525),sK191(U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525)),U_9533)) )
| ( hAPP(hAPP(U_9529,U_9535),U_9537) = U_9531
& U_9533 = c_Orderings_Obot__class_Obot(tc_fun(U_9525,tc_HOL_Obool)) )
| ~ c_Nitpick_Ofold__graph_H(U_9525,U_9527,U_9529,U_9531,U_9533,hAPP(hAPP(U_9529,U_9535),U_9537)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK191]),skolemize(U_9515,sK191(U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525))],[f_2627_3]) ).
fof(f_2627_5,plain,
( ! [U_9538,U_9536,U_9534,U_9532,U_9530,U_9528,U_9526] :
( c_Nitpick_Ofold__graph_H(U_9526,U_9528,U_9530,U_9532,U_9534,hAPP(hAPP(U_9530,U_9536),U_9538))
| ( ! [U_9517] :
( ! [U_9516] :
( ~ c_Nitpick_Ofold__graph_H(U_9526,U_9528,U_9530,U_9532,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9526,tc_HOL_Obool)),U_9534),hAPP(hAPP(c_Set_Oinsert(U_9526),U_9517),c_Orderings_Obot__class_Obot(tc_fun(U_9526,tc_HOL_Obool)))),U_9516)
| hAPP(hAPP(U_9530,U_9536),U_9538) != hAPP(hAPP(U_9530,U_9517),U_9516) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9526),U_9517),U_9534)) )
& ( hAPP(hAPP(U_9530,U_9536),U_9538) != U_9532
| U_9534 != c_Orderings_Obot__class_Obot(tc_fun(U_9526,tc_HOL_Obool)) ) ) )
& ! [U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525] :
( ( c_Nitpick_Ofold__graph_H(U_9525,U_9527,U_9529,U_9531,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9525,tc_HOL_Obool)),U_9533),hAPP(hAPP(c_Set_Oinsert(U_9525),sK191(U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525)),c_Orderings_Obot__class_Obot(tc_fun(U_9525,tc_HOL_Obool)))),sK192(U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525))
& hAPP(hAPP(U_9529,U_9535),U_9537) = hAPP(hAPP(U_9529,sK191(U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525)),sK192(U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525))
& hBOOL(hAPP(hAPP(c_member(U_9525),sK191(U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525)),U_9533)) )
| ( hAPP(hAPP(U_9529,U_9535),U_9537) = U_9531
& U_9533 = c_Orderings_Obot__class_Obot(tc_fun(U_9525,tc_HOL_Obool)) )
| ~ c_Nitpick_Ofold__graph_H(U_9525,U_9527,U_9529,U_9531,U_9533,hAPP(hAPP(U_9529,U_9535),U_9537)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK192]),skolemize(U_9514,sK192(U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525))],[f_2627_4]) ).
cnf(f_2627_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_9525),sK191(U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525)),U_9533))
| U_9533 = c_Orderings_Obot__class_Obot(tc_fun(U_9525,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(U_9525,U_9527,U_9529,U_9531,U_9533,hAPP(hAPP(U_9529,U_9535),U_9537)) ),
inference(clausify,[status(thm)],[f_2627_5]) ).
cnf(f_2627_7,plain,
( hAPP(hAPP(U_9529,U_9535),U_9537) = hAPP(hAPP(U_9529,sK191(U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525)),sK192(U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525))
| U_9533 = c_Orderings_Obot__class_Obot(tc_fun(U_9525,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(U_9525,U_9527,U_9529,U_9531,U_9533,hAPP(hAPP(U_9529,U_9535),U_9537)) ),
inference(clausify,[status(thm)],[f_2627_5]) ).
cnf(f_2627_8,plain,
( c_Nitpick_Ofold__graph_H(U_9525,U_9527,U_9529,U_9531,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9525,tc_HOL_Obool)),U_9533),hAPP(hAPP(c_Set_Oinsert(U_9525),sK191(U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525)),c_Orderings_Obot__class_Obot(tc_fun(U_9525,tc_HOL_Obool)))),sK192(U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525))
| U_9533 = c_Orderings_Obot__class_Obot(tc_fun(U_9525,tc_HOL_Obool))
| ~ c_Nitpick_Ofold__graph_H(U_9525,U_9527,U_9529,U_9531,U_9533,hAPP(hAPP(U_9529,U_9535),U_9537)) ),
inference(clausify,[status(thm)],[f_2627_5]) ).
cnf(f_2627_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_9525),sK191(U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525)),U_9533))
| hAPP(hAPP(U_9529,U_9535),U_9537) = U_9531
| ~ c_Nitpick_Ofold__graph_H(U_9525,U_9527,U_9529,U_9531,U_9533,hAPP(hAPP(U_9529,U_9535),U_9537)) ),
inference(clausify,[status(thm)],[f_2627_5]) ).
cnf(f_2627_10,plain,
( hAPP(hAPP(U_9529,U_9535),U_9537) = hAPP(hAPP(U_9529,sK191(U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525)),sK192(U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525))
| hAPP(hAPP(U_9529,U_9535),U_9537) = U_9531
| ~ c_Nitpick_Ofold__graph_H(U_9525,U_9527,U_9529,U_9531,U_9533,hAPP(hAPP(U_9529,U_9535),U_9537)) ),
inference(clausify,[status(thm)],[f_2627_5]) ).
cnf(f_2627_11,plain,
( c_Nitpick_Ofold__graph_H(U_9525,U_9527,U_9529,U_9531,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9525,tc_HOL_Obool)),U_9533),hAPP(hAPP(c_Set_Oinsert(U_9525),sK191(U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525)),c_Orderings_Obot__class_Obot(tc_fun(U_9525,tc_HOL_Obool)))),sK192(U_9537,U_9535,U_9533,U_9531,U_9529,U_9527,U_9525))
| hAPP(hAPP(U_9529,U_9535),U_9537) = U_9531
| ~ c_Nitpick_Ofold__graph_H(U_9525,U_9527,U_9529,U_9531,U_9533,hAPP(hAPP(U_9529,U_9535),U_9537)) ),
inference(clausify,[status(thm)],[f_2627_5]) ).
cnf(f_2627_12,plain,
( hAPP(hAPP(U_9530,U_9536),U_9538) != U_9532
| U_9534 != c_Orderings_Obot__class_Obot(tc_fun(U_9526,tc_HOL_Obool))
| c_Nitpick_Ofold__graph_H(U_9526,U_9528,U_9530,U_9532,U_9534,hAPP(hAPP(U_9530,U_9536),U_9538)) ),
inference(clausify,[status(thm)],[f_2627_5]) ).
cnf(f_2627_13,plain,
( ~ c_Nitpick_Ofold__graph_H(U_9526,U_9528,U_9530,U_9532,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9526,tc_HOL_Obool)),U_9534),hAPP(hAPP(c_Set_Oinsert(U_9526),U_9517),c_Orderings_Obot__class_Obot(tc_fun(U_9526,tc_HOL_Obool)))),U_9516)
| hAPP(hAPP(U_9530,U_9536),U_9538) != hAPP(hAPP(U_9530,U_9517),U_9516)
| ~ hBOOL(hAPP(hAPP(c_member(U_9526),U_9517),U_9534))
| c_Nitpick_Ofold__graph_H(U_9526,U_9528,U_9530,U_9532,U_9534,hAPP(hAPP(U_9530,U_9536),U_9538)) ),
inference(clausify,[status(thm)],[f_2627_5]) ).
fof(f_2628_1,plain,
! [V_x_2,T_b] :
( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Osingleton]) ).
fof(f_2628_2,plain,
! [U_9540,U_9539] :
( c_Big__Operators_Olinorder__class_OMin(U_9539,hAPP(hAPP(c_Set_Oinsert(U_9539),U_9540),c_Orderings_Obot__class_Obot(tc_fun(U_9539,tc_HOL_Obool)))) = U_9540
| ~ class_Orderings_Olinorder(U_9539) ),
inference(variable_rename,[status(thm)],[f_2628_1]) ).
cnf(f_2628_3,plain,
( c_Big__Operators_Olinorder__class_OMin(U_9539,hAPP(hAPP(c_Set_Oinsert(U_9539),U_9540),c_Orderings_Obot__class_Obot(tc_fun(U_9539,tc_HOL_Obool)))) = U_9540
| ~ class_Orderings_Olinorder(U_9539) ),
inference(clausify,[status(thm)],[f_2628_2]) ).
fof(f_2629_1,plain,
! [V_x_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min__le]) ).
fof(f_2629_2,plain,
! [U_9543,U_9542,U_9541] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9541),c_Big__Operators_Olinorder__class_OMin(U_9541,U_9542)),U_9543))
| ~ hBOOL(hAPP(hAPP(c_member(U_9541),U_9543),U_9542))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9541),U_9542))
| ~ class_Orderings_Olinorder(U_9541) ),
inference(variable_rename,[status(thm)],[f_2629_1]) ).
cnf(f_2629_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9541),c_Big__Operators_Olinorder__class_OMin(U_9541,U_9542)),U_9543))
| ~ hBOOL(hAPP(hAPP(c_member(U_9541),U_9543),U_9542))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9541),U_9542))
| ~ class_Orderings_Olinorder(U_9541) ),
inference(clausify,[status(thm)],[f_2629_2]) ).
fof(f_2630_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min__in]) ).
fof(f_2630_2,plain,
! [U_9545,U_9544] :
( hBOOL(hAPP(hAPP(c_member(U_9544),c_Big__Operators_Olinorder__class_OMin(U_9544,U_9545)),U_9545))
| U_9545 = c_Orderings_Obot__class_Obot(tc_fun(U_9544,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9544),U_9545))
| ~ class_Orderings_Olinorder(U_9544) ),
inference(variable_rename,[status(thm)],[f_2630_1]) ).
cnf(f_2630_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_9544),c_Big__Operators_Olinorder__class_OMin(U_9544,U_9545)),U_9545))
| U_9545 = c_Orderings_Obot__class_Obot(tc_fun(U_9544,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9544),U_9545))
| ~ class_Orderings_Olinorder(U_9544) ),
inference(clausify,[status(thm)],[f_2630_2]) ).
fof(f_2631_1,plain,
! [V_x_2,V_A_2,T_b] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oin__idem]) ).
fof(f_2631_2,plain,
! [U_9548,U_9547,U_9546] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9546),U_9548),c_Big__Operators_Olinorder__class_OMin(U_9546,U_9547)) = c_Big__Operators_Olinorder__class_OMin(U_9546,U_9547)
| ~ hBOOL(hAPP(hAPP(c_member(U_9546),U_9548),U_9547))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9546),U_9547))
| ~ class_Orderings_Olinorder(U_9546) ),
inference(variable_rename,[status(thm)],[f_2631_1]) ).
cnf(f_2631_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9546),U_9548),c_Big__Operators_Olinorder__class_OMin(U_9546,U_9547)) = c_Big__Operators_Olinorder__class_OMin(U_9546,U_9547)
| ~ hBOOL(hAPP(hAPP(c_member(U_9546),U_9548),U_9547))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9546),U_9547))
| ~ class_Orderings_Olinorder(U_9546) ),
inference(clausify,[status(thm)],[f_2631_2]) ).
fof(f_2632_1,plain,
! [V_N_2,V_M_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_M_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| V_M_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min__antimono]) ).
fof(f_2632_2,plain,
! [U_9551,U_9550,U_9549] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9549),c_Big__Operators_Olinorder__class_OMin(U_9549,U_9551)),c_Big__Operators_Olinorder__class_OMin(U_9549,U_9550)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9549),U_9551))
| U_9550 = c_Orderings_Obot__class_Obot(tc_fun(U_9549,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9549,tc_HOL_Obool)),U_9550),U_9551))
| ~ class_Orderings_Olinorder(U_9549) ),
inference(variable_rename,[status(thm)],[f_2632_1]) ).
cnf(f_2632_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9549),c_Big__Operators_Olinorder__class_OMin(U_9549,U_9551)),c_Big__Operators_Olinorder__class_OMin(U_9549,U_9550)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9549),U_9551))
| U_9550 = c_Orderings_Obot__class_Obot(tc_fun(U_9549,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9549,tc_HOL_Obool)),U_9550),U_9551))
| ~ class_Orderings_Olinorder(U_9549) ),
inference(clausify,[status(thm)],[f_2632_2]) ).
fof(f_2633_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min__insert]) ).
fof(f_2633_2,plain,
! [U_9554,U_9553,U_9552] :
( c_Big__Operators_Olinorder__class_OMin(U_9552,hAPP(hAPP(c_Set_Oinsert(U_9552),U_9554),U_9553)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9552),U_9554),c_Big__Operators_Olinorder__class_OMin(U_9552,U_9553))
| U_9553 = c_Orderings_Obot__class_Obot(tc_fun(U_9552,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9552),U_9553))
| ~ class_Orderings_Olinorder(U_9552) ),
inference(variable_rename,[status(thm)],[f_2633_1]) ).
cnf(f_2633_3,plain,
( c_Big__Operators_Olinorder__class_OMin(U_9552,hAPP(hAPP(c_Set_Oinsert(U_9552),U_9554),U_9553)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9552),U_9554),c_Big__Operators_Olinorder__class_OMin(U_9552,U_9553))
| U_9553 = c_Orderings_Obot__class_Obot(tc_fun(U_9552,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9552),U_9553))
| ~ class_Orderings_Olinorder(U_9552) ),
inference(clausify,[status(thm)],[f_2633_2]) ).
fof(f_2634_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Osubset__idem]) ).
fof(f_2634_2,plain,
! [U_9557,U_9556,U_9555] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9555),c_Big__Operators_Olinorder__class_OMin(U_9555,U_9557)),c_Big__Operators_Olinorder__class_OMin(U_9555,U_9556)) = c_Big__Operators_Olinorder__class_OMin(U_9555,U_9556)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9555,tc_HOL_Obool)),U_9557),U_9556))
| U_9557 = c_Orderings_Obot__class_Obot(tc_fun(U_9555,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9555),U_9556))
| ~ class_Orderings_Olinorder(U_9555) ),
inference(variable_rename,[status(thm)],[f_2634_1]) ).
cnf(f_2634_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9555),c_Big__Operators_Olinorder__class_OMin(U_9555,U_9557)),c_Big__Operators_Olinorder__class_OMin(U_9555,U_9556)) = c_Big__Operators_Olinorder__class_OMin(U_9555,U_9556)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9555,tc_HOL_Obool)),U_9557),U_9556))
| U_9557 = c_Orderings_Obot__class_Obot(tc_fun(U_9555,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9555),U_9556))
| ~ class_Orderings_Olinorder(U_9555) ),
inference(clausify,[status(thm)],[f_2634_2]) ).
fof(f_2635_1,plain,
! [V_B_2,V_A_2,T_b] :
( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min__Un]) ).
fof(f_2635_2,plain,
! [U_9560,U_9559,U_9558] :
( c_Big__Operators_Olinorder__class_OMin(U_9558,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9558,tc_HOL_Obool)),U_9559),U_9560)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9558),c_Big__Operators_Olinorder__class_OMin(U_9558,U_9559)),c_Big__Operators_Olinorder__class_OMin(U_9558,U_9560))
| U_9560 = c_Orderings_Obot__class_Obot(tc_fun(U_9558,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9558),U_9560))
| U_9559 = c_Orderings_Obot__class_Obot(tc_fun(U_9558,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9558),U_9559))
| ~ class_Orderings_Olinorder(U_9558) ),
inference(variable_rename,[status(thm)],[f_2635_1]) ).
cnf(f_2635_3,plain,
( c_Big__Operators_Olinorder__class_OMin(U_9558,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9558,tc_HOL_Obool)),U_9559),U_9560)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9558),c_Big__Operators_Olinorder__class_OMin(U_9558,U_9559)),c_Big__Operators_Olinorder__class_OMin(U_9558,U_9560))
| U_9560 = c_Orderings_Obot__class_Obot(tc_fun(U_9558,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9558),U_9560))
| U_9559 = c_Orderings_Obot__class_Obot(tc_fun(U_9558,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9558),U_9559))
| ~ class_Orderings_Olinorder(U_9558) ),
inference(clausify,[status(thm)],[f_2635_2]) ).
fof(f_2636_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oinsert]) ).
fof(f_2636_2,plain,
! [U_9563,U_9562,U_9561] :
( c_Big__Operators_Olinorder__class_OMin(U_9561,hAPP(hAPP(c_Set_Oinsert(U_9561),U_9563),U_9562)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9561),U_9563),c_Big__Operators_Olinorder__class_OMin(U_9561,U_9562))
| U_9562 = c_Orderings_Obot__class_Obot(tc_fun(U_9561,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_9561),U_9563),U_9562))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9561),U_9562))
| ~ class_Orderings_Olinorder(U_9561) ),
inference(variable_rename,[status(thm)],[f_2636_1]) ).
cnf(f_2636_3,plain,
( c_Big__Operators_Olinorder__class_OMin(U_9561,hAPP(hAPP(c_Set_Oinsert(U_9561),U_9563),U_9562)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9561),U_9563),c_Big__Operators_Olinorder__class_OMin(U_9561,U_9562))
| U_9562 = c_Orderings_Obot__class_Obot(tc_fun(U_9561,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_9561),U_9563),U_9562))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9561),U_9562))
| ~ class_Orderings_Olinorder(U_9561) ),
inference(clausify,[status(thm)],[f_2636_2]) ).
fof(f_2637_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oinsert__remove]) ).
fof(f_2637_2,plain,
! [U_9566,U_9565,U_9564] :
( ( ( c_Big__Operators_Olinorder__class_OMin(U_9564,hAPP(hAPP(c_Set_Oinsert(U_9564),U_9566),U_9565)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9564),U_9566),c_Big__Operators_Olinorder__class_OMin(U_9564,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9564,tc_HOL_Obool)),U_9565),hAPP(hAPP(c_Set_Oinsert(U_9564),U_9566),c_Orderings_Obot__class_Obot(tc_fun(U_9564,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9564,tc_HOL_Obool)),U_9565),hAPP(hAPP(c_Set_Oinsert(U_9564),U_9566),c_Orderings_Obot__class_Obot(tc_fun(U_9564,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9564,tc_HOL_Obool)) )
& ( c_Big__Operators_Olinorder__class_OMin(U_9564,hAPP(hAPP(c_Set_Oinsert(U_9564),U_9566),U_9565)) = U_9566
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9564,tc_HOL_Obool)),U_9565),hAPP(hAPP(c_Set_Oinsert(U_9564),U_9566),c_Orderings_Obot__class_Obot(tc_fun(U_9564,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9564,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9564),U_9565))
| ~ class_Orderings_Olinorder(U_9564) ),
inference(variable_rename,[status(thm)],[f_2637_1]) ).
cnf(f_2637_3,plain,
( c_Big__Operators_Olinorder__class_OMin(U_9564,hAPP(hAPP(c_Set_Oinsert(U_9564),U_9566),U_9565)) = U_9566
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9564,tc_HOL_Obool)),U_9565),hAPP(hAPP(c_Set_Oinsert(U_9564),U_9566),c_Orderings_Obot__class_Obot(tc_fun(U_9564,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9564,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9564),U_9565))
| ~ class_Orderings_Olinorder(U_9564) ),
inference(clausify,[status(thm)],[f_2637_2]) ).
cnf(f_2637_4,plain,
( c_Big__Operators_Olinorder__class_OMin(U_9564,hAPP(hAPP(c_Set_Oinsert(U_9564),U_9566),U_9565)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9564),U_9566),c_Big__Operators_Olinorder__class_OMin(U_9564,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9564,tc_HOL_Obool)),U_9565),hAPP(hAPP(c_Set_Oinsert(U_9564),U_9566),c_Orderings_Obot__class_Obot(tc_fun(U_9564,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9564,tc_HOL_Obool)),U_9565),hAPP(hAPP(c_Set_Oinsert(U_9564),U_9566),c_Orderings_Obot__class_Obot(tc_fun(U_9564,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9564,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9564),U_9565))
| ~ class_Orderings_Olinorder(U_9564) ),
inference(clausify,[status(thm)],[f_2637_2]) ).
fof(f_2638_1,plain,
! [V_S_2,T_b] :
( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2))
| V_S_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_minus__Min__eq__Max]) ).
fof(f_2638_2,plain,
! [U_9568,U_9567] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_9567),c_Big__Operators_Olinorder__class_OMin(U_9567,U_9568)) = c_Big__Operators_Olinorder__class_OMax(U_9567,hAPP(c_Set_Oimage(U_9567,U_9567,c_Groups_Ouminus__class_Ouminus(U_9567)),U_9568))
| U_9568 = c_Orderings_Obot__class_Obot(tc_fun(U_9567,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9567),U_9568))
| ~ class_Groups_Olinordered__ab__group__add(U_9567) ),
inference(variable_rename,[status(thm)],[f_2638_1]) ).
cnf(f_2638_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_9567),c_Big__Operators_Olinorder__class_OMin(U_9567,U_9568)) = c_Big__Operators_Olinorder__class_OMax(U_9567,hAPP(c_Set_Oimage(U_9567,U_9567,c_Groups_Ouminus__class_Ouminus(U_9567)),U_9568))
| U_9568 = c_Orderings_Obot__class_Obot(tc_fun(U_9567,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9567),U_9568))
| ~ class_Groups_Olinordered__ab__group__add(U_9567) ),
inference(clausify,[status(thm)],[f_2638_2]) ).
fof(f_2639_1,plain,
! [V_S_2,T_b] :
( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2))
| V_S_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Olinordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_minus__Max__eq__Min]) ).
fof(f_2639_2,plain,
! [U_9570,U_9569] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_9569),c_Big__Operators_Olinorder__class_OMax(U_9569,U_9570)) = c_Big__Operators_Olinorder__class_OMin(U_9569,hAPP(c_Set_Oimage(U_9569,U_9569,c_Groups_Ouminus__class_Ouminus(U_9569)),U_9570))
| U_9570 = c_Orderings_Obot__class_Obot(tc_fun(U_9569,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9569),U_9570))
| ~ class_Groups_Olinordered__ab__group__add(U_9569) ),
inference(variable_rename,[status(thm)],[f_2639_1]) ).
cnf(f_2639_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_9569),c_Big__Operators_Olinorder__class_OMax(U_9569,U_9570)) = c_Big__Operators_Olinorder__class_OMin(U_9569,hAPP(c_Set_Oimage(U_9569,U_9569,c_Groups_Ouminus__class_Ouminus(U_9569)),U_9570))
| U_9570 = c_Orderings_Obot__class_Obot(tc_fun(U_9569,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9569),U_9570))
| ~ class_Groups_Olinordered__ab__group__add(U_9569) ),
inference(clausify,[status(thm)],[f_2639_2]) ).
fof(f_2640_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2))
| ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oclosed]) ).
fof(f_2640_2,plain,
! [U_9574,U_9573] :
( hBOOL(hAPP(hAPP(c_member(U_9573),c_Big__Operators_Olinorder__class_OMin(U_9573,U_9574)),U_9574))
| ? [U_9572,U_9571] : ~ hBOOL(hAPP(hAPP(c_member(U_9573),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9573),U_9572),U_9571)),hAPP(hAPP(c_Set_Oinsert(U_9573),U_9572),hAPP(hAPP(c_Set_Oinsert(U_9573),U_9571),c_Orderings_Obot__class_Obot(tc_fun(U_9573,tc_HOL_Obool))))))
| U_9574 = c_Orderings_Obot__class_Obot(tc_fun(U_9573,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9573),U_9574))
| ~ class_Orderings_Olinorder(U_9573) ),
inference(variable_rename,[status(thm)],[f_2640_1]) ).
fof(f_2640_3,plain,
! [U_9574,U_9573] :
( hBOOL(hAPP(hAPP(c_member(U_9573),c_Big__Operators_Olinorder__class_OMin(U_9573,U_9574)),U_9574))
| ? [U_9571] : ~ hBOOL(hAPP(hAPP(c_member(U_9573),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9573),sK193(U_9574,U_9573)),U_9571)),hAPP(hAPP(c_Set_Oinsert(U_9573),sK193(U_9574,U_9573)),hAPP(hAPP(c_Set_Oinsert(U_9573),U_9571),c_Orderings_Obot__class_Obot(tc_fun(U_9573,tc_HOL_Obool))))))
| U_9574 = c_Orderings_Obot__class_Obot(tc_fun(U_9573,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9573),U_9574))
| ~ class_Orderings_Olinorder(U_9573) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK193]),skolemize(U_9572,sK193(U_9574,U_9573))],[f_2640_2]) ).
fof(f_2640_4,plain,
! [U_9574,U_9573] :
( hBOOL(hAPP(hAPP(c_member(U_9573),c_Big__Operators_Olinorder__class_OMin(U_9573,U_9574)),U_9574))
| ~ hBOOL(hAPP(hAPP(c_member(U_9573),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9573),sK193(U_9574,U_9573)),sK194(U_9574,U_9573))),hAPP(hAPP(c_Set_Oinsert(U_9573),sK193(U_9574,U_9573)),hAPP(hAPP(c_Set_Oinsert(U_9573),sK194(U_9574,U_9573)),c_Orderings_Obot__class_Obot(tc_fun(U_9573,tc_HOL_Obool))))))
| U_9574 = c_Orderings_Obot__class_Obot(tc_fun(U_9573,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9573),U_9574))
| ~ class_Orderings_Olinorder(U_9573) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK194]),skolemize(U_9571,sK194(U_9574,U_9573))],[f_2640_3]) ).
cnf(f_2640_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9573),c_Big__Operators_Olinorder__class_OMin(U_9573,U_9574)),U_9574))
| ~ hBOOL(hAPP(hAPP(c_member(U_9573),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9573),sK193(U_9574,U_9573)),sK194(U_9574,U_9573))),hAPP(hAPP(c_Set_Oinsert(U_9573),sK193(U_9574,U_9573)),hAPP(hAPP(c_Set_Oinsert(U_9573),sK194(U_9574,U_9573)),c_Orderings_Obot__class_Obot(tc_fun(U_9573,tc_HOL_Obool))))))
| U_9574 = c_Orderings_Obot__class_Obot(tc_fun(U_9573,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9573),U_9574))
| ~ class_Orderings_Olinorder(U_9573) ),
inference(clausify,[status(thm)],[f_2640_4]) ).
fof(f_2641_1,plain,
! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_b_H_2)),V_s_2))
| V_a_2 != V_a_H_2 )
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2)) ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_b_H_2)),V_s_2))
& V_a_2 = V_a_H_2 )
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_in__lex__prod]) ).
fof(f_2641_2,plain,
! [U_9582,U_9581,U_9580,U_9579,U_9578,U_9577,U_9576,U_9575] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_9575,U_9576),tc_prod(U_9575,U_9576))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_9575,U_9576),tc_prod(U_9575,U_9576)),hAPP(hAPP(c_Product__Type_OPair(U_9575,U_9576),U_9577),U_9578)),hAPP(hAPP(c_Product__Type_OPair(U_9575,U_9576),U_9579),U_9580))),c_Wellfounded_Olex__prod(U_9575,U_9576,U_9581,U_9582)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9576,U_9576)),hAPP(hAPP(c_Product__Type_OPair(U_9576,U_9576),U_9578),U_9580)),U_9582))
| U_9577 != U_9579 )
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9575,U_9575)),hAPP(hAPP(c_Product__Type_OPair(U_9575,U_9575),U_9577),U_9579)),U_9581)) ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9576,U_9576)),hAPP(hAPP(c_Product__Type_OPair(U_9576,U_9576),U_9578),U_9580)),U_9582))
& U_9577 = U_9579 )
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_9575,U_9575)),hAPP(hAPP(c_Product__Type_OPair(U_9575,U_9575),U_9577),U_9579)),U_9581))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_9575,U_9576),tc_prod(U_9575,U_9576))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_9575,U_9576),tc_prod(U_9575,U_9576)),hAPP(hAPP(c_Product__Type_OPair(U_9575,U_9576),U_9577),U_9578)),hAPP(hAPP(c_Product__Type_OPair(U_9575,U_9576),U_9579),U_9580))),c_Wellfounded_Olex__prod(U_9575,U_9576,U_9581,U_9582))) ) ),
inference(variable_rename,[status(thm)],[f_2641_1]) ).
fof(f_2641_3,plain,
( ! [U_9598,U_9596,U_9594,U_9592,U_9590,U_9588,U_9586,U_9584] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_9584,U_9586),tc_prod(U_9584,U_9586))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_9584,U_9586),tc_prod(U_9584,U_9586)),hAPP(hAPP(c_Product__Type_OPair(U_9584,U_9586),U_9588),U_9590)),hAPP(hAPP(c_Product__Type_OPair(U_9584,U_9586),U_9592),U_9594))),c_Wellfounded_Olex__prod(U_9584,U_9586,U_9596,U_9598)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9586,U_9586)),hAPP(hAPP(c_Product__Type_OPair(U_9586,U_9586),U_9590),U_9594)),U_9598))
| U_9588 != U_9592 )
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9584,U_9584)),hAPP(hAPP(c_Product__Type_OPair(U_9584,U_9584),U_9588),U_9592)),U_9596)) ) )
& ! [U_9597,U_9595,U_9593,U_9591,U_9589,U_9587,U_9585,U_9583] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9585,U_9585)),hAPP(hAPP(c_Product__Type_OPair(U_9585,U_9585),U_9589),U_9593)),U_9597))
& U_9587 = U_9591 )
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_9583,U_9583)),hAPP(hAPP(c_Product__Type_OPair(U_9583,U_9583),U_9587),U_9591)),U_9595))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_9583,U_9585),tc_prod(U_9583,U_9585))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_9583,U_9585),tc_prod(U_9583,U_9585)),hAPP(hAPP(c_Product__Type_OPair(U_9583,U_9585),U_9587),U_9589)),hAPP(hAPP(c_Product__Type_OPair(U_9583,U_9585),U_9591),U_9593))),c_Wellfounded_Olex__prod(U_9583,U_9585,U_9595,U_9597))) ) ),
inference(miniscope,[status(thm)],[f_2641_2]) ).
cnf(f_2641_4,plain,
( U_9587 = U_9591
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_9583,U_9583)),hAPP(hAPP(c_Product__Type_OPair(U_9583,U_9583),U_9587),U_9591)),U_9595))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_9583,U_9585),tc_prod(U_9583,U_9585))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_9583,U_9585),tc_prod(U_9583,U_9585)),hAPP(hAPP(c_Product__Type_OPair(U_9583,U_9585),U_9587),U_9589)),hAPP(hAPP(c_Product__Type_OPair(U_9583,U_9585),U_9591),U_9593))),c_Wellfounded_Olex__prod(U_9583,U_9585,U_9595,U_9597))) ),
inference(clausify,[status(thm)],[f_2641_3]) ).
cnf(f_2641_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9585,U_9585)),hAPP(hAPP(c_Product__Type_OPair(U_9585,U_9585),U_9589),U_9593)),U_9597))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_9583,U_9583)),hAPP(hAPP(c_Product__Type_OPair(U_9583,U_9583),U_9587),U_9591)),U_9595))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_9583,U_9585),tc_prod(U_9583,U_9585))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_9583,U_9585),tc_prod(U_9583,U_9585)),hAPP(hAPP(c_Product__Type_OPair(U_9583,U_9585),U_9587),U_9589)),hAPP(hAPP(c_Product__Type_OPair(U_9583,U_9585),U_9591),U_9593))),c_Wellfounded_Olex__prod(U_9583,U_9585,U_9595,U_9597))) ),
inference(clausify,[status(thm)],[f_2641_3]) ).
cnf(f_2641_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9584,U_9584)),hAPP(hAPP(c_Product__Type_OPair(U_9584,U_9584),U_9588),U_9592)),U_9596))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_9584,U_9586),tc_prod(U_9584,U_9586))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_9584,U_9586),tc_prod(U_9584,U_9586)),hAPP(hAPP(c_Product__Type_OPair(U_9584,U_9586),U_9588),U_9590)),hAPP(hAPP(c_Product__Type_OPair(U_9584,U_9586),U_9592),U_9594))),c_Wellfounded_Olex__prod(U_9584,U_9586,U_9596,U_9598))) ),
inference(clausify,[status(thm)],[f_2641_3]) ).
cnf(f_2641_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9586,U_9586)),hAPP(hAPP(c_Product__Type_OPair(U_9586,U_9586),U_9590),U_9594)),U_9598))
| U_9588 != U_9592
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_9584,U_9586),tc_prod(U_9584,U_9586))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_9584,U_9586),tc_prod(U_9584,U_9586)),hAPP(hAPP(c_Product__Type_OPair(U_9584,U_9586),U_9588),U_9590)),hAPP(hAPP(c_Product__Type_OPair(U_9584,U_9586),U_9592),U_9594))),c_Wellfounded_Olex__prod(U_9584,U_9586,U_9596,U_9598))) ),
inference(clausify,[status(thm)],[f_2641_3]) ).
fof(f_2642_1,plain,
! [V_B_2,V_A_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_b)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_b))) ) ),
inference(fof_nnf,[status(thm)],[fact_in__finite__psubset]) ).
fof(f_2642_2,plain,
! [U_9601,U_9600,U_9599] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9599,tc_HOL_Obool),tc_fun(U_9599,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9599,tc_HOL_Obool),tc_fun(U_9599,tc_HOL_Obool)),U_9600),U_9601)),c_Wellfounded_Ofinite__psubset(U_9599)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9599),U_9601))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9599,tc_HOL_Obool)),U_9600),U_9601)) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9599),U_9601))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9599,tc_HOL_Obool)),U_9600),U_9601)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9599,tc_HOL_Obool),tc_fun(U_9599,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9599,tc_HOL_Obool),tc_fun(U_9599,tc_HOL_Obool)),U_9600),U_9601)),c_Wellfounded_Ofinite__psubset(U_9599))) ) ),
inference(variable_rename,[status(thm)],[f_2642_1]) ).
fof(f_2642_3,plain,
( ! [U_9607,U_9605,U_9603] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9603,tc_HOL_Obool),tc_fun(U_9603,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9603,tc_HOL_Obool),tc_fun(U_9603,tc_HOL_Obool)),U_9605),U_9607)),c_Wellfounded_Ofinite__psubset(U_9603)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9603),U_9607))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9603,tc_HOL_Obool)),U_9605),U_9607)) )
& ! [U_9606,U_9604,U_9602] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9602),U_9606))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9602,tc_HOL_Obool)),U_9604),U_9606)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9602,tc_HOL_Obool),tc_fun(U_9602,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9602,tc_HOL_Obool),tc_fun(U_9602,tc_HOL_Obool)),U_9604),U_9606)),c_Wellfounded_Ofinite__psubset(U_9602))) ) ),
inference(miniscope,[status(thm)],[f_2642_2]) ).
cnf(f_2642_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9602,tc_HOL_Obool)),U_9604),U_9606))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9602,tc_HOL_Obool),tc_fun(U_9602,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9602,tc_HOL_Obool),tc_fun(U_9602,tc_HOL_Obool)),U_9604),U_9606)),c_Wellfounded_Ofinite__psubset(U_9602))) ),
inference(clausify,[status(thm)],[f_2642_3]) ).
cnf(f_2642_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9602),U_9606))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9602,tc_HOL_Obool),tc_fun(U_9602,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9602,tc_HOL_Obool),tc_fun(U_9602,tc_HOL_Obool)),U_9604),U_9606)),c_Wellfounded_Ofinite__psubset(U_9602))) ),
inference(clausify,[status(thm)],[f_2642_3]) ).
cnf(f_2642_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9603,tc_HOL_Obool),tc_fun(U_9603,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9603,tc_HOL_Obool),tc_fun(U_9603,tc_HOL_Obool)),U_9605),U_9607)),c_Wellfounded_Ofinite__psubset(U_9603)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9603),U_9607))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9603,tc_HOL_Obool)),U_9605),U_9607)) ),
inference(clausify,[status(thm)],[f_2642_3]) ).
fof(f_2643_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oremove]) ).
fof(f_2643_2,plain,
! [U_9610,U_9609,U_9608] :
( ( ( c_Big__Operators_Olattice_OSup__fin(U_9608,c_Orderings_Oord__class_Omax(U_9608),U_9609) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9608),U_9610),c_Big__Operators_Olattice_OSup__fin(U_9608,c_Orderings_Oord__class_Omax(U_9608),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9608,tc_HOL_Obool)),U_9609),hAPP(hAPP(c_Set_Oinsert(U_9608),U_9610),c_Orderings_Obot__class_Obot(tc_fun(U_9608,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9608,tc_HOL_Obool)),U_9609),hAPP(hAPP(c_Set_Oinsert(U_9608),U_9610),c_Orderings_Obot__class_Obot(tc_fun(U_9608,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9608,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OSup__fin(U_9608,c_Orderings_Oord__class_Omax(U_9608),U_9609) = U_9610
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9608,tc_HOL_Obool)),U_9609),hAPP(hAPP(c_Set_Oinsert(U_9608),U_9610),c_Orderings_Obot__class_Obot(tc_fun(U_9608,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9608,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9608),U_9610),U_9609))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9608),U_9609))
| ~ class_Orderings_Olinorder(U_9608) ),
inference(variable_rename,[status(thm)],[f_2643_1]) ).
cnf(f_2643_3,plain,
( c_Big__Operators_Olattice_OSup__fin(U_9608,c_Orderings_Oord__class_Omax(U_9608),U_9609) = U_9610
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9608,tc_HOL_Obool)),U_9609),hAPP(hAPP(c_Set_Oinsert(U_9608),U_9610),c_Orderings_Obot__class_Obot(tc_fun(U_9608,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9608,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9608),U_9610),U_9609))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9608),U_9609))
| ~ class_Orderings_Olinorder(U_9608) ),
inference(clausify,[status(thm)],[f_2643_2]) ).
cnf(f_2643_4,plain,
( c_Big__Operators_Olattice_OSup__fin(U_9608,c_Orderings_Oord__class_Omax(U_9608),U_9609) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9608),U_9610),c_Big__Operators_Olattice_OSup__fin(U_9608,c_Orderings_Oord__class_Omax(U_9608),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9608,tc_HOL_Obool)),U_9609),hAPP(hAPP(c_Set_Oinsert(U_9608),U_9610),c_Orderings_Obot__class_Obot(tc_fun(U_9608,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9608,tc_HOL_Obool)),U_9609),hAPP(hAPP(c_Set_Oinsert(U_9608),U_9610),c_Orderings_Obot__class_Obot(tc_fun(U_9608,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9608,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9608),U_9610),U_9609))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9608),U_9609))
| ~ class_Orderings_Olinorder(U_9608) ),
inference(clausify,[status(thm)],[f_2643_2]) ).
fof(f_2644_1,plain,
! [V_x_2,V_A_2,T_b] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oin__idem]) ).
fof(f_2644_2,plain,
! [U_9613,U_9612,U_9611] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9611),U_9613),c_Big__Operators_Olattice_OSup__fin(U_9611,c_Orderings_Oord__class_Omax(U_9611),U_9612)) = c_Big__Operators_Olattice_OSup__fin(U_9611,c_Orderings_Oord__class_Omax(U_9611),U_9612)
| ~ hBOOL(hAPP(hAPP(c_member(U_9611),U_9613),U_9612))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9611),U_9612))
| ~ class_Orderings_Olinorder(U_9611) ),
inference(variable_rename,[status(thm)],[f_2644_1]) ).
cnf(f_2644_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9611),U_9613),c_Big__Operators_Olattice_OSup__fin(U_9611,c_Orderings_Oord__class_Omax(U_9611),U_9612)) = c_Big__Operators_Olattice_OSup__fin(U_9611,c_Orderings_Oord__class_Omax(U_9611),U_9612)
| ~ hBOOL(hAPP(hAPP(c_member(U_9611),U_9613),U_9612))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9611),U_9612))
| ~ class_Orderings_Olinorder(U_9611) ),
inference(clausify,[status(thm)],[f_2644_2]) ).
fof(f_2645_1,plain,
! [V_x_2,T_b] :
( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osingleton]) ).
fof(f_2645_2,plain,
! [U_9615,U_9614] :
( c_Big__Operators_Olattice_OSup__fin(U_9614,c_Orderings_Oord__class_Omax(U_9614),hAPP(hAPP(c_Set_Oinsert(U_9614),U_9615),c_Orderings_Obot__class_Obot(tc_fun(U_9614,tc_HOL_Obool)))) = U_9615
| ~ class_Orderings_Olinorder(U_9614) ),
inference(variable_rename,[status(thm)],[f_2645_1]) ).
cnf(f_2645_3,plain,
( c_Big__Operators_Olattice_OSup__fin(U_9614,c_Orderings_Oord__class_Omax(U_9614),hAPP(hAPP(c_Set_Oinsert(U_9614),U_9615),c_Orderings_Obot__class_Obot(tc_fun(U_9614,tc_HOL_Obool)))) = U_9615
| ~ class_Orderings_Olinorder(U_9614) ),
inference(clausify,[status(thm)],[f_2645_2]) ).
fof(f_2646_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__idem]) ).
fof(f_2646_2,plain,
! [U_9618,U_9617,U_9616] :
( c_Big__Operators_Olattice_OSup__fin(U_9616,c_Orderings_Oord__class_Omax(U_9616),hAPP(hAPP(c_Set_Oinsert(U_9616),U_9618),U_9617)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9616),U_9618),c_Big__Operators_Olattice_OSup__fin(U_9616,c_Orderings_Oord__class_Omax(U_9616),U_9617))
| U_9617 = c_Orderings_Obot__class_Obot(tc_fun(U_9616,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9616),U_9617))
| ~ class_Orderings_Olinorder(U_9616) ),
inference(variable_rename,[status(thm)],[f_2646_1]) ).
cnf(f_2646_3,plain,
( c_Big__Operators_Olattice_OSup__fin(U_9616,c_Orderings_Oord__class_Omax(U_9616),hAPP(hAPP(c_Set_Oinsert(U_9616),U_9618),U_9617)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9616),U_9618),c_Big__Operators_Olattice_OSup__fin(U_9616,c_Orderings_Oord__class_Omax(U_9616),U_9617))
| U_9617 = c_Orderings_Obot__class_Obot(tc_fun(U_9616,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9616),U_9617))
| ~ class_Orderings_Olinorder(U_9616) ),
inference(clausify,[status(thm)],[f_2646_2]) ).
fof(f_2647_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osubset__idem]) ).
fof(f_2647_2,plain,
! [U_9621,U_9620,U_9619] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9619),c_Big__Operators_Olattice_OSup__fin(U_9619,c_Orderings_Oord__class_Omax(U_9619),U_9621)),c_Big__Operators_Olattice_OSup__fin(U_9619,c_Orderings_Oord__class_Omax(U_9619),U_9620)) = c_Big__Operators_Olattice_OSup__fin(U_9619,c_Orderings_Oord__class_Omax(U_9619),U_9620)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9619,tc_HOL_Obool)),U_9621),U_9620))
| U_9621 = c_Orderings_Obot__class_Obot(tc_fun(U_9619,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9619),U_9620))
| ~ class_Orderings_Olinorder(U_9619) ),
inference(variable_rename,[status(thm)],[f_2647_1]) ).
cnf(f_2647_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9619),c_Big__Operators_Olattice_OSup__fin(U_9619,c_Orderings_Oord__class_Omax(U_9619),U_9621)),c_Big__Operators_Olattice_OSup__fin(U_9619,c_Orderings_Oord__class_Omax(U_9619),U_9620)) = c_Big__Operators_Olattice_OSup__fin(U_9619,c_Orderings_Oord__class_Omax(U_9619),U_9620)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9619,tc_HOL_Obool)),U_9621),U_9620))
| U_9621 = c_Orderings_Obot__class_Obot(tc_fun(U_9619,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9619),U_9620))
| ~ class_Orderings_Olinorder(U_9619) ),
inference(clausify,[status(thm)],[f_2647_2]) ).
fof(f_2648_1,plain,
! [V_a_2,V_A_2,T_b] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = V_a_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup__absorb]) ).
fof(f_2648_2,plain,
! [U_9624,U_9623,U_9622] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9622),U_9624),c_Big__Operators_Olattice_OSup__fin(U_9622,c_Orderings_Oord__class_Omax(U_9622),U_9623)) = U_9624
| ~ hBOOL(hAPP(hAPP(c_member(U_9622),U_9624),U_9623))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9622),U_9623))
| ~ class_Orderings_Olinorder(U_9622) ),
inference(variable_rename,[status(thm)],[f_2648_1]) ).
cnf(f_2648_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9622),U_9624),c_Big__Operators_Olattice_OSup__fin(U_9622,c_Orderings_Oord__class_Omax(U_9622),U_9623)) = U_9624
| ~ hBOOL(hAPP(hAPP(c_member(U_9622),U_9624),U_9623))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9622),U_9623))
| ~ class_Orderings_Olinorder(U_9622) ),
inference(clausify,[status(thm)],[f_2648_2]) ).
fof(f_2649_1,plain,
! [V_B_2,V_A_2,T_b] :
( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__idem]) ).
fof(f_2649_2,plain,
! [U_9627,U_9626,U_9625] :
( c_Big__Operators_Olattice_OSup__fin(U_9625,c_Orderings_Oord__class_Omax(U_9625),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9625,tc_HOL_Obool)),U_9626),U_9627)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9625),c_Big__Operators_Olattice_OSup__fin(U_9625,c_Orderings_Oord__class_Omax(U_9625),U_9626)),c_Big__Operators_Olattice_OSup__fin(U_9625,c_Orderings_Oord__class_Omax(U_9625),U_9627))
| U_9627 = c_Orderings_Obot__class_Obot(tc_fun(U_9625,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9625),U_9627))
| U_9626 = c_Orderings_Obot__class_Obot(tc_fun(U_9625,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9625),U_9626))
| ~ class_Orderings_Olinorder(U_9625) ),
inference(variable_rename,[status(thm)],[f_2649_1]) ).
cnf(f_2649_3,plain,
( c_Big__Operators_Olattice_OSup__fin(U_9625,c_Orderings_Oord__class_Omax(U_9625),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9625,tc_HOL_Obool)),U_9626),U_9627)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9625),c_Big__Operators_Olattice_OSup__fin(U_9625,c_Orderings_Oord__class_Omax(U_9625),U_9626)),c_Big__Operators_Olattice_OSup__fin(U_9625,c_Orderings_Oord__class_Omax(U_9625),U_9627))
| U_9627 = c_Orderings_Obot__class_Obot(tc_fun(U_9625,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9625),U_9627))
| U_9626 = c_Orderings_Obot__class_Obot(tc_fun(U_9625,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9625),U_9626))
| ~ class_Orderings_Olinorder(U_9625) ),
inference(clausify,[status(thm)],[f_2649_2]) ).
fof(f_2650_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert]) ).
fof(f_2650_2,plain,
! [U_9630,U_9629,U_9628] :
( c_Big__Operators_Olattice_OSup__fin(U_9628,c_Orderings_Oord__class_Omax(U_9628),hAPP(hAPP(c_Set_Oinsert(U_9628),U_9630),U_9629)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9628),U_9630),c_Big__Operators_Olattice_OSup__fin(U_9628,c_Orderings_Oord__class_Omax(U_9628),U_9629))
| U_9629 = c_Orderings_Obot__class_Obot(tc_fun(U_9628,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_9628),U_9630),U_9629))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9628),U_9629))
| ~ class_Orderings_Olinorder(U_9628) ),
inference(variable_rename,[status(thm)],[f_2650_1]) ).
cnf(f_2650_3,plain,
( c_Big__Operators_Olattice_OSup__fin(U_9628,c_Orderings_Oord__class_Omax(U_9628),hAPP(hAPP(c_Set_Oinsert(U_9628),U_9630),U_9629)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9628),U_9630),c_Big__Operators_Olattice_OSup__fin(U_9628,c_Orderings_Oord__class_Omax(U_9628),U_9629))
| U_9629 = c_Orderings_Obot__class_Obot(tc_fun(U_9628,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_9628),U_9630),U_9629))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9628),U_9629))
| ~ class_Orderings_Olinorder(U_9628) ),
inference(clausify,[status(thm)],[f_2650_2]) ).
fof(f_2651_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__remove]) ).
fof(f_2651_2,plain,
! [U_9633,U_9632,U_9631] :
( ( ( c_Big__Operators_Olattice_OSup__fin(U_9631,c_Orderings_Oord__class_Omax(U_9631),hAPP(hAPP(c_Set_Oinsert(U_9631),U_9633),U_9632)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9631),U_9633),c_Big__Operators_Olattice_OSup__fin(U_9631,c_Orderings_Oord__class_Omax(U_9631),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9631,tc_HOL_Obool)),U_9632),hAPP(hAPP(c_Set_Oinsert(U_9631),U_9633),c_Orderings_Obot__class_Obot(tc_fun(U_9631,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9631,tc_HOL_Obool)),U_9632),hAPP(hAPP(c_Set_Oinsert(U_9631),U_9633),c_Orderings_Obot__class_Obot(tc_fun(U_9631,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9631,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OSup__fin(U_9631,c_Orderings_Oord__class_Omax(U_9631),hAPP(hAPP(c_Set_Oinsert(U_9631),U_9633),U_9632)) = U_9633
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9631,tc_HOL_Obool)),U_9632),hAPP(hAPP(c_Set_Oinsert(U_9631),U_9633),c_Orderings_Obot__class_Obot(tc_fun(U_9631,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9631,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9631),U_9632))
| ~ class_Orderings_Olinorder(U_9631) ),
inference(variable_rename,[status(thm)],[f_2651_1]) ).
cnf(f_2651_3,plain,
( c_Big__Operators_Olattice_OSup__fin(U_9631,c_Orderings_Oord__class_Omax(U_9631),hAPP(hAPP(c_Set_Oinsert(U_9631),U_9633),U_9632)) = U_9633
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9631,tc_HOL_Obool)),U_9632),hAPP(hAPP(c_Set_Oinsert(U_9631),U_9633),c_Orderings_Obot__class_Obot(tc_fun(U_9631,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9631,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9631),U_9632))
| ~ class_Orderings_Olinorder(U_9631) ),
inference(clausify,[status(thm)],[f_2651_2]) ).
cnf(f_2651_4,plain,
( c_Big__Operators_Olattice_OSup__fin(U_9631,c_Orderings_Oord__class_Omax(U_9631),hAPP(hAPP(c_Set_Oinsert(U_9631),U_9633),U_9632)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9631),U_9633),c_Big__Operators_Olattice_OSup__fin(U_9631,c_Orderings_Oord__class_Omax(U_9631),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9631,tc_HOL_Obool)),U_9632),hAPP(hAPP(c_Set_Oinsert(U_9631),U_9633),c_Orderings_Obot__class_Obot(tc_fun(U_9631,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9631,tc_HOL_Obool)),U_9632),hAPP(hAPP(c_Set_Oinsert(U_9631),U_9633),c_Orderings_Obot__class_Obot(tc_fun(U_9631,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9631,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9631),U_9632))
| ~ class_Orderings_Olinorder(U_9631) ),
inference(clausify,[status(thm)],[f_2651_2]) ).
fof(f_2652_1,plain,
! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_P_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
| ~ hBOOL(hAPP(V_P_2,V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_same__fstI]) ).
fof(f_2652_2,plain,
! [U_9640,U_9639,U_9638,U_9637,U_9636,U_9635,U_9634] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_9640,U_9636),tc_prod(U_9640,U_9636))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_9640,U_9636),tc_prod(U_9640,U_9636)),hAPP(hAPP(c_Product__Type_OPair(U_9640,U_9636),U_9635),U_9637)),hAPP(hAPP(c_Product__Type_OPair(U_9640,U_9636),U_9635),U_9638))),c_Recdef_Osame__fst(U_9640,U_9636,U_9634,U_9639)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9636,U_9636)),hAPP(hAPP(c_Product__Type_OPair(U_9636,U_9636),U_9637),U_9638)),hAPP(U_9639,U_9635)))
| ~ hBOOL(hAPP(U_9634,U_9635)) ),
inference(variable_rename,[status(thm)],[f_2652_1]) ).
cnf(f_2652_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_9640,U_9636),tc_prod(U_9640,U_9636))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_9640,U_9636),tc_prod(U_9640,U_9636)),hAPP(hAPP(c_Product__Type_OPair(U_9640,U_9636),U_9635),U_9637)),hAPP(hAPP(c_Product__Type_OPair(U_9640,U_9636),U_9635),U_9638))),c_Recdef_Osame__fst(U_9640,U_9636,U_9634,U_9639)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9636,U_9636)),hAPP(hAPP(c_Product__Type_OPair(U_9636,U_9636),U_9637),U_9638)),hAPP(U_9639,U_9635)))
| ~ hBOOL(hAPP(U_9634,U_9635)) ),
inference(clausify,[status(thm)],[f_2652_2]) ).
fof(f_2653_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),V_A_2))
| ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oclosed]) ).
fof(f_2653_2,plain,
! [U_9644,U_9643] :
( hBOOL(hAPP(hAPP(c_member(U_9643),c_Big__Operators_Olattice_OSup__fin(U_9643,c_Orderings_Oord__class_Omax(U_9643),U_9644)),U_9644))
| ? [U_9642,U_9641] : ~ hBOOL(hAPP(hAPP(c_member(U_9643),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9643),U_9642),U_9641)),hAPP(hAPP(c_Set_Oinsert(U_9643),U_9642),hAPP(hAPP(c_Set_Oinsert(U_9643),U_9641),c_Orderings_Obot__class_Obot(tc_fun(U_9643,tc_HOL_Obool))))))
| U_9644 = c_Orderings_Obot__class_Obot(tc_fun(U_9643,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9643),U_9644))
| ~ class_Orderings_Olinorder(U_9643) ),
inference(variable_rename,[status(thm)],[f_2653_1]) ).
fof(f_2653_3,plain,
! [U_9644,U_9643] :
( hBOOL(hAPP(hAPP(c_member(U_9643),c_Big__Operators_Olattice_OSup__fin(U_9643,c_Orderings_Oord__class_Omax(U_9643),U_9644)),U_9644))
| ? [U_9641] : ~ hBOOL(hAPP(hAPP(c_member(U_9643),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9643),sK195(U_9644,U_9643)),U_9641)),hAPP(hAPP(c_Set_Oinsert(U_9643),sK195(U_9644,U_9643)),hAPP(hAPP(c_Set_Oinsert(U_9643),U_9641),c_Orderings_Obot__class_Obot(tc_fun(U_9643,tc_HOL_Obool))))))
| U_9644 = c_Orderings_Obot__class_Obot(tc_fun(U_9643,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9643),U_9644))
| ~ class_Orderings_Olinorder(U_9643) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK195]),skolemize(U_9642,sK195(U_9644,U_9643))],[f_2653_2]) ).
fof(f_2653_4,plain,
! [U_9644,U_9643] :
( hBOOL(hAPP(hAPP(c_member(U_9643),c_Big__Operators_Olattice_OSup__fin(U_9643,c_Orderings_Oord__class_Omax(U_9643),U_9644)),U_9644))
| ~ hBOOL(hAPP(hAPP(c_member(U_9643),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9643),sK195(U_9644,U_9643)),sK196(U_9644,U_9643))),hAPP(hAPP(c_Set_Oinsert(U_9643),sK195(U_9644,U_9643)),hAPP(hAPP(c_Set_Oinsert(U_9643),sK196(U_9644,U_9643)),c_Orderings_Obot__class_Obot(tc_fun(U_9643,tc_HOL_Obool))))))
| U_9644 = c_Orderings_Obot__class_Obot(tc_fun(U_9643,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9643),U_9644))
| ~ class_Orderings_Olinorder(U_9643) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK196]),skolemize(U_9641,sK196(U_9644,U_9643))],[f_2653_3]) ).
cnf(f_2653_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9643),c_Big__Operators_Olattice_OSup__fin(U_9643,c_Orderings_Oord__class_Omax(U_9643),U_9644)),U_9644))
| ~ hBOOL(hAPP(hAPP(c_member(U_9643),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9643),sK195(U_9644,U_9643)),sK196(U_9644,U_9643))),hAPP(hAPP(c_Set_Oinsert(U_9643),sK195(U_9644,U_9643)),hAPP(hAPP(c_Set_Oinsert(U_9643),sK196(U_9644,U_9643)),c_Orderings_Obot__class_Obot(tc_fun(U_9643,tc_HOL_Obool))))))
| U_9644 = c_Orderings_Obot__class_Obot(tc_fun(U_9643,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9643),U_9644))
| ~ class_Orderings_Olinorder(U_9643) ),
inference(clausify,[status(thm)],[f_2653_4]) ).
fof(f_2654_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__le__Sup]) ).
fof(f_2654_2,plain,
! [U_9646,U_9645] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9645),c_Big__Operators_Olattice_OInf__fin(U_9645,c_Orderings_Oord__class_Omin(U_9645),U_9646)),c_Big__Operators_Olattice_OSup__fin(U_9645,c_Orderings_Oord__class_Omax(U_9645),U_9646)))
| U_9646 = c_Orderings_Obot__class_Obot(tc_fun(U_9645,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9645),U_9646))
| ~ class_Orderings_Olinorder(U_9645) ),
inference(variable_rename,[status(thm)],[f_2654_1]) ).
cnf(f_2654_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9645),c_Big__Operators_Olattice_OInf__fin(U_9645,c_Orderings_Oord__class_Omin(U_9645),U_9646)),c_Big__Operators_Olattice_OSup__fin(U_9645,c_Orderings_Oord__class_Omax(U_9645),U_9646)))
| U_9646 = c_Orderings_Obot__class_Obot(tc_fun(U_9645,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9645),U_9646))
| ~ class_Orderings_Olinorder(U_9645) ),
inference(clausify,[status(thm)],[f_2654_2]) ).
fof(f_2655_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oremove]) ).
fof(f_2655_2,plain,
! [U_9649,U_9648,U_9647] :
( ( ( c_Big__Operators_Olattice_OInf__fin(U_9647,c_Orderings_Oord__class_Omin(U_9647),U_9648) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9647),U_9649),c_Big__Operators_Olattice_OInf__fin(U_9647,c_Orderings_Oord__class_Omin(U_9647),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9647,tc_HOL_Obool)),U_9648),hAPP(hAPP(c_Set_Oinsert(U_9647),U_9649),c_Orderings_Obot__class_Obot(tc_fun(U_9647,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9647,tc_HOL_Obool)),U_9648),hAPP(hAPP(c_Set_Oinsert(U_9647),U_9649),c_Orderings_Obot__class_Obot(tc_fun(U_9647,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9647,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OInf__fin(U_9647,c_Orderings_Oord__class_Omin(U_9647),U_9648) = U_9649
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9647,tc_HOL_Obool)),U_9648),hAPP(hAPP(c_Set_Oinsert(U_9647),U_9649),c_Orderings_Obot__class_Obot(tc_fun(U_9647,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9647,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_9647),U_9649),U_9648))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9647),U_9648))
| ~ class_Orderings_Olinorder(U_9647) ),
inference(variable_rename,[status(thm)],[f_2655_1]) ).
cnf(f_2655_3,plain,
( c_Big__Operators_Olattice_OInf__fin(U_9647,c_Orderings_Oord__class_Omin(U_9647),U_9648) = U_9649
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9647,tc_HOL_Obool)),U_9648),hAPP(hAPP(c_Set_Oinsert(U_9647),U_9649),c_Orderings_Obot__class_Obot(tc_fun(U_9647,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9647,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9647),U_9649),U_9648))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9647),U_9648))
| ~ class_Orderings_Olinorder(U_9647) ),
inference(clausify,[status(thm)],[f_2655_2]) ).
cnf(f_2655_4,plain,
( c_Big__Operators_Olattice_OInf__fin(U_9647,c_Orderings_Oord__class_Omin(U_9647),U_9648) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9647),U_9649),c_Big__Operators_Olattice_OInf__fin(U_9647,c_Orderings_Oord__class_Omin(U_9647),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9647,tc_HOL_Obool)),U_9648),hAPP(hAPP(c_Set_Oinsert(U_9647),U_9649),c_Orderings_Obot__class_Obot(tc_fun(U_9647,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9647,tc_HOL_Obool)),U_9648),hAPP(hAPP(c_Set_Oinsert(U_9647),U_9649),c_Orderings_Obot__class_Obot(tc_fun(U_9647,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9647,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_9647),U_9649),U_9648))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9647),U_9648))
| ~ class_Orderings_Olinorder(U_9647) ),
inference(clausify,[status(thm)],[f_2655_2]) ).
fof(f_2656_1,plain,
! [V_x_2,V_A_2,T_b] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oin__idem]) ).
fof(f_2656_2,plain,
! [U_9652,U_9651,U_9650] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9650),U_9652),c_Big__Operators_Olattice_OInf__fin(U_9650,c_Orderings_Oord__class_Omin(U_9650),U_9651)) = c_Big__Operators_Olattice_OInf__fin(U_9650,c_Orderings_Oord__class_Omin(U_9650),U_9651)
| ~ hBOOL(hAPP(hAPP(c_member(U_9650),U_9652),U_9651))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9650),U_9651))
| ~ class_Orderings_Olinorder(U_9650) ),
inference(variable_rename,[status(thm)],[f_2656_1]) ).
cnf(f_2656_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9650),U_9652),c_Big__Operators_Olattice_OInf__fin(U_9650,c_Orderings_Oord__class_Omin(U_9650),U_9651)) = c_Big__Operators_Olattice_OInf__fin(U_9650,c_Orderings_Oord__class_Omin(U_9650),U_9651)
| ~ hBOOL(hAPP(hAPP(c_member(U_9650),U_9652),U_9651))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9650),U_9651))
| ~ class_Orderings_Olinorder(U_9650) ),
inference(clausify,[status(thm)],[f_2656_2]) ).
fof(f_2657_1,plain,
! [V_x_2,T_b] :
( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osingleton]) ).
fof(f_2657_2,plain,
! [U_9654,U_9653] :
( c_Big__Operators_Olattice_OInf__fin(U_9653,c_Orderings_Oord__class_Omin(U_9653),hAPP(hAPP(c_Set_Oinsert(U_9653),U_9654),c_Orderings_Obot__class_Obot(tc_fun(U_9653,tc_HOL_Obool)))) = U_9654
| ~ class_Orderings_Olinorder(U_9653) ),
inference(variable_rename,[status(thm)],[f_2657_1]) ).
cnf(f_2657_3,plain,
( c_Big__Operators_Olattice_OInf__fin(U_9653,c_Orderings_Oord__class_Omin(U_9653),hAPP(hAPP(c_Set_Oinsert(U_9653),U_9654),c_Orderings_Obot__class_Obot(tc_fun(U_9653,tc_HOL_Obool)))) = U_9654
| ~ class_Orderings_Olinorder(U_9653) ),
inference(clausify,[status(thm)],[f_2657_2]) ).
fof(f_2658_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__idem]) ).
fof(f_2658_2,plain,
! [U_9657,U_9656,U_9655] :
( c_Big__Operators_Olattice_OInf__fin(U_9655,c_Orderings_Oord__class_Omin(U_9655),hAPP(hAPP(c_Set_Oinsert(U_9655),U_9657),U_9656)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9655),U_9657),c_Big__Operators_Olattice_OInf__fin(U_9655,c_Orderings_Oord__class_Omin(U_9655),U_9656))
| U_9656 = c_Orderings_Obot__class_Obot(tc_fun(U_9655,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9655),U_9656))
| ~ class_Orderings_Olinorder(U_9655) ),
inference(variable_rename,[status(thm)],[f_2658_1]) ).
cnf(f_2658_3,plain,
( c_Big__Operators_Olattice_OInf__fin(U_9655,c_Orderings_Oord__class_Omin(U_9655),hAPP(hAPP(c_Set_Oinsert(U_9655),U_9657),U_9656)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9655),U_9657),c_Big__Operators_Olattice_OInf__fin(U_9655,c_Orderings_Oord__class_Omin(U_9655),U_9656))
| U_9656 = c_Orderings_Obot__class_Obot(tc_fun(U_9655,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9655),U_9656))
| ~ class_Orderings_Olinorder(U_9655) ),
inference(clausify,[status(thm)],[f_2658_2]) ).
fof(f_2659_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osubset__idem]) ).
fof(f_2659_2,plain,
! [U_9660,U_9659,U_9658] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9658),c_Big__Operators_Olattice_OInf__fin(U_9658,c_Orderings_Oord__class_Omin(U_9658),U_9660)),c_Big__Operators_Olattice_OInf__fin(U_9658,c_Orderings_Oord__class_Omin(U_9658),U_9659)) = c_Big__Operators_Olattice_OInf__fin(U_9658,c_Orderings_Oord__class_Omin(U_9658),U_9659)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9658,tc_HOL_Obool)),U_9660),U_9659))
| U_9660 = c_Orderings_Obot__class_Obot(tc_fun(U_9658,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9658),U_9659))
| ~ class_Orderings_Olinorder(U_9658) ),
inference(variable_rename,[status(thm)],[f_2659_1]) ).
cnf(f_2659_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9658),c_Big__Operators_Olattice_OInf__fin(U_9658,c_Orderings_Oord__class_Omin(U_9658),U_9660)),c_Big__Operators_Olattice_OInf__fin(U_9658,c_Orderings_Oord__class_Omin(U_9658),U_9659)) = c_Big__Operators_Olattice_OInf__fin(U_9658,c_Orderings_Oord__class_Omin(U_9658),U_9659)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9658,tc_HOL_Obool)),U_9660),U_9659))
| U_9660 = c_Orderings_Obot__class_Obot(tc_fun(U_9658,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9658),U_9659))
| ~ class_Orderings_Olinorder(U_9658) ),
inference(clausify,[status(thm)],[f_2659_2]) ).
fof(f_2660_1,plain,
! [V_a_2,V_A_2,T_b] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = V_a_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf__absorb]) ).
fof(f_2660_2,plain,
! [U_9663,U_9662,U_9661] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9661),U_9663),c_Big__Operators_Olattice_OInf__fin(U_9661,c_Orderings_Oord__class_Omin(U_9661),U_9662)) = U_9663
| ~ hBOOL(hAPP(hAPP(c_member(U_9661),U_9663),U_9662))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9661),U_9662))
| ~ class_Orderings_Olinorder(U_9661) ),
inference(variable_rename,[status(thm)],[f_2660_1]) ).
cnf(f_2660_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9661),U_9663),c_Big__Operators_Olattice_OInf__fin(U_9661,c_Orderings_Oord__class_Omin(U_9661),U_9662)) = U_9663
| ~ hBOOL(hAPP(hAPP(c_member(U_9661),U_9663),U_9662))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9661),U_9662))
| ~ class_Orderings_Olinorder(U_9661) ),
inference(clausify,[status(thm)],[f_2660_2]) ).
fof(f_2661_1,plain,
! [V_B_2,V_A_2,T_b] :
( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__idem]) ).
fof(f_2661_2,plain,
! [U_9666,U_9665,U_9664] :
( c_Big__Operators_Olattice_OInf__fin(U_9664,c_Orderings_Oord__class_Omin(U_9664),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9664,tc_HOL_Obool)),U_9665),U_9666)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9664),c_Big__Operators_Olattice_OInf__fin(U_9664,c_Orderings_Oord__class_Omin(U_9664),U_9665)),c_Big__Operators_Olattice_OInf__fin(U_9664,c_Orderings_Oord__class_Omin(U_9664),U_9666))
| U_9666 = c_Orderings_Obot__class_Obot(tc_fun(U_9664,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9664),U_9666))
| U_9665 = c_Orderings_Obot__class_Obot(tc_fun(U_9664,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9664),U_9665))
| ~ class_Orderings_Olinorder(U_9664) ),
inference(variable_rename,[status(thm)],[f_2661_1]) ).
cnf(f_2661_3,plain,
( c_Big__Operators_Olattice_OInf__fin(U_9664,c_Orderings_Oord__class_Omin(U_9664),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9664,tc_HOL_Obool)),U_9665),U_9666)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9664),c_Big__Operators_Olattice_OInf__fin(U_9664,c_Orderings_Oord__class_Omin(U_9664),U_9665)),c_Big__Operators_Olattice_OInf__fin(U_9664,c_Orderings_Oord__class_Omin(U_9664),U_9666))
| U_9666 = c_Orderings_Obot__class_Obot(tc_fun(U_9664,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9664),U_9666))
| U_9665 = c_Orderings_Obot__class_Obot(tc_fun(U_9664,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9664),U_9665))
| ~ class_Orderings_Olinorder(U_9664) ),
inference(clausify,[status(thm)],[f_2661_2]) ).
fof(f_2662_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert]) ).
fof(f_2662_2,plain,
! [U_9669,U_9668,U_9667] :
( c_Big__Operators_Olattice_OInf__fin(U_9667,c_Orderings_Oord__class_Omin(U_9667),hAPP(hAPP(c_Set_Oinsert(U_9667),U_9669),U_9668)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9667),U_9669),c_Big__Operators_Olattice_OInf__fin(U_9667,c_Orderings_Oord__class_Omin(U_9667),U_9668))
| U_9668 = c_Orderings_Obot__class_Obot(tc_fun(U_9667,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_9667),U_9669),U_9668))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9667),U_9668))
| ~ class_Orderings_Olinorder(U_9667) ),
inference(variable_rename,[status(thm)],[f_2662_1]) ).
cnf(f_2662_3,plain,
( c_Big__Operators_Olattice_OInf__fin(U_9667,c_Orderings_Oord__class_Omin(U_9667),hAPP(hAPP(c_Set_Oinsert(U_9667),U_9669),U_9668)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9667),U_9669),c_Big__Operators_Olattice_OInf__fin(U_9667,c_Orderings_Oord__class_Omin(U_9667),U_9668))
| U_9668 = c_Orderings_Obot__class_Obot(tc_fun(U_9667,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_9667),U_9669),U_9668))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9667),U_9668))
| ~ class_Orderings_Olinorder(U_9667) ),
inference(clausify,[status(thm)],[f_2662_2]) ).
fof(f_2663_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__remove]) ).
fof(f_2663_2,plain,
! [U_9672,U_9671,U_9670] :
( ( ( c_Big__Operators_Olattice_OInf__fin(U_9670,c_Orderings_Oord__class_Omin(U_9670),hAPP(hAPP(c_Set_Oinsert(U_9670),U_9672),U_9671)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9670),U_9672),c_Big__Operators_Olattice_OInf__fin(U_9670,c_Orderings_Oord__class_Omin(U_9670),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9670,tc_HOL_Obool)),U_9671),hAPP(hAPP(c_Set_Oinsert(U_9670),U_9672),c_Orderings_Obot__class_Obot(tc_fun(U_9670,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9670,tc_HOL_Obool)),U_9671),hAPP(hAPP(c_Set_Oinsert(U_9670),U_9672),c_Orderings_Obot__class_Obot(tc_fun(U_9670,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9670,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice_OInf__fin(U_9670,c_Orderings_Oord__class_Omin(U_9670),hAPP(hAPP(c_Set_Oinsert(U_9670),U_9672),U_9671)) = U_9672
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9670,tc_HOL_Obool)),U_9671),hAPP(hAPP(c_Set_Oinsert(U_9670),U_9672),c_Orderings_Obot__class_Obot(tc_fun(U_9670,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9670,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9670),U_9671))
| ~ class_Orderings_Olinorder(U_9670) ),
inference(variable_rename,[status(thm)],[f_2663_1]) ).
cnf(f_2663_3,plain,
( c_Big__Operators_Olattice_OInf__fin(U_9670,c_Orderings_Oord__class_Omin(U_9670),hAPP(hAPP(c_Set_Oinsert(U_9670),U_9672),U_9671)) = U_9672
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9670,tc_HOL_Obool)),U_9671),hAPP(hAPP(c_Set_Oinsert(U_9670),U_9672),c_Orderings_Obot__class_Obot(tc_fun(U_9670,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9670,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9670),U_9671))
| ~ class_Orderings_Olinorder(U_9670) ),
inference(clausify,[status(thm)],[f_2663_2]) ).
cnf(f_2663_4,plain,
( c_Big__Operators_Olattice_OInf__fin(U_9670,c_Orderings_Oord__class_Omin(U_9670),hAPP(hAPP(c_Set_Oinsert(U_9670),U_9672),U_9671)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9670),U_9672),c_Big__Operators_Olattice_OInf__fin(U_9670,c_Orderings_Oord__class_Omin(U_9670),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9670,tc_HOL_Obool)),U_9671),hAPP(hAPP(c_Set_Oinsert(U_9670),U_9672),c_Orderings_Obot__class_Obot(tc_fun(U_9670,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9670,tc_HOL_Obool)),U_9671),hAPP(hAPP(c_Set_Oinsert(U_9670),U_9672),c_Orderings_Obot__class_Obot(tc_fun(U_9670,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9670,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9670),U_9671))
| ~ class_Orderings_Olinorder(U_9670) ),
inference(clausify,[status(thm)],[f_2663_2]) ).
fof(f_2664_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),V_A_2))
| ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oclosed]) ).
fof(f_2664_2,plain,
! [U_9676,U_9675] :
( hBOOL(hAPP(hAPP(c_member(U_9675),c_Big__Operators_Olattice_OInf__fin(U_9675,c_Orderings_Oord__class_Omin(U_9675),U_9676)),U_9676))
| ? [U_9674,U_9673] : ~ hBOOL(hAPP(hAPP(c_member(U_9675),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9675),U_9674),U_9673)),hAPP(hAPP(c_Set_Oinsert(U_9675),U_9674),hAPP(hAPP(c_Set_Oinsert(U_9675),U_9673),c_Orderings_Obot__class_Obot(tc_fun(U_9675,tc_HOL_Obool))))))
| U_9676 = c_Orderings_Obot__class_Obot(tc_fun(U_9675,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9675),U_9676))
| ~ class_Orderings_Olinorder(U_9675) ),
inference(variable_rename,[status(thm)],[f_2664_1]) ).
fof(f_2664_3,plain,
! [U_9676,U_9675] :
( hBOOL(hAPP(hAPP(c_member(U_9675),c_Big__Operators_Olattice_OInf__fin(U_9675,c_Orderings_Oord__class_Omin(U_9675),U_9676)),U_9676))
| ? [U_9673] : ~ hBOOL(hAPP(hAPP(c_member(U_9675),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9675),sK197(U_9676,U_9675)),U_9673)),hAPP(hAPP(c_Set_Oinsert(U_9675),sK197(U_9676,U_9675)),hAPP(hAPP(c_Set_Oinsert(U_9675),U_9673),c_Orderings_Obot__class_Obot(tc_fun(U_9675,tc_HOL_Obool))))))
| U_9676 = c_Orderings_Obot__class_Obot(tc_fun(U_9675,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9675),U_9676))
| ~ class_Orderings_Olinorder(U_9675) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK197]),skolemize(U_9674,sK197(U_9676,U_9675))],[f_2664_2]) ).
fof(f_2664_4,plain,
! [U_9676,U_9675] :
( hBOOL(hAPP(hAPP(c_member(U_9675),c_Big__Operators_Olattice_OInf__fin(U_9675,c_Orderings_Oord__class_Omin(U_9675),U_9676)),U_9676))
| ~ hBOOL(hAPP(hAPP(c_member(U_9675),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9675),sK197(U_9676,U_9675)),sK198(U_9676,U_9675))),hAPP(hAPP(c_Set_Oinsert(U_9675),sK197(U_9676,U_9675)),hAPP(hAPP(c_Set_Oinsert(U_9675),sK198(U_9676,U_9675)),c_Orderings_Obot__class_Obot(tc_fun(U_9675,tc_HOL_Obool))))))
| U_9676 = c_Orderings_Obot__class_Obot(tc_fun(U_9675,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9675),U_9676))
| ~ class_Orderings_Olinorder(U_9675) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK198]),skolemize(U_9673,sK198(U_9676,U_9675))],[f_2664_3]) ).
cnf(f_2664_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9675),c_Big__Operators_Olattice_OInf__fin(U_9675,c_Orderings_Oord__class_Omin(U_9675),U_9676)),U_9676))
| ~ hBOOL(hAPP(hAPP(c_member(U_9675),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9675),sK197(U_9676,U_9675)),sK198(U_9676,U_9675))),hAPP(hAPP(c_Set_Oinsert(U_9675),sK197(U_9676,U_9675)),hAPP(hAPP(c_Set_Oinsert(U_9675),sK198(U_9676,U_9675)),c_Orderings_Obot__class_Obot(tc_fun(U_9675,tc_HOL_Obool))))))
| U_9676 = c_Orderings_Obot__class_Obot(tc_fun(U_9675,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9675),U_9676))
| ~ class_Orderings_Olinorder(U_9675) ),
inference(clausify,[status(thm)],[f_2664_4]) ).
fof(f_2665_1,plain,
! [V_A_2,V_F_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2))
| ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Oclosed]) ).
fof(f_2665_2,plain,
! [U_9682,U_9681,U_9680,U_9679] :
( hBOOL(hAPP(hAPP(c_member(U_9679),hAPP(U_9681,U_9682)),U_9682))
| ? [U_9678,U_9677] : ~ hBOOL(hAPP(hAPP(c_member(U_9679),hAPP(hAPP(U_9680,U_9678),U_9677)),hAPP(hAPP(c_Set_Oinsert(U_9679),U_9678),hAPP(hAPP(c_Set_Oinsert(U_9679),U_9677),c_Orderings_Obot__class_Obot(tc_fun(U_9679,tc_HOL_Obool))))))
| U_9682 = c_Orderings_Obot__class_Obot(tc_fun(U_9679,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9679),U_9682))
| ~ c_Finite__Set_Ofolding__one(U_9679,U_9680,U_9681) ),
inference(variable_rename,[status(thm)],[f_2665_1]) ).
fof(f_2665_3,plain,
! [U_9682,U_9681,U_9680,U_9679] :
( hBOOL(hAPP(hAPP(c_member(U_9679),hAPP(U_9681,U_9682)),U_9682))
| ? [U_9677] : ~ hBOOL(hAPP(hAPP(c_member(U_9679),hAPP(hAPP(U_9680,sK199(U_9682,U_9681,U_9680,U_9679)),U_9677)),hAPP(hAPP(c_Set_Oinsert(U_9679),sK199(U_9682,U_9681,U_9680,U_9679)),hAPP(hAPP(c_Set_Oinsert(U_9679),U_9677),c_Orderings_Obot__class_Obot(tc_fun(U_9679,tc_HOL_Obool))))))
| U_9682 = c_Orderings_Obot__class_Obot(tc_fun(U_9679,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9679),U_9682))
| ~ c_Finite__Set_Ofolding__one(U_9679,U_9680,U_9681) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK199]),skolemize(U_9678,sK199(U_9682,U_9681,U_9680,U_9679))],[f_2665_2]) ).
fof(f_2665_4,plain,
! [U_9682,U_9681,U_9680,U_9679] :
( hBOOL(hAPP(hAPP(c_member(U_9679),hAPP(U_9681,U_9682)),U_9682))
| ~ hBOOL(hAPP(hAPP(c_member(U_9679),hAPP(hAPP(U_9680,sK199(U_9682,U_9681,U_9680,U_9679)),sK200(U_9682,U_9681,U_9680,U_9679))),hAPP(hAPP(c_Set_Oinsert(U_9679),sK199(U_9682,U_9681,U_9680,U_9679)),hAPP(hAPP(c_Set_Oinsert(U_9679),sK200(U_9682,U_9681,U_9680,U_9679)),c_Orderings_Obot__class_Obot(tc_fun(U_9679,tc_HOL_Obool))))))
| U_9682 = c_Orderings_Obot__class_Obot(tc_fun(U_9679,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9679),U_9682))
| ~ c_Finite__Set_Ofolding__one(U_9679,U_9680,U_9681) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK200]),skolemize(U_9677,sK200(U_9682,U_9681,U_9680,U_9679))],[f_2665_3]) ).
cnf(f_2665_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9679),hAPP(U_9681,U_9682)),U_9682))
| ~ hBOOL(hAPP(hAPP(c_member(U_9679),hAPP(hAPP(U_9680,sK199(U_9682,U_9681,U_9680,U_9679)),sK200(U_9682,U_9681,U_9680,U_9679))),hAPP(hAPP(c_Set_Oinsert(U_9679),sK199(U_9682,U_9681,U_9680,U_9679)),hAPP(hAPP(c_Set_Oinsert(U_9679),sK200(U_9682,U_9681,U_9680,U_9679)),c_Orderings_Obot__class_Obot(tc_fun(U_9679,tc_HOL_Obool))))))
| U_9682 = c_Orderings_Obot__class_Obot(tc_fun(U_9679,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9679),U_9682))
| ~ c_Finite__Set_Ofolding__one(U_9679,U_9680,U_9681) ),
inference(clausify,[status(thm)],[f_2665_4]) ).
fof(f_2666_1,plain,
! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
( ( hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
& ( hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_fun__upd__image]) ).
fof(f_2666_2,plain,
! [U_9688,U_9687,U_9686,U_9685,U_9684,U_9683] :
( ( hAPP(c_Set_Oimage(U_9683,U_9686,c_Fun_Ofun__upd(U_9683,U_9686,U_9687,U_9684,U_9688)),U_9685) = hAPP(c_Set_Oimage(U_9683,U_9686,U_9687),U_9685)
| hBOOL(hAPP(hAPP(c_member(U_9683),U_9684),U_9685)) )
& ( hAPP(c_Set_Oimage(U_9683,U_9686,c_Fun_Ofun__upd(U_9683,U_9686,U_9687,U_9684,U_9688)),U_9685) = hAPP(hAPP(c_Set_Oinsert(U_9686),U_9688),hAPP(c_Set_Oimage(U_9683,U_9686,U_9687),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9683,tc_HOL_Obool)),U_9685),hAPP(hAPP(c_Set_Oinsert(U_9683),U_9684),c_Orderings_Obot__class_Obot(tc_fun(U_9683,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_9683),U_9684),U_9685)) ) ),
inference(variable_rename,[status(thm)],[f_2666_1]) ).
fof(f_2666_3,plain,
( ! [U_9700,U_9698,U_9696,U_9694,U_9692,U_9690] :
( hAPP(c_Set_Oimage(U_9690,U_9696,c_Fun_Ofun__upd(U_9690,U_9696,U_9698,U_9692,U_9700)),U_9694) = hAPP(c_Set_Oimage(U_9690,U_9696,U_9698),U_9694)
| hBOOL(hAPP(hAPP(c_member(U_9690),U_9692),U_9694)) )
& ! [U_9699,U_9697,U_9695,U_9693,U_9691,U_9689] :
( hAPP(c_Set_Oimage(U_9689,U_9695,c_Fun_Ofun__upd(U_9689,U_9695,U_9697,U_9691,U_9699)),U_9693) = hAPP(hAPP(c_Set_Oinsert(U_9695),U_9699),hAPP(c_Set_Oimage(U_9689,U_9695,U_9697),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9689,tc_HOL_Obool)),U_9693),hAPP(hAPP(c_Set_Oinsert(U_9689),U_9691),c_Orderings_Obot__class_Obot(tc_fun(U_9689,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_9689),U_9691),U_9693)) ) ),
inference(miniscope,[status(thm)],[f_2666_2]) ).
cnf(f_2666_4,plain,
( hAPP(c_Set_Oimage(U_9689,U_9695,c_Fun_Ofun__upd(U_9689,U_9695,U_9697,U_9691,U_9699)),U_9693) = hAPP(hAPP(c_Set_Oinsert(U_9695),U_9699),hAPP(c_Set_Oimage(U_9689,U_9695,U_9697),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9689,tc_HOL_Obool)),U_9693),hAPP(hAPP(c_Set_Oinsert(U_9689),U_9691),c_Orderings_Obot__class_Obot(tc_fun(U_9689,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_9689),U_9691),U_9693)) ),
inference(clausify,[status(thm)],[f_2666_3]) ).
cnf(f_2666_5,plain,
( hAPP(c_Set_Oimage(U_9690,U_9696,c_Fun_Ofun__upd(U_9690,U_9696,U_9698,U_9692,U_9700)),U_9694) = hAPP(c_Set_Oimage(U_9690,U_9696,U_9698),U_9694)
| hBOOL(hAPP(hAPP(c_member(U_9690),U_9692),U_9694)) ),
inference(clausify,[status(thm)],[f_2666_3]) ).
fof(f_2667_1,plain,
! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__gen__delta]) ).
fof(f_2667_2,plain,
! [U_9706,U_9705,U_9704,U_9703,U_9702,U_9701] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9702,U_9701),hAPP(hAPP(c_COMBC(U_9702,U_9701,U_9701),hAPP(hAPP(c_COMBS(U_9702,U_9701,tc_fun(U_9701,U_9701)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9701,tc_fun(U_9701,U_9701)),U_9702),c_If(U_9701)),hAPP(hAPP(c_COMBC(U_9702,U_9702,tc_HOL_Obool),c_fequal),U_9704))),U_9705)),U_9706)),U_9703) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9701),U_9706),hAPP(c_Finite__Set_Ocard(U_9702),U_9703))
| hBOOL(hAPP(hAPP(c_member(U_9702),U_9704),U_9703)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9702,U_9701),hAPP(hAPP(c_COMBC(U_9702,U_9701,U_9701),hAPP(hAPP(c_COMBS(U_9702,U_9701,tc_fun(U_9701,U_9701)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9701,tc_fun(U_9701,U_9701)),U_9702),c_If(U_9701)),hAPP(hAPP(c_COMBC(U_9702,U_9702,tc_HOL_Obool),c_fequal),U_9704))),U_9705)),U_9706)),U_9703) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9701),hAPP(U_9705,U_9704)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9701),U_9706),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9702),U_9703)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_member(U_9702),U_9704),U_9703)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9702),U_9703))
| ~ class_Groups_Ocomm__monoid__mult(U_9701) ),
inference(variable_rename,[status(thm)],[f_2667_1]) ).
cnf(f_2667_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9702,U_9701),hAPP(hAPP(c_COMBC(U_9702,U_9701,U_9701),hAPP(hAPP(c_COMBS(U_9702,U_9701,tc_fun(U_9701,U_9701)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9701,tc_fun(U_9701,U_9701)),U_9702),c_If(U_9701)),hAPP(hAPP(c_COMBC(U_9702,U_9702,tc_HOL_Obool),c_fequal),U_9704))),U_9705)),U_9706)),U_9703) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9701),hAPP(U_9705,U_9704)),hAPP(hAPP(c_Power_Opower__class_Opower(U_9701),U_9706),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9702),U_9703)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ hBOOL(hAPP(hAPP(c_member(U_9702),U_9704),U_9703))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9702),U_9703))
| ~ class_Groups_Ocomm__monoid__mult(U_9701) ),
inference(clausify,[status(thm)],[f_2667_2]) ).
cnf(f_2667_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9702,U_9701),hAPP(hAPP(c_COMBC(U_9702,U_9701,U_9701),hAPP(hAPP(c_COMBS(U_9702,U_9701,tc_fun(U_9701,U_9701)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9701,tc_fun(U_9701,U_9701)),U_9702),c_If(U_9701)),hAPP(hAPP(c_COMBC(U_9702,U_9702,tc_HOL_Obool),c_fequal),U_9704))),U_9705)),U_9706)),U_9703) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9701),U_9706),hAPP(c_Finite__Set_Ocard(U_9702),U_9703))
| hBOOL(hAPP(hAPP(c_member(U_9702),U_9704),U_9703))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9702),U_9703))
| ~ class_Groups_Ocomm__monoid__mult(U_9701) ),
inference(clausify,[status(thm)],[f_2667_2]) ).
fof(f_2668_1,plain,
! [V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,hAPP(V_f_2,V_x_2)) = V_f_2,
inference(fof_nnf,[status(thm)],[fact_fun__upd__triv]) ).
fof(f_2668_2,plain,
! [U_9710,U_9709,U_9708,U_9707] : c_Fun_Ofun__upd(U_9707,U_9708,U_9709,U_9710,hAPP(U_9709,U_9710)) = U_9709,
inference(variable_rename,[status(thm)],[f_2668_1]) ).
cnf(f_2668_3,plain,
c_Fun_Ofun__upd(U_9707,U_9708,U_9709,U_9710,hAPP(U_9709,U_9710)) = U_9709,
inference(clausify,[status(thm)],[f_2668_2]) ).
fof(f_2669_1,plain,
! [V_A_2,V_f_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_b)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I2_J]) ).
fof(f_2669_2,plain,
! [U_9713,U_9712,U_9711] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_9711),U_9712),U_9713) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_9711),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9711,tc_Int_Oint),U_9712),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9713))
| ~ class_Groups_Ocomm__monoid__mult(U_9711)
| ~ class_Groups_Ocomm__monoid__add(U_9711) ),
inference(variable_rename,[status(thm)],[f_2669_1]) ).
cnf(f_2669_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_9711),U_9712),U_9713) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_9711),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9711,tc_Int_Oint),U_9712),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9713))
| ~ class_Groups_Ocomm__monoid__mult(U_9711)
| ~ class_Groups_Ocomm__monoid__add(U_9711) ),
inference(clausify,[status(thm)],[f_2669_2]) ).
fof(f_2670_1,plain,
! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
( ( hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = hAPP(V_f_2,V_x_2)
| V_x_2 = V_a_2 )
& ( hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2
| V_x_2 != V_a_2 ) ),
inference(fof_nnf,[status(thm)],[fact_fun__upd__def]) ).
fof(f_2670_2,plain,
! [U_9719,U_9718,U_9717,U_9716,U_9715,U_9714] :
( ( hAPP(c_Fun_Ofun__upd(U_9716,U_9717,U_9718,U_9715,U_9719),U_9714) = hAPP(U_9718,U_9714)
| U_9714 = U_9715 )
& ( hAPP(c_Fun_Ofun__upd(U_9716,U_9717,U_9718,U_9715,U_9719),U_9714) = U_9719
| U_9714 != U_9715 ) ),
inference(variable_rename,[status(thm)],[f_2670_1]) ).
fof(f_2670_3,plain,
( ! [U_9731,U_9729,U_9727,U_9725,U_9723,U_9721] :
( hAPP(c_Fun_Ofun__upd(U_9725,U_9727,U_9729,U_9723,U_9731),U_9721) = hAPP(U_9729,U_9721)
| U_9721 = U_9723 )
& ! [U_9730,U_9728,U_9726,U_9724,U_9722,U_9720] :
( hAPP(c_Fun_Ofun__upd(U_9724,U_9726,U_9728,U_9722,U_9730),U_9720) = U_9730
| U_9720 != U_9722 ) ),
inference(miniscope,[status(thm)],[f_2670_2]) ).
cnf(f_2670_4,plain,
( hAPP(c_Fun_Ofun__upd(U_9724,U_9726,U_9728,U_9722,U_9730),U_9720) = U_9730
| U_9720 != U_9722 ),
inference(clausify,[status(thm)],[f_2670_3]) ).
cnf(f_2670_5,plain,
( hAPP(c_Fun_Ofun__upd(U_9725,U_9727,U_9729,U_9723,U_9731),U_9721) = hAPP(U_9729,U_9721)
| U_9721 = U_9723 ),
inference(clausify,[status(thm)],[f_2670_3]) ).
fof(f_2671_1,plain,
! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
( ( c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2
| hAPP(V_f_2,V_x_2) != V_y_2 )
& ( hAPP(V_f_2,V_x_2) = V_y_2
| c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) != V_f_2 ) ),
inference(fof_nnf,[status(thm)],[fact_fun__upd__idem__iff]) ).
fof(f_2671_2,plain,
! [U_9736,U_9735,U_9734,U_9733,U_9732] :
( ( c_Fun_Ofun__upd(U_9732,U_9733,U_9734,U_9735,U_9736) = U_9734
| hAPP(U_9734,U_9735) != U_9736 )
& ( hAPP(U_9734,U_9735) = U_9736
| c_Fun_Ofun__upd(U_9732,U_9733,U_9734,U_9735,U_9736) != U_9734 ) ),
inference(variable_rename,[status(thm)],[f_2671_1]) ).
fof(f_2671_3,plain,
( ! [U_9746,U_9744,U_9742] :
( ! [U_9740,U_9738] : c_Fun_Ofun__upd(U_9738,U_9740,U_9742,U_9744,U_9746) = U_9742
| hAPP(U_9742,U_9744) != U_9746 )
& ! [U_9745,U_9743,U_9741] :
( ! [U_9739,U_9737] : c_Fun_Ofun__upd(U_9737,U_9739,U_9741,U_9743,U_9745) != U_9741
| hAPP(U_9741,U_9743) = U_9745 ) ),
inference(miniscope,[status(thm)],[f_2671_2]) ).
cnf(f_2671_4,plain,
( c_Fun_Ofun__upd(U_9737,U_9739,U_9741,U_9743,U_9745) != U_9741
| hAPP(U_9741,U_9743) = U_9745 ),
inference(clausify,[status(thm)],[f_2671_3]) ).
cnf(f_2671_5,plain,
( c_Fun_Ofun__upd(U_9738,U_9740,U_9742,U_9744,U_9746) = U_9742
| hAPP(U_9742,U_9744) != U_9746 ),
inference(clausify,[status(thm)],[f_2671_3]) ).
fof(f_2672_1,plain,
! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_z_2),
inference(fof_nnf,[status(thm)],[fact_fun__upd__upd]) ).
fof(f_2672_2,plain,
! [U_9752,U_9751,U_9750,U_9749,U_9748,U_9747] : c_Fun_Ofun__upd(U_9747,U_9748,c_Fun_Ofun__upd(U_9747,U_9748,U_9749,U_9750,U_9751),U_9750,U_9752) = c_Fun_Ofun__upd(U_9747,U_9748,U_9749,U_9750,U_9752),
inference(variable_rename,[status(thm)],[f_2672_1]) ).
cnf(f_2672_3,plain,
c_Fun_Ofun__upd(U_9747,U_9748,c_Fun_Ofun__upd(U_9747,U_9748,U_9749,U_9750,U_9751),U_9750,U_9752) = c_Fun_Ofun__upd(U_9747,U_9748,U_9749,U_9750,U_9752),
inference(clausify,[status(thm)],[f_2672_2]) ).
fof(f_2673_1,plain,
! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2),V_x_2) = V_y_2,
inference(fof_nnf,[status(thm)],[fact_fun__upd__same]) ).
fof(f_2673_2,plain,
! [U_9757,U_9756,U_9755,U_9754,U_9753] : hAPP(c_Fun_Ofun__upd(U_9753,U_9754,U_9755,U_9756,U_9757),U_9756) = U_9757,
inference(variable_rename,[status(thm)],[f_2673_1]) ).
cnf(f_2673_3,plain,
hAPP(c_Fun_Ofun__upd(U_9753,U_9754,U_9755,U_9756,U_9757),U_9756) = U_9757,
inference(clausify,[status(thm)],[f_2673_2]) ).
fof(f_2674_1,plain,
! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
( ( hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2)
| V_z_2 = V_x_2 )
& ( hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2
| V_z_2 != V_x_2 ) ),
inference(fof_nnf,[status(thm)],[fact_fun__upd__apply]) ).
fof(f_2674_2,plain,
! [U_9763,U_9762,U_9761,U_9760,U_9759,U_9758] :
( ( hAPP(c_Fun_Ofun__upd(U_9760,U_9761,U_9762,U_9759,U_9763),U_9758) = hAPP(U_9762,U_9758)
| U_9758 = U_9759 )
& ( hAPP(c_Fun_Ofun__upd(U_9760,U_9761,U_9762,U_9759,U_9763),U_9758) = U_9763
| U_9758 != U_9759 ) ),
inference(variable_rename,[status(thm)],[f_2674_1]) ).
fof(f_2674_3,plain,
( ! [U_9775,U_9773,U_9771,U_9769,U_9767,U_9765] :
( hAPP(c_Fun_Ofun__upd(U_9769,U_9771,U_9773,U_9767,U_9775),U_9765) = hAPP(U_9773,U_9765)
| U_9765 = U_9767 )
& ! [U_9774,U_9772,U_9770,U_9768,U_9766,U_9764] :
( hAPP(c_Fun_Ofun__upd(U_9768,U_9770,U_9772,U_9766,U_9774),U_9764) = U_9774
| U_9764 != U_9766 ) ),
inference(miniscope,[status(thm)],[f_2674_2]) ).
cnf(f_2674_4,plain,
( hAPP(c_Fun_Ofun__upd(U_9768,U_9770,U_9772,U_9766,U_9774),U_9764) = U_9774
| U_9764 != U_9766 ),
inference(clausify,[status(thm)],[f_2674_3]) ).
cnf(f_2674_5,plain,
( hAPP(c_Fun_Ofun__upd(U_9769,U_9771,U_9773,U_9767,U_9775),U_9765) = hAPP(U_9773,U_9765)
| U_9765 = U_9767 ),
inference(clausify,[status(thm)],[f_2674_3]) ).
fof(f_2675_1,plain,
! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] :
( c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_a_2,V_b_2),V_c_2,V_d_2) = c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,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_2675_2,plain,
! [U_9782,U_9781,U_9780,U_9779,U_9778,U_9777,U_9776] :
( c_Fun_Ofun__upd(U_9778,U_9779,c_Fun_Ofun__upd(U_9778,U_9779,U_9780,U_9776,U_9781),U_9777,U_9782) = c_Fun_Ofun__upd(U_9778,U_9779,c_Fun_Ofun__upd(U_9778,U_9779,U_9780,U_9777,U_9782),U_9776,U_9781)
| U_9776 = U_9777 ),
inference(variable_rename,[status(thm)],[f_2675_1]) ).
cnf(f_2675_3,plain,
( c_Fun_Ofun__upd(U_9778,U_9779,c_Fun_Ofun__upd(U_9778,U_9779,U_9780,U_9776,U_9781),U_9777,U_9782) = c_Fun_Ofun__upd(U_9778,U_9779,c_Fun_Ofun__upd(U_9778,U_9779,U_9780,U_9777,U_9782),U_9776,U_9781)
| U_9776 = U_9777 ),
inference(clausify,[status(thm)],[f_2675_2]) ).
fof(f_2676_1,plain,
! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
( hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2)
| V_z_2 = V_x_2 ),
inference(fof_nnf,[status(thm)],[fact_fun__upd__other]) ).
fof(f_2676_2,plain,
! [U_9788,U_9787,U_9786,U_9785,U_9784,U_9783] :
( hAPP(c_Fun_Ofun__upd(U_9785,U_9786,U_9787,U_9784,U_9788),U_9783) = hAPP(U_9787,U_9783)
| U_9783 = U_9784 ),
inference(variable_rename,[status(thm)],[f_2676_1]) ).
cnf(f_2676_3,plain,
( hAPP(c_Fun_Ofun__upd(U_9785,U_9786,U_9787,U_9784,U_9788),U_9783) = hAPP(U_9787,U_9783)
| U_9783 = U_9784 ),
inference(clausify,[status(thm)],[f_2676_2]) ).
fof(f_2677_1,plain,
! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
( c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2
| hAPP(V_f_2,V_x_2) != V_y_2 ),
inference(fof_nnf,[status(thm)],[fact_fun__upd__idem]) ).
fof(f_2677_2,plain,
! [U_9793,U_9792,U_9791,U_9790,U_9789] :
( c_Fun_Ofun__upd(U_9792,U_9793,U_9789,U_9790,U_9791) = U_9789
| hAPP(U_9789,U_9790) != U_9791 ),
inference(variable_rename,[status(thm)],[f_2677_1]) ).
cnf(f_2677_3,plain,
( c_Fun_Ofun__upd(U_9792,U_9793,U_9789,U_9790,U_9791) = U_9789
| hAPP(U_9789,U_9790) != U_9791 ),
inference(clausify,[status(thm)],[f_2677_2]) ).
fof(f_2678_1,plain,
! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setprod__timesf]) ).
fof(f_2678_2,plain,
! [U_9798,U_9797,U_9796,U_9795,U_9794] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9795,U_9794),hAPP(hAPP(c_COMBS(U_9795,U_9794,U_9794),hAPP(hAPP(c_COMBB(U_9794,tc_fun(U_9794,U_9794),U_9795),c_Groups_Otimes__class_Otimes(U_9794)),U_9796)),U_9797)),U_9798) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9794),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9795,U_9794),U_9796),U_9798)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9795,U_9794),U_9797),U_9798))
| ~ class_Groups_Ocomm__monoid__mult(U_9794) ),
inference(variable_rename,[status(thm)],[f_2678_1]) ).
cnf(f_2678_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9795,U_9794),hAPP(hAPP(c_COMBS(U_9795,U_9794,U_9794),hAPP(hAPP(c_COMBB(U_9794,tc_fun(U_9794,U_9794),U_9795),c_Groups_Otimes__class_Otimes(U_9794)),U_9796)),U_9797)),U_9798) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9794),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9795,U_9794),U_9796),U_9798)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9795,U_9794),U_9797),U_9798))
| ~ class_Groups_Ocomm__monoid__mult(U_9794) ),
inference(clausify,[status(thm)],[f_2678_2]) ).
fof(f_2679_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2)
| ~ class_Rings_Oring__1(T_b)
| ~ class_Groups_Ocomm__monoid__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int__setprod]) ).
fof(f_2679_2,plain,
! [U_9802,U_9801,U_9800,U_9799] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_9799),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9800,tc_Int_Oint),U_9801),U_9802)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9800,U_9799),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_9799,U_9800),c_Int_Oring__1__class_Oof__int(U_9799)),U_9801)),U_9802)
| ~ class_Rings_Oring__1(U_9799)
| ~ class_Groups_Ocomm__monoid__mult(U_9799) ),
inference(variable_rename,[status(thm)],[f_2679_1]) ).
cnf(f_2679_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_9799),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9800,tc_Int_Oint),U_9801),U_9802)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9800,U_9799),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_9799,U_9800),c_Int_Oring__1__class_Oof__int(U_9799)),U_9801)),U_9802)
| ~ class_Rings_Oring__1(U_9799)
| ~ class_Groups_Ocomm__monoid__mult(U_9799) ),
inference(clausify,[status(thm)],[f_2679_2]) ).
fof(f_2680_1,plain,
! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod2_I2_J]) ).
fof(f_2680_2,plain,
! [U_9805,U_9804,U_9803] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9803,tc_Nat_Onat),U_9804),U_9805) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9803,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_9803),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9804)),U_9805)),
inference(variable_rename,[status(thm)],[f_2680_1]) ).
cnf(f_2680_3,plain,
hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9803,tc_Nat_Onat),U_9804),U_9805) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9803,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_9803),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9804)),U_9805)),
inference(clausify,[status(thm)],[f_2680_2]) ).
fof(f_2681_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2)
| ~ class_Rings_Osemiring__1(T_b)
| ~ class_Groups_Ocomm__monoid__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__setprod]) ).
fof(f_2681_2,plain,
! [U_9809,U_9808,U_9807,U_9806] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9806),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9807,tc_Nat_Onat),U_9808),U_9809)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9807,U_9806),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9806,U_9807),c_Nat_Osemiring__1__class_Oof__nat(U_9806)),U_9808)),U_9809)
| ~ class_Rings_Osemiring__1(U_9806)
| ~ class_Groups_Ocomm__monoid__mult(U_9806) ),
inference(variable_rename,[status(thm)],[f_2681_1]) ).
cnf(f_2681_3,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_9806),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9807,tc_Nat_Onat),U_9808),U_9809)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9807,U_9806),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_9806,U_9807),c_Nat_Osemiring__1__class_Oof__nat(U_9806)),U_9808)),U_9809)
| ~ class_Rings_Osemiring__1(U_9806)
| ~ class_Groups_Ocomm__monoid__mult(U_9806) ),
inference(clausify,[status(thm)],[f_2681_2]) ).
fof(f_2682_1,plain,
! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2),
inference(fof_nnf,[status(thm)],[fact_int__setprod]) ).
fof(f_2682_2,plain,
! [U_9812,U_9811,U_9810] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9810,tc_Nat_Onat),U_9811),U_9812)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9810,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_9810),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9811)),U_9812),
inference(variable_rename,[status(thm)],[f_2682_1]) ).
cnf(f_2682_3,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9810,tc_Nat_Onat),U_9811),U_9812)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9810,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_9810),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_9811)),U_9812),
inference(clausify,[status(thm)],[f_2682_2]) ).
fof(f_2683_1,plain,
! [V_A_2,T_c,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Oone__class_Oone(T_b))),V_A_2) = c_Groups_Oone__class_Oone(T_b)
| ~ class_Groups_Ocomm__monoid__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setprod__1]) ).
fof(f_2683_2,plain,
! [U_9815,U_9814,U_9813] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9814,U_9813),hAPP(c_COMBK(U_9813,U_9814),c_Groups_Oone__class_Oone(U_9813))),U_9815) = c_Groups_Oone__class_Oone(U_9813)
| ~ class_Groups_Ocomm__monoid__mult(U_9813) ),
inference(variable_rename,[status(thm)],[f_2683_1]) ).
cnf(f_2683_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9814,U_9813),hAPP(c_COMBK(U_9813,U_9814),c_Groups_Oone__class_Oone(U_9813))),U_9815) = c_Groups_Oone__class_Oone(U_9813)
| ~ class_Groups_Ocomm__monoid__mult(U_9813) ),
inference(clausify,[status(thm)],[f_2683_2]) ).
fof(f_2684_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)
| ~ class_Fields_Olinordered__field(T_b) ),
inference(fof_nnf,[status(thm)],[fact_abs__setprod]) ).
fof(f_2684_2,plain,
! [U_9819,U_9818,U_9817,U_9816] :
( hAPP(c_Groups_Oabs__class_Oabs(U_9816),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9817,U_9816),U_9818),U_9819)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9817,U_9816),hAPP(hAPP(c_COMBB(U_9816,U_9816,U_9817),c_Groups_Oabs__class_Oabs(U_9816)),U_9818)),U_9819)
| ~ class_Fields_Olinordered__field(U_9816) ),
inference(variable_rename,[status(thm)],[f_2684_1]) ).
cnf(f_2684_3,plain,
( hAPP(c_Groups_Oabs__class_Oabs(U_9816),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9817,U_9816),U_9818),U_9819)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9817,U_9816),hAPP(hAPP(c_COMBB(U_9816,U_9816,U_9817),c_Groups_Oabs__class_Oabs(U_9816)),U_9818)),U_9819)
| ~ class_Fields_Olinordered__field(U_9816) ),
inference(clausify,[status(thm)],[f_2684_2]) ).
fof(f_2685_1,plain,
! [V_f_2,V_A_2,T_b,T_c] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
| ! [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) != c_Groups_Ozero__class_Ozero(T_c) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Rings_Ono__zero__divisors(T_c)
| ~ class_Rings_Ocomm__semiring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__zero__iff]) ).
fof(f_2685_2,plain,
! [U_9825,U_9824,U_9823,U_9822] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9823,U_9822),U_9825),U_9824) = c_Groups_Ozero__class_Ozero(U_9822)
| ! [U_9821] :
( hAPP(U_9825,U_9821) != c_Groups_Ozero__class_Ozero(U_9822)
| ~ hBOOL(hAPP(hAPP(c_member(U_9823),U_9821),U_9824)) ) )
& ( ? [U_9820] :
( hAPP(U_9825,U_9820) = c_Groups_Ozero__class_Ozero(U_9822)
& hBOOL(hAPP(hAPP(c_member(U_9823),U_9820),U_9824)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9823,U_9822),U_9825),U_9824) != c_Groups_Ozero__class_Ozero(U_9822) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9823),U_9824))
| ~ class_Rings_Ono__zero__divisors(U_9822)
| ~ class_Rings_Ocomm__semiring__1(U_9822) ),
inference(variable_rename,[status(thm)],[f_2685_1]) ).
fof(f_2685_3,plain,
! [U_9825,U_9824,U_9823,U_9822] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9823,U_9822),U_9825),U_9824) = c_Groups_Ozero__class_Ozero(U_9822)
| ! [U_9821] :
( hAPP(U_9825,U_9821) != c_Groups_Ozero__class_Ozero(U_9822)
| ~ hBOOL(hAPP(hAPP(c_member(U_9823),U_9821),U_9824)) ) )
& ( ( hAPP(U_9825,sK201(U_9825,U_9824,U_9823,U_9822)) = c_Groups_Ozero__class_Ozero(U_9822)
& hBOOL(hAPP(hAPP(c_member(U_9823),sK201(U_9825,U_9824,U_9823,U_9822)),U_9824)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9823,U_9822),U_9825),U_9824) != c_Groups_Ozero__class_Ozero(U_9822) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9823),U_9824))
| ~ class_Rings_Ono__zero__divisors(U_9822)
| ~ class_Rings_Ocomm__semiring__1(U_9822) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK201]),skolemize(U_9820,sK201(U_9825,U_9824,U_9823,U_9822))],[f_2685_2]) ).
cnf(f_2685_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_9823),sK201(U_9825,U_9824,U_9823,U_9822)),U_9824))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9823,U_9822),U_9825),U_9824) != c_Groups_Ozero__class_Ozero(U_9822)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9823),U_9824))
| ~ class_Rings_Ono__zero__divisors(U_9822)
| ~ class_Rings_Ocomm__semiring__1(U_9822) ),
inference(clausify,[status(thm)],[f_2685_3]) ).
cnf(f_2685_5,plain,
( hAPP(U_9825,sK201(U_9825,U_9824,U_9823,U_9822)) = c_Groups_Ozero__class_Ozero(U_9822)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9823,U_9822),U_9825),U_9824) != c_Groups_Ozero__class_Ozero(U_9822)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9823),U_9824))
| ~ class_Rings_Ono__zero__divisors(U_9822)
| ~ class_Rings_Ocomm__semiring__1(U_9822) ),
inference(clausify,[status(thm)],[f_2685_3]) ).
cnf(f_2685_6,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9823,U_9822),U_9825),U_9824) = c_Groups_Ozero__class_Ozero(U_9822)
| hAPP(U_9825,U_9821) != c_Groups_Ozero__class_Ozero(U_9822)
| ~ hBOOL(hAPP(hAPP(c_member(U_9823),U_9821),U_9824))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9823),U_9824))
| ~ class_Rings_Ono__zero__divisors(U_9822)
| ~ class_Rings_Ocomm__semiring__1(U_9822) ),
inference(clausify,[status(thm)],[f_2685_3]) ).
fof(f_2686_1,plain,
! [V_f_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
| ! [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Rings_Ocomm__semiring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__zero]) ).
fof(f_2686_2,plain,
! [U_9830,U_9829,U_9828,U_9827] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9828,U_9827),U_9830),U_9829) = c_Groups_Ozero__class_Ozero(U_9827)
| ! [U_9826] :
( hAPP(U_9830,U_9826) != c_Groups_Ozero__class_Ozero(U_9827)
| ~ hBOOL(hAPP(hAPP(c_member(U_9828),U_9826),U_9829)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9828),U_9829))
| ~ class_Rings_Ocomm__semiring__1(U_9827) ),
inference(variable_rename,[status(thm)],[f_2686_1]) ).
cnf(f_2686_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9828,U_9827),U_9830),U_9829) = c_Groups_Ozero__class_Ozero(U_9827)
| hAPP(U_9830,U_9826) != c_Groups_Ozero__class_Ozero(U_9827)
| ~ hBOOL(hAPP(hAPP(c_member(U_9828),U_9826),U_9829))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9828),U_9829))
| ~ class_Rings_Ocomm__semiring__1(U_9827) ),
inference(clausify,[status(thm)],[f_2686_2]) ).
fof(f_2687_1,plain,
! [V_g_2,T_c,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b)
| ~ class_Groups_Ocomm__monoid__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Oempty]) ).
fof(f_2687_2,plain,
! [U_9833,U_9832,U_9831] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9832,U_9831),U_9833),c_Orderings_Obot__class_Obot(tc_fun(U_9832,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_9831)
| ~ class_Groups_Ocomm__monoid__mult(U_9831) ),
inference(variable_rename,[status(thm)],[f_2687_1]) ).
cnf(f_2687_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9832,U_9831),U_9833),c_Orderings_Obot__class_Obot(tc_fun(U_9832,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_9831)
| ~ class_Groups_Ocomm__monoid__mult(U_9831) ),
inference(clausify,[status(thm)],[f_2687_2]) ).
fof(f_2688_1,plain,
! [V_f_2,T_c,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b)
| ~ class_Groups_Ocomm__monoid__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setprod__empty]) ).
fof(f_2688_2,plain,
! [U_9836,U_9835,U_9834] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9835,U_9834),U_9836),c_Orderings_Obot__class_Obot(tc_fun(U_9835,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_9834)
| ~ class_Groups_Ocomm__monoid__mult(U_9834) ),
inference(variable_rename,[status(thm)],[f_2688_1]) ).
cnf(f_2688_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9835,U_9834),U_9836),c_Orderings_Obot__class_Obot(tc_fun(U_9835,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_9834)
| ~ class_Groups_Ocomm__monoid__mult(U_9834) ),
inference(clausify,[status(thm)],[f_2688_2]) ).
fof(f_2689_1,plain,
! [V_g_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Oinfinite]) ).
fof(f_2689_2,plain,
! [U_9840,U_9839,U_9838,U_9837] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9838,U_9837),U_9840),U_9839) = c_Groups_Oone__class_Oone(U_9837)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_9838),U_9839))
| ~ class_Groups_Ocomm__monoid__mult(U_9837) ),
inference(variable_rename,[status(thm)],[f_2689_1]) ).
cnf(f_2689_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9838,U_9837),U_9840),U_9839) = c_Groups_Oone__class_Oone(U_9837)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_9838),U_9839))
| ~ class_Groups_Ocomm__monoid__mult(U_9837) ),
inference(clausify,[status(thm)],[f_2689_2]) ).
fof(f_2690_1,plain,
! [V_f_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_c)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__infinite]) ).
fof(f_2690_2,plain,
! [U_9844,U_9843,U_9842,U_9841] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9842,U_9841),U_9844),U_9843) = c_Groups_Oone__class_Oone(U_9841)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_9842),U_9843))
| ~ class_Groups_Ocomm__monoid__mult(U_9841) ),
inference(variable_rename,[status(thm)],[f_2690_1]) ).
cnf(f_2690_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9842,U_9841),U_9844),U_9843) = c_Groups_Oone__class_Oone(U_9841)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_9842),U_9843))
| ~ class_Groups_Ocomm__monoid__mult(U_9841) ),
inference(clausify,[status(thm)],[f_2690_2]) ).
fof(f_2691_1,plain,
! [V_f_2,V_F_2,T_b] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) ) )
& ( ! [B_x] :
( hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_F_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_setprod__eq__1__iff]) ).
fof(f_2691_2,plain,
! [U_9849,U_9848,U_9847] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9847,tc_Nat_Onat),U_9849),U_9848) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ? [U_9846] :
( hAPP(U_9849,U_9846) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_9847),U_9846),U_9848)) ) )
& ( ! [U_9845] :
( hAPP(U_9849,U_9845) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_9847),U_9845),U_9848)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9847,tc_Nat_Onat),U_9849),U_9848) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9847),U_9848)) ),
inference(variable_rename,[status(thm)],[f_2691_1]) ).
fof(f_2691_3,plain,
! [U_9849,U_9848,U_9847] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9847,tc_Nat_Onat),U_9849),U_9848) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ( hAPP(U_9849,sK202(U_9849,U_9848,U_9847)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_9847),sK202(U_9849,U_9848,U_9847)),U_9848)) ) )
& ( ! [U_9845] :
( hAPP(U_9849,U_9845) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_9847),U_9845),U_9848)) )
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9847,tc_Nat_Onat),U_9849),U_9848) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9847),U_9848)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK202]),skolemize(U_9846,sK202(U_9849,U_9848,U_9847))],[f_2691_2]) ).
cnf(f_2691_4,plain,
( hAPP(U_9849,U_9845) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(U_9847),U_9845),U_9848))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9847,tc_Nat_Onat),U_9849),U_9848) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9847),U_9848)) ),
inference(clausify,[status(thm)],[f_2691_3]) ).
cnf(f_2691_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9847),sK202(U_9849,U_9848,U_9847)),U_9848))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9847,tc_Nat_Onat),U_9849),U_9848) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9847),U_9848)) ),
inference(clausify,[status(thm)],[f_2691_3]) ).
cnf(f_2691_6,plain,
( hAPP(U_9849,sK202(U_9849,U_9848,U_9847)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9847,tc_Nat_Onat),U_9849),U_9848) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9847),U_9848)) ),
inference(clausify,[status(thm)],[f_2691_3]) ).
fof(f_2692_1,plain,
! [V_f_2,V_A_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,tc_Nat_Onat),V_f_2),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))
| ~ c_Nat__Transfer_Onat__set(V_A_2)
| ~ class_Groups_Ocomm__monoid__mult(T_b)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I2_J]) ).
fof(f_2692_2,plain,
! [U_9852,U_9851,U_9850] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_9850),U_9852),U_9851) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_9850),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_9850,tc_Nat_Onat),U_9852),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9851))
| ~ c_Nat__Transfer_Onat__set(U_9851)
| ~ class_Groups_Ocomm__monoid__mult(U_9850)
| ~ class_Groups_Ocomm__monoid__add(U_9850) ),
inference(variable_rename,[status(thm)],[f_2692_1]) ).
cnf(f_2692_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_9850),U_9852),U_9851) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_9850),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_9850,tc_Nat_Onat),U_9852),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9851))
| ~ c_Nat__Transfer_Onat__set(U_9851)
| ~ class_Groups_Ocomm__monoid__mult(U_9850)
| ~ class_Groups_Ocomm__monoid__add(U_9850) ),
inference(clausify,[status(thm)],[f_2692_2]) ).
fof(f_2693_1,plain,
! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Odistrib]) ).
fof(f_2693_2,plain,
! [U_9857,U_9856,U_9855,U_9854,U_9853] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9854,U_9853),hAPP(hAPP(c_COMBS(U_9854,U_9853,U_9853),hAPP(hAPP(c_COMBB(U_9853,tc_fun(U_9853,U_9853),U_9854),c_Groups_Otimes__class_Otimes(U_9853)),U_9856)),U_9857)),U_9855) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9853),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9854,U_9853),U_9856),U_9855)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9854,U_9853),U_9857),U_9855))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9854),U_9855))
| ~ class_Groups_Ocomm__monoid__mult(U_9853) ),
inference(variable_rename,[status(thm)],[f_2693_1]) ).
cnf(f_2693_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9854,U_9853),hAPP(hAPP(c_COMBS(U_9854,U_9853,U_9853),hAPP(hAPP(c_COMBB(U_9853,tc_fun(U_9853,U_9853),U_9854),c_Groups_Otimes__class_Otimes(U_9853)),U_9856)),U_9857)),U_9855) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9853),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9854,U_9853),U_9856),U_9855)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9854,U_9853),U_9857),U_9855))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9854),U_9855))
| ~ class_Groups_Ocomm__monoid__mult(U_9853) ),
inference(clausify,[status(thm)],[f_2693_2]) ).
fof(f_2694_1,plain,
! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Rings_Oinverse__class_Odivide(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Fields_Ofield__inverse__zero(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__dividef]) ).
fof(f_2694_2,plain,
! [U_9862,U_9861,U_9860,U_9859,U_9858] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9859,U_9858),hAPP(hAPP(c_COMBS(U_9859,U_9858,U_9858),hAPP(hAPP(c_COMBB(U_9858,tc_fun(U_9858,U_9858),U_9859),c_Rings_Oinverse__class_Odivide(U_9858)),U_9861)),U_9862)),U_9860) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9858),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9859,U_9858),U_9861),U_9860)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9859,U_9858),U_9862),U_9860))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9859),U_9860))
| ~ class_Fields_Ofield__inverse__zero(U_9858) ),
inference(variable_rename,[status(thm)],[f_2694_1]) ).
cnf(f_2694_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9859,U_9858),hAPP(hAPP(c_COMBS(U_9859,U_9858,U_9858),hAPP(hAPP(c_COMBB(U_9858,tc_fun(U_9858,U_9858),U_9859),c_Rings_Oinverse__class_Odivide(U_9858)),U_9861)),U_9862)),U_9860) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9858),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9859,U_9858),U_9861),U_9860)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9859,U_9858),U_9862),U_9860))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9859),U_9860))
| ~ class_Fields_Ofield__inverse__zero(U_9858) ),
inference(clausify,[status(thm)],[f_2694_2]) ).
fof(f_2695_1,plain,
! [V_f_2,V_i_2,V_A_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,V_i_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Rings_Ocomm__semiring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_dvd__setprod]) ).
fof(f_2695_2,plain,
! [U_9867,U_9866,U_9865,U_9864,U_9863] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_9863),hAPP(U_9867,U_9866)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9864,U_9863),U_9867),U_9865)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9864),U_9866),U_9865))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9864),U_9865))
| ~ class_Rings_Ocomm__semiring__1(U_9863) ),
inference(variable_rename,[status(thm)],[f_2695_1]) ).
cnf(f_2695_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_9863),hAPP(U_9867,U_9866)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9864,U_9863),U_9867),U_9865)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9864),U_9866),U_9865))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9864),U_9865))
| ~ class_Rings_Ocomm__semiring__1(U_9863) ),
inference(clausify,[status(thm)],[f_2695_2]) ).
fof(f_2696_1,plain,
! [V_f_2,V_S_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) ),
inference(fof_nnf,[status(thm)],[fact_setprod__pos__nat__iff]) ).
fof(f_2696_2,plain,
! [U_9872,U_9871,U_9870] :
( ( ( 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_9870,tc_Nat_Onat),U_9872),U_9871)))
| ? [U_9869] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_9872,U_9869)))
& hBOOL(hAPP(hAPP(c_member(U_9870),U_9869),U_9871)) ) )
& ( ! [U_9868] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_9872,U_9868)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9870),U_9868),U_9871)) )
| ~ 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_9870,tc_Nat_Onat),U_9872),U_9871))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9870),U_9871)) ),
inference(variable_rename,[status(thm)],[f_2696_1]) ).
fof(f_2696_3,plain,
! [U_9872,U_9871,U_9870] :
( ( ( 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_9870,tc_Nat_Onat),U_9872),U_9871)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_9872,sK203(U_9872,U_9871,U_9870))))
& hBOOL(hAPP(hAPP(c_member(U_9870),sK203(U_9872,U_9871,U_9870)),U_9871)) ) )
& ( ! [U_9868] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_9872,U_9868)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9870),U_9868),U_9871)) )
| ~ 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_9870,tc_Nat_Onat),U_9872),U_9871))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9870),U_9871)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK203]),skolemize(U_9869,sK203(U_9872,U_9871,U_9870))],[f_2696_2]) ).
cnf(f_2696_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_9872,U_9868)))
| ~ hBOOL(hAPP(hAPP(c_member(U_9870),U_9868),U_9871))
| ~ 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_9870,tc_Nat_Onat),U_9872),U_9871)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9870),U_9871)) ),
inference(clausify,[status(thm)],[f_2696_3]) ).
cnf(f_2696_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_9870),sK203(U_9872,U_9871,U_9870)),U_9871))
| 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_9870,tc_Nat_Onat),U_9872),U_9871)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9870),U_9871)) ),
inference(clausify,[status(thm)],[f_2696_3]) ).
cnf(f_2696_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_9872,sK203(U_9872,U_9871,U_9870))))
| 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_9870,tc_Nat_Onat),U_9872),U_9871)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9870),U_9871)) ),
inference(clausify,[status(thm)],[f_2696_3]) ).
fof(f_2697_1,plain,
! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ class_Rings_Odvd(T_c)
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__dvd__setprod__subset]) ).
fof(f_2697_2,plain,
! [U_9877,U_9876,U_9875,U_9874,U_9873] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_9873),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9874,U_9873),U_9877),U_9876)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9874,U_9873),U_9877),U_9875)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9874,tc_HOL_Obool)),U_9876),U_9875))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9874),U_9875))
| ~ class_Rings_Odvd(U_9873)
| ~ class_Groups_Ocomm__monoid__mult(U_9873) ),
inference(variable_rename,[status(thm)],[f_2697_1]) ).
cnf(f_2697_3,plain,
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_9873),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9874,U_9873),U_9877),U_9876)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9874,U_9873),U_9877),U_9875)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9874,tc_HOL_Obool)),U_9876),U_9875))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9874),U_9875))
| ~ class_Rings_Odvd(U_9873)
| ~ class_Groups_Ocomm__monoid__mult(U_9873) ),
inference(clausify,[status(thm)],[f_2697_2]) ).
fof(f_2698_1,plain,
! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__delta_H]) ).
fof(f_2698_2,plain,
! [U_9882,U_9881,U_9880,U_9879,U_9878] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9879,U_9878),hAPP(hAPP(c_COMBC(U_9879,U_9878,U_9878),hAPP(hAPP(c_COMBS(U_9879,U_9878,tc_fun(U_9878,U_9878)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9878,tc_fun(U_9878,U_9878)),U_9879),c_If(U_9878)),hAPP(c_fequal,U_9881))),U_9882)),c_Groups_Oone__class_Oone(U_9878))),U_9880) = c_Groups_Oone__class_Oone(U_9878)
| hBOOL(hAPP(hAPP(c_member(U_9879),U_9881),U_9880)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9879,U_9878),hAPP(hAPP(c_COMBC(U_9879,U_9878,U_9878),hAPP(hAPP(c_COMBS(U_9879,U_9878,tc_fun(U_9878,U_9878)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9878,tc_fun(U_9878,U_9878)),U_9879),c_If(U_9878)),hAPP(c_fequal,U_9881))),U_9882)),c_Groups_Oone__class_Oone(U_9878))),U_9880) = hAPP(U_9882,U_9881)
| ~ hBOOL(hAPP(hAPP(c_member(U_9879),U_9881),U_9880)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9879),U_9880))
| ~ class_Groups_Ocomm__monoid__mult(U_9878) ),
inference(variable_rename,[status(thm)],[f_2698_1]) ).
cnf(f_2698_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9879,U_9878),hAPP(hAPP(c_COMBC(U_9879,U_9878,U_9878),hAPP(hAPP(c_COMBS(U_9879,U_9878,tc_fun(U_9878,U_9878)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9878,tc_fun(U_9878,U_9878)),U_9879),c_If(U_9878)),hAPP(c_fequal,U_9881))),U_9882)),c_Groups_Oone__class_Oone(U_9878))),U_9880) = hAPP(U_9882,U_9881)
| ~ hBOOL(hAPP(hAPP(c_member(U_9879),U_9881),U_9880))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9879),U_9880))
| ~ class_Groups_Ocomm__monoid__mult(U_9878) ),
inference(clausify,[status(thm)],[f_2698_2]) ).
cnf(f_2698_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9879,U_9878),hAPP(hAPP(c_COMBC(U_9879,U_9878,U_9878),hAPP(hAPP(c_COMBS(U_9879,U_9878,tc_fun(U_9878,U_9878)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9878,tc_fun(U_9878,U_9878)),U_9879),c_If(U_9878)),hAPP(c_fequal,U_9881))),U_9882)),c_Groups_Oone__class_Oone(U_9878))),U_9880) = c_Groups_Oone__class_Oone(U_9878)
| hBOOL(hAPP(hAPP(c_member(U_9879),U_9881),U_9880))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9879),U_9880))
| ~ class_Groups_Ocomm__monoid__mult(U_9878) ),
inference(clausify,[status(thm)],[f_2698_2]) ).
fof(f_2699_1,plain,
! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__delta]) ).
fof(f_2699_2,plain,
! [U_9887,U_9886,U_9885,U_9884,U_9883] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9884,U_9883),hAPP(hAPP(c_COMBC(U_9884,U_9883,U_9883),hAPP(hAPP(c_COMBS(U_9884,U_9883,tc_fun(U_9883,U_9883)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9883,tc_fun(U_9883,U_9883)),U_9884),c_If(U_9883)),hAPP(hAPP(c_COMBC(U_9884,U_9884,tc_HOL_Obool),c_fequal),U_9886))),U_9887)),c_Groups_Oone__class_Oone(U_9883))),U_9885) = c_Groups_Oone__class_Oone(U_9883)
| hBOOL(hAPP(hAPP(c_member(U_9884),U_9886),U_9885)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9884,U_9883),hAPP(hAPP(c_COMBC(U_9884,U_9883,U_9883),hAPP(hAPP(c_COMBS(U_9884,U_9883,tc_fun(U_9883,U_9883)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9883,tc_fun(U_9883,U_9883)),U_9884),c_If(U_9883)),hAPP(hAPP(c_COMBC(U_9884,U_9884,tc_HOL_Obool),c_fequal),U_9886))),U_9887)),c_Groups_Oone__class_Oone(U_9883))),U_9885) = hAPP(U_9887,U_9886)
| ~ hBOOL(hAPP(hAPP(c_member(U_9884),U_9886),U_9885)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9884),U_9885))
| ~ class_Groups_Ocomm__monoid__mult(U_9883) ),
inference(variable_rename,[status(thm)],[f_2699_1]) ).
cnf(f_2699_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9884,U_9883),hAPP(hAPP(c_COMBC(U_9884,U_9883,U_9883),hAPP(hAPP(c_COMBS(U_9884,U_9883,tc_fun(U_9883,U_9883)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9883,tc_fun(U_9883,U_9883)),U_9884),c_If(U_9883)),hAPP(hAPP(c_COMBC(U_9884,U_9884,tc_HOL_Obool),c_fequal),U_9886))),U_9887)),c_Groups_Oone__class_Oone(U_9883))),U_9885) = hAPP(U_9887,U_9886)
| ~ hBOOL(hAPP(hAPP(c_member(U_9884),U_9886),U_9885))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9884),U_9885))
| ~ class_Groups_Ocomm__monoid__mult(U_9883) ),
inference(clausify,[status(thm)],[f_2699_2]) ).
cnf(f_2699_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9884,U_9883),hAPP(hAPP(c_COMBC(U_9884,U_9883,U_9883),hAPP(hAPP(c_COMBS(U_9884,U_9883,tc_fun(U_9883,U_9883)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_9883,tc_fun(U_9883,U_9883)),U_9884),c_If(U_9883)),hAPP(hAPP(c_COMBC(U_9884,U_9884,tc_HOL_Obool),c_fequal),U_9886))),U_9887)),c_Groups_Oone__class_Oone(U_9883))),U_9885) = c_Groups_Oone__class_Oone(U_9883)
| hBOOL(hAPP(hAPP(c_member(U_9884),U_9886),U_9885))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9884),U_9885))
| ~ class_Groups_Ocomm__monoid__mult(U_9883) ),
inference(clausify,[status(thm)],[f_2699_2]) ).
fof(f_2700_1,plain,
! [V_y_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_COMBK(T_c,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_y_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__constant]) ).
fof(f_2700_2,plain,
! [U_9891,U_9890,U_9889,U_9888] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9889,U_9888),hAPP(c_COMBK(U_9888,U_9889),U_9891)),U_9890) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9888),U_9891),hAPP(c_Finite__Set_Ocard(U_9889),U_9890))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9889),U_9890))
| ~ class_Groups_Ocomm__monoid__mult(U_9888) ),
inference(variable_rename,[status(thm)],[f_2700_1]) ).
cnf(f_2700_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9889,U_9888),hAPP(c_COMBK(U_9888,U_9889),U_9891)),U_9890) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9888),U_9891),hAPP(c_Finite__Set_Ocard(U_9889),U_9890))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9889),U_9890))
| ~ class_Groups_Ocomm__monoid__mult(U_9888) ),
inference(clausify,[status(thm)],[f_2700_2]) ).
fof(f_2701_1,plain,
! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__insert]) ).
fof(f_2701_2,plain,
! [U_9896,U_9895,U_9894,U_9893,U_9892] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9893,U_9892),U_9896),hAPP(hAPP(c_Set_Oinsert(U_9893),U_9895),U_9894)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9892),hAPP(U_9896,U_9895)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9893,U_9892),U_9896),U_9894))
| hBOOL(hAPP(hAPP(c_member(U_9893),U_9895),U_9894))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9893),U_9894))
| ~ class_Groups_Ocomm__monoid__mult(U_9892) ),
inference(variable_rename,[status(thm)],[f_2701_1]) ).
cnf(f_2701_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9893,U_9892),U_9896),hAPP(hAPP(c_Set_Oinsert(U_9893),U_9895),U_9894)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9892),hAPP(U_9896,U_9895)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9893,U_9892),U_9896),U_9894))
| hBOOL(hAPP(hAPP(c_member(U_9893),U_9895),U_9894))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9893),U_9894))
| ~ class_Groups_Ocomm__monoid__mult(U_9892) ),
inference(clausify,[status(thm)],[f_2701_2]) ).
fof(f_2702_1,plain,
! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Oinsert]) ).
fof(f_2702_2,plain,
! [U_9901,U_9900,U_9899,U_9898,U_9897] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9898,U_9897),U_9901),hAPP(hAPP(c_Set_Oinsert(U_9898),U_9900),U_9899)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9897),hAPP(U_9901,U_9900)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9898,U_9897),U_9901),U_9899))
| hBOOL(hAPP(hAPP(c_member(U_9898),U_9900),U_9899))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9898),U_9899))
| ~ class_Groups_Ocomm__monoid__mult(U_9897) ),
inference(variable_rename,[status(thm)],[f_2702_1]) ).
cnf(f_2702_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9898,U_9897),U_9901),hAPP(hAPP(c_Set_Oinsert(U_9898),U_9900),U_9899)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9897),hAPP(U_9901,U_9900)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9898,U_9897),U_9901),U_9899))
| hBOOL(hAPP(hAPP(c_member(U_9898),U_9900),U_9899))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9898),U_9899))
| ~ class_Groups_Ocomm__monoid__mult(U_9897) ),
inference(clausify,[status(thm)],[f_2702_2]) ).
fof(f_2703_1,plain,
! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Oinsert__remove]) ).
fof(f_2703_2,plain,
! [U_9906,U_9905,U_9904,U_9903,U_9902] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9903,U_9902),U_9905),hAPP(hAPP(c_Set_Oinsert(U_9903),U_9906),U_9904)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9902),hAPP(U_9905,U_9906)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9903,U_9902),U_9905),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9903,tc_HOL_Obool)),U_9904),hAPP(hAPP(c_Set_Oinsert(U_9903),U_9906),c_Orderings_Obot__class_Obot(tc_fun(U_9903,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9903),U_9904))
| ~ class_Groups_Ocomm__monoid__mult(U_9902) ),
inference(variable_rename,[status(thm)],[f_2703_1]) ).
cnf(f_2703_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9903,U_9902),U_9905),hAPP(hAPP(c_Set_Oinsert(U_9903),U_9906),U_9904)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9902),hAPP(U_9905,U_9906)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9903,U_9902),U_9905),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9903,tc_HOL_Obool)),U_9904),hAPP(hAPP(c_Set_Oinsert(U_9903),U_9906),c_Orderings_Obot__class_Obot(tc_fun(U_9903,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9903),U_9904))
| ~ class_Groups_Ocomm__monoid__mult(U_9902) ),
inference(clausify,[status(thm)],[f_2703_2]) ).
fof(f_2704_1,plain,
! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Oremove]) ).
fof(f_2704_2,plain,
! [U_9911,U_9910,U_9909,U_9908,U_9907] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9908,U_9907),U_9911),U_9909) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9907),hAPP(U_9911,U_9910)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9908,U_9907),U_9911),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9908,tc_HOL_Obool)),U_9909),hAPP(hAPP(c_Set_Oinsert(U_9908),U_9910),c_Orderings_Obot__class_Obot(tc_fun(U_9908,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_9908),U_9910),U_9909))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9908),U_9909))
| ~ class_Groups_Ocomm__monoid__mult(U_9907) ),
inference(variable_rename,[status(thm)],[f_2704_1]) ).
cnf(f_2704_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9908,U_9907),U_9911),U_9909) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_9907),hAPP(U_9911,U_9910)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9908,U_9907),U_9911),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9908,tc_HOL_Obool)),U_9909),hAPP(hAPP(c_Set_Oinsert(U_9908),U_9910),c_Orderings_Obot__class_Obot(tc_fun(U_9908,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_9908),U_9910),U_9909))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9908),U_9909))
| ~ class_Groups_Ocomm__monoid__mult(U_9907) ),
inference(clausify,[status(thm)],[f_2704_2]) ).
fof(f_2705_1,plain,
! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) )
| hAPP(V_f_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_c)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Fields_Ofield(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__diff1]) ).
fof(f_2705_2,plain,
! [U_9916,U_9915,U_9914,U_9913,U_9912] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9913,U_9912),U_9915),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9913,tc_HOL_Obool)),U_9914),hAPP(hAPP(c_Set_Oinsert(U_9913),U_9916),c_Orderings_Obot__class_Obot(tc_fun(U_9913,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9913,U_9912),U_9915),U_9914)
| hBOOL(hAPP(hAPP(c_member(U_9913),U_9916),U_9914)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9913,U_9912),U_9915),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9913,tc_HOL_Obool)),U_9914),hAPP(hAPP(c_Set_Oinsert(U_9913),U_9916),c_Orderings_Obot__class_Obot(tc_fun(U_9913,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9912),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9913,U_9912),U_9915),U_9914)),hAPP(U_9915,U_9916))
| ~ hBOOL(hAPP(hAPP(c_member(U_9913),U_9916),U_9914)) ) )
| hAPP(U_9915,U_9916) = c_Groups_Ozero__class_Ozero(U_9912)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9913),U_9914))
| ~ class_Fields_Ofield(U_9912) ),
inference(variable_rename,[status(thm)],[f_2705_1]) ).
cnf(f_2705_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9913,U_9912),U_9915),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9913,tc_HOL_Obool)),U_9914),hAPP(hAPP(c_Set_Oinsert(U_9913),U_9916),c_Orderings_Obot__class_Obot(tc_fun(U_9913,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_9912),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9913,U_9912),U_9915),U_9914)),hAPP(U_9915,U_9916))
| ~ hBOOL(hAPP(hAPP(c_member(U_9913),U_9916),U_9914))
| hAPP(U_9915,U_9916) = c_Groups_Ozero__class_Ozero(U_9912)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9913),U_9914))
| ~ class_Fields_Ofield(U_9912) ),
inference(clausify,[status(thm)],[f_2705_2]) ).
cnf(f_2705_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9913,U_9912),U_9915),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9913,tc_HOL_Obool)),U_9914),hAPP(hAPP(c_Set_Oinsert(U_9913),U_9916),c_Orderings_Obot__class_Obot(tc_fun(U_9913,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9913,U_9912),U_9915),U_9914)
| hBOOL(hAPP(hAPP(c_member(U_9913),U_9916),U_9914))
| hAPP(U_9915,U_9916) = c_Groups_Ozero__class_Ozero(U_9912)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9913),U_9914))
| ~ class_Fields_Ofield(U_9912) ),
inference(clausify,[status(thm)],[f_2705_2]) ).
fof(f_2706_1,plain,
! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) != V_B_2
| ? [B_i] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__nonneg__leq__bound]) ).
fof(f_2706_2,plain,
! [U_9923,U_9922,U_9921,U_9920,U_9919,U_9918] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9918),hAPP(U_9921,U_9923)),U_9922))
| ~ hBOOL(hAPP(hAPP(c_member(U_9919),U_9923),U_9920))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9919,U_9918),U_9921),U_9920) != U_9922
| ? [U_9917] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9918),c_Groups_Ozero__class_Ozero(U_9918)),hAPP(U_9921,U_9917)))
& hBOOL(hAPP(hAPP(c_member(U_9919),U_9917),U_9920)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9919),U_9920))
| ~ class_Groups_Oordered__ab__group__add(U_9918) ),
inference(variable_rename,[status(thm)],[f_2706_1]) ).
fof(f_2706_3,plain,
! [U_9923,U_9922,U_9921,U_9920,U_9919,U_9918] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9918),hAPP(U_9921,U_9923)),U_9922))
| ~ hBOOL(hAPP(hAPP(c_member(U_9919),U_9923),U_9920))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9919,U_9918),U_9921),U_9920) != U_9922
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9918),c_Groups_Ozero__class_Ozero(U_9918)),hAPP(U_9921,sK204(U_9923,U_9922,U_9921,U_9920,U_9919,U_9918))))
& hBOOL(hAPP(hAPP(c_member(U_9919),sK204(U_9923,U_9922,U_9921,U_9920,U_9919,U_9918)),U_9920)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9919),U_9920))
| ~ class_Groups_Oordered__ab__group__add(U_9918) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK204]),skolemize(U_9917,sK204(U_9923,U_9922,U_9921,U_9920,U_9919,U_9918))],[f_2706_2]) ).
cnf(f_2706_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_9919),sK204(U_9923,U_9922,U_9921,U_9920,U_9919,U_9918)),U_9920))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9918),hAPP(U_9921,U_9923)),U_9922))
| ~ hBOOL(hAPP(hAPP(c_member(U_9919),U_9923),U_9920))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9919,U_9918),U_9921),U_9920) != U_9922
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9919),U_9920))
| ~ class_Groups_Oordered__ab__group__add(U_9918) ),
inference(clausify,[status(thm)],[f_2706_3]) ).
cnf(f_2706_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9918),c_Groups_Ozero__class_Ozero(U_9918)),hAPP(U_9921,sK204(U_9923,U_9922,U_9921,U_9920,U_9919,U_9918))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9918),hAPP(U_9921,U_9923)),U_9922))
| ~ hBOOL(hAPP(hAPP(c_member(U_9919),U_9923),U_9920))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9919,U_9918),U_9921),U_9920) != U_9922
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9919),U_9920))
| ~ class_Groups_Oordered__ab__group__add(U_9918) ),
inference(clausify,[status(thm)],[f_2706_3]) ).
fof(f_2707_1,plain,
! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
( hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) != c_Groups_Ozero__class_Ozero(T_c)
| ? [B_i] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
| ~ class_Groups_Oordered__ab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__nonneg__0]) ).
fof(f_2707_2,plain,
! [U_9929,U_9928,U_9927,U_9926,U_9925] :
( hAPP(U_9928,U_9929) = c_Groups_Ozero__class_Ozero(U_9925)
| ~ hBOOL(hAPP(hAPP(c_member(U_9926),U_9929),U_9927))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9926,U_9925),U_9928),U_9927) != c_Groups_Ozero__class_Ozero(U_9925)
| ? [U_9924] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9925),c_Groups_Ozero__class_Ozero(U_9925)),hAPP(U_9928,U_9924)))
& hBOOL(hAPP(hAPP(c_member(U_9926),U_9924),U_9927)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9926),U_9927))
| ~ class_Groups_Oordered__ab__group__add(U_9925) ),
inference(variable_rename,[status(thm)],[f_2707_1]) ).
fof(f_2707_3,plain,
! [U_9929,U_9928,U_9927,U_9926,U_9925] :
( hAPP(U_9928,U_9929) = c_Groups_Ozero__class_Ozero(U_9925)
| ~ hBOOL(hAPP(hAPP(c_member(U_9926),U_9929),U_9927))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9926,U_9925),U_9928),U_9927) != c_Groups_Ozero__class_Ozero(U_9925)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9925),c_Groups_Ozero__class_Ozero(U_9925)),hAPP(U_9928,sK205(U_9929,U_9928,U_9927,U_9926,U_9925))))
& hBOOL(hAPP(hAPP(c_member(U_9926),sK205(U_9929,U_9928,U_9927,U_9926,U_9925)),U_9927)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9926),U_9927))
| ~ class_Groups_Oordered__ab__group__add(U_9925) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK205]),skolemize(U_9924,sK205(U_9929,U_9928,U_9927,U_9926,U_9925))],[f_2707_2]) ).
cnf(f_2707_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_9926),sK205(U_9929,U_9928,U_9927,U_9926,U_9925)),U_9927))
| hAPP(U_9928,U_9929) = c_Groups_Ozero__class_Ozero(U_9925)
| ~ hBOOL(hAPP(hAPP(c_member(U_9926),U_9929),U_9927))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9926,U_9925),U_9928),U_9927) != c_Groups_Ozero__class_Ozero(U_9925)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9926),U_9927))
| ~ class_Groups_Oordered__ab__group__add(U_9925) ),
inference(clausify,[status(thm)],[f_2707_3]) ).
cnf(f_2707_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9925),c_Groups_Ozero__class_Ozero(U_9925)),hAPP(U_9928,sK205(U_9929,U_9928,U_9927,U_9926,U_9925))))
| hAPP(U_9928,U_9929) = c_Groups_Ozero__class_Ozero(U_9925)
| ~ hBOOL(hAPP(hAPP(c_member(U_9926),U_9929),U_9927))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_9926,U_9925),U_9928),U_9927) != c_Groups_Ozero__class_Ozero(U_9925)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9926),U_9927))
| ~ class_Groups_Oordered__ab__group__add(U_9925) ),
inference(clausify,[status(thm)],[f_2707_3]) ).
fof(f_2708_1,plain,
! [V_t_2,V_s_2,V_b_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_pair__lessI2]) ).
fof(f_2708_2,plain,
! [U_9933,U_9932,U_9931,U_9930] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9930),U_9932)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9931),U_9933))),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9932),U_9933))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9930),U_9931)) ),
inference(variable_rename,[status(thm)],[f_2708_1]) ).
cnf(f_2708_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9930),U_9932)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9931),U_9933))),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9932),U_9933))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9930),U_9931)) ),
inference(clausify,[status(thm)],[f_2708_2]) ).
fof(f_2709_1,plain,
! [V_N_2,V_h_2,T_b] :
( hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ohom__commute]) ).
fof(f_2709_2,plain,
! [U_9938,U_9937,U_9936] :
( hAPP(U_9937,c_Big__Operators_Olattice_OSup__fin(U_9936,c_Orderings_Oord__class_Omax(U_9936),U_9938)) = c_Big__Operators_Olattice_OSup__fin(U_9936,c_Orderings_Oord__class_Omax(U_9936),hAPP(c_Set_Oimage(U_9936,U_9936,U_9937),U_9938))
| U_9938 = c_Orderings_Obot__class_Obot(tc_fun(U_9936,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9936),U_9938))
| ? [U_9935,U_9934] : hAPP(U_9937,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9936),U_9935),U_9934)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9936),hAPP(U_9937,U_9935)),hAPP(U_9937,U_9934))
| ~ class_Orderings_Olinorder(U_9936) ),
inference(variable_rename,[status(thm)],[f_2709_1]) ).
fof(f_2709_3,plain,
! [U_9938,U_9937,U_9936] :
( hAPP(U_9937,c_Big__Operators_Olattice_OSup__fin(U_9936,c_Orderings_Oord__class_Omax(U_9936),U_9938)) = c_Big__Operators_Olattice_OSup__fin(U_9936,c_Orderings_Oord__class_Omax(U_9936),hAPP(c_Set_Oimage(U_9936,U_9936,U_9937),U_9938))
| U_9938 = c_Orderings_Obot__class_Obot(tc_fun(U_9936,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9936),U_9938))
| ? [U_9934] : hAPP(U_9937,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9936),sK206(U_9938,U_9937,U_9936)),U_9934)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9936),hAPP(U_9937,sK206(U_9938,U_9937,U_9936))),hAPP(U_9937,U_9934))
| ~ class_Orderings_Olinorder(U_9936) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK206]),skolemize(U_9935,sK206(U_9938,U_9937,U_9936))],[f_2709_2]) ).
fof(f_2709_4,plain,
! [U_9938,U_9937,U_9936] :
( hAPP(U_9937,c_Big__Operators_Olattice_OSup__fin(U_9936,c_Orderings_Oord__class_Omax(U_9936),U_9938)) = c_Big__Operators_Olattice_OSup__fin(U_9936,c_Orderings_Oord__class_Omax(U_9936),hAPP(c_Set_Oimage(U_9936,U_9936,U_9937),U_9938))
| U_9938 = c_Orderings_Obot__class_Obot(tc_fun(U_9936,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9936),U_9938))
| hAPP(U_9937,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9936),sK206(U_9938,U_9937,U_9936)),sK207(U_9938,U_9937,U_9936))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9936),hAPP(U_9937,sK206(U_9938,U_9937,U_9936))),hAPP(U_9937,sK207(U_9938,U_9937,U_9936)))
| ~ class_Orderings_Olinorder(U_9936) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK207]),skolemize(U_9934,sK207(U_9938,U_9937,U_9936))],[f_2709_3]) ).
cnf(f_2709_5,plain,
( hAPP(U_9937,c_Big__Operators_Olattice_OSup__fin(U_9936,c_Orderings_Oord__class_Omax(U_9936),U_9938)) = c_Big__Operators_Olattice_OSup__fin(U_9936,c_Orderings_Oord__class_Omax(U_9936),hAPP(c_Set_Oimage(U_9936,U_9936,U_9937),U_9938))
| U_9938 = c_Orderings_Obot__class_Obot(tc_fun(U_9936,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9936),U_9938))
| hAPP(U_9937,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9936),sK206(U_9938,U_9937,U_9936)),sK207(U_9938,U_9937,U_9936))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9936),hAPP(U_9937,sK206(U_9938,U_9937,U_9936))),hAPP(U_9937,sK207(U_9938,U_9937,U_9936)))
| ~ class_Orderings_Olinorder(U_9936) ),
inference(clausify,[status(thm)],[f_2709_4]) ).
fof(f_2710_1,plain,
! [V_t_2,V_s_2,V_b_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_pair__lessI1]) ).
fof(f_2710_2,plain,
! [U_9942,U_9941,U_9940,U_9939] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9939),U_9941)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9940),U_9942))),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9939),U_9940)) ),
inference(variable_rename,[status(thm)],[f_2710_1]) ).
cnf(f_2710_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9939),U_9941)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9940),U_9942))),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9939),U_9940)) ),
inference(clausify,[status(thm)],[f_2710_2]) ).
fof(f_2711_1,plain,
! [V_t_2,V_s_2,V_b_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_pair__leqI2]) ).
fof(f_2711_2,plain,
! [U_9946,U_9945,U_9944,U_9943] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9943),U_9945)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9944),U_9946))),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9945),U_9946))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9943),U_9944)) ),
inference(variable_rename,[status(thm)],[f_2711_1]) ).
cnf(f_2711_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9943),U_9945)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9944),U_9946))),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9945),U_9946))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9943),U_9944)) ),
inference(clausify,[status(thm)],[f_2711_2]) ).
fof(f_2712_1,plain,
! [V_X_2,V_x_2,V_Y_2,V_y_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_X_2)),V_Y_2)),c_FunDef_Omax__strict))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),V_Y_2)),c_FunDef_Omax__strict))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) ),
inference(fof_nnf,[status(thm)],[fact_smax__insertI]) ).
fof(f_2712_2,plain,
! [U_9950,U_9949,U_9948,U_9947] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9949),U_9950)),U_9948)),c_FunDef_Omax__strict))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_9950),U_9948)),c_FunDef_Omax__strict))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9949),U_9947)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9947),U_9948)) ),
inference(variable_rename,[status(thm)],[f_2712_1]) ).
cnf(f_2712_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9949),U_9950)),U_9948)),c_FunDef_Omax__strict))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_9950),U_9948)),c_FunDef_Omax__strict))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9949),U_9947)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9947),U_9948)) ),
inference(clausify,[status(thm)],[f_2712_2]) ).
fof(f_2713_1,plain,
! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__strict))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__strict))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) ),
inference(fof_nnf,[status(thm)],[fact_smin__insertI]) ).
fof(f_2713_2,plain,
! [U_9954,U_9953,U_9952,U_9951] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_9952),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9953),U_9954))),c_FunDef_Omin__strict))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_9952),U_9954)),c_FunDef_Omin__strict))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9951),U_9953)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9951),U_9952)) ),
inference(variable_rename,[status(thm)],[f_2713_1]) ).
cnf(f_2713_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_9952),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9953),U_9954))),c_FunDef_Omin__strict))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_9952),U_9954)),c_FunDef_Omin__strict))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9951),U_9953)),c_FunDef_Opair__less))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9951),U_9952)) ),
inference(clausify,[status(thm)],[f_2713_2]) ).
fof(f_2714_1,plain,
! [V_t_2,V_s_2,V_b_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_a_2),V_s_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_b_2),V_t_2))),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_pair__leqI1]) ).
fof(f_2714_2,plain,
! [U_9958,U_9957,U_9956,U_9955] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9955),U_9957)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9956),U_9958))),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9955),U_9956)) ),
inference(variable_rename,[status(thm)],[f_2714_1]) ).
cnf(f_2714_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9955),U_9957)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9956),U_9958))),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9955),U_9956)) ),
inference(clausify,[status(thm)],[f_2714_2]) ).
fof(f_2715_1,plain,
! [V_Y_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_Y_2)),c_FunDef_Omax__strict))
| V_Y_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) ),
inference(fof_nnf,[status(thm)],[fact_smax__emptyI]) ).
fof(f_2715_2,plain,
! [U_9959] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),U_9959)),c_FunDef_Omax__strict))
| U_9959 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9959)) ),
inference(variable_rename,[status(thm)],[f_2715_1]) ).
cnf(f_2715_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),U_9959)),c_FunDef_Omax__strict))
| U_9959 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9959)) ),
inference(clausify,[status(thm)],[f_2715_2]) ).
fof(f_2716_1,plain,
! [V_X_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
| V_X_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_smin__emptyI]) ).
fof(f_2716_2,plain,
! [U_9960] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_9960),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
| U_9960 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_2716_1]) ).
cnf(f_2716_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_9960),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
| U_9960 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2716_2]) ).
fof(f_2717_1,plain,
! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))),c_FunDef_Omin__weak))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omin__weak))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) ),
inference(fof_nnf,[status(thm)],[fact_wmin__insertI]) ).
fof(f_2717_2,plain,
! [U_9964,U_9963,U_9962,U_9961] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_9962),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9963),U_9964))),c_FunDef_Omin__weak))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_9962),U_9964)),c_FunDef_Omin__weak))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9961),U_9963)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9961),U_9962)) ),
inference(variable_rename,[status(thm)],[f_2717_1]) ).
cnf(f_2717_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_9962),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9963),U_9964))),c_FunDef_Omin__weak))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_9962),U_9964)),c_FunDef_Omin__weak))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9961),U_9963)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9961),U_9962)) ),
inference(clausify,[status(thm)],[f_2717_2]) ).
fof(f_2718_1,plain,
! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)),V_YS_2)),c_FunDef_Omax__weak))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_XS_2),V_YS_2)),c_FunDef_Omax__weak))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) ),
inference(fof_nnf,[status(thm)],[fact_wmax__insertI]) ).
fof(f_2718_2,plain,
! [U_9968,U_9967,U_9966,U_9965] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9967),U_9968)),U_9966)),c_FunDef_Omax__weak))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_9968),U_9966)),c_FunDef_Omax__weak))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9967),U_9965)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9965),U_9966)) ),
inference(variable_rename,[status(thm)],[f_2718_1]) ).
cnf(f_2718_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9967),U_9968)),U_9966)),c_FunDef_Omax__weak))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_9968),U_9966)),c_FunDef_Omax__weak))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9967),U_9965)),c_FunDef_Opair__leq))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9965),U_9966)) ),
inference(clausify,[status(thm)],[f_2718_2]) ).
fof(f_2719_1,plain,
! [V_f_2,V_A_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),V_f_2),V_A_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2))
| ? [B_x] :
( ~ c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod2_I2_J]) ).
fof(f_2719_2,plain,
! [U_9972,U_9971,U_9970] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9970,tc_Int_Oint),U_9972),U_9971) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9970,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_9970),c_Int_Onat),U_9972)),U_9971))
| ? [U_9969] :
( ~ c_Nat__Transfer_Ois__nat(hAPP(U_9972,U_9969))
& hBOOL(hAPP(hAPP(c_member(U_9970),U_9969),U_9971)) ) ),
inference(variable_rename,[status(thm)],[f_2719_1]) ).
fof(f_2719_3,plain,
! [U_9972,U_9971,U_9970] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9970,tc_Int_Oint),U_9972),U_9971) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9970,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_9970),c_Int_Onat),U_9972)),U_9971))
| ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_9972,sK208(U_9972,U_9971,U_9970)))
& hBOOL(hAPP(hAPP(c_member(U_9970),sK208(U_9972,U_9971,U_9970)),U_9971)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK208]),skolemize(U_9969,sK208(U_9972,U_9971,U_9970))],[f_2719_2]) ).
cnf(f_2719_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_9970),sK208(U_9972,U_9971,U_9970)),U_9971))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9970,tc_Int_Oint),U_9972),U_9971) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9970,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_9970),c_Int_Onat),U_9972)),U_9971)) ),
inference(clausify,[status(thm)],[f_2719_3]) ).
cnf(f_2719_5,plain,
( ~ c_Nat__Transfer_Ois__nat(hAPP(U_9972,sK208(U_9972,U_9971,U_9970)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9970,tc_Int_Oint),U_9972),U_9971) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_9970,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_9970),c_Int_Onat),U_9972)),U_9971)) ),
inference(clausify,[status(thm)],[f_2719_3]) ).
fof(f_2720_1,plain,
! [V_X_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),V_X_2)),c_FunDef_Omax__weak))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) ),
inference(fof_nnf,[status(thm)],[fact_wmax__emptyI]) ).
fof(f_2720_2,plain,
! [U_9973] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),U_9973)),c_FunDef_Omax__weak))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9973)) ),
inference(variable_rename,[status(thm)],[f_2720_1]) ).
cnf(f_2720_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),U_9973)),c_FunDef_Omax__weak))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9973)) ),
inference(clausify,[status(thm)],[f_2720_2]) ).
fof(f_2721_1,plain,
! [V_X_2] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_X_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
inference(fof_nnf,[status(thm)],[fact_wmin__emptyI]) ).
fof(f_2721_2,plain,
! [U_9974] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_9974),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
inference(variable_rename,[status(thm)],[f_2721_1]) ).
cnf(f_2721_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_9974),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__weak)),
inference(clausify,[status(thm)],[f_2721_2]) ).
fof(f_2722_1,plain,
c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_min__weak__def]) ).
cnf(f_2722_2,plain,
c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_2722_1]) ).
fof(f_2723_1,plain,
c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_max__weak__def]) ).
cnf(f_2723_2,plain,
c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_2723_1]) ).
fof(f_2724_1,plain,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)),
inference(fof_nnf,[status(thm)],[fact_min__rpair__set]) ).
cnf(f_2724_2,plain,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)),
inference(clausify,[status(thm)],[f_2724_1]) ).
fof(f_2725_1,plain,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
inference(fof_nnf,[status(thm)],[fact_max__rpair__set]) ).
cnf(f_2725_2,plain,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
inference(clausify,[status(thm)],[f_2725_1]) ).
fof(f_2726_1,plain,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(fof_nnf,[status(thm)],[fact_max__strict__def]) ).
cnf(f_2726_2,plain,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(clausify,[status(thm)],[f_2726_1]) ).
fof(f_2727_1,plain,
! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_b,V_R_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_max__ext__additive]) ).
fof(f_2727_2,plain,
! [U_9980,U_9979,U_9978,U_9977,U_9976,U_9975] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9975,tc_HOL_Obool),tc_fun(U_9975,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9975,tc_HOL_Obool),tc_fun(U_9975,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9975,tc_HOL_Obool)),U_9976),U_9979)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9975,tc_HOL_Obool)),U_9977),U_9980))),c_Wellfounded_Omax__ext(U_9975,U_9978)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9975,tc_HOL_Obool),tc_fun(U_9975,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9975,tc_HOL_Obool),tc_fun(U_9975,tc_HOL_Obool)),U_9979),U_9980)),c_Wellfounded_Omax__ext(U_9975,U_9978)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9975,tc_HOL_Obool),tc_fun(U_9975,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9975,tc_HOL_Obool),tc_fun(U_9975,tc_HOL_Obool)),U_9976),U_9977)),c_Wellfounded_Omax__ext(U_9975,U_9978))) ),
inference(variable_rename,[status(thm)],[f_2727_1]) ).
cnf(f_2727_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9975,tc_HOL_Obool),tc_fun(U_9975,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9975,tc_HOL_Obool),tc_fun(U_9975,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9975,tc_HOL_Obool)),U_9976),U_9979)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9975,tc_HOL_Obool)),U_9977),U_9980))),c_Wellfounded_Omax__ext(U_9975,U_9978)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9975,tc_HOL_Obool),tc_fun(U_9975,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9975,tc_HOL_Obool),tc_fun(U_9975,tc_HOL_Obool)),U_9979),U_9980)),c_Wellfounded_Omax__ext(U_9975,U_9978)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9975,tc_HOL_Obool),tc_fun(U_9975,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9975,tc_HOL_Obool),tc_fun(U_9975,tc_HOL_Obool)),U_9976),U_9977)),c_Wellfounded_Omax__ext(U_9975,U_9978))) ),
inference(clausify,[status(thm)],[f_2727_2]) ).
fof(f_2728_1,plain,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(fof_nnf,[status(thm)],[fact_min__strict__def]) ).
cnf(f_2728_2,plain,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(clausify,[status(thm)],[f_2728_1]) ).
fof(f_2729_1,plain,
! [V_xa_2,V_x_2,V_R_2,T_b] :
( ( c_Wellfounded_Omax__extp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_R_2),V_x_2,V_xa_2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
| ~ c_Wellfounded_Omax__extp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_R_2),V_x_2,V_xa_2) ) ),
inference(fof_nnf,[status(thm)],[fact_max__extp__max__ext__eq]) ).
fof(f_2729_2,plain,
! [U_9984,U_9983,U_9982,U_9981] :
( ( c_Wellfounded_Omax__extp(U_9981,hAPP(hAPP(c_COMBC(U_9981,tc_fun(tc_prod(U_9981,U_9981),tc_HOL_Obool),tc_fun(U_9981,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9981,tc_fun(tc_fun(tc_prod(U_9981,U_9981),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9981,U_9981),tc_HOL_Obool),tc_fun(U_9981,tc_HOL_Obool)),U_9981),c_COMBC(U_9981,tc_fun(tc_prod(U_9981,U_9981),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9981,tc_prod(U_9981,U_9981)),tc_fun(U_9981,tc_fun(tc_fun(tc_prod(U_9981,U_9981),tc_HOL_Obool),tc_HOL_Obool)),U_9981),hAPP(c_COMBB(tc_prod(U_9981,U_9981),tc_fun(tc_fun(tc_prod(U_9981,U_9981),tc_HOL_Obool),tc_HOL_Obool),U_9981),c_member(tc_prod(U_9981,U_9981)))),c_Product__Type_OPair(U_9981,U_9981)))),U_9982),U_9983,U_9984)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9981,tc_HOL_Obool),tc_fun(U_9981,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9981,tc_HOL_Obool),tc_fun(U_9981,tc_HOL_Obool)),U_9983),U_9984)),c_Wellfounded_Omax__ext(U_9981,U_9982))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9981,tc_HOL_Obool),tc_fun(U_9981,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9981,tc_HOL_Obool),tc_fun(U_9981,tc_HOL_Obool)),U_9983),U_9984)),c_Wellfounded_Omax__ext(U_9981,U_9982)))
| ~ c_Wellfounded_Omax__extp(U_9981,hAPP(hAPP(c_COMBC(U_9981,tc_fun(tc_prod(U_9981,U_9981),tc_HOL_Obool),tc_fun(U_9981,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9981,tc_fun(tc_fun(tc_prod(U_9981,U_9981),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9981,U_9981),tc_HOL_Obool),tc_fun(U_9981,tc_HOL_Obool)),U_9981),c_COMBC(U_9981,tc_fun(tc_prod(U_9981,U_9981),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9981,tc_prod(U_9981,U_9981)),tc_fun(U_9981,tc_fun(tc_fun(tc_prod(U_9981,U_9981),tc_HOL_Obool),tc_HOL_Obool)),U_9981),hAPP(c_COMBB(tc_prod(U_9981,U_9981),tc_fun(tc_fun(tc_prod(U_9981,U_9981),tc_HOL_Obool),tc_HOL_Obool),U_9981),c_member(tc_prod(U_9981,U_9981)))),c_Product__Type_OPair(U_9981,U_9981)))),U_9982),U_9983,U_9984) ) ),
inference(variable_rename,[status(thm)],[f_2729_1]) ).
fof(f_2729_3,plain,
( ! [U_9992,U_9990,U_9988,U_9986] :
( c_Wellfounded_Omax__extp(U_9986,hAPP(hAPP(c_COMBC(U_9986,tc_fun(tc_prod(U_9986,U_9986),tc_HOL_Obool),tc_fun(U_9986,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9986,tc_fun(tc_fun(tc_prod(U_9986,U_9986),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9986,U_9986),tc_HOL_Obool),tc_fun(U_9986,tc_HOL_Obool)),U_9986),c_COMBC(U_9986,tc_fun(tc_prod(U_9986,U_9986),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9986,tc_prod(U_9986,U_9986)),tc_fun(U_9986,tc_fun(tc_fun(tc_prod(U_9986,U_9986),tc_HOL_Obool),tc_HOL_Obool)),U_9986),hAPP(c_COMBB(tc_prod(U_9986,U_9986),tc_fun(tc_fun(tc_prod(U_9986,U_9986),tc_HOL_Obool),tc_HOL_Obool),U_9986),c_member(tc_prod(U_9986,U_9986)))),c_Product__Type_OPair(U_9986,U_9986)))),U_9988),U_9990,U_9992)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9986,tc_HOL_Obool),tc_fun(U_9986,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9986,tc_HOL_Obool),tc_fun(U_9986,tc_HOL_Obool)),U_9990),U_9992)),c_Wellfounded_Omax__ext(U_9986,U_9988))) )
& ! [U_9991,U_9989,U_9987,U_9985] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9985,tc_HOL_Obool),tc_fun(U_9985,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9985,tc_HOL_Obool),tc_fun(U_9985,tc_HOL_Obool)),U_9989),U_9991)),c_Wellfounded_Omax__ext(U_9985,U_9987)))
| ~ c_Wellfounded_Omax__extp(U_9985,hAPP(hAPP(c_COMBC(U_9985,tc_fun(tc_prod(U_9985,U_9985),tc_HOL_Obool),tc_fun(U_9985,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9985,tc_fun(tc_fun(tc_prod(U_9985,U_9985),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9985,U_9985),tc_HOL_Obool),tc_fun(U_9985,tc_HOL_Obool)),U_9985),c_COMBC(U_9985,tc_fun(tc_prod(U_9985,U_9985),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9985,tc_prod(U_9985,U_9985)),tc_fun(U_9985,tc_fun(tc_fun(tc_prod(U_9985,U_9985),tc_HOL_Obool),tc_HOL_Obool)),U_9985),hAPP(c_COMBB(tc_prod(U_9985,U_9985),tc_fun(tc_fun(tc_prod(U_9985,U_9985),tc_HOL_Obool),tc_HOL_Obool),U_9985),c_member(tc_prod(U_9985,U_9985)))),c_Product__Type_OPair(U_9985,U_9985)))),U_9987),U_9989,U_9991) ) ),
inference(miniscope,[status(thm)],[f_2729_2]) ).
cnf(f_2729_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9985,tc_HOL_Obool),tc_fun(U_9985,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9985,tc_HOL_Obool),tc_fun(U_9985,tc_HOL_Obool)),U_9989),U_9991)),c_Wellfounded_Omax__ext(U_9985,U_9987)))
| ~ c_Wellfounded_Omax__extp(U_9985,hAPP(hAPP(c_COMBC(U_9985,tc_fun(tc_prod(U_9985,U_9985),tc_HOL_Obool),tc_fun(U_9985,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9985,tc_fun(tc_fun(tc_prod(U_9985,U_9985),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9985,U_9985),tc_HOL_Obool),tc_fun(U_9985,tc_HOL_Obool)),U_9985),c_COMBC(U_9985,tc_fun(tc_prod(U_9985,U_9985),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9985,tc_prod(U_9985,U_9985)),tc_fun(U_9985,tc_fun(tc_fun(tc_prod(U_9985,U_9985),tc_HOL_Obool),tc_HOL_Obool)),U_9985),hAPP(c_COMBB(tc_prod(U_9985,U_9985),tc_fun(tc_fun(tc_prod(U_9985,U_9985),tc_HOL_Obool),tc_HOL_Obool),U_9985),c_member(tc_prod(U_9985,U_9985)))),c_Product__Type_OPair(U_9985,U_9985)))),U_9987),U_9989,U_9991) ),
inference(clausify,[status(thm)],[f_2729_3]) ).
cnf(f_2729_5,plain,
( c_Wellfounded_Omax__extp(U_9986,hAPP(hAPP(c_COMBC(U_9986,tc_fun(tc_prod(U_9986,U_9986),tc_HOL_Obool),tc_fun(U_9986,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9986,tc_fun(tc_fun(tc_prod(U_9986,U_9986),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9986,U_9986),tc_HOL_Obool),tc_fun(U_9986,tc_HOL_Obool)),U_9986),c_COMBC(U_9986,tc_fun(tc_prod(U_9986,U_9986),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9986,tc_prod(U_9986,U_9986)),tc_fun(U_9986,tc_fun(tc_fun(tc_prod(U_9986,U_9986),tc_HOL_Obool),tc_HOL_Obool)),U_9986),hAPP(c_COMBB(tc_prod(U_9986,U_9986),tc_fun(tc_fun(tc_prod(U_9986,U_9986),tc_HOL_Obool),tc_HOL_Obool),U_9986),c_member(tc_prod(U_9986,U_9986)))),c_Product__Type_OPair(U_9986,U_9986)))),U_9988),U_9990,U_9992)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9986,tc_HOL_Obool),tc_fun(U_9986,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9986,tc_HOL_Obool),tc_fun(U_9986,tc_HOL_Obool)),U_9990),U_9992)),c_Wellfounded_Omax__ext(U_9986,U_9988))) ),
inference(clausify,[status(thm)],[f_2729_3]) ).
fof(f_2730_1,plain,
! [V_y_2,V_x_2] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Wellfounded_Oless__than)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__than__iff]) ).
fof(f_2730_2,plain,
! [U_9994,U_9993] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9993),U_9994)),c_Wellfounded_Oless__than))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9993),U_9994)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9993),U_9994))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9993),U_9994)),c_Wellfounded_Oless__than)) ) ),
inference(variable_rename,[status(thm)],[f_2730_1]) ).
fof(f_2730_3,plain,
( ! [U_9998,U_9996] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9996),U_9998)),c_Wellfounded_Oless__than))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9996),U_9998)) )
& ! [U_9997,U_9995] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9995),U_9997))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9995),U_9997)),c_Wellfounded_Oless__than)) ) ),
inference(miniscope,[status(thm)],[f_2730_2]) ).
cnf(f_2730_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9995),U_9997))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9995),U_9997)),c_Wellfounded_Oless__than)) ),
inference(clausify,[status(thm)],[f_2730_3]) ).
cnf(f_2730_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9996),U_9998)),c_Wellfounded_Oless__than))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9996),U_9998)) ),
inference(clausify,[status(thm)],[f_2730_3]) ).
fof(f_2731_1,plain,
! [V_v_2,V_u_2,V_y_2,V_x_2] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2))),c_Int_Ointrel))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2))),c_Int_Ointrel)) ) ),
inference(fof_nnf,[status(thm)],[fact_intrel__iff]) ).
fof(f_2731_2,plain,
! [U_10002,U_10001,U_10000,U_9999] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9999),U_10000)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10001),U_10002))),c_Int_Ointrel))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9999),U_10002) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10001),U_10000) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_9999),U_10002) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10001),U_10000)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_9999),U_10000)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10001),U_10002))),c_Int_Ointrel)) ) ),
inference(variable_rename,[status(thm)],[f_2731_1]) ).
fof(f_2731_3,plain,
( ! [U_10010,U_10008,U_10006,U_10004] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10004),U_10006)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10008),U_10010))),c_Int_Ointrel))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10004),U_10010) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10008),U_10006) )
& ! [U_10009,U_10007,U_10005,U_10003] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10003),U_10009) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10007),U_10005)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10003),U_10005)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10007),U_10009))),c_Int_Ointrel)) ) ),
inference(miniscope,[status(thm)],[f_2731_2]) ).
cnf(f_2731_4,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10003),U_10009) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10007),U_10005)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10003),U_10005)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10007),U_10009))),c_Int_Ointrel)) ),
inference(clausify,[status(thm)],[f_2731_3]) ).
cnf(f_2731_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10004),U_10006)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10008),U_10010))),c_Int_Ointrel))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10004),U_10010) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10008),U_10006) ),
inference(clausify,[status(thm)],[f_2731_3]) ).
fof(f_2732_1,plain,
! [V_f_2,T_c,V_P_2,T_b] :
( c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_P_2),V_f_2))
| ~ c_FunDef_Oreduction__pair(T_b,V_P_2) ),
inference(fof_nnf,[status(thm)],[fact_rp__inv__image__rp]) ).
fof(f_2732_2,plain,
! [U_10014,U_10013,U_10012,U_10011] :
( c_FunDef_Oreduction__pair(U_10013,hAPP(hAPP(c_FunDef_Orp__inv__image(U_10011,U_10013),U_10012),U_10014))
| ~ c_FunDef_Oreduction__pair(U_10011,U_10012) ),
inference(variable_rename,[status(thm)],[f_2732_1]) ).
cnf(f_2732_3,plain,
( c_FunDef_Oreduction__pair(U_10013,hAPP(hAPP(c_FunDef_Orp__inv__image(U_10011,U_10013),U_10012),U_10014))
| ~ c_FunDef_Oreduction__pair(U_10011,U_10012) ),
inference(clausify,[status(thm)],[f_2732_2]) ).
fof(f_2733_1,plain,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
inference(fof_nnf,[status(thm)],[fact_pair__less__def]) ).
cnf(f_2733_2,plain,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
inference(clausify,[status(thm)],[f_2733_1]) ).
fof(f_2734_1,plain,
! [V_R_2,V_f_2,T_b] : c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_b),T_b),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_b,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(tc_Nat_Onat,T_b)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_prod(tc_Nat_Onat,T_b)),T_b),c_Product__Type_OPair(tc_Nat_Onat,T_b)),V_f_2)),c_COMBI(T_b))),
inference(fof_nnf,[status(thm)],[fact_mlex__prod__def]) ).
fof(f_2734_2,plain,
! [U_10017,U_10016,U_10015] : c_Wellfounded_Omlex__prod(U_10015,U_10016,U_10017) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_10015),U_10015),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_10015,c_Wellfounded_Oless__than,U_10017)),hAPP(hAPP(c_COMBS(U_10015,U_10015,tc_prod(tc_Nat_Onat,U_10015)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10015,tc_prod(tc_Nat_Onat,U_10015)),U_10015),c_Product__Type_OPair(tc_Nat_Onat,U_10015)),U_10016)),c_COMBI(U_10015))),
inference(variable_rename,[status(thm)],[f_2734_1]) ).
cnf(f_2734_3,plain,
c_Wellfounded_Omlex__prod(U_10015,U_10016,U_10017) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_10015),U_10015),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_10015,c_Wellfounded_Oless__than,U_10017)),hAPP(hAPP(c_COMBS(U_10015,U_10015,tc_prod(tc_Nat_Onat,U_10015)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_10015,tc_prod(tc_Nat_Onat,U_10015)),U_10015),c_Product__Type_OPair(tc_Nat_Onat,U_10015)),U_10016)),c_COMBI(U_10015))),
inference(clausify,[status(thm)],[f_2734_2]) ).
fof(f_2735_1,plain,
! [T_c,T_b] : c_FunDef_Orp__inv__image(T_b,T_c) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBS(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(T_c,T_b)),c_Product__Type_OPair(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),c_Relation_Oinv__image(T_b,T_c))))),c_Relation_Oinv__image(T_b,T_c))),
inference(fof_nnf,[status(thm)],[fact_rp__inv__image__def]) ).
fof(f_2735_2,plain,
! [U_10019,U_10018] : c_FunDef_Orp__inv__image(U_10018,U_10019) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool),tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool),tc_fun(tc_fun(U_10019,U_10018),tc_prod(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool),tc_fun(tc_fun(U_10019,U_10018),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool),tc_fun(tc_fun(U_10019,U_10018),tc_prod(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_10019,U_10018),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)),tc_fun(tc_fun(U_10019,U_10018),tc_prod(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool),tc_fun(tc_fun(U_10019,U_10018),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool),tc_fun(tc_fun(U_10019,U_10018),tc_prod(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool))))),tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_10019,U_10018),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)),tc_fun(tc_fun(U_10019,U_10018),tc_prod(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool))),tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10019,U_10018),tc_fun(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_10019,U_10018),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)),tc_fun(tc_fun(U_10019,U_10018),tc_prod(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)))),tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool)),c_COMBS(tc_fun(U_10019,U_10018),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10019,U_10018),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)),tc_fun(tc_fun(U_10019,U_10018),tc_fun(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)))),tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool))),tc_fun(U_10019,U_10018)),c_Product__Type_OPair(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)))),c_Relation_Oinv__image(U_10018,U_10019))))),c_Relation_Oinv__image(U_10018,U_10019))),
inference(variable_rename,[status(thm)],[f_2735_1]) ).
cnf(f_2735_3,plain,
c_FunDef_Orp__inv__image(U_10018,U_10019) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool),tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool),tc_fun(tc_fun(U_10019,U_10018),tc_prod(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool),tc_fun(tc_fun(U_10019,U_10018),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool),tc_fun(tc_fun(U_10019,U_10018),tc_prod(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_10019,U_10018),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)),tc_fun(tc_fun(U_10019,U_10018),tc_prod(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool),tc_fun(tc_fun(U_10019,U_10018),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool),tc_fun(tc_fun(U_10019,U_10018),tc_prod(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool))))),tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_10019,U_10018),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)),tc_fun(tc_fun(U_10019,U_10018),tc_prod(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool))),tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10019,U_10018),tc_fun(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_10019,U_10018),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)),tc_fun(tc_fun(U_10019,U_10018),tc_prod(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)))),tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool)),c_COMBS(tc_fun(U_10019,U_10018),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10019,U_10018),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)),tc_fun(tc_fun(U_10019,U_10018),tc_fun(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)))),tc_fun(tc_prod(U_10018,U_10018),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool))),tc_fun(U_10019,U_10018)),c_Product__Type_OPair(tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool),tc_fun(tc_prod(U_10019,U_10019),tc_HOL_Obool)))),c_Relation_Oinv__image(U_10018,U_10019))))),c_Relation_Oinv__image(U_10018,U_10019))),
inference(clausify,[status(thm)],[f_2735_2]) ).
fof(f_2736_1,plain,
! [V_N_2,V_h_2,T_b] :
( hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ohom__commute]) ).
fof(f_2736_2,plain,
! [U_10024,U_10023,U_10022] :
( hAPP(U_10023,c_Big__Operators_Olattice_OInf__fin(U_10022,c_Orderings_Oord__class_Omin(U_10022),U_10024)) = c_Big__Operators_Olattice_OInf__fin(U_10022,c_Orderings_Oord__class_Omin(U_10022),hAPP(c_Set_Oimage(U_10022,U_10022,U_10023),U_10024))
| U_10024 = c_Orderings_Obot__class_Obot(tc_fun(U_10022,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10022),U_10024))
| ? [U_10021,U_10020] : hAPP(U_10023,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10022),U_10021),U_10020)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10022),hAPP(U_10023,U_10021)),hAPP(U_10023,U_10020))
| ~ class_Orderings_Olinorder(U_10022) ),
inference(variable_rename,[status(thm)],[f_2736_1]) ).
fof(f_2736_3,plain,
! [U_10024,U_10023,U_10022] :
( hAPP(U_10023,c_Big__Operators_Olattice_OInf__fin(U_10022,c_Orderings_Oord__class_Omin(U_10022),U_10024)) = c_Big__Operators_Olattice_OInf__fin(U_10022,c_Orderings_Oord__class_Omin(U_10022),hAPP(c_Set_Oimage(U_10022,U_10022,U_10023),U_10024))
| U_10024 = c_Orderings_Obot__class_Obot(tc_fun(U_10022,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10022),U_10024))
| ? [U_10020] : hAPP(U_10023,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10022),sK209(U_10024,U_10023,U_10022)),U_10020)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10022),hAPP(U_10023,sK209(U_10024,U_10023,U_10022))),hAPP(U_10023,U_10020))
| ~ class_Orderings_Olinorder(U_10022) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK209]),skolemize(U_10021,sK209(U_10024,U_10023,U_10022))],[f_2736_2]) ).
fof(f_2736_4,plain,
! [U_10024,U_10023,U_10022] :
( hAPP(U_10023,c_Big__Operators_Olattice_OInf__fin(U_10022,c_Orderings_Oord__class_Omin(U_10022),U_10024)) = c_Big__Operators_Olattice_OInf__fin(U_10022,c_Orderings_Oord__class_Omin(U_10022),hAPP(c_Set_Oimage(U_10022,U_10022,U_10023),U_10024))
| U_10024 = c_Orderings_Obot__class_Obot(tc_fun(U_10022,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10022),U_10024))
| hAPP(U_10023,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10022),sK209(U_10024,U_10023,U_10022)),sK210(U_10024,U_10023,U_10022))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10022),hAPP(U_10023,sK209(U_10024,U_10023,U_10022))),hAPP(U_10023,sK210(U_10024,U_10023,U_10022)))
| ~ class_Orderings_Olinorder(U_10022) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK210]),skolemize(U_10020,sK210(U_10024,U_10023,U_10022))],[f_2736_3]) ).
cnf(f_2736_5,plain,
( hAPP(U_10023,c_Big__Operators_Olattice_OInf__fin(U_10022,c_Orderings_Oord__class_Omin(U_10022),U_10024)) = c_Big__Operators_Olattice_OInf__fin(U_10022,c_Orderings_Oord__class_Omin(U_10022),hAPP(c_Set_Oimage(U_10022,U_10022,U_10023),U_10024))
| U_10024 = c_Orderings_Obot__class_Obot(tc_fun(U_10022,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10022),U_10024))
| hAPP(U_10023,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10022),sK209(U_10024,U_10023,U_10022)),sK210(U_10024,U_10023,U_10022))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10022),hAPP(U_10023,sK209(U_10024,U_10023,U_10022))),hAPP(U_10023,sK210(U_10024,U_10023,U_10022)))
| ~ class_Orderings_Olinorder(U_10022) ),
inference(clausify,[status(thm)],[f_2736_4]) ).
fof(f_2737_1,plain,
! [V_N_2,V_h_2,T_b] :
( hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Ohom__commute]) ).
fof(f_2737_2,plain,
! [U_10029,U_10028,U_10027] :
( hAPP(U_10028,c_Big__Operators_Olinorder__class_OMax(U_10027,U_10029)) = c_Big__Operators_Olinorder__class_OMax(U_10027,hAPP(c_Set_Oimage(U_10027,U_10027,U_10028),U_10029))
| U_10029 = c_Orderings_Obot__class_Obot(tc_fun(U_10027,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10027),U_10029))
| ? [U_10026,U_10025] : hAPP(U_10028,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10027),U_10026),U_10025)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10027),hAPP(U_10028,U_10026)),hAPP(U_10028,U_10025))
| ~ class_Orderings_Olinorder(U_10027) ),
inference(variable_rename,[status(thm)],[f_2737_1]) ).
fof(f_2737_3,plain,
! [U_10029,U_10028,U_10027] :
( hAPP(U_10028,c_Big__Operators_Olinorder__class_OMax(U_10027,U_10029)) = c_Big__Operators_Olinorder__class_OMax(U_10027,hAPP(c_Set_Oimage(U_10027,U_10027,U_10028),U_10029))
| U_10029 = c_Orderings_Obot__class_Obot(tc_fun(U_10027,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10027),U_10029))
| ? [U_10025] : hAPP(U_10028,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10027),sK211(U_10029,U_10028,U_10027)),U_10025)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10027),hAPP(U_10028,sK211(U_10029,U_10028,U_10027))),hAPP(U_10028,U_10025))
| ~ class_Orderings_Olinorder(U_10027) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK211]),skolemize(U_10026,sK211(U_10029,U_10028,U_10027))],[f_2737_2]) ).
fof(f_2737_4,plain,
! [U_10029,U_10028,U_10027] :
( hAPP(U_10028,c_Big__Operators_Olinorder__class_OMax(U_10027,U_10029)) = c_Big__Operators_Olinorder__class_OMax(U_10027,hAPP(c_Set_Oimage(U_10027,U_10027,U_10028),U_10029))
| U_10029 = c_Orderings_Obot__class_Obot(tc_fun(U_10027,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10027),U_10029))
| hAPP(U_10028,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10027),sK211(U_10029,U_10028,U_10027)),sK212(U_10029,U_10028,U_10027))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10027),hAPP(U_10028,sK211(U_10029,U_10028,U_10027))),hAPP(U_10028,sK212(U_10029,U_10028,U_10027)))
| ~ class_Orderings_Olinorder(U_10027) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK212]),skolemize(U_10025,sK212(U_10029,U_10028,U_10027))],[f_2737_3]) ).
cnf(f_2737_5,plain,
( hAPP(U_10028,c_Big__Operators_Olinorder__class_OMax(U_10027,U_10029)) = c_Big__Operators_Olinorder__class_OMax(U_10027,hAPP(c_Set_Oimage(U_10027,U_10027,U_10028),U_10029))
| U_10029 = c_Orderings_Obot__class_Obot(tc_fun(U_10027,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10027),U_10029))
| hAPP(U_10028,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10027),sK211(U_10029,U_10028,U_10027)),sK212(U_10029,U_10028,U_10027))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10027),hAPP(U_10028,sK211(U_10029,U_10028,U_10027))),hAPP(U_10028,sK212(U_10029,U_10028,U_10027)))
| ~ class_Orderings_Olinorder(U_10027) ),
inference(clausify,[status(thm)],[f_2737_4]) ).
fof(f_2738_1,plain,
! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than),
inference(fof_nnf,[status(thm)],[fact_measure__def]) ).
fof(f_2738_2,plain,
! [U_10030] : c_Wellfounded_Omeasure(U_10030) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_10030),c_Wellfounded_Oless__than),
inference(variable_rename,[status(thm)],[f_2738_1]) ).
cnf(f_2738_3,plain,
c_Wellfounded_Omeasure(U_10030) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_10030),c_Wellfounded_Oless__than),
inference(clausify,[status(thm)],[f_2738_2]) ).
fof(f_2739_1,plain,
! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_in__inv__image]) ).
fof(f_2739_2,plain,
! [U_10036,U_10035,U_10034,U_10033,U_10032,U_10031] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10031,U_10031)),hAPP(hAPP(c_Product__Type_OPair(U_10031,U_10031),U_10032),U_10033)),hAPP(hAPP(c_Relation_Oinv__image(U_10034,U_10031),U_10035),U_10036)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10034,U_10034)),hAPP(hAPP(c_Product__Type_OPair(U_10034,U_10034),hAPP(U_10036,U_10032)),hAPP(U_10036,U_10033))),U_10035)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10034,U_10034)),hAPP(hAPP(c_Product__Type_OPair(U_10034,U_10034),hAPP(U_10036,U_10032)),hAPP(U_10036,U_10033))),U_10035))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10031,U_10031)),hAPP(hAPP(c_Product__Type_OPair(U_10031,U_10031),U_10032),U_10033)),hAPP(hAPP(c_Relation_Oinv__image(U_10034,U_10031),U_10035),U_10036))) ) ),
inference(variable_rename,[status(thm)],[f_2739_1]) ).
fof(f_2739_3,plain,
( ! [U_10048,U_10046,U_10044,U_10042,U_10040] :
( ! [U_10038] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_10038,U_10038)),hAPP(hAPP(c_Product__Type_OPair(U_10038,U_10038),U_10040),U_10042)),hAPP(hAPP(c_Relation_Oinv__image(U_10044,U_10038),U_10046),U_10048)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10044,U_10044)),hAPP(hAPP(c_Product__Type_OPair(U_10044,U_10044),hAPP(U_10048,U_10040)),hAPP(U_10048,U_10042))),U_10046)) )
& ! [U_10047,U_10045,U_10043,U_10041,U_10039] :
( ! [U_10037] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10037,U_10037)),hAPP(hAPP(c_Product__Type_OPair(U_10037,U_10037),U_10039),U_10041)),hAPP(hAPP(c_Relation_Oinv__image(U_10043,U_10037),U_10045),U_10047)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_10043,U_10043)),hAPP(hAPP(c_Product__Type_OPair(U_10043,U_10043),hAPP(U_10047,U_10039)),hAPP(U_10047,U_10041))),U_10045)) ) ),
inference(miniscope,[status(thm)],[f_2739_2]) ).
cnf(f_2739_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10037,U_10037)),hAPP(hAPP(c_Product__Type_OPair(U_10037,U_10037),U_10039),U_10041)),hAPP(hAPP(c_Relation_Oinv__image(U_10043,U_10037),U_10045),U_10047)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_10043,U_10043)),hAPP(hAPP(c_Product__Type_OPair(U_10043,U_10043),hAPP(U_10047,U_10039)),hAPP(U_10047,U_10041))),U_10045)) ),
inference(clausify,[status(thm)],[f_2739_3]) ).
cnf(f_2739_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10038,U_10038)),hAPP(hAPP(c_Product__Type_OPair(U_10038,U_10038),U_10040),U_10042)),hAPP(hAPP(c_Relation_Oinv__image(U_10044,U_10038),U_10046),U_10048)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10044,U_10044)),hAPP(hAPP(c_Product__Type_OPair(U_10044,U_10044),hAPP(U_10048,U_10040)),hAPP(U_10048,U_10042))),U_10046)) ),
inference(clausify,[status(thm)],[f_2739_3]) ).
fof(f_2740_1,plain,
! [V_N_2,V_h_2,T_b] :
( hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Ohom__commute]) ).
fof(f_2740_2,plain,
! [U_10053,U_10052,U_10051] :
( hAPP(U_10052,c_Big__Operators_Olinorder__class_OMin(U_10051,U_10053)) = c_Big__Operators_Olinorder__class_OMin(U_10051,hAPP(c_Set_Oimage(U_10051,U_10051,U_10052),U_10053))
| U_10053 = c_Orderings_Obot__class_Obot(tc_fun(U_10051,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10051),U_10053))
| ? [U_10050,U_10049] : hAPP(U_10052,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10051),U_10050),U_10049)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10051),hAPP(U_10052,U_10050)),hAPP(U_10052,U_10049))
| ~ class_Orderings_Olinorder(U_10051) ),
inference(variable_rename,[status(thm)],[f_2740_1]) ).
fof(f_2740_3,plain,
! [U_10053,U_10052,U_10051] :
( hAPP(U_10052,c_Big__Operators_Olinorder__class_OMin(U_10051,U_10053)) = c_Big__Operators_Olinorder__class_OMin(U_10051,hAPP(c_Set_Oimage(U_10051,U_10051,U_10052),U_10053))
| U_10053 = c_Orderings_Obot__class_Obot(tc_fun(U_10051,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10051),U_10053))
| ? [U_10049] : hAPP(U_10052,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10051),sK213(U_10053,U_10052,U_10051)),U_10049)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10051),hAPP(U_10052,sK213(U_10053,U_10052,U_10051))),hAPP(U_10052,U_10049))
| ~ class_Orderings_Olinorder(U_10051) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK213]),skolemize(U_10050,sK213(U_10053,U_10052,U_10051))],[f_2740_2]) ).
fof(f_2740_4,plain,
! [U_10053,U_10052,U_10051] :
( hAPP(U_10052,c_Big__Operators_Olinorder__class_OMin(U_10051,U_10053)) = c_Big__Operators_Olinorder__class_OMin(U_10051,hAPP(c_Set_Oimage(U_10051,U_10051,U_10052),U_10053))
| U_10053 = c_Orderings_Obot__class_Obot(tc_fun(U_10051,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10051),U_10053))
| hAPP(U_10052,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10051),sK213(U_10053,U_10052,U_10051)),sK214(U_10053,U_10052,U_10051))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10051),hAPP(U_10052,sK213(U_10053,U_10052,U_10051))),hAPP(U_10052,sK214(U_10053,U_10052,U_10051)))
| ~ class_Orderings_Olinorder(U_10051) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK214]),skolemize(U_10049,sK214(U_10053,U_10052,U_10051))],[f_2740_3]) ).
cnf(f_2740_5,plain,
( hAPP(U_10052,c_Big__Operators_Olinorder__class_OMin(U_10051,U_10053)) = c_Big__Operators_Olinorder__class_OMin(U_10051,hAPP(c_Set_Oimage(U_10051,U_10051,U_10052),U_10053))
| U_10053 = c_Orderings_Obot__class_Obot(tc_fun(U_10051,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10051),U_10053))
| hAPP(U_10052,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10051),sK213(U_10053,U_10052,U_10051)),sK214(U_10053,U_10052,U_10051))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10051),hAPP(U_10052,sK213(U_10053,U_10052,U_10051))),hAPP(U_10052,sK214(U_10053,U_10052,U_10051)))
| ~ class_Orderings_Olinorder(U_10051) ),
inference(clausify,[status(thm)],[f_2740_4]) ).
fof(f_2741_1,plain,
! [V_N_2,V_h_2,T_b] :
( hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ohom__commute]) ).
fof(f_2741_2,plain,
! [U_10058,U_10057,U_10056] :
( hAPP(U_10057,c_Big__Operators_Olattice__class_OSup__fin(U_10056,U_10058)) = c_Big__Operators_Olattice__class_OSup__fin(U_10056,hAPP(c_Set_Oimage(U_10056,U_10056,U_10057),U_10058))
| U_10058 = c_Orderings_Obot__class_Obot(tc_fun(U_10056,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10056),U_10058))
| ? [U_10055,U_10054] : hAPP(U_10057,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10056),U_10055),U_10054)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10056),hAPP(U_10057,U_10055)),hAPP(U_10057,U_10054))
| ~ class_Lattices_Olattice(U_10056) ),
inference(variable_rename,[status(thm)],[f_2741_1]) ).
fof(f_2741_3,plain,
! [U_10058,U_10057,U_10056] :
( hAPP(U_10057,c_Big__Operators_Olattice__class_OSup__fin(U_10056,U_10058)) = c_Big__Operators_Olattice__class_OSup__fin(U_10056,hAPP(c_Set_Oimage(U_10056,U_10056,U_10057),U_10058))
| U_10058 = c_Orderings_Obot__class_Obot(tc_fun(U_10056,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10056),U_10058))
| ? [U_10054] : hAPP(U_10057,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10056),sK215(U_10058,U_10057,U_10056)),U_10054)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10056),hAPP(U_10057,sK215(U_10058,U_10057,U_10056))),hAPP(U_10057,U_10054))
| ~ class_Lattices_Olattice(U_10056) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK215]),skolemize(U_10055,sK215(U_10058,U_10057,U_10056))],[f_2741_2]) ).
fof(f_2741_4,plain,
! [U_10058,U_10057,U_10056] :
( hAPP(U_10057,c_Big__Operators_Olattice__class_OSup__fin(U_10056,U_10058)) = c_Big__Operators_Olattice__class_OSup__fin(U_10056,hAPP(c_Set_Oimage(U_10056,U_10056,U_10057),U_10058))
| U_10058 = c_Orderings_Obot__class_Obot(tc_fun(U_10056,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10056),U_10058))
| hAPP(U_10057,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10056),sK215(U_10058,U_10057,U_10056)),sK216(U_10058,U_10057,U_10056))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10056),hAPP(U_10057,sK215(U_10058,U_10057,U_10056))),hAPP(U_10057,sK216(U_10058,U_10057,U_10056)))
| ~ class_Lattices_Olattice(U_10056) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK216]),skolemize(U_10054,sK216(U_10058,U_10057,U_10056))],[f_2741_3]) ).
cnf(f_2741_5,plain,
( hAPP(U_10057,c_Big__Operators_Olattice__class_OSup__fin(U_10056,U_10058)) = c_Big__Operators_Olattice__class_OSup__fin(U_10056,hAPP(c_Set_Oimage(U_10056,U_10056,U_10057),U_10058))
| U_10058 = c_Orderings_Obot__class_Obot(tc_fun(U_10056,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10056),U_10058))
| hAPP(U_10057,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10056),sK215(U_10058,U_10057,U_10056)),sK216(U_10058,U_10057,U_10056))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10056),hAPP(U_10057,sK215(U_10058,U_10057,U_10056))),hAPP(U_10057,sK216(U_10058,U_10057,U_10056)))
| ~ class_Lattices_Olattice(U_10056) ),
inference(clausify,[status(thm)],[f_2741_4]) ).
fof(f_2742_1,plain,
! [V_r_2,T_b] :
( ( c_Relation_Oirrefl(T_b,V_r_2)
| ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
& ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
| ~ c_Relation_Oirrefl(T_b,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_irrefl__def]) ).
fof(f_2742_2,plain,
! [U_10062,U_10061] :
( ( c_Relation_Oirrefl(U_10061,U_10062)
| ? [U_10060] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_10061,U_10061)),hAPP(hAPP(c_Product__Type_OPair(U_10061,U_10061),U_10060),U_10060)),U_10062)) )
& ( ! [U_10059] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10061,U_10061)),hAPP(hAPP(c_Product__Type_OPair(U_10061,U_10061),U_10059),U_10059)),U_10062))
| ~ c_Relation_Oirrefl(U_10061,U_10062) ) ),
inference(variable_rename,[status(thm)],[f_2742_1]) ).
fof(f_2742_3,plain,
( ! [U_10066,U_10064] :
( c_Relation_Oirrefl(U_10064,U_10066)
| ? [U_10060] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_10064,U_10064)),hAPP(hAPP(c_Product__Type_OPair(U_10064,U_10064),U_10060),U_10060)),U_10066)) )
& ! [U_10065,U_10063] :
( ! [U_10059] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10063,U_10063)),hAPP(hAPP(c_Product__Type_OPair(U_10063,U_10063),U_10059),U_10059)),U_10065))
| ~ c_Relation_Oirrefl(U_10063,U_10065) ) ),
inference(miniscope,[status(thm)],[f_2742_2]) ).
fof(f_2742_4,plain,
( ! [U_10066,U_10064] :
( c_Relation_Oirrefl(U_10064,U_10066)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_10064,U_10064)),hAPP(hAPP(c_Product__Type_OPair(U_10064,U_10064),sK217(U_10066,U_10064)),sK217(U_10066,U_10064))),U_10066)) )
& ! [U_10065,U_10063] :
( ! [U_10059] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10063,U_10063)),hAPP(hAPP(c_Product__Type_OPair(U_10063,U_10063),U_10059),U_10059)),U_10065))
| ~ c_Relation_Oirrefl(U_10063,U_10065) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK217]),skolemize(U_10060,sK217(U_10066,U_10064))],[f_2742_3]) ).
cnf(f_2742_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10063,U_10063)),hAPP(hAPP(c_Product__Type_OPair(U_10063,U_10063),U_10059),U_10059)),U_10065))
| ~ c_Relation_Oirrefl(U_10063,U_10065) ),
inference(clausify,[status(thm)],[f_2742_4]) ).
cnf(f_2742_6,plain,
( c_Relation_Oirrefl(U_10064,U_10066)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_10064,U_10064)),hAPP(hAPP(c_Product__Type_OPair(U_10064,U_10064),sK217(U_10066,U_10064)),sK217(U_10066,U_10064))),U_10066)) ),
inference(clausify,[status(thm)],[f_2742_4]) ).
fof(f_2743_1,plain,
! [V_r_2,V_b_2,V_a_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_b),V_r_2)),
inference(fof_nnf,[status(thm)],[fact_Field__insert]) ).
fof(f_2743_2,plain,
! [U_10070,U_10069,U_10068,U_10067] : hAPP(c_Relation_OField(U_10067),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10067,U_10067)),hAPP(hAPP(c_Product__Type_OPair(U_10067,U_10067),U_10068),U_10069)),U_10070)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10067,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10067),U_10068),hAPP(hAPP(c_Set_Oinsert(U_10067),U_10069),c_Orderings_Obot__class_Obot(tc_fun(U_10067,tc_HOL_Obool))))),hAPP(c_Relation_OField(U_10067),U_10070)),
inference(variable_rename,[status(thm)],[f_2743_1]) ).
cnf(f_2743_3,plain,
hAPP(c_Relation_OField(U_10067),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10067,U_10067)),hAPP(hAPP(c_Product__Type_OPair(U_10067,U_10067),U_10068),U_10069)),U_10070)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10067,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10067),U_10068),hAPP(hAPP(c_Set_Oinsert(U_10067),U_10069),c_Orderings_Obot__class_Obot(tc_fun(U_10067,tc_HOL_Obool))))),hAPP(c_Relation_OField(U_10067),U_10070)),
inference(clausify,[status(thm)],[f_2743_2]) ).
fof(f_2744_1,plain,
! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2)
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_c)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__mono__one__left]) ).
fof(f_2744_2,plain,
! [U_10076,U_10075,U_10074,U_10073,U_10072] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10073,U_10072),U_10076),U_10075) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10073,U_10072),U_10076),U_10074)
| ? [U_10071] :
( hAPP(U_10076,U_10071) != c_Groups_Oone__class_Oone(U_10072)
& hBOOL(hAPP(hAPP(c_member(U_10073),U_10071),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10073,tc_HOL_Obool)),U_10074),U_10075))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10073,tc_HOL_Obool)),U_10075),U_10074))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10073),U_10074))
| ~ class_Groups_Ocomm__monoid__mult(U_10072) ),
inference(variable_rename,[status(thm)],[f_2744_1]) ).
fof(f_2744_3,plain,
! [U_10076,U_10075,U_10074,U_10073,U_10072] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10073,U_10072),U_10076),U_10075) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10073,U_10072),U_10076),U_10074)
| ( hAPP(U_10076,sK218(U_10076,U_10075,U_10074,U_10073,U_10072)) != c_Groups_Oone__class_Oone(U_10072)
& hBOOL(hAPP(hAPP(c_member(U_10073),sK218(U_10076,U_10075,U_10074,U_10073,U_10072)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10073,tc_HOL_Obool)),U_10074),U_10075))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10073,tc_HOL_Obool)),U_10075),U_10074))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10073),U_10074))
| ~ class_Groups_Ocomm__monoid__mult(U_10072) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK218]),skolemize(U_10071,sK218(U_10076,U_10075,U_10074,U_10073,U_10072))],[f_2744_2]) ).
cnf(f_2744_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_10073),sK218(U_10076,U_10075,U_10074,U_10073,U_10072)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10073,tc_HOL_Obool)),U_10074),U_10075)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10073,U_10072),U_10076),U_10075) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10073,U_10072),U_10076),U_10074)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10073,tc_HOL_Obool)),U_10075),U_10074))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10073),U_10074))
| ~ class_Groups_Ocomm__monoid__mult(U_10072) ),
inference(clausify,[status(thm)],[f_2744_3]) ).
cnf(f_2744_5,plain,
( hAPP(U_10076,sK218(U_10076,U_10075,U_10074,U_10073,U_10072)) != c_Groups_Oone__class_Oone(U_10072)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10073,U_10072),U_10076),U_10075) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10073,U_10072),U_10076),U_10074)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10073,tc_HOL_Obool)),U_10075),U_10074))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10073),U_10074))
| ~ class_Groups_Ocomm__monoid__mult(U_10072) ),
inference(clausify,[status(thm)],[f_2744_3]) ).
fof(f_2745_1,plain,
! [T_b] : hAPP(c_Relation_OField(T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Field__empty]) ).
fof(f_2745_2,plain,
! [U_10077] : hAPP(c_Relation_OField(U_10077),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10077,U_10077),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_10077,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2745_1]) ).
cnf(f_2745_3,plain,
hAPP(c_Relation_OField(U_10077),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10077,U_10077),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_10077,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2745_2]) ).
fof(f_2746_1,plain,
! [V_s_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ),
inference(fof_nnf,[status(thm)],[fact_mono__Field]) ).
fof(f_2746_2,plain,
! [U_10080,U_10079,U_10078] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10078,tc_HOL_Obool)),hAPP(c_Relation_OField(U_10078),U_10079)),hAPP(c_Relation_OField(U_10078),U_10080)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10078,U_10078),tc_HOL_Obool)),U_10079),U_10080)) ),
inference(variable_rename,[status(thm)],[f_2746_1]) ).
cnf(f_2746_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10078,tc_HOL_Obool)),hAPP(c_Relation_OField(U_10078),U_10079)),hAPP(c_Relation_OField(U_10078),U_10080)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10078,U_10078),tc_HOL_Obool)),U_10079),U_10080)) ),
inference(clausify,[status(thm)],[f_2746_2]) ).
fof(f_2747_1,plain,
! [V_s_2,V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2)),
inference(fof_nnf,[status(thm)],[fact_Field__Un]) ).
fof(f_2747_2,plain,
! [U_10083,U_10082,U_10081] : hAPP(c_Relation_OField(U_10081),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10081,U_10081),tc_HOL_Obool)),U_10082),U_10083)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10081,tc_HOL_Obool)),hAPP(c_Relation_OField(U_10081),U_10082)),hAPP(c_Relation_OField(U_10081),U_10083)),
inference(variable_rename,[status(thm)],[f_2747_1]) ).
cnf(f_2747_3,plain,
hAPP(c_Relation_OField(U_10081),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10081,U_10081),tc_HOL_Obool)),U_10082),U_10083)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10081,tc_HOL_Obool)),hAPP(c_Relation_OField(U_10081),U_10082)),hAPP(c_Relation_OField(U_10081),U_10083)),
inference(clausify,[status(thm)],[f_2747_2]) ).
fof(f_2748_1,plain,
! [V_r_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__Field]) ).
fof(f_2748_2,plain,
! [U_10085,U_10084] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10084),hAPP(c_Relation_OField(U_10084),U_10085)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_10084,U_10084)),U_10085)) ),
inference(variable_rename,[status(thm)],[f_2748_1]) ).
cnf(f_2748_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10084),hAPP(c_Relation_OField(U_10084),U_10085)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_10084,U_10084)),U_10085)) ),
inference(clausify,[status(thm)],[f_2748_2]) ).
fof(f_2749_1,plain,
! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2)
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_c)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__mono__one__right]) ).
fof(f_2749_2,plain,
! [U_10091,U_10090,U_10089,U_10088,U_10087] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10088,U_10087),U_10091),U_10089) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10088,U_10087),U_10091),U_10090)
| ? [U_10086] :
( hAPP(U_10091,U_10086) != c_Groups_Oone__class_Oone(U_10087)
& hBOOL(hAPP(hAPP(c_member(U_10088),U_10086),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10088,tc_HOL_Obool)),U_10089),U_10090))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10088,tc_HOL_Obool)),U_10090),U_10089))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10088),U_10089))
| ~ class_Groups_Ocomm__monoid__mult(U_10087) ),
inference(variable_rename,[status(thm)],[f_2749_1]) ).
fof(f_2749_3,plain,
! [U_10091,U_10090,U_10089,U_10088,U_10087] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10088,U_10087),U_10091),U_10089) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10088,U_10087),U_10091),U_10090)
| ( hAPP(U_10091,sK219(U_10091,U_10090,U_10089,U_10088,U_10087)) != c_Groups_Oone__class_Oone(U_10087)
& hBOOL(hAPP(hAPP(c_member(U_10088),sK219(U_10091,U_10090,U_10089,U_10088,U_10087)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10088,tc_HOL_Obool)),U_10089),U_10090))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10088,tc_HOL_Obool)),U_10090),U_10089))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10088),U_10089))
| ~ class_Groups_Ocomm__monoid__mult(U_10087) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK219]),skolemize(U_10086,sK219(U_10091,U_10090,U_10089,U_10088,U_10087))],[f_2749_2]) ).
cnf(f_2749_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_10088),sK219(U_10091,U_10090,U_10089,U_10088,U_10087)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10088,tc_HOL_Obool)),U_10089),U_10090)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10088,U_10087),U_10091),U_10089) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10088,U_10087),U_10091),U_10090)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10088,tc_HOL_Obool)),U_10090),U_10089))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10088),U_10089))
| ~ class_Groups_Ocomm__monoid__mult(U_10087) ),
inference(clausify,[status(thm)],[f_2749_3]) ).
cnf(f_2749_5,plain,
( hAPP(U_10091,sK219(U_10091,U_10090,U_10089,U_10088,U_10087)) != c_Groups_Oone__class_Oone(U_10087)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10088,U_10087),U_10091),U_10089) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10088,U_10087),U_10091),U_10090)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10088,tc_HOL_Obool)),U_10090),U_10089))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10088),U_10089))
| ~ class_Groups_Ocomm__monoid__mult(U_10087) ),
inference(clausify,[status(thm)],[f_2749_3]) ).
fof(f_2750_1,plain,
! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2)
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__mono__zero__left]) ).
fof(f_2750_2,plain,
! [U_10097,U_10096,U_10095,U_10094,U_10093] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10094,U_10093),U_10097),U_10096) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10094,U_10093),U_10097),U_10095)
| ? [U_10092] :
( hAPP(U_10097,U_10092) != c_Groups_Ozero__class_Ozero(U_10093)
& hBOOL(hAPP(hAPP(c_member(U_10094),U_10092),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10094,tc_HOL_Obool)),U_10095),U_10096))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10094,tc_HOL_Obool)),U_10096),U_10095))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10094),U_10095))
| ~ class_Groups_Ocomm__monoid__add(U_10093) ),
inference(variable_rename,[status(thm)],[f_2750_1]) ).
fof(f_2750_3,plain,
! [U_10097,U_10096,U_10095,U_10094,U_10093] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10094,U_10093),U_10097),U_10096) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10094,U_10093),U_10097),U_10095)
| ( hAPP(U_10097,sK220(U_10097,U_10096,U_10095,U_10094,U_10093)) != c_Groups_Ozero__class_Ozero(U_10093)
& hBOOL(hAPP(hAPP(c_member(U_10094),sK220(U_10097,U_10096,U_10095,U_10094,U_10093)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10094,tc_HOL_Obool)),U_10095),U_10096))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10094,tc_HOL_Obool)),U_10096),U_10095))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10094),U_10095))
| ~ class_Groups_Ocomm__monoid__add(U_10093) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK220]),skolemize(U_10092,sK220(U_10097,U_10096,U_10095,U_10094,U_10093))],[f_2750_2]) ).
cnf(f_2750_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_10094),sK220(U_10097,U_10096,U_10095,U_10094,U_10093)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10094,tc_HOL_Obool)),U_10095),U_10096)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10094,U_10093),U_10097),U_10096) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10094,U_10093),U_10097),U_10095)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10094,tc_HOL_Obool)),U_10096),U_10095))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10094),U_10095))
| ~ class_Groups_Ocomm__monoid__add(U_10093) ),
inference(clausify,[status(thm)],[f_2750_3]) ).
cnf(f_2750_5,plain,
( hAPP(U_10097,sK220(U_10097,U_10096,U_10095,U_10094,U_10093)) != c_Groups_Ozero__class_Ozero(U_10093)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10094,U_10093),U_10097),U_10096) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10094,U_10093),U_10097),U_10095)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10094,tc_HOL_Obool)),U_10096),U_10095))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10094),U_10095))
| ~ class_Groups_Ocomm__monoid__add(U_10093) ),
inference(clausify,[status(thm)],[f_2750_3]) ).
fof(f_2751_1,plain,
! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__mono__zero__right]) ).
fof(f_2751_2,plain,
! [U_10103,U_10102,U_10101,U_10100,U_10099] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10100,U_10099),U_10103),U_10101) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10100,U_10099),U_10103),U_10102)
| ? [U_10098] :
( hAPP(U_10103,U_10098) != c_Groups_Ozero__class_Ozero(U_10099)
& hBOOL(hAPP(hAPP(c_member(U_10100),U_10098),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10100,tc_HOL_Obool)),U_10101),U_10102))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10100,tc_HOL_Obool)),U_10102),U_10101))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10100),U_10101))
| ~ class_Groups_Ocomm__monoid__add(U_10099) ),
inference(variable_rename,[status(thm)],[f_2751_1]) ).
fof(f_2751_3,plain,
! [U_10103,U_10102,U_10101,U_10100,U_10099] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10100,U_10099),U_10103),U_10101) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10100,U_10099),U_10103),U_10102)
| ( hAPP(U_10103,sK221(U_10103,U_10102,U_10101,U_10100,U_10099)) != c_Groups_Ozero__class_Ozero(U_10099)
& hBOOL(hAPP(hAPP(c_member(U_10100),sK221(U_10103,U_10102,U_10101,U_10100,U_10099)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10100,tc_HOL_Obool)),U_10101),U_10102))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10100,tc_HOL_Obool)),U_10102),U_10101))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10100),U_10101))
| ~ class_Groups_Ocomm__monoid__add(U_10099) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK221]),skolemize(U_10098,sK221(U_10103,U_10102,U_10101,U_10100,U_10099))],[f_2751_2]) ).
cnf(f_2751_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_10100),sK221(U_10103,U_10102,U_10101,U_10100,U_10099)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10100,tc_HOL_Obool)),U_10101),U_10102)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10100,U_10099),U_10103),U_10101) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10100,U_10099),U_10103),U_10102)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10100,tc_HOL_Obool)),U_10102),U_10101))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10100),U_10101))
| ~ class_Groups_Ocomm__monoid__add(U_10099) ),
inference(clausify,[status(thm)],[f_2751_3]) ).
cnf(f_2751_5,plain,
( hAPP(U_10103,sK221(U_10103,U_10102,U_10101,U_10100,U_10099)) != c_Groups_Ozero__class_Ozero(U_10099)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10100,U_10099),U_10103),U_10101) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10100,U_10099),U_10103),U_10102)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10100,tc_HOL_Obool)),U_10102),U_10101))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10100),U_10101))
| ~ class_Groups_Ocomm__monoid__add(U_10099) ),
inference(clausify,[status(thm)],[f_2751_3]) ).
fof(f_2752_1,plain,
! [V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Pow]) ).
fof(f_2752_2,plain,
! [U_10105,U_10104] :
( hAPP(c_Finite__Set_Ocard(tc_fun(U_10104,tc_HOL_Obool)),hAPP(c_Set_OPow(U_10104),U_10105)) = 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_10104),U_10105))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10104),U_10105)) ),
inference(variable_rename,[status(thm)],[f_2752_1]) ).
cnf(f_2752_3,plain,
( hAPP(c_Finite__Set_Ocard(tc_fun(U_10104,tc_HOL_Obool)),hAPP(c_Set_OPow(U_10104),U_10105)) = 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_10104),U_10105))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10104),U_10105)) ),
inference(clausify,[status(thm)],[f_2752_2]) ).
fof(f_2753_1,plain,
! [V_P_2,V_A_2,T_b] :
( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
| ? [B_a,B_A] :
( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
& hBOOL(hAPP(V_P_2,B_A))
& hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A)) )
| ~ hBOOL(hAPP(V_P_2,V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__empty__induct]) ).
fof(f_2753_2,plain,
! [U_10110,U_10109,U_10108] :
( hBOOL(hAPP(U_10110,c_Orderings_Obot__class_Obot(tc_fun(U_10108,tc_HOL_Obool))))
| ? [U_10107,U_10106] :
( ~ hBOOL(hAPP(U_10110,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10108,tc_HOL_Obool)),U_10106),hAPP(hAPP(c_Set_Oinsert(U_10108),U_10107),c_Orderings_Obot__class_Obot(tc_fun(U_10108,tc_HOL_Obool))))))
& hBOOL(hAPP(U_10110,U_10106))
& hBOOL(hAPP(hAPP(c_member(U_10108),U_10107),U_10106))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_10108),U_10106)) )
| ~ hBOOL(hAPP(U_10110,U_10109))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10108),U_10109)) ),
inference(variable_rename,[status(thm)],[f_2753_1]) ).
fof(f_2753_3,plain,
! [U_10110,U_10109,U_10108] :
( hBOOL(hAPP(U_10110,c_Orderings_Obot__class_Obot(tc_fun(U_10108,tc_HOL_Obool))))
| ? [U_10106] :
( ~ hBOOL(hAPP(U_10110,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10108,tc_HOL_Obool)),U_10106),hAPP(hAPP(c_Set_Oinsert(U_10108),sK222(U_10110,U_10109,U_10108)),c_Orderings_Obot__class_Obot(tc_fun(U_10108,tc_HOL_Obool))))))
& hBOOL(hAPP(U_10110,U_10106))
& hBOOL(hAPP(hAPP(c_member(U_10108),sK222(U_10110,U_10109,U_10108)),U_10106))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_10108),U_10106)) )
| ~ hBOOL(hAPP(U_10110,U_10109))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10108),U_10109)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK222]),skolemize(U_10107,sK222(U_10110,U_10109,U_10108))],[f_2753_2]) ).
fof(f_2753_4,plain,
! [U_10110,U_10109,U_10108] :
( hBOOL(hAPP(U_10110,c_Orderings_Obot__class_Obot(tc_fun(U_10108,tc_HOL_Obool))))
| ( ~ hBOOL(hAPP(U_10110,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10108,tc_HOL_Obool)),sK223(U_10110,U_10109,U_10108)),hAPP(hAPP(c_Set_Oinsert(U_10108),sK222(U_10110,U_10109,U_10108)),c_Orderings_Obot__class_Obot(tc_fun(U_10108,tc_HOL_Obool))))))
& hBOOL(hAPP(U_10110,sK223(U_10110,U_10109,U_10108)))
& hBOOL(hAPP(hAPP(c_member(U_10108),sK222(U_10110,U_10109,U_10108)),sK223(U_10110,U_10109,U_10108)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_10108),sK223(U_10110,U_10109,U_10108))) )
| ~ hBOOL(hAPP(U_10110,U_10109))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10108),U_10109)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK223]),skolemize(U_10106,sK223(U_10110,U_10109,U_10108))],[f_2753_3]) ).
cnf(f_2753_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10108),sK223(U_10110,U_10109,U_10108)))
| hBOOL(hAPP(U_10110,c_Orderings_Obot__class_Obot(tc_fun(U_10108,tc_HOL_Obool))))
| ~ hBOOL(hAPP(U_10110,U_10109))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10108),U_10109)) ),
inference(clausify,[status(thm)],[f_2753_4]) ).
cnf(f_2753_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_10108),sK222(U_10110,U_10109,U_10108)),sK223(U_10110,U_10109,U_10108)))
| hBOOL(hAPP(U_10110,c_Orderings_Obot__class_Obot(tc_fun(U_10108,tc_HOL_Obool))))
| ~ hBOOL(hAPP(U_10110,U_10109))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10108),U_10109)) ),
inference(clausify,[status(thm)],[f_2753_4]) ).
cnf(f_2753_7,plain,
( hBOOL(hAPP(U_10110,sK223(U_10110,U_10109,U_10108)))
| hBOOL(hAPP(U_10110,c_Orderings_Obot__class_Obot(tc_fun(U_10108,tc_HOL_Obool))))
| ~ hBOOL(hAPP(U_10110,U_10109))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10108),U_10109)) ),
inference(clausify,[status(thm)],[f_2753_4]) ).
cnf(f_2753_8,plain,
( ~ hBOOL(hAPP(U_10110,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10108,tc_HOL_Obool)),sK223(U_10110,U_10109,U_10108)),hAPP(hAPP(c_Set_Oinsert(U_10108),sK222(U_10110,U_10109,U_10108)),c_Orderings_Obot__class_Obot(tc_fun(U_10108,tc_HOL_Obool))))))
| hBOOL(hAPP(U_10110,c_Orderings_Obot__class_Obot(tc_fun(U_10108,tc_HOL_Obool))))
| ~ hBOOL(hAPP(U_10110,U_10109))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10108),U_10109)) ),
inference(clausify,[status(thm)],[f_2753_4]) ).
fof(f_2754_1,plain,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ounion__idem]) ).
fof(f_2754_2,plain,
! [U_10115,U_10114,U_10113,U_10112,U_10111] :
( hAPP(U_10113,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10111,tc_HOL_Obool)),U_10114),U_10115)) = hAPP(hAPP(U_10112,hAPP(U_10113,U_10114)),hAPP(U_10113,U_10115))
| U_10115 = c_Orderings_Obot__class_Obot(tc_fun(U_10111,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10111),U_10115))
| U_10114 = c_Orderings_Obot__class_Obot(tc_fun(U_10111,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10111),U_10114))
| ~ c_Finite__Set_Ofolding__one__idem(U_10111,U_10112,U_10113) ),
inference(variable_rename,[status(thm)],[f_2754_1]) ).
cnf(f_2754_3,plain,
( hAPP(U_10113,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10111,tc_HOL_Obool)),U_10114),U_10115)) = hAPP(hAPP(U_10112,hAPP(U_10113,U_10114)),hAPP(U_10113,U_10115))
| U_10115 = c_Orderings_Obot__class_Obot(tc_fun(U_10111,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10111),U_10115))
| U_10114 = c_Orderings_Obot__class_Obot(tc_fun(U_10111,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10111),U_10114))
| ~ c_Finite__Set_Ofolding__one__idem(U_10111,U_10112,U_10113) ),
inference(clausify,[status(thm)],[f_2754_2]) ).
fof(f_2755_1,plain,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_PowI]) ).
fof(f_2755_2,plain,
! [U_10118,U_10117,U_10116] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10116,tc_HOL_Obool)),U_10117),hAPP(c_Set_OPow(U_10116),U_10118)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10116,tc_HOL_Obool)),U_10117),U_10118)) ),
inference(variable_rename,[status(thm)],[f_2755_1]) ).
cnf(f_2755_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10116,tc_HOL_Obool)),U_10117),hAPP(c_Set_OPow(U_10116),U_10118)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10116,tc_HOL_Obool)),U_10117),U_10118)) ),
inference(clausify,[status(thm)],[f_2755_2]) ).
fof(f_2756_1,plain,
! [V_A_2,T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Pow__iff]) ).
fof(f_2756_2,plain,
! [U_10120,U_10119] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_10119,tc_HOL_Obool)),hAPP(c_Set_OPow(U_10119),U_10120)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10119),U_10120)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10119),U_10120))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_10119,tc_HOL_Obool)),hAPP(c_Set_OPow(U_10119),U_10120))) ) ),
inference(variable_rename,[status(thm)],[f_2756_1]) ).
fof(f_2756_3,plain,
( ! [U_10124,U_10122] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_10122,tc_HOL_Obool)),hAPP(c_Set_OPow(U_10122),U_10124)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10122),U_10124)) )
& ! [U_10123,U_10121] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10121),U_10123))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_10121,tc_HOL_Obool)),hAPP(c_Set_OPow(U_10121),U_10123))) ) ),
inference(miniscope,[status(thm)],[f_2756_2]) ).
cnf(f_2756_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10121),U_10123))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_10121,tc_HOL_Obool)),hAPP(c_Set_OPow(U_10121),U_10123))) ),
inference(clausify,[status(thm)],[f_2756_3]) ).
cnf(f_2756_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_10122,tc_HOL_Obool)),hAPP(c_Set_OPow(U_10122),U_10124)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10122),U_10124)) ),
inference(clausify,[status(thm)],[f_2756_3]) ).
fof(f_2757_1,plain,
! [V_A_2,T_b,B_f] : hAPP(c_Set_Oimage(T_b,tc_fun(T_b,tc_HOL_Obool),B_f),V_A_2) != hAPP(c_Set_OPow(T_b),V_A_2),
inference(fof_nnf,[status(thm)],[fact_Cantors__paradox]) ).
fof(f_2757_2,plain,
! [U_10127,U_10126,U_10125] : hAPP(c_Set_Oimage(U_10126,tc_fun(U_10126,tc_HOL_Obool),U_10125),U_10127) != hAPP(c_Set_OPow(U_10126),U_10127),
inference(variable_rename,[status(thm)],[f_2757_1]) ).
cnf(f_2757_3,plain,
hAPP(c_Set_Oimage(U_10126,tc_fun(U_10126,tc_HOL_Obool),U_10125),U_10127) != hAPP(c_Set_OPow(U_10126),U_10127),
inference(clausify,[status(thm)],[f_2757_2]) ).
fof(f_2758_1,plain,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2)) = hAPP(c_Set_OPow(T_b),V_B_2)
| hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) != V_B_2 ),
inference(fof_nnf,[status(thm)],[fact_image__Pow__surj]) ).
fof(f_2758_2,plain,
! [U_10132,U_10131,U_10130,U_10129,U_10128] :
( hAPP(c_Set_Oimage(tc_fun(U_10128,tc_HOL_Obool),tc_fun(U_10129,tc_HOL_Obool),c_Set_Oimage(U_10128,U_10129,U_10130)),hAPP(c_Set_OPow(U_10128),U_10131)) = hAPP(c_Set_OPow(U_10129),U_10132)
| hAPP(c_Set_Oimage(U_10128,U_10129,U_10130),U_10131) != U_10132 ),
inference(variable_rename,[status(thm)],[f_2758_1]) ).
cnf(f_2758_3,plain,
( hAPP(c_Set_Oimage(tc_fun(U_10128,tc_HOL_Obool),tc_fun(U_10129,tc_HOL_Obool),c_Set_Oimage(U_10128,U_10129,U_10130)),hAPP(c_Set_OPow(U_10128),U_10131)) = hAPP(c_Set_OPow(U_10129),U_10132)
| hAPP(c_Set_Oimage(U_10128,U_10129,U_10130),U_10131) != U_10132 ),
inference(clausify,[status(thm)],[f_2758_2]) ).
fof(f_2759_1,plain,
! [V_x_2,V_F_2,V_f_2,T_b] :
( hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2
| ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oidem]) ).
fof(f_2759_2,plain,
! [U_10136,U_10135,U_10134,U_10133] :
( hAPP(hAPP(U_10134,U_10136),U_10136) = U_10136
| ~ c_Finite__Set_Ofolding__one__idem(U_10133,U_10134,U_10135) ),
inference(variable_rename,[status(thm)],[f_2759_1]) ).
fof(f_2759_3,plain,
! [U_10136,U_10135,U_10134] :
( ! [U_10133] : ~ c_Finite__Set_Ofolding__one__idem(U_10133,U_10134,U_10135)
| hAPP(hAPP(U_10134,U_10136),U_10136) = U_10136 ),
inference(miniscope,[status(thm)],[f_2759_2]) ).
cnf(f_2759_4,plain,
( ~ c_Finite__Set_Ofolding__one__idem(U_10133,U_10134,U_10135)
| hAPP(hAPP(U_10134,U_10136),U_10136) = U_10136 ),
inference(clausify,[status(thm)],[f_2759_3]) ).
fof(f_2760_1,plain,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_PowD]) ).
fof(f_2760_2,plain,
! [U_10139,U_10138,U_10137] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10137,tc_HOL_Obool)),U_10138),U_10139))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10137,tc_HOL_Obool)),U_10138),hAPP(c_Set_OPow(U_10137),U_10139))) ),
inference(variable_rename,[status(thm)],[f_2760_1]) ).
cnf(f_2760_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10137,tc_HOL_Obool)),U_10138),U_10139))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10137,tc_HOL_Obool)),U_10138),hAPP(c_Set_OPow(U_10137),U_10139))) ),
inference(clausify,[status(thm)],[f_2760_2]) ).
fof(f_2761_1,plain,
! [V_B_2,V_A_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Pow__iff]) ).
fof(f_2761_2,plain,
! [U_10142,U_10141,U_10140] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10140,tc_HOL_Obool)),U_10141),hAPP(c_Set_OPow(U_10140),U_10142)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10140,tc_HOL_Obool)),U_10141),U_10142)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10140,tc_HOL_Obool)),U_10141),U_10142))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10140,tc_HOL_Obool)),U_10141),hAPP(c_Set_OPow(U_10140),U_10142))) ) ),
inference(variable_rename,[status(thm)],[f_2761_1]) ).
fof(f_2761_3,plain,
( ! [U_10148,U_10146,U_10144] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10144,tc_HOL_Obool)),U_10146),hAPP(c_Set_OPow(U_10144),U_10148)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10144,tc_HOL_Obool)),U_10146),U_10148)) )
& ! [U_10147,U_10145,U_10143] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10143,tc_HOL_Obool)),U_10145),U_10147))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10143,tc_HOL_Obool)),U_10145),hAPP(c_Set_OPow(U_10143),U_10147))) ) ),
inference(miniscope,[status(thm)],[f_2761_2]) ).
cnf(f_2761_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10143,tc_HOL_Obool)),U_10145),U_10147))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10143,tc_HOL_Obool)),U_10145),hAPP(c_Set_OPow(U_10143),U_10147))) ),
inference(clausify,[status(thm)],[f_2761_3]) ).
cnf(f_2761_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10144,tc_HOL_Obool)),U_10146),hAPP(c_Set_OPow(U_10144),U_10148)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10144,tc_HOL_Obool)),U_10146),U_10148)) ),
inference(clausify,[status(thm)],[f_2761_3]) ).
fof(f_2762_1,plain,
! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_A_2))),
inference(fof_nnf,[status(thm)],[fact_Pow__top]) ).
fof(f_2762_2,plain,
! [U_10150,U_10149] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_10149,tc_HOL_Obool)),U_10150),hAPP(c_Set_OPow(U_10149),U_10150))),
inference(variable_rename,[status(thm)],[f_2762_1]) ).
cnf(f_2762_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(U_10149,tc_HOL_Obool)),U_10150),hAPP(c_Set_OPow(U_10149),U_10150))),
inference(clausify,[status(thm)],[f_2762_2]) ).
fof(f_2763_1,plain,
! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Pow__not__empty]) ).
fof(f_2763_2,plain,
! [U_10152,U_10151] : hAPP(c_Set_OPow(U_10151),U_10152) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10151,tc_HOL_Obool),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2763_1]) ).
cnf(f_2763_3,plain,
hAPP(c_Set_OPow(U_10151),U_10152) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10151,tc_HOL_Obool),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2763_2]) ).
fof(f_2764_1,plain,
! [V_B_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Set_OPow(T_b),V_B_2))),
inference(fof_nnf,[status(thm)],[fact_Pow__bottom]) ).
fof(f_2764_2,plain,
! [U_10154,U_10153] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_10153,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_10153,tc_HOL_Obool))),hAPP(c_Set_OPow(U_10153),U_10154))),
inference(variable_rename,[status(thm)],[f_2764_1]) ).
cnf(f_2764_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(U_10153,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_10153,tc_HOL_Obool))),hAPP(c_Set_OPow(U_10153),U_10154))),
inference(clausify,[status(thm)],[f_2764_2]) ).
fof(f_2765_1,plain,
! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_Pow__empty]) ).
fof(f_2765_2,plain,
! [U_10155] : hAPP(c_Set_OPow(U_10155),c_Orderings_Obot__class_Obot(tc_fun(U_10155,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_10155,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_10155,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10155,tc_HOL_Obool),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_2765_1]) ).
cnf(f_2765_3,plain,
hAPP(c_Set_OPow(U_10155),c_Orderings_Obot__class_Obot(tc_fun(U_10155,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_10155,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_10155,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10155,tc_HOL_Obool),tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_2765_2]) ).
fof(f_2766_1,plain,
! [V_A_2,V_a_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_b),V_a_2)),hAPP(c_Set_OPow(T_b),V_A_2))),
inference(fof_nnf,[status(thm)],[fact_Pow__insert]) ).
fof(f_2766_2,plain,
! [U_10158,U_10157,U_10156] : hAPP(c_Set_OPow(U_10156),hAPP(hAPP(c_Set_Oinsert(U_10156),U_10157),U_10158)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_10156,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_10156),U_10158)),hAPP(c_Set_Oimage(tc_fun(U_10156,tc_HOL_Obool),tc_fun(U_10156,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_10156),U_10157)),hAPP(c_Set_OPow(U_10156),U_10158))),
inference(variable_rename,[status(thm)],[f_2766_1]) ).
cnf(f_2766_3,plain,
hAPP(c_Set_OPow(U_10156),hAPP(hAPP(c_Set_Oinsert(U_10156),U_10157),U_10158)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_10156,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_10156),U_10158)),hAPP(c_Set_Oimage(tc_fun(U_10156,tc_HOL_Obool),tc_fun(U_10156,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_10156),U_10157)),hAPP(c_Set_OPow(U_10156),U_10158))),
inference(clausify,[status(thm)],[f_2766_2]) ).
fof(f_2767_1,plain,
! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Pow__INT__eq]) ).
fof(f_2767_2,plain,
! [U_10162,U_10161,U_10160,U_10159] : hAPP(c_Set_OPow(U_10159),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10160,tc_fun(U_10159,tc_HOL_Obool)),U_10161),U_10162)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10160,tc_fun(tc_fun(U_10159,tc_HOL_Obool),tc_HOL_Obool)),U_10161),hAPP(hAPP(c_COMBB(tc_fun(U_10159,tc_HOL_Obool),tc_fun(tc_fun(U_10159,tc_HOL_Obool),tc_HOL_Obool),U_10160),c_Set_OPow(U_10159)),U_10162)),
inference(variable_rename,[status(thm)],[f_2767_1]) ).
cnf(f_2767_3,plain,
hAPP(c_Set_OPow(U_10159),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10160,tc_fun(U_10159,tc_HOL_Obool)),U_10161),U_10162)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10160,tc_fun(tc_fun(U_10159,tc_HOL_Obool),tc_HOL_Obool)),U_10161),hAPP(hAPP(c_COMBB(tc_fun(U_10159,tc_HOL_Obool),tc_fun(tc_fun(U_10159,tc_HOL_Obool),tc_HOL_Obool),U_10160),c_Set_OPow(U_10159)),U_10162)),
inference(clausify,[status(thm)],[f_2767_2]) ).
fof(f_2768_1,plain,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Pow__mono]) ).
fof(f_2768_2,plain,
! [U_10165,U_10164,U_10163] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10163,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_10163),U_10164)),hAPP(c_Set_OPow(U_10163),U_10165)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10163,tc_HOL_Obool)),U_10164),U_10165)) ),
inference(variable_rename,[status(thm)],[f_2768_1]) ).
cnf(f_2768_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10163,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_10163),U_10164)),hAPP(c_Set_OPow(U_10163),U_10165)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10163,tc_HOL_Obool)),U_10164),U_10165)) ),
inference(clausify,[status(thm)],[f_2768_2]) ).
fof(f_2769_1,plain,
! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_Un__Pow__subset]) ).
fof(f_2769_2,plain,
! [U_10168,U_10167,U_10166] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10166,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_10166,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_10166),U_10167)),hAPP(c_Set_OPow(U_10166),U_10168))),hAPP(c_Set_OPow(U_10166),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10166,tc_HOL_Obool)),U_10167),U_10168)))),
inference(variable_rename,[status(thm)],[f_2769_1]) ).
cnf(f_2769_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10166,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_10166,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_10166),U_10167)),hAPP(c_Set_OPow(U_10166),U_10168))),hAPP(c_Set_OPow(U_10166),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10166,tc_HOL_Obool)),U_10167),U_10168)))),
inference(clausify,[status(thm)],[f_2769_2]) ).
fof(f_2770_1,plain,
! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_UN__Pow__subset]) ).
fof(f_2770_2,plain,
! [U_10172,U_10171,U_10170,U_10169] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10169,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10170,tc_fun(tc_fun(U_10169,tc_HOL_Obool),tc_HOL_Obool)),U_10171),hAPP(hAPP(c_COMBB(tc_fun(U_10169,tc_HOL_Obool),tc_fun(tc_fun(U_10169,tc_HOL_Obool),tc_HOL_Obool),U_10170),c_Set_OPow(U_10169)),U_10172))),hAPP(c_Set_OPow(U_10169),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10170,tc_fun(U_10169,tc_HOL_Obool)),U_10171),U_10172)))),
inference(variable_rename,[status(thm)],[f_2770_1]) ).
cnf(f_2770_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10169,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10170,tc_fun(tc_fun(U_10169,tc_HOL_Obool),tc_HOL_Obool)),U_10171),hAPP(hAPP(c_COMBB(tc_fun(U_10169,tc_HOL_Obool),tc_fun(tc_fun(U_10169,tc_HOL_Obool),tc_HOL_Obool),U_10170),c_Set_OPow(U_10169)),U_10172))),hAPP(c_Set_OPow(U_10169),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10170,tc_fun(U_10169,tc_HOL_Obool)),U_10171),U_10172)))),
inference(clausify,[status(thm)],[f_2770_2]) ).
fof(f_2771_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( hBOOL(hAPP(c_Predicate_OPowp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2)))
| ~ hBOOL(hAPP(c_Predicate_OPowp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Powp__Pow__eq]) ).
fof(f_2771_2,plain,
! [U_10175,U_10174,U_10173] :
( ( hBOOL(hAPP(c_Predicate_OPowp(U_10173,hAPP(hAPP(c_COMBC(U_10173,tc_fun(U_10173,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10173)),U_10174)),U_10175))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10173,tc_HOL_Obool)),U_10175),hAPP(c_Set_OPow(U_10173),U_10174))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10173,tc_HOL_Obool)),U_10175),hAPP(c_Set_OPow(U_10173),U_10174)))
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_10173,hAPP(hAPP(c_COMBC(U_10173,tc_fun(U_10173,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10173)),U_10174)),U_10175)) ) ),
inference(variable_rename,[status(thm)],[f_2771_1]) ).
fof(f_2771_3,plain,
( ! [U_10181,U_10179,U_10177] :
( hBOOL(hAPP(c_Predicate_OPowp(U_10177,hAPP(hAPP(c_COMBC(U_10177,tc_fun(U_10177,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10177)),U_10179)),U_10181))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10177,tc_HOL_Obool)),U_10181),hAPP(c_Set_OPow(U_10177),U_10179))) )
& ! [U_10180,U_10178,U_10176] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10176,tc_HOL_Obool)),U_10180),hAPP(c_Set_OPow(U_10176),U_10178)))
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_10176,hAPP(hAPP(c_COMBC(U_10176,tc_fun(U_10176,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10176)),U_10178)),U_10180)) ) ),
inference(miniscope,[status(thm)],[f_2771_2]) ).
cnf(f_2771_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10176,tc_HOL_Obool)),U_10180),hAPP(c_Set_OPow(U_10176),U_10178)))
| ~ hBOOL(hAPP(c_Predicate_OPowp(U_10176,hAPP(hAPP(c_COMBC(U_10176,tc_fun(U_10176,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10176)),U_10178)),U_10180)) ),
inference(clausify,[status(thm)],[f_2771_3]) ).
cnf(f_2771_5,plain,
( hBOOL(hAPP(c_Predicate_OPowp(U_10177,hAPP(hAPP(c_COMBC(U_10177,tc_fun(U_10177,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10177)),U_10179)),U_10181))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10177,tc_HOL_Obool)),U_10181),hAPP(c_Set_OPow(U_10177),U_10179))) ),
inference(clausify,[status(thm)],[f_2771_3]) ).
fof(f_2772_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2))),hAPP(c_Set_OPow(T_b),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_image__Pow__mono]) ).
fof(f_2772_2,plain,
! [U_10186,U_10185,U_10184,U_10183,U_10182] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10182,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_10183,tc_HOL_Obool),tc_fun(U_10182,tc_HOL_Obool),c_Set_Oimage(U_10183,U_10182,U_10184)),hAPP(c_Set_OPow(U_10183),U_10185))),hAPP(c_Set_OPow(U_10182),U_10186)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10182,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10183,U_10182,U_10184),U_10185)),U_10186)) ),
inference(variable_rename,[status(thm)],[f_2772_1]) ).
cnf(f_2772_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_10182,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_10183,tc_HOL_Obool),tc_fun(U_10182,tc_HOL_Obool),c_Set_Oimage(U_10183,U_10182,U_10184)),hAPP(c_Set_OPow(U_10183),U_10185))),hAPP(c_Set_OPow(U_10182),U_10186)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10182,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10183,U_10182,U_10184),U_10185)),U_10186)) ),
inference(clausify,[status(thm)],[f_2772_2]) ).
fof(f_2773_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oin__idem]) ).
fof(f_2773_2,plain,
! [U_10191,U_10190,U_10189,U_10188,U_10187] :
( hAPP(hAPP(U_10188,U_10191),hAPP(U_10189,U_10190)) = hAPP(U_10189,U_10190)
| ~ hBOOL(hAPP(hAPP(c_member(U_10187),U_10191),U_10190))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10187),U_10190))
| ~ c_Finite__Set_Ofolding__one__idem(U_10187,U_10188,U_10189) ),
inference(variable_rename,[status(thm)],[f_2773_1]) ).
cnf(f_2773_3,plain,
( hAPP(hAPP(U_10188,U_10191),hAPP(U_10189,U_10190)) = hAPP(U_10189,U_10190)
| ~ hBOOL(hAPP(hAPP(c_member(U_10187),U_10191),U_10190))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10187),U_10190))
| ~ c_Finite__Set_Ofolding__one__idem(U_10187,U_10188,U_10189) ),
inference(clausify,[status(thm)],[f_2773_2]) ).
fof(f_2774_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oinsert__idem]) ).
fof(f_2774_2,plain,
! [U_10196,U_10195,U_10194,U_10193,U_10192] :
( hAPP(U_10194,hAPP(hAPP(c_Set_Oinsert(U_10192),U_10196),U_10195)) = hAPP(hAPP(U_10193,U_10196),hAPP(U_10194,U_10195))
| U_10195 = c_Orderings_Obot__class_Obot(tc_fun(U_10192,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10192),U_10195))
| ~ c_Finite__Set_Ofolding__one__idem(U_10192,U_10193,U_10194) ),
inference(variable_rename,[status(thm)],[f_2774_1]) ).
cnf(f_2774_3,plain,
( hAPP(U_10194,hAPP(hAPP(c_Set_Oinsert(U_10192),U_10196),U_10195)) = hAPP(hAPP(U_10193,U_10196),hAPP(U_10194,U_10195))
| U_10195 = c_Orderings_Obot__class_Obot(tc_fun(U_10192,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10192),U_10195))
| ~ c_Finite__Set_Ofolding__one__idem(U_10192,U_10193,U_10194) ),
inference(clausify,[status(thm)],[f_2774_2]) ).
fof(f_2775_1,plain,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
( hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Osubset__idem]) ).
fof(f_2775_2,plain,
! [U_10201,U_10200,U_10199,U_10198,U_10197] :
( hAPP(hAPP(U_10198,hAPP(U_10199,U_10201)),hAPP(U_10199,U_10200)) = hAPP(U_10199,U_10200)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10197,tc_HOL_Obool)),U_10201),U_10200))
| U_10201 = c_Orderings_Obot__class_Obot(tc_fun(U_10197,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10197),U_10200))
| ~ c_Finite__Set_Ofolding__one__idem(U_10197,U_10198,U_10199) ),
inference(variable_rename,[status(thm)],[f_2775_1]) ).
cnf(f_2775_3,plain,
( hAPP(hAPP(U_10198,hAPP(U_10199,U_10201)),hAPP(U_10199,U_10200)) = hAPP(U_10199,U_10200)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10197,tc_HOL_Obool)),U_10201),U_10200))
| U_10201 = c_Orderings_Obot__class_Obot(tc_fun(U_10197,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10197),U_10200))
| ~ c_Finite__Set_Ofolding__one__idem(U_10197,U_10198,U_10199) ),
inference(clausify,[status(thm)],[f_2775_2]) ).
fof(f_2776_1,plain,
! [V_P_2,V_A_2,V_F_2,T_b] :
( hBOOL(hAPP(V_P_2,V_F_2))
| ? [B_a,B_F] :
( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F)))
& hBOOL(hAPP(V_P_2,B_F))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
& hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) )
| ~ hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__subset__induct]) ).
fof(f_2776_2,plain,
! [U_10207,U_10206,U_10205,U_10204] :
( hBOOL(hAPP(U_10207,U_10205))
| ? [U_10203,U_10202] :
( ~ hBOOL(hAPP(U_10207,hAPP(hAPP(c_Set_Oinsert(U_10204),U_10203),U_10202)))
& hBOOL(hAPP(U_10207,U_10202))
& ~ hBOOL(hAPP(hAPP(c_member(U_10204),U_10203),U_10202))
& hBOOL(hAPP(hAPP(c_member(U_10204),U_10203),U_10206))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_10204),U_10202)) )
| ~ hBOOL(hAPP(U_10207,c_Orderings_Obot__class_Obot(tc_fun(U_10204,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10204,tc_HOL_Obool)),U_10205),U_10206))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10204),U_10205)) ),
inference(variable_rename,[status(thm)],[f_2776_1]) ).
fof(f_2776_3,plain,
! [U_10207,U_10206,U_10205,U_10204] :
( hBOOL(hAPP(U_10207,U_10205))
| ? [U_10202] :
( ~ hBOOL(hAPP(U_10207,hAPP(hAPP(c_Set_Oinsert(U_10204),sK224(U_10207,U_10206,U_10205,U_10204)),U_10202)))
& hBOOL(hAPP(U_10207,U_10202))
& ~ hBOOL(hAPP(hAPP(c_member(U_10204),sK224(U_10207,U_10206,U_10205,U_10204)),U_10202))
& hBOOL(hAPP(hAPP(c_member(U_10204),sK224(U_10207,U_10206,U_10205,U_10204)),U_10206))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_10204),U_10202)) )
| ~ hBOOL(hAPP(U_10207,c_Orderings_Obot__class_Obot(tc_fun(U_10204,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10204,tc_HOL_Obool)),U_10205),U_10206))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10204),U_10205)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK224]),skolemize(U_10203,sK224(U_10207,U_10206,U_10205,U_10204))],[f_2776_2]) ).
fof(f_2776_4,plain,
! [U_10207,U_10206,U_10205,U_10204] :
( hBOOL(hAPP(U_10207,U_10205))
| ( ~ hBOOL(hAPP(U_10207,hAPP(hAPP(c_Set_Oinsert(U_10204),sK224(U_10207,U_10206,U_10205,U_10204)),sK225(U_10207,U_10206,U_10205,U_10204))))
& hBOOL(hAPP(U_10207,sK225(U_10207,U_10206,U_10205,U_10204)))
& ~ hBOOL(hAPP(hAPP(c_member(U_10204),sK224(U_10207,U_10206,U_10205,U_10204)),sK225(U_10207,U_10206,U_10205,U_10204)))
& hBOOL(hAPP(hAPP(c_member(U_10204),sK224(U_10207,U_10206,U_10205,U_10204)),U_10206))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_10204),sK225(U_10207,U_10206,U_10205,U_10204))) )
| ~ hBOOL(hAPP(U_10207,c_Orderings_Obot__class_Obot(tc_fun(U_10204,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10204,tc_HOL_Obool)),U_10205),U_10206))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10204),U_10205)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK225]),skolemize(U_10202,sK225(U_10207,U_10206,U_10205,U_10204))],[f_2776_3]) ).
cnf(f_2776_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10204),sK225(U_10207,U_10206,U_10205,U_10204)))
| hBOOL(hAPP(U_10207,U_10205))
| ~ hBOOL(hAPP(U_10207,c_Orderings_Obot__class_Obot(tc_fun(U_10204,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10204,tc_HOL_Obool)),U_10205),U_10206))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10204),U_10205)) ),
inference(clausify,[status(thm)],[f_2776_4]) ).
cnf(f_2776_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_10204),sK224(U_10207,U_10206,U_10205,U_10204)),U_10206))
| hBOOL(hAPP(U_10207,U_10205))
| ~ hBOOL(hAPP(U_10207,c_Orderings_Obot__class_Obot(tc_fun(U_10204,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10204,tc_HOL_Obool)),U_10205),U_10206))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10204),U_10205)) ),
inference(clausify,[status(thm)],[f_2776_4]) ).
cnf(f_2776_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_10204),sK224(U_10207,U_10206,U_10205,U_10204)),sK225(U_10207,U_10206,U_10205,U_10204)))
| hBOOL(hAPP(U_10207,U_10205))
| ~ hBOOL(hAPP(U_10207,c_Orderings_Obot__class_Obot(tc_fun(U_10204,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10204,tc_HOL_Obool)),U_10205),U_10206))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10204),U_10205)) ),
inference(clausify,[status(thm)],[f_2776_4]) ).
cnf(f_2776_8,plain,
( hBOOL(hAPP(U_10207,sK225(U_10207,U_10206,U_10205,U_10204)))
| hBOOL(hAPP(U_10207,U_10205))
| ~ hBOOL(hAPP(U_10207,c_Orderings_Obot__class_Obot(tc_fun(U_10204,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10204,tc_HOL_Obool)),U_10205),U_10206))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10204),U_10205)) ),
inference(clausify,[status(thm)],[f_2776_4]) ).
cnf(f_2776_9,plain,
( ~ hBOOL(hAPP(U_10207,hAPP(hAPP(c_Set_Oinsert(U_10204),sK224(U_10207,U_10206,U_10205,U_10204)),sK225(U_10207,U_10206,U_10205,U_10204))))
| hBOOL(hAPP(U_10207,U_10205))
| ~ hBOOL(hAPP(U_10207,c_Orderings_Obot__class_Obot(tc_fun(U_10204,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10204,tc_HOL_Obool)),U_10205),U_10206))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10204),U_10205)) ),
inference(clausify,[status(thm)],[f_2776_4]) ).
fof(f_2777_1,plain,
! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_c)
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__strict__mono]) ).
fof(f_2777_2,plain,
! [U_10213,U_10212,U_10211,U_10210,U_10209] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10209),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10210,U_10209),U_10212),U_10211)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10210,U_10209),U_10213),U_10211)))
| ? [U_10208] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10209),hAPP(U_10212,U_10208)),hAPP(U_10213,U_10208)))
& hBOOL(hAPP(hAPP(c_member(U_10210),U_10208),U_10211)) )
| U_10211 = c_Orderings_Obot__class_Obot(tc_fun(U_10210,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10210),U_10211))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_10209)
| ~ class_Groups_Ocomm__monoid__add(U_10209) ),
inference(variable_rename,[status(thm)],[f_2777_1]) ).
fof(f_2777_3,plain,
! [U_10213,U_10212,U_10211,U_10210,U_10209] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10209),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10210,U_10209),U_10212),U_10211)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10210,U_10209),U_10213),U_10211)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10209),hAPP(U_10212,sK226(U_10213,U_10212,U_10211,U_10210,U_10209))),hAPP(U_10213,sK226(U_10213,U_10212,U_10211,U_10210,U_10209))))
& hBOOL(hAPP(hAPP(c_member(U_10210),sK226(U_10213,U_10212,U_10211,U_10210,U_10209)),U_10211)) )
| U_10211 = c_Orderings_Obot__class_Obot(tc_fun(U_10210,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10210),U_10211))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_10209)
| ~ class_Groups_Ocomm__monoid__add(U_10209) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK226]),skolemize(U_10208,sK226(U_10213,U_10212,U_10211,U_10210,U_10209))],[f_2777_2]) ).
cnf(f_2777_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_10210),sK226(U_10213,U_10212,U_10211,U_10210,U_10209)),U_10211))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10209),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10210,U_10209),U_10212),U_10211)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10210,U_10209),U_10213),U_10211)))
| U_10211 = c_Orderings_Obot__class_Obot(tc_fun(U_10210,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10210),U_10211))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_10209)
| ~ class_Groups_Ocomm__monoid__add(U_10209) ),
inference(clausify,[status(thm)],[f_2777_3]) ).
cnf(f_2777_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10209),hAPP(U_10212,sK226(U_10213,U_10212,U_10211,U_10210,U_10209))),hAPP(U_10213,sK226(U_10213,U_10212,U_10211,U_10210,U_10209))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10209),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10210,U_10209),U_10212),U_10211)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_10210,U_10209),U_10213),U_10211)))
| U_10211 = c_Orderings_Obot__class_Obot(tc_fun(U_10210,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10210),U_10211))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_10209)
| ~ class_Groups_Ocomm__monoid__add(U_10209) ),
inference(clausify,[status(thm)],[f_2777_3]) ).
fof(f_2778_1,plain,
! [V_y_2,V_x_2] :
( ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_Int_Ointrel)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_y_2)),c_Int_Ointrel))
| hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) != hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
inference(fof_nnf,[status(thm)],[fact_equiv__intrel__iff]) ).
fof(f_2778_2,plain,
! [U_10215,U_10214] :
( ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_10214),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_10215),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_10214),U_10215)),c_Int_Ointrel)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_10214),U_10215)),c_Int_Ointrel))
| hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_10214),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) != hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_10215),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[f_2778_1]) ).
fof(f_2778_3,plain,
( ! [U_10219,U_10217] :
( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_10217),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_10219),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_10217),U_10219)),c_Int_Ointrel)) )
& ! [U_10218,U_10216] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_10216),U_10218)),c_Int_Ointrel))
| hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_10216),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) != hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_10218),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
inference(miniscope,[status(thm)],[f_2778_2]) ).
cnf(f_2778_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_10216),U_10218)),c_Int_Ointrel))
| hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_10216),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) != hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_10218),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_2778_3]) ).
cnf(f_2778_5,plain,
( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_10217),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_10219),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_10217),U_10219)),c_Int_Ointrel)) ),
inference(clausify,[status(thm)],[f_2778_3]) ).
fof(f_2779_1,plain,
! [V_B_2,V_A_2,T_d,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Image__UN]) ).
fof(f_2779_2,plain,
! [U_10225,U_10224,U_10223,U_10222,U_10221,U_10220] : hAPP(c_Relation_OImage(U_10220,U_10221,U_10222),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10223,tc_fun(U_10220,tc_HOL_Obool)),U_10224),U_10225)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10223,tc_fun(U_10221,tc_HOL_Obool)),U_10224),hAPP(hAPP(c_COMBB(tc_fun(U_10220,tc_HOL_Obool),tc_fun(U_10221,tc_HOL_Obool),U_10223),c_Relation_OImage(U_10220,U_10221,U_10222)),U_10225)),
inference(variable_rename,[status(thm)],[f_2779_1]) ).
cnf(f_2779_3,plain,
hAPP(c_Relation_OImage(U_10220,U_10221,U_10222),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10223,tc_fun(U_10220,tc_HOL_Obool)),U_10224),U_10225)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10223,tc_fun(U_10221,tc_HOL_Obool)),U_10224),hAPP(hAPP(c_COMBB(tc_fun(U_10220,tc_HOL_Obool),tc_fun(U_10221,tc_HOL_Obool),U_10223),c_Relation_OImage(U_10220,U_10221,U_10222)),U_10225)),
inference(clausify,[status(thm)],[f_2779_2]) ).
fof(f_2780_1,plain,
! [V_B_2,V_A_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Image__Un]) ).
fof(f_2780_2,plain,
! [U_10230,U_10229,U_10228,U_10227,U_10226] : hAPP(c_Relation_OImage(U_10226,U_10227,U_10228),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10226,tc_HOL_Obool)),U_10229),U_10230)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10227,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10226,U_10227,U_10228),U_10229)),hAPP(c_Relation_OImage(U_10226,U_10227,U_10228),U_10230)),
inference(variable_rename,[status(thm)],[f_2780_1]) ).
cnf(f_2780_3,plain,
hAPP(c_Relation_OImage(U_10226,U_10227,U_10228),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10226,tc_HOL_Obool)),U_10229),U_10230)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10227,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10226,U_10227,U_10228),U_10229)),hAPP(c_Relation_OImage(U_10226,U_10227,U_10228),U_10230)),
inference(clausify,[status(thm)],[f_2780_2]) ).
fof(f_2781_1,plain,
! [V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Image__empty]) ).
fof(f_2781_2,plain,
! [U_10233,U_10232,U_10231] : hAPP(c_Relation_OImage(U_10231,U_10232,U_10233),c_Orderings_Obot__class_Obot(tc_fun(U_10231,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_10232,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2781_1]) ).
cnf(f_2781_3,plain,
hAPP(c_Relation_OImage(U_10231,U_10232,U_10233),c_Orderings_Obot__class_Obot(tc_fun(U_10231,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_10232,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2781_2]) ).
fof(f_2782_1,plain,
! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_Image__mono]) ).
fof(f_2782_2,plain,
! [U_10239,U_10238,U_10237,U_10236,U_10235,U_10234] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10235,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10234,U_10235,U_10236),U_10238)),hAPP(c_Relation_OImage(U_10234,U_10235,U_10237),U_10239)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10234,tc_HOL_Obool)),U_10238),U_10239))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10234,U_10235),tc_HOL_Obool)),U_10236),U_10237)) ),
inference(variable_rename,[status(thm)],[f_2782_1]) ).
cnf(f_2782_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10235,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10234,U_10235,U_10236),U_10238)),hAPP(c_Relation_OImage(U_10234,U_10235,U_10237),U_10239)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10234,tc_HOL_Obool)),U_10238),U_10239))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10234,U_10235),tc_HOL_Obool)),U_10236),U_10237)) ),
inference(clausify,[status(thm)],[f_2782_2]) ).
fof(f_2783_1,plain,
! [V_A_2,V_S_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_S_2),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Un__Image]) ).
fof(f_2783_2,plain,
! [U_10244,U_10243,U_10242,U_10241,U_10240] : hAPP(c_Relation_OImage(U_10240,U_10241,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10240,U_10241),tc_HOL_Obool)),U_10242),U_10243)),U_10244) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10241,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10240,U_10241,U_10242),U_10244)),hAPP(c_Relation_OImage(U_10240,U_10241,U_10243),U_10244)),
inference(variable_rename,[status(thm)],[f_2783_1]) ).
cnf(f_2783_3,plain,
hAPP(c_Relation_OImage(U_10240,U_10241,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10240,U_10241),tc_HOL_Obool)),U_10242),U_10243)),U_10244) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10241,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10240,U_10241,U_10242),U_10244)),hAPP(c_Relation_OImage(U_10240,U_10241,U_10243),U_10244)),
inference(clausify,[status(thm)],[f_2783_2]) ).
fof(f_2784_1,plain,
! [V_B_2,V_A_2,T_d,V_r_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_Image__INT__subset]) ).
fof(f_2784_2,plain,
! [U_10250,U_10249,U_10248,U_10247,U_10246,U_10245] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10245,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10246,U_10245,U_10247),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10248,tc_fun(U_10246,tc_HOL_Obool)),U_10249),U_10250))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10248,tc_fun(U_10245,tc_HOL_Obool)),U_10249),hAPP(hAPP(c_COMBB(tc_fun(U_10246,tc_HOL_Obool),tc_fun(U_10245,tc_HOL_Obool),U_10248),c_Relation_OImage(U_10246,U_10245,U_10247)),U_10250)))),
inference(variable_rename,[status(thm)],[f_2784_1]) ).
cnf(f_2784_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10245,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10246,U_10245,U_10247),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10248,tc_fun(U_10246,tc_HOL_Obool)),U_10249),U_10250))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10248,tc_fun(U_10245,tc_HOL_Obool)),U_10249),hAPP(hAPP(c_COMBB(tc_fun(U_10246,tc_HOL_Obool),tc_fun(U_10245,tc_HOL_Obool),U_10248),c_Relation_OImage(U_10246,U_10245,U_10247)),U_10250)))),
inference(clausify,[status(thm)],[f_2784_2]) ).
fof(f_2785_1,plain,
! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_rev__ImageI]) ).
fof(f_2785_2,plain,
! [U_10256,U_10255,U_10254,U_10253,U_10252,U_10251] :
( hBOOL(hAPP(hAPP(c_member(U_10254),U_10255),hAPP(c_Relation_OImage(U_10251,U_10254,U_10256),U_10253)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10251,U_10254)),hAPP(hAPP(c_Product__Type_OPair(U_10251,U_10254),U_10252),U_10255)),U_10256))
| ~ hBOOL(hAPP(hAPP(c_member(U_10251),U_10252),U_10253)) ),
inference(variable_rename,[status(thm)],[f_2785_1]) ).
cnf(f_2785_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_10254),U_10255),hAPP(c_Relation_OImage(U_10251,U_10254,U_10256),U_10253)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10251,U_10254)),hAPP(hAPP(c_Product__Type_OPair(U_10251,U_10254),U_10252),U_10255)),U_10256))
| ~ hBOOL(hAPP(hAPP(c_member(U_10251),U_10252),U_10253)) ),
inference(clausify,[status(thm)],[f_2785_2]) ).
fof(f_2786_1,plain,
! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Image__iff]) ).
fof(f_2786_2,plain,
! [U_10263,U_10262,U_10261,U_10260,U_10259] :
( ( hBOOL(hAPP(hAPP(c_member(U_10259),U_10260),hAPP(c_Relation_OImage(U_10261,U_10259,U_10262),U_10263)))
| ! [U_10258] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10261,U_10259)),hAPP(hAPP(c_Product__Type_OPair(U_10261,U_10259),U_10258),U_10260)),U_10262))
| ~ hBOOL(hAPP(hAPP(c_member(U_10261),U_10258),U_10263)) ) )
& ( ? [U_10257] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10261,U_10259)),hAPP(hAPP(c_Product__Type_OPair(U_10261,U_10259),U_10257),U_10260)),U_10262))
& hBOOL(hAPP(hAPP(c_member(U_10261),U_10257),U_10263)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_10259),U_10260),hAPP(c_Relation_OImage(U_10261,U_10259,U_10262),U_10263))) ) ),
inference(variable_rename,[status(thm)],[f_2786_1]) ).
fof(f_2786_3,plain,
( ! [U_10273,U_10271,U_10269,U_10267,U_10265] :
( hBOOL(hAPP(hAPP(c_member(U_10265),U_10267),hAPP(c_Relation_OImage(U_10269,U_10265,U_10271),U_10273)))
| ! [U_10258] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10269,U_10265)),hAPP(hAPP(c_Product__Type_OPair(U_10269,U_10265),U_10258),U_10267)),U_10271))
| ~ hBOOL(hAPP(hAPP(c_member(U_10269),U_10258),U_10273)) ) )
& ! [U_10272,U_10270,U_10268,U_10266,U_10264] :
( ? [U_10257] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10268,U_10264)),hAPP(hAPP(c_Product__Type_OPair(U_10268,U_10264),U_10257),U_10266)),U_10270))
& hBOOL(hAPP(hAPP(c_member(U_10268),U_10257),U_10272)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_10264),U_10266),hAPP(c_Relation_OImage(U_10268,U_10264,U_10270),U_10272))) ) ),
inference(miniscope,[status(thm)],[f_2786_2]) ).
fof(f_2786_4,plain,
( ! [U_10273,U_10271,U_10269,U_10267,U_10265] :
( hBOOL(hAPP(hAPP(c_member(U_10265),U_10267),hAPP(c_Relation_OImage(U_10269,U_10265,U_10271),U_10273)))
| ! [U_10258] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10269,U_10265)),hAPP(hAPP(c_Product__Type_OPair(U_10269,U_10265),U_10258),U_10267)),U_10271))
| ~ hBOOL(hAPP(hAPP(c_member(U_10269),U_10258),U_10273)) ) )
& ! [U_10272,U_10270,U_10268,U_10266,U_10264] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10268,U_10264)),hAPP(hAPP(c_Product__Type_OPair(U_10268,U_10264),sK227(U_10272,U_10270,U_10268,U_10266,U_10264)),U_10266)),U_10270))
& hBOOL(hAPP(hAPP(c_member(U_10268),sK227(U_10272,U_10270,U_10268,U_10266,U_10264)),U_10272)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_10264),U_10266),hAPP(c_Relation_OImage(U_10268,U_10264,U_10270),U_10272))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK227]),skolemize(U_10257,sK227(U_10272,U_10270,U_10268,U_10266,U_10264))],[f_2786_3]) ).
cnf(f_2786_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_10268),sK227(U_10272,U_10270,U_10268,U_10266,U_10264)),U_10272))
| ~ hBOOL(hAPP(hAPP(c_member(U_10264),U_10266),hAPP(c_Relation_OImage(U_10268,U_10264,U_10270),U_10272))) ),
inference(clausify,[status(thm)],[f_2786_4]) ).
cnf(f_2786_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10268,U_10264)),hAPP(hAPP(c_Product__Type_OPair(U_10268,U_10264),sK227(U_10272,U_10270,U_10268,U_10266,U_10264)),U_10266)),U_10270))
| ~ hBOOL(hAPP(hAPP(c_member(U_10264),U_10266),hAPP(c_Relation_OImage(U_10268,U_10264,U_10270),U_10272))) ),
inference(clausify,[status(thm)],[f_2786_4]) ).
cnf(f_2786_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_10265),U_10267),hAPP(c_Relation_OImage(U_10269,U_10265,U_10271),U_10273)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10269,U_10265)),hAPP(hAPP(c_Product__Type_OPair(U_10269,U_10265),U_10258),U_10267)),U_10271))
| ~ hBOOL(hAPP(hAPP(c_member(U_10269),U_10258),U_10273)) ),
inference(clausify,[status(thm)],[f_2786_4]) ).
fof(f_2787_1,plain,
! [V_B_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Relation_OImage(T_c,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),
inference(fof_nnf,[status(thm)],[fact_Image__eq__UN]) ).
fof(f_2787_2,plain,
! [U_10277,U_10276,U_10275,U_10274] : hAPP(c_Relation_OImage(U_10274,U_10275,U_10276),U_10277) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10274,tc_fun(U_10275,tc_HOL_Obool)),U_10277),hAPP(hAPP(c_COMBB(tc_fun(U_10274,tc_HOL_Obool),tc_fun(U_10275,tc_HOL_Obool),U_10274),c_Relation_OImage(U_10274,U_10275,U_10276)),hAPP(hAPP(c_COMBC(U_10274,tc_fun(U_10274,tc_HOL_Obool),tc_fun(U_10274,tc_HOL_Obool)),c_Set_Oinsert(U_10274)),c_Orderings_Obot__class_Obot(tc_fun(U_10274,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_2787_1]) ).
cnf(f_2787_3,plain,
hAPP(c_Relation_OImage(U_10274,U_10275,U_10276),U_10277) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10274,tc_fun(U_10275,tc_HOL_Obool)),U_10277),hAPP(hAPP(c_COMBB(tc_fun(U_10274,tc_HOL_Obool),tc_fun(U_10275,tc_HOL_Obool),U_10274),c_Relation_OImage(U_10274,U_10275,U_10276)),hAPP(hAPP(c_COMBC(U_10274,tc_fun(U_10274,tc_HOL_Obool),tc_fun(U_10274,tc_HOL_Obool)),c_Set_Oinsert(U_10274)),c_Orderings_Obot__class_Obot(tc_fun(U_10274,tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_2787_2]) ).
fof(f_2788_1,plain,
! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ),
inference(fof_nnf,[status(thm)],[fact_Image__singleton__iff]) ).
fof(f_2788_2,plain,
! [U_10282,U_10281,U_10280,U_10279,U_10278] :
( ( hBOOL(hAPP(hAPP(c_member(U_10278),U_10279),hAPP(c_Relation_OImage(U_10280,U_10278,U_10281),hAPP(hAPP(c_Set_Oinsert(U_10280),U_10282),c_Orderings_Obot__class_Obot(tc_fun(U_10280,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10280,U_10278)),hAPP(hAPP(c_Product__Type_OPair(U_10280,U_10278),U_10282),U_10279)),U_10281)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10280,U_10278)),hAPP(hAPP(c_Product__Type_OPair(U_10280,U_10278),U_10282),U_10279)),U_10281))
| ~ hBOOL(hAPP(hAPP(c_member(U_10278),U_10279),hAPP(c_Relation_OImage(U_10280,U_10278,U_10281),hAPP(hAPP(c_Set_Oinsert(U_10280),U_10282),c_Orderings_Obot__class_Obot(tc_fun(U_10280,tc_HOL_Obool)))))) ) ),
inference(variable_rename,[status(thm)],[f_2788_1]) ).
fof(f_2788_3,plain,
( ! [U_10292,U_10290,U_10288,U_10286,U_10284] :
( hBOOL(hAPP(hAPP(c_member(U_10284),U_10286),hAPP(c_Relation_OImage(U_10288,U_10284,U_10290),hAPP(hAPP(c_Set_Oinsert(U_10288),U_10292),c_Orderings_Obot__class_Obot(tc_fun(U_10288,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10288,U_10284)),hAPP(hAPP(c_Product__Type_OPair(U_10288,U_10284),U_10292),U_10286)),U_10290)) )
& ! [U_10291,U_10289,U_10287,U_10285,U_10283] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10287,U_10283)),hAPP(hAPP(c_Product__Type_OPair(U_10287,U_10283),U_10291),U_10285)),U_10289))
| ~ hBOOL(hAPP(hAPP(c_member(U_10283),U_10285),hAPP(c_Relation_OImage(U_10287,U_10283,U_10289),hAPP(hAPP(c_Set_Oinsert(U_10287),U_10291),c_Orderings_Obot__class_Obot(tc_fun(U_10287,tc_HOL_Obool)))))) ) ),
inference(miniscope,[status(thm)],[f_2788_2]) ).
cnf(f_2788_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10287,U_10283)),hAPP(hAPP(c_Product__Type_OPair(U_10287,U_10283),U_10291),U_10285)),U_10289))
| ~ hBOOL(hAPP(hAPP(c_member(U_10283),U_10285),hAPP(c_Relation_OImage(U_10287,U_10283,U_10289),hAPP(hAPP(c_Set_Oinsert(U_10287),U_10291),c_Orderings_Obot__class_Obot(tc_fun(U_10287,tc_HOL_Obool)))))) ),
inference(clausify,[status(thm)],[f_2788_3]) ).
cnf(f_2788_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_10284),U_10286),hAPP(c_Relation_OImage(U_10288,U_10284,U_10290),hAPP(hAPP(c_Set_Oinsert(U_10288),U_10292),c_Orderings_Obot__class_Obot(tc_fun(U_10288,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10288,U_10284)),hAPP(hAPP(c_Product__Type_OPair(U_10288,U_10284),U_10292),U_10286)),U_10290)) ),
inference(clausify,[status(thm)],[f_2788_3]) ).
fof(f_2789_1,plain,
! [V_j_2,V_i_2,T_b] :
( hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_i_2),V_j_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_j_2))
| ~ class_Rings_Oring__1(T_b) ),
inference(fof_nnf,[status(thm)],[fact_of__int]) ).
fof(f_2789_2,plain,
! [U_10295,U_10294,U_10293] :
( hAPP(c_Int_Oring__1__class_Oof__int(U_10293),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10294),U_10295)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10293),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10293),U_10294)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10293),U_10295))
| ~ class_Rings_Oring__1(U_10293) ),
inference(variable_rename,[status(thm)],[f_2789_1]) ).
cnf(f_2789_3,plain,
( hAPP(c_Int_Oring__1__class_Oof__int(U_10293),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10294),U_10295)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10293),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10293),U_10294)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10293),U_10295))
| ~ class_Rings_Oring__1(U_10293) ),
inference(clausify,[status(thm)],[f_2789_2]) ).
fof(f_2790_1,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(fof_nnf,[status(thm)],[fact_One__int__def]) ).
cnf(f_2790_2,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_2790_1]) ).
fof(f_2791_1,plain,
! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_v_2))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y_2),V_u_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(fof_nnf,[status(thm)],[fact_mult]) ).
fof(f_2791_2,plain,
! [U_10299,U_10298,U_10297,U_10296] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10296),U_10297)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10298),U_10299)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10296),U_10298)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10297),U_10299))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10296),U_10299)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10297),U_10298)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_2791_1]) ).
cnf(f_2791_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10296),U_10297)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10298),U_10299)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10296),U_10298)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10297),U_10299))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10296),U_10299)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_10297),U_10298)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_2791_2]) ).
fof(f_2792_1,plain,
! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2,
inference(fof_nnf,[status(thm)],[fact_Rep__Integ__inverse]) ).
fof(f_2792_2,plain,
! [U_10300] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_10300)) = U_10300,
inference(variable_rename,[status(thm)],[f_2792_1]) ).
cnf(f_2792_3,plain,
hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_10300)) = U_10300,
inference(clausify,[status(thm)],[f_2792_2]) ).
fof(f_2793_1,plain,
! [V_y_2,V_x_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_y_2),V_x_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(fof_nnf,[status(thm)],[fact_minus]) ).
fof(f_2793_2,plain,
! [U_10302,U_10301] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10301),U_10302)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10302),U_10301)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_2793_1]) ).
cnf(f_2793_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10301),U_10302)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10302),U_10301)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_2793_2]) ).
fof(f_2794_1,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(fof_nnf,[status(thm)],[fact_Zero__int__def]) ).
cnf(f_2794_2,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_2794_1]) ).
fof(f_2795_1,plain,
! [V_m_2] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(fof_nnf,[status(thm)],[fact_int__def]) ).
fof(f_2795_2,plain,
! [U_10303] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10303) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10303),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_2795_1]) ).
cnf(f_2795_3,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_10303) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10303),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_2795_2]) ).
fof(f_2796_1,plain,
! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),V_v_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(fof_nnf,[status(thm)],[fact_add]) ).
fof(f_2796_2,plain,
! [U_10307,U_10306,U_10305,U_10304] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10304),U_10305)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10306),U_10307)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10304),U_10306)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10305),U_10307))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_2796_1]) ).
cnf(f_2796_3,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10304),U_10305)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10306),U_10307)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10304),U_10306)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10305),U_10307))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_2796_2]) ).
fof(f_2797_1,plain,
! [V_y_2,V_x_2] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2),
inference(fof_nnf,[status(thm)],[fact_nat]) ).
fof(f_2797_2,plain,
! [U_10309,U_10308] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10308),U_10309)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10308),U_10309),
inference(variable_rename,[status(thm)],[f_2797_1]) ).
cnf(f_2797_3,plain,
hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10308),U_10309)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10308),U_10309),
inference(clausify,[status(thm)],[f_2797_2]) ).
fof(f_2798_1,plain,
! [V_z_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z_2) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,V_z_2)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
inference(fof_nnf,[status(thm)],[fact_minus__int__def]) ).
fof(f_2798_2,plain,
! [U_10310] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10310) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_10310)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
inference(variable_rename,[status(thm)],[f_2798_1]) ).
cnf(f_2798_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_10310) = hAPP(c_Int_OAbs__Integ,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_10310)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
inference(clausify,[status(thm)],[f_2798_2]) ).
fof(f_2799_1,plain,
! [V_v_2,V_u_2,V_y_2,V_x_2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
inference(fof_nnf,[status(thm)],[fact_less]) ).
fof(f_2799_2,plain,
! [U_10314,U_10313,U_10312,U_10311] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10311),U_10312)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10313),U_10314)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10311),U_10314)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10313),U_10312))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10311),U_10314)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10313),U_10312)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10311),U_10312)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10313),U_10314)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
inference(variable_rename,[status(thm)],[f_2799_1]) ).
fof(f_2799_3,plain,
( ! [U_10322,U_10320,U_10318,U_10316] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10316),U_10318)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10320),U_10322)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10316),U_10322)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10320),U_10318))) )
& ! [U_10321,U_10319,U_10317,U_10315] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10315),U_10321)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10319),U_10317)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10315),U_10317)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10319),U_10321)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
inference(miniscope,[status(thm)],[f_2799_2]) ).
cnf(f_2799_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10315),U_10321)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10319),U_10317)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10315),U_10317)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10319),U_10321)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ),
inference(clausify,[status(thm)],[f_2799_3]) ).
cnf(f_2799_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10316),U_10318)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10320),U_10322)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10316),U_10322)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10320),U_10318))) ),
inference(clausify,[status(thm)],[f_2799_3]) ).
fof(f_2800_1,plain,
! [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))) )
& ( 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)))
| ~ 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))))))) ) ),
inference(fof_nnf,[status(thm)],[fact_le]) ).
fof(f_2800_2,plain,
! [U_10326,U_10325,U_10324,U_10323] :
( ( 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),U_10323),U_10324)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10325),U_10326)),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),U_10323),U_10326)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10325),U_10324))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10323),U_10326)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10325),U_10324)))
| ~ 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),U_10323),U_10324)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10325),U_10326)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
inference(variable_rename,[status(thm)],[f_2800_1]) ).
fof(f_2800_3,plain,
( ! [U_10334,U_10332,U_10330,U_10328] :
( 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),U_10328),U_10330)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10332),U_10334)),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),U_10328),U_10334)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10332),U_10330))) )
& ! [U_10333,U_10331,U_10329,U_10327] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10327),U_10333)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10331),U_10329)))
| ~ 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),U_10327),U_10329)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10331),U_10333)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
inference(miniscope,[status(thm)],[f_2800_2]) ).
cnf(f_2800_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_10327),U_10333)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10331),U_10329)))
| ~ 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),U_10327),U_10329)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10331),U_10333)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ),
inference(clausify,[status(thm)],[f_2800_3]) ).
cnf(f_2800_5,plain,
( 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),U_10328),U_10330)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10332),U_10334)),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),U_10328),U_10334)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_10332),U_10330))) ),
inference(clausify,[status(thm)],[f_2800_3]) ).
fof(f_2801_1,plain,
! [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))))),
inference(fof_nnf,[status(thm)],[fact_eq__Abs__Integ]) ).
fof(f_2801_2,plain,
! [U_10337] :
? [U_10336,U_10335] : U_10337 = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_10336),U_10335)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_2801_1]) ).
fof(f_2801_3,plain,
! [U_10337] :
? [U_10335] : U_10337 = 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),sK228(U_10337)),U_10335)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK228]),skolemize(U_10336,sK228(U_10337))],[f_2801_2]) ).
fof(f_2801_4,plain,
! [U_10337] : U_10337 = 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),sK228(U_10337)),sK229(U_10337))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK229]),skolemize(U_10335,sK229(U_10337))],[f_2801_3]) ).
cnf(f_2801_5,plain,
U_10337 = 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),sK228(U_10337)),sK229(U_10337))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_2801_4]) ).
fof(f_2802_1,plain,
! [V_r_2,V_A_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_quotient__def]) ).
fof(f_2802_2,plain,
! [U_10340,U_10339,U_10338] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10338),U_10339),U_10340) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10338,tc_fun(tc_fun(U_10338,tc_HOL_Obool),tc_HOL_Obool)),U_10339),hAPP(hAPP(c_COMBC(U_10338,tc_fun(tc_fun(U_10338,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10338,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10338,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_10338,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10338,tc_HOL_Obool),tc_HOL_Obool)),U_10338),c_Set_Oinsert(tc_fun(U_10338,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10338,tc_HOL_Obool),tc_fun(U_10338,tc_HOL_Obool),U_10338),c_Relation_OImage(U_10338,U_10338,U_10340)),hAPP(hAPP(c_COMBC(U_10338,tc_fun(U_10338,tc_HOL_Obool),tc_fun(U_10338,tc_HOL_Obool)),c_Set_Oinsert(U_10338)),c_Orderings_Obot__class_Obot(tc_fun(U_10338,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10338,tc_HOL_Obool),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_2802_1]) ).
cnf(f_2802_3,plain,
hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10338),U_10339),U_10340) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10338,tc_fun(tc_fun(U_10338,tc_HOL_Obool),tc_HOL_Obool)),U_10339),hAPP(hAPP(c_COMBC(U_10338,tc_fun(tc_fun(U_10338,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10338,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10338,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_10338,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_10338,tc_HOL_Obool),tc_HOL_Obool)),U_10338),c_Set_Oinsert(tc_fun(U_10338,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10338,tc_HOL_Obool),tc_fun(U_10338,tc_HOL_Obool),U_10338),c_Relation_OImage(U_10338,U_10338,U_10340)),hAPP(hAPP(c_COMBC(U_10338,tc_fun(U_10338,tc_HOL_Obool),tc_fun(U_10338,tc_HOL_Obool)),c_Set_Oinsert(U_10338)),c_Orderings_Obot__class_Obot(tc_fun(U_10338,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10338,tc_HOL_Obool),tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_2802_2]) ).
fof(f_2803_1,plain,
! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_ImageE]) ).
fof(f_2803_2,plain,
! [U_10346,U_10345,U_10344,U_10343,U_10342] :
( ? [U_10341] :
( hBOOL(hAPP(hAPP(c_member(U_10344),U_10341),U_10346))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_10344,U_10342)),hAPP(hAPP(c_Product__Type_OPair(U_10344,U_10342),U_10341),U_10343)),U_10345)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_10342),U_10343),hAPP(c_Relation_OImage(U_10344,U_10342,U_10345),U_10346))) ),
inference(variable_rename,[status(thm)],[f_2803_1]) ).
fof(f_2803_3,plain,
! [U_10346,U_10345,U_10344,U_10343,U_10342] :
( ( hBOOL(hAPP(hAPP(c_member(U_10344),sK230(U_10346,U_10345,U_10344,U_10343,U_10342)),U_10346))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_10344,U_10342)),hAPP(hAPP(c_Product__Type_OPair(U_10344,U_10342),sK230(U_10346,U_10345,U_10344,U_10343,U_10342)),U_10343)),U_10345)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_10342),U_10343),hAPP(c_Relation_OImage(U_10344,U_10342,U_10345),U_10346))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK230]),skolemize(U_10341,sK230(U_10346,U_10345,U_10344,U_10343,U_10342))],[f_2803_2]) ).
cnf(f_2803_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10344,U_10342)),hAPP(hAPP(c_Product__Type_OPair(U_10344,U_10342),sK230(U_10346,U_10345,U_10344,U_10343,U_10342)),U_10343)),U_10345))
| ~ hBOOL(hAPP(hAPP(c_member(U_10342),U_10343),hAPP(c_Relation_OImage(U_10344,U_10342,U_10345),U_10346))) ),
inference(clausify,[status(thm)],[f_2803_3]) ).
cnf(f_2803_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_10344),sK230(U_10346,U_10345,U_10344,U_10343,U_10342)),U_10346))
| ~ hBOOL(hAPP(hAPP(c_member(U_10342),U_10343),hAPP(c_Relation_OImage(U_10344,U_10342,U_10345),U_10346))) ),
inference(clausify,[status(thm)],[f_2803_3]) ).
fof(f_2804_1,plain,
! [V_r_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_quotient__empty]) ).
fof(f_2804_2,plain,
! [U_10348,U_10347] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10347),c_Orderings_Obot__class_Obot(tc_fun(U_10347,tc_HOL_Obool))),U_10348) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10347,tc_HOL_Obool),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2804_1]) ).
cnf(f_2804_3,plain,
hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10347),c_Orderings_Obot__class_Obot(tc_fun(U_10347,tc_HOL_Obool))),U_10348) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10347,tc_HOL_Obool),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2804_2]) ).
fof(f_2805_1,plain,
! [V_r_2,V_A_2,T_b] :
( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_quotient__is__empty2]) ).
fof(f_2805_2,plain,
! [U_10351,U_10350,U_10349] :
( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10349,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10349),U_10350),U_10351)
| U_10350 != c_Orderings_Obot__class_Obot(tc_fun(U_10349,tc_HOL_Obool)) )
& ( U_10350 = c_Orderings_Obot__class_Obot(tc_fun(U_10349,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10349,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10349),U_10350),U_10351) ) ),
inference(variable_rename,[status(thm)],[f_2805_1]) ).
fof(f_2805_3,plain,
( ! [U_10357,U_10355,U_10353] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10353,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10353),U_10355),U_10357)
| U_10355 != c_Orderings_Obot__class_Obot(tc_fun(U_10353,tc_HOL_Obool)) )
& ! [U_10356,U_10354,U_10352] :
( U_10354 = c_Orderings_Obot__class_Obot(tc_fun(U_10352,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10352,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10352),U_10354),U_10356) ) ),
inference(miniscope,[status(thm)],[f_2805_2]) ).
cnf(f_2805_4,plain,
( U_10354 = c_Orderings_Obot__class_Obot(tc_fun(U_10352,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10352,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10352),U_10354),U_10356) ),
inference(clausify,[status(thm)],[f_2805_3]) ).
cnf(f_2805_5,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10353,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10353),U_10355),U_10357)
| U_10355 != c_Orderings_Obot__class_Obot(tc_fun(U_10353,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2805_3]) ).
fof(f_2806_1,plain,
! [V_r_2,V_A_2,T_b] :
( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_quotient__is__empty]) ).
fof(f_2806_2,plain,
! [U_10360,U_10359,U_10358] :
( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10358),U_10359),U_10360) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10358,tc_HOL_Obool),tc_HOL_Obool))
| U_10359 != c_Orderings_Obot__class_Obot(tc_fun(U_10358,tc_HOL_Obool)) )
& ( U_10359 = c_Orderings_Obot__class_Obot(tc_fun(U_10358,tc_HOL_Obool))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10358),U_10359),U_10360) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10358,tc_HOL_Obool),tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2806_1]) ).
fof(f_2806_3,plain,
( ! [U_10366,U_10364,U_10362] :
( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10362),U_10364),U_10366) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10362,tc_HOL_Obool),tc_HOL_Obool))
| U_10364 != c_Orderings_Obot__class_Obot(tc_fun(U_10362,tc_HOL_Obool)) )
& ! [U_10365,U_10363,U_10361] :
( U_10363 = c_Orderings_Obot__class_Obot(tc_fun(U_10361,tc_HOL_Obool))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10361),U_10363),U_10365) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10361,tc_HOL_Obool),tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2806_2]) ).
cnf(f_2806_4,plain,
( U_10363 = c_Orderings_Obot__class_Obot(tc_fun(U_10361,tc_HOL_Obool))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10361),U_10363),U_10365) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10361,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2806_3]) ).
cnf(f_2806_5,plain,
( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10362),U_10364),U_10366) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10362,tc_HOL_Obool),tc_HOL_Obool))
| U_10364 != c_Orderings_Obot__class_Obot(tc_fun(U_10362,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2806_3]) ).
fof(f_2807_1,plain,
! [V_r_2,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_quotientI]) ).
fof(f_2807_2,plain,
! [U_10370,U_10369,U_10368,U_10367] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10367,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10367,U_10367,U_10370),hAPP(hAPP(c_Set_Oinsert(U_10367),U_10368),c_Orderings_Obot__class_Obot(tc_fun(U_10367,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10367),U_10369),U_10370)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10367),U_10368),U_10369)) ),
inference(variable_rename,[status(thm)],[f_2807_1]) ).
cnf(f_2807_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_10367,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10367,U_10367,U_10370),hAPP(hAPP(c_Set_Oinsert(U_10367),U_10368),c_Orderings_Obot__class_Obot(tc_fun(U_10367,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10367),U_10369),U_10370)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10367),U_10368),U_10369)) ),
inference(clausify,[status(thm)],[f_2807_2]) ).
fof(f_2808_1,plain,
! [V_r_2,V_x_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_singleton__quotient]) ).
fof(f_2808_2,plain,
! [U_10373,U_10372,U_10371] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10371),hAPP(hAPP(c_Set_Oinsert(U_10371),U_10372),c_Orderings_Obot__class_Obot(tc_fun(U_10371,tc_HOL_Obool)))),U_10373) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_10371,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10371,U_10371,U_10373),hAPP(hAPP(c_Set_Oinsert(U_10371),U_10372),c_Orderings_Obot__class_Obot(tc_fun(U_10371,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10371,tc_HOL_Obool),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_2808_1]) ).
cnf(f_2808_3,plain,
hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10371),hAPP(hAPP(c_Set_Oinsert(U_10371),U_10372),c_Orderings_Obot__class_Obot(tc_fun(U_10371,tc_HOL_Obool)))),U_10373) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_10371,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10371,U_10371,U_10373),hAPP(hAPP(c_Set_Oinsert(U_10371),U_10372),c_Orderings_Obot__class_Obot(tc_fun(U_10371,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_10371,tc_HOL_Obool),tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_2808_2]) ).
fof(f_2809_1,plain,
! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_subset__equiv__class]) ).
fof(f_2809_2,plain,
! [U_10378,U_10377,U_10376,U_10375,U_10374] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10374,U_10374)),hAPP(hAPP(c_Product__Type_OPair(U_10374,U_10374),U_10378),U_10377)),U_10376))
| ~ hBOOL(hAPP(hAPP(c_member(U_10374),U_10377),U_10375))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10374,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10374,U_10374,U_10376),hAPP(hAPP(c_Set_Oinsert(U_10374),U_10377),c_Orderings_Obot__class_Obot(tc_fun(U_10374,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_10374,U_10374,U_10376),hAPP(hAPP(c_Set_Oinsert(U_10374),U_10378),c_Orderings_Obot__class_Obot(tc_fun(U_10374,tc_HOL_Obool))))))
| ~ c_Equiv__Relations_Oequiv(U_10374,U_10375,U_10376) ),
inference(variable_rename,[status(thm)],[f_2809_1]) ).
cnf(f_2809_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10374,U_10374)),hAPP(hAPP(c_Product__Type_OPair(U_10374,U_10374),U_10378),U_10377)),U_10376))
| ~ hBOOL(hAPP(hAPP(c_member(U_10374),U_10377),U_10375))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10374,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10374,U_10374,U_10376),hAPP(hAPP(c_Set_Oinsert(U_10374),U_10377),c_Orderings_Obot__class_Obot(tc_fun(U_10374,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_10374,U_10374,U_10376),hAPP(hAPP(c_Set_Oinsert(U_10374),U_10378),c_Orderings_Obot__class_Obot(tc_fun(U_10374,tc_HOL_Obool))))))
| ~ c_Equiv__Relations_Oequiv(U_10374,U_10375,U_10376) ),
inference(clausify,[status(thm)],[f_2809_2]) ).
fof(f_2810_1,plain,
! [V_r_2,V_A_2,V_X_2,T_b] :
( ? [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
& V_X_2 = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_quotientE]) ).
fof(f_2810_2,plain,
! [U_10383,U_10382,U_10381,U_10380] :
( ? [U_10379] :
( hBOOL(hAPP(hAPP(c_member(U_10380),U_10379),U_10382))
& U_10381 = hAPP(c_Relation_OImage(U_10380,U_10380,U_10383),hAPP(hAPP(c_Set_Oinsert(U_10380),U_10379),c_Orderings_Obot__class_Obot(tc_fun(U_10380,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10380,tc_HOL_Obool)),U_10381),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10380),U_10382),U_10383))) ),
inference(variable_rename,[status(thm)],[f_2810_1]) ).
fof(f_2810_3,plain,
! [U_10383,U_10382,U_10381,U_10380] :
( ( hBOOL(hAPP(hAPP(c_member(U_10380),sK231(U_10383,U_10382,U_10381,U_10380)),U_10382))
& U_10381 = hAPP(c_Relation_OImage(U_10380,U_10380,U_10383),hAPP(hAPP(c_Set_Oinsert(U_10380),sK231(U_10383,U_10382,U_10381,U_10380)),c_Orderings_Obot__class_Obot(tc_fun(U_10380,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10380,tc_HOL_Obool)),U_10381),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10380),U_10382),U_10383))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK231]),skolemize(U_10379,sK231(U_10383,U_10382,U_10381,U_10380))],[f_2810_2]) ).
cnf(f_2810_4,plain,
( U_10381 = hAPP(c_Relation_OImage(U_10380,U_10380,U_10383),hAPP(hAPP(c_Set_Oinsert(U_10380),sK231(U_10383,U_10382,U_10381,U_10380)),c_Orderings_Obot__class_Obot(tc_fun(U_10380,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10380,tc_HOL_Obool)),U_10381),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10380),U_10382),U_10383))) ),
inference(clausify,[status(thm)],[f_2810_3]) ).
cnf(f_2810_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_10380),sK231(U_10383,U_10382,U_10381,U_10380)),U_10382))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10380,tc_HOL_Obool)),U_10381),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10380),U_10382),U_10383))) ),
inference(clausify,[status(thm)],[f_2810_3]) ).
fof(f_2811_1,plain,
! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_Id__on__def]) ).
fof(f_2811_2,plain,
! [U_10385,U_10384] : c_Relation_OId__on(U_10384,U_10385) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10384,tc_fun(tc_prod(U_10384,U_10384),tc_HOL_Obool)),U_10385),hAPP(hAPP(c_COMBC(U_10384,tc_fun(tc_prod(U_10384,U_10384),tc_HOL_Obool),tc_fun(tc_prod(U_10384,U_10384),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(U_10384,U_10384),tc_fun(tc_fun(tc_prod(U_10384,U_10384),tc_HOL_Obool),tc_fun(tc_prod(U_10384,U_10384),tc_HOL_Obool)),U_10384),c_Set_Oinsert(tc_prod(U_10384,U_10384))),hAPP(hAPP(c_COMBS(U_10384,U_10384,tc_prod(U_10384,U_10384)),c_Product__Type_OPair(U_10384,U_10384)),c_COMBI(U_10384)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10384,U_10384),tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_2811_1]) ).
cnf(f_2811_3,plain,
c_Relation_OId__on(U_10384,U_10385) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10384,tc_fun(tc_prod(U_10384,U_10384),tc_HOL_Obool)),U_10385),hAPP(hAPP(c_COMBC(U_10384,tc_fun(tc_prod(U_10384,U_10384),tc_HOL_Obool),tc_fun(tc_prod(U_10384,U_10384),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(U_10384,U_10384),tc_fun(tc_fun(tc_prod(U_10384,U_10384),tc_HOL_Obool),tc_fun(tc_prod(U_10384,U_10384),tc_HOL_Obool)),U_10384),c_Set_Oinsert(tc_prod(U_10384,U_10384))),hAPP(hAPP(c_COMBS(U_10384,U_10384,tc_prod(U_10384,U_10384)),c_Product__Type_OPair(U_10384,U_10384)),c_COMBI(U_10384)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10384,U_10384),tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_2811_2]) ).
fof(f_2812_1,plain,
! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),c_fequal))),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Id__on__def_H]) ).
fof(f_2812_2,plain,
! [U_10387,U_10386] : c_Relation_OId__on(U_10386,U_10387) = hAPP(c_Product__Type_Oprod_Oprod__case(U_10386,U_10386,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_10386,tc_HOL_Obool,tc_fun(U_10386,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10386,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(U_10386,tc_HOL_Obool)),U_10386),c_COMBC(U_10386,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10386,tc_HOL_Obool),tc_fun(U_10386,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_10386),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10386),c_fconj)),c_fequal))),U_10387)),
inference(variable_rename,[status(thm)],[f_2812_1]) ).
cnf(f_2812_3,plain,
c_Relation_OId__on(U_10386,U_10387) = hAPP(c_Product__Type_Oprod_Oprod__case(U_10386,U_10386,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_10386,tc_HOL_Obool,tc_fun(U_10386,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10386,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(U_10386,tc_HOL_Obool)),U_10386),c_COMBC(U_10386,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10386,tc_HOL_Obool),tc_fun(U_10386,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_10386),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10386),c_fconj)),c_fequal))),U_10387)),
inference(clausify,[status(thm)],[f_2812_2]) ).
fof(f_2813_1,plain,
! [T_b] : c_Relation_OId__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Id__on__empty]) ).
fof(f_2813_2,plain,
! [U_10388] : c_Relation_OId__on(U_10388,c_Orderings_Obot__class_Obot(tc_fun(U_10388,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10388,U_10388),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2813_1]) ).
cnf(f_2813_3,plain,
c_Relation_OId__on(U_10388,c_Orderings_Obot__class_Obot(tc_fun(U_10388,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10388,U_10388),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2813_2]) ).
fof(f_2814_1,plain,
! [V_A_2,T_b,V_b_2,V_a_2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId__on(T_b,V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| V_a_2 != V_b_2 ),
inference(fof_nnf,[status(thm)],[fact_Id__on__eqI]) ).
fof(f_2814_2,plain,
! [U_10392,U_10391,U_10390,U_10389] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10391,U_10391)),hAPP(hAPP(c_Product__Type_OPair(U_10391,U_10391),U_10389),U_10390)),c_Relation_OId__on(U_10391,U_10392)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10391),U_10389),U_10392))
| U_10389 != U_10390 ),
inference(variable_rename,[status(thm)],[f_2814_1]) ).
cnf(f_2814_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10391,U_10391)),hAPP(hAPP(c_Product__Type_OPair(U_10391,U_10391),U_10389),U_10390)),c_Relation_OId__on(U_10391,U_10392)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10391),U_10389),U_10392))
| U_10389 != U_10390 ),
inference(clausify,[status(thm)],[f_2814_2]) ).
fof(f_2815_1,plain,
! [V_A_2,V_y_2,V_x_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| V_x_2 != V_y_2 )
& ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
& V_x_2 = V_y_2 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Id__on__iff]) ).
fof(f_2815_2,plain,
! [U_10396,U_10395,U_10394,U_10393] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10393,U_10393)),hAPP(hAPP(c_Product__Type_OPair(U_10393,U_10393),U_10394),U_10395)),c_Relation_OId__on(U_10393,U_10396)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10393),U_10394),U_10396))
| U_10394 != U_10395 )
& ( ( hBOOL(hAPP(hAPP(c_member(U_10393),U_10394),U_10396))
& U_10394 = U_10395 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10393,U_10393)),hAPP(hAPP(c_Product__Type_OPair(U_10393,U_10393),U_10394),U_10395)),c_Relation_OId__on(U_10393,U_10396))) ) ),
inference(variable_rename,[status(thm)],[f_2815_1]) ).
fof(f_2815_3,plain,
( ! [U_10404,U_10402,U_10400,U_10398] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10398,U_10398)),hAPP(hAPP(c_Product__Type_OPair(U_10398,U_10398),U_10400),U_10402)),c_Relation_OId__on(U_10398,U_10404)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10398),U_10400),U_10404))
| U_10400 != U_10402 )
& ! [U_10403,U_10401,U_10399,U_10397] :
( ( hBOOL(hAPP(hAPP(c_member(U_10397),U_10399),U_10403))
& U_10399 = U_10401 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10397,U_10397)),hAPP(hAPP(c_Product__Type_OPair(U_10397,U_10397),U_10399),U_10401)),c_Relation_OId__on(U_10397,U_10403))) ) ),
inference(miniscope,[status(thm)],[f_2815_2]) ).
cnf(f_2815_4,plain,
( U_10399 = U_10401
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10397,U_10397)),hAPP(hAPP(c_Product__Type_OPair(U_10397,U_10397),U_10399),U_10401)),c_Relation_OId__on(U_10397,U_10403))) ),
inference(clausify,[status(thm)],[f_2815_3]) ).
cnf(f_2815_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_10397),U_10399),U_10403))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10397,U_10397)),hAPP(hAPP(c_Product__Type_OPair(U_10397,U_10397),U_10399),U_10401)),c_Relation_OId__on(U_10397,U_10403))) ),
inference(clausify,[status(thm)],[f_2815_3]) ).
cnf(f_2815_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10398,U_10398)),hAPP(hAPP(c_Product__Type_OPair(U_10398,U_10398),U_10400),U_10402)),c_Relation_OId__on(U_10398,U_10404)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10398),U_10400),U_10404))
| U_10400 != U_10402 ),
inference(clausify,[status(thm)],[f_2815_3]) ).
fof(f_2816_1,plain,
! [V_a_2,V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_equiv__class__self]) ).
fof(f_2816_2,plain,
! [U_10408,U_10407,U_10406,U_10405] :
( hBOOL(hAPP(hAPP(c_member(U_10405),U_10408),hAPP(c_Relation_OImage(U_10405,U_10405,U_10407),hAPP(hAPP(c_Set_Oinsert(U_10405),U_10408),c_Orderings_Obot__class_Obot(tc_fun(U_10405,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_10405),U_10408),U_10406))
| ~ c_Equiv__Relations_Oequiv(U_10405,U_10406,U_10407) ),
inference(variable_rename,[status(thm)],[f_2816_1]) ).
cnf(f_2816_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_10405),U_10408),hAPP(c_Relation_OImage(U_10405,U_10405,U_10407),hAPP(hAPP(c_Set_Oinsert(U_10405),U_10408),c_Orderings_Obot__class_Obot(tc_fun(U_10405,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_10405),U_10408),U_10406))
| ~ c_Equiv__Relations_Oequiv(U_10405,U_10406,U_10407) ),
inference(clausify,[status(thm)],[f_2816_2]) ).
fof(f_2817_1,plain,
! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
| ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_equiv__class__eq]) ).
fof(f_2817_2,plain,
! [U_10413,U_10412,U_10411,U_10410,U_10409] :
( hAPP(c_Relation_OImage(U_10409,U_10409,U_10411),hAPP(hAPP(c_Set_Oinsert(U_10409),U_10412),c_Orderings_Obot__class_Obot(tc_fun(U_10409,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_10409,U_10409,U_10411),hAPP(hAPP(c_Set_Oinsert(U_10409),U_10413),c_Orderings_Obot__class_Obot(tc_fun(U_10409,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10409,U_10409)),hAPP(hAPP(c_Product__Type_OPair(U_10409,U_10409),U_10412),U_10413)),U_10411))
| ~ c_Equiv__Relations_Oequiv(U_10409,U_10410,U_10411) ),
inference(variable_rename,[status(thm)],[f_2817_1]) ).
cnf(f_2817_3,plain,
( hAPP(c_Relation_OImage(U_10409,U_10409,U_10411),hAPP(hAPP(c_Set_Oinsert(U_10409),U_10412),c_Orderings_Obot__class_Obot(tc_fun(U_10409,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_10409,U_10409,U_10411),hAPP(hAPP(c_Set_Oinsert(U_10409),U_10413),c_Orderings_Obot__class_Obot(tc_fun(U_10409,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10409,U_10409)),hAPP(hAPP(c_Product__Type_OPair(U_10409,U_10409),U_10412),U_10413)),U_10411))
| ~ c_Equiv__Relations_Oequiv(U_10409,U_10410,U_10411) ),
inference(clausify,[status(thm)],[f_2817_2]) ).
fof(f_2818_1,plain,
! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
( ( ( V_X_2 = V_Y_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
| V_X_2 != V_Y_2 ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
| ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_quotient__eq__iff]) ).
fof(f_2818_2,plain,
! [U_10420,U_10419,U_10418,U_10417,U_10416,U_10415,U_10414] :
( ( ( U_10417 = U_10418
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10414,U_10414)),hAPP(hAPP(c_Product__Type_OPair(U_10414,U_10414),U_10419),U_10420)),U_10416)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10414,U_10414)),hAPP(hAPP(c_Product__Type_OPair(U_10414,U_10414),U_10419),U_10420)),U_10416))
| U_10417 != U_10418 ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_10414),U_10420),U_10418))
| ~ hBOOL(hAPP(hAPP(c_member(U_10414),U_10419),U_10417))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10414,tc_HOL_Obool)),U_10418),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10414),U_10415),U_10416)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10414,tc_HOL_Obool)),U_10417),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10414),U_10415),U_10416)))
| ~ c_Equiv__Relations_Oequiv(U_10414,U_10415,U_10416) ),
inference(variable_rename,[status(thm)],[f_2818_1]) ).
cnf(f_2818_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10414,U_10414)),hAPP(hAPP(c_Product__Type_OPair(U_10414,U_10414),U_10419),U_10420)),U_10416))
| U_10417 != U_10418
| ~ hBOOL(hAPP(hAPP(c_member(U_10414),U_10420),U_10418))
| ~ hBOOL(hAPP(hAPP(c_member(U_10414),U_10419),U_10417))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10414,tc_HOL_Obool)),U_10418),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10414),U_10415),U_10416)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10414,tc_HOL_Obool)),U_10417),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10414),U_10415),U_10416)))
| ~ c_Equiv__Relations_Oequiv(U_10414,U_10415,U_10416) ),
inference(clausify,[status(thm)],[f_2818_2]) ).
cnf(f_2818_4,plain,
( U_10417 = U_10418
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10414,U_10414)),hAPP(hAPP(c_Product__Type_OPair(U_10414,U_10414),U_10419),U_10420)),U_10416))
| ~ hBOOL(hAPP(hAPP(c_member(U_10414),U_10420),U_10418))
| ~ hBOOL(hAPP(hAPP(c_member(U_10414),U_10419),U_10417))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10414,tc_HOL_Obool)),U_10418),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10414),U_10415),U_10416)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10414,tc_HOL_Obool)),U_10417),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10414),U_10415),U_10416)))
| ~ c_Equiv__Relations_Oequiv(U_10414,U_10415,U_10416) ),
inference(clausify,[status(thm)],[f_2818_2]) ).
fof(f_2819_1,plain,
! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
( V_X_2 = V_Y_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
| ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_quotient__eqI]) ).
fof(f_2819_2,plain,
! [U_10427,U_10426,U_10425,U_10424,U_10423,U_10422,U_10421] :
( U_10424 = U_10425
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10421,U_10421)),hAPP(hAPP(c_Product__Type_OPair(U_10421,U_10421),U_10426),U_10427)),U_10423))
| ~ hBOOL(hAPP(hAPP(c_member(U_10421),U_10427),U_10425))
| ~ hBOOL(hAPP(hAPP(c_member(U_10421),U_10426),U_10424))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10421,tc_HOL_Obool)),U_10425),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10421),U_10422),U_10423)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10421,tc_HOL_Obool)),U_10424),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10421),U_10422),U_10423)))
| ~ c_Equiv__Relations_Oequiv(U_10421,U_10422,U_10423) ),
inference(variable_rename,[status(thm)],[f_2819_1]) ).
cnf(f_2819_3,plain,
( U_10424 = U_10425
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10421,U_10421)),hAPP(hAPP(c_Product__Type_OPair(U_10421,U_10421),U_10426),U_10427)),U_10423))
| ~ hBOOL(hAPP(hAPP(c_member(U_10421),U_10427),U_10425))
| ~ hBOOL(hAPP(hAPP(c_member(U_10421),U_10426),U_10424))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10421,tc_HOL_Obool)),U_10425),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10421),U_10422),U_10423)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_10421,tc_HOL_Obool)),U_10424),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10421),U_10422),U_10423)))
| ~ c_Equiv__Relations_Oequiv(U_10421,U_10422,U_10423) ),
inference(clausify,[status(thm)],[f_2819_2]) ).
fof(f_2820_1,plain,
! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
| ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
| hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_eq__equiv__class]) ).
fof(f_2820_2,plain,
! [U_10432,U_10431,U_10430,U_10429,U_10428] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10428,U_10428)),hAPP(hAPP(c_Product__Type_OPair(U_10428,U_10428),U_10430),U_10431)),U_10429))
| ~ hBOOL(hAPP(hAPP(c_member(U_10428),U_10431),U_10432))
| ~ c_Equiv__Relations_Oequiv(U_10428,U_10432,U_10429)
| hAPP(c_Relation_OImage(U_10428,U_10428,U_10429),hAPP(hAPP(c_Set_Oinsert(U_10428),U_10430),c_Orderings_Obot__class_Obot(tc_fun(U_10428,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_10428,U_10428,U_10429),hAPP(hAPP(c_Set_Oinsert(U_10428),U_10431),c_Orderings_Obot__class_Obot(tc_fun(U_10428,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_2820_1]) ).
cnf(f_2820_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10428,U_10428)),hAPP(hAPP(c_Product__Type_OPair(U_10428,U_10428),U_10430),U_10431)),U_10429))
| ~ hBOOL(hAPP(hAPP(c_member(U_10428),U_10431),U_10432))
| ~ c_Equiv__Relations_Oequiv(U_10428,U_10432,U_10429)
| hAPP(c_Relation_OImage(U_10428,U_10428,U_10429),hAPP(hAPP(c_Set_Oinsert(U_10428),U_10430),c_Orderings_Obot__class_Obot(tc_fun(U_10428,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_10428,U_10428,U_10429),hAPP(hAPP(c_Set_Oinsert(U_10428),U_10431),c_Orderings_Obot__class_Obot(tc_fun(U_10428,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_2820_2]) ).
fof(f_2821_1,plain,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
( ( ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
| hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff]) ).
fof(f_2821_2,plain,
! [U_10437,U_10436,U_10435,U_10434,U_10433] :
( ( ( hAPP(c_Relation_OImage(U_10433,U_10433,U_10435),hAPP(hAPP(c_Set_Oinsert(U_10433),U_10436),c_Orderings_Obot__class_Obot(tc_fun(U_10433,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_10433,U_10433,U_10435),hAPP(hAPP(c_Set_Oinsert(U_10433),U_10437),c_Orderings_Obot__class_Obot(tc_fun(U_10433,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10433,U_10433)),hAPP(hAPP(c_Product__Type_OPair(U_10433,U_10433),U_10436),U_10437)),U_10435)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10433,U_10433)),hAPP(hAPP(c_Product__Type_OPair(U_10433,U_10433),U_10436),U_10437)),U_10435))
| hAPP(c_Relation_OImage(U_10433,U_10433,U_10435),hAPP(hAPP(c_Set_Oinsert(U_10433),U_10436),c_Orderings_Obot__class_Obot(tc_fun(U_10433,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_10433,U_10433,U_10435),hAPP(hAPP(c_Set_Oinsert(U_10433),U_10437),c_Orderings_Obot__class_Obot(tc_fun(U_10433,tc_HOL_Obool)))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_10433),U_10437),U_10434))
| ~ hBOOL(hAPP(hAPP(c_member(U_10433),U_10436),U_10434))
| ~ c_Equiv__Relations_Oequiv(U_10433,U_10434,U_10435) ),
inference(variable_rename,[status(thm)],[f_2821_1]) ).
cnf(f_2821_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10433,U_10433)),hAPP(hAPP(c_Product__Type_OPair(U_10433,U_10433),U_10436),U_10437)),U_10435))
| hAPP(c_Relation_OImage(U_10433,U_10433,U_10435),hAPP(hAPP(c_Set_Oinsert(U_10433),U_10436),c_Orderings_Obot__class_Obot(tc_fun(U_10433,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_10433,U_10433,U_10435),hAPP(hAPP(c_Set_Oinsert(U_10433),U_10437),c_Orderings_Obot__class_Obot(tc_fun(U_10433,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(U_10433),U_10437),U_10434))
| ~ hBOOL(hAPP(hAPP(c_member(U_10433),U_10436),U_10434))
| ~ c_Equiv__Relations_Oequiv(U_10433,U_10434,U_10435) ),
inference(clausify,[status(thm)],[f_2821_2]) ).
cnf(f_2821_4,plain,
( hAPP(c_Relation_OImage(U_10433,U_10433,U_10435),hAPP(hAPP(c_Set_Oinsert(U_10433),U_10436),c_Orderings_Obot__class_Obot(tc_fun(U_10433,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_10433,U_10433,U_10435),hAPP(hAPP(c_Set_Oinsert(U_10433),U_10437),c_Orderings_Obot__class_Obot(tc_fun(U_10433,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10433,U_10433)),hAPP(hAPP(c_Product__Type_OPair(U_10433,U_10433),U_10436),U_10437)),U_10435))
| ~ hBOOL(hAPP(hAPP(c_member(U_10433),U_10437),U_10434))
| ~ hBOOL(hAPP(hAPP(c_member(U_10433),U_10436),U_10434))
| ~ c_Equiv__Relations_Oequiv(U_10433,U_10434,U_10435) ),
inference(clausify,[status(thm)],[f_2821_2]) ).
fof(f_2822_1,plain,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) )
& ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
& hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) )
| ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_equiv__class__eq__iff]) ).
fof(f_2822_2,plain,
! [U_10442,U_10441,U_10440,U_10439,U_10438] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10438,U_10438)),hAPP(hAPP(c_Product__Type_OPair(U_10438,U_10438),U_10441),U_10442)),U_10440))
| ~ hBOOL(hAPP(hAPP(c_member(U_10438),U_10442),U_10439))
| ~ hBOOL(hAPP(hAPP(c_member(U_10438),U_10441),U_10439))
| hAPP(c_Relation_OImage(U_10438,U_10438,U_10440),hAPP(hAPP(c_Set_Oinsert(U_10438),U_10441),c_Orderings_Obot__class_Obot(tc_fun(U_10438,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_10438,U_10438,U_10440),hAPP(hAPP(c_Set_Oinsert(U_10438),U_10442),c_Orderings_Obot__class_Obot(tc_fun(U_10438,tc_HOL_Obool)))) )
& ( ( hBOOL(hAPP(hAPP(c_member(U_10438),U_10442),U_10439))
& hBOOL(hAPP(hAPP(c_member(U_10438),U_10441),U_10439))
& hAPP(c_Relation_OImage(U_10438,U_10438,U_10440),hAPP(hAPP(c_Set_Oinsert(U_10438),U_10441),c_Orderings_Obot__class_Obot(tc_fun(U_10438,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_10438,U_10438,U_10440),hAPP(hAPP(c_Set_Oinsert(U_10438),U_10442),c_Orderings_Obot__class_Obot(tc_fun(U_10438,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10438,U_10438)),hAPP(hAPP(c_Product__Type_OPair(U_10438,U_10438),U_10441),U_10442)),U_10440)) ) )
| ~ c_Equiv__Relations_Oequiv(U_10438,U_10439,U_10440) ),
inference(variable_rename,[status(thm)],[f_2822_1]) ).
cnf(f_2822_3,plain,
( hAPP(c_Relation_OImage(U_10438,U_10438,U_10440),hAPP(hAPP(c_Set_Oinsert(U_10438),U_10441),c_Orderings_Obot__class_Obot(tc_fun(U_10438,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_10438,U_10438,U_10440),hAPP(hAPP(c_Set_Oinsert(U_10438),U_10442),c_Orderings_Obot__class_Obot(tc_fun(U_10438,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10438,U_10438)),hAPP(hAPP(c_Product__Type_OPair(U_10438,U_10438),U_10441),U_10442)),U_10440))
| ~ c_Equiv__Relations_Oequiv(U_10438,U_10439,U_10440) ),
inference(clausify,[status(thm)],[f_2822_2]) ).
cnf(f_2822_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_10438),U_10441),U_10439))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10438,U_10438)),hAPP(hAPP(c_Product__Type_OPair(U_10438,U_10438),U_10441),U_10442)),U_10440))
| ~ c_Equiv__Relations_Oequiv(U_10438,U_10439,U_10440) ),
inference(clausify,[status(thm)],[f_2822_2]) ).
cnf(f_2822_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_10438),U_10442),U_10439))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10438,U_10438)),hAPP(hAPP(c_Product__Type_OPair(U_10438,U_10438),U_10441),U_10442)),U_10440))
| ~ c_Equiv__Relations_Oequiv(U_10438,U_10439,U_10440) ),
inference(clausify,[status(thm)],[f_2822_2]) ).
cnf(f_2822_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10438,U_10438)),hAPP(hAPP(c_Product__Type_OPair(U_10438,U_10438),U_10441),U_10442)),U_10440))
| ~ hBOOL(hAPP(hAPP(c_member(U_10438),U_10442),U_10439))
| ~ hBOOL(hAPP(hAPP(c_member(U_10438),U_10441),U_10439))
| hAPP(c_Relation_OImage(U_10438,U_10438,U_10440),hAPP(hAPP(c_Set_Oinsert(U_10438),U_10441),c_Orderings_Obot__class_Obot(tc_fun(U_10438,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_10438,U_10438,U_10440),hAPP(hAPP(c_Set_Oinsert(U_10438),U_10442),c_Orderings_Obot__class_Obot(tc_fun(U_10438,tc_HOL_Obool))))
| ~ c_Equiv__Relations_Oequiv(U_10438,U_10439,U_10440) ),
inference(clausify,[status(thm)],[f_2822_2]) ).
fof(f_2823_1,plain,
! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
| ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_equiv__class__subset]) ).
fof(f_2823_2,plain,
! [U_10447,U_10446,U_10445,U_10444,U_10443] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10443,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10443,U_10443,U_10445),hAPP(hAPP(c_Set_Oinsert(U_10443),U_10446),c_Orderings_Obot__class_Obot(tc_fun(U_10443,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_10443,U_10443,U_10445),hAPP(hAPP(c_Set_Oinsert(U_10443),U_10447),c_Orderings_Obot__class_Obot(tc_fun(U_10443,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10443,U_10443)),hAPP(hAPP(c_Product__Type_OPair(U_10443,U_10443),U_10446),U_10447)),U_10445))
| ~ c_Equiv__Relations_Oequiv(U_10443,U_10444,U_10445) ),
inference(variable_rename,[status(thm)],[f_2823_1]) ).
cnf(f_2823_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10443,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10443,U_10443,U_10445),hAPP(hAPP(c_Set_Oinsert(U_10443),U_10446),c_Orderings_Obot__class_Obot(tc_fun(U_10443,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_10443,U_10443,U_10445),hAPP(hAPP(c_Set_Oinsert(U_10443),U_10447),c_Orderings_Obot__class_Obot(tc_fun(U_10443,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10443,U_10443)),hAPP(hAPP(c_Product__Type_OPair(U_10443,U_10443),U_10446),U_10447)),U_10445))
| ~ c_Equiv__Relations_Oequiv(U_10443,U_10444,U_10445) ),
inference(clausify,[status(thm)],[f_2823_2]) ).
fof(f_2824_1,plain,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
( ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) != hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff2]) ).
fof(f_2824_2,plain,
! [U_10452,U_10451,U_10450,U_10449,U_10448] :
( ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10448),hAPP(hAPP(c_Set_Oinsert(U_10448),U_10451),c_Orderings_Obot__class_Obot(tc_fun(U_10448,tc_HOL_Obool)))),U_10450) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10448),hAPP(hAPP(c_Set_Oinsert(U_10448),U_10452),c_Orderings_Obot__class_Obot(tc_fun(U_10448,tc_HOL_Obool)))),U_10450)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10448,U_10448)),hAPP(hAPP(c_Product__Type_OPair(U_10448,U_10448),U_10451),U_10452)),U_10450)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10448,U_10448)),hAPP(hAPP(c_Product__Type_OPair(U_10448,U_10448),U_10451),U_10452)),U_10450))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10448),hAPP(hAPP(c_Set_Oinsert(U_10448),U_10451),c_Orderings_Obot__class_Obot(tc_fun(U_10448,tc_HOL_Obool)))),U_10450) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10448),hAPP(hAPP(c_Set_Oinsert(U_10448),U_10452),c_Orderings_Obot__class_Obot(tc_fun(U_10448,tc_HOL_Obool)))),U_10450) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_10448),U_10452),U_10449))
| ~ hBOOL(hAPP(hAPP(c_member(U_10448),U_10451),U_10449))
| ~ c_Equiv__Relations_Oequiv(U_10448,U_10449,U_10450) ),
inference(variable_rename,[status(thm)],[f_2824_1]) ).
cnf(f_2824_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10448,U_10448)),hAPP(hAPP(c_Product__Type_OPair(U_10448,U_10448),U_10451),U_10452)),U_10450))
| hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10448),hAPP(hAPP(c_Set_Oinsert(U_10448),U_10451),c_Orderings_Obot__class_Obot(tc_fun(U_10448,tc_HOL_Obool)))),U_10450) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10448),hAPP(hAPP(c_Set_Oinsert(U_10448),U_10452),c_Orderings_Obot__class_Obot(tc_fun(U_10448,tc_HOL_Obool)))),U_10450)
| ~ hBOOL(hAPP(hAPP(c_member(U_10448),U_10452),U_10449))
| ~ hBOOL(hAPP(hAPP(c_member(U_10448),U_10451),U_10449))
| ~ c_Equiv__Relations_Oequiv(U_10448,U_10449,U_10450) ),
inference(clausify,[status(thm)],[f_2824_2]) ).
cnf(f_2824_4,plain,
( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10448),hAPP(hAPP(c_Set_Oinsert(U_10448),U_10451),c_Orderings_Obot__class_Obot(tc_fun(U_10448,tc_HOL_Obool)))),U_10450) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_10448),hAPP(hAPP(c_Set_Oinsert(U_10448),U_10452),c_Orderings_Obot__class_Obot(tc_fun(U_10448,tc_HOL_Obool)))),U_10450)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10448,U_10448)),hAPP(hAPP(c_Product__Type_OPair(U_10448,U_10448),U_10451),U_10452)),U_10450))
| ~ hBOOL(hAPP(hAPP(c_member(U_10448),U_10452),U_10449))
| ~ hBOOL(hAPP(hAPP(c_member(U_10448),U_10451),U_10449))
| ~ c_Equiv__Relations_Oequiv(U_10448,U_10449,U_10450) ),
inference(clausify,[status(thm)],[f_2824_2]) ).
fof(f_2825_1,plain,
! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
| ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_UN__equiv__class]) ).
fof(f_2825_2,plain,
! [U_10458,U_10457,U_10456,U_10455,U_10454,U_10453] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10453,tc_fun(U_10456,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10453,U_10453,U_10455),hAPP(hAPP(c_Set_Oinsert(U_10453),U_10458),c_Orderings_Obot__class_Obot(tc_fun(U_10453,tc_HOL_Obool))))),U_10457) = hAPP(U_10457,U_10458)
| ~ hBOOL(hAPP(hAPP(c_member(U_10453),U_10458),U_10454))
| ~ c_Equiv__Relations_Ocongruent(U_10453,tc_fun(U_10456,tc_HOL_Obool),U_10455,U_10457)
| ~ c_Equiv__Relations_Oequiv(U_10453,U_10454,U_10455) ),
inference(variable_rename,[status(thm)],[f_2825_1]) ).
cnf(f_2825_3,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10453,tc_fun(U_10456,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10453,U_10453,U_10455),hAPP(hAPP(c_Set_Oinsert(U_10453),U_10458),c_Orderings_Obot__class_Obot(tc_fun(U_10453,tc_HOL_Obool))))),U_10457) = hAPP(U_10457,U_10458)
| ~ hBOOL(hAPP(hAPP(c_member(U_10453),U_10458),U_10454))
| ~ c_Equiv__Relations_Ocongruent(U_10453,tc_fun(U_10456,tc_HOL_Obool),U_10455,U_10457)
| ~ c_Equiv__Relations_Oequiv(U_10453,U_10454,U_10455) ),
inference(clausify,[status(thm)],[f_2825_2]) ).
fof(f_2826_1,plain,
! [V_a2_2,V_a1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
| ~ c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
| ~ c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
| ~ c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) ),
inference(fof_nnf,[status(thm)],[fact_UN__equiv__class2]) ).
fof(f_2826_2,plain,
! [U_10468,U_10467,U_10466,U_10465,U_10464,U_10463,U_10462,U_10461,U_10460,U_10459] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10459,tc_fun(U_10465,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10459,U_10459,U_10461),hAPP(hAPP(c_Set_Oinsert(U_10459),U_10467),c_Orderings_Obot__class_Obot(tc_fun(U_10459,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_10462,tc_fun(U_10465,tc_HOL_Obool)),tc_fun(U_10465,tc_HOL_Obool),U_10459),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10462,tc_fun(U_10465,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10462,U_10462,U_10464),hAPP(hAPP(c_Set_Oinsert(U_10462),U_10468),c_Orderings_Obot__class_Obot(tc_fun(U_10462,tc_HOL_Obool)))))),U_10466)) = hAPP(hAPP(U_10466,U_10467),U_10468)
| ~ hBOOL(hAPP(hAPP(c_member(U_10462),U_10468),U_10463))
| ~ hBOOL(hAPP(hAPP(c_member(U_10459),U_10467),U_10460))
| ~ c_Equiv__Relations_Ocongruent2(U_10459,U_10462,tc_fun(U_10465,tc_HOL_Obool),U_10461,U_10464,U_10466)
| ~ c_Equiv__Relations_Oequiv(U_10462,U_10463,U_10464)
| ~ c_Equiv__Relations_Oequiv(U_10459,U_10460,U_10461) ),
inference(variable_rename,[status(thm)],[f_2826_1]) ).
cnf(f_2826_3,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10459,tc_fun(U_10465,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10459,U_10459,U_10461),hAPP(hAPP(c_Set_Oinsert(U_10459),U_10467),c_Orderings_Obot__class_Obot(tc_fun(U_10459,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_10462,tc_fun(U_10465,tc_HOL_Obool)),tc_fun(U_10465,tc_HOL_Obool),U_10459),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10462,tc_fun(U_10465,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10462,U_10462,U_10464),hAPP(hAPP(c_Set_Oinsert(U_10462),U_10468),c_Orderings_Obot__class_Obot(tc_fun(U_10462,tc_HOL_Obool)))))),U_10466)) = hAPP(hAPP(U_10466,U_10467),U_10468)
| ~ hBOOL(hAPP(hAPP(c_member(U_10462),U_10468),U_10463))
| ~ hBOOL(hAPP(hAPP(c_member(U_10459),U_10467),U_10460))
| ~ c_Equiv__Relations_Ocongruent2(U_10459,U_10462,tc_fun(U_10465,tc_HOL_Obool),U_10461,U_10464,U_10466)
| ~ c_Equiv__Relations_Oequiv(U_10462,U_10463,U_10464)
| ~ c_Equiv__Relations_Oequiv(U_10459,U_10460,U_10461) ),
inference(clausify,[status(thm)],[f_2826_2]) ).
fof(f_2827_1,plain,
! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
| ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_equiv__class__nondisjoint]) ).
fof(f_2827_2,plain,
! [U_10474,U_10473,U_10472,U_10471,U_10470,U_10469] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10469,U_10469)),hAPP(hAPP(c_Product__Type_OPair(U_10469,U_10469),U_10473),U_10474)),U_10471))
| ~ hBOOL(hAPP(hAPP(c_member(U_10469),U_10472),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10469,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10469,U_10469,U_10471),hAPP(hAPP(c_Set_Oinsert(U_10469),U_10473),c_Orderings_Obot__class_Obot(tc_fun(U_10469,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_10469,U_10469,U_10471),hAPP(hAPP(c_Set_Oinsert(U_10469),U_10474),c_Orderings_Obot__class_Obot(tc_fun(U_10469,tc_HOL_Obool)))))))
| ~ c_Equiv__Relations_Oequiv(U_10469,U_10470,U_10471) ),
inference(variable_rename,[status(thm)],[f_2827_1]) ).
cnf(f_2827_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10469,U_10469)),hAPP(hAPP(c_Product__Type_OPair(U_10469,U_10469),U_10473),U_10474)),U_10471))
| ~ hBOOL(hAPP(hAPP(c_member(U_10469),U_10472),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10469,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10469,U_10469,U_10471),hAPP(hAPP(c_Set_Oinsert(U_10469),U_10473),c_Orderings_Obot__class_Obot(tc_fun(U_10469,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_10469,U_10469,U_10471),hAPP(hAPP(c_Set_Oinsert(U_10469),U_10474),c_Orderings_Obot__class_Obot(tc_fun(U_10469,tc_HOL_Obool)))))))
| ~ c_Equiv__Relations_Oequiv(U_10469,U_10470,U_10471) ),
inference(clausify,[status(thm)],[f_2827_2]) ).
fof(f_2828_1,plain,
! [V_x_2,V_B_2,V_A_2,T_b] :
( ( hBOOL(hAPP(V_B_2,V_x_2))
& hBOOL(hAPP(V_A_2,V_x_2)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf1E]) ).
fof(f_2828_2,plain,
! [U_10478,U_10477,U_10476,U_10475] :
( ( hBOOL(hAPP(U_10477,U_10478))
& hBOOL(hAPP(U_10476,U_10478)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10475,tc_HOL_Obool)),U_10476),U_10477),U_10478)) ),
inference(variable_rename,[status(thm)],[f_2828_1]) ).
fof(f_2828_3,plain,
! [U_10478,U_10477,U_10476] :
( ! [U_10475] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10475,tc_HOL_Obool)),U_10476),U_10477),U_10478))
| ( hBOOL(hAPP(U_10477,U_10478))
& hBOOL(hAPP(U_10476,U_10478)) ) ),
inference(miniscope,[status(thm)],[f_2828_2]) ).
cnf(f_2828_4,plain,
( hBOOL(hAPP(U_10476,U_10478))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10475,tc_HOL_Obool)),U_10476),U_10477),U_10478)) ),
inference(clausify,[status(thm)],[f_2828_3]) ).
cnf(f_2828_5,plain,
( hBOOL(hAPP(U_10477,U_10478))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10475,tc_HOL_Obool)),U_10476),U_10477),U_10478)) ),
inference(clausify,[status(thm)],[f_2828_3]) ).
fof(f_2829_1,plain,
! [T_b,V_B_2,V_x_2,V_A_2] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
| ~ hBOOL(hAPP(V_B_2,V_x_2))
| ~ hBOOL(hAPP(V_A_2,V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf1I]) ).
fof(f_2829_2,plain,
! [U_10482,U_10481,U_10480,U_10479] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10482,tc_HOL_Obool)),U_10479),U_10481),U_10480))
| ~ hBOOL(hAPP(U_10481,U_10480))
| ~ hBOOL(hAPP(U_10479,U_10480)) ),
inference(variable_rename,[status(thm)],[f_2829_1]) ).
cnf(f_2829_3,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10482,tc_HOL_Obool)),U_10479),U_10481),U_10480))
| ~ hBOOL(hAPP(U_10481,U_10480))
| ~ hBOOL(hAPP(U_10479,U_10480)) ),
inference(clausify,[status(thm)],[f_2829_2]) ).
fof(f_2830_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_IntE]) ).
fof(f_2830_2,plain,
! [U_10486,U_10485,U_10484,U_10483] :
( ( hBOOL(hAPP(hAPP(c_member(U_10483),U_10484),U_10486))
& hBOOL(hAPP(hAPP(c_member(U_10483),U_10484),U_10485)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_10483),U_10484),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10483,tc_HOL_Obool)),U_10485),U_10486))) ),
inference(variable_rename,[status(thm)],[f_2830_1]) ).
cnf(f_2830_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_10483),U_10484),U_10485))
| ~ hBOOL(hAPP(hAPP(c_member(U_10483),U_10484),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10483,tc_HOL_Obool)),U_10485),U_10486))) ),
inference(clausify,[status(thm)],[f_2830_2]) ).
cnf(f_2830_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_10483),U_10484),U_10486))
| ~ hBOOL(hAPP(hAPP(c_member(U_10483),U_10484),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10483,tc_HOL_Obool)),U_10485),U_10486))) ),
inference(clausify,[status(thm)],[f_2830_2]) ).
fof(f_2831_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_IntI]) ).
fof(f_2831_2,plain,
! [U_10490,U_10489,U_10488,U_10487] :
( hBOOL(hAPP(hAPP(c_member(U_10487),U_10488),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10487,tc_HOL_Obool)),U_10489),U_10490)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10487),U_10488),U_10490))
| ~ hBOOL(hAPP(hAPP(c_member(U_10487),U_10488),U_10489)) ),
inference(variable_rename,[status(thm)],[f_2831_1]) ).
cnf(f_2831_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_10487),U_10488),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10487,tc_HOL_Obool)),U_10489),U_10490)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10487),U_10488),U_10490))
| ~ hBOOL(hAPP(hAPP(c_member(U_10487),U_10488),U_10489)) ),
inference(clausify,[status(thm)],[f_2831_2]) ).
fof(f_2832_1,plain,
! [V_G_2,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_G_2)))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2))
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Int]) ).
fof(f_2832_2,plain,
! [U_10493,U_10492,U_10491] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10491),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10491,tc_HOL_Obool)),U_10492),U_10493)))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10491),U_10493))
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10491),U_10492)) ) ),
inference(variable_rename,[status(thm)],[f_2832_1]) ).
cnf(f_2832_3,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10491),U_10492))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_10491),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10491,tc_HOL_Obool)),U_10492),U_10493))) ),
inference(clausify,[status(thm)],[f_2832_2]) ).
cnf(f_2832_4,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10491),U_10493))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_10491),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10491,tc_HOL_Obool)),U_10492),U_10493))) ),
inference(clausify,[status(thm)],[f_2832_2]) ).
fof(f_2833_1,plain,
! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))),
inference(fof_nnf,[status(thm)],[fact_Int__UN__distrib2]) ).
fof(f_2833_2,plain,
! [U_10500,U_10499,U_10498,U_10497,U_10496,U_10495,U_10494] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10494,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10495,tc_fun(U_10494,tc_HOL_Obool)),U_10496),U_10497)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10498,tc_fun(U_10494,tc_HOL_Obool)),U_10499),U_10500)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10495,tc_fun(U_10494,tc_HOL_Obool)),U_10496),hAPP(hAPP(c_COMBB(tc_fun(U_10498,tc_fun(U_10494,tc_HOL_Obool)),tc_fun(U_10494,tc_HOL_Obool),U_10495),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10498,tc_fun(U_10494,tc_HOL_Obool)),U_10499)),hAPP(hAPP(c_COMBC(U_10495,tc_fun(U_10498,tc_fun(U_10494,tc_HOL_Obool)),tc_fun(U_10498,tc_fun(U_10494,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10494,tc_HOL_Obool),tc_fun(U_10494,tc_HOL_Obool)),tc_fun(tc_fun(U_10498,tc_fun(U_10494,tc_HOL_Obool)),tc_fun(U_10498,tc_fun(U_10494,tc_HOL_Obool))),U_10495),c_COMBB(tc_fun(U_10494,tc_HOL_Obool),tc_fun(U_10494,tc_HOL_Obool),U_10498)),hAPP(hAPP(c_COMBB(tc_fun(U_10494,tc_HOL_Obool),tc_fun(tc_fun(U_10494,tc_HOL_Obool),tc_fun(U_10494,tc_HOL_Obool)),U_10495),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10494,tc_HOL_Obool))),U_10497))),U_10500))),
inference(variable_rename,[status(thm)],[f_2833_1]) ).
cnf(f_2833_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10494,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10495,tc_fun(U_10494,tc_HOL_Obool)),U_10496),U_10497)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10498,tc_fun(U_10494,tc_HOL_Obool)),U_10499),U_10500)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10495,tc_fun(U_10494,tc_HOL_Obool)),U_10496),hAPP(hAPP(c_COMBB(tc_fun(U_10498,tc_fun(U_10494,tc_HOL_Obool)),tc_fun(U_10494,tc_HOL_Obool),U_10495),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10498,tc_fun(U_10494,tc_HOL_Obool)),U_10499)),hAPP(hAPP(c_COMBC(U_10495,tc_fun(U_10498,tc_fun(U_10494,tc_HOL_Obool)),tc_fun(U_10498,tc_fun(U_10494,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10494,tc_HOL_Obool),tc_fun(U_10494,tc_HOL_Obool)),tc_fun(tc_fun(U_10498,tc_fun(U_10494,tc_HOL_Obool)),tc_fun(U_10498,tc_fun(U_10494,tc_HOL_Obool))),U_10495),c_COMBB(tc_fun(U_10494,tc_HOL_Obool),tc_fun(U_10494,tc_HOL_Obool),U_10498)),hAPP(hAPP(c_COMBB(tc_fun(U_10494,tc_HOL_Obool),tc_fun(tc_fun(U_10494,tc_HOL_Obool),tc_fun(U_10494,tc_HOL_Obool)),U_10495),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10494,tc_HOL_Obool))),U_10497))),U_10500))),
inference(clausify,[status(thm)],[f_2833_2]) ).
fof(f_2834_1,plain,
! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I4_J]) ).
fof(f_2834_2,plain,
! [U_10505,U_10504,U_10503,U_10502,U_10501] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10501,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10502,tc_fun(U_10501,tc_HOL_Obool)),U_10503),U_10504)),U_10505) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10502,tc_fun(U_10501,tc_HOL_Obool)),U_10503),hAPP(hAPP(c_COMBC(U_10502,tc_fun(U_10501,tc_HOL_Obool),tc_fun(U_10501,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10501,tc_HOL_Obool),tc_fun(tc_fun(U_10501,tc_HOL_Obool),tc_fun(U_10501,tc_HOL_Obool)),U_10502),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10501,tc_HOL_Obool))),U_10504)),U_10505)),
inference(variable_rename,[status(thm)],[f_2834_1]) ).
cnf(f_2834_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10501,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10502,tc_fun(U_10501,tc_HOL_Obool)),U_10503),U_10504)),U_10505) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10502,tc_fun(U_10501,tc_HOL_Obool)),U_10503),hAPP(hAPP(c_COMBC(U_10502,tc_fun(U_10501,tc_HOL_Obool),tc_fun(U_10501,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10501,tc_HOL_Obool),tc_fun(tc_fun(U_10501,tc_HOL_Obool),tc_fun(U_10501,tc_HOL_Obool)),U_10502),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10501,tc_HOL_Obool))),U_10504)),U_10505)),
inference(clausify,[status(thm)],[f_2834_2]) ).
fof(f_2835_1,plain,
! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Int__UN__distrib]) ).
fof(f_2835_2,plain,
! [U_10510,U_10509,U_10508,U_10507,U_10506] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10506,tc_HOL_Obool)),U_10507),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10508,tc_fun(U_10506,tc_HOL_Obool)),U_10509),U_10510)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10508,tc_fun(U_10506,tc_HOL_Obool)),U_10509),hAPP(hAPP(c_COMBB(tc_fun(U_10506,tc_HOL_Obool),tc_fun(U_10506,tc_HOL_Obool),U_10508),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10506,tc_HOL_Obool)),U_10507)),U_10510)),
inference(variable_rename,[status(thm)],[f_2835_1]) ).
cnf(f_2835_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10506,tc_HOL_Obool)),U_10507),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10508,tc_fun(U_10506,tc_HOL_Obool)),U_10509),U_10510)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10508,tc_fun(U_10506,tc_HOL_Obool)),U_10509),hAPP(hAPP(c_COMBB(tc_fun(U_10506,tc_HOL_Obool),tc_fun(U_10506,tc_HOL_Obool),U_10508),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10506,tc_HOL_Obool)),U_10507)),U_10510)),
inference(clausify,[status(thm)],[f_2835_2]) ).
fof(f_2836_1,plain,
! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I5_J]) ).
fof(f_2836_2,plain,
! [U_10515,U_10514,U_10513,U_10512,U_10511] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10511,tc_HOL_Obool)),U_10512),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10513,tc_fun(U_10511,tc_HOL_Obool)),U_10514),U_10515)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10513,tc_fun(U_10511,tc_HOL_Obool)),U_10514),hAPP(hAPP(c_COMBB(tc_fun(U_10511,tc_HOL_Obool),tc_fun(U_10511,tc_HOL_Obool),U_10513),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10511,tc_HOL_Obool)),U_10512)),U_10515)),
inference(variable_rename,[status(thm)],[f_2836_1]) ).
cnf(f_2836_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10511,tc_HOL_Obool)),U_10512),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10513,tc_fun(U_10511,tc_HOL_Obool)),U_10514),U_10515)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10513,tc_fun(U_10511,tc_HOL_Obool)),U_10514),hAPP(hAPP(c_COMBB(tc_fun(U_10511,tc_HOL_Obool),tc_fun(U_10511,tc_HOL_Obool),U_10513),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10511,tc_HOL_Obool)),U_10512)),U_10515)),
inference(clausify,[status(thm)],[f_2836_2]) ).
fof(f_2837_1,plain,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I4_J]) ).
fof(f_2837_2,plain,
! [U_10520,U_10519,U_10518,U_10517,U_10516] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10516,tc_fun(U_10517,tc_HOL_Obool)),U_10518),hAPP(hAPP(c_COMBC(U_10516,tc_fun(U_10517,tc_HOL_Obool),tc_fun(U_10517,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10517,tc_HOL_Obool),tc_fun(tc_fun(U_10517,tc_HOL_Obool),tc_fun(U_10517,tc_HOL_Obool)),U_10516),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10517,tc_HOL_Obool))),U_10519)),U_10520)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10517,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10516,tc_fun(U_10517,tc_HOL_Obool)),U_10518),U_10519)),U_10520),
inference(variable_rename,[status(thm)],[f_2837_1]) ).
cnf(f_2837_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10516,tc_fun(U_10517,tc_HOL_Obool)),U_10518),hAPP(hAPP(c_COMBC(U_10516,tc_fun(U_10517,tc_HOL_Obool),tc_fun(U_10517,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10517,tc_HOL_Obool),tc_fun(tc_fun(U_10517,tc_HOL_Obool),tc_fun(U_10517,tc_HOL_Obool)),U_10516),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10517,tc_HOL_Obool))),U_10519)),U_10520)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10517,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10516,tc_fun(U_10517,tc_HOL_Obool)),U_10518),U_10519)),U_10520),
inference(clausify,[status(thm)],[f_2837_2]) ).
fof(f_2838_1,plain,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I5_J]) ).
fof(f_2838_2,plain,
! [U_10525,U_10524,U_10523,U_10522,U_10521] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10521,tc_fun(U_10522,tc_HOL_Obool)),U_10523),hAPP(hAPP(c_COMBB(tc_fun(U_10522,tc_HOL_Obool),tc_fun(U_10522,tc_HOL_Obool),U_10521),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10522,tc_HOL_Obool)),U_10524)),U_10525)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10522,tc_HOL_Obool)),U_10524),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10521,tc_fun(U_10522,tc_HOL_Obool)),U_10523),U_10525)),
inference(variable_rename,[status(thm)],[f_2838_1]) ).
cnf(f_2838_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10521,tc_fun(U_10522,tc_HOL_Obool)),U_10523),hAPP(hAPP(c_COMBB(tc_fun(U_10522,tc_HOL_Obool),tc_fun(U_10522,tc_HOL_Obool),U_10521),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10522,tc_HOL_Obool)),U_10524)),U_10525)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10522,tc_HOL_Obool)),U_10524),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_10521,tc_fun(U_10522,tc_HOL_Obool)),U_10523),U_10525)),
inference(clausify,[status(thm)],[f_2838_2]) ).
fof(f_2839_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Pow__Int__eq]) ).
fof(f_2839_2,plain,
! [U_10528,U_10527,U_10526] : hAPP(c_Set_OPow(U_10526),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10526,tc_HOL_Obool)),U_10527),U_10528)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_10526,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_10526),U_10527)),hAPP(c_Set_OPow(U_10526),U_10528)),
inference(variable_rename,[status(thm)],[f_2839_1]) ).
cnf(f_2839_3,plain,
hAPP(c_Set_OPow(U_10526),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10526,tc_HOL_Obool)),U_10527),U_10528)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_10526,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_10526),U_10527)),hAPP(c_Set_OPow(U_10526),U_10528)),
inference(clausify,[status(thm)],[f_2839_2]) ).
fof(f_2840_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_2840_2,plain,
! [U_10530,U_10529] :
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_10529),U_10530))
| ~ c_Nat__Transfer_Onat__set(U_10530)
| ~ c_Nat__Transfer_Onat__set(U_10529) ),
inference(variable_rename,[status(thm)],[f_2840_1]) ).
cnf(f_2840_3,plain,
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_10529),U_10530))
| ~ c_Nat__Transfer_Onat__set(U_10530)
| ~ c_Nat__Transfer_Onat__set(U_10529) ),
inference(clausify,[status(thm)],[f_2840_2]) ).
fof(f_2841_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_2841_2,plain,
! [U_10534,U_10533,U_10532,U_10531] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10531),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10531),U_10534),U_10532)),U_10533))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10531),U_10532),U_10533))
| ~ class_Lattices_Osemilattice__inf(U_10531) ),
inference(variable_rename,[status(thm)],[f_2841_1]) ).
cnf(f_2841_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10531),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10531),U_10534),U_10532)),U_10533))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10531),U_10532),U_10533))
| ~ class_Lattices_Osemilattice__inf(U_10531) ),
inference(clausify,[status(thm)],[f_2841_2]) ).
fof(f_2842_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_2842_2,plain,
! [U_10538,U_10537,U_10536,U_10535] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10535),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10535),U_10536),U_10538)),U_10537))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10535),U_10536),U_10537))
| ~ class_Lattices_Osemilattice__inf(U_10535) ),
inference(variable_rename,[status(thm)],[f_2842_1]) ).
cnf(f_2842_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10535),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10535),U_10536),U_10538)),U_10537))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10535),U_10536),U_10537))
| ~ class_Lattices_Osemilattice__inf(U_10535) ),
inference(clausify,[status(thm)],[f_2842_2]) ).
fof(f_2843_1,plain,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(V_B_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf1D2]) ).
fof(f_2843_2,plain,
! [U_10542,U_10541,U_10540,U_10539] :
( hBOOL(hAPP(U_10541,U_10542))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10539,tc_HOL_Obool)),U_10540),U_10541),U_10542)) ),
inference(variable_rename,[status(thm)],[f_2843_1]) ).
fof(f_2843_3,plain,
! [U_10542,U_10541] :
( ! [U_10540,U_10539] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10539,tc_HOL_Obool)),U_10540),U_10541),U_10542))
| hBOOL(hAPP(U_10541,U_10542)) ),
inference(miniscope,[status(thm)],[f_2843_2]) ).
cnf(f_2843_4,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10539,tc_HOL_Obool)),U_10540),U_10541),U_10542))
| hBOOL(hAPP(U_10541,U_10542)) ),
inference(clausify,[status(thm)],[f_2843_3]) ).
fof(f_2844_1,plain,
! [V_x_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(V_A_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf1D1]) ).
fof(f_2844_2,plain,
! [U_10546,U_10545,U_10544,U_10543] :
( hBOOL(hAPP(U_10544,U_10546))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10543,tc_HOL_Obool)),U_10544),U_10545),U_10546)) ),
inference(variable_rename,[status(thm)],[f_2844_1]) ).
fof(f_2844_3,plain,
! [U_10546,U_10545,U_10544] :
( ! [U_10543] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10543,tc_HOL_Obool)),U_10544),U_10545),U_10546))
| hBOOL(hAPP(U_10544,U_10546)) ),
inference(miniscope,[status(thm)],[f_2844_2]) ).
cnf(f_2844_4,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10543,tc_HOL_Obool)),U_10544),U_10545),U_10546))
| hBOOL(hAPP(U_10544,U_10546)) ),
inference(clausify,[status(thm)],[f_2844_3]) ).
fof(f_2845_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_2845_2,plain,
! [U_10548,U_10547] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10547),U_10548),U_10548) = U_10548
| ~ class_Lattices_Olattice(U_10547) ),
inference(variable_rename,[status(thm)],[f_2845_1]) ).
cnf(f_2845_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10547),U_10548),U_10548) = U_10548
| ~ class_Lattices_Olattice(U_10547) ),
inference(clausify,[status(thm)],[f_2845_2]) ).
fof(f_2846_1,plain,
! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__fun__def]) ).
fof(f_2846_2,plain,
! [U_10553,U_10552,U_10551,U_10550,U_10549] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10550,U_10549)),U_10551),U_10552),U_10553) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10549),hAPP(U_10551,U_10553)),hAPP(U_10552,U_10553))
| ~ class_Lattices_Olattice(U_10549) ),
inference(variable_rename,[status(thm)],[f_2846_1]) ).
cnf(f_2846_3,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10550,U_10549)),U_10551),U_10552),U_10553) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10549),hAPP(U_10551,U_10553)),hAPP(U_10552,U_10553))
| ~ class_Lattices_Olattice(U_10549) ),
inference(clausify,[status(thm)],[f_2846_2]) ).
fof(f_2847_1,plain,
! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__apply]) ).
fof(f_2847_2,plain,
! [U_10558,U_10557,U_10556,U_10555,U_10554] :
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10555,U_10554)),U_10556),U_10557),U_10558) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10554),hAPP(U_10556,U_10558)),hAPP(U_10557,U_10558))
| ~ class_Lattices_Olattice(U_10554) ),
inference(variable_rename,[status(thm)],[f_2847_1]) ).
cnf(f_2847_3,plain,
( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10555,U_10554)),U_10556),U_10557),U_10558) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10554),hAPP(U_10556,U_10558)),hAPP(U_10557,U_10558))
| ~ class_Lattices_Olattice(U_10554) ),
inference(clausify,[status(thm)],[f_2847_2]) ).
fof(f_2848_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_2848_2,plain,
! [U_10562,U_10561,U_10560,U_10559] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10559),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10559),U_10560),U_10561)),U_10562) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10559),U_10560),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10559),U_10561),U_10562))
| ~ class_Lattices_Osemilattice__inf(U_10559) ),
inference(variable_rename,[status(thm)],[f_2848_1]) ).
cnf(f_2848_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10559),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10559),U_10560),U_10561)),U_10562) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10559),U_10560),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10559),U_10561),U_10562))
| ~ class_Lattices_Osemilattice__inf(U_10559) ),
inference(clausify,[status(thm)],[f_2848_2]) ).
fof(f_2849_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_2849_2,plain,
! [U_10566,U_10565,U_10564,U_10563] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10563),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10563),U_10564),U_10565)),U_10566) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10563),U_10564),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10563),U_10565),U_10566))
| ~ class_Lattices_Olattice(U_10563) ),
inference(variable_rename,[status(thm)],[f_2849_1]) ).
cnf(f_2849_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10563),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10563),U_10564),U_10565)),U_10566) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10563),U_10564),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10563),U_10565),U_10566))
| ~ class_Lattices_Olattice(U_10563) ),
inference(clausify,[status(thm)],[f_2849_2]) ).
fof(f_2850_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_2850_2,plain,
! [U_10570,U_10569,U_10568,U_10567] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10567),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10567),U_10568),U_10569)),U_10570) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10567),U_10568),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10567),U_10569),U_10570))
| ~ class_Lattices_Osemilattice__inf(U_10567) ),
inference(variable_rename,[status(thm)],[f_2850_1]) ).
cnf(f_2850_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10567),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10567),U_10568),U_10569)),U_10570) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10567),U_10568),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10567),U_10569),U_10570))
| ~ class_Lattices_Osemilattice__inf(U_10567) ),
inference(clausify,[status(thm)],[f_2850_2]) ).
fof(f_2851_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_2851_2,plain,
! [U_10574,U_10573,U_10572,U_10571] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10571),U_10572),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10571),U_10573),U_10574)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10571),U_10573),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10571),U_10572),U_10574))
| ~ class_Lattices_Osemilattice__inf(U_10571) ),
inference(variable_rename,[status(thm)],[f_2851_1]) ).
cnf(f_2851_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10571),U_10572),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10571),U_10573),U_10574)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10571),U_10573),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10571),U_10572),U_10574))
| ~ class_Lattices_Osemilattice__inf(U_10571) ),
inference(clausify,[status(thm)],[f_2851_2]) ).
fof(f_2852_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_2852_2,plain,
! [U_10578,U_10577,U_10576,U_10575] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10575),U_10576),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10575),U_10577),U_10578)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10575),U_10577),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10575),U_10576),U_10578))
| ~ class_Lattices_Olattice(U_10575) ),
inference(variable_rename,[status(thm)],[f_2852_1]) ).
cnf(f_2852_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10575),U_10576),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10575),U_10577),U_10578)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10575),U_10577),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10575),U_10576),U_10578))
| ~ class_Lattices_Olattice(U_10575) ),
inference(clausify,[status(thm)],[f_2852_2]) ).
fof(f_2853_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_2853_2,plain,
! [U_10582,U_10581,U_10580,U_10579] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10579),U_10580),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10579),U_10581),U_10582)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10579),U_10581),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10579),U_10580),U_10582))
| ~ class_Lattices_Osemilattice__inf(U_10579) ),
inference(variable_rename,[status(thm)],[f_2853_1]) ).
cnf(f_2853_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10579),U_10580),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10579),U_10581),U_10582)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10579),U_10581),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10579),U_10580),U_10582))
| ~ class_Lattices_Osemilattice__inf(U_10579) ),
inference(clausify,[status(thm)],[f_2853_2]) ).
fof(f_2854_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_2854_2,plain,
! [U_10585,U_10584,U_10583] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10583),U_10584),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10583),U_10584),U_10585)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10583),U_10584),U_10585)
| ~ class_Lattices_Osemilattice__inf(U_10583) ),
inference(variable_rename,[status(thm)],[f_2854_1]) ).
cnf(f_2854_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10583),U_10584),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10583),U_10584),U_10585)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10583),U_10584),U_10585)
| ~ class_Lattices_Osemilattice__inf(U_10583) ),
inference(clausify,[status(thm)],[f_2854_2]) ).
fof(f_2855_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_2855_2,plain,
! [U_10588,U_10587,U_10586] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10586),U_10587),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10586),U_10587),U_10588)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10586),U_10587),U_10588)
| ~ class_Lattices_Olattice(U_10586) ),
inference(variable_rename,[status(thm)],[f_2855_1]) ).
cnf(f_2855_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10586),U_10587),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10586),U_10587),U_10588)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10586),U_10587),U_10588)
| ~ class_Lattices_Olattice(U_10586) ),
inference(clausify,[status(thm)],[f_2855_2]) ).
fof(f_2856_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_2856_2,plain,
! [U_10591,U_10590,U_10589] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10589),U_10590),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10589),U_10590),U_10591)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10589),U_10590),U_10591)
| ~ class_Lattices_Osemilattice__inf(U_10589) ),
inference(variable_rename,[status(thm)],[f_2856_1]) ).
cnf(f_2856_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10589),U_10590),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10589),U_10590),U_10591)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10589),U_10590),U_10591)
| ~ class_Lattices_Osemilattice__inf(U_10589) ),
inference(clausify,[status(thm)],[f_2856_2]) ).
fof(f_2857_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_2857_2,plain,
! [U_10594,U_10593,U_10592] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10592),U_10593),U_10594) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10592),U_10594),U_10593)
| ~ class_Lattices_Osemilattice__inf(U_10592) ),
inference(variable_rename,[status(thm)],[f_2857_1]) ).
cnf(f_2857_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10592),U_10593),U_10594) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10592),U_10594),U_10593)
| ~ class_Lattices_Osemilattice__inf(U_10592) ),
inference(clausify,[status(thm)],[f_2857_2]) ).
fof(f_2858_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_2858_2,plain,
! [U_10597,U_10596,U_10595] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10595),U_10596),U_10597) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10595),U_10597),U_10596)
| ~ class_Lattices_Olattice(U_10595) ),
inference(variable_rename,[status(thm)],[f_2858_1]) ).
cnf(f_2858_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10595),U_10596),U_10597) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10595),U_10597),U_10596)
| ~ class_Lattices_Olattice(U_10595) ),
inference(clausify,[status(thm)],[f_2858_2]) ).
fof(f_2859_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_2859_2,plain,
! [U_10600,U_10599,U_10598] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10598),U_10599),U_10600) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10598),U_10600),U_10599)
| ~ class_Lattices_Osemilattice__inf(U_10598) ),
inference(variable_rename,[status(thm)],[f_2859_1]) ).
cnf(f_2859_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10598),U_10599),U_10600) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10598),U_10600),U_10599)
| ~ class_Lattices_Osemilattice__inf(U_10598) ),
inference(clausify,[status(thm)],[f_2859_2]) ).
fof(f_2860_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_2860_2,plain,
! [U_10602,U_10601] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10601),U_10602),U_10602) = U_10602
| ~ class_Lattices_Osemilattice__inf(U_10601) ),
inference(variable_rename,[status(thm)],[f_2860_1]) ).
cnf(f_2860_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10601),U_10602),U_10602) = U_10602
| ~ class_Lattices_Osemilattice__inf(U_10601) ),
inference(clausify,[status(thm)],[f_2860_2]) ).
fof(f_2861_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_2861_2,plain,
! [U_10604,U_10603] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10603),U_10604),U_10604) = U_10604
| ~ class_Lattices_Osemilattice__inf(U_10603) ),
inference(variable_rename,[status(thm)],[f_2861_1]) ).
cnf(f_2861_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10603),U_10604),U_10604) = U_10604
| ~ class_Lattices_Osemilattice__inf(U_10603) ),
inference(clausify,[status(thm)],[f_2861_2]) ).
fof(f_2862_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Int__assoc]) ).
fof(f_2862_2,plain,
! [U_10608,U_10607,U_10606,U_10605] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10605,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10605,tc_HOL_Obool)),U_10606),U_10607)),U_10608) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10605,tc_HOL_Obool)),U_10606),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10605,tc_HOL_Obool)),U_10607),U_10608)),
inference(variable_rename,[status(thm)],[f_2862_1]) ).
cnf(f_2862_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10605,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10605,tc_HOL_Obool)),U_10606),U_10607)),U_10608) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10605,tc_HOL_Obool)),U_10606),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10605,tc_HOL_Obool)),U_10607),U_10608)),
inference(clausify,[status(thm)],[f_2862_2]) ).
fof(f_2863_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Int__left__commute]) ).
fof(f_2863_2,plain,
! [U_10612,U_10611,U_10610,U_10609] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10609,tc_HOL_Obool)),U_10610),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10609,tc_HOL_Obool)),U_10611),U_10612)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10609,tc_HOL_Obool)),U_10611),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10609,tc_HOL_Obool)),U_10610),U_10612)),
inference(variable_rename,[status(thm)],[f_2863_1]) ).
cnf(f_2863_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10609,tc_HOL_Obool)),U_10610),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10609,tc_HOL_Obool)),U_10611),U_10612)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10609,tc_HOL_Obool)),U_10611),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10609,tc_HOL_Obool)),U_10610),U_10612)),
inference(clausify,[status(thm)],[f_2863_2]) ).
fof(f_2864_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
inference(fof_nnf,[status(thm)],[fact_Int__left__absorb]) ).
fof(f_2864_2,plain,
! [U_10615,U_10614,U_10613] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10613,tc_HOL_Obool)),U_10614),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10613,tc_HOL_Obool)),U_10614),U_10615)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10613,tc_HOL_Obool)),U_10614),U_10615),
inference(variable_rename,[status(thm)],[f_2864_1]) ).
cnf(f_2864_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10613,tc_HOL_Obool)),U_10614),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10613,tc_HOL_Obool)),U_10614),U_10615)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10613,tc_HOL_Obool)),U_10614),U_10615),
inference(clausify,[status(thm)],[f_2864_2]) ).
fof(f_2865_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2),
inference(fof_nnf,[status(thm)],[fact_Int__commute]) ).
fof(f_2865_2,plain,
! [U_10618,U_10617,U_10616] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10616,tc_HOL_Obool)),U_10617),U_10618) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10616,tc_HOL_Obool)),U_10618),U_10617),
inference(variable_rename,[status(thm)],[f_2865_1]) ).
cnf(f_2865_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10616,tc_HOL_Obool)),U_10617),U_10618) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10616,tc_HOL_Obool)),U_10618),U_10617),
inference(clausify,[status(thm)],[f_2865_2]) ).
fof(f_2866_1,plain,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Int__absorb]) ).
fof(f_2866_2,plain,
! [U_10620,U_10619] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10619,tc_HOL_Obool)),U_10620),U_10620) = U_10620,
inference(variable_rename,[status(thm)],[f_2866_1]) ).
cnf(f_2866_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10619,tc_HOL_Obool)),U_10620),U_10620) = U_10620,
inference(clausify,[status(thm)],[f_2866_2]) ).
fof(f_2867_1,plain,
! [T_b] :
( c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b)
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Lattices_Osemilattice__inf(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__min]) ).
fof(f_2867_2,plain,
! [U_10621] :
( c_Lattices_Osemilattice__inf__class_Oinf(U_10621) = c_Orderings_Oord__class_Omin(U_10621)
| ~ class_Orderings_Olinorder(U_10621)
| ~ class_Lattices_Osemilattice__inf(U_10621) ),
inference(variable_rename,[status(thm)],[f_2867_1]) ).
cnf(f_2867_3,plain,
( c_Lattices_Osemilattice__inf__class_Oinf(U_10621) = c_Orderings_Oord__class_Omin(U_10621)
| ~ class_Orderings_Olinorder(U_10621)
| ~ class_Lattices_Osemilattice__inf(U_10621) ),
inference(clausify,[status(thm)],[f_2867_2]) ).
fof(f_2868_1,plain,
! [V_B_2,V_C_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2),
inference(fof_nnf,[status(thm)],[fact_Diff__Int2]) ).
fof(f_2868_2,plain,
! [U_10625,U_10624,U_10623,U_10622] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10622,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10622,tc_HOL_Obool)),U_10623),U_10624)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10622,tc_HOL_Obool)),U_10625),U_10624)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10622,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10622,tc_HOL_Obool)),U_10623),U_10624)),U_10625),
inference(variable_rename,[status(thm)],[f_2868_1]) ).
cnf(f_2868_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10622,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10622,tc_HOL_Obool)),U_10623),U_10624)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10622,tc_HOL_Obool)),U_10625),U_10624)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10622,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10622,tc_HOL_Obool)),U_10623),U_10624)),U_10625),
inference(clausify,[status(thm)],[f_2868_2]) ).
fof(f_2869_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Diff__Int__distrib2]) ).
fof(f_2869_2,plain,
! [U_10629,U_10628,U_10627,U_10626] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10626,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10626,tc_HOL_Obool)),U_10627),U_10628)),U_10629) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10626,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10626,tc_HOL_Obool)),U_10627),U_10629)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10626,tc_HOL_Obool)),U_10628),U_10629)),
inference(variable_rename,[status(thm)],[f_2869_1]) ).
cnf(f_2869_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10626,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10626,tc_HOL_Obool)),U_10627),U_10628)),U_10629) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10626,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10626,tc_HOL_Obool)),U_10627),U_10629)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10626,tc_HOL_Obool)),U_10628),U_10629)),
inference(clausify,[status(thm)],[f_2869_2]) ).
fof(f_2870_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Int__Diff]) ).
fof(f_2870_2,plain,
! [U_10633,U_10632,U_10631,U_10630] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10630,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10630,tc_HOL_Obool)),U_10631),U_10632)),U_10633) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10630,tc_HOL_Obool)),U_10631),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10630,tc_HOL_Obool)),U_10632),U_10633)),
inference(variable_rename,[status(thm)],[f_2870_1]) ).
cnf(f_2870_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10630,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10630,tc_HOL_Obool)),U_10631),U_10632)),U_10633) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10630,tc_HOL_Obool)),U_10631),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10630,tc_HOL_Obool)),U_10632),U_10633)),
inference(clausify,[status(thm)],[f_2870_2]) ).
fof(f_2871_1,plain,
! [V_B_2,V_A_2,V_C_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Diff__Int__distrib]) ).
fof(f_2871_2,plain,
! [U_10637,U_10636,U_10635,U_10634] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10634,tc_HOL_Obool)),U_10635),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10634,tc_HOL_Obool)),U_10636),U_10637)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10634,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10634,tc_HOL_Obool)),U_10635),U_10636)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10634,tc_HOL_Obool)),U_10635),U_10637)),
inference(variable_rename,[status(thm)],[f_2871_1]) ).
cnf(f_2871_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10634,tc_HOL_Obool)),U_10635),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10634,tc_HOL_Obool)),U_10636),U_10637)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10634,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10634,tc_HOL_Obool)),U_10635),U_10636)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10634,tc_HOL_Obool)),U_10635),U_10637)),
inference(clausify,[status(thm)],[f_2871_2]) ).
fof(f_2872_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_2872_2,plain,
! [U_10641,U_10640,U_10639,U_10638] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10638),U_10639),U_10641))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10638),U_10639),U_10640)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10638),U_10639),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10638),U_10640),U_10641)))
| ~ class_Lattices_Osemilattice__inf(U_10638) ),
inference(variable_rename,[status(thm)],[f_2872_1]) ).
cnf(f_2872_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10638),U_10639),U_10640))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10638),U_10639),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10638),U_10640),U_10641)))
| ~ class_Lattices_Osemilattice__inf(U_10638) ),
inference(clausify,[status(thm)],[f_2872_2]) ).
cnf(f_2872_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10638),U_10639),U_10641))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10638),U_10639),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10638),U_10640),U_10641)))
| ~ class_Lattices_Osemilattice__inf(U_10638) ),
inference(clausify,[status(thm)],[f_2872_2]) ).
fof(f_2873_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_2873_2,plain,
! [U_10646,U_10645,U_10644,U_10643,U_10642] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10642),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10642),U_10643),U_10645)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10642),U_10644),U_10646)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10642),U_10645),U_10646))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10642),U_10643),U_10644))
| ~ class_Lattices_Osemilattice__inf(U_10642) ),
inference(variable_rename,[status(thm)],[f_2873_1]) ).
cnf(f_2873_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10642),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10642),U_10643),U_10645)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10642),U_10644),U_10646)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10642),U_10645),U_10646))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10642),U_10643),U_10644))
| ~ class_Lattices_Osemilattice__inf(U_10642) ),
inference(clausify,[status(thm)],[f_2873_2]) ).
fof(f_2874_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_2874_2,plain,
! [U_10650,U_10649,U_10648,U_10647] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10647),U_10648),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10647),U_10649),U_10650)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10647),U_10648),U_10650))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10647),U_10648),U_10649))
| ~ class_Lattices_Osemilattice__inf(U_10647) ),
inference(variable_rename,[status(thm)],[f_2874_1]) ).
cnf(f_2874_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10647),U_10648),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10647),U_10649),U_10650)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10647),U_10648),U_10650))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10647),U_10648),U_10649))
| ~ class_Lattices_Osemilattice__inf(U_10647) ),
inference(clausify,[status(thm)],[f_2874_2]) ).
fof(f_2875_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_2875_2,plain,
! [U_10654,U_10653,U_10652,U_10651] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10651),U_10652),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10651),U_10653),U_10654)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10651),U_10652),U_10654))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10651),U_10652),U_10653))
| ~ class_Lattices_Osemilattice__inf(U_10651) ),
inference(variable_rename,[status(thm)],[f_2875_1]) ).
cnf(f_2875_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10651),U_10652),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10651),U_10653),U_10654)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10651),U_10652),U_10654))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10651),U_10652),U_10653))
| ~ class_Lattices_Osemilattice__inf(U_10651) ),
inference(clausify,[status(thm)],[f_2875_2]) ).
fof(f_2876_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_2876_2,plain,
! [U_10657,U_10656,U_10655] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10655),U_10657),U_10656) = U_10656
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10655),U_10656),U_10657))
| ~ class_Lattices_Osemilattice__inf(U_10655) ),
inference(variable_rename,[status(thm)],[f_2876_1]) ).
cnf(f_2876_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10655),U_10657),U_10656) = U_10656
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10655),U_10656),U_10657))
| ~ class_Lattices_Osemilattice__inf(U_10655) ),
inference(clausify,[status(thm)],[f_2876_2]) ).
fof(f_2877_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_2877_2,plain,
! [U_10660,U_10659,U_10658] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10658),U_10659),U_10660) = U_10659
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10658),U_10659),U_10660))
| ~ class_Lattices_Osemilattice__inf(U_10658) ),
inference(variable_rename,[status(thm)],[f_2877_1]) ).
cnf(f_2877_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10658),U_10659),U_10660) = U_10659
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10658),U_10659),U_10660))
| ~ class_Lattices_Osemilattice__inf(U_10658) ),
inference(clausify,[status(thm)],[f_2877_2]) ).
fof(f_2878_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_2878_2,plain,
! [U_10664,U_10663,U_10662,U_10661] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10661),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10661),U_10664),U_10662)),U_10663))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10661),U_10662),U_10663))
| ~ class_Lattices_Osemilattice__inf(U_10661) ),
inference(variable_rename,[status(thm)],[f_2878_1]) ).
cnf(f_2878_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10661),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10661),U_10664),U_10662)),U_10663))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10661),U_10662),U_10663))
| ~ class_Lattices_Osemilattice__inf(U_10661) ),
inference(clausify,[status(thm)],[f_2878_2]) ).
fof(f_2879_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_2879_2,plain,
! [U_10668,U_10667,U_10666,U_10665] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10665),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10665),U_10666),U_10668)),U_10667))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10665),U_10666),U_10667))
| ~ class_Lattices_Osemilattice__inf(U_10665) ),
inference(variable_rename,[status(thm)],[f_2879_1]) ).
cnf(f_2879_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10665),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10665),U_10666),U_10668)),U_10667))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10665),U_10666),U_10667))
| ~ class_Lattices_Osemilattice__inf(U_10665) ),
inference(clausify,[status(thm)],[f_2879_2]) ).
fof(f_2880_1,plain,
! [V_z_2,V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_y_2),V_z_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_y_2),V_z_2))) ) )
| ~ class_Lattices_Osemilattice__inf(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__inf__iff]) ).
fof(f_2880_2,plain,
! [U_10672,U_10671,U_10670,U_10669] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10669),U_10670),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10669),U_10671),U_10672)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10669),U_10670),U_10672))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10669),U_10670),U_10671)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10669),U_10670),U_10672))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10669),U_10670),U_10671)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10669),U_10670),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10669),U_10671),U_10672))) ) )
| ~ class_Lattices_Osemilattice__inf(U_10669) ),
inference(variable_rename,[status(thm)],[f_2880_1]) ).
cnf(f_2880_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10669),U_10670),U_10671))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10669),U_10670),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10669),U_10671),U_10672)))
| ~ class_Lattices_Osemilattice__inf(U_10669) ),
inference(clausify,[status(thm)],[f_2880_2]) ).
cnf(f_2880_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10669),U_10670),U_10672))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10669),U_10670),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10669),U_10671),U_10672)))
| ~ class_Lattices_Osemilattice__inf(U_10669) ),
inference(clausify,[status(thm)],[f_2880_2]) ).
cnf(f_2880_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10669),U_10670),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10669),U_10671),U_10672)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10669),U_10670),U_10672))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10669),U_10670),U_10671))
| ~ class_Lattices_Osemilattice__inf(U_10669) ),
inference(clausify,[status(thm)],[f_2880_2]) ).
fof(f_2881_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) != V_x_2 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) )
| ~ class_Lattices_Osemilattice__inf(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__inf]) ).
fof(f_2881_2,plain,
! [U_10675,U_10674,U_10673] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10673),U_10674),U_10675))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10673),U_10674),U_10675) != U_10674 )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10673),U_10674),U_10675) = U_10674
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10673),U_10674),U_10675)) ) )
| ~ class_Lattices_Osemilattice__inf(U_10673) ),
inference(variable_rename,[status(thm)],[f_2881_1]) ).
cnf(f_2881_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10673),U_10674),U_10675) = U_10674
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10673),U_10674),U_10675))
| ~ class_Lattices_Osemilattice__inf(U_10673) ),
inference(clausify,[status(thm)],[f_2881_2]) ).
cnf(f_2881_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10673),U_10674),U_10675))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10673),U_10674),U_10675) != U_10674
| ~ class_Lattices_Osemilattice__inf(U_10673) ),
inference(clausify,[status(thm)],[f_2881_2]) ).
fof(f_2882_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_2882_2,plain,
! [U_10678,U_10677,U_10676] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10676),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10676),U_10677),U_10678)),U_10678))
| ~ class_Lattices_Osemilattice__inf(U_10676) ),
inference(variable_rename,[status(thm)],[f_2882_1]) ).
cnf(f_2882_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10676),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10676),U_10677),U_10678)),U_10678))
| ~ class_Lattices_Osemilattice__inf(U_10676) ),
inference(clausify,[status(thm)],[f_2882_2]) ).
fof(f_2883_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_2883_2,plain,
! [U_10681,U_10680,U_10679] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10679),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10679),U_10680),U_10681)),U_10681))
| ~ class_Lattices_Olattice(U_10679) ),
inference(variable_rename,[status(thm)],[f_2883_1]) ).
cnf(f_2883_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10679),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10679),U_10680),U_10681)),U_10681))
| ~ class_Lattices_Olattice(U_10679) ),
inference(clausify,[status(thm)],[f_2883_2]) ).
fof(f_2884_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_2884_2,plain,
! [U_10684,U_10683,U_10682] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10682),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10682),U_10683),U_10684)),U_10683))
| ~ class_Lattices_Osemilattice__inf(U_10682) ),
inference(variable_rename,[status(thm)],[f_2884_1]) ).
cnf(f_2884_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10682),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10682),U_10683),U_10684)),U_10683))
| ~ class_Lattices_Osemilattice__inf(U_10682) ),
inference(clausify,[status(thm)],[f_2884_2]) ).
fof(f_2885_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_2885_2,plain,
! [U_10687,U_10686,U_10685] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10685),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10685),U_10686),U_10687)),U_10686))
| ~ class_Lattices_Olattice(U_10685) ),
inference(variable_rename,[status(thm)],[f_2885_1]) ).
cnf(f_2885_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10685),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10685),U_10686),U_10687)),U_10686))
| ~ class_Lattices_Olattice(U_10685) ),
inference(clausify,[status(thm)],[f_2885_2]) ).
fof(f_2886_1,plain,
! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Int__lower1]) ).
fof(f_2886_2,plain,
! [U_10690,U_10689,U_10688] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10688,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10688,tc_HOL_Obool)),U_10689),U_10690)),U_10689)),
inference(variable_rename,[status(thm)],[f_2886_1]) ).
cnf(f_2886_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10688,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10688,tc_HOL_Obool)),U_10689),U_10690)),U_10689)),
inference(clausify,[status(thm)],[f_2886_2]) ).
fof(f_2887_1,plain,
! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Int__lower2]) ).
fof(f_2887_2,plain,
! [U_10693,U_10692,U_10691] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10691,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10691,tc_HOL_Obool)),U_10692),U_10693)),U_10693)),
inference(variable_rename,[status(thm)],[f_2887_1]) ).
cnf(f_2887_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10691,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10691,tc_HOL_Obool)),U_10692),U_10693)),U_10693)),
inference(clausify,[status(thm)],[f_2887_2]) ).
fof(f_2888_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__absorb2]) ).
fof(f_2888_2,plain,
! [U_10696,U_10695,U_10694] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10694,tc_HOL_Obool)),U_10695),U_10696) = U_10695
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10694,tc_HOL_Obool)),U_10695),U_10696)) ),
inference(variable_rename,[status(thm)],[f_2888_1]) ).
cnf(f_2888_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10694,tc_HOL_Obool)),U_10695),U_10696) = U_10695
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10694,tc_HOL_Obool)),U_10695),U_10696)) ),
inference(clausify,[status(thm)],[f_2888_2]) ).
fof(f_2889_1,plain,
! [V_A_2,V_B_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__absorb1]) ).
fof(f_2889_2,plain,
! [U_10699,U_10698,U_10697] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10697,tc_HOL_Obool)),U_10699),U_10698) = U_10698
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10697,tc_HOL_Obool)),U_10698),U_10699)) ),
inference(variable_rename,[status(thm)],[f_2889_1]) ).
cnf(f_2889_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10697,tc_HOL_Obool)),U_10699),U_10698) = U_10698
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10697,tc_HOL_Obool)),U_10698),U_10699)) ),
inference(clausify,[status(thm)],[f_2889_2]) ).
fof(f_2890_1,plain,
! [V_B_2,V_A_2,V_C_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__greatest]) ).
fof(f_2890_2,plain,
! [U_10703,U_10702,U_10701,U_10700] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10700,tc_HOL_Obool)),U_10701),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10700,tc_HOL_Obool)),U_10702),U_10703)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10700,tc_HOL_Obool)),U_10701),U_10703))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10700,tc_HOL_Obool)),U_10701),U_10702)) ),
inference(variable_rename,[status(thm)],[f_2890_1]) ).
cnf(f_2890_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10700,tc_HOL_Obool)),U_10701),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10700,tc_HOL_Obool)),U_10702),U_10703)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10700,tc_HOL_Obool)),U_10701),U_10703))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10700,tc_HOL_Obool)),U_10701),U_10702)) ),
inference(clausify,[status(thm)],[f_2890_2]) ).
fof(f_2891_1,plain,
! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__mono]) ).
fof(f_2891_2,plain,
! [U_10708,U_10707,U_10706,U_10705,U_10704] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10704,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10704,tc_HOL_Obool)),U_10705),U_10707)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10704,tc_HOL_Obool)),U_10706),U_10708)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10704,tc_HOL_Obool)),U_10707),U_10708))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10704,tc_HOL_Obool)),U_10705),U_10706)) ),
inference(variable_rename,[status(thm)],[f_2891_1]) ).
cnf(f_2891_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10704,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10704,tc_HOL_Obool)),U_10705),U_10707)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10704,tc_HOL_Obool)),U_10706),U_10708)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10704,tc_HOL_Obool)),U_10707),U_10708))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10704,tc_HOL_Obool)),U_10705),U_10706)) ),
inference(clausify,[status(thm)],[f_2891_2]) ).
fof(f_2892_1,plain,
! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_INT__Int__distrib]) ).
fof(f_2892_2,plain,
! [U_10713,U_10712,U_10711,U_10710,U_10709] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10709,tc_fun(U_10710,tc_HOL_Obool)),U_10711),hAPP(hAPP(c_COMBS(U_10709,tc_fun(U_10710,tc_HOL_Obool),tc_fun(U_10710,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10710,tc_HOL_Obool),tc_fun(tc_fun(U_10710,tc_HOL_Obool),tc_fun(U_10710,tc_HOL_Obool)),U_10709),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10710,tc_HOL_Obool))),U_10712)),U_10713)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10710,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10709,tc_fun(U_10710,tc_HOL_Obool)),U_10711),U_10712)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10709,tc_fun(U_10710,tc_HOL_Obool)),U_10711),U_10713)),
inference(variable_rename,[status(thm)],[f_2892_1]) ).
cnf(f_2892_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10709,tc_fun(U_10710,tc_HOL_Obool)),U_10711),hAPP(hAPP(c_COMBS(U_10709,tc_fun(U_10710,tc_HOL_Obool),tc_fun(U_10710,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10710,tc_HOL_Obool),tc_fun(tc_fun(U_10710,tc_HOL_Obool),tc_fun(U_10710,tc_HOL_Obool)),U_10709),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10710,tc_HOL_Obool))),U_10712)),U_10713)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10710,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10709,tc_fun(U_10710,tc_HOL_Obool)),U_10711),U_10712)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10709,tc_fun(U_10710,tc_HOL_Obool)),U_10711),U_10713)),
inference(clausify,[status(thm)],[f_2892_2]) ).
fof(f_2893_1,plain,
! [V_x_2,V_S_2,V_R_2,T_b] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_inf__Int__eq]) ).
fof(f_2893_2,plain,
! [U_10717,U_10716,U_10715,U_10714] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10714,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10714,tc_fun(U_10714,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10714)),U_10715)),hAPP(hAPP(c_COMBC(U_10714,tc_fun(U_10714,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10714)),U_10716)),U_10717))
| ~ hBOOL(hAPP(hAPP(c_member(U_10714),U_10717),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10714,tc_HOL_Obool)),U_10715),U_10716))) )
& ( hBOOL(hAPP(hAPP(c_member(U_10714),U_10717),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10714,tc_HOL_Obool)),U_10715),U_10716)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10714,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10714,tc_fun(U_10714,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10714)),U_10715)),hAPP(hAPP(c_COMBC(U_10714,tc_fun(U_10714,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10714)),U_10716)),U_10717)) ) ),
inference(variable_rename,[status(thm)],[f_2893_1]) ).
fof(f_2893_3,plain,
( ! [U_10725,U_10723,U_10721,U_10719] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10719,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10719,tc_fun(U_10719,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10719)),U_10721)),hAPP(hAPP(c_COMBC(U_10719,tc_fun(U_10719,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10719)),U_10723)),U_10725))
| ~ hBOOL(hAPP(hAPP(c_member(U_10719),U_10725),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10719,tc_HOL_Obool)),U_10721),U_10723))) )
& ! [U_10724,U_10722,U_10720,U_10718] :
( hBOOL(hAPP(hAPP(c_member(U_10718),U_10724),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10718,tc_HOL_Obool)),U_10720),U_10722)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10718,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10718,tc_fun(U_10718,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10718)),U_10720)),hAPP(hAPP(c_COMBC(U_10718,tc_fun(U_10718,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10718)),U_10722)),U_10724)) ) ),
inference(miniscope,[status(thm)],[f_2893_2]) ).
cnf(f_2893_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_10718),U_10724),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10718,tc_HOL_Obool)),U_10720),U_10722)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10718,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10718,tc_fun(U_10718,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10718)),U_10720)),hAPP(hAPP(c_COMBC(U_10718,tc_fun(U_10718,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10718)),U_10722)),U_10724)) ),
inference(clausify,[status(thm)],[f_2893_3]) ).
cnf(f_2893_5,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10719,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10719,tc_fun(U_10719,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10719)),U_10721)),hAPP(hAPP(c_COMBC(U_10719,tc_fun(U_10719,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10719)),U_10723)),U_10725))
| ~ hBOOL(hAPP(hAPP(c_member(U_10719),U_10725),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10719,tc_HOL_Obool)),U_10721),U_10723))) ),
inference(clausify,[status(thm)],[f_2893_3]) ).
fof(f_2894_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_IntD2]) ).
fof(f_2894_2,plain,
! [U_10729,U_10728,U_10727,U_10726] :
( hBOOL(hAPP(hAPP(c_member(U_10726),U_10727),U_10729))
| ~ hBOOL(hAPP(hAPP(c_member(U_10726),U_10727),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10726,tc_HOL_Obool)),U_10728),U_10729))) ),
inference(variable_rename,[status(thm)],[f_2894_1]) ).
cnf(f_2894_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_10726),U_10727),U_10729))
| ~ hBOOL(hAPP(hAPP(c_member(U_10726),U_10727),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10726,tc_HOL_Obool)),U_10728),U_10729))) ),
inference(clausify,[status(thm)],[f_2894_2]) ).
fof(f_2895_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_IntD1]) ).
fof(f_2895_2,plain,
! [U_10733,U_10732,U_10731,U_10730] :
( hBOOL(hAPP(hAPP(c_member(U_10730),U_10731),U_10732))
| ~ hBOOL(hAPP(hAPP(c_member(U_10730),U_10731),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10730,tc_HOL_Obool)),U_10732),U_10733))) ),
inference(variable_rename,[status(thm)],[f_2895_1]) ).
cnf(f_2895_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_10730),U_10731),U_10732))
| ~ hBOOL(hAPP(hAPP(c_member(U_10730),U_10731),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10730,tc_HOL_Obool)),U_10732),U_10733))) ),
inference(clausify,[status(thm)],[f_2895_2]) ).
fof(f_2896_1,plain,
! [V_B_2,V_A_2,V_c_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
& ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Int__iff]) ).
fof(f_2896_2,plain,
! [U_10737,U_10736,U_10735,U_10734] :
( ( hBOOL(hAPP(hAPP(c_member(U_10734),U_10735),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10734,tc_HOL_Obool)),U_10736),U_10737)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10734),U_10735),U_10737))
| ~ hBOOL(hAPP(hAPP(c_member(U_10734),U_10735),U_10736)) )
& ( ( hBOOL(hAPP(hAPP(c_member(U_10734),U_10735),U_10737))
& hBOOL(hAPP(hAPP(c_member(U_10734),U_10735),U_10736)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_10734),U_10735),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10734,tc_HOL_Obool)),U_10736),U_10737))) ) ),
inference(variable_rename,[status(thm)],[f_2896_1]) ).
fof(f_2896_3,plain,
( ! [U_10745,U_10743,U_10741,U_10739] :
( hBOOL(hAPP(hAPP(c_member(U_10739),U_10741),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10739,tc_HOL_Obool)),U_10743),U_10745)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10739),U_10741),U_10745))
| ~ hBOOL(hAPP(hAPP(c_member(U_10739),U_10741),U_10743)) )
& ! [U_10744,U_10742,U_10740,U_10738] :
( ( hBOOL(hAPP(hAPP(c_member(U_10738),U_10740),U_10744))
& hBOOL(hAPP(hAPP(c_member(U_10738),U_10740),U_10742)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_10738),U_10740),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10738,tc_HOL_Obool)),U_10742),U_10744))) ) ),
inference(miniscope,[status(thm)],[f_2896_2]) ).
cnf(f_2896_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_10738),U_10740),U_10742))
| ~ hBOOL(hAPP(hAPP(c_member(U_10738),U_10740),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10738,tc_HOL_Obool)),U_10742),U_10744))) ),
inference(clausify,[status(thm)],[f_2896_3]) ).
cnf(f_2896_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_10738),U_10740),U_10744))
| ~ hBOOL(hAPP(hAPP(c_member(U_10738),U_10740),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10738,tc_HOL_Obool)),U_10742),U_10744))) ),
inference(clausify,[status(thm)],[f_2896_3]) ).
cnf(f_2896_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_10739),U_10741),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10739,tc_HOL_Obool)),U_10743),U_10745)))
| ~ hBOOL(hAPP(hAPP(c_member(U_10739),U_10741),U_10745))
| ~ hBOOL(hAPP(hAPP(c_member(U_10739),U_10741),U_10743)) ),
inference(clausify,[status(thm)],[f_2896_3]) ).
fof(f_2897_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_2897_2,plain,
! [U_10749,U_10748,U_10747,U_10746] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10746),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10746),U_10747),U_10748)),U_10749) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10746),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10746),U_10747),U_10749)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10746),U_10748),U_10749))
| ~ class_Lattices_Odistrib__lattice(U_10746) ),
inference(variable_rename,[status(thm)],[f_2897_1]) ).
cnf(f_2897_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10746),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10746),U_10747),U_10748)),U_10749) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10746),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10746),U_10747),U_10749)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10746),U_10748),U_10749))
| ~ class_Lattices_Odistrib__lattice(U_10746) ),
inference(clausify,[status(thm)],[f_2897_2]) ).
fof(f_2898_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_2898_2,plain,
! [U_10753,U_10752,U_10751,U_10750] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10750),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10750),U_10751),U_10752)),U_10753) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10750),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10750),U_10751),U_10753)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10750),U_10752),U_10753))
| ~ class_Lattices_Odistrib__lattice(U_10750) ),
inference(variable_rename,[status(thm)],[f_2898_1]) ).
cnf(f_2898_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10750),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10750),U_10751),U_10752)),U_10753) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10750),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10750),U_10751),U_10753)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10750),U_10752),U_10753))
| ~ class_Lattices_Odistrib__lattice(U_10750) ),
inference(clausify,[status(thm)],[f_2898_2]) ).
fof(f_2899_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_2899_2,plain,
! [U_10757,U_10756,U_10755,U_10754] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10754),U_10755),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10754),U_10756),U_10757)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10754),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10754),U_10755),U_10756)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10754),U_10755),U_10757))
| ~ class_Lattices_Odistrib__lattice(U_10754) ),
inference(variable_rename,[status(thm)],[f_2899_1]) ).
cnf(f_2899_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10754),U_10755),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10754),U_10756),U_10757)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10754),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10754),U_10755),U_10756)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10754),U_10755),U_10757))
| ~ class_Lattices_Odistrib__lattice(U_10754) ),
inference(clausify,[status(thm)],[f_2899_2]) ).
fof(f_2900_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_2900_2,plain,
! [U_10761,U_10760,U_10759,U_10758] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10758),U_10759),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10758),U_10760),U_10761)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10758),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10758),U_10759),U_10760)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10758),U_10759),U_10761))
| ~ class_Lattices_Odistrib__lattice(U_10758) ),
inference(variable_rename,[status(thm)],[f_2900_1]) ).
cnf(f_2900_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10758),U_10759),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10758),U_10760),U_10761)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10758),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10758),U_10759),U_10760)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10758),U_10759),U_10761))
| ~ class_Lattices_Odistrib__lattice(U_10758) ),
inference(clausify,[status(thm)],[f_2900_2]) ).
fof(f_2901_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_2901_2,plain,
! [U_10764,U_10763,U_10762] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10762),U_10763),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10762),U_10763),U_10764)) = U_10763
| ~ class_Lattices_Olattice(U_10762) ),
inference(variable_rename,[status(thm)],[f_2901_1]) ).
cnf(f_2901_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10762),U_10763),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10762),U_10763),U_10764)) = U_10763
| ~ class_Lattices_Olattice(U_10762) ),
inference(clausify,[status(thm)],[f_2901_2]) ).
fof(f_2902_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_2902_2,plain,
! [U_10767,U_10766,U_10765] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10765),U_10766),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10765),U_10766),U_10767)) = U_10766
| ~ class_Lattices_Olattice(U_10765) ),
inference(variable_rename,[status(thm)],[f_2902_1]) ).
cnf(f_2902_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10765),U_10766),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10765),U_10766),U_10767)) = U_10766
| ~ class_Lattices_Olattice(U_10765) ),
inference(clausify,[status(thm)],[f_2902_2]) ).
fof(f_2903_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Un__Int__crazy]) ).
fof(f_2903_2,plain,
! [U_10771,U_10770,U_10769,U_10768] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10768,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10768,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10768,tc_HOL_Obool)),U_10769),U_10770)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10768,tc_HOL_Obool)),U_10770),U_10771))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10768,tc_HOL_Obool)),U_10771),U_10769)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10768,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10768,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10768,tc_HOL_Obool)),U_10769),U_10770)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10768,tc_HOL_Obool)),U_10770),U_10771))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10768,tc_HOL_Obool)),U_10771),U_10769)),
inference(variable_rename,[status(thm)],[f_2903_1]) ).
cnf(f_2903_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10768,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10768,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10768,tc_HOL_Obool)),U_10769),U_10770)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10768,tc_HOL_Obool)),U_10770),U_10771))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10768,tc_HOL_Obool)),U_10771),U_10769)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10768,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10768,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10768,tc_HOL_Obool)),U_10769),U_10770)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10768,tc_HOL_Obool)),U_10770),U_10771))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10768,tc_HOL_Obool)),U_10771),U_10769)),
inference(clausify,[status(thm)],[f_2903_2]) ).
fof(f_2904_1,plain,
! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Un__Int__distrib2]) ).
fof(f_2904_2,plain,
! [U_10775,U_10774,U_10773,U_10772] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10772,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10772,tc_HOL_Obool)),U_10773),U_10774)),U_10775) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10772,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10772,tc_HOL_Obool)),U_10773),U_10775)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10772,tc_HOL_Obool)),U_10774),U_10775)),
inference(variable_rename,[status(thm)],[f_2904_1]) ).
cnf(f_2904_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10772,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10772,tc_HOL_Obool)),U_10773),U_10774)),U_10775) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10772,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10772,tc_HOL_Obool)),U_10773),U_10775)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10772,tc_HOL_Obool)),U_10774),U_10775)),
inference(clausify,[status(thm)],[f_2904_2]) ).
fof(f_2905_1,plain,
! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Int__Un__distrib2]) ).
fof(f_2905_2,plain,
! [U_10779,U_10778,U_10777,U_10776] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10776,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10776,tc_HOL_Obool)),U_10777),U_10778)),U_10779) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10776,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10776,tc_HOL_Obool)),U_10777),U_10779)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10776,tc_HOL_Obool)),U_10778),U_10779)),
inference(variable_rename,[status(thm)],[f_2905_1]) ).
cnf(f_2905_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10776,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10776,tc_HOL_Obool)),U_10777),U_10778)),U_10779) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10776,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10776,tc_HOL_Obool)),U_10777),U_10779)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10776,tc_HOL_Obool)),U_10778),U_10779)),
inference(clausify,[status(thm)],[f_2905_2]) ).
fof(f_2906_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Un__Int__distrib]) ).
fof(f_2906_2,plain,
! [U_10783,U_10782,U_10781,U_10780] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10780,tc_HOL_Obool)),U_10781),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10780,tc_HOL_Obool)),U_10782),U_10783)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10780,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10780,tc_HOL_Obool)),U_10781),U_10782)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10780,tc_HOL_Obool)),U_10781),U_10783)),
inference(variable_rename,[status(thm)],[f_2906_1]) ).
cnf(f_2906_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10780,tc_HOL_Obool)),U_10781),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10780,tc_HOL_Obool)),U_10782),U_10783)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10780,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10780,tc_HOL_Obool)),U_10781),U_10782)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10780,tc_HOL_Obool)),U_10781),U_10783)),
inference(clausify,[status(thm)],[f_2906_2]) ).
fof(f_2907_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Int__Un__distrib]) ).
fof(f_2907_2,plain,
! [U_10787,U_10786,U_10785,U_10784] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10784,tc_HOL_Obool)),U_10785),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10784,tc_HOL_Obool)),U_10786),U_10787)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10784,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10784,tc_HOL_Obool)),U_10785),U_10786)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10784,tc_HOL_Obool)),U_10785),U_10787)),
inference(variable_rename,[status(thm)],[f_2907_1]) ).
cnf(f_2907_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10784,tc_HOL_Obool)),U_10785),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10784,tc_HOL_Obool)),U_10786),U_10787)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10784,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10784,tc_HOL_Obool)),U_10785),U_10786)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10784,tc_HOL_Obool)),U_10785),U_10787)),
inference(clausify,[status(thm)],[f_2907_2]) ).
fof(f_2908_1,plain,
! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Int__empty__left]) ).
fof(f_2908_2,plain,
! [U_10789,U_10788] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10788,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_10788,tc_HOL_Obool))),U_10789) = c_Orderings_Obot__class_Obot(tc_fun(U_10788,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2908_1]) ).
cnf(f_2908_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10788,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_10788,tc_HOL_Obool))),U_10789) = c_Orderings_Obot__class_Obot(tc_fun(U_10788,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2908_2]) ).
fof(f_2909_1,plain,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Int__empty__right]) ).
fof(f_2909_2,plain,
! [U_10791,U_10790] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10790,tc_HOL_Obool)),U_10791),c_Orderings_Obot__class_Obot(tc_fun(U_10790,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_10790,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2909_1]) ).
cnf(f_2909_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10790,tc_HOL_Obool)),U_10791),c_Orderings_Obot__class_Obot(tc_fun(U_10790,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_10790,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2909_2]) ).
fof(f_2910_1,plain,
! [V_B_2,V_A_2,T_b] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ? [B_x] :
( ? [B_xa] :
( B_x = B_xa
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2)) )
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ! [B_x] :
( ! [B_xa] :
( B_x != B_xa
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_disjoint__iff__not__equal]) ).
fof(f_2910_2,plain,
! [U_10798,U_10797,U_10796] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10796,tc_HOL_Obool)),U_10797),U_10798) = c_Orderings_Obot__class_Obot(tc_fun(U_10796,tc_HOL_Obool))
| ? [U_10795] :
( ? [U_10794] :
( U_10795 = U_10794
& hBOOL(hAPP(hAPP(c_member(U_10796),U_10794),U_10798)) )
& hBOOL(hAPP(hAPP(c_member(U_10796),U_10795),U_10797)) ) )
& ( ! [U_10793] :
( ! [U_10792] :
( U_10793 != U_10792
| ~ hBOOL(hAPP(hAPP(c_member(U_10796),U_10792),U_10798)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_10796),U_10793),U_10797)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10796,tc_HOL_Obool)),U_10797),U_10798) != c_Orderings_Obot__class_Obot(tc_fun(U_10796,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2910_1]) ).
fof(f_2910_3,plain,
( ! [U_10804,U_10802,U_10800] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10800,tc_HOL_Obool)),U_10802),U_10804) = c_Orderings_Obot__class_Obot(tc_fun(U_10800,tc_HOL_Obool))
| ? [U_10795] :
( ? [U_10794] :
( U_10795 = U_10794
& hBOOL(hAPP(hAPP(c_member(U_10800),U_10794),U_10804)) )
& hBOOL(hAPP(hAPP(c_member(U_10800),U_10795),U_10802)) ) )
& ! [U_10803,U_10801,U_10799] :
( ! [U_10793] :
( ! [U_10792] :
( U_10793 != U_10792
| ~ hBOOL(hAPP(hAPP(c_member(U_10799),U_10792),U_10803)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_10799),U_10793),U_10801)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10799,tc_HOL_Obool)),U_10801),U_10803) != c_Orderings_Obot__class_Obot(tc_fun(U_10799,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2910_2]) ).
fof(f_2910_4,plain,
( ! [U_10804,U_10802,U_10800] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10800,tc_HOL_Obool)),U_10802),U_10804) = c_Orderings_Obot__class_Obot(tc_fun(U_10800,tc_HOL_Obool))
| ( ? [U_10794] :
( sK232(U_10804,U_10802,U_10800) = U_10794
& hBOOL(hAPP(hAPP(c_member(U_10800),U_10794),U_10804)) )
& hBOOL(hAPP(hAPP(c_member(U_10800),sK232(U_10804,U_10802,U_10800)),U_10802)) ) )
& ! [U_10803,U_10801,U_10799] :
( ! [U_10793] :
( ! [U_10792] :
( U_10793 != U_10792
| ~ hBOOL(hAPP(hAPP(c_member(U_10799),U_10792),U_10803)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_10799),U_10793),U_10801)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10799,tc_HOL_Obool)),U_10801),U_10803) != c_Orderings_Obot__class_Obot(tc_fun(U_10799,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK232]),skolemize(U_10795,sK232(U_10804,U_10802,U_10800))],[f_2910_3]) ).
fof(f_2910_5,plain,
( ! [U_10804,U_10802,U_10800] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10800,tc_HOL_Obool)),U_10802),U_10804) = c_Orderings_Obot__class_Obot(tc_fun(U_10800,tc_HOL_Obool))
| ( sK232(U_10804,U_10802,U_10800) = sK233(U_10804,U_10802,U_10800)
& hBOOL(hAPP(hAPP(c_member(U_10800),sK233(U_10804,U_10802,U_10800)),U_10804))
& hBOOL(hAPP(hAPP(c_member(U_10800),sK232(U_10804,U_10802,U_10800)),U_10802)) ) )
& ! [U_10803,U_10801,U_10799] :
( ! [U_10793] :
( ! [U_10792] :
( U_10793 != U_10792
| ~ hBOOL(hAPP(hAPP(c_member(U_10799),U_10792),U_10803)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_10799),U_10793),U_10801)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10799,tc_HOL_Obool)),U_10801),U_10803) != c_Orderings_Obot__class_Obot(tc_fun(U_10799,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK233]),skolemize(U_10794,sK233(U_10804,U_10802,U_10800))],[f_2910_4]) ).
cnf(f_2910_6,plain,
( U_10793 != U_10792
| ~ hBOOL(hAPP(hAPP(c_member(U_10799),U_10792),U_10803))
| ~ hBOOL(hAPP(hAPP(c_member(U_10799),U_10793),U_10801))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10799,tc_HOL_Obool)),U_10801),U_10803) != c_Orderings_Obot__class_Obot(tc_fun(U_10799,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2910_5]) ).
cnf(f_2910_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_10800),sK232(U_10804,U_10802,U_10800)),U_10802))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10800,tc_HOL_Obool)),U_10802),U_10804) = c_Orderings_Obot__class_Obot(tc_fun(U_10800,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2910_5]) ).
cnf(f_2910_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_10800),sK233(U_10804,U_10802,U_10800)),U_10804))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10800,tc_HOL_Obool)),U_10802),U_10804) = c_Orderings_Obot__class_Obot(tc_fun(U_10800,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2910_5]) ).
cnf(f_2910_9,plain,
( sK232(U_10804,U_10802,U_10800) = sK233(U_10804,U_10802,U_10800)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10800,tc_HOL_Obool)),U_10802),U_10804) = c_Orderings_Obot__class_Obot(tc_fun(U_10800,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2910_5]) ).
fof(f_2911_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_2911_2,plain,
! [U_10806,U_10805] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10805),c_Orderings_Obot__class_Obot(U_10805)),U_10806) = c_Orderings_Obot__class_Obot(U_10805)
| ~ class_Lattices_Obounded__lattice__bot(U_10805) ),
inference(variable_rename,[status(thm)],[f_2911_1]) ).
cnf(f_2911_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10805),c_Orderings_Obot__class_Obot(U_10805)),U_10806) = c_Orderings_Obot__class_Obot(U_10805)
| ~ class_Lattices_Obounded__lattice__bot(U_10805) ),
inference(clausify,[status(thm)],[f_2911_2]) ).
fof(f_2912_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_2912_2,plain,
! [U_10808,U_10807] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10807),U_10808),c_Orderings_Obot__class_Obot(U_10807)) = c_Orderings_Obot__class_Obot(U_10807)
| ~ class_Lattices_Obounded__lattice__bot(U_10807) ),
inference(variable_rename,[status(thm)],[f_2912_1]) ).
cnf(f_2912_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10807),U_10808),c_Orderings_Obot__class_Obot(U_10807)) = c_Orderings_Obot__class_Obot(U_10807)
| ~ class_Lattices_Obounded__lattice__bot(U_10807) ),
inference(clausify,[status(thm)],[f_2912_2]) ).
fof(f_2913_1,plain,
! [V_B_2,V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_insert__inter__insert]) ).
fof(f_2913_2,plain,
! [U_10812,U_10811,U_10810,U_10809] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10809,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10809),U_10810),U_10811)),hAPP(hAPP(c_Set_Oinsert(U_10809),U_10810),U_10812)) = hAPP(hAPP(c_Set_Oinsert(U_10809),U_10810),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10809,tc_HOL_Obool)),U_10811),U_10812)),
inference(variable_rename,[status(thm)],[f_2913_1]) ).
cnf(f_2913_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10809,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10809),U_10810),U_10811)),hAPP(hAPP(c_Set_Oinsert(U_10809),U_10810),U_10812)) = hAPP(hAPP(c_Set_Oinsert(U_10809),U_10810),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10809,tc_HOL_Obool)),U_10811),U_10812)),
inference(clausify,[status(thm)],[f_2913_2]) ).
fof(f_2914_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_2914_2,plain,
! [U_10816,U_10815,U_10814,U_10813] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10813),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10813),U_10814),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10813),U_10815),U_10816))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10813),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10813),U_10814),U_10815)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10813),U_10814),U_10816))))
| ~ class_Lattices_Olattice(U_10813) ),
inference(variable_rename,[status(thm)],[f_2914_1]) ).
cnf(f_2914_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10813),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10813),U_10814),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10813),U_10815),U_10816))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10813),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10813),U_10814),U_10815)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10813),U_10814),U_10816))))
| ~ class_Lattices_Olattice(U_10813) ),
inference(clausify,[status(thm)],[f_2914_2]) ).
fof(f_2915_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_2915_2,plain,
! [U_10820,U_10819,U_10818,U_10817] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10817),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10817),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10817),U_10818),U_10819)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10817),U_10818),U_10820))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10817),U_10818),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10817),U_10819),U_10820))))
| ~ class_Lattices_Olattice(U_10817) ),
inference(variable_rename,[status(thm)],[f_2915_1]) ).
cnf(f_2915_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10817),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10817),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10817),U_10818),U_10819)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10817),U_10818),U_10820))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10817),U_10818),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10817),U_10819),U_10820))))
| ~ class_Lattices_Olattice(U_10817) ),
inference(clausify,[status(thm)],[f_2915_2]) ).
fof(f_2916_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_2916_2,plain,
! [U_10822,U_10821] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10821),hAPP(c_Groups_Ouminus__class_Ouminus(U_10821),U_10822)),U_10822) = c_Orderings_Obot__class_Obot(U_10821)
| ~ class_Lattices_Oboolean__algebra(U_10821) ),
inference(variable_rename,[status(thm)],[f_2916_1]) ).
cnf(f_2916_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10821),hAPP(c_Groups_Ouminus__class_Ouminus(U_10821),U_10822)),U_10822) = c_Orderings_Obot__class_Obot(U_10821)
| ~ class_Lattices_Oboolean__algebra(U_10821) ),
inference(clausify,[status(thm)],[f_2916_2]) ).
fof(f_2917_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_2917_2,plain,
! [U_10824,U_10823] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10823),U_10824),hAPP(c_Groups_Ouminus__class_Ouminus(U_10823),U_10824)) = c_Orderings_Obot__class_Obot(U_10823)
| ~ class_Lattices_Oboolean__algebra(U_10823) ),
inference(variable_rename,[status(thm)],[f_2917_1]) ).
cnf(f_2917_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10823),U_10824),hAPP(c_Groups_Ouminus__class_Ouminus(U_10823),U_10824)) = c_Orderings_Obot__class_Obot(U_10823)
| ~ class_Lattices_Oboolean__algebra(U_10823) ),
inference(clausify,[status(thm)],[f_2917_2]) ).
fof(f_2918_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_2918_2,plain,
! [U_10827,U_10826,U_10825] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10825),U_10826),U_10827) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10825),U_10826),hAPP(c_Groups_Ouminus__class_Ouminus(U_10825),U_10827))
| ~ class_Lattices_Oboolean__algebra(U_10825) ),
inference(variable_rename,[status(thm)],[f_2918_1]) ).
cnf(f_2918_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_10825),U_10826),U_10827) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10825),U_10826),hAPP(c_Groups_Ouminus__class_Ouminus(U_10825),U_10827))
| ~ class_Lattices_Oboolean__algebra(U_10825) ),
inference(clausify,[status(thm)],[f_2918_2]) ).
fof(f_2919_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_2919_2,plain,
! [U_10830,U_10829,U_10828] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_10828),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10828),U_10829),U_10830)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10828),hAPP(c_Groups_Ouminus__class_Ouminus(U_10828),U_10829)),hAPP(c_Groups_Ouminus__class_Ouminus(U_10828),U_10830))
| ~ class_Lattices_Oboolean__algebra(U_10828) ),
inference(variable_rename,[status(thm)],[f_2919_1]) ).
cnf(f_2919_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_10828),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10828),U_10829),U_10830)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10828),hAPP(c_Groups_Ouminus__class_Ouminus(U_10828),U_10829)),hAPP(c_Groups_Ouminus__class_Ouminus(U_10828),U_10830))
| ~ class_Lattices_Oboolean__algebra(U_10828) ),
inference(clausify,[status(thm)],[f_2919_2]) ).
fof(f_2920_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_2920_2,plain,
! [U_10833,U_10832,U_10831] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_10831),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10831),U_10832),U_10833)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10831),hAPP(c_Groups_Ouminus__class_Ouminus(U_10831),U_10832)),hAPP(c_Groups_Ouminus__class_Ouminus(U_10831),U_10833))
| ~ class_Lattices_Oboolean__algebra(U_10831) ),
inference(variable_rename,[status(thm)],[f_2920_1]) ).
cnf(f_2920_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_10831),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10831),U_10832),U_10833)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10831),hAPP(c_Groups_Ouminus__class_Ouminus(U_10831),U_10832)),hAPP(c_Groups_Ouminus__class_Ouminus(U_10831),U_10833))
| ~ class_Lattices_Oboolean__algebra(U_10831) ),
inference(clausify,[status(thm)],[f_2920_2]) ).
fof(f_2921_1,plain,
! [V_B_2,V_A_2,V_a_2,T_b] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__right]) ).
fof(f_2921_2,plain,
! [U_10837,U_10836,U_10835,U_10834] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10834,tc_HOL_Obool)),U_10836),hAPP(hAPP(c_Set_Oinsert(U_10834),U_10835),U_10837)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10834,tc_HOL_Obool)),U_10836),U_10837)
| hBOOL(hAPP(hAPP(c_member(U_10834),U_10835),U_10836)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10834,tc_HOL_Obool)),U_10836),hAPP(hAPP(c_Set_Oinsert(U_10834),U_10835),U_10837)) = hAPP(hAPP(c_Set_Oinsert(U_10834),U_10835),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10834,tc_HOL_Obool)),U_10836),U_10837))
| ~ hBOOL(hAPP(hAPP(c_member(U_10834),U_10835),U_10836)) ) ),
inference(variable_rename,[status(thm)],[f_2921_1]) ).
fof(f_2921_3,plain,
( ! [U_10845,U_10843,U_10841,U_10839] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10839,tc_HOL_Obool)),U_10843),hAPP(hAPP(c_Set_Oinsert(U_10839),U_10841),U_10845)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10839,tc_HOL_Obool)),U_10843),U_10845)
| hBOOL(hAPP(hAPP(c_member(U_10839),U_10841),U_10843)) )
& ! [U_10844,U_10842,U_10840,U_10838] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10838,tc_HOL_Obool)),U_10842),hAPP(hAPP(c_Set_Oinsert(U_10838),U_10840),U_10844)) = hAPP(hAPP(c_Set_Oinsert(U_10838),U_10840),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10838,tc_HOL_Obool)),U_10842),U_10844))
| ~ hBOOL(hAPP(hAPP(c_member(U_10838),U_10840),U_10842)) ) ),
inference(miniscope,[status(thm)],[f_2921_2]) ).
cnf(f_2921_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10838,tc_HOL_Obool)),U_10842),hAPP(hAPP(c_Set_Oinsert(U_10838),U_10840),U_10844)) = hAPP(hAPP(c_Set_Oinsert(U_10838),U_10840),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10838,tc_HOL_Obool)),U_10842),U_10844))
| ~ hBOOL(hAPP(hAPP(c_member(U_10838),U_10840),U_10842)) ),
inference(clausify,[status(thm)],[f_2921_3]) ).
cnf(f_2921_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10839,tc_HOL_Obool)),U_10843),hAPP(hAPP(c_Set_Oinsert(U_10839),U_10841),U_10845)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10839,tc_HOL_Obool)),U_10843),U_10845)
| hBOOL(hAPP(hAPP(c_member(U_10839),U_10841),U_10843)) ),
inference(clausify,[status(thm)],[f_2921_3]) ).
fof(f_2922_1,plain,
! [V_B_2,V_C_2,V_a_2,T_b] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__left]) ).
fof(f_2922_2,plain,
! [U_10849,U_10848,U_10847,U_10846] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10846,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10846),U_10847),U_10849)),U_10848) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10846,tc_HOL_Obool)),U_10849),U_10848)
| hBOOL(hAPP(hAPP(c_member(U_10846),U_10847),U_10848)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10846,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10846),U_10847),U_10849)),U_10848) = hAPP(hAPP(c_Set_Oinsert(U_10846),U_10847),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10846,tc_HOL_Obool)),U_10849),U_10848))
| ~ hBOOL(hAPP(hAPP(c_member(U_10846),U_10847),U_10848)) ) ),
inference(variable_rename,[status(thm)],[f_2922_1]) ).
fof(f_2922_3,plain,
( ! [U_10857,U_10855,U_10853,U_10851] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10851,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10851),U_10853),U_10857)),U_10855) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10851,tc_HOL_Obool)),U_10857),U_10855)
| hBOOL(hAPP(hAPP(c_member(U_10851),U_10853),U_10855)) )
& ! [U_10856,U_10854,U_10852,U_10850] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10850,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10850),U_10852),U_10856)),U_10854) = hAPP(hAPP(c_Set_Oinsert(U_10850),U_10852),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10850,tc_HOL_Obool)),U_10856),U_10854))
| ~ hBOOL(hAPP(hAPP(c_member(U_10850),U_10852),U_10854)) ) ),
inference(miniscope,[status(thm)],[f_2922_2]) ).
cnf(f_2922_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10850,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10850),U_10852),U_10856)),U_10854) = hAPP(hAPP(c_Set_Oinsert(U_10850),U_10852),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10850,tc_HOL_Obool)),U_10856),U_10854))
| ~ hBOOL(hAPP(hAPP(c_member(U_10850),U_10852),U_10854)) ),
inference(clausify,[status(thm)],[f_2922_3]) ).
cnf(f_2922_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10851,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10851),U_10853),U_10857)),U_10855) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10851,tc_HOL_Obool)),U_10857),U_10855)
| hBOOL(hAPP(hAPP(c_member(U_10851),U_10853),U_10855)) ),
inference(clausify,[status(thm)],[f_2922_3]) ).
fof(f_2923_1,plain,
! [V_B_2,V_A_2,V_a_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if0]) ).
fof(f_2923_2,plain,
! [U_10861,U_10860,U_10859,U_10858] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10858,tc_HOL_Obool)),U_10860),hAPP(hAPP(c_Set_Oinsert(U_10858),U_10859),U_10861)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10858,tc_HOL_Obool)),U_10860),U_10861)
| hBOOL(hAPP(hAPP(c_member(U_10858),U_10859),U_10860)) ),
inference(variable_rename,[status(thm)],[f_2923_1]) ).
cnf(f_2923_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10858,tc_HOL_Obool)),U_10860),hAPP(hAPP(c_Set_Oinsert(U_10858),U_10859),U_10861)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10858,tc_HOL_Obool)),U_10860),U_10861)
| hBOOL(hAPP(hAPP(c_member(U_10858),U_10859),U_10860)) ),
inference(clausify,[status(thm)],[f_2923_2]) ).
fof(f_2924_1,plain,
! [V_B_2,V_C_2,V_a_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if0]) ).
fof(f_2924_2,plain,
! [U_10865,U_10864,U_10863,U_10862] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10862,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10862),U_10863),U_10865)),U_10864) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10862,tc_HOL_Obool)),U_10865),U_10864)
| hBOOL(hAPP(hAPP(c_member(U_10862),U_10863),U_10864)) ),
inference(variable_rename,[status(thm)],[f_2924_1]) ).
cnf(f_2924_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10862,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10862),U_10863),U_10865)),U_10864) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10862,tc_HOL_Obool)),U_10865),U_10864)
| hBOOL(hAPP(hAPP(c_member(U_10862),U_10863),U_10864)) ),
inference(clausify,[status(thm)],[f_2924_2]) ).
fof(f_2925_1,plain,
! [V_B_2,V_A_2,V_a_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if1]) ).
fof(f_2925_2,plain,
! [U_10869,U_10868,U_10867,U_10866] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10866,tc_HOL_Obool)),U_10868),hAPP(hAPP(c_Set_Oinsert(U_10866),U_10867),U_10869)) = hAPP(hAPP(c_Set_Oinsert(U_10866),U_10867),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10866,tc_HOL_Obool)),U_10868),U_10869))
| ~ hBOOL(hAPP(hAPP(c_member(U_10866),U_10867),U_10868)) ),
inference(variable_rename,[status(thm)],[f_2925_1]) ).
cnf(f_2925_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10866,tc_HOL_Obool)),U_10868),hAPP(hAPP(c_Set_Oinsert(U_10866),U_10867),U_10869)) = hAPP(hAPP(c_Set_Oinsert(U_10866),U_10867),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10866,tc_HOL_Obool)),U_10868),U_10869))
| ~ hBOOL(hAPP(hAPP(c_member(U_10866),U_10867),U_10868)) ),
inference(clausify,[status(thm)],[f_2925_2]) ).
fof(f_2926_1,plain,
! [V_B_2,V_C_2,V_a_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if1]) ).
fof(f_2926_2,plain,
! [U_10873,U_10872,U_10871,U_10870] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10870,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10870),U_10871),U_10873)),U_10872) = hAPP(hAPP(c_Set_Oinsert(U_10870),U_10871),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10870,tc_HOL_Obool)),U_10873),U_10872))
| ~ hBOOL(hAPP(hAPP(c_member(U_10870),U_10871),U_10872)) ),
inference(variable_rename,[status(thm)],[f_2926_1]) ).
cnf(f_2926_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10870,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10870),U_10871),U_10873)),U_10872) = hAPP(hAPP(c_Set_Oinsert(U_10870),U_10871),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10870,tc_HOL_Obool)),U_10873),U_10872))
| ~ hBOOL(hAPP(hAPP(c_member(U_10870),U_10871),U_10872)) ),
inference(clausify,[status(thm)],[f_2926_2]) ).
fof(f_2927_1,plain,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
| ~ class_Lattices_Osemilattice__inf(T_b)
| ~ class_Lattices_Osemilattice__inf(T_c) ),
inference(fof_nnf,[status(thm)],[fact_mono__inf]) ).
fof(f_2927_2,plain,
! [U_10878,U_10877,U_10876,U_10875,U_10874] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10874),hAPP(U_10876,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10875),U_10877),U_10878))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10874),hAPP(U_10876,U_10877)),hAPP(U_10876,U_10878))))
| ~ c_Orderings_Oorder__class_Omono(U_10875,U_10874,U_10876)
| ~ class_Lattices_Osemilattice__inf(U_10875)
| ~ class_Lattices_Osemilattice__inf(U_10874) ),
inference(variable_rename,[status(thm)],[f_2927_1]) ).
cnf(f_2927_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10874),hAPP(U_10876,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10875),U_10877),U_10878))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10874),hAPP(U_10876,U_10877)),hAPP(U_10876,U_10878))))
| ~ c_Orderings_Oorder__class_Omono(U_10875,U_10874,U_10876)
| ~ class_Lattices_Osemilattice__inf(U_10875)
| ~ class_Lattices_Osemilattice__inf(U_10874) ),
inference(clausify,[status(thm)],[f_2927_2]) ).
fof(f_2928_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_image__Int__subset]) ).
fof(f_2928_2,plain,
! [U_10883,U_10882,U_10881,U_10880,U_10879] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10879,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10880,U_10879,U_10881),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10880,tc_HOL_Obool)),U_10882),U_10883))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10879,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10880,U_10879,U_10881),U_10882)),hAPP(c_Set_Oimage(U_10880,U_10879,U_10881),U_10883)))),
inference(variable_rename,[status(thm)],[f_2928_1]) ).
cnf(f_2928_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10879,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10880,U_10879,U_10881),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10880,tc_HOL_Obool)),U_10882),U_10883))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10879,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_10880,U_10879,U_10881),U_10882)),hAPP(c_Set_Oimage(U_10880,U_10879,U_10881),U_10883)))),
inference(clausify,[status(thm)],[f_2928_2]) ).
fof(f_2929_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_Diff__triv]) ).
fof(f_2929_2,plain,
! [U_10886,U_10885,U_10884] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10884,tc_HOL_Obool)),U_10885),U_10886) = U_10885
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10884,tc_HOL_Obool)),U_10885),U_10886) != c_Orderings_Obot__class_Obot(tc_fun(U_10884,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_2929_1]) ).
cnf(f_2929_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10884,tc_HOL_Obool)),U_10885),U_10886) = U_10885
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10884,tc_HOL_Obool)),U_10885),U_10886) != c_Orderings_Obot__class_Obot(tc_fun(U_10884,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2929_2]) ).
fof(f_2930_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Diff__disjoint]) ).
fof(f_2930_2,plain,
! [U_10889,U_10888,U_10887] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10887,tc_HOL_Obool)),U_10888),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10887,tc_HOL_Obool)),U_10889),U_10888)) = c_Orderings_Obot__class_Obot(tc_fun(U_10887,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2930_1]) ).
cnf(f_2930_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10887,tc_HOL_Obool)),U_10888),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10887,tc_HOL_Obool)),U_10889),U_10888)) = c_Orderings_Obot__class_Obot(tc_fun(U_10887,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2930_2]) ).
fof(f_2931_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Un__Int__assoc__eq]) ).
fof(f_2931_2,plain,
! [U_10893,U_10892,U_10891,U_10890] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10890,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10890,tc_HOL_Obool)),U_10891),U_10892)),U_10893) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10890,tc_HOL_Obool)),U_10891),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10890,tc_HOL_Obool)),U_10892),U_10893))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10890,tc_HOL_Obool)),U_10893),U_10891)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10890,tc_HOL_Obool)),U_10893),U_10891))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10890,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10890,tc_HOL_Obool)),U_10891),U_10892)),U_10893) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10890,tc_HOL_Obool)),U_10891),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10890,tc_HOL_Obool)),U_10892),U_10893)) ) ),
inference(variable_rename,[status(thm)],[f_2931_1]) ).
fof(f_2931_3,plain,
( ! [U_10901,U_10899,U_10897,U_10895] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10895,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10895,tc_HOL_Obool)),U_10897),U_10899)),U_10901) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10895,tc_HOL_Obool)),U_10897),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10895,tc_HOL_Obool)),U_10899),U_10901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10895,tc_HOL_Obool)),U_10901),U_10897)) )
& ! [U_10900,U_10898,U_10896,U_10894] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10894,tc_HOL_Obool)),U_10900),U_10896))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10894,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10894,tc_HOL_Obool)),U_10896),U_10898)),U_10900) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10894,tc_HOL_Obool)),U_10896),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10894,tc_HOL_Obool)),U_10898),U_10900)) ) ),
inference(miniscope,[status(thm)],[f_2931_2]) ).
cnf(f_2931_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10894,tc_HOL_Obool)),U_10900),U_10896))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10894,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10894,tc_HOL_Obool)),U_10896),U_10898)),U_10900) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10894,tc_HOL_Obool)),U_10896),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10894,tc_HOL_Obool)),U_10898),U_10900)) ),
inference(clausify,[status(thm)],[f_2931_3]) ).
cnf(f_2931_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10895,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10895,tc_HOL_Obool)),U_10897),U_10899)),U_10901) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10895,tc_HOL_Obool)),U_10897),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10895,tc_HOL_Obool)),U_10899),U_10901))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10895,tc_HOL_Obool)),U_10901),U_10897)) ),
inference(clausify,[status(thm)],[f_2931_3]) ).
fof(f_2932_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Un__Diff__Int]) ).
fof(f_2932_2,plain,
! [U_10904,U_10903,U_10902] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10902,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10902,tc_HOL_Obool)),U_10903),U_10904)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10902,tc_HOL_Obool)),U_10903),U_10904)) = U_10903,
inference(variable_rename,[status(thm)],[f_2932_1]) ).
cnf(f_2932_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10902,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10902,tc_HOL_Obool)),U_10903),U_10904)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10902,tc_HOL_Obool)),U_10903),U_10904)) = U_10903,
inference(clausify,[status(thm)],[f_2932_2]) ).
fof(f_2933_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Diff__Un]) ).
fof(f_2933_2,plain,
! [U_10908,U_10907,U_10906,U_10905] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10905,tc_HOL_Obool)),U_10906),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10905,tc_HOL_Obool)),U_10907),U_10908)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10905,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10905,tc_HOL_Obool)),U_10906),U_10907)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10905,tc_HOL_Obool)),U_10906),U_10908)),
inference(variable_rename,[status(thm)],[f_2933_1]) ).
cnf(f_2933_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10905,tc_HOL_Obool)),U_10906),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10905,tc_HOL_Obool)),U_10907),U_10908)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10905,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10905,tc_HOL_Obool)),U_10906),U_10907)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10905,tc_HOL_Obool)),U_10906),U_10908)),
inference(clausify,[status(thm)],[f_2933_2]) ).
fof(f_2934_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Diff__Int]) ).
fof(f_2934_2,plain,
! [U_10912,U_10911,U_10910,U_10909] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10909,tc_HOL_Obool)),U_10910),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10909,tc_HOL_Obool)),U_10911),U_10912)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10909,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10909,tc_HOL_Obool)),U_10910),U_10911)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10909,tc_HOL_Obool)),U_10910),U_10912)),
inference(variable_rename,[status(thm)],[f_2934_1]) ).
cnf(f_2934_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10909,tc_HOL_Obool)),U_10910),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10909,tc_HOL_Obool)),U_10911),U_10912)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10909,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10909,tc_HOL_Obool)),U_10910),U_10911)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10909,tc_HOL_Obool)),U_10910),U_10912)),
inference(clausify,[status(thm)],[f_2934_2]) ).
fof(f_2935_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I11_J]) ).
fof(f_2935_2,plain,
! [U_10916,U_10915,U_10914,U_10913] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10913,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10913,U_10914),U_10915)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10913,U_10915),U_10916)) = c_Orderings_Obot__class_Obot(tc_fun(U_10913,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_10913) ),
inference(variable_rename,[status(thm)],[f_2935_1]) ).
cnf(f_2935_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10913,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10913,U_10914),U_10915)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_10913,U_10915),U_10916)) = c_Orderings_Obot__class_Obot(tc_fun(U_10913,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_10913) ),
inference(clausify,[status(thm)],[f_2935_2]) ).
fof(f_2936_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_2936_2,plain,
! [U_10918,U_10917] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_10917),U_10918) = 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_10917)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10918))),
inference(variable_rename,[status(thm)],[f_2936_1]) ).
cnf(f_2936_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_10917),U_10918) = 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_10917)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10918))),
inference(clausify,[status(thm)],[f_2936_2]) ).
fof(f_2937_1,plain,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Compl__disjoint]) ).
fof(f_2937_2,plain,
! [U_10920,U_10919] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10919,tc_HOL_Obool)),U_10920),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10919,tc_HOL_Obool)),U_10920)) = c_Orderings_Obot__class_Obot(tc_fun(U_10919,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2937_1]) ).
cnf(f_2937_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10919,tc_HOL_Obool)),U_10920),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10919,tc_HOL_Obool)),U_10920)) = c_Orderings_Obot__class_Obot(tc_fun(U_10919,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2937_2]) ).
fof(f_2938_1,plain,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Compl__disjoint2]) ).
fof(f_2938_2,plain,
! [U_10922,U_10921] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10921,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10921,tc_HOL_Obool)),U_10922)),U_10922) = c_Orderings_Obot__class_Obot(tc_fun(U_10921,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_2938_1]) ).
cnf(f_2938_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10921,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10921,tc_HOL_Obool)),U_10922)),U_10922) = c_Orderings_Obot__class_Obot(tc_fun(U_10921,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_2938_2]) ).
fof(f_2939_1,plain,
! [V_B_2,V_A_2,V_R_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_Image__Int__subset]) ).
fof(f_2939_2,plain,
! [U_10927,U_10926,U_10925,U_10924,U_10923] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10923,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10924,U_10923,U_10925),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10924,tc_HOL_Obool)),U_10926),U_10927))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10923,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10924,U_10923,U_10925),U_10926)),hAPP(c_Relation_OImage(U_10924,U_10923,U_10925),U_10927)))),
inference(variable_rename,[status(thm)],[f_2939_1]) ).
cnf(f_2939_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10923,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10924,U_10923,U_10925),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10924,tc_HOL_Obool)),U_10926),U_10927))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10923,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_10924,U_10923,U_10925),U_10926)),hAPP(c_Relation_OImage(U_10924,U_10923,U_10925),U_10927)))),
inference(clausify,[status(thm)],[f_2939_2]) ).
fof(f_2940_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Compl__Int]) ).
fof(f_2940_2,plain,
! [U_10930,U_10929,U_10928] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10928,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10928,tc_HOL_Obool)),U_10929),U_10930)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10928,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10928,tc_HOL_Obool)),U_10929)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10928,tc_HOL_Obool)),U_10930)),
inference(variable_rename,[status(thm)],[f_2940_1]) ).
cnf(f_2940_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10928,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10928,tc_HOL_Obool)),U_10929),U_10930)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10928,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10928,tc_HOL_Obool)),U_10929)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10928,tc_HOL_Obool)),U_10930)),
inference(clausify,[status(thm)],[f_2940_2]) ).
fof(f_2941_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Compl__Un]) ).
fof(f_2941_2,plain,
! [U_10933,U_10932,U_10931] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10931,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10931,tc_HOL_Obool)),U_10932),U_10933)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10931,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10931,tc_HOL_Obool)),U_10932)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10931,tc_HOL_Obool)),U_10933)),
inference(variable_rename,[status(thm)],[f_2941_1]) ).
cnf(f_2941_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10931,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10931,tc_HOL_Obool)),U_10932),U_10933)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10931,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10931,tc_HOL_Obool)),U_10932)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10931,tc_HOL_Obool)),U_10933)),
inference(clausify,[status(thm)],[f_2941_2]) ).
fof(f_2942_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
inference(fof_nnf,[status(thm)],[fact_Diff__Compl]) ).
fof(f_2942_2,plain,
! [U_10936,U_10935,U_10934] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10934,tc_HOL_Obool)),U_10935),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10934,tc_HOL_Obool)),U_10936)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10934,tc_HOL_Obool)),U_10935),U_10936),
inference(variable_rename,[status(thm)],[f_2942_1]) ).
cnf(f_2942_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10934,tc_HOL_Obool)),U_10935),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10934,tc_HOL_Obool)),U_10936)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10934,tc_HOL_Obool)),U_10935),U_10936),
inference(clausify,[status(thm)],[f_2942_2]) ).
fof(f_2943_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Diff__eq]) ).
fof(f_2943_2,plain,
! [U_10939,U_10938,U_10937] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10937,tc_HOL_Obool)),U_10938),U_10939) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10937,tc_HOL_Obool)),U_10938),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10937,tc_HOL_Obool)),U_10939)),
inference(variable_rename,[status(thm)],[f_2943_1]) ).
cnf(f_2943_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10937,tc_HOL_Obool)),U_10938),U_10939) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10937,tc_HOL_Obool)),U_10938),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10937,tc_HOL_Obool)),U_10939)),
inference(clausify,[status(thm)],[f_2943_2]) ).
fof(f_2944_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I14_J]) ).
fof(f_2944_2,plain,
! [U_10943,U_10942,U_10941,U_10940] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10940,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10940,U_10941,U_10942)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10940,U_10942,U_10943)) = c_Orderings_Obot__class_Obot(tc_fun(U_10940,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_10940) ),
inference(variable_rename,[status(thm)],[f_2944_1]) ).
cnf(f_2944_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10940,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10940,U_10941,U_10942)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10940,U_10942,U_10943)) = c_Orderings_Obot__class_Obot(tc_fun(U_10940,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_10940) ),
inference(clausify,[status(thm)],[f_2944_2]) ).
fof(f_2945_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_mono__Int]) ).
fof(f_2945_2,plain,
! [U_10948,U_10947,U_10946,U_10945,U_10944] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10945,tc_HOL_Obool)),hAPP(U_10946,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10944,tc_HOL_Obool)),U_10947),U_10948))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10945,tc_HOL_Obool)),hAPP(U_10946,U_10947)),hAPP(U_10946,U_10948))))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_10944,tc_HOL_Obool),tc_fun(U_10945,tc_HOL_Obool),U_10946) ),
inference(variable_rename,[status(thm)],[f_2945_1]) ).
cnf(f_2945_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10945,tc_HOL_Obool)),hAPP(U_10946,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10944,tc_HOL_Obool)),U_10947),U_10948))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10945,tc_HOL_Obool)),hAPP(U_10946,U_10947)),hAPP(U_10946,U_10948))))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_10944,tc_HOL_Obool),tc_fun(U_10945,tc_HOL_Obool),U_10946) ),
inference(clausify,[status(thm)],[f_2945_2]) ).
fof(f_2946_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
inference(fof_nnf,[status(thm)],[fact_Image__Id__on]) ).
fof(f_2946_2,plain,
! [U_10951,U_10950,U_10949] : hAPP(c_Relation_OImage(U_10949,U_10949,c_Relation_OId__on(U_10949,U_10950)),U_10951) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10949,tc_HOL_Obool)),U_10950),U_10951),
inference(variable_rename,[status(thm)],[f_2946_1]) ).
cnf(f_2946_3,plain,
hAPP(c_Relation_OImage(U_10949,U_10949,c_Relation_OId__on(U_10949,U_10950)),U_10951) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10949,tc_HOL_Obool)),U_10950),U_10951),
inference(clausify,[status(thm)],[f_2946_2]) ).
fof(f_2947_1,plain,
! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2)) ),
inference(fof_nnf,[status(thm)],[fact_INT__absorb]) ).
fof(f_2947_2,plain,
! [U_10956,U_10955,U_10954,U_10953,U_10952] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10955,tc_HOL_Obool)),hAPP(U_10956,U_10953)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10952,tc_fun(U_10955,tc_HOL_Obool)),U_10954),U_10956)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10952,tc_fun(U_10955,tc_HOL_Obool)),U_10954),U_10956)
| ~ hBOOL(hAPP(hAPP(c_member(U_10952),U_10953),U_10954)) ),
inference(variable_rename,[status(thm)],[f_2947_1]) ).
cnf(f_2947_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10955,tc_HOL_Obool)),hAPP(U_10956,U_10953)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10952,tc_fun(U_10955,tc_HOL_Obool)),U_10954),U_10956)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10952,tc_fun(U_10955,tc_HOL_Obool)),U_10954),U_10956)
| ~ hBOOL(hAPP(hAPP(c_member(U_10952),U_10953),U_10954)) ),
inference(clausify,[status(thm)],[f_2947_2]) ).
fof(f_2948_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I1_J]) ).
fof(f_2948_2,plain,
! [U_10961,U_10960,U_10959,U_10958,U_10957] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10959,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10958,tc_fun(U_10959,tc_HOL_Obool)),U_10957),U_10960)),U_10961) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10958,tc_fun(U_10959,tc_HOL_Obool)),U_10957),hAPP(hAPP(c_COMBC(U_10958,tc_fun(U_10959,tc_HOL_Obool),tc_fun(U_10959,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10959,tc_HOL_Obool),tc_fun(tc_fun(U_10959,tc_HOL_Obool),tc_fun(U_10959,tc_HOL_Obool)),U_10958),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10959,tc_HOL_Obool))),U_10960)),U_10961))
| U_10957 = c_Orderings_Obot__class_Obot(tc_fun(U_10958,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10959,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10958,tc_fun(U_10959,tc_HOL_Obool)),U_10957),U_10960)),U_10961) = U_10961
| U_10957 != c_Orderings_Obot__class_Obot(tc_fun(U_10958,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2948_1]) ).
fof(f_2948_3,plain,
( ! [U_10971,U_10969,U_10967,U_10965,U_10963] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10967,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10965,tc_fun(U_10967,tc_HOL_Obool)),U_10963),U_10969)),U_10971) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10965,tc_fun(U_10967,tc_HOL_Obool)),U_10963),hAPP(hAPP(c_COMBC(U_10965,tc_fun(U_10967,tc_HOL_Obool),tc_fun(U_10967,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10967,tc_HOL_Obool),tc_fun(tc_fun(U_10967,tc_HOL_Obool),tc_fun(U_10967,tc_HOL_Obool)),U_10965),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10967,tc_HOL_Obool))),U_10969)),U_10971))
| U_10963 = c_Orderings_Obot__class_Obot(tc_fun(U_10965,tc_HOL_Obool)) )
& ! [U_10970,U_10968,U_10966,U_10964,U_10962] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10966,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10964,tc_fun(U_10966,tc_HOL_Obool)),U_10962),U_10968)),U_10970) = U_10970
| U_10962 != c_Orderings_Obot__class_Obot(tc_fun(U_10964,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2948_2]) ).
cnf(f_2948_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10966,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10964,tc_fun(U_10966,tc_HOL_Obool)),U_10962),U_10968)),U_10970) = U_10970
| U_10962 != c_Orderings_Obot__class_Obot(tc_fun(U_10964,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2948_3]) ).
cnf(f_2948_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10967,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10965,tc_fun(U_10967,tc_HOL_Obool)),U_10963),U_10969)),U_10971) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10965,tc_fun(U_10967,tc_HOL_Obool)),U_10963),hAPP(hAPP(c_COMBC(U_10965,tc_fun(U_10967,tc_HOL_Obool),tc_fun(U_10967,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10967,tc_HOL_Obool),tc_fun(tc_fun(U_10967,tc_HOL_Obool),tc_fun(U_10967,tc_HOL_Obool)),U_10965),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10967,tc_HOL_Obool))),U_10969)),U_10971))
| U_10963 = c_Orderings_Obot__class_Obot(tc_fun(U_10965,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2948_3]) ).
fof(f_2949_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I2_J]) ).
fof(f_2949_2,plain,
! [U_10976,U_10975,U_10974,U_10973,U_10972] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10974,tc_HOL_Obool)),U_10975),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10973,tc_fun(U_10974,tc_HOL_Obool)),U_10972),U_10976)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10973,tc_fun(U_10974,tc_HOL_Obool)),U_10972),hAPP(hAPP(c_COMBB(tc_fun(U_10974,tc_HOL_Obool),tc_fun(U_10974,tc_HOL_Obool),U_10973),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10974,tc_HOL_Obool)),U_10975)),U_10976))
| U_10972 = c_Orderings_Obot__class_Obot(tc_fun(U_10973,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10974,tc_HOL_Obool)),U_10975),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10973,tc_fun(U_10974,tc_HOL_Obool)),U_10972),U_10976)) = U_10975
| U_10972 != c_Orderings_Obot__class_Obot(tc_fun(U_10973,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2949_1]) ).
fof(f_2949_3,plain,
( ! [U_10986,U_10984,U_10982,U_10980,U_10978] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10982,tc_HOL_Obool)),U_10984),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10980,tc_fun(U_10982,tc_HOL_Obool)),U_10978),U_10986)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10980,tc_fun(U_10982,tc_HOL_Obool)),U_10978),hAPP(hAPP(c_COMBB(tc_fun(U_10982,tc_HOL_Obool),tc_fun(U_10982,tc_HOL_Obool),U_10980),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10982,tc_HOL_Obool)),U_10984)),U_10986))
| U_10978 = c_Orderings_Obot__class_Obot(tc_fun(U_10980,tc_HOL_Obool)) )
& ! [U_10985,U_10983,U_10981,U_10979,U_10977] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10981,tc_HOL_Obool)),U_10983),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10979,tc_fun(U_10981,tc_HOL_Obool)),U_10977),U_10985)) = U_10983
| U_10977 != c_Orderings_Obot__class_Obot(tc_fun(U_10979,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2949_2]) ).
cnf(f_2949_4,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10981,tc_HOL_Obool)),U_10983),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10979,tc_fun(U_10981,tc_HOL_Obool)),U_10977),U_10985)) = U_10983
| U_10977 != c_Orderings_Obot__class_Obot(tc_fun(U_10979,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2949_3]) ).
cnf(f_2949_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10982,tc_HOL_Obool)),U_10984),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10980,tc_fun(U_10982,tc_HOL_Obool)),U_10978),U_10986)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10980,tc_fun(U_10982,tc_HOL_Obool)),U_10978),hAPP(hAPP(c_COMBB(tc_fun(U_10982,tc_HOL_Obool),tc_fun(U_10982,tc_HOL_Obool),U_10980),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10982,tc_HOL_Obool)),U_10984)),U_10986))
| U_10978 = c_Orderings_Obot__class_Obot(tc_fun(U_10980,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2949_3]) ).
fof(f_2950_1,plain,
! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_INT__insert]) ).
fof(f_2950_2,plain,
! [U_10991,U_10990,U_10989,U_10988,U_10987] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10987,tc_fun(U_10988,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10987),U_10989),U_10990)),U_10991) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10988,tc_HOL_Obool)),hAPP(U_10991,U_10989)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10987,tc_fun(U_10988,tc_HOL_Obool)),U_10990),U_10991)),
inference(variable_rename,[status(thm)],[f_2950_1]) ).
cnf(f_2950_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10987,tc_fun(U_10988,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10987),U_10989),U_10990)),U_10991) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10988,tc_HOL_Obool)),hAPP(U_10991,U_10989)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10987,tc_fun(U_10988,tc_HOL_Obool)),U_10990),U_10991)),
inference(clausify,[status(thm)],[f_2950_2]) ).
fof(f_2951_1,plain,
! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)),
inference(fof_nnf,[status(thm)],[fact_INT__Un]) ).
fof(f_2951_2,plain,
! [U_10996,U_10995,U_10994,U_10993,U_10992] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10992,tc_fun(U_10993,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10992,tc_HOL_Obool)),U_10994),U_10995)),U_10996) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10993,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10992,tc_fun(U_10993,tc_HOL_Obool)),U_10994),U_10996)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10992,tc_fun(U_10993,tc_HOL_Obool)),U_10995),U_10996)),
inference(variable_rename,[status(thm)],[f_2951_1]) ).
cnf(f_2951_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10992,tc_fun(U_10993,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10992,tc_HOL_Obool)),U_10994),U_10995)),U_10996) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10993,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10992,tc_fun(U_10993,tc_HOL_Obool)),U_10994),U_10996)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_10992,tc_fun(U_10993,tc_HOL_Obool)),U_10995),U_10996)),
inference(clausify,[status(thm)],[f_2951_2]) ).
fof(f_2952_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_2952_2,plain,
! [U_10998,U_10997] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_10997),U_10998) = 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_10997)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10998)))
| ~ c_Nat__Transfer_Onat__set(U_10998)
| ~ c_Nat__Transfer_Onat__set(U_10997) ),
inference(variable_rename,[status(thm)],[f_2952_1]) ).
cnf(f_2952_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_10997),U_10998) = 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_10997)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10998)))
| ~ c_Nat__Transfer_Onat__set(U_10998)
| ~ c_Nat__Transfer_Onat__set(U_10997) ),
inference(clausify,[status(thm)],[f_2952_2]) ).
fof(f_2953_1,plain,
! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
( c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
| ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2) ),
inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent]) ).
fof(f_2953_2,plain,
! [U_11006,U_11005,U_11004,U_11003,U_11002,U_11001,U_11000,U_10999] :
( c_Equiv__Relations_Ocongruent(U_11002,U_11003,U_11004,hAPP(U_11005,U_11006))
| ~ hBOOL(hAPP(hAPP(c_member(U_10999),U_11006),U_11000))
| ~ c_Equiv__Relations_Ocongruent2(U_10999,U_11002,U_11003,U_11001,U_11004,U_11005)
| ~ c_Equiv__Relations_Oequiv(U_10999,U_11000,U_11001) ),
inference(variable_rename,[status(thm)],[f_2953_1]) ).
cnf(f_2953_3,plain,
( c_Equiv__Relations_Ocongruent(U_11002,U_11003,U_11004,hAPP(U_11005,U_11006))
| ~ hBOOL(hAPP(hAPP(c_member(U_10999),U_11006),U_11000))
| ~ c_Equiv__Relations_Ocongruent2(U_10999,U_11002,U_11003,U_11001,U_11004,U_11005)
| ~ c_Equiv__Relations_Oequiv(U_10999,U_11000,U_11001) ),
inference(clausify,[status(thm)],[f_2953_2]) ).
fof(f_2954_1,plain,
! [V_a_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = V_a_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__Sup__absorb]) ).
fof(f_2954_2,plain,
! [U_11009,U_11008,U_11007] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11007),U_11009),c_Big__Operators_Olattice__class_OSup__fin(U_11007,U_11008)) = U_11009
| ~ hBOOL(hAPP(hAPP(c_member(U_11007),U_11009),U_11008))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11007),U_11008))
| ~ class_Lattices_Olattice(U_11007) ),
inference(variable_rename,[status(thm)],[f_2954_1]) ).
cnf(f_2954_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11007),U_11009),c_Big__Operators_Olattice__class_OSup__fin(U_11007,U_11008)) = U_11009
| ~ hBOOL(hAPP(hAPP(c_member(U_11007),U_11009),U_11008))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11007),U_11008))
| ~ class_Lattices_Olattice(U_11007) ),
inference(clausify,[status(thm)],[f_2954_2]) ).
fof(f_2955_1,plain,
! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Lattices_Osemilattice__inf(T_c) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Omono__inf]) ).
fof(f_2955_2,plain,
! [U_11014,U_11013,U_11012,U_11011,U_11010] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11010),hAPP(U_11012,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11011),U_11013),U_11014))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11010),hAPP(U_11012,U_11013)),hAPP(U_11012,U_11014))))
| ~ c_Orderings_Oorder__class_Omono(U_11011,U_11010,U_11012)
| ~ class_Orderings_Olinorder(U_11011)
| ~ class_Lattices_Osemilattice__inf(U_11010) ),
inference(variable_rename,[status(thm)],[f_2955_1]) ).
cnf(f_2955_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11010),hAPP(U_11012,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11011),U_11013),U_11014))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11010),hAPP(U_11012,U_11013)),hAPP(U_11012,U_11014))))
| ~ c_Orderings_Oorder__class_Omono(U_11011,U_11010,U_11012)
| ~ class_Orderings_Olinorder(U_11011)
| ~ class_Lattices_Osemilattice__inf(U_11010) ),
inference(clausify,[status(thm)],[f_2955_2]) ).
fof(f_2956_1,plain,
! [V_B_2,V_A_2,T_b] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_disjoint__eq__subset__Compl]) ).
fof(f_2956_2,plain,
! [U_11017,U_11016,U_11015] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11015,tc_HOL_Obool)),U_11016),U_11017) = c_Orderings_Obot__class_Obot(tc_fun(U_11015,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11015,tc_HOL_Obool)),U_11016),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11015,tc_HOL_Obool)),U_11017))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11015,tc_HOL_Obool)),U_11016),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11015,tc_HOL_Obool)),U_11017)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11015,tc_HOL_Obool)),U_11016),U_11017) != c_Orderings_Obot__class_Obot(tc_fun(U_11015,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_2956_1]) ).
fof(f_2956_3,plain,
( ! [U_11023,U_11021,U_11019] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11019,tc_HOL_Obool)),U_11021),U_11023) = c_Orderings_Obot__class_Obot(tc_fun(U_11019,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11019,tc_HOL_Obool)),U_11021),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11019,tc_HOL_Obool)),U_11023))) )
& ! [U_11022,U_11020,U_11018] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11018,tc_HOL_Obool)),U_11020),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11018,tc_HOL_Obool)),U_11022)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11018,tc_HOL_Obool)),U_11020),U_11022) != c_Orderings_Obot__class_Obot(tc_fun(U_11018,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_2956_2]) ).
cnf(f_2956_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11018,tc_HOL_Obool)),U_11020),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11018,tc_HOL_Obool)),U_11022)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11018,tc_HOL_Obool)),U_11020),U_11022) != c_Orderings_Obot__class_Obot(tc_fun(U_11018,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_2956_3]) ).
cnf(f_2956_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11019,tc_HOL_Obool)),U_11021),U_11023) = c_Orderings_Obot__class_Obot(tc_fun(U_11019,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11019,tc_HOL_Obool)),U_11021),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11019,tc_HOL_Obool)),U_11023))) ),
inference(clausify,[status(thm)],[f_2956_3]) ).
fof(f_2957_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I15_J]) ).
fof(f_2957_2,plain,
! [U_11027,U_11026,U_11025,U_11024] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11024,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11024,U_11025),U_11026)),c_SetInterval_Oord__class_OatLeastAtMost(U_11024,U_11026,U_11027)) = c_Orderings_Obot__class_Obot(tc_fun(U_11024,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11024) ),
inference(variable_rename,[status(thm)],[f_2957_1]) ).
cnf(f_2957_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11024,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11024,U_11025),U_11026)),c_SetInterval_Oord__class_OatLeastAtMost(U_11024,U_11026,U_11027)) = c_Orderings_Obot__class_Obot(tc_fun(U_11024,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11024) ),
inference(clausify,[status(thm)],[f_2957_2]) ).
fof(f_2958_1,plain,
! [V_P_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_P_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_P_2))),V_P_2))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lfp__induct]) ).
fof(f_2958_2,plain,
! [U_11030,U_11029,U_11028] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11028),c_Inductive_Ocomplete__lattice__class_Olfp(U_11028,U_11029)),U_11030))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11028),hAPP(U_11029,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11028),c_Inductive_Ocomplete__lattice__class_Olfp(U_11028,U_11029)),U_11030))),U_11030))
| ~ c_Orderings_Oorder__class_Omono(U_11028,U_11028,U_11029)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_11028) ),
inference(variable_rename,[status(thm)],[f_2958_1]) ).
cnf(f_2958_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11028),c_Inductive_Ocomplete__lattice__class_Olfp(U_11028,U_11029)),U_11030))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11028),hAPP(U_11029,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11028),c_Inductive_Ocomplete__lattice__class_Olfp(U_11028,U_11029)),U_11030))),U_11030))
| ~ c_Orderings_Oorder__class_Omono(U_11028,U_11028,U_11029)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_11028) ),
inference(clausify,[status(thm)],[f_2958_2]) ).
fof(f_2959_1,plain,
! [V_P_2,V_f_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_A_2),V_P_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_A_2),V_P_2))),V_P_2))
| ~ c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
| V_A_2 != c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_def__lfp__induct]) ).
fof(f_2959_2,plain,
! [U_11034,U_11033,U_11032,U_11031] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11031),U_11032),U_11034))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11031),hAPP(U_11033,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11031),U_11032),U_11034))),U_11034))
| ~ c_Orderings_Oorder__class_Omono(U_11031,U_11031,U_11033)
| U_11032 != c_Inductive_Ocomplete__lattice__class_Olfp(U_11031,U_11033)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_11031) ),
inference(variable_rename,[status(thm)],[f_2959_1]) ).
cnf(f_2959_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11031),U_11032),U_11034))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11031),hAPP(U_11033,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11031),U_11032),U_11034))),U_11034))
| ~ c_Orderings_Oorder__class_Omono(U_11031,U_11031,U_11033)
| U_11032 != c_Inductive_Ocomplete__lattice__class_Olfp(U_11031,U_11033)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_11031) ),
inference(clausify,[status(thm)],[f_2959_2]) ).
fof(f_2960_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMost]) ).
fof(f_2960_2,plain,
! [U_11039,U_11038,U_11037,U_11036,U_11035] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11035,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11035,U_11036,U_11037)),c_SetInterval_Oord__class_OatLeastAtMost(U_11035,U_11038,U_11039)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11035,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11035),U_11036),U_11038),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11035),U_11037),U_11039))
| ~ class_Orderings_Olinorder(U_11035) ),
inference(variable_rename,[status(thm)],[f_2960_1]) ).
cnf(f_2960_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11035,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11035,U_11036,U_11037)),c_SetInterval_Oord__class_OatLeastAtMost(U_11035,U_11038,U_11039)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11035,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11035),U_11036),U_11038),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11035),U_11037),U_11039))
| ~ class_Orderings_Olinorder(U_11035) ),
inference(clausify,[status(thm)],[f_2960_2]) ).
fof(f_2961_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastLessThan]) ).
fof(f_2961_2,plain,
! [U_11044,U_11043,U_11042,U_11041,U_11040] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11040,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11040,U_11041),U_11042)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11040,U_11043),U_11044)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11040,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11040),U_11041),U_11043)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11040),U_11042),U_11044))
| ~ class_Orderings_Olinorder(U_11040) ),
inference(variable_rename,[status(thm)],[f_2961_1]) ).
cnf(f_2961_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11040,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11040,U_11041),U_11042)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11040,U_11043),U_11044)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11040,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11040),U_11041),U_11043)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11040),U_11042),U_11044))
| ~ class_Orderings_Olinorder(U_11040) ),
inference(clausify,[status(thm)],[f_2961_2]) ).
fof(f_2962_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I4_J]) ).
fof(f_2962_2,plain,
! [U_11047,U_11046,U_11045] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11045,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11045),U_11046)),c_SetInterval_Oord__class_OatLeastAtMost(U_11045,U_11046,U_11047)) = c_Orderings_Obot__class_Obot(tc_fun(U_11045,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11045) ),
inference(variable_rename,[status(thm)],[f_2962_1]) ).
cnf(f_2962_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11045,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11045),U_11046)),c_SetInterval_Oord__class_OatLeastAtMost(U_11045,U_11046,U_11047)) = c_Orderings_Obot__class_Obot(tc_fun(U_11045,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11045) ),
inference(clausify,[status(thm)],[f_2962_2]) ).
fof(f_2963_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I2_J]) ).
fof(f_2963_2,plain,
! [U_11050,U_11049,U_11048] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11048,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11048),U_11049)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11048,U_11049),U_11050)) = c_Orderings_Obot__class_Obot(tc_fun(U_11048,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11048) ),
inference(variable_rename,[status(thm)],[f_2963_1]) ).
cnf(f_2963_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11048,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_11048),U_11049)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11048,U_11049),U_11050)) = c_Orderings_Obot__class_Obot(tc_fun(U_11048,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11048) ),
inference(clausify,[status(thm)],[f_2963_2]) ).
fof(f_2964_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I16_J]) ).
fof(f_2964_2,plain,
! [U_11054,U_11053,U_11052,U_11051] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11051,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11051,U_11052,U_11053)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11051,U_11053,U_11054)) = c_Orderings_Obot__class_Obot(tc_fun(U_11051,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11051) ),
inference(variable_rename,[status(thm)],[f_2964_1]) ).
cnf(f_2964_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11051,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11051,U_11052,U_11053)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11051,U_11053,U_11054)) = c_Orderings_Obot__class_Obot(tc_fun(U_11051,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11051) ),
inference(clausify,[status(thm)],[f_2964_2]) ).
fof(f_2965_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I13_J]) ).
fof(f_2965_2,plain,
! [U_11058,U_11057,U_11056,U_11055] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11055,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11055,U_11056,U_11057)),c_SetInterval_Oord__class_OatLeastAtMost(U_11055,U_11057,U_11058)) = c_Orderings_Obot__class_Obot(tc_fun(U_11055,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11055) ),
inference(variable_rename,[status(thm)],[f_2965_1]) ).
cnf(f_2965_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11055,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11055,U_11056,U_11057)),c_SetInterval_Oord__class_OatLeastAtMost(U_11055,U_11057,U_11058)) = c_Orderings_Obot__class_Obot(tc_fun(U_11055,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11055) ),
inference(clausify,[status(thm)],[f_2965_2]) ).
fof(f_2966_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I12_J]) ).
fof(f_2966_2,plain,
! [U_11062,U_11061,U_11060,U_11059] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11059,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11059,U_11060,U_11061)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11059,U_11061,U_11062)) = c_Orderings_Obot__class_Obot(tc_fun(U_11059,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11059) ),
inference(variable_rename,[status(thm)],[f_2966_1]) ).
cnf(f_2966_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11059,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11059,U_11060,U_11061)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11059,U_11061,U_11062)) = c_Orderings_Obot__class_Obot(tc_fun(U_11059,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11059) ),
inference(clausify,[status(thm)],[f_2966_2]) ).
fof(f_2967_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__greaterThanAtMost]) ).
fof(f_2967_2,plain,
! [U_11067,U_11066,U_11065,U_11064,U_11063] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11063,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11063,U_11064,U_11065)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11063,U_11066,U_11067)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_11063,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11063),U_11064),U_11066),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11063),U_11065),U_11067))
| ~ class_Orderings_Olinorder(U_11063) ),
inference(variable_rename,[status(thm)],[f_2967_1]) ).
cnf(f_2967_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11063,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11063,U_11064,U_11065)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11063,U_11066,U_11067)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_11063,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11063),U_11064),U_11066),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11063),U_11065),U_11067))
| ~ class_Orderings_Olinorder(U_11063) ),
inference(clausify,[status(thm)],[f_2967_2]) ).
fof(f_2968_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I9_J]) ).
fof(f_2968_2,plain,
! [U_11071,U_11070,U_11069,U_11068] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11068,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11068,U_11069,U_11070)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11068,U_11070),U_11071)) = c_Orderings_Obot__class_Obot(tc_fun(U_11068,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11068) ),
inference(variable_rename,[status(thm)],[f_2968_1]) ).
cnf(f_2968_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11068,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11068,U_11069,U_11070)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11068,U_11070),U_11071)) = c_Orderings_Obot__class_Obot(tc_fun(U_11068,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11068) ),
inference(clausify,[status(thm)],[f_2968_2]) ).
fof(f_2969_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__greaterThanLessThan]) ).
fof(f_2969_2,plain,
! [U_11076,U_11075,U_11074,U_11073,U_11072] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11072,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11072,U_11073,U_11074)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11072,U_11075,U_11076)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_11072,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11072),U_11073),U_11075),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11072),U_11074),U_11076))
| ~ class_Orderings_Olinorder(U_11072) ),
inference(variable_rename,[status(thm)],[f_2969_1]) ).
cnf(f_2969_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11072,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11072,U_11073,U_11074)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11072,U_11075,U_11076)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_11072,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11072),U_11073),U_11075),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11072),U_11074),U_11076))
| ~ class_Orderings_Olinorder(U_11072) ),
inference(clausify,[status(thm)],[f_2969_2]) ).
fof(f_2970_1,plain,
! [V_d_2,V_c_2,V_b_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR1]) ).
fof(f_2970_2,plain,
! [U_11080,U_11079,U_11078,U_11077] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11077,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11077),U_11078)),c_SetInterval_Oord__class_OatLeastAtMost(U_11077,U_11079,U_11080)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11077,U_11079,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11077),U_11078),U_11080))
| ~ class_Orderings_Olinorder(U_11077) ),
inference(variable_rename,[status(thm)],[f_2970_1]) ).
cnf(f_2970_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11077,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11077),U_11078)),c_SetInterval_Oord__class_OatLeastAtMost(U_11077,U_11079,U_11080)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11077,U_11079,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11077),U_11078),U_11080))
| ~ class_Orderings_Olinorder(U_11077) ),
inference(clausify,[status(thm)],[f_2970_2]) ).
fof(f_2971_1,plain,
! [V_d_2,V_b_2,V_a_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL1]) ).
fof(f_2971_2,plain,
! [U_11084,U_11083,U_11082,U_11081] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11081,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11081,U_11082,U_11083)),hAPP(c_SetInterval_Oord__class_OatMost(U_11081),U_11084)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11081,U_11082,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11081),U_11083),U_11084))
| ~ class_Orderings_Olinorder(U_11081) ),
inference(variable_rename,[status(thm)],[f_2971_1]) ).
cnf(f_2971_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11081,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11081,U_11082,U_11083)),hAPP(c_SetInterval_Oord__class_OatMost(U_11081),U_11084)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11081,U_11082,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11081),U_11083),U_11084))
| ~ class_Orderings_Olinorder(U_11081) ),
inference(clausify,[status(thm)],[f_2971_2]) ).
fof(f_2972_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I8_J]) ).
fof(f_2972_2,plain,
! [U_11087,U_11086,U_11085] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11085,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11085,U_11086),U_11087)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11085),U_11087)) = c_Orderings_Obot__class_Obot(tc_fun(U_11085,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11085) ),
inference(variable_rename,[status(thm)],[f_2972_1]) ).
cnf(f_2972_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11085,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11085,U_11086),U_11087)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11085),U_11087)) = c_Orderings_Obot__class_Obot(tc_fun(U_11085,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11085) ),
inference(clausify,[status(thm)],[f_2972_2]) ).
fof(f_2973_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I7_J]) ).
fof(f_2973_2,plain,
! [U_11090,U_11089,U_11088] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11088,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11088,U_11089,U_11090)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11088),U_11090)) = c_Orderings_Obot__class_Obot(tc_fun(U_11088,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11088) ),
inference(variable_rename,[status(thm)],[f_2973_1]) ).
cnf(f_2973_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11088,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11088,U_11089,U_11090)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11088),U_11090)) = c_Orderings_Obot__class_Obot(tc_fun(U_11088,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11088) ),
inference(clausify,[status(thm)],[f_2973_2]) ).
fof(f_2974_1,plain,
! [V_d_2,V_c_2,V_a_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_d_2)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR2]) ).
fof(f_2974_2,plain,
! [U_11094,U_11093,U_11092,U_11091] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11091,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11091),U_11092)),c_SetInterval_Oord__class_OatLeastAtMost(U_11091,U_11093,U_11094)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11091,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11091),U_11092),U_11093),U_11094)
| ~ class_Orderings_Olinorder(U_11091) ),
inference(variable_rename,[status(thm)],[f_2974_1]) ).
cnf(f_2974_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11091,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11091),U_11092)),c_SetInterval_Oord__class_OatLeastAtMost(U_11091,U_11093,U_11094)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11091,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11091),U_11092),U_11093),U_11094)
| ~ class_Orderings_Olinorder(U_11091) ),
inference(clausify,[status(thm)],[f_2974_2]) ).
fof(f_2975_1,plain,
! [V_c_2,V_b_2,V_a_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_b_2)
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL2]) ).
fof(f_2975_2,plain,
! [U_11098,U_11097,U_11096,U_11095] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11095,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11095,U_11096,U_11097)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11095),U_11098)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11095,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11095),U_11096),U_11098),U_11097)
| ~ class_Orderings_Olinorder(U_11095) ),
inference(variable_rename,[status(thm)],[f_2975_1]) ).
cnf(f_2975_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11095,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11095,U_11096,U_11097)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11095),U_11098)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11095,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11095),U_11096),U_11098),U_11097)
| ~ class_Orderings_Olinorder(U_11095) ),
inference(clausify,[status(thm)],[f_2975_2]) ).
fof(f_2976_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I3_J]) ).
fof(f_2976_2,plain,
! [U_11101,U_11100,U_11099] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11099,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11099),U_11100)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11099,U_11100,U_11101)) = c_Orderings_Obot__class_Obot(tc_fun(U_11099,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11099) ),
inference(variable_rename,[status(thm)],[f_2976_1]) ).
cnf(f_2976_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11099,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11099),U_11100)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11099,U_11100,U_11101)) = c_Orderings_Obot__class_Obot(tc_fun(U_11099,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11099) ),
inference(clausify,[status(thm)],[f_2976_2]) ).
fof(f_2977_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I1_J]) ).
fof(f_2977_2,plain,
! [U_11104,U_11103,U_11102] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11102,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11102),U_11103)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11102,U_11103,U_11104)) = c_Orderings_Obot__class_Obot(tc_fun(U_11102,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11102) ),
inference(variable_rename,[status(thm)],[f_2977_1]) ).
cnf(f_2977_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11102,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11102),U_11103)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11102,U_11103,U_11104)) = c_Orderings_Obot__class_Obot(tc_fun(U_11102,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11102) ),
inference(clausify,[status(thm)],[f_2977_2]) ).
fof(f_2978_1,plain,
! [V_u_2,V_m_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I10_J]) ).
fof(f_2978_2,plain,
! [U_11108,U_11107,U_11106,U_11105] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11105,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11105,U_11106,U_11107)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11105,U_11107,U_11108)) = c_Orderings_Obot__class_Obot(tc_fun(U_11105,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11105) ),
inference(variable_rename,[status(thm)],[f_2978_1]) ).
cnf(f_2978_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11105,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11105,U_11106,U_11107)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11105,U_11107,U_11108)) = c_Orderings_Obot__class_Obot(tc_fun(U_11105,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11105) ),
inference(clausify,[status(thm)],[f_2978_2]) ).
fof(f_2979_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I6_J]) ).
fof(f_2979_2,plain,
! [U_11111,U_11110,U_11109] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11109,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11109,U_11110,U_11111)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11109),U_11111)) = c_Orderings_Obot__class_Obot(tc_fun(U_11109,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11109) ),
inference(variable_rename,[status(thm)],[f_2979_1]) ).
cnf(f_2979_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11109,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11109,U_11110,U_11111)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11109),U_11111)) = c_Orderings_Obot__class_Obot(tc_fun(U_11109,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11109) ),
inference(clausify,[status(thm)],[f_2979_2]) ).
fof(f_2980_1,plain,
! [V_u_2,V_l_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I5_J]) ).
fof(f_2980_2,plain,
! [U_11114,U_11113,U_11112] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11112,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11112,U_11113,U_11114)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11112),U_11114)) = c_Orderings_Obot__class_Obot(tc_fun(U_11112,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11112) ),
inference(variable_rename,[status(thm)],[f_2980_1]) ).
cnf(f_2980_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11112,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11112,U_11113,U_11114)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_11112),U_11114)) = c_Orderings_Obot__class_Obot(tc_fun(U_11112,tc_HOL_Obool))
| ~ class_Orderings_Oorder(U_11112) ),
inference(clausify,[status(thm)],[f_2980_2]) ).
fof(f_2981_1,plain,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__inter]) ).
fof(f_2981_2,plain,
! [U_11122,U_11121,U_11120,U_11119,U_11118,U_11117,U_11116,U_11115] :
( hAPP(hAPP(U_11117,hAPP(U_11120,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11116,tc_HOL_Obool)),U_11121),U_11122))),hAPP(U_11120,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11116,tc_HOL_Obool)),U_11121),U_11122))) = hAPP(hAPP(U_11117,hAPP(U_11120,U_11121)),hAPP(U_11120,U_11122))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11116),U_11122))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11116),U_11121))
| ~ c_Finite__Set_Ofolding__image__simple(U_11115,U_11116,U_11117,U_11118,U_11119,U_11120) ),
inference(variable_rename,[status(thm)],[f_2981_1]) ).
fof(f_2981_3,plain,
! [U_11122,U_11121,U_11120,U_11119,U_11118,U_11117,U_11116] :
( ! [U_11115] : ~ c_Finite__Set_Ofolding__image__simple(U_11115,U_11116,U_11117,U_11118,U_11119,U_11120)
| hAPP(hAPP(U_11117,hAPP(U_11120,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11116,tc_HOL_Obool)),U_11121),U_11122))),hAPP(U_11120,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11116,tc_HOL_Obool)),U_11121),U_11122))) = hAPP(hAPP(U_11117,hAPP(U_11120,U_11121)),hAPP(U_11120,U_11122))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11116),U_11122))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11116),U_11121)) ),
inference(miniscope,[status(thm)],[f_2981_2]) ).
cnf(f_2981_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_11115,U_11116,U_11117,U_11118,U_11119,U_11120)
| hAPP(hAPP(U_11117,hAPP(U_11120,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11116,tc_HOL_Obool)),U_11121),U_11122))),hAPP(U_11120,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11116,tc_HOL_Obool)),U_11121),U_11122))) = hAPP(hAPP(U_11117,hAPP(U_11120,U_11121)),hAPP(U_11120,U_11122))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11116),U_11122))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11116),U_11121)) ),
inference(clausify,[status(thm)],[f_2981_3]) ).
fof(f_2982_1,plain,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__Un__Int]) ).
fof(f_2982_2,plain,
! [U_11127,U_11126,U_11125,U_11124,U_11123] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11123),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11124,U_11123),U_11127),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11124,tc_HOL_Obool)),U_11125),U_11126))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11124,U_11123),U_11127),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11124,tc_HOL_Obool)),U_11125),U_11126))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11123),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11124,U_11123),U_11127),U_11125)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11124,U_11123),U_11127),U_11126))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11124),U_11126))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11124),U_11125))
| ~ class_Groups_Ocomm__monoid__add(U_11123) ),
inference(variable_rename,[status(thm)],[f_2982_1]) ).
cnf(f_2982_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11123),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11124,U_11123),U_11127),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11124,tc_HOL_Obool)),U_11125),U_11126))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11124,U_11123),U_11127),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11124,tc_HOL_Obool)),U_11125),U_11126))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11123),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11124,U_11123),U_11127),U_11125)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11124,U_11123),U_11127),U_11126))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11124),U_11126))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11124),U_11125))
| ~ class_Groups_Ocomm__monoid__add(U_11123) ),
inference(clausify,[status(thm)],[f_2982_2]) ).
fof(f_2983_1,plain,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__Un__Int]) ).
fof(f_2983_2,plain,
! [U_11132,U_11131,U_11130,U_11129,U_11128] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11128),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11129,U_11128),U_11132),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11129,tc_HOL_Obool)),U_11130),U_11131))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11129,U_11128),U_11132),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11129,tc_HOL_Obool)),U_11130),U_11131))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11128),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11129,U_11128),U_11132),U_11130)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11129,U_11128),U_11132),U_11131))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11129),U_11131))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11129),U_11130))
| ~ class_Groups_Ocomm__monoid__mult(U_11128) ),
inference(variable_rename,[status(thm)],[f_2983_1]) ).
cnf(f_2983_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11128),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11129,U_11128),U_11132),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11129,tc_HOL_Obool)),U_11130),U_11131))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11129,U_11128),U_11132),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11129,tc_HOL_Obool)),U_11130),U_11131))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11128),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11129,U_11128),U_11132),U_11130)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11129,U_11128),U_11132),U_11131))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11129),U_11131))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11129),U_11130))
| ~ class_Groups_Ocomm__monoid__mult(U_11128) ),
inference(clausify,[status(thm)],[f_2983_2]) ).
fof(f_2984_1,plain,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__inter]) ).
fof(f_2984_2,plain,
! [U_11137,U_11136,U_11135,U_11134,U_11133] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11133),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11134,U_11133),U_11137),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11134,tc_HOL_Obool)),U_11135),U_11136))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11134,U_11133),U_11137),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11134,tc_HOL_Obool)),U_11135),U_11136))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11133),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11134,U_11133),U_11137),U_11135)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11134,U_11133),U_11137),U_11136))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11134),U_11136))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11134),U_11135))
| ~ class_Groups_Ocomm__monoid__mult(U_11133) ),
inference(variable_rename,[status(thm)],[f_2984_1]) ).
cnf(f_2984_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11133),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11134,U_11133),U_11137),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11134,tc_HOL_Obool)),U_11135),U_11136))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11134,U_11133),U_11137),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11134,tc_HOL_Obool)),U_11135),U_11136))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11133),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11134,U_11133),U_11137),U_11135)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11134,U_11133),U_11137),U_11136))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11134),U_11136))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11134),U_11135))
| ~ class_Groups_Ocomm__monoid__mult(U_11133) ),
inference(clausify,[status(thm)],[f_2984_2]) ).
fof(f_2985_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card_Ounion__inter]) ).
fof(f_2985_2,plain,
! [U_11140,U_11139,U_11138] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11138),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11138,tc_HOL_Obool)),U_11139),U_11140))),hAPP(c_Finite__Set_Ocard(U_11138),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11138,tc_HOL_Obool)),U_11139),U_11140))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11138),U_11139)),hAPP(c_Finite__Set_Ocard(U_11138),U_11140))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11138),U_11140))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11138),U_11139)) ),
inference(variable_rename,[status(thm)],[f_2985_1]) ).
cnf(f_2985_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11138),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11138,tc_HOL_Obool)),U_11139),U_11140))),hAPP(c_Finite__Set_Ocard(U_11138),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11138,tc_HOL_Obool)),U_11139),U_11140))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11138),U_11139)),hAPP(c_Finite__Set_Ocard(U_11138),U_11140))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11138),U_11140))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11138),U_11139)) ),
inference(clausify,[status(thm)],[f_2985_2]) ).
fof(f_2986_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Un__Int]) ).
fof(f_2986_2,plain,
! [U_11143,U_11142,U_11141] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11141),U_11142)),hAPP(c_Finite__Set_Ocard(U_11141),U_11143)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11141),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11141,tc_HOL_Obool)),U_11142),U_11143))),hAPP(c_Finite__Set_Ocard(U_11141),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11141,tc_HOL_Obool)),U_11142),U_11143)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11141),U_11143))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11141),U_11142)) ),
inference(variable_rename,[status(thm)],[f_2986_1]) ).
cnf(f_2986_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11141),U_11142)),hAPP(c_Finite__Set_Ocard(U_11141),U_11143)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11141),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11141,tc_HOL_Obool)),U_11142),U_11143))),hAPP(c_Finite__Set_Ocard(U_11141),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11141,tc_HOL_Obool)),U_11142),U_11143)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11141),U_11143))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11141),U_11142)) ),
inference(clausify,[status(thm)],[f_2986_2]) ).
fof(f_2987_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_card__Diff__subset__Int]) ).
fof(f_2987_2,plain,
! [U_11146,U_11145,U_11144] :
( hAPP(c_Finite__Set_Ocard(U_11144),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11144,tc_HOL_Obool)),U_11145),U_11146)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11144),U_11145)),hAPP(c_Finite__Set_Ocard(U_11144),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11144,tc_HOL_Obool)),U_11145),U_11146)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11144),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11144,tc_HOL_Obool)),U_11145),U_11146))) ),
inference(variable_rename,[status(thm)],[f_2987_1]) ).
cnf(f_2987_3,plain,
( hAPP(c_Finite__Set_Ocard(U_11144),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11144,tc_HOL_Obool)),U_11145),U_11146)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11144),U_11145)),hAPP(c_Finite__Set_Ocard(U_11144),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11144,tc_HOL_Obool)),U_11145),U_11146)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11144),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11144,tc_HOL_Obool)),U_11145),U_11146))) ),
inference(clausify,[status(thm)],[f_2987_2]) ).
fof(f_2988_1,plain,
! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set]) ).
fof(f_2988_2,plain,
! [U_11151,U_11150,U_11149,U_11148,U_11147] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11148,U_11147),U_11150),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11148,tc_HOL_Obool)),U_11149),U_11151)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11148,U_11147),hAPP(hAPP(c_COMBC(U_11148,U_11147,U_11147),hAPP(hAPP(c_COMBS(U_11148,U_11147,tc_fun(U_11147,U_11147)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11147,tc_fun(U_11147,U_11147)),U_11148),c_If(U_11147)),hAPP(hAPP(c_COMBC(U_11148,tc_fun(U_11148,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11148)),U_11151))),U_11150)),c_Groups_Ozero__class_Ozero(U_11147))),U_11149)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11148),U_11149))
| ~ class_Groups_Ocomm__monoid__add(U_11147) ),
inference(variable_rename,[status(thm)],[f_2988_1]) ).
cnf(f_2988_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11148,U_11147),U_11150),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11148,tc_HOL_Obool)),U_11149),U_11151)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11148,U_11147),hAPP(hAPP(c_COMBC(U_11148,U_11147,U_11147),hAPP(hAPP(c_COMBS(U_11148,U_11147,tc_fun(U_11147,U_11147)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11147,tc_fun(U_11147,U_11147)),U_11148),c_If(U_11147)),hAPP(hAPP(c_COMBC(U_11148,tc_fun(U_11148,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11148)),U_11151))),U_11150)),c_Groups_Ozero__class_Ozero(U_11147))),U_11149)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11148),U_11149))
| ~ class_Groups_Ocomm__monoid__add(U_11147) ),
inference(clausify,[status(thm)],[f_2988_2]) ).
fof(f_2989_1,plain,
! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| V_X_2 = V_Y_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
| ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_quotient__disj]) ).
fof(f_2989_2,plain,
! [U_11156,U_11155,U_11154,U_11153,U_11152] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11152,tc_HOL_Obool)),U_11155),U_11156) = c_Orderings_Obot__class_Obot(tc_fun(U_11152,tc_HOL_Obool))
| U_11155 = U_11156
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11152,tc_HOL_Obool)),U_11156),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11152),U_11153),U_11154)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11152,tc_HOL_Obool)),U_11155),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11152),U_11153),U_11154)))
| ~ c_Equiv__Relations_Oequiv(U_11152,U_11153,U_11154) ),
inference(variable_rename,[status(thm)],[f_2989_1]) ).
cnf(f_2989_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11152,tc_HOL_Obool)),U_11155),U_11156) = c_Orderings_Obot__class_Obot(tc_fun(U_11152,tc_HOL_Obool))
| U_11155 = U_11156
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11152,tc_HOL_Obool)),U_11156),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11152),U_11153),U_11154)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11152,tc_HOL_Obool)),U_11155),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11152),U_11153),U_11154)))
| ~ c_Equiv__Relations_Oequiv(U_11152,U_11153,U_11154) ),
inference(clausify,[status(thm)],[f_2989_2]) ).
fof(f_2990_1,plain,
! [V_na_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_na_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_na_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_na_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_atMost__Int__atLeast]) ).
fof(f_2990_2,plain,
! [U_11158,U_11157] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11157,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11157),U_11158)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11157),U_11158)) = hAPP(hAPP(c_Set_Oinsert(U_11157),U_11158),c_Orderings_Obot__class_Obot(tc_fun(U_11157,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_11157) ),
inference(variable_rename,[status(thm)],[f_2990_1]) ).
cnf(f_2990_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11157,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_11157),U_11158)),hAPP(c_SetInterval_Oord__class_OatLeast(U_11157),U_11158)) = hAPP(hAPP(c_Set_Oinsert(U_11157),U_11158),c_Orderings_Obot__class_Obot(tc_fun(U_11157,tc_HOL_Obool)))
| ~ class_Orderings_Oorder(U_11157) ),
inference(clausify,[status(thm)],[f_2990_2]) ).
fof(f_2991_1,plain,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__disjoint]) ).
fof(f_2991_2,plain,
! [U_11166,U_11165,U_11164,U_11163,U_11162,U_11161,U_11160,U_11159] :
( hAPP(U_11164,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11160,tc_HOL_Obool)),U_11165),U_11166)) = hAPP(hAPP(U_11161,hAPP(U_11164,U_11165)),hAPP(U_11164,U_11166))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11160,tc_HOL_Obool)),U_11165),U_11166) != c_Orderings_Obot__class_Obot(tc_fun(U_11160,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11160),U_11166))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11160),U_11165))
| ~ c_Finite__Set_Ofolding__image__simple(U_11159,U_11160,U_11161,U_11162,U_11163,U_11164) ),
inference(variable_rename,[status(thm)],[f_2991_1]) ).
fof(f_2991_3,plain,
! [U_11166,U_11165,U_11164,U_11163,U_11162,U_11161,U_11160] :
( ! [U_11159] : ~ c_Finite__Set_Ofolding__image__simple(U_11159,U_11160,U_11161,U_11162,U_11163,U_11164)
| hAPP(U_11164,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11160,tc_HOL_Obool)),U_11165),U_11166)) = hAPP(hAPP(U_11161,hAPP(U_11164,U_11165)),hAPP(U_11164,U_11166))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11160,tc_HOL_Obool)),U_11165),U_11166) != c_Orderings_Obot__class_Obot(tc_fun(U_11160,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11160),U_11166))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11160),U_11165)) ),
inference(miniscope,[status(thm)],[f_2991_2]) ).
cnf(f_2991_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple(U_11159,U_11160,U_11161,U_11162,U_11163,U_11164)
| hAPP(U_11164,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11160,tc_HOL_Obool)),U_11165),U_11166)) = hAPP(hAPP(U_11161,hAPP(U_11164,U_11165)),hAPP(U_11164,U_11166))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11160,tc_HOL_Obool)),U_11165),U_11166) != c_Orderings_Obot__class_Obot(tc_fun(U_11160,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11160),U_11166))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11160),U_11165)) ),
inference(clausify,[status(thm)],[f_2991_3]) ).
fof(f_2992_1,plain,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
( hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__inter]) ).
fof(f_2992_2,plain,
! [U_11171,U_11170,U_11169,U_11168,U_11167] :
( hAPP(hAPP(U_11168,hAPP(U_11169,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11167,tc_HOL_Obool)),U_11170),U_11171))),hAPP(U_11169,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11167,tc_HOL_Obool)),U_11170),U_11171))) = hAPP(hAPP(U_11168,hAPP(U_11169,U_11170)),hAPP(U_11169,U_11171))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11167,tc_HOL_Obool)),U_11170),U_11171) = c_Orderings_Obot__class_Obot(tc_fun(U_11167,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11167),U_11171))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11167),U_11170))
| ~ c_Finite__Set_Ofolding__one(U_11167,U_11168,U_11169) ),
inference(variable_rename,[status(thm)],[f_2992_1]) ).
cnf(f_2992_3,plain,
( hAPP(hAPP(U_11168,hAPP(U_11169,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11167,tc_HOL_Obool)),U_11170),U_11171))),hAPP(U_11169,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11167,tc_HOL_Obool)),U_11170),U_11171))) = hAPP(hAPP(U_11168,hAPP(U_11169,U_11170)),hAPP(U_11169,U_11171))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11167,tc_HOL_Obool)),U_11170),U_11171) = c_Orderings_Obot__class_Obot(tc_fun(U_11167,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11167),U_11171))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11167),U_11170))
| ~ c_Finite__Set_Ofolding__one(U_11167,U_11168,U_11169) ),
inference(clausify,[status(thm)],[f_2992_2]) ).
fof(f_2993_1,plain,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__disjoint]) ).
fof(f_2993_2,plain,
! [U_11176,U_11175,U_11174,U_11173,U_11172] :
( hAPP(U_11174,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11172,tc_HOL_Obool)),U_11175),U_11176)) = hAPP(hAPP(U_11173,hAPP(U_11174,U_11175)),hAPP(U_11174,U_11176))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11172,tc_HOL_Obool)),U_11175),U_11176) != c_Orderings_Obot__class_Obot(tc_fun(U_11172,tc_HOL_Obool))
| U_11176 = c_Orderings_Obot__class_Obot(tc_fun(U_11172,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11172),U_11176))
| U_11175 = c_Orderings_Obot__class_Obot(tc_fun(U_11172,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11172),U_11175))
| ~ c_Finite__Set_Ofolding__one(U_11172,U_11173,U_11174) ),
inference(variable_rename,[status(thm)],[f_2993_1]) ).
cnf(f_2993_3,plain,
( hAPP(U_11174,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11172,tc_HOL_Obool)),U_11175),U_11176)) = hAPP(hAPP(U_11173,hAPP(U_11174,U_11175)),hAPP(U_11174,U_11176))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11172,tc_HOL_Obool)),U_11175),U_11176) != c_Orderings_Obot__class_Obot(tc_fun(U_11172,tc_HOL_Obool))
| U_11176 = c_Orderings_Obot__class_Obot(tc_fun(U_11172,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11172),U_11176))
| U_11175 = c_Orderings_Obot__class_Obot(tc_fun(U_11172,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11172),U_11175))
| ~ c_Finite__Set_Ofolding__one(U_11172,U_11173,U_11174) ),
inference(clausify,[status(thm)],[f_2993_2]) ).
fof(f_2994_1,plain,
! [V_f_2,V_r_2,T_c,T_b] :
( ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2))),V_f_2)),B_x))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2))),V_f_2)),B_x))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) )
| ~ c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ) ),
inference(fof_nnf,[status(thm)],[fact_congruent__def]) ).
fof(f_2994_2,plain,
! [U_11182,U_11181,U_11180,U_11179] :
( ( c_Equiv__Relations_Ocongruent(U_11179,U_11180,U_11181,U_11182)
| ? [U_11178] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11179,U_11179,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11179,tc_fun(U_11179,U_11180),tc_fun(U_11179,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11180,tc_HOL_Obool),tc_fun(tc_fun(U_11179,U_11180),tc_fun(U_11179,tc_HOL_Obool)),U_11179),c_COMBB(U_11180,tc_HOL_Obool,U_11179)),hAPP(hAPP(c_COMBB(U_11180,tc_fun(U_11180,tc_HOL_Obool),U_11179),c_fequal),U_11182))),U_11182)),U_11178))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_11179,U_11179)),U_11178),U_11181)) ) )
& ( ! [U_11177] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11179,U_11179,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11179,tc_fun(U_11179,U_11180),tc_fun(U_11179,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11180,tc_HOL_Obool),tc_fun(tc_fun(U_11179,U_11180),tc_fun(U_11179,tc_HOL_Obool)),U_11179),c_COMBB(U_11180,tc_HOL_Obool,U_11179)),hAPP(hAPP(c_COMBB(U_11180,tc_fun(U_11180,tc_HOL_Obool),U_11179),c_fequal),U_11182))),U_11182)),U_11177))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11179,U_11179)),U_11177),U_11181)) )
| ~ c_Equiv__Relations_Ocongruent(U_11179,U_11180,U_11181,U_11182) ) ),
inference(variable_rename,[status(thm)],[f_2994_1]) ).
fof(f_2994_3,plain,
( ! [U_11190,U_11188,U_11186,U_11184] :
( c_Equiv__Relations_Ocongruent(U_11184,U_11186,U_11188,U_11190)
| ? [U_11178] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11184,U_11184,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11184,tc_fun(U_11184,U_11186),tc_fun(U_11184,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11186,tc_HOL_Obool),tc_fun(tc_fun(U_11184,U_11186),tc_fun(U_11184,tc_HOL_Obool)),U_11184),c_COMBB(U_11186,tc_HOL_Obool,U_11184)),hAPP(hAPP(c_COMBB(U_11186,tc_fun(U_11186,tc_HOL_Obool),U_11184),c_fequal),U_11190))),U_11190)),U_11178))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_11184,U_11184)),U_11178),U_11188)) ) )
& ! [U_11189,U_11187,U_11185,U_11183] :
( ! [U_11177] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11183,U_11183,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11183,tc_fun(U_11183,U_11185),tc_fun(U_11183,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11185,tc_HOL_Obool),tc_fun(tc_fun(U_11183,U_11185),tc_fun(U_11183,tc_HOL_Obool)),U_11183),c_COMBB(U_11185,tc_HOL_Obool,U_11183)),hAPP(hAPP(c_COMBB(U_11185,tc_fun(U_11185,tc_HOL_Obool),U_11183),c_fequal),U_11189))),U_11189)),U_11177))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11183,U_11183)),U_11177),U_11187)) )
| ~ c_Equiv__Relations_Ocongruent(U_11183,U_11185,U_11187,U_11189) ) ),
inference(miniscope,[status(thm)],[f_2994_2]) ).
fof(f_2994_4,plain,
( ! [U_11190,U_11188,U_11186,U_11184] :
( c_Equiv__Relations_Ocongruent(U_11184,U_11186,U_11188,U_11190)
| ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11184,U_11184,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11184,tc_fun(U_11184,U_11186),tc_fun(U_11184,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11186,tc_HOL_Obool),tc_fun(tc_fun(U_11184,U_11186),tc_fun(U_11184,tc_HOL_Obool)),U_11184),c_COMBB(U_11186,tc_HOL_Obool,U_11184)),hAPP(hAPP(c_COMBB(U_11186,tc_fun(U_11186,tc_HOL_Obool),U_11184),c_fequal),U_11190))),U_11190)),sK234(U_11190,U_11188,U_11186,U_11184)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_11184,U_11184)),sK234(U_11190,U_11188,U_11186,U_11184)),U_11188)) ) )
& ! [U_11189,U_11187,U_11185,U_11183] :
( ! [U_11177] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11183,U_11183,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11183,tc_fun(U_11183,U_11185),tc_fun(U_11183,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11185,tc_HOL_Obool),tc_fun(tc_fun(U_11183,U_11185),tc_fun(U_11183,tc_HOL_Obool)),U_11183),c_COMBB(U_11185,tc_HOL_Obool,U_11183)),hAPP(hAPP(c_COMBB(U_11185,tc_fun(U_11185,tc_HOL_Obool),U_11183),c_fequal),U_11189))),U_11189)),U_11177))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11183,U_11183)),U_11177),U_11187)) )
| ~ c_Equiv__Relations_Ocongruent(U_11183,U_11185,U_11187,U_11189) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK234]),skolemize(U_11178,sK234(U_11190,U_11188,U_11186,U_11184))],[f_2994_3]) ).
cnf(f_2994_5,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11183,U_11183,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11183,tc_fun(U_11183,U_11185),tc_fun(U_11183,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11185,tc_HOL_Obool),tc_fun(tc_fun(U_11183,U_11185),tc_fun(U_11183,tc_HOL_Obool)),U_11183),c_COMBB(U_11185,tc_HOL_Obool,U_11183)),hAPP(hAPP(c_COMBB(U_11185,tc_fun(U_11185,tc_HOL_Obool),U_11183),c_fequal),U_11189))),U_11189)),U_11177))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11183,U_11183)),U_11177),U_11187))
| ~ c_Equiv__Relations_Ocongruent(U_11183,U_11185,U_11187,U_11189) ),
inference(clausify,[status(thm)],[f_2994_4]) ).
cnf(f_2994_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11184,U_11184)),sK234(U_11190,U_11188,U_11186,U_11184)),U_11188))
| c_Equiv__Relations_Ocongruent(U_11184,U_11186,U_11188,U_11190) ),
inference(clausify,[status(thm)],[f_2994_4]) ).
cnf(f_2994_7,plain,
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11184,U_11184,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11184,tc_fun(U_11184,U_11186),tc_fun(U_11184,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11186,tc_HOL_Obool),tc_fun(tc_fun(U_11184,U_11186),tc_fun(U_11184,tc_HOL_Obool)),U_11184),c_COMBB(U_11186,tc_HOL_Obool,U_11184)),hAPP(hAPP(c_COMBB(U_11186,tc_fun(U_11186,tc_HOL_Obool),U_11184),c_fequal),U_11190))),U_11190)),sK234(U_11190,U_11188,U_11186,U_11184)))
| c_Equiv__Relations_Ocongruent(U_11184,U_11186,U_11188,U_11190) ),
inference(clausify,[status(thm)],[f_2994_4]) ).
fof(f_2995_1,plain,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__Un__disjoint]) ).
fof(f_2995_2,plain,
! [U_11195,U_11194,U_11193,U_11192,U_11191] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11192,U_11191),U_11195),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11192,tc_HOL_Obool)),U_11193),U_11194)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11191),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11192,U_11191),U_11195),U_11193)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11192,U_11191),U_11195),U_11194))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11192,tc_HOL_Obool)),U_11193),U_11194) != c_Orderings_Obot__class_Obot(tc_fun(U_11192,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11192),U_11194))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11192),U_11193))
| ~ class_Groups_Ocomm__monoid__add(U_11191) ),
inference(variable_rename,[status(thm)],[f_2995_1]) ).
cnf(f_2995_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11192,U_11191),U_11195),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11192,tc_HOL_Obool)),U_11193),U_11194)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11191),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11192,U_11191),U_11195),U_11193)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11192,U_11191),U_11195),U_11194))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11192,tc_HOL_Obool)),U_11193),U_11194) != c_Orderings_Obot__class_Obot(tc_fun(U_11192,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11192),U_11194))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11192),U_11193))
| ~ class_Groups_Ocomm__monoid__add(U_11191) ),
inference(clausify,[status(thm)],[f_2995_2]) ).
fof(f_2996_1,plain,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Oab__group__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__Un]) ).
fof(f_2996_2,plain,
! [U_11200,U_11199,U_11198,U_11197,U_11196] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11197,U_11196),U_11200),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11197,tc_HOL_Obool)),U_11198),U_11199)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11196),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11196),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11197,U_11196),U_11200),U_11198)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11197,U_11196),U_11200),U_11199))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11197,U_11196),U_11200),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11197,tc_HOL_Obool)),U_11198),U_11199)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11197),U_11199))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11197),U_11198))
| ~ class_Groups_Oab__group__add(U_11196) ),
inference(variable_rename,[status(thm)],[f_2996_1]) ).
cnf(f_2996_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11197,U_11196),U_11200),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11197,tc_HOL_Obool)),U_11198),U_11199)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11196),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11196),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11197,U_11196),U_11200),U_11198)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11197,U_11196),U_11200),U_11199))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11197,U_11196),U_11200),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11197,tc_HOL_Obool)),U_11198),U_11199)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11197),U_11199))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11197),U_11198))
| ~ class_Groups_Oab__group__add(U_11196) ),
inference(clausify,[status(thm)],[f_2996_2]) ).
fof(f_2997_1,plain,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__disjoint]) ).
fof(f_2997_2,plain,
! [U_11205,U_11204,U_11203,U_11202,U_11201] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11202,U_11201),U_11205),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11202,tc_HOL_Obool)),U_11203),U_11204)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11201),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11202,U_11201),U_11205),U_11203)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11202,U_11201),U_11205),U_11204))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11202,tc_HOL_Obool)),U_11203),U_11204) != c_Orderings_Obot__class_Obot(tc_fun(U_11202,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11202),U_11204))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11202),U_11203))
| ~ class_Groups_Ocomm__monoid__mult(U_11201) ),
inference(variable_rename,[status(thm)],[f_2997_1]) ).
cnf(f_2997_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11202,U_11201),U_11205),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11202,tc_HOL_Obool)),U_11203),U_11204)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11201),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11202,U_11201),U_11205),U_11203)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11202,U_11201),U_11205),U_11204))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11202,tc_HOL_Obool)),U_11203),U_11204) != c_Orderings_Obot__class_Obot(tc_fun(U_11202,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11202),U_11204))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11202),U_11203))
| ~ class_Groups_Ocomm__monoid__mult(U_11201) ),
inference(clausify,[status(thm)],[f_2997_2]) ).
fof(f_2998_1,plain,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__Un__disjoint]) ).
fof(f_2998_2,plain,
! [U_11210,U_11209,U_11208,U_11207,U_11206] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11207,U_11206),U_11210),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11207,tc_HOL_Obool)),U_11208),U_11209)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11206),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11207,U_11206),U_11210),U_11208)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11207,U_11206),U_11210),U_11209))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11207,tc_HOL_Obool)),U_11208),U_11209) != c_Orderings_Obot__class_Obot(tc_fun(U_11207,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11207),U_11209))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11207),U_11208))
| ~ class_Groups_Ocomm__monoid__mult(U_11206) ),
inference(variable_rename,[status(thm)],[f_2998_1]) ).
cnf(f_2998_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11207,U_11206),U_11210),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11207,tc_HOL_Obool)),U_11208),U_11209)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11206),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11207,U_11206),U_11210),U_11208)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11207,U_11206),U_11210),U_11209))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11207,tc_HOL_Obool)),U_11208),U_11209) != c_Orderings_Obot__class_Obot(tc_fun(U_11207,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11207),U_11209))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11207),U_11208))
| ~ class_Groups_Ocomm__monoid__mult(U_11206) ),
inference(clausify,[status(thm)],[f_2998_2]) ).
fof(f_2999_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__Un__disjoint]) ).
fof(f_2999_2,plain,
! [U_11213,U_11212,U_11211] :
( hAPP(c_Finite__Set_Ocard(U_11211),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11211,tc_HOL_Obool)),U_11212),U_11213)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11211),U_11212)),hAPP(c_Finite__Set_Ocard(U_11211),U_11213))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11211,tc_HOL_Obool)),U_11212),U_11213) != c_Orderings_Obot__class_Obot(tc_fun(U_11211,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11211),U_11213))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11211),U_11212)) ),
inference(variable_rename,[status(thm)],[f_2999_1]) ).
cnf(f_2999_3,plain,
( hAPP(c_Finite__Set_Ocard(U_11211),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11211,tc_HOL_Obool)),U_11212),U_11213)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11211),U_11212)),hAPP(c_Finite__Set_Ocard(U_11211),U_11213))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11211,tc_HOL_Obool)),U_11212),U_11213) != c_Orderings_Obot__class_Obot(tc_fun(U_11211,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11211),U_11213))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11211),U_11212)) ),
inference(clausify,[status(thm)],[f_2999_2]) ).
fof(f_3000_1,plain,
! [V_B_2,V_A_2,T_b] :
( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__disjoint]) ).
fof(f_3000_2,plain,
! [U_11216,U_11215,U_11214] :
( c_Big__Operators_Olattice__class_OSup__fin(U_11214,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11214,tc_HOL_Obool)),U_11215),U_11216)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11214),c_Big__Operators_Olattice__class_OSup__fin(U_11214,U_11215)),c_Big__Operators_Olattice__class_OSup__fin(U_11214,U_11216))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11214,tc_HOL_Obool)),U_11215),U_11216) != c_Orderings_Obot__class_Obot(tc_fun(U_11214,tc_HOL_Obool))
| U_11216 = c_Orderings_Obot__class_Obot(tc_fun(U_11214,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11214),U_11216))
| U_11215 = c_Orderings_Obot__class_Obot(tc_fun(U_11214,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11214),U_11215))
| ~ class_Lattices_Olattice(U_11214) ),
inference(variable_rename,[status(thm)],[f_3000_1]) ).
cnf(f_3000_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_11214,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11214,tc_HOL_Obool)),U_11215),U_11216)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11214),c_Big__Operators_Olattice__class_OSup__fin(U_11214,U_11215)),c_Big__Operators_Olattice__class_OSup__fin(U_11214,U_11216))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11214,tc_HOL_Obool)),U_11215),U_11216) != c_Orderings_Obot__class_Obot(tc_fun(U_11214,tc_HOL_Obool))
| U_11216 = c_Orderings_Obot__class_Obot(tc_fun(U_11214,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11214),U_11216))
| U_11215 = c_Orderings_Obot__class_Obot(tc_fun(U_11214,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11214),U_11215))
| ~ class_Lattices_Olattice(U_11214) ),
inference(clausify,[status(thm)],[f_3000_2]) ).
fof(f_3001_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__inter]) ).
fof(f_3001_2,plain,
! [U_11219,U_11218,U_11217] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11217),c_Big__Operators_Olattice__class_OSup__fin(U_11217,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11217,tc_HOL_Obool)),U_11218),U_11219))),c_Big__Operators_Olattice__class_OSup__fin(U_11217,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11217,tc_HOL_Obool)),U_11218),U_11219))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11217),c_Big__Operators_Olattice__class_OSup__fin(U_11217,U_11218)),c_Big__Operators_Olattice__class_OSup__fin(U_11217,U_11219))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11217,tc_HOL_Obool)),U_11218),U_11219) = c_Orderings_Obot__class_Obot(tc_fun(U_11217,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11217),U_11219))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11217),U_11218))
| ~ class_Lattices_Olattice(U_11217) ),
inference(variable_rename,[status(thm)],[f_3001_1]) ).
cnf(f_3001_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11217),c_Big__Operators_Olattice__class_OSup__fin(U_11217,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11217,tc_HOL_Obool)),U_11218),U_11219))),c_Big__Operators_Olattice__class_OSup__fin(U_11217,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11217,tc_HOL_Obool)),U_11218),U_11219))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11217),c_Big__Operators_Olattice__class_OSup__fin(U_11217,U_11218)),c_Big__Operators_Olattice__class_OSup__fin(U_11217,U_11219))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11217,tc_HOL_Obool)),U_11218),U_11219) = c_Orderings_Obot__class_Obot(tc_fun(U_11217,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11217),U_11219))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11217),U_11218))
| ~ class_Lattices_Olattice(U_11217) ),
inference(clausify,[status(thm)],[f_3001_2]) ).
fof(f_3002_1,plain,
! [V_B_2,V_A_2,T_b] :
( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Ounion__disjoint]) ).
fof(f_3002_2,plain,
! [U_11222,U_11221,U_11220] :
( c_Big__Operators_Olinorder__class_OMin(U_11220,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11220,tc_HOL_Obool)),U_11221),U_11222)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11220),c_Big__Operators_Olinorder__class_OMin(U_11220,U_11221)),c_Big__Operators_Olinorder__class_OMin(U_11220,U_11222))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11220,tc_HOL_Obool)),U_11221),U_11222) != c_Orderings_Obot__class_Obot(tc_fun(U_11220,tc_HOL_Obool))
| U_11222 = c_Orderings_Obot__class_Obot(tc_fun(U_11220,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11220),U_11222))
| U_11221 = c_Orderings_Obot__class_Obot(tc_fun(U_11220,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11220),U_11221))
| ~ class_Orderings_Olinorder(U_11220) ),
inference(variable_rename,[status(thm)],[f_3002_1]) ).
cnf(f_3002_3,plain,
( c_Big__Operators_Olinorder__class_OMin(U_11220,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11220,tc_HOL_Obool)),U_11221),U_11222)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11220),c_Big__Operators_Olinorder__class_OMin(U_11220,U_11221)),c_Big__Operators_Olinorder__class_OMin(U_11220,U_11222))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11220,tc_HOL_Obool)),U_11221),U_11222) != c_Orderings_Obot__class_Obot(tc_fun(U_11220,tc_HOL_Obool))
| U_11222 = c_Orderings_Obot__class_Obot(tc_fun(U_11220,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11220),U_11222))
| U_11221 = c_Orderings_Obot__class_Obot(tc_fun(U_11220,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11220),U_11221))
| ~ class_Orderings_Olinorder(U_11220) ),
inference(clausify,[status(thm)],[f_3002_2]) ).
fof(f_3003_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Ounion__inter]) ).
fof(f_3003_2,plain,
! [U_11225,U_11224,U_11223] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11223),c_Big__Operators_Olinorder__class_OMin(U_11223,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11223,tc_HOL_Obool)),U_11224),U_11225))),c_Big__Operators_Olinorder__class_OMin(U_11223,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11223,tc_HOL_Obool)),U_11224),U_11225))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11223),c_Big__Operators_Olinorder__class_OMin(U_11223,U_11224)),c_Big__Operators_Olinorder__class_OMin(U_11223,U_11225))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11223,tc_HOL_Obool)),U_11224),U_11225) = c_Orderings_Obot__class_Obot(tc_fun(U_11223,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11223),U_11225))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11223),U_11224))
| ~ class_Orderings_Olinorder(U_11223) ),
inference(variable_rename,[status(thm)],[f_3003_1]) ).
cnf(f_3003_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11223),c_Big__Operators_Olinorder__class_OMin(U_11223,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11223,tc_HOL_Obool)),U_11224),U_11225))),c_Big__Operators_Olinorder__class_OMin(U_11223,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11223,tc_HOL_Obool)),U_11224),U_11225))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11223),c_Big__Operators_Olinorder__class_OMin(U_11223,U_11224)),c_Big__Operators_Olinorder__class_OMin(U_11223,U_11225))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11223,tc_HOL_Obool)),U_11224),U_11225) = c_Orderings_Obot__class_Obot(tc_fun(U_11223,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11223),U_11225))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11223),U_11224))
| ~ class_Orderings_Olinorder(U_11223) ),
inference(clausify,[status(thm)],[f_3003_2]) ).
fof(f_3004_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Ounion__inter]) ).
fof(f_3004_2,plain,
! [U_11228,U_11227,U_11226] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11226),c_Big__Operators_Olinorder__class_OMax(U_11226,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11226,tc_HOL_Obool)),U_11227),U_11228))),c_Big__Operators_Olinorder__class_OMax(U_11226,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11226,tc_HOL_Obool)),U_11227),U_11228))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11226),c_Big__Operators_Olinorder__class_OMax(U_11226,U_11227)),c_Big__Operators_Olinorder__class_OMax(U_11226,U_11228))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11226,tc_HOL_Obool)),U_11227),U_11228) = c_Orderings_Obot__class_Obot(tc_fun(U_11226,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11226),U_11228))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11226),U_11227))
| ~ class_Orderings_Olinorder(U_11226) ),
inference(variable_rename,[status(thm)],[f_3004_1]) ).
cnf(f_3004_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11226),c_Big__Operators_Olinorder__class_OMax(U_11226,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11226,tc_HOL_Obool)),U_11227),U_11228))),c_Big__Operators_Olinorder__class_OMax(U_11226,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11226,tc_HOL_Obool)),U_11227),U_11228))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11226),c_Big__Operators_Olinorder__class_OMax(U_11226,U_11227)),c_Big__Operators_Olinorder__class_OMax(U_11226,U_11228))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11226,tc_HOL_Obool)),U_11227),U_11228) = c_Orderings_Obot__class_Obot(tc_fun(U_11226,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11226),U_11228))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11226),U_11227))
| ~ class_Orderings_Olinorder(U_11226) ),
inference(clausify,[status(thm)],[f_3004_2]) ).
fof(f_3005_1,plain,
! [V_B_2,V_A_2,T_b] :
( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Ounion__disjoint]) ).
fof(f_3005_2,plain,
! [U_11231,U_11230,U_11229] :
( c_Big__Operators_Olinorder__class_OMax(U_11229,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11229,tc_HOL_Obool)),U_11230),U_11231)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11229),c_Big__Operators_Olinorder__class_OMax(U_11229,U_11230)),c_Big__Operators_Olinorder__class_OMax(U_11229,U_11231))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11229,tc_HOL_Obool)),U_11230),U_11231) != c_Orderings_Obot__class_Obot(tc_fun(U_11229,tc_HOL_Obool))
| U_11231 = c_Orderings_Obot__class_Obot(tc_fun(U_11229,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11229),U_11231))
| U_11230 = c_Orderings_Obot__class_Obot(tc_fun(U_11229,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11229),U_11230))
| ~ class_Orderings_Olinorder(U_11229) ),
inference(variable_rename,[status(thm)],[f_3005_1]) ).
cnf(f_3005_3,plain,
( c_Big__Operators_Olinorder__class_OMax(U_11229,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11229,tc_HOL_Obool)),U_11230),U_11231)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11229),c_Big__Operators_Olinorder__class_OMax(U_11229,U_11230)),c_Big__Operators_Olinorder__class_OMax(U_11229,U_11231))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11229,tc_HOL_Obool)),U_11230),U_11231) != c_Orderings_Obot__class_Obot(tc_fun(U_11229,tc_HOL_Obool))
| U_11231 = c_Orderings_Obot__class_Obot(tc_fun(U_11229,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11229),U_11231))
| U_11230 = c_Orderings_Obot__class_Obot(tc_fun(U_11229,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11229),U_11230))
| ~ class_Orderings_Olinorder(U_11229) ),
inference(clausify,[status(thm)],[f_3005_2]) ).
fof(f_3006_1,plain,
! [V_B_2,V_A_2,T_b] :
( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__disjoint]) ).
fof(f_3006_2,plain,
! [U_11234,U_11233,U_11232] :
( c_Big__Operators_Olattice_OInf__fin(U_11232,c_Orderings_Oord__class_Omin(U_11232),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11232,tc_HOL_Obool)),U_11233),U_11234)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11232),c_Big__Operators_Olattice_OInf__fin(U_11232,c_Orderings_Oord__class_Omin(U_11232),U_11233)),c_Big__Operators_Olattice_OInf__fin(U_11232,c_Orderings_Oord__class_Omin(U_11232),U_11234))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11232,tc_HOL_Obool)),U_11233),U_11234) != c_Orderings_Obot__class_Obot(tc_fun(U_11232,tc_HOL_Obool))
| U_11234 = c_Orderings_Obot__class_Obot(tc_fun(U_11232,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11232),U_11234))
| U_11233 = c_Orderings_Obot__class_Obot(tc_fun(U_11232,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11232),U_11233))
| ~ class_Orderings_Olinorder(U_11232) ),
inference(variable_rename,[status(thm)],[f_3006_1]) ).
cnf(f_3006_3,plain,
( c_Big__Operators_Olattice_OInf__fin(U_11232,c_Orderings_Oord__class_Omin(U_11232),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11232,tc_HOL_Obool)),U_11233),U_11234)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11232),c_Big__Operators_Olattice_OInf__fin(U_11232,c_Orderings_Oord__class_Omin(U_11232),U_11233)),c_Big__Operators_Olattice_OInf__fin(U_11232,c_Orderings_Oord__class_Omin(U_11232),U_11234))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11232,tc_HOL_Obool)),U_11233),U_11234) != c_Orderings_Obot__class_Obot(tc_fun(U_11232,tc_HOL_Obool))
| U_11234 = c_Orderings_Obot__class_Obot(tc_fun(U_11232,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11232),U_11234))
| U_11233 = c_Orderings_Obot__class_Obot(tc_fun(U_11232,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11232),U_11233))
| ~ class_Orderings_Olinorder(U_11232) ),
inference(clausify,[status(thm)],[f_3006_2]) ).
fof(f_3007_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__inter]) ).
fof(f_3007_2,plain,
! [U_11237,U_11236,U_11235] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11235),c_Big__Operators_Olattice_OInf__fin(U_11235,c_Orderings_Oord__class_Omin(U_11235),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11235,tc_HOL_Obool)),U_11236),U_11237))),c_Big__Operators_Olattice_OInf__fin(U_11235,c_Orderings_Oord__class_Omin(U_11235),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11235,tc_HOL_Obool)),U_11236),U_11237))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11235),c_Big__Operators_Olattice_OInf__fin(U_11235,c_Orderings_Oord__class_Omin(U_11235),U_11236)),c_Big__Operators_Olattice_OInf__fin(U_11235,c_Orderings_Oord__class_Omin(U_11235),U_11237))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11235,tc_HOL_Obool)),U_11236),U_11237) = c_Orderings_Obot__class_Obot(tc_fun(U_11235,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11235),U_11237))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11235),U_11236))
| ~ class_Orderings_Olinorder(U_11235) ),
inference(variable_rename,[status(thm)],[f_3007_1]) ).
cnf(f_3007_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11235),c_Big__Operators_Olattice_OInf__fin(U_11235,c_Orderings_Oord__class_Omin(U_11235),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11235,tc_HOL_Obool)),U_11236),U_11237))),c_Big__Operators_Olattice_OInf__fin(U_11235,c_Orderings_Oord__class_Omin(U_11235),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11235,tc_HOL_Obool)),U_11236),U_11237))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11235),c_Big__Operators_Olattice_OInf__fin(U_11235,c_Orderings_Oord__class_Omin(U_11235),U_11236)),c_Big__Operators_Olattice_OInf__fin(U_11235,c_Orderings_Oord__class_Omin(U_11235),U_11237))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11235,tc_HOL_Obool)),U_11236),U_11237) = c_Orderings_Obot__class_Obot(tc_fun(U_11235,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11235),U_11237))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11235),U_11236))
| ~ class_Orderings_Olinorder(U_11235) ),
inference(clausify,[status(thm)],[f_3007_2]) ).
fof(f_3008_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__inter]) ).
fof(f_3008_2,plain,
! [U_11240,U_11239,U_11238] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11238),c_Big__Operators_Olattice_OSup__fin(U_11238,c_Orderings_Oord__class_Omax(U_11238),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11238,tc_HOL_Obool)),U_11239),U_11240))),c_Big__Operators_Olattice_OSup__fin(U_11238,c_Orderings_Oord__class_Omax(U_11238),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11238,tc_HOL_Obool)),U_11239),U_11240))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11238),c_Big__Operators_Olattice_OSup__fin(U_11238,c_Orderings_Oord__class_Omax(U_11238),U_11239)),c_Big__Operators_Olattice_OSup__fin(U_11238,c_Orderings_Oord__class_Omax(U_11238),U_11240))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11238,tc_HOL_Obool)),U_11239),U_11240) = c_Orderings_Obot__class_Obot(tc_fun(U_11238,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11238),U_11240))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11238),U_11239))
| ~ class_Orderings_Olinorder(U_11238) ),
inference(variable_rename,[status(thm)],[f_3008_1]) ).
cnf(f_3008_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11238),c_Big__Operators_Olattice_OSup__fin(U_11238,c_Orderings_Oord__class_Omax(U_11238),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11238,tc_HOL_Obool)),U_11239),U_11240))),c_Big__Operators_Olattice_OSup__fin(U_11238,c_Orderings_Oord__class_Omax(U_11238),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11238,tc_HOL_Obool)),U_11239),U_11240))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11238),c_Big__Operators_Olattice_OSup__fin(U_11238,c_Orderings_Oord__class_Omax(U_11238),U_11239)),c_Big__Operators_Olattice_OSup__fin(U_11238,c_Orderings_Oord__class_Omax(U_11238),U_11240))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11238,tc_HOL_Obool)),U_11239),U_11240) = c_Orderings_Obot__class_Obot(tc_fun(U_11238,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11238),U_11240))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11238),U_11239))
| ~ class_Orderings_Olinorder(U_11238) ),
inference(clausify,[status(thm)],[f_3008_2]) ).
fof(f_3009_1,plain,
! [V_B_2,V_A_2,T_b] :
( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__disjoint]) ).
fof(f_3009_2,plain,
! [U_11243,U_11242,U_11241] :
( c_Big__Operators_Olattice_OSup__fin(U_11241,c_Orderings_Oord__class_Omax(U_11241),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11241,tc_HOL_Obool)),U_11242),U_11243)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11241),c_Big__Operators_Olattice_OSup__fin(U_11241,c_Orderings_Oord__class_Omax(U_11241),U_11242)),c_Big__Operators_Olattice_OSup__fin(U_11241,c_Orderings_Oord__class_Omax(U_11241),U_11243))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11241,tc_HOL_Obool)),U_11242),U_11243) != c_Orderings_Obot__class_Obot(tc_fun(U_11241,tc_HOL_Obool))
| U_11243 = c_Orderings_Obot__class_Obot(tc_fun(U_11241,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11241),U_11243))
| U_11242 = c_Orderings_Obot__class_Obot(tc_fun(U_11241,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11241),U_11242))
| ~ class_Orderings_Olinorder(U_11241) ),
inference(variable_rename,[status(thm)],[f_3009_1]) ).
cnf(f_3009_3,plain,
( c_Big__Operators_Olattice_OSup__fin(U_11241,c_Orderings_Oord__class_Omax(U_11241),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11241,tc_HOL_Obool)),U_11242),U_11243)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11241),c_Big__Operators_Olattice_OSup__fin(U_11241,c_Orderings_Oord__class_Omax(U_11241),U_11242)),c_Big__Operators_Olattice_OSup__fin(U_11241,c_Orderings_Oord__class_Omax(U_11241),U_11243))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11241,tc_HOL_Obool)),U_11242),U_11243) != c_Orderings_Obot__class_Obot(tc_fun(U_11241,tc_HOL_Obool))
| U_11243 = c_Orderings_Obot__class_Obot(tc_fun(U_11241,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11241),U_11243))
| U_11242 = c_Orderings_Obot__class_Obot(tc_fun(U_11241,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11241),U_11242))
| ~ class_Orderings_Olinorder(U_11241) ),
inference(clausify,[status(thm)],[f_3009_2]) ).
fof(f_3010_1,plain,
! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_d,T_c,T_b] :
( 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_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y2_2),V_z2_2)),V_r2_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y1_2),V_z1_2)),V_r1_2))
| ~ c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_congruent2D]) ).
fof(f_3010_2,plain,
! [U_11253,U_11252,U_11251,U_11250,U_11249,U_11248,U_11247,U_11246,U_11245,U_11244] :
( hAPP(hAPP(U_11249,U_11250),U_11252) = hAPP(hAPP(U_11249,U_11251),U_11253)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11245,U_11245)),hAPP(hAPP(c_Product__Type_OPair(U_11245,U_11245),U_11252),U_11253)),U_11248))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11244,U_11244)),hAPP(hAPP(c_Product__Type_OPair(U_11244,U_11244),U_11250),U_11251)),U_11247))
| ~ c_Equiv__Relations_Ocongruent2(U_11244,U_11245,U_11246,U_11247,U_11248,U_11249) ),
inference(variable_rename,[status(thm)],[f_3010_1]) ).
cnf(f_3010_3,plain,
( hAPP(hAPP(U_11249,U_11250),U_11252) = hAPP(hAPP(U_11249,U_11251),U_11253)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11245,U_11245)),hAPP(hAPP(c_Product__Type_OPair(U_11245,U_11245),U_11252),U_11253)),U_11248))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11244,U_11244)),hAPP(hAPP(c_Product__Type_OPair(U_11244,U_11244),U_11250),U_11251)),U_11247))
| ~ c_Equiv__Relations_Ocongruent2(U_11244,U_11245,U_11246,U_11247,U_11248,U_11249) ),
inference(clausify,[status(thm)],[f_3010_2]) ).
fof(f_3011_1,plain,
! [V_f_2,V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__Un__nat]) ).
fof(f_3011_2,plain,
! [U_11257,U_11256,U_11255,U_11254] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11254,tc_Nat_Onat),U_11257),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11254,tc_HOL_Obool)),U_11255),U_11256)) = 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_11254,tc_Nat_Onat),U_11257),U_11255)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11254,tc_Nat_Onat),U_11257),U_11256))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11254,tc_Nat_Onat),U_11257),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11254,tc_HOL_Obool)),U_11255),U_11256)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11254),U_11256))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11254),U_11255)) ),
inference(variable_rename,[status(thm)],[f_3011_1]) ).
cnf(f_3011_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11254,tc_Nat_Onat),U_11257),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11254,tc_HOL_Obool)),U_11255),U_11256)) = 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_11254,tc_Nat_Onat),U_11257),U_11255)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11254,tc_Nat_Onat),U_11257),U_11256))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11254,tc_Nat_Onat),U_11257),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11254,tc_HOL_Obool)),U_11255),U_11256)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11254),U_11256))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11254),U_11255)) ),
inference(clausify,[status(thm)],[f_3011_2]) ).
fof(f_3012_1,plain,
! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
( hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_r_2))
| ~ c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_congruentD]) ).
fof(f_3012_2,plain,
! [U_11263,U_11262,U_11261,U_11260,U_11259,U_11258] :
( hAPP(U_11261,U_11262) = hAPP(U_11261,U_11263)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11258,U_11258)),hAPP(hAPP(c_Product__Type_OPair(U_11258,U_11258),U_11262),U_11263)),U_11260))
| ~ c_Equiv__Relations_Ocongruent(U_11258,U_11259,U_11260,U_11261) ),
inference(variable_rename,[status(thm)],[f_3012_1]) ).
cnf(f_3012_3,plain,
( hAPP(U_11261,U_11262) = hAPP(U_11261,U_11263)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11258,U_11258)),hAPP(hAPP(c_Product__Type_OPair(U_11258,U_11258),U_11262),U_11263)),U_11260))
| ~ c_Equiv__Relations_Ocongruent(U_11258,U_11259,U_11260,U_11261) ),
inference(clausify,[status(thm)],[f_3012_2]) ).
fof(f_3013_1,plain,
! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_d,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
| ~ c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
| ~ c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
| ~ c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) ),
inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent__UN]) ).
fof(f_3013_2,plain,
! [U_11272,U_11271,U_11270,U_11269,U_11268,U_11267,U_11266,U_11265,U_11264] :
( c_Equiv__Relations_Ocongruent(U_11264,tc_fun(U_11270,tc_HOL_Obool),U_11266,hAPP(hAPP(c_COMBB(tc_fun(U_11267,tc_fun(U_11270,tc_HOL_Obool)),tc_fun(U_11270,tc_HOL_Obool),U_11264),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11267,tc_fun(U_11270,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11267,U_11267,U_11269),hAPP(hAPP(c_Set_Oinsert(U_11267),U_11272),c_Orderings_Obot__class_Obot(tc_fun(U_11267,tc_HOL_Obool)))))),U_11271))
| ~ hBOOL(hAPP(hAPP(c_member(U_11267),U_11272),U_11268))
| ~ c_Equiv__Relations_Ocongruent2(U_11264,U_11267,tc_fun(U_11270,tc_HOL_Obool),U_11266,U_11269,U_11271)
| ~ c_Equiv__Relations_Oequiv(U_11267,U_11268,U_11269)
| ~ c_Equiv__Relations_Oequiv(U_11264,U_11265,U_11266) ),
inference(variable_rename,[status(thm)],[f_3013_1]) ).
cnf(f_3013_3,plain,
( c_Equiv__Relations_Ocongruent(U_11264,tc_fun(U_11270,tc_HOL_Obool),U_11266,hAPP(hAPP(c_COMBB(tc_fun(U_11267,tc_fun(U_11270,tc_HOL_Obool)),tc_fun(U_11270,tc_HOL_Obool),U_11264),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11267,tc_fun(U_11270,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_11267,U_11267,U_11269),hAPP(hAPP(c_Set_Oinsert(U_11267),U_11272),c_Orderings_Obot__class_Obot(tc_fun(U_11267,tc_HOL_Obool)))))),U_11271))
| ~ hBOOL(hAPP(hAPP(c_member(U_11267),U_11272),U_11268))
| ~ c_Equiv__Relations_Ocongruent2(U_11264,U_11267,tc_fun(U_11270,tc_HOL_Obool),U_11266,U_11269,U_11271)
| ~ c_Equiv__Relations_Oequiv(U_11267,U_11268,U_11269)
| ~ c_Equiv__Relations_Oequiv(U_11264,U_11265,U_11266) ),
inference(clausify,[status(thm)],[f_3013_2]) ).
fof(f_3014_1,plain,
! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
( V_X_2 = V_Y_2
| ? [B_x] :
( ? [B_y] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
& hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
& hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) )
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_Y_2),V_f_2)
| ~ c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
| ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__inject]) ).
fof(f_3014_2,plain,
! [U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275] :
( U_11280 = U_11281
| ? [U_11274] :
( ? [U_11273] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11275,U_11275)),hAPP(hAPP(c_Product__Type_OPair(U_11275,U_11275),U_11274),U_11273)),U_11277))
& hAPP(U_11279,U_11274) = hAPP(U_11279,U_11273)
& hBOOL(hAPP(hAPP(c_member(U_11275),U_11273),U_11276)) )
& hBOOL(hAPP(hAPP(c_member(U_11275),U_11274),U_11276)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11275,tc_HOL_Obool)),U_11281),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11275),U_11276),U_11277)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11275,tc_HOL_Obool)),U_11280),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11275),U_11276),U_11277)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11275,tc_fun(U_11278,tc_HOL_Obool)),U_11280),U_11279) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11275,tc_fun(U_11278,tc_HOL_Obool)),U_11281),U_11279)
| ~ c_Equiv__Relations_Ocongruent(U_11275,tc_fun(U_11278,tc_HOL_Obool),U_11277,U_11279)
| ~ c_Equiv__Relations_Oequiv(U_11275,U_11276,U_11277) ),
inference(variable_rename,[status(thm)],[f_3014_1]) ).
fof(f_3014_3,plain,
! [U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275] :
( U_11280 = U_11281
| ( ? [U_11273] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11275,U_11275)),hAPP(hAPP(c_Product__Type_OPair(U_11275,U_11275),sK235(U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275)),U_11273)),U_11277))
& hAPP(U_11279,sK235(U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275)) = hAPP(U_11279,U_11273)
& hBOOL(hAPP(hAPP(c_member(U_11275),U_11273),U_11276)) )
& hBOOL(hAPP(hAPP(c_member(U_11275),sK235(U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275)),U_11276)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11275,tc_HOL_Obool)),U_11281),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11275),U_11276),U_11277)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11275,tc_HOL_Obool)),U_11280),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11275),U_11276),U_11277)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11275,tc_fun(U_11278,tc_HOL_Obool)),U_11280),U_11279) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11275,tc_fun(U_11278,tc_HOL_Obool)),U_11281),U_11279)
| ~ c_Equiv__Relations_Ocongruent(U_11275,tc_fun(U_11278,tc_HOL_Obool),U_11277,U_11279)
| ~ c_Equiv__Relations_Oequiv(U_11275,U_11276,U_11277) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK235]),skolemize(U_11274,sK235(U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275))],[f_3014_2]) ).
fof(f_3014_4,plain,
! [U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275] :
( U_11280 = U_11281
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11275,U_11275)),hAPP(hAPP(c_Product__Type_OPair(U_11275,U_11275),sK235(U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275)),sK236(U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275))),U_11277))
& hAPP(U_11279,sK235(U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275)) = hAPP(U_11279,sK236(U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275))
& hBOOL(hAPP(hAPP(c_member(U_11275),sK236(U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275)),U_11276))
& hBOOL(hAPP(hAPP(c_member(U_11275),sK235(U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275)),U_11276)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11275,tc_HOL_Obool)),U_11281),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11275),U_11276),U_11277)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11275,tc_HOL_Obool)),U_11280),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11275),U_11276),U_11277)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11275,tc_fun(U_11278,tc_HOL_Obool)),U_11280),U_11279) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11275,tc_fun(U_11278,tc_HOL_Obool)),U_11281),U_11279)
| ~ c_Equiv__Relations_Ocongruent(U_11275,tc_fun(U_11278,tc_HOL_Obool),U_11277,U_11279)
| ~ c_Equiv__Relations_Oequiv(U_11275,U_11276,U_11277) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK236]),skolemize(U_11273,sK236(U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275))],[f_3014_3]) ).
cnf(f_3014_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_11275),sK235(U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275)),U_11276))
| U_11280 = U_11281
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11275,tc_HOL_Obool)),U_11281),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11275),U_11276),U_11277)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11275,tc_HOL_Obool)),U_11280),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11275),U_11276),U_11277)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11275,tc_fun(U_11278,tc_HOL_Obool)),U_11280),U_11279) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11275,tc_fun(U_11278,tc_HOL_Obool)),U_11281),U_11279)
| ~ c_Equiv__Relations_Ocongruent(U_11275,tc_fun(U_11278,tc_HOL_Obool),U_11277,U_11279)
| ~ c_Equiv__Relations_Oequiv(U_11275,U_11276,U_11277) ),
inference(clausify,[status(thm)],[f_3014_4]) ).
cnf(f_3014_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_11275),sK236(U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275)),U_11276))
| U_11280 = U_11281
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11275,tc_HOL_Obool)),U_11281),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11275),U_11276),U_11277)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11275,tc_HOL_Obool)),U_11280),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11275),U_11276),U_11277)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11275,tc_fun(U_11278,tc_HOL_Obool)),U_11280),U_11279) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11275,tc_fun(U_11278,tc_HOL_Obool)),U_11281),U_11279)
| ~ c_Equiv__Relations_Ocongruent(U_11275,tc_fun(U_11278,tc_HOL_Obool),U_11277,U_11279)
| ~ c_Equiv__Relations_Oequiv(U_11275,U_11276,U_11277) ),
inference(clausify,[status(thm)],[f_3014_4]) ).
cnf(f_3014_7,plain,
( hAPP(U_11279,sK235(U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275)) = hAPP(U_11279,sK236(U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275))
| U_11280 = U_11281
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11275,tc_HOL_Obool)),U_11281),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11275),U_11276),U_11277)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11275,tc_HOL_Obool)),U_11280),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11275),U_11276),U_11277)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11275,tc_fun(U_11278,tc_HOL_Obool)),U_11280),U_11279) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11275,tc_fun(U_11278,tc_HOL_Obool)),U_11281),U_11279)
| ~ c_Equiv__Relations_Ocongruent(U_11275,tc_fun(U_11278,tc_HOL_Obool),U_11277,U_11279)
| ~ c_Equiv__Relations_Oequiv(U_11275,U_11276,U_11277) ),
inference(clausify,[status(thm)],[f_3014_4]) ).
cnf(f_3014_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11275,U_11275)),hAPP(hAPP(c_Product__Type_OPair(U_11275,U_11275),sK235(U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275)),sK236(U_11281,U_11280,U_11279,U_11278,U_11277,U_11276,U_11275))),U_11277))
| U_11280 = U_11281
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11275,tc_HOL_Obool)),U_11281),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11275),U_11276),U_11277)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11275,tc_HOL_Obool)),U_11280),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11275),U_11276),U_11277)))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11275,tc_fun(U_11278,tc_HOL_Obool)),U_11280),U_11279) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11275,tc_fun(U_11278,tc_HOL_Obool)),U_11281),U_11279)
| ~ c_Equiv__Relations_Ocongruent(U_11275,tc_fun(U_11278,tc_HOL_Obool),U_11277,U_11279)
| ~ c_Equiv__Relations_Oequiv(U_11275,U_11276,U_11277) ),
inference(clausify,[status(thm)],[f_3014_4]) ).
fof(f_3015_1,plain,
! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2))
| ? [B_x1] :
( ? [B_x2] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2)) )
& hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A2_2),V_r2_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A1_2),V_r1_2)))
| ~ c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
| ~ c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
| ~ c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2) ),
inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__type2]) ).
fof(f_3015_2,plain,
! [U_11294,U_11293,U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286,U_11285,U_11284] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11290,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11284,tc_fun(U_11290,tc_HOL_Obool)),U_11292),hAPP(hAPP(c_COMBB(tc_fun(U_11287,tc_fun(U_11290,tc_HOL_Obool)),tc_fun(U_11290,tc_HOL_Obool),U_11284),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11287,tc_fun(U_11290,tc_HOL_Obool)),U_11293)),U_11291))),U_11294))
| ? [U_11283] :
( ? [U_11282] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11290,tc_HOL_Obool)),hAPP(hAPP(U_11291,U_11283),U_11282)),U_11294))
& hBOOL(hAPP(hAPP(c_member(U_11287),U_11282),U_11288)) )
& hBOOL(hAPP(hAPP(c_member(U_11284),U_11283),U_11285)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11287,tc_HOL_Obool)),U_11293),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11287),U_11288),U_11289)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11284,tc_HOL_Obool)),U_11292),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11284),U_11285),U_11286)))
| ~ c_Equiv__Relations_Ocongruent2(U_11284,U_11287,tc_fun(U_11290,tc_HOL_Obool),U_11286,U_11289,U_11291)
| ~ c_Equiv__Relations_Oequiv(U_11287,U_11288,U_11289)
| ~ c_Equiv__Relations_Oequiv(U_11284,U_11285,U_11286) ),
inference(variable_rename,[status(thm)],[f_3015_1]) ).
fof(f_3015_3,plain,
! [U_11294,U_11293,U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286,U_11285,U_11284] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11290,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11284,tc_fun(U_11290,tc_HOL_Obool)),U_11292),hAPP(hAPP(c_COMBB(tc_fun(U_11287,tc_fun(U_11290,tc_HOL_Obool)),tc_fun(U_11290,tc_HOL_Obool),U_11284),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11287,tc_fun(U_11290,tc_HOL_Obool)),U_11293)),U_11291))),U_11294))
| ( ? [U_11282] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11290,tc_HOL_Obool)),hAPP(hAPP(U_11291,sK237(U_11294,U_11293,U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286,U_11285,U_11284)),U_11282)),U_11294))
& hBOOL(hAPP(hAPP(c_member(U_11287),U_11282),U_11288)) )
& hBOOL(hAPP(hAPP(c_member(U_11284),sK237(U_11294,U_11293,U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286,U_11285,U_11284)),U_11285)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11287,tc_HOL_Obool)),U_11293),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11287),U_11288),U_11289)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11284,tc_HOL_Obool)),U_11292),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11284),U_11285),U_11286)))
| ~ c_Equiv__Relations_Ocongruent2(U_11284,U_11287,tc_fun(U_11290,tc_HOL_Obool),U_11286,U_11289,U_11291)
| ~ c_Equiv__Relations_Oequiv(U_11287,U_11288,U_11289)
| ~ c_Equiv__Relations_Oequiv(U_11284,U_11285,U_11286) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK237]),skolemize(U_11283,sK237(U_11294,U_11293,U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286,U_11285,U_11284))],[f_3015_2]) ).
fof(f_3015_4,plain,
! [U_11294,U_11293,U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286,U_11285,U_11284] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11290,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11284,tc_fun(U_11290,tc_HOL_Obool)),U_11292),hAPP(hAPP(c_COMBB(tc_fun(U_11287,tc_fun(U_11290,tc_HOL_Obool)),tc_fun(U_11290,tc_HOL_Obool),U_11284),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11287,tc_fun(U_11290,tc_HOL_Obool)),U_11293)),U_11291))),U_11294))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11290,tc_HOL_Obool)),hAPP(hAPP(U_11291,sK237(U_11294,U_11293,U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286,U_11285,U_11284)),sK238(U_11294,U_11293,U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286,U_11285,U_11284))),U_11294))
& hBOOL(hAPP(hAPP(c_member(U_11287),sK238(U_11294,U_11293,U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286,U_11285,U_11284)),U_11288))
& hBOOL(hAPP(hAPP(c_member(U_11284),sK237(U_11294,U_11293,U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286,U_11285,U_11284)),U_11285)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11287,tc_HOL_Obool)),U_11293),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11287),U_11288),U_11289)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11284,tc_HOL_Obool)),U_11292),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11284),U_11285),U_11286)))
| ~ c_Equiv__Relations_Ocongruent2(U_11284,U_11287,tc_fun(U_11290,tc_HOL_Obool),U_11286,U_11289,U_11291)
| ~ c_Equiv__Relations_Oequiv(U_11287,U_11288,U_11289)
| ~ c_Equiv__Relations_Oequiv(U_11284,U_11285,U_11286) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK238]),skolemize(U_11282,sK238(U_11294,U_11293,U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286,U_11285,U_11284))],[f_3015_3]) ).
cnf(f_3015_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_11284),sK237(U_11294,U_11293,U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286,U_11285,U_11284)),U_11285))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_11290,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11284,tc_fun(U_11290,tc_HOL_Obool)),U_11292),hAPP(hAPP(c_COMBB(tc_fun(U_11287,tc_fun(U_11290,tc_HOL_Obool)),tc_fun(U_11290,tc_HOL_Obool),U_11284),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11287,tc_fun(U_11290,tc_HOL_Obool)),U_11293)),U_11291))),U_11294))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11287,tc_HOL_Obool)),U_11293),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11287),U_11288),U_11289)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11284,tc_HOL_Obool)),U_11292),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11284),U_11285),U_11286)))
| ~ c_Equiv__Relations_Ocongruent2(U_11284,U_11287,tc_fun(U_11290,tc_HOL_Obool),U_11286,U_11289,U_11291)
| ~ c_Equiv__Relations_Oequiv(U_11287,U_11288,U_11289)
| ~ c_Equiv__Relations_Oequiv(U_11284,U_11285,U_11286) ),
inference(clausify,[status(thm)],[f_3015_4]) ).
cnf(f_3015_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_11287),sK238(U_11294,U_11293,U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286,U_11285,U_11284)),U_11288))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_11290,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11284,tc_fun(U_11290,tc_HOL_Obool)),U_11292),hAPP(hAPP(c_COMBB(tc_fun(U_11287,tc_fun(U_11290,tc_HOL_Obool)),tc_fun(U_11290,tc_HOL_Obool),U_11284),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11287,tc_fun(U_11290,tc_HOL_Obool)),U_11293)),U_11291))),U_11294))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11287,tc_HOL_Obool)),U_11293),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11287),U_11288),U_11289)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11284,tc_HOL_Obool)),U_11292),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11284),U_11285),U_11286)))
| ~ c_Equiv__Relations_Ocongruent2(U_11284,U_11287,tc_fun(U_11290,tc_HOL_Obool),U_11286,U_11289,U_11291)
| ~ c_Equiv__Relations_Oequiv(U_11287,U_11288,U_11289)
| ~ c_Equiv__Relations_Oequiv(U_11284,U_11285,U_11286) ),
inference(clausify,[status(thm)],[f_3015_4]) ).
cnf(f_3015_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11290,tc_HOL_Obool)),hAPP(hAPP(U_11291,sK237(U_11294,U_11293,U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286,U_11285,U_11284)),sK238(U_11294,U_11293,U_11292,U_11291,U_11290,U_11289,U_11288,U_11287,U_11286,U_11285,U_11284))),U_11294))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_11290,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11284,tc_fun(U_11290,tc_HOL_Obool)),U_11292),hAPP(hAPP(c_COMBB(tc_fun(U_11287,tc_fun(U_11290,tc_HOL_Obool)),tc_fun(U_11290,tc_HOL_Obool),U_11284),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11287,tc_fun(U_11290,tc_HOL_Obool)),U_11293)),U_11291))),U_11294))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11287,tc_HOL_Obool)),U_11293),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11287),U_11288),U_11289)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11284,tc_HOL_Obool)),U_11292),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11284),U_11285),U_11286)))
| ~ c_Equiv__Relations_Ocongruent2(U_11284,U_11287,tc_fun(U_11290,tc_HOL_Obool),U_11286,U_11289,U_11291)
| ~ c_Equiv__Relations_Oequiv(U_11287,U_11288,U_11289)
| ~ c_Equiv__Relations_Oequiv(U_11284,U_11285,U_11286) ),
inference(clausify,[status(thm)],[f_3015_4]) ).
fof(f_3016_1,plain,
! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
| ~ c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
| ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__type]) ).
fof(f_3016_2,plain,
! [U_11302,U_11301,U_11300,U_11299,U_11298,U_11297,U_11296] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11299,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11296,tc_fun(U_11299,tc_HOL_Obool)),U_11301),U_11300)),U_11302))
| ? [U_11295] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11299,tc_HOL_Obool)),hAPP(U_11300,U_11295)),U_11302))
& hBOOL(hAPP(hAPP(c_member(U_11296),U_11295),U_11297)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11296,tc_HOL_Obool)),U_11301),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11296),U_11297),U_11298)))
| ~ c_Equiv__Relations_Ocongruent(U_11296,tc_fun(U_11299,tc_HOL_Obool),U_11298,U_11300)
| ~ c_Equiv__Relations_Oequiv(U_11296,U_11297,U_11298) ),
inference(variable_rename,[status(thm)],[f_3016_1]) ).
fof(f_3016_3,plain,
! [U_11302,U_11301,U_11300,U_11299,U_11298,U_11297,U_11296] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11299,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11296,tc_fun(U_11299,tc_HOL_Obool)),U_11301),U_11300)),U_11302))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11299,tc_HOL_Obool)),hAPP(U_11300,sK239(U_11302,U_11301,U_11300,U_11299,U_11298,U_11297,U_11296))),U_11302))
& hBOOL(hAPP(hAPP(c_member(U_11296),sK239(U_11302,U_11301,U_11300,U_11299,U_11298,U_11297,U_11296)),U_11297)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11296,tc_HOL_Obool)),U_11301),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11296),U_11297),U_11298)))
| ~ c_Equiv__Relations_Ocongruent(U_11296,tc_fun(U_11299,tc_HOL_Obool),U_11298,U_11300)
| ~ c_Equiv__Relations_Oequiv(U_11296,U_11297,U_11298) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK239]),skolemize(U_11295,sK239(U_11302,U_11301,U_11300,U_11299,U_11298,U_11297,U_11296))],[f_3016_2]) ).
cnf(f_3016_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11296),sK239(U_11302,U_11301,U_11300,U_11299,U_11298,U_11297,U_11296)),U_11297))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_11299,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11296,tc_fun(U_11299,tc_HOL_Obool)),U_11301),U_11300)),U_11302))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11296,tc_HOL_Obool)),U_11301),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11296),U_11297),U_11298)))
| ~ c_Equiv__Relations_Ocongruent(U_11296,tc_fun(U_11299,tc_HOL_Obool),U_11298,U_11300)
| ~ c_Equiv__Relations_Oequiv(U_11296,U_11297,U_11298) ),
inference(clausify,[status(thm)],[f_3016_3]) ).
cnf(f_3016_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11299,tc_HOL_Obool)),hAPP(U_11300,sK239(U_11302,U_11301,U_11300,U_11299,U_11298,U_11297,U_11296))),U_11302))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_11299,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11296,tc_fun(U_11299,tc_HOL_Obool)),U_11301),U_11300)),U_11302))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11296,tc_HOL_Obool)),U_11301),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11296),U_11297),U_11298)))
| ~ c_Equiv__Relations_Ocongruent(U_11296,tc_fun(U_11299,tc_HOL_Obool),U_11298,U_11300)
| ~ c_Equiv__Relations_Oequiv(U_11296,U_11297,U_11298) ),
inference(clausify,[status(thm)],[f_3016_3]) ).
fof(f_3017_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]) ).
cnf(f_3017_2,plain,
c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_3017_1]) ).
fof(f_3018_1,plain,
! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_S_2)),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2]) ).
fof(f_3018_2,plain,
! [U_11308,U_11307,U_11306,U_11305,U_11304,U_11303] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11303,tc_fun(U_11304,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11303,tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_fun(U_11304,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11304,tc_fun(tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_fun(U_11304,tc_HOL_Obool)),U_11303),c_COMBC(U_11304,tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11304,tc_prod(U_11303,U_11304)),tc_fun(U_11304,tc_fun(tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_HOL_Obool)),U_11303),hAPP(c_COMBB(tc_prod(U_11303,U_11304),tc_fun(tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_HOL_Obool),U_11304),c_member(tc_prod(U_11303,U_11304)))),c_Product__Type_OPair(U_11303,U_11304)))),U_11305)),hAPP(hAPP(c_COMBC(U_11303,tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_fun(U_11304,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11304,tc_fun(tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_fun(U_11304,tc_HOL_Obool)),U_11303),c_COMBC(U_11304,tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11304,tc_prod(U_11303,U_11304)),tc_fun(U_11304,tc_fun(tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_HOL_Obool)),U_11303),hAPP(c_COMBB(tc_prod(U_11303,U_11304),tc_fun(tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_HOL_Obool),U_11304),c_member(tc_prod(U_11303,U_11304)))),c_Product__Type_OPair(U_11303,U_11304)))),U_11306)),U_11307),U_11308))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11303,U_11304)),hAPP(hAPP(c_Product__Type_OPair(U_11303,U_11304),U_11307),U_11308)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool)),U_11305),U_11306))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11303,U_11304)),hAPP(hAPP(c_Product__Type_OPair(U_11303,U_11304),U_11307),U_11308)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool)),U_11305),U_11306)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11303,tc_fun(U_11304,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11303,tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_fun(U_11304,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11304,tc_fun(tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_fun(U_11304,tc_HOL_Obool)),U_11303),c_COMBC(U_11304,tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11304,tc_prod(U_11303,U_11304)),tc_fun(U_11304,tc_fun(tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_HOL_Obool)),U_11303),hAPP(c_COMBB(tc_prod(U_11303,U_11304),tc_fun(tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_HOL_Obool),U_11304),c_member(tc_prod(U_11303,U_11304)))),c_Product__Type_OPair(U_11303,U_11304)))),U_11305)),hAPP(hAPP(c_COMBC(U_11303,tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_fun(U_11304,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11304,tc_fun(tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_fun(U_11304,tc_HOL_Obool)),U_11303),c_COMBC(U_11304,tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11304,tc_prod(U_11303,U_11304)),tc_fun(U_11304,tc_fun(tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_HOL_Obool)),U_11303),hAPP(c_COMBB(tc_prod(U_11303,U_11304),tc_fun(tc_fun(tc_prod(U_11303,U_11304),tc_HOL_Obool),tc_HOL_Obool),U_11304),c_member(tc_prod(U_11303,U_11304)))),c_Product__Type_OPair(U_11303,U_11304)))),U_11306)),U_11307),U_11308)) ) ),
inference(variable_rename,[status(thm)],[f_3018_1]) ).
fof(f_3018_3,plain,
( ! [U_11320,U_11318,U_11316,U_11314,U_11312,U_11310] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11310,tc_fun(U_11312,tc_HOL_Obool))),hAPP(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)),hAPP(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_11316)),U_11318),U_11320))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11310,U_11312)),hAPP(hAPP(c_Product__Type_OPair(U_11310,U_11312),U_11318),U_11320)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool)),U_11314),U_11316))) )
& ! [U_11319,U_11317,U_11315,U_11313,U_11311,U_11309] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11309,U_11311)),hAPP(hAPP(c_Product__Type_OPair(U_11309,U_11311),U_11317),U_11319)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool)),U_11313),U_11315)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11309,tc_fun(U_11311,tc_HOL_Obool))),hAPP(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)),hAPP(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_11315)),U_11317),U_11319)) ) ),
inference(miniscope,[status(thm)],[f_3018_2]) ).
cnf(f_3018_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11309,U_11311)),hAPP(hAPP(c_Product__Type_OPair(U_11309,U_11311),U_11317),U_11319)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11309,U_11311),tc_HOL_Obool)),U_11313),U_11315)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11309,tc_fun(U_11311,tc_HOL_Obool))),hAPP(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)),hAPP(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_11315)),U_11317),U_11319)) ),
inference(clausify,[status(thm)],[f_3018_3]) ).
cnf(f_3018_5,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11310,tc_fun(U_11312,tc_HOL_Obool))),hAPP(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)),hAPP(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_11316)),U_11318),U_11320))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11310,U_11312)),hAPP(hAPP(c_Product__Type_OPair(U_11310,U_11312),U_11318),U_11320)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11310,U_11312),tc_HOL_Obool)),U_11314),U_11316))) ),
inference(clausify,[status(thm)],[f_3018_3]) ).
fof(f_3019_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card_Ounion__inter__neutral]) ).
fof(f_3019_2,plain,
! [U_11324,U_11323,U_11322] :
( hAPP(c_Finite__Set_Ocard(U_11322),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11322,tc_HOL_Obool)),U_11323),U_11324)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11322),U_11323)),hAPP(c_Finite__Set_Ocard(U_11322),U_11324))
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [U_11321] : hBOOL(hAPP(hAPP(c_member(U_11322),U_11321),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11322,tc_HOL_Obool)),U_11323),U_11324))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11322),U_11324))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11322),U_11323)) ),
inference(variable_rename,[status(thm)],[f_3019_1]) ).
fof(f_3019_3,plain,
! [U_11324,U_11323,U_11322] :
( hAPP(c_Finite__Set_Ocard(U_11322),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11322,tc_HOL_Obool)),U_11323),U_11324)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11322),U_11323)),hAPP(c_Finite__Set_Ocard(U_11322),U_11324))
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(U_11322),sK240(U_11324,U_11323,U_11322)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11322,tc_HOL_Obool)),U_11323),U_11324))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11322),U_11324))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11322),U_11323)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK240]),skolemize(U_11321,sK240(U_11324,U_11323,U_11322))],[f_3019_2]) ).
cnf(f_3019_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11322),sK240(U_11324,U_11323,U_11322)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11322,tc_HOL_Obool)),U_11323),U_11324)))
| hAPP(c_Finite__Set_Ocard(U_11322),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11322,tc_HOL_Obool)),U_11323),U_11324)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11322),U_11323)),hAPP(c_Finite__Set_Ocard(U_11322),U_11324))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11322),U_11324))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11322),U_11323)) ),
inference(clausify,[status(thm)],[f_3019_3]) ).
cnf(f_3019_5,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Finite__Set_Ocard(U_11322),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11322,tc_HOL_Obool)),U_11323),U_11324)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11322),U_11323)),hAPP(c_Finite__Set_Ocard(U_11322),U_11324))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11322),U_11324))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11322),U_11323)) ),
inference(clausify,[status(thm)],[f_3019_3]) ).
fof(f_3020_1,plain,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ? [B_x] :
( hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Fields_Ofield(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__Un]) ).
fof(f_3020_2,plain,
! [U_11330,U_11329,U_11328,U_11327,U_11326] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11327,U_11326),U_11330),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11327,tc_HOL_Obool)),U_11328),U_11329)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11326),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11327,U_11326),U_11330),U_11328)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11327,U_11326),U_11330),U_11329))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11327,U_11326),U_11330),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11327,tc_HOL_Obool)),U_11328),U_11329)))
| ? [U_11325] :
( hAPP(U_11330,U_11325) = c_Groups_Ozero__class_Ozero(U_11326)
& hBOOL(hAPP(hAPP(c_member(U_11327),U_11325),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11327,tc_HOL_Obool)),U_11328),U_11329))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11327),U_11329))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11327),U_11328))
| ~ class_Fields_Ofield(U_11326) ),
inference(variable_rename,[status(thm)],[f_3020_1]) ).
fof(f_3020_3,plain,
! [U_11330,U_11329,U_11328,U_11327,U_11326] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11327,U_11326),U_11330),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11327,tc_HOL_Obool)),U_11328),U_11329)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11326),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11327,U_11326),U_11330),U_11328)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11327,U_11326),U_11330),U_11329))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11327,U_11326),U_11330),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11327,tc_HOL_Obool)),U_11328),U_11329)))
| ( hAPP(U_11330,sK241(U_11330,U_11329,U_11328,U_11327,U_11326)) = c_Groups_Ozero__class_Ozero(U_11326)
& hBOOL(hAPP(hAPP(c_member(U_11327),sK241(U_11330,U_11329,U_11328,U_11327,U_11326)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11327,tc_HOL_Obool)),U_11328),U_11329))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11327),U_11329))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11327),U_11328))
| ~ class_Fields_Ofield(U_11326) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK241]),skolemize(U_11325,sK241(U_11330,U_11329,U_11328,U_11327,U_11326))],[f_3020_2]) ).
cnf(f_3020_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11327),sK241(U_11330,U_11329,U_11328,U_11327,U_11326)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11327,tc_HOL_Obool)),U_11328),U_11329)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11327,U_11326),U_11330),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11327,tc_HOL_Obool)),U_11328),U_11329)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11326),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11327,U_11326),U_11330),U_11328)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11327,U_11326),U_11330),U_11329))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11327,U_11326),U_11330),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11327,tc_HOL_Obool)),U_11328),U_11329)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11327),U_11329))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11327),U_11328))
| ~ class_Fields_Ofield(U_11326) ),
inference(clausify,[status(thm)],[f_3020_3]) ).
cnf(f_3020_5,plain,
( hAPP(U_11330,sK241(U_11330,U_11329,U_11328,U_11327,U_11326)) = c_Groups_Ozero__class_Ozero(U_11326)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11327,U_11326),U_11330),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11327,tc_HOL_Obool)),U_11328),U_11329)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11326),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11327,U_11326),U_11330),U_11328)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11327,U_11326),U_11330),U_11329))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11327,U_11326),U_11330),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11327,tc_HOL_Obool)),U_11328),U_11329)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11327),U_11329))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11327),U_11328))
| ~ class_Fields_Ofield(U_11326) ),
inference(clausify,[status(thm)],[f_3020_3]) ).
fof(f_3021_1,plain,
! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2))
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_c)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__Un__one]) ).
fof(f_3021_2,plain,
! [U_11336,U_11335,U_11334,U_11333,U_11332] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11333,U_11332),U_11336),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11333,tc_HOL_Obool)),U_11334),U_11335)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11332),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11333,U_11332),U_11336),U_11334)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11333,U_11332),U_11336),U_11335))
| ? [U_11331] :
( hAPP(U_11336,U_11331) != c_Groups_Oone__class_Oone(U_11332)
& hBOOL(hAPP(hAPP(c_member(U_11333),U_11331),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11333,tc_HOL_Obool)),U_11334),U_11335))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11333),U_11335))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11333),U_11334))
| ~ class_Groups_Ocomm__monoid__mult(U_11332) ),
inference(variable_rename,[status(thm)],[f_3021_1]) ).
fof(f_3021_3,plain,
! [U_11336,U_11335,U_11334,U_11333,U_11332] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11333,U_11332),U_11336),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11333,tc_HOL_Obool)),U_11334),U_11335)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11332),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11333,U_11332),U_11336),U_11334)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11333,U_11332),U_11336),U_11335))
| ( hAPP(U_11336,sK242(U_11336,U_11335,U_11334,U_11333,U_11332)) != c_Groups_Oone__class_Oone(U_11332)
& hBOOL(hAPP(hAPP(c_member(U_11333),sK242(U_11336,U_11335,U_11334,U_11333,U_11332)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11333,tc_HOL_Obool)),U_11334),U_11335))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11333),U_11335))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11333),U_11334))
| ~ class_Groups_Ocomm__monoid__mult(U_11332) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK242]),skolemize(U_11331,sK242(U_11336,U_11335,U_11334,U_11333,U_11332))],[f_3021_2]) ).
cnf(f_3021_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11333),sK242(U_11336,U_11335,U_11334,U_11333,U_11332)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11333,tc_HOL_Obool)),U_11334),U_11335)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11333,U_11332),U_11336),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11333,tc_HOL_Obool)),U_11334),U_11335)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11332),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11333,U_11332),U_11336),U_11334)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11333,U_11332),U_11336),U_11335))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11333),U_11335))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11333),U_11334))
| ~ class_Groups_Ocomm__monoid__mult(U_11332) ),
inference(clausify,[status(thm)],[f_3021_3]) ).
cnf(f_3021_5,plain,
( hAPP(U_11336,sK242(U_11336,U_11335,U_11334,U_11333,U_11332)) != c_Groups_Oone__class_Oone(U_11332)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11333,U_11332),U_11336),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11333,tc_HOL_Obool)),U_11334),U_11335)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11332),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11333,U_11332),U_11336),U_11334)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11333,U_11332),U_11336),U_11335))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11333),U_11335))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11333),U_11334))
| ~ class_Groups_Ocomm__monoid__mult(U_11332) ),
inference(clausify,[status(thm)],[f_3021_3]) ).
fof(f_3022_1,plain,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
& hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf2E]) ).
fof(f_3022_2,plain,
! [U_11342,U_11341,U_11340,U_11339,U_11338,U_11337] :
( ( hBOOL(hAPP(hAPP(U_11340,U_11341),U_11342))
& hBOOL(hAPP(hAPP(U_11339,U_11341),U_11342)) )
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11337,tc_fun(U_11338,tc_HOL_Obool))),U_11339),U_11340),U_11341),U_11342)) ),
inference(variable_rename,[status(thm)],[f_3022_1]) ).
fof(f_3022_3,plain,
! [U_11342,U_11341,U_11340,U_11339] :
( ! [U_11338,U_11337] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11337,tc_fun(U_11338,tc_HOL_Obool))),U_11339),U_11340),U_11341),U_11342))
| ( hBOOL(hAPP(hAPP(U_11340,U_11341),U_11342))
& hBOOL(hAPP(hAPP(U_11339,U_11341),U_11342)) ) ),
inference(miniscope,[status(thm)],[f_3022_2]) ).
cnf(f_3022_4,plain,
( hBOOL(hAPP(hAPP(U_11339,U_11341),U_11342))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11337,tc_fun(U_11338,tc_HOL_Obool))),U_11339),U_11340),U_11341),U_11342)) ),
inference(clausify,[status(thm)],[f_3022_3]) ).
cnf(f_3022_5,plain,
( hBOOL(hAPP(hAPP(U_11340,U_11341),U_11342))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11337,tc_fun(U_11338,tc_HOL_Obool))),U_11339),U_11340),U_11341),U_11342)) ),
inference(clausify,[status(thm)],[f_3022_3]) ).
fof(f_3023_1,plain,
! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf2I]) ).
fof(f_3023_2,plain,
! [U_11348,U_11347,U_11346,U_11345,U_11344,U_11343] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11347,tc_fun(U_11348,tc_HOL_Obool))),U_11343),U_11346),U_11344),U_11345))
| ~ hBOOL(hAPP(hAPP(U_11346,U_11344),U_11345))
| ~ hBOOL(hAPP(hAPP(U_11343,U_11344),U_11345)) ),
inference(variable_rename,[status(thm)],[f_3023_1]) ).
cnf(f_3023_3,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11347,tc_fun(U_11348,tc_HOL_Obool))),U_11343),U_11346),U_11344),U_11345))
| ~ hBOOL(hAPP(hAPP(U_11346,U_11344),U_11345))
| ~ hBOOL(hAPP(hAPP(U_11343,U_11344),U_11345)) ),
inference(clausify,[status(thm)],[f_3023_2]) ).
fof(f_3024_1,plain,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf2D2]) ).
fof(f_3024_2,plain,
! [U_11354,U_11353,U_11352,U_11351,U_11350,U_11349] :
( hBOOL(hAPP(hAPP(U_11352,U_11353),U_11354))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11349,tc_fun(U_11350,tc_HOL_Obool))),U_11351),U_11352),U_11353),U_11354)) ),
inference(variable_rename,[status(thm)],[f_3024_1]) ).
fof(f_3024_3,plain,
! [U_11354,U_11353,U_11352] :
( ! [U_11351,U_11350,U_11349] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11349,tc_fun(U_11350,tc_HOL_Obool))),U_11351),U_11352),U_11353),U_11354))
| hBOOL(hAPP(hAPP(U_11352,U_11353),U_11354)) ),
inference(miniscope,[status(thm)],[f_3024_2]) ).
cnf(f_3024_4,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11349,tc_fun(U_11350,tc_HOL_Obool))),U_11351),U_11352),U_11353),U_11354))
| hBOOL(hAPP(hAPP(U_11352,U_11353),U_11354)) ),
inference(clausify,[status(thm)],[f_3024_3]) ).
fof(f_3025_1,plain,
! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_inf2D1]) ).
fof(f_3025_2,plain,
! [U_11360,U_11359,U_11358,U_11357,U_11356,U_11355] :
( hBOOL(hAPP(hAPP(U_11357,U_11359),U_11360))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11355,tc_fun(U_11356,tc_HOL_Obool))),U_11357),U_11358),U_11359),U_11360)) ),
inference(variable_rename,[status(thm)],[f_3025_1]) ).
fof(f_3025_3,plain,
! [U_11360,U_11359,U_11358,U_11357] :
( ! [U_11356,U_11355] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11355,tc_fun(U_11356,tc_HOL_Obool))),U_11357),U_11358),U_11359),U_11360))
| hBOOL(hAPP(hAPP(U_11357,U_11359),U_11360)) ),
inference(miniscope,[status(thm)],[f_3025_2]) ).
cnf(f_3025_4,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11355,tc_fun(U_11356,tc_HOL_Obool))),U_11357),U_11358),U_11359),U_11360))
| hBOOL(hAPP(hAPP(U_11357,U_11359),U_11360)) ),
inference(clausify,[status(thm)],[f_3025_3]) ).
fof(f_3026_1,plain,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2))
| ? [B_x] :
( hAPP(V_g_2,B_x) != c_Groups_Oone__class_Oone(T_c)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__inter__neutral]) ).
fof(f_3026_2,plain,
! [U_11366,U_11365,U_11364,U_11363,U_11362] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11363,U_11362),U_11366),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11363,tc_HOL_Obool)),U_11364),U_11365)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11362),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11363,U_11362),U_11366),U_11364)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11363,U_11362),U_11366),U_11365))
| ? [U_11361] :
( hAPP(U_11366,U_11361) != c_Groups_Oone__class_Oone(U_11362)
& hBOOL(hAPP(hAPP(c_member(U_11363),U_11361),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11363,tc_HOL_Obool)),U_11364),U_11365))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11363),U_11365))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11363),U_11364))
| ~ class_Groups_Ocomm__monoid__mult(U_11362) ),
inference(variable_rename,[status(thm)],[f_3026_1]) ).
fof(f_3026_3,plain,
! [U_11366,U_11365,U_11364,U_11363,U_11362] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11363,U_11362),U_11366),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11363,tc_HOL_Obool)),U_11364),U_11365)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11362),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11363,U_11362),U_11366),U_11364)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11363,U_11362),U_11366),U_11365))
| ( hAPP(U_11366,sK243(U_11366,U_11365,U_11364,U_11363,U_11362)) != c_Groups_Oone__class_Oone(U_11362)
& hBOOL(hAPP(hAPP(c_member(U_11363),sK243(U_11366,U_11365,U_11364,U_11363,U_11362)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11363,tc_HOL_Obool)),U_11364),U_11365))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11363),U_11365))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11363),U_11364))
| ~ class_Groups_Ocomm__monoid__mult(U_11362) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK243]),skolemize(U_11361,sK243(U_11366,U_11365,U_11364,U_11363,U_11362))],[f_3026_2]) ).
cnf(f_3026_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11363),sK243(U_11366,U_11365,U_11364,U_11363,U_11362)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11363,tc_HOL_Obool)),U_11364),U_11365)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11363,U_11362),U_11366),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11363,tc_HOL_Obool)),U_11364),U_11365)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11362),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11363,U_11362),U_11366),U_11364)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11363,U_11362),U_11366),U_11365))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11363),U_11365))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11363),U_11364))
| ~ class_Groups_Ocomm__monoid__mult(U_11362) ),
inference(clausify,[status(thm)],[f_3026_3]) ).
cnf(f_3026_5,plain,
( hAPP(U_11366,sK243(U_11366,U_11365,U_11364,U_11363,U_11362)) != c_Groups_Oone__class_Oone(U_11362)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11363,U_11362),U_11366),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11363,tc_HOL_Obool)),U_11364),U_11365)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11362),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11363,U_11362),U_11366),U_11364)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11363,U_11362),U_11366),U_11365))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11363),U_11365))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11363),U_11364))
| ~ class_Groups_Ocomm__monoid__mult(U_11362) ),
inference(clausify,[status(thm)],[f_3026_3]) ).
fof(f_3027_1,plain,
! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2))
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__Un__zero]) ).
fof(f_3027_2,plain,
! [U_11372,U_11371,U_11370,U_11369,U_11368] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11369,U_11368),U_11372),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11369,tc_HOL_Obool)),U_11370),U_11371)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11368),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11369,U_11368),U_11372),U_11370)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11369,U_11368),U_11372),U_11371))
| ? [U_11367] :
( hAPP(U_11372,U_11367) != c_Groups_Ozero__class_Ozero(U_11368)
& hBOOL(hAPP(hAPP(c_member(U_11369),U_11367),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11369,tc_HOL_Obool)),U_11370),U_11371))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11369),U_11371))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11369),U_11370))
| ~ class_Groups_Ocomm__monoid__add(U_11368) ),
inference(variable_rename,[status(thm)],[f_3027_1]) ).
fof(f_3027_3,plain,
! [U_11372,U_11371,U_11370,U_11369,U_11368] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11369,U_11368),U_11372),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11369,tc_HOL_Obool)),U_11370),U_11371)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11368),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11369,U_11368),U_11372),U_11370)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11369,U_11368),U_11372),U_11371))
| ( hAPP(U_11372,sK244(U_11372,U_11371,U_11370,U_11369,U_11368)) != c_Groups_Ozero__class_Ozero(U_11368)
& hBOOL(hAPP(hAPP(c_member(U_11369),sK244(U_11372,U_11371,U_11370,U_11369,U_11368)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11369,tc_HOL_Obool)),U_11370),U_11371))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11369),U_11371))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11369),U_11370))
| ~ class_Groups_Ocomm__monoid__add(U_11368) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK244]),skolemize(U_11367,sK244(U_11372,U_11371,U_11370,U_11369,U_11368))],[f_3027_2]) ).
cnf(f_3027_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11369),sK244(U_11372,U_11371,U_11370,U_11369,U_11368)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11369,tc_HOL_Obool)),U_11370),U_11371)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11369,U_11368),U_11372),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11369,tc_HOL_Obool)),U_11370),U_11371)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11368),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11369,U_11368),U_11372),U_11370)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11369,U_11368),U_11372),U_11371))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11369),U_11371))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11369),U_11370))
| ~ class_Groups_Ocomm__monoid__add(U_11368) ),
inference(clausify,[status(thm)],[f_3027_3]) ).
cnf(f_3027_5,plain,
( hAPP(U_11372,sK244(U_11372,U_11371,U_11370,U_11369,U_11368)) != c_Groups_Ozero__class_Ozero(U_11368)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11369,U_11368),U_11372),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11369,tc_HOL_Obool)),U_11370),U_11371)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11368),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11369,U_11368),U_11372),U_11370)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11369,U_11368),U_11372),U_11371))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11369),U_11371))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11369),U_11370))
| ~ class_Groups_Ocomm__monoid__add(U_11368) ),
inference(clausify,[status(thm)],[f_3027_3]) ).
fof(f_3028_1,plain,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2))
| ? [B_x] :
( hAPP(V_g_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Ounion__inter__neutral]) ).
fof(f_3028_2,plain,
! [U_11378,U_11377,U_11376,U_11375,U_11374] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11375,U_11374),U_11378),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11375,tc_HOL_Obool)),U_11376),U_11377)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11374),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11375,U_11374),U_11378),U_11376)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11375,U_11374),U_11378),U_11377))
| ? [U_11373] :
( hAPP(U_11378,U_11373) != c_Groups_Ozero__class_Ozero(U_11374)
& hBOOL(hAPP(hAPP(c_member(U_11375),U_11373),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11375,tc_HOL_Obool)),U_11376),U_11377))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11375),U_11377))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11375),U_11376))
| ~ class_Groups_Ocomm__monoid__add(U_11374) ),
inference(variable_rename,[status(thm)],[f_3028_1]) ).
fof(f_3028_3,plain,
! [U_11378,U_11377,U_11376,U_11375,U_11374] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11375,U_11374),U_11378),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11375,tc_HOL_Obool)),U_11376),U_11377)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11374),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11375,U_11374),U_11378),U_11376)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11375,U_11374),U_11378),U_11377))
| ( hAPP(U_11378,sK245(U_11378,U_11377,U_11376,U_11375,U_11374)) != c_Groups_Ozero__class_Ozero(U_11374)
& hBOOL(hAPP(hAPP(c_member(U_11375),sK245(U_11378,U_11377,U_11376,U_11375,U_11374)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11375,tc_HOL_Obool)),U_11376),U_11377))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11375),U_11377))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11375),U_11376))
| ~ class_Groups_Ocomm__monoid__add(U_11374) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK245]),skolemize(U_11373,sK245(U_11378,U_11377,U_11376,U_11375,U_11374))],[f_3028_2]) ).
cnf(f_3028_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11375),sK245(U_11378,U_11377,U_11376,U_11375,U_11374)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11375,tc_HOL_Obool)),U_11376),U_11377)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11375,U_11374),U_11378),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11375,tc_HOL_Obool)),U_11376),U_11377)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11374),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11375,U_11374),U_11378),U_11376)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11375,U_11374),U_11378),U_11377))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11375),U_11377))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11375),U_11376))
| ~ class_Groups_Ocomm__monoid__add(U_11374) ),
inference(clausify,[status(thm)],[f_3028_3]) ).
cnf(f_3028_5,plain,
( hAPP(U_11378,sK245(U_11378,U_11377,U_11376,U_11375,U_11374)) != c_Groups_Ozero__class_Ozero(U_11374)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11375,U_11374),U_11378),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11375,tc_HOL_Obool)),U_11376),U_11377)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_11374),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11375,U_11374),U_11378),U_11376)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11375,U_11374),U_11378),U_11377))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11375),U_11377))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11375),U_11376))
| ~ class_Groups_Ocomm__monoid__add(U_11374) ),
inference(clausify,[status(thm)],[f_3028_3]) ).
fof(f_3029_1,plain,
! [V_r_2,V_A_2,T_b] :
( ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),B_x))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) ) )
& ( ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
& ! [B_x] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),B_x))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2)) ) )
| ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_refl__on__def_H]) ).
fof(f_3029_2,plain,
! [U_11385,U_11384,U_11383] :
( ( c_Relation_Orefl__on(U_11383,U_11384,U_11385)
| ? [U_11382] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11383,U_11383)),hAPP(hAPP(c_Product__Type_OPair(U_11383,U_11383),U_11382),U_11382)),U_11385))
& hBOOL(hAPP(hAPP(c_member(U_11383),U_11382),U_11384)) )
| ? [U_11381] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11383,U_11383,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11383,tc_fun(U_11383,tc_HOL_Obool),tc_fun(U_11383,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11383,tc_HOL_Obool),tc_fun(U_11383,tc_HOL_Obool)),U_11383),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11383)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11383),c_fconj),hAPP(hAPP(c_COMBC(U_11383,tc_fun(U_11383,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11383)),U_11384)))),hAPP(hAPP(c_COMBC(U_11383,tc_fun(U_11383,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11383)),U_11384))),U_11381))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_11383,U_11383)),U_11381),U_11385)) ) )
& ( ( ! [U_11380] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11383,U_11383)),hAPP(hAPP(c_Product__Type_OPair(U_11383,U_11383),U_11380),U_11380)),U_11385))
| ~ hBOOL(hAPP(hAPP(c_member(U_11383),U_11380),U_11384)) )
& ! [U_11379] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11383,U_11383,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11383,tc_fun(U_11383,tc_HOL_Obool),tc_fun(U_11383,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11383,tc_HOL_Obool),tc_fun(U_11383,tc_HOL_Obool)),U_11383),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11383)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11383),c_fconj),hAPP(hAPP(c_COMBC(U_11383,tc_fun(U_11383,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11383)),U_11384)))),hAPP(hAPP(c_COMBC(U_11383,tc_fun(U_11383,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11383)),U_11384))),U_11379))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11383,U_11383)),U_11379),U_11385)) ) )
| ~ c_Relation_Orefl__on(U_11383,U_11384,U_11385) ) ),
inference(variable_rename,[status(thm)],[f_3029_1]) ).
fof(f_3029_3,plain,
( ! [U_11391,U_11389,U_11387] :
( c_Relation_Orefl__on(U_11387,U_11389,U_11391)
| ? [U_11382] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11387,U_11387)),hAPP(hAPP(c_Product__Type_OPair(U_11387,U_11387),U_11382),U_11382)),U_11391))
& hBOOL(hAPP(hAPP(c_member(U_11387),U_11382),U_11389)) )
| ? [U_11381] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11387,U_11387,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11387,tc_fun(U_11387,tc_HOL_Obool),tc_fun(U_11387,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11387,tc_HOL_Obool),tc_fun(U_11387,tc_HOL_Obool)),U_11387),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11387)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11387),c_fconj),hAPP(hAPP(c_COMBC(U_11387,tc_fun(U_11387,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11387)),U_11389)))),hAPP(hAPP(c_COMBC(U_11387,tc_fun(U_11387,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11387)),U_11389))),U_11381))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_11387,U_11387)),U_11381),U_11391)) ) )
& ! [U_11390,U_11388,U_11386] :
( ( ! [U_11380] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11386,U_11386)),hAPP(hAPP(c_Product__Type_OPair(U_11386,U_11386),U_11380),U_11380)),U_11390))
| ~ hBOOL(hAPP(hAPP(c_member(U_11386),U_11380),U_11388)) )
& ! [U_11379] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11386,U_11386,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11386,tc_fun(U_11386,tc_HOL_Obool),tc_fun(U_11386,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11386,tc_HOL_Obool),tc_fun(U_11386,tc_HOL_Obool)),U_11386),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11386)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11386),c_fconj),hAPP(hAPP(c_COMBC(U_11386,tc_fun(U_11386,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11386)),U_11388)))),hAPP(hAPP(c_COMBC(U_11386,tc_fun(U_11386,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11386)),U_11388))),U_11379))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11386,U_11386)),U_11379),U_11390)) ) )
| ~ c_Relation_Orefl__on(U_11386,U_11388,U_11390) ) ),
inference(miniscope,[status(thm)],[f_3029_2]) ).
fof(f_3029_4,plain,
( ! [U_11391,U_11389,U_11387] :
( c_Relation_Orefl__on(U_11387,U_11389,U_11391)
| ? [U_11382] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11387,U_11387)),hAPP(hAPP(c_Product__Type_OPair(U_11387,U_11387),U_11382),U_11382)),U_11391))
& hBOOL(hAPP(hAPP(c_member(U_11387),U_11382),U_11389)) )
| ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11387,U_11387,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11387,tc_fun(U_11387,tc_HOL_Obool),tc_fun(U_11387,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11387,tc_HOL_Obool),tc_fun(U_11387,tc_HOL_Obool)),U_11387),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11387)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11387),c_fconj),hAPP(hAPP(c_COMBC(U_11387,tc_fun(U_11387,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11387)),U_11389)))),hAPP(hAPP(c_COMBC(U_11387,tc_fun(U_11387,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11387)),U_11389))),sK246(U_11391,U_11389,U_11387)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_11387,U_11387)),sK246(U_11391,U_11389,U_11387)),U_11391)) ) )
& ! [U_11390,U_11388,U_11386] :
( ( ! [U_11380] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11386,U_11386)),hAPP(hAPP(c_Product__Type_OPair(U_11386,U_11386),U_11380),U_11380)),U_11390))
| ~ hBOOL(hAPP(hAPP(c_member(U_11386),U_11380),U_11388)) )
& ! [U_11379] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11386,U_11386,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11386,tc_fun(U_11386,tc_HOL_Obool),tc_fun(U_11386,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11386,tc_HOL_Obool),tc_fun(U_11386,tc_HOL_Obool)),U_11386),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11386)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11386),c_fconj),hAPP(hAPP(c_COMBC(U_11386,tc_fun(U_11386,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11386)),U_11388)))),hAPP(hAPP(c_COMBC(U_11386,tc_fun(U_11386,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11386)),U_11388))),U_11379))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11386,U_11386)),U_11379),U_11390)) ) )
| ~ c_Relation_Orefl__on(U_11386,U_11388,U_11390) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK246]),skolemize(U_11381,sK246(U_11391,U_11389,U_11387))],[f_3029_3]) ).
fof(f_3029_5,plain,
( ! [U_11391,U_11389,U_11387] :
( c_Relation_Orefl__on(U_11387,U_11389,U_11391)
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11387,U_11387)),hAPP(hAPP(c_Product__Type_OPair(U_11387,U_11387),sK247(U_11391,U_11389,U_11387)),sK247(U_11391,U_11389,U_11387))),U_11391))
& hBOOL(hAPP(hAPP(c_member(U_11387),sK247(U_11391,U_11389,U_11387)),U_11389)) )
| ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11387,U_11387,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11387,tc_fun(U_11387,tc_HOL_Obool),tc_fun(U_11387,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11387,tc_HOL_Obool),tc_fun(U_11387,tc_HOL_Obool)),U_11387),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11387)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11387),c_fconj),hAPP(hAPP(c_COMBC(U_11387,tc_fun(U_11387,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11387)),U_11389)))),hAPP(hAPP(c_COMBC(U_11387,tc_fun(U_11387,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11387)),U_11389))),sK246(U_11391,U_11389,U_11387)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_11387,U_11387)),sK246(U_11391,U_11389,U_11387)),U_11391)) ) )
& ! [U_11390,U_11388,U_11386] :
( ( ! [U_11380] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11386,U_11386)),hAPP(hAPP(c_Product__Type_OPair(U_11386,U_11386),U_11380),U_11380)),U_11390))
| ~ hBOOL(hAPP(hAPP(c_member(U_11386),U_11380),U_11388)) )
& ! [U_11379] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11386,U_11386,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11386,tc_fun(U_11386,tc_HOL_Obool),tc_fun(U_11386,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11386,tc_HOL_Obool),tc_fun(U_11386,tc_HOL_Obool)),U_11386),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11386)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11386),c_fconj),hAPP(hAPP(c_COMBC(U_11386,tc_fun(U_11386,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11386)),U_11388)))),hAPP(hAPP(c_COMBC(U_11386,tc_fun(U_11386,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11386)),U_11388))),U_11379))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11386,U_11386)),U_11379),U_11390)) ) )
| ~ c_Relation_Orefl__on(U_11386,U_11388,U_11390) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK247]),skolemize(U_11382,sK247(U_11391,U_11389,U_11387))],[f_3029_4]) ).
cnf(f_3029_6,plain,
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11386,U_11386,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11386,tc_fun(U_11386,tc_HOL_Obool),tc_fun(U_11386,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11386,tc_HOL_Obool),tc_fun(U_11386,tc_HOL_Obool)),U_11386),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11386)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11386),c_fconj),hAPP(hAPP(c_COMBC(U_11386,tc_fun(U_11386,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11386)),U_11388)))),hAPP(hAPP(c_COMBC(U_11386,tc_fun(U_11386,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11386)),U_11388))),U_11379))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11386,U_11386)),U_11379),U_11390))
| ~ c_Relation_Orefl__on(U_11386,U_11388,U_11390) ),
inference(clausify,[status(thm)],[f_3029_5]) ).
cnf(f_3029_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11386,U_11386)),hAPP(hAPP(c_Product__Type_OPair(U_11386,U_11386),U_11380),U_11380)),U_11390))
| ~ hBOOL(hAPP(hAPP(c_member(U_11386),U_11380),U_11388))
| ~ c_Relation_Orefl__on(U_11386,U_11388,U_11390) ),
inference(clausify,[status(thm)],[f_3029_5]) ).
cnf(f_3029_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_11387),sK247(U_11391,U_11389,U_11387)),U_11389))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_11387,U_11387)),sK246(U_11391,U_11389,U_11387)),U_11391))
| c_Relation_Orefl__on(U_11387,U_11389,U_11391) ),
inference(clausify,[status(thm)],[f_3029_5]) ).
cnf(f_3029_9,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11387,U_11387)),hAPP(hAPP(c_Product__Type_OPair(U_11387,U_11387),sK247(U_11391,U_11389,U_11387)),sK247(U_11391,U_11389,U_11387))),U_11391))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_11387,U_11387)),sK246(U_11391,U_11389,U_11387)),U_11391))
| c_Relation_Orefl__on(U_11387,U_11389,U_11391) ),
inference(clausify,[status(thm)],[f_3029_5]) ).
cnf(f_3029_10,plain,
( hBOOL(hAPP(hAPP(c_member(U_11387),sK247(U_11391,U_11389,U_11387)),U_11389))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11387,U_11387,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11387,tc_fun(U_11387,tc_HOL_Obool),tc_fun(U_11387,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11387,tc_HOL_Obool),tc_fun(U_11387,tc_HOL_Obool)),U_11387),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11387)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11387),c_fconj),hAPP(hAPP(c_COMBC(U_11387,tc_fun(U_11387,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11387)),U_11389)))),hAPP(hAPP(c_COMBC(U_11387,tc_fun(U_11387,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11387)),U_11389))),sK246(U_11391,U_11389,U_11387)))
| c_Relation_Orefl__on(U_11387,U_11389,U_11391) ),
inference(clausify,[status(thm)],[f_3029_5]) ).
cnf(f_3029_11,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11387,U_11387)),hAPP(hAPP(c_Product__Type_OPair(U_11387,U_11387),sK247(U_11391,U_11389,U_11387)),sK247(U_11391,U_11389,U_11387))),U_11391))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_11387,U_11387,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11387,tc_fun(U_11387,tc_HOL_Obool),tc_fun(U_11387,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11387,tc_HOL_Obool),tc_fun(U_11387,tc_HOL_Obool)),U_11387),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11387)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11387),c_fconj),hAPP(hAPP(c_COMBC(U_11387,tc_fun(U_11387,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11387)),U_11389)))),hAPP(hAPP(c_COMBC(U_11387,tc_fun(U_11387,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11387)),U_11389))),sK246(U_11391,U_11389,U_11387)))
| c_Relation_Orefl__on(U_11387,U_11389,U_11391) ),
inference(clausify,[status(thm)],[f_3029_5]) ).
fof(f_3030_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oremove]) ).
fof(f_3030_2,plain,
! [U_11394,U_11393,U_11392] :
( ( ( c_Big__Operators_Olattice__class_OInf__fin(U_11392,U_11393) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11392),U_11394),c_Big__Operators_Olattice__class_OInf__fin(U_11392,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11392,tc_HOL_Obool)),U_11393),hAPP(hAPP(c_Set_Oinsert(U_11392),U_11394),c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11392,tc_HOL_Obool)),U_11393),hAPP(hAPP(c_Set_Oinsert(U_11392),U_11394),c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OInf__fin(U_11392,U_11393) = U_11394
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11392,tc_HOL_Obool)),U_11393),hAPP(hAPP(c_Set_Oinsert(U_11392),U_11394),c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_11392),U_11394),U_11393))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11392),U_11393))
| ~ class_Lattices_Olattice(U_11392) ),
inference(variable_rename,[status(thm)],[f_3030_1]) ).
cnf(f_3030_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_11392,U_11393) = U_11394
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11392,tc_HOL_Obool)),U_11393),hAPP(hAPP(c_Set_Oinsert(U_11392),U_11394),c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_11392),U_11394),U_11393))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11392),U_11393))
| ~ class_Lattices_Olattice(U_11392) ),
inference(clausify,[status(thm)],[f_3030_2]) ).
cnf(f_3030_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_11392,U_11393) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11392),U_11394),c_Big__Operators_Olattice__class_OInf__fin(U_11392,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11392,tc_HOL_Obool)),U_11393),hAPP(hAPP(c_Set_Oinsert(U_11392),U_11394),c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11392,tc_HOL_Obool)),U_11393),hAPP(hAPP(c_Set_Oinsert(U_11392),U_11394),c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_11392,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_11392),U_11394),U_11393))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11392),U_11393))
| ~ class_Lattices_Olattice(U_11392) ),
inference(clausify,[status(thm)],[f_3030_2]) ).
fof(f_3031_1,plain,
! [V_k_2,V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_b),B_x)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) )
| ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_equiv__imp__dvd__card]) ).
fof(f_3031_2,plain,
! [U_11399,U_11398,U_11397,U_11396] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_11399),hAPP(c_Finite__Set_Ocard(U_11396),U_11397)))
| ? [U_11395] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_11399),hAPP(c_Finite__Set_Ocard(U_11396),U_11395)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_11396,tc_HOL_Obool)),U_11395),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11396),U_11397),U_11398))) )
| ~ c_Equiv__Relations_Oequiv(U_11396,U_11397,U_11398)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11396),U_11397)) ),
inference(variable_rename,[status(thm)],[f_3031_1]) ).
fof(f_3031_3,plain,
! [U_11399,U_11398,U_11397,U_11396] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_11399),hAPP(c_Finite__Set_Ocard(U_11396),U_11397)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_11399),hAPP(c_Finite__Set_Ocard(U_11396),sK248(U_11399,U_11398,U_11397,U_11396))))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_11396,tc_HOL_Obool)),sK248(U_11399,U_11398,U_11397,U_11396)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11396),U_11397),U_11398))) )
| ~ c_Equiv__Relations_Oequiv(U_11396,U_11397,U_11398)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11396),U_11397)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK248]),skolemize(U_11395,sK248(U_11399,U_11398,U_11397,U_11396))],[f_3031_2]) ).
cnf(f_3031_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11396,tc_HOL_Obool)),sK248(U_11399,U_11398,U_11397,U_11396)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11396),U_11397),U_11398)))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_11399),hAPP(c_Finite__Set_Ocard(U_11396),U_11397)))
| ~ c_Equiv__Relations_Oequiv(U_11396,U_11397,U_11398)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11396),U_11397)) ),
inference(clausify,[status(thm)],[f_3031_3]) ).
cnf(f_3031_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_11399),hAPP(c_Finite__Set_Ocard(U_11396),sK248(U_11399,U_11398,U_11397,U_11396))))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_11399),hAPP(c_Finite__Set_Ocard(U_11396),U_11397)))
| ~ c_Equiv__Relations_Oequiv(U_11396,U_11397,U_11398)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11396),U_11397)) ),
inference(clausify,[status(thm)],[f_3031_3]) ).
fof(f_3032_1,plain,
! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)),
inference(fof_nnf,[status(thm)],[fact_refl__on__Id__on]) ).
fof(f_3032_2,plain,
! [U_11401,U_11400] : c_Relation_Orefl__on(U_11400,U_11401,c_Relation_OId__on(U_11400,U_11401)),
inference(variable_rename,[status(thm)],[f_3032_1]) ).
cnf(f_3032_3,plain,
c_Relation_Orefl__on(U_11400,U_11401,c_Relation_OId__on(U_11400,U_11401)),
inference(clausify,[status(thm)],[f_3032_2]) ).
fof(f_3033_1,plain,
! [V_x_2,T_b] :
( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osingleton]) ).
fof(f_3033_2,plain,
! [U_11403,U_11402] :
( c_Big__Operators_Olattice__class_OInf__fin(U_11402,hAPP(hAPP(c_Set_Oinsert(U_11402),U_11403),c_Orderings_Obot__class_Obot(tc_fun(U_11402,tc_HOL_Obool)))) = U_11403
| ~ class_Lattices_Olattice(U_11402) ),
inference(variable_rename,[status(thm)],[f_3033_1]) ).
cnf(f_3033_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_11402,hAPP(hAPP(c_Set_Oinsert(U_11402),U_11403),c_Orderings_Obot__class_Obot(tc_fun(U_11402,tc_HOL_Obool)))) = U_11403
| ~ class_Lattices_Olattice(U_11402) ),
inference(clausify,[status(thm)],[f_3033_2]) ).
fof(f_3034_1,plain,
! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_refl__on__empty]) ).
fof(f_3034_2,plain,
! [U_11404] : c_Relation_Orefl__on(U_11404,c_Orderings_Obot__class_Obot(tc_fun(U_11404,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11404,U_11404),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_3034_1]) ).
cnf(f_3034_3,plain,
c_Relation_Orefl__on(U_11404,c_Orderings_Obot__class_Obot(tc_fun(U_11404,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_11404,U_11404),tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_3034_2]) ).
fof(f_3035_1,plain,
! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
| ~ c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
| ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_refl__on__Un]) ).
fof(f_3035_2,plain,
! [U_11409,U_11408,U_11407,U_11406,U_11405] :
( c_Relation_Orefl__on(U_11405,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11405,tc_HOL_Obool)),U_11406),U_11408),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11405,U_11405),tc_HOL_Obool)),U_11407),U_11409))
| ~ c_Relation_Orefl__on(U_11405,U_11408,U_11409)
| ~ c_Relation_Orefl__on(U_11405,U_11406,U_11407) ),
inference(variable_rename,[status(thm)],[f_3035_1]) ).
cnf(f_3035_3,plain,
( c_Relation_Orefl__on(U_11405,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11405,tc_HOL_Obool)),U_11406),U_11408),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11405,U_11405),tc_HOL_Obool)),U_11407),U_11409))
| ~ c_Relation_Orefl__on(U_11405,U_11408,U_11409)
| ~ c_Relation_Orefl__on(U_11405,U_11406,U_11407) ),
inference(clausify,[status(thm)],[f_3035_2]) ).
fof(f_3036_1,plain,
! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
( c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
| ~ c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
| ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_refl__on__Int]) ).
fof(f_3036_2,plain,
! [U_11414,U_11413,U_11412,U_11411,U_11410] :
( c_Relation_Orefl__on(U_11410,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11410,tc_HOL_Obool)),U_11411),U_11413),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11410,U_11410),tc_HOL_Obool)),U_11412),U_11414))
| ~ c_Relation_Orefl__on(U_11410,U_11413,U_11414)
| ~ c_Relation_Orefl__on(U_11410,U_11411,U_11412) ),
inference(variable_rename,[status(thm)],[f_3036_1]) ).
cnf(f_3036_3,plain,
( c_Relation_Orefl__on(U_11410,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11410,tc_HOL_Obool)),U_11411),U_11413),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11410,U_11410),tc_HOL_Obool)),U_11412),U_11414))
| ~ c_Relation_Orefl__on(U_11410,U_11413,U_11414)
| ~ c_Relation_Orefl__on(U_11410,U_11411,U_11412) ),
inference(clausify,[status(thm)],[f_3036_2]) ).
fof(f_3037_1,plain,
! [V_a_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = V_a_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sup__Inf__absorb]) ).
fof(f_3037_2,plain,
! [U_11417,U_11416,U_11415] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11415),U_11417),c_Big__Operators_Olattice__class_OInf__fin(U_11415,U_11416)) = U_11417
| ~ hBOOL(hAPP(hAPP(c_member(U_11415),U_11417),U_11416))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11415),U_11416))
| ~ class_Lattices_Olattice(U_11415) ),
inference(variable_rename,[status(thm)],[f_3037_1]) ).
cnf(f_3037_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11415),U_11417),c_Big__Operators_Olattice__class_OInf__fin(U_11415,U_11416)) = U_11417
| ~ hBOOL(hAPP(hAPP(c_member(U_11415),U_11417),U_11416))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11415),U_11416))
| ~ class_Lattices_Olattice(U_11415) ),
inference(clausify,[status(thm)],[f_3037_2]) ).
fof(f_3038_1,plain,
! [V_x_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oin__idem]) ).
fof(f_3038_2,plain,
! [U_11420,U_11419,U_11418] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11418),U_11420),c_Big__Operators_Olattice__class_OInf__fin(U_11418,U_11419)) = c_Big__Operators_Olattice__class_OInf__fin(U_11418,U_11419)
| ~ hBOOL(hAPP(hAPP(c_member(U_11418),U_11420),U_11419))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11418),U_11419))
| ~ class_Lattices_Olattice(U_11418) ),
inference(variable_rename,[status(thm)],[f_3038_1]) ).
cnf(f_3038_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11418),U_11420),c_Big__Operators_Olattice__class_OInf__fin(U_11418,U_11419)) = c_Big__Operators_Olattice__class_OInf__fin(U_11418,U_11419)
| ~ hBOOL(hAPP(hAPP(c_member(U_11418),U_11420),U_11419))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11418),U_11419))
| ~ class_Lattices_Olattice(U_11418) ),
inference(clausify,[status(thm)],[f_3038_2]) ).
fof(f_3039_1,plain,
! [V_a_2,V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_refl__onD]) ).
fof(f_3039_2,plain,
! [U_11424,U_11423,U_11422,U_11421] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11421,U_11421)),hAPP(hAPP(c_Product__Type_OPair(U_11421,U_11421),U_11424),U_11424)),U_11423))
| ~ hBOOL(hAPP(hAPP(c_member(U_11421),U_11424),U_11422))
| ~ c_Relation_Orefl__on(U_11421,U_11422,U_11423) ),
inference(variable_rename,[status(thm)],[f_3039_1]) ).
cnf(f_3039_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11421,U_11421)),hAPP(hAPP(c_Product__Type_OPair(U_11421,U_11421),U_11424),U_11424)),U_11423))
| ~ hBOOL(hAPP(hAPP(c_member(U_11421),U_11424),U_11422))
| ~ c_Relation_Orefl__on(U_11421,U_11422,U_11423) ),
inference(clausify,[status(thm)],[f_3039_2]) ).
fof(f_3040_1,plain,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
| ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_refl__onD1]) ).
fof(f_3040_2,plain,
! [U_11429,U_11428,U_11427,U_11426,U_11425] :
( hBOOL(hAPP(hAPP(c_member(U_11425),U_11428),U_11426))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11425,U_11425)),hAPP(hAPP(c_Product__Type_OPair(U_11425,U_11425),U_11428),U_11429)),U_11427))
| ~ c_Relation_Orefl__on(U_11425,U_11426,U_11427) ),
inference(variable_rename,[status(thm)],[f_3040_1]) ).
cnf(f_3040_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_11425),U_11428),U_11426))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11425,U_11425)),hAPP(hAPP(c_Product__Type_OPair(U_11425,U_11425),U_11428),U_11429)),U_11427))
| ~ c_Relation_Orefl__on(U_11425,U_11426,U_11427) ),
inference(clausify,[status(thm)],[f_3040_2]) ).
fof(f_3041_1,plain,
! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
| ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_refl__onD2]) ).
fof(f_3041_2,plain,
! [U_11434,U_11433,U_11432,U_11431,U_11430] :
( hBOOL(hAPP(hAPP(c_member(U_11430),U_11434),U_11431))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11430,U_11430)),hAPP(hAPP(c_Product__Type_OPair(U_11430,U_11430),U_11433),U_11434)),U_11432))
| ~ c_Relation_Orefl__on(U_11430,U_11431,U_11432) ),
inference(variable_rename,[status(thm)],[f_3041_1]) ).
cnf(f_3041_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_11430),U_11434),U_11431))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11430,U_11430)),hAPP(hAPP(c_Product__Type_OPair(U_11430,U_11430),U_11433),U_11434)),U_11432))
| ~ c_Relation_Orefl__on(U_11430,U_11431,U_11432) ),
inference(clausify,[status(thm)],[f_3041_2]) ).
fof(f_3042_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__idem]) ).
fof(f_3042_2,plain,
! [U_11437,U_11436,U_11435] :
( c_Big__Operators_Olattice__class_OInf__fin(U_11435,hAPP(hAPP(c_Set_Oinsert(U_11435),U_11437),U_11436)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11435),U_11437),c_Big__Operators_Olattice__class_OInf__fin(U_11435,U_11436))
| U_11436 = c_Orderings_Obot__class_Obot(tc_fun(U_11435,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11435),U_11436))
| ~ class_Lattices_Olattice(U_11435) ),
inference(variable_rename,[status(thm)],[f_3042_1]) ).
cnf(f_3042_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_11435,hAPP(hAPP(c_Set_Oinsert(U_11435),U_11437),U_11436)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11435),U_11437),c_Big__Operators_Olattice__class_OInf__fin(U_11435,U_11436))
| U_11436 = c_Orderings_Obot__class_Obot(tc_fun(U_11435,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11435),U_11436))
| ~ class_Lattices_Olattice(U_11435) ),
inference(clausify,[status(thm)],[f_3042_2]) ).
fof(f_3043_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osubset__idem]) ).
fof(f_3043_2,plain,
! [U_11440,U_11439,U_11438] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11438),c_Big__Operators_Olattice__class_OInf__fin(U_11438,U_11440)),c_Big__Operators_Olattice__class_OInf__fin(U_11438,U_11439)) = c_Big__Operators_Olattice__class_OInf__fin(U_11438,U_11439)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11438,tc_HOL_Obool)),U_11440),U_11439))
| U_11440 = c_Orderings_Obot__class_Obot(tc_fun(U_11438,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11438),U_11439))
| ~ class_Lattices_Olattice(U_11438) ),
inference(variable_rename,[status(thm)],[f_3043_1]) ).
cnf(f_3043_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11438),c_Big__Operators_Olattice__class_OInf__fin(U_11438,U_11440)),c_Big__Operators_Olattice__class_OInf__fin(U_11438,U_11439)) = c_Big__Operators_Olattice__class_OInf__fin(U_11438,U_11439)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11438,tc_HOL_Obool)),U_11440),U_11439))
| U_11440 = c_Orderings_Obot__class_Obot(tc_fun(U_11438,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11438),U_11439))
| ~ class_Lattices_Olattice(U_11438) ),
inference(clausify,[status(thm)],[f_3043_2]) ).
fof(f_3044_1,plain,
! [V_B_2,V_A_2,T_b] :
( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__idem]) ).
fof(f_3044_2,plain,
! [U_11443,U_11442,U_11441] :
( c_Big__Operators_Olattice__class_OInf__fin(U_11441,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11441,tc_HOL_Obool)),U_11442),U_11443)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11441),c_Big__Operators_Olattice__class_OInf__fin(U_11441,U_11442)),c_Big__Operators_Olattice__class_OInf__fin(U_11441,U_11443))
| U_11443 = c_Orderings_Obot__class_Obot(tc_fun(U_11441,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11441),U_11443))
| U_11442 = c_Orderings_Obot__class_Obot(tc_fun(U_11441,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11441),U_11442))
| ~ class_Lattices_Olattice(U_11441) ),
inference(variable_rename,[status(thm)],[f_3044_1]) ).
cnf(f_3044_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_11441,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11441,tc_HOL_Obool)),U_11442),U_11443)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11441),c_Big__Operators_Olattice__class_OInf__fin(U_11441,U_11442)),c_Big__Operators_Olattice__class_OInf__fin(U_11441,U_11443))
| U_11443 = c_Orderings_Obot__class_Obot(tc_fun(U_11441,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11441),U_11443))
| U_11442 = c_Orderings_Obot__class_Obot(tc_fun(U_11441,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11441),U_11442))
| ~ class_Lattices_Olattice(U_11441) ),
inference(clausify,[status(thm)],[f_3044_2]) ).
fof(f_3045_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__le__Sup]) ).
fof(f_3045_2,plain,
! [U_11445,U_11444] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11444),c_Big__Operators_Olattice__class_OInf__fin(U_11444,U_11445)),c_Big__Operators_Olattice__class_OSup__fin(U_11444,U_11445)))
| U_11445 = c_Orderings_Obot__class_Obot(tc_fun(U_11444,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11444),U_11445))
| ~ class_Lattices_Olattice(U_11444) ),
inference(variable_rename,[status(thm)],[f_3045_1]) ).
cnf(f_3045_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11444),c_Big__Operators_Olattice__class_OInf__fin(U_11444,U_11445)),c_Big__Operators_Olattice__class_OSup__fin(U_11444,U_11445)))
| U_11445 = c_Orderings_Obot__class_Obot(tc_fun(U_11444,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11444),U_11445))
| ~ class_Lattices_Olattice(U_11444) ),
inference(clausify,[status(thm)],[f_3045_2]) ).
fof(f_3046_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert]) ).
fof(f_3046_2,plain,
! [U_11448,U_11447,U_11446] :
( c_Big__Operators_Olattice__class_OInf__fin(U_11446,hAPP(hAPP(c_Set_Oinsert(U_11446),U_11448),U_11447)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11446),U_11448),c_Big__Operators_Olattice__class_OInf__fin(U_11446,U_11447))
| U_11447 = c_Orderings_Obot__class_Obot(tc_fun(U_11446,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_11446),U_11448),U_11447))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11446),U_11447))
| ~ class_Lattices_Olattice(U_11446) ),
inference(variable_rename,[status(thm)],[f_3046_1]) ).
cnf(f_3046_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_11446,hAPP(hAPP(c_Set_Oinsert(U_11446),U_11448),U_11447)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11446),U_11448),c_Big__Operators_Olattice__class_OInf__fin(U_11446,U_11447))
| U_11447 = c_Orderings_Obot__class_Obot(tc_fun(U_11446,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_11446),U_11448),U_11447))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11446),U_11447))
| ~ class_Lattices_Olattice(U_11446) ),
inference(clausify,[status(thm)],[f_3046_2]) ).
fof(f_3047_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__remove]) ).
fof(f_3047_2,plain,
! [U_11451,U_11450,U_11449] :
( ( ( c_Big__Operators_Olattice__class_OInf__fin(U_11449,hAPP(hAPP(c_Set_Oinsert(U_11449),U_11451),U_11450)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11449),U_11451),c_Big__Operators_Olattice__class_OInf__fin(U_11449,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11449,tc_HOL_Obool)),U_11450),hAPP(hAPP(c_Set_Oinsert(U_11449),U_11451),c_Orderings_Obot__class_Obot(tc_fun(U_11449,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11449,tc_HOL_Obool)),U_11450),hAPP(hAPP(c_Set_Oinsert(U_11449),U_11451),c_Orderings_Obot__class_Obot(tc_fun(U_11449,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_11449,tc_HOL_Obool)) )
& ( c_Big__Operators_Olattice__class_OInf__fin(U_11449,hAPP(hAPP(c_Set_Oinsert(U_11449),U_11451),U_11450)) = U_11451
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11449,tc_HOL_Obool)),U_11450),hAPP(hAPP(c_Set_Oinsert(U_11449),U_11451),c_Orderings_Obot__class_Obot(tc_fun(U_11449,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_11449,tc_HOL_Obool)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11449),U_11450))
| ~ class_Lattices_Olattice(U_11449) ),
inference(variable_rename,[status(thm)],[f_3047_1]) ).
cnf(f_3047_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_11449,hAPP(hAPP(c_Set_Oinsert(U_11449),U_11451),U_11450)) = U_11451
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11449,tc_HOL_Obool)),U_11450),hAPP(hAPP(c_Set_Oinsert(U_11449),U_11451),c_Orderings_Obot__class_Obot(tc_fun(U_11449,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_11449,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11449),U_11450))
| ~ class_Lattices_Olattice(U_11449) ),
inference(clausify,[status(thm)],[f_3047_2]) ).
cnf(f_3047_4,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_11449,hAPP(hAPP(c_Set_Oinsert(U_11449),U_11451),U_11450)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11449),U_11451),c_Big__Operators_Olattice__class_OInf__fin(U_11449,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11449,tc_HOL_Obool)),U_11450),hAPP(hAPP(c_Set_Oinsert(U_11449),U_11451),c_Orderings_Obot__class_Obot(tc_fun(U_11449,tc_HOL_Obool))))))
| hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11449,tc_HOL_Obool)),U_11450),hAPP(hAPP(c_Set_Oinsert(U_11449),U_11451),c_Orderings_Obot__class_Obot(tc_fun(U_11449,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_11449,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11449),U_11450))
| ~ class_Lattices_Olattice(U_11449) ),
inference(clausify,[status(thm)],[f_3047_2]) ).
fof(f_3048_1,plain,
! [V_B_2,V_A_2,T_b] :
( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__disjoint]) ).
fof(f_3048_2,plain,
! [U_11454,U_11453,U_11452] :
( c_Big__Operators_Olattice__class_OInf__fin(U_11452,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11452,tc_HOL_Obool)),U_11453),U_11454)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11452),c_Big__Operators_Olattice__class_OInf__fin(U_11452,U_11453)),c_Big__Operators_Olattice__class_OInf__fin(U_11452,U_11454))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11452,tc_HOL_Obool)),U_11453),U_11454) != c_Orderings_Obot__class_Obot(tc_fun(U_11452,tc_HOL_Obool))
| U_11454 = c_Orderings_Obot__class_Obot(tc_fun(U_11452,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11452),U_11454))
| U_11453 = c_Orderings_Obot__class_Obot(tc_fun(U_11452,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11452),U_11453))
| ~ class_Lattices_Olattice(U_11452) ),
inference(variable_rename,[status(thm)],[f_3048_1]) ).
cnf(f_3048_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_11452,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11452,tc_HOL_Obool)),U_11453),U_11454)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11452),c_Big__Operators_Olattice__class_OInf__fin(U_11452,U_11453)),c_Big__Operators_Olattice__class_OInf__fin(U_11452,U_11454))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11452,tc_HOL_Obool)),U_11453),U_11454) != c_Orderings_Obot__class_Obot(tc_fun(U_11452,tc_HOL_Obool))
| U_11454 = c_Orderings_Obot__class_Obot(tc_fun(U_11452,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11452),U_11454))
| U_11453 = c_Orderings_Obot__class_Obot(tc_fun(U_11452,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11452),U_11453))
| ~ class_Lattices_Olattice(U_11452) ),
inference(clausify,[status(thm)],[f_3048_2]) ).
fof(f_3049_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__inter]) ).
fof(f_3049_2,plain,
! [U_11457,U_11456,U_11455] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11455),c_Big__Operators_Olattice__class_OInf__fin(U_11455,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11455,tc_HOL_Obool)),U_11456),U_11457))),c_Big__Operators_Olattice__class_OInf__fin(U_11455,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11455,tc_HOL_Obool)),U_11456),U_11457))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11455),c_Big__Operators_Olattice__class_OInf__fin(U_11455,U_11456)),c_Big__Operators_Olattice__class_OInf__fin(U_11455,U_11457))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11455,tc_HOL_Obool)),U_11456),U_11457) = c_Orderings_Obot__class_Obot(tc_fun(U_11455,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11455),U_11457))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11455),U_11456))
| ~ class_Lattices_Olattice(U_11455) ),
inference(variable_rename,[status(thm)],[f_3049_1]) ).
cnf(f_3049_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11455),c_Big__Operators_Olattice__class_OInf__fin(U_11455,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11455,tc_HOL_Obool)),U_11456),U_11457))),c_Big__Operators_Olattice__class_OInf__fin(U_11455,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11455,tc_HOL_Obool)),U_11456),U_11457))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11455),c_Big__Operators_Olattice__class_OInf__fin(U_11455,U_11456)),c_Big__Operators_Olattice__class_OInf__fin(U_11455,U_11457))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11455,tc_HOL_Obool)),U_11456),U_11457) = c_Orderings_Obot__class_Obot(tc_fun(U_11455,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11455),U_11457))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11455),U_11456))
| ~ class_Lattices_Olattice(U_11455) ),
inference(clausify,[status(thm)],[f_3049_2]) ).
fof(f_3050_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2))
| ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oclosed]) ).
fof(f_3050_2,plain,
! [U_11461,U_11460] :
( hBOOL(hAPP(hAPP(c_member(U_11460),c_Big__Operators_Olattice__class_OInf__fin(U_11460,U_11461)),U_11461))
| ? [U_11459,U_11458] : ~ hBOOL(hAPP(hAPP(c_member(U_11460),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11460),U_11459),U_11458)),hAPP(hAPP(c_Set_Oinsert(U_11460),U_11459),hAPP(hAPP(c_Set_Oinsert(U_11460),U_11458),c_Orderings_Obot__class_Obot(tc_fun(U_11460,tc_HOL_Obool))))))
| U_11461 = c_Orderings_Obot__class_Obot(tc_fun(U_11460,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11460),U_11461))
| ~ class_Lattices_Olattice(U_11460) ),
inference(variable_rename,[status(thm)],[f_3050_1]) ).
fof(f_3050_3,plain,
! [U_11461,U_11460] :
( hBOOL(hAPP(hAPP(c_member(U_11460),c_Big__Operators_Olattice__class_OInf__fin(U_11460,U_11461)),U_11461))
| ? [U_11458] : ~ hBOOL(hAPP(hAPP(c_member(U_11460),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11460),sK249(U_11461,U_11460)),U_11458)),hAPP(hAPP(c_Set_Oinsert(U_11460),sK249(U_11461,U_11460)),hAPP(hAPP(c_Set_Oinsert(U_11460),U_11458),c_Orderings_Obot__class_Obot(tc_fun(U_11460,tc_HOL_Obool))))))
| U_11461 = c_Orderings_Obot__class_Obot(tc_fun(U_11460,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11460),U_11461))
| ~ class_Lattices_Olattice(U_11460) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK249]),skolemize(U_11459,sK249(U_11461,U_11460))],[f_3050_2]) ).
fof(f_3050_4,plain,
! [U_11461,U_11460] :
( hBOOL(hAPP(hAPP(c_member(U_11460),c_Big__Operators_Olattice__class_OInf__fin(U_11460,U_11461)),U_11461))
| ~ hBOOL(hAPP(hAPP(c_member(U_11460),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11460),sK249(U_11461,U_11460)),sK250(U_11461,U_11460))),hAPP(hAPP(c_Set_Oinsert(U_11460),sK249(U_11461,U_11460)),hAPP(hAPP(c_Set_Oinsert(U_11460),sK250(U_11461,U_11460)),c_Orderings_Obot__class_Obot(tc_fun(U_11460,tc_HOL_Obool))))))
| U_11461 = c_Orderings_Obot__class_Obot(tc_fun(U_11460,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11460),U_11461))
| ~ class_Lattices_Olattice(U_11460) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK250]),skolemize(U_11458,sK250(U_11461,U_11460))],[f_3050_3]) ).
cnf(f_3050_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_11460),c_Big__Operators_Olattice__class_OInf__fin(U_11460,U_11461)),U_11461))
| ~ hBOOL(hAPP(hAPP(c_member(U_11460),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11460),sK249(U_11461,U_11460)),sK250(U_11461,U_11460))),hAPP(hAPP(c_Set_Oinsert(U_11460),sK249(U_11461,U_11460)),hAPP(hAPP(c_Set_Oinsert(U_11460),sK250(U_11461,U_11460)),c_Orderings_Obot__class_Obot(tc_fun(U_11460,tc_HOL_Obool))))))
| U_11461 = c_Orderings_Obot__class_Obot(tc_fun(U_11460,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11460),U_11461))
| ~ class_Lattices_Olattice(U_11460) ),
inference(clausify,[status(thm)],[f_3050_4]) ).
fof(f_3051_1,plain,
! [V_r_2,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
| ~ c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__quotient__disjoint]) ).
fof(f_3051_2,plain,
! [U_11464,U_11463,U_11462] :
( hAPP(c_Finite__Set_Ocard(tc_fun(U_11462,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11462),U_11463),U_11464)) = hAPP(c_Finite__Set_Ocard(U_11462),U_11463)
| ~ c_Fun_Oinj__on(U_11462,tc_fun(tc_fun(U_11462,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11462,tc_fun(tc_prod(U_11462,U_11462),tc_HOL_Obool),tc_fun(tc_fun(U_11462,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11462,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11462,U_11462),tc_HOL_Obool),tc_fun(tc_fun(U_11462,tc_HOL_Obool),tc_HOL_Obool)),U_11462),c_Equiv__Relations_Oquotient(U_11462)),hAPP(hAPP(c_COMBC(U_11462,tc_fun(U_11462,tc_HOL_Obool),tc_fun(U_11462,tc_HOL_Obool)),c_Set_Oinsert(U_11462)),c_Orderings_Obot__class_Obot(tc_fun(U_11462,tc_HOL_Obool))))),U_11464),U_11463)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11462),U_11463)) ),
inference(variable_rename,[status(thm)],[f_3051_1]) ).
cnf(f_3051_3,plain,
( hAPP(c_Finite__Set_Ocard(tc_fun(U_11462,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11462),U_11463),U_11464)) = hAPP(c_Finite__Set_Ocard(U_11462),U_11463)
| ~ c_Fun_Oinj__on(U_11462,tc_fun(tc_fun(U_11462,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11462,tc_fun(tc_prod(U_11462,U_11462),tc_HOL_Obool),tc_fun(tc_fun(U_11462,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11462,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11462,U_11462),tc_HOL_Obool),tc_fun(tc_fun(U_11462,tc_HOL_Obool),tc_HOL_Obool)),U_11462),c_Equiv__Relations_Oquotient(U_11462)),hAPP(hAPP(c_COMBC(U_11462,tc_fun(U_11462,tc_HOL_Obool),tc_fun(U_11462,tc_HOL_Obool)),c_Set_Oinsert(U_11462)),c_Orderings_Obot__class_Obot(tc_fun(U_11462,tc_HOL_Obool))))),U_11464),U_11463)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11462),U_11463)) ),
inference(clausify,[status(thm)],[f_3051_2]) ).
fof(f_3052_1,plain,
! [V_A_2,V_c_2,T_b] :
( ? [B_x] :
( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_Id__onE]) ).
fof(f_3052_2,plain,
! [U_11468,U_11467,U_11466] :
( ? [U_11465] :
( U_11467 = hAPP(hAPP(c_Product__Type_OPair(U_11466,U_11466),U_11465),U_11465)
& hBOOL(hAPP(hAPP(c_member(U_11466),U_11465),U_11468)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11466,U_11466)),U_11467),c_Relation_OId__on(U_11466,U_11468))) ),
inference(variable_rename,[status(thm)],[f_3052_1]) ).
fof(f_3052_3,plain,
! [U_11468,U_11467,U_11466] :
( ( U_11467 = hAPP(hAPP(c_Product__Type_OPair(U_11466,U_11466),sK251(U_11468,U_11467,U_11466)),sK251(U_11468,U_11467,U_11466))
& hBOOL(hAPP(hAPP(c_member(U_11466),sK251(U_11468,U_11467,U_11466)),U_11468)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11466,U_11466)),U_11467),c_Relation_OId__on(U_11466,U_11468))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK251]),skolemize(U_11465,sK251(U_11468,U_11467,U_11466))],[f_3052_2]) ).
cnf(f_3052_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11466),sK251(U_11468,U_11467,U_11466)),U_11468))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11466,U_11466)),U_11467),c_Relation_OId__on(U_11466,U_11468))) ),
inference(clausify,[status(thm)],[f_3052_3]) ).
cnf(f_3052_5,plain,
( U_11467 = hAPP(hAPP(c_Product__Type_OPair(U_11466,U_11466),sK251(U_11468,U_11467,U_11466)),sK251(U_11468,U_11467,U_11466))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11466,U_11466)),U_11467),c_Relation_OId__on(U_11466,U_11468))) ),
inference(clausify,[status(thm)],[f_3052_3]) ).
fof(f_3053_1,plain,
! [V_f_2,T_c,T_b] : c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_inj__on__empty]) ).
fof(f_3053_2,plain,
! [U_11471,U_11470,U_11469] : c_Fun_Oinj__on(U_11469,U_11470,U_11471,c_Orderings_Obot__class_Obot(tc_fun(U_11469,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_3053_1]) ).
cnf(f_3053_3,plain,
c_Fun_Oinj__on(U_11469,U_11470,U_11471,c_Orderings_Obot__class_Obot(tc_fun(U_11469,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_3053_2]) ).
fof(f_3054_1,plain,
! [V_A_2,T_b] :
( c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2)
| ~ class_Groups_Oordered__ab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inj__uminus]) ).
fof(f_3054_2,plain,
! [U_11473,U_11472] :
( c_Fun_Oinj__on(U_11472,U_11472,c_Groups_Ouminus__class_Ouminus(U_11472),U_11473)
| ~ class_Groups_Oordered__ab__group__add(U_11472) ),
inference(variable_rename,[status(thm)],[f_3054_1]) ).
cnf(f_3054_3,plain,
( c_Fun_Oinj__on(U_11472,U_11472,c_Groups_Ouminus__class_Ouminus(U_11472),U_11473)
| ~ class_Groups_Oordered__ab__group__add(U_11472) ),
inference(clausify,[status(thm)],[f_3054_2]) ).
fof(f_3055_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__Int]) ).
fof(f_3055_2,plain,
! [U_11478,U_11477,U_11476,U_11475,U_11474] :
( c_Fun_Oinj__on(U_11474,U_11475,U_11476,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11474,tc_HOL_Obool)),U_11477),U_11478))
| ~ c_Fun_Oinj__on(U_11474,U_11475,U_11476,U_11478)
| ~ c_Fun_Oinj__on(U_11474,U_11475,U_11476,U_11477) ),
inference(variable_rename,[status(thm)],[f_3055_1]) ).
cnf(f_3055_3,plain,
( c_Fun_Oinj__on(U_11474,U_11475,U_11476,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11474,tc_HOL_Obool)),U_11477),U_11478))
| ~ c_Fun_Oinj__on(U_11474,U_11475,U_11476,U_11478)
| ~ c_Fun_Oinj__on(U_11474,U_11475,U_11476,U_11477) ),
inference(clausify,[status(thm)],[f_3055_2]) ).
fof(f_3056_1,plain,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| V_x_2 = V_y_2
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__contraD]) ).
fof(f_3056_2,plain,
! [U_11484,U_11483,U_11482,U_11481,U_11480,U_11479] :
( hAPP(U_11481,U_11483) != hAPP(U_11481,U_11484)
| ~ hBOOL(hAPP(hAPP(c_member(U_11479),U_11484),U_11482))
| ~ hBOOL(hAPP(hAPP(c_member(U_11479),U_11483),U_11482))
| U_11483 = U_11484
| ~ c_Fun_Oinj__on(U_11479,U_11480,U_11481,U_11482) ),
inference(variable_rename,[status(thm)],[f_3056_1]) ).
cnf(f_3056_3,plain,
( hAPP(U_11481,U_11483) != hAPP(U_11481,U_11484)
| ~ hBOOL(hAPP(hAPP(c_member(U_11479),U_11484),U_11482))
| ~ hBOOL(hAPP(hAPP(c_member(U_11479),U_11483),U_11482))
| U_11483 = U_11484
| ~ c_Fun_Oinj__on(U_11479,U_11480,U_11481,U_11482) ),
inference(clausify,[status(thm)],[f_3056_2]) ).
fof(f_3057_1,plain,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( ( ( 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_b),V_y_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__iff]) ).
fof(f_3057_2,plain,
! [U_11490,U_11489,U_11488,U_11487,U_11486,U_11485] :
( ( ( hAPP(U_11487,U_11489) = hAPP(U_11487,U_11490)
| U_11489 != U_11490 )
& ( U_11489 = U_11490
| hAPP(U_11487,U_11489) != hAPP(U_11487,U_11490) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_11485),U_11490),U_11488))
| ~ hBOOL(hAPP(hAPP(c_member(U_11485),U_11489),U_11488))
| ~ c_Fun_Oinj__on(U_11485,U_11486,U_11487,U_11488) ),
inference(variable_rename,[status(thm)],[f_3057_1]) ).
cnf(f_3057_3,plain,
( U_11489 = U_11490
| hAPP(U_11487,U_11489) != hAPP(U_11487,U_11490)
| ~ hBOOL(hAPP(hAPP(c_member(U_11485),U_11490),U_11488))
| ~ hBOOL(hAPP(hAPP(c_member(U_11485),U_11489),U_11488))
| ~ c_Fun_Oinj__on(U_11485,U_11486,U_11487,U_11488) ),
inference(clausify,[status(thm)],[f_3057_2]) ).
cnf(f_3057_4,plain,
( hAPP(U_11487,U_11489) = hAPP(U_11487,U_11490)
| U_11489 != U_11490
| ~ hBOOL(hAPP(hAPP(c_member(U_11485),U_11490),U_11488))
| ~ hBOOL(hAPP(hAPP(c_member(U_11485),U_11489),U_11488))
| ~ c_Fun_Oinj__on(U_11485,U_11486,U_11487,U_11488) ),
inference(clausify,[status(thm)],[f_3057_2]) ).
fof(f_3058_1,plain,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__onD]) ).
fof(f_3058_2,plain,
! [U_11496,U_11495,U_11494,U_11493,U_11492,U_11491] :
( U_11495 = U_11496
| ~ hBOOL(hAPP(hAPP(c_member(U_11491),U_11496),U_11494))
| ~ hBOOL(hAPP(hAPP(c_member(U_11491),U_11495),U_11494))
| hAPP(U_11493,U_11495) != hAPP(U_11493,U_11496)
| ~ c_Fun_Oinj__on(U_11491,U_11492,U_11493,U_11494) ),
inference(variable_rename,[status(thm)],[f_3058_1]) ).
cnf(f_3058_3,plain,
( U_11495 = U_11496
| ~ hBOOL(hAPP(hAPP(c_member(U_11491),U_11496),U_11494))
| ~ hBOOL(hAPP(hAPP(c_member(U_11491),U_11495),U_11494))
| hAPP(U_11493,U_11495) != hAPP(U_11493,U_11496)
| ~ c_Fun_Oinj__on(U_11491,U_11492,U_11493,U_11494) ),
inference(clausify,[status(thm)],[f_3058_2]) ).
fof(f_3059_1,plain,
! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) ),
inference(fof_nnf,[status(thm)],[fact_subset__inj__on]) ).
fof(f_3059_2,plain,
! [U_11501,U_11500,U_11499,U_11498,U_11497] :
( c_Fun_Oinj__on(U_11497,U_11498,U_11499,U_11501)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11497,tc_HOL_Obool)),U_11501),U_11500))
| ~ c_Fun_Oinj__on(U_11497,U_11498,U_11499,U_11500) ),
inference(variable_rename,[status(thm)],[f_3059_1]) ).
cnf(f_3059_3,plain,
( c_Fun_Oinj__on(U_11497,U_11498,U_11499,U_11501)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11497,tc_HOL_Obool)),U_11501),U_11500))
| ~ c_Fun_Oinj__on(U_11497,U_11498,U_11499,U_11500) ),
inference(clausify,[status(thm)],[f_3059_2]) ).
fof(f_3060_1,plain,
! [V_A_2,V_f_2,T_b,T_c] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
| ~ c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Orderings_Oorder(T_c) ),
inference(fof_nnf,[status(thm)],[fact_strict__mono__imp__inj__on]) ).
fof(f_3060_2,plain,
! [U_11505,U_11504,U_11503,U_11502] :
( c_Fun_Oinj__on(U_11503,U_11502,U_11504,U_11505)
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_11503,U_11502,U_11504)
| ~ class_Orderings_Olinorder(U_11503)
| ~ class_Orderings_Oorder(U_11502) ),
inference(variable_rename,[status(thm)],[f_3060_1]) ).
cnf(f_3060_3,plain,
( c_Fun_Oinj__on(U_11503,U_11502,U_11504,U_11505)
| ~ c_Orderings_Oorder__class_Ostrict__mono(U_11503,U_11502,U_11504)
| ~ class_Orderings_Olinorder(U_11503)
| ~ class_Orderings_Oorder(U_11502) ),
inference(clausify,[status(thm)],[f_3060_2]) ).
fof(f_3061_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__diff]) ).
fof(f_3061_2,plain,
! [U_11510,U_11509,U_11508,U_11507,U_11506] :
( c_Fun_Oinj__on(U_11506,U_11507,U_11508,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11506,tc_HOL_Obool)),U_11509),U_11510))
| ~ c_Fun_Oinj__on(U_11506,U_11507,U_11508,U_11509) ),
inference(variable_rename,[status(thm)],[f_3061_1]) ).
cnf(f_3061_3,plain,
( c_Fun_Oinj__on(U_11506,U_11507,U_11508,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11506,tc_HOL_Obool)),U_11509),U_11510))
| ~ c_Fun_Oinj__on(U_11506,U_11507,U_11508,U_11509) ),
inference(clausify,[status(thm)],[f_3061_2]) ).
fof(f_3062_1,plain,
! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2),
inference(fof_nnf,[status(thm)],[fact_inj__on__id2]) ).
fof(f_3062_2,plain,
! [U_11512,U_11511] : c_Fun_Oinj__on(U_11511,U_11511,c_COMBI(U_11511),U_11512),
inference(variable_rename,[status(thm)],[f_3062_1]) ).
cnf(f_3062_3,plain,
c_Fun_Oinj__on(U_11511,U_11511,c_COMBI(U_11511),U_11512),
inference(clausify,[status(thm)],[f_3062_2]) ).
fof(f_3063_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
| ? [B_x] :
( ? [B_xa] :
( B_x != B_xa
& hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
& hBOOL(hAPP(hAPP(c_member(T_b),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_b),B_xa),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__def]) ).
fof(f_3063_2,plain,
! [U_11520,U_11519,U_11518,U_11517] :
( ( c_Fun_Oinj__on(U_11517,U_11518,U_11519,U_11520)
| ? [U_11516] :
( ? [U_11515] :
( U_11516 != U_11515
& hAPP(U_11519,U_11516) = hAPP(U_11519,U_11515)
& hBOOL(hAPP(hAPP(c_member(U_11517),U_11515),U_11520)) )
& hBOOL(hAPP(hAPP(c_member(U_11517),U_11516),U_11520)) ) )
& ( ! [U_11514] :
( ! [U_11513] :
( U_11514 = U_11513
| hAPP(U_11519,U_11514) != hAPP(U_11519,U_11513)
| ~ hBOOL(hAPP(hAPP(c_member(U_11517),U_11513),U_11520)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_11517),U_11514),U_11520)) )
| ~ c_Fun_Oinj__on(U_11517,U_11518,U_11519,U_11520) ) ),
inference(variable_rename,[status(thm)],[f_3063_1]) ).
fof(f_3063_3,plain,
( ! [U_11528,U_11526,U_11524,U_11522] :
( c_Fun_Oinj__on(U_11522,U_11524,U_11526,U_11528)
| ? [U_11516] :
( ? [U_11515] :
( U_11516 != U_11515
& hAPP(U_11526,U_11516) = hAPP(U_11526,U_11515)
& hBOOL(hAPP(hAPP(c_member(U_11522),U_11515),U_11528)) )
& hBOOL(hAPP(hAPP(c_member(U_11522),U_11516),U_11528)) ) )
& ! [U_11527,U_11525,U_11523,U_11521] :
( ! [U_11514] :
( ! [U_11513] :
( U_11514 = U_11513
| hAPP(U_11525,U_11514) != hAPP(U_11525,U_11513)
| ~ hBOOL(hAPP(hAPP(c_member(U_11521),U_11513),U_11527)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_11521),U_11514),U_11527)) )
| ~ c_Fun_Oinj__on(U_11521,U_11523,U_11525,U_11527) ) ),
inference(miniscope,[status(thm)],[f_3063_2]) ).
fof(f_3063_4,plain,
( ! [U_11528,U_11526,U_11524,U_11522] :
( c_Fun_Oinj__on(U_11522,U_11524,U_11526,U_11528)
| ( ? [U_11515] :
( sK252(U_11528,U_11526,U_11524,U_11522) != U_11515
& hAPP(U_11526,sK252(U_11528,U_11526,U_11524,U_11522)) = hAPP(U_11526,U_11515)
& hBOOL(hAPP(hAPP(c_member(U_11522),U_11515),U_11528)) )
& hBOOL(hAPP(hAPP(c_member(U_11522),sK252(U_11528,U_11526,U_11524,U_11522)),U_11528)) ) )
& ! [U_11527,U_11525,U_11523,U_11521] :
( ! [U_11514] :
( ! [U_11513] :
( U_11514 = U_11513
| hAPP(U_11525,U_11514) != hAPP(U_11525,U_11513)
| ~ hBOOL(hAPP(hAPP(c_member(U_11521),U_11513),U_11527)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_11521),U_11514),U_11527)) )
| ~ c_Fun_Oinj__on(U_11521,U_11523,U_11525,U_11527) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK252]),skolemize(U_11516,sK252(U_11528,U_11526,U_11524,U_11522))],[f_3063_3]) ).
fof(f_3063_5,plain,
( ! [U_11528,U_11526,U_11524,U_11522] :
( c_Fun_Oinj__on(U_11522,U_11524,U_11526,U_11528)
| ( sK252(U_11528,U_11526,U_11524,U_11522) != sK253(U_11528,U_11526,U_11524,U_11522)
& hAPP(U_11526,sK252(U_11528,U_11526,U_11524,U_11522)) = hAPP(U_11526,sK253(U_11528,U_11526,U_11524,U_11522))
& hBOOL(hAPP(hAPP(c_member(U_11522),sK253(U_11528,U_11526,U_11524,U_11522)),U_11528))
& hBOOL(hAPP(hAPP(c_member(U_11522),sK252(U_11528,U_11526,U_11524,U_11522)),U_11528)) ) )
& ! [U_11527,U_11525,U_11523,U_11521] :
( ! [U_11514] :
( ! [U_11513] :
( U_11514 = U_11513
| hAPP(U_11525,U_11514) != hAPP(U_11525,U_11513)
| ~ hBOOL(hAPP(hAPP(c_member(U_11521),U_11513),U_11527)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_11521),U_11514),U_11527)) )
| ~ c_Fun_Oinj__on(U_11521,U_11523,U_11525,U_11527) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK253]),skolemize(U_11515,sK253(U_11528,U_11526,U_11524,U_11522))],[f_3063_4]) ).
cnf(f_3063_6,plain,
( U_11514 = U_11513
| hAPP(U_11525,U_11514) != hAPP(U_11525,U_11513)
| ~ hBOOL(hAPP(hAPP(c_member(U_11521),U_11513),U_11527))
| ~ hBOOL(hAPP(hAPP(c_member(U_11521),U_11514),U_11527))
| ~ c_Fun_Oinj__on(U_11521,U_11523,U_11525,U_11527) ),
inference(clausify,[status(thm)],[f_3063_5]) ).
cnf(f_3063_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_11522),sK252(U_11528,U_11526,U_11524,U_11522)),U_11528))
| c_Fun_Oinj__on(U_11522,U_11524,U_11526,U_11528) ),
inference(clausify,[status(thm)],[f_3063_5]) ).
cnf(f_3063_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_11522),sK253(U_11528,U_11526,U_11524,U_11522)),U_11528))
| c_Fun_Oinj__on(U_11522,U_11524,U_11526,U_11528) ),
inference(clausify,[status(thm)],[f_3063_5]) ).
cnf(f_3063_9,plain,
( hAPP(U_11526,sK252(U_11528,U_11526,U_11524,U_11522)) = hAPP(U_11526,sK253(U_11528,U_11526,U_11524,U_11522))
| c_Fun_Oinj__on(U_11522,U_11524,U_11526,U_11528) ),
inference(clausify,[status(thm)],[f_3063_5]) ).
cnf(f_3063_10,plain,
( sK252(U_11528,U_11526,U_11524,U_11522) != sK253(U_11528,U_11526,U_11524,U_11522)
| c_Fun_Oinj__on(U_11522,U_11524,U_11526,U_11528) ),
inference(clausify,[status(thm)],[f_3063_5]) ).
fof(f_3064_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__imageD]) ).
fof(f_3064_2,plain,
! [U_11532,U_11531,U_11530,U_11529] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11530),U_11532))
| ~ c_Fun_Oinj__on(U_11530,U_11529,U_11531,U_11532)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11529),hAPP(c_Set_Oimage(U_11530,U_11529,U_11531),U_11532))) ),
inference(variable_rename,[status(thm)],[f_3064_1]) ).
cnf(f_3064_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11530),U_11532))
| ~ c_Fun_Oinj__on(U_11530,U_11529,U_11531,U_11532)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11529),hAPP(c_Set_Oimage(U_11530,U_11529,U_11531),U_11532))) ),
inference(clausify,[status(thm)],[f_3064_2]) ).
fof(f_3065_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( ( ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
| V_A_2 != V_B_2 )
& ( V_A_2 = V_B_2
| hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) != hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) ) )
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__Un__image__eq__iff]) ).
fof(f_3065_2,plain,
! [U_11537,U_11536,U_11535,U_11534,U_11533] :
( ( ( hAPP(c_Set_Oimage(U_11533,U_11534,U_11535),U_11536) = hAPP(c_Set_Oimage(U_11533,U_11534,U_11535),U_11537)
| U_11536 != U_11537 )
& ( U_11536 = U_11537
| hAPP(c_Set_Oimage(U_11533,U_11534,U_11535),U_11536) != hAPP(c_Set_Oimage(U_11533,U_11534,U_11535),U_11537) ) )
| ~ c_Fun_Oinj__on(U_11533,U_11534,U_11535,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11533,tc_HOL_Obool)),U_11536),U_11537)) ),
inference(variable_rename,[status(thm)],[f_3065_1]) ).
cnf(f_3065_3,plain,
( U_11536 = U_11537
| hAPP(c_Set_Oimage(U_11533,U_11534,U_11535),U_11536) != hAPP(c_Set_Oimage(U_11533,U_11534,U_11535),U_11537)
| ~ c_Fun_Oinj__on(U_11533,U_11534,U_11535,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11533,tc_HOL_Obool)),U_11536),U_11537)) ),
inference(clausify,[status(thm)],[f_3065_2]) ).
cnf(f_3065_4,plain,
( hAPP(c_Set_Oimage(U_11533,U_11534,U_11535),U_11536) = hAPP(c_Set_Oimage(U_11533,U_11534,U_11535),U_11537)
| U_11536 != U_11537
| ~ c_Fun_Oinj__on(U_11533,U_11534,U_11535,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11533,tc_HOL_Obool)),U_11536),U_11537)) ),
inference(clausify,[status(thm)],[f_3065_2]) ).
fof(f_3066_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_card__image]) ).
fof(f_3066_2,plain,
! [U_11541,U_11540,U_11539,U_11538] :
( hAPP(c_Finite__Set_Ocard(U_11539),hAPP(c_Set_Oimage(U_11538,U_11539,U_11540),U_11541)) = hAPP(c_Finite__Set_Ocard(U_11538),U_11541)
| ~ c_Fun_Oinj__on(U_11538,U_11539,U_11540,U_11541) ),
inference(variable_rename,[status(thm)],[f_3066_1]) ).
cnf(f_3066_3,plain,
( hAPP(c_Finite__Set_Ocard(U_11539),hAPP(c_Set_Oimage(U_11538,U_11539,U_11540),U_11541)) = hAPP(c_Finite__Set_Ocard(U_11538),U_11541)
| ~ c_Fun_Oinj__on(U_11538,U_11539,U_11540,U_11541) ),
inference(clausify,[status(thm)],[f_3066_2]) ).
fof(f_3067_1,plain,
! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset]) ).
fof(f_3067_2,plain,
! [U_11546,U_11545,U_11544,U_11543,U_11542] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11543,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11542,U_11543,U_11544),U_11546)),hAPP(c_Set_Oimage(U_11542,U_11543,U_11544),U_11545)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11542,tc_HOL_Obool)),U_11546),U_11545))
| ~ c_Fun_Oinj__on(U_11542,U_11543,U_11544,U_11545) ),
inference(variable_rename,[status(thm)],[f_3067_1]) ).
cnf(f_3067_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11543,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11542,U_11543,U_11544),U_11546)),hAPP(c_Set_Oimage(U_11542,U_11543,U_11544),U_11545)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11542,tc_HOL_Obool)),U_11546),U_11545))
| ~ c_Fun_Oinj__on(U_11542,U_11543,U_11544,U_11545) ),
inference(clausify,[status(thm)],[f_3067_2]) ).
fof(f_3068_1,plain,
! [V_f_2,V_A_2,T_b] :
( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__surj__inj]) ).
fof(f_3068_2,plain,
! [U_11549,U_11548,U_11547] :
( c_Fun_Oinj__on(U_11547,U_11547,U_11549,U_11548)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11547,tc_HOL_Obool)),U_11548),hAPP(c_Set_Oimage(U_11547,U_11547,U_11549),U_11548)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11547),U_11548)) ),
inference(variable_rename,[status(thm)],[f_3068_1]) ).
cnf(f_3068_3,plain,
( c_Fun_Oinj__on(U_11547,U_11547,U_11549,U_11548)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11547,tc_HOL_Obool)),U_11548),hAPP(c_Set_Oimage(U_11547,U_11547,U_11549),U_11548)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11547),U_11548)) ),
inference(clausify,[status(thm)],[f_3068_2]) ).
fof(f_3069_1,plain,
! [V_f_2,V_A_2,T_b] :
( hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2
| ~ c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_endo__inj__surj]) ).
fof(f_3069_2,plain,
! [U_11552,U_11551,U_11550] :
( hAPP(c_Set_Oimage(U_11550,U_11550,U_11552),U_11551) = U_11551
| ~ c_Fun_Oinj__on(U_11550,U_11550,U_11552,U_11551)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11550,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11550,U_11550,U_11552),U_11551)),U_11551))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11550),U_11551)) ),
inference(variable_rename,[status(thm)],[f_3069_1]) ).
cnf(f_3069_3,plain,
( hAPP(c_Set_Oimage(U_11550,U_11550,U_11552),U_11551) = U_11551
| ~ c_Fun_Oinj__on(U_11550,U_11550,U_11552,U_11551)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11550,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11550,U_11550,U_11552),U_11551)),U_11551))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11550),U_11551)) ),
inference(clausify,[status(thm)],[f_3069_2]) ).
fof(f_3070_1,plain,
! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__image__Int]) ).
fof(f_3070_2,plain,
! [U_11558,U_11557,U_11556,U_11555,U_11554,U_11553] :
( hAPP(c_Set_Oimage(U_11553,U_11554,U_11555),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11553,tc_HOL_Obool)),U_11557),U_11558)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11554,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11553,U_11554,U_11555),U_11557)),hAPP(c_Set_Oimage(U_11553,U_11554,U_11555),U_11558))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11553,tc_HOL_Obool)),U_11558),U_11556))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11553,tc_HOL_Obool)),U_11557),U_11556))
| ~ c_Fun_Oinj__on(U_11553,U_11554,U_11555,U_11556) ),
inference(variable_rename,[status(thm)],[f_3070_1]) ).
cnf(f_3070_3,plain,
( hAPP(c_Set_Oimage(U_11553,U_11554,U_11555),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11553,tc_HOL_Obool)),U_11557),U_11558)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11554,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11553,U_11554,U_11555),U_11557)),hAPP(c_Set_Oimage(U_11553,U_11554,U_11555),U_11558))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11553,tc_HOL_Obool)),U_11558),U_11556))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11553,tc_HOL_Obool)),U_11557),U_11556))
| ~ c_Fun_Oinj__on(U_11553,U_11554,U_11555,U_11556) ),
inference(clausify,[status(thm)],[f_3070_2]) ).
fof(f_3071_1,plain,
! [V_f_2,T_c,V_A_2,T_b] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
| hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) != hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on]) ).
fof(f_3071_2,plain,
! [U_11562,U_11561,U_11560,U_11559] :
( c_Fun_Oinj__on(U_11559,U_11561,U_11562,U_11560)
| hAPP(c_Finite__Set_Ocard(U_11561),hAPP(c_Set_Oimage(U_11559,U_11561,U_11562),U_11560)) != hAPP(c_Finite__Set_Ocard(U_11559),U_11560)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11559),U_11560)) ),
inference(variable_rename,[status(thm)],[f_3071_1]) ).
cnf(f_3071_3,plain,
( c_Fun_Oinj__on(U_11559,U_11561,U_11562,U_11560)
| hAPP(c_Finite__Set_Ocard(U_11561),hAPP(c_Set_Oimage(U_11559,U_11561,U_11562),U_11560)) != hAPP(c_Finite__Set_Ocard(U_11559),U_11560)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11559),U_11560)) ),
inference(clausify,[status(thm)],[f_3071_2]) ).
fof(f_3072_1,plain,
! [V_f_2,T_c,V_A_2,T_b] :
( ( ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
| hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) != hAPP(c_Finite__Set_Ocard(T_b),V_A_2) )
& ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__iff__eq__card]) ).
fof(f_3072_2,plain,
! [U_11566,U_11565,U_11564,U_11563] :
( ( ( c_Fun_Oinj__on(U_11563,U_11565,U_11566,U_11564)
| hAPP(c_Finite__Set_Ocard(U_11565),hAPP(c_Set_Oimage(U_11563,U_11565,U_11566),U_11564)) != hAPP(c_Finite__Set_Ocard(U_11563),U_11564) )
& ( hAPP(c_Finite__Set_Ocard(U_11565),hAPP(c_Set_Oimage(U_11563,U_11565,U_11566),U_11564)) = hAPP(c_Finite__Set_Ocard(U_11563),U_11564)
| ~ c_Fun_Oinj__on(U_11563,U_11565,U_11566,U_11564) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11563),U_11564)) ),
inference(variable_rename,[status(thm)],[f_3072_1]) ).
cnf(f_3072_3,plain,
( hAPP(c_Finite__Set_Ocard(U_11565),hAPP(c_Set_Oimage(U_11563,U_11565,U_11566),U_11564)) = hAPP(c_Finite__Set_Ocard(U_11563),U_11564)
| ~ c_Fun_Oinj__on(U_11563,U_11565,U_11566,U_11564)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11563),U_11564)) ),
inference(clausify,[status(thm)],[f_3072_2]) ).
cnf(f_3072_4,plain,
( c_Fun_Oinj__on(U_11563,U_11565,U_11566,U_11564)
| hAPP(c_Finite__Set_Ocard(U_11565),hAPP(c_Set_Oimage(U_11563,U_11565,U_11566),U_11564)) != hAPP(c_Finite__Set_Ocard(U_11563),U_11564)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11563),U_11564)) ),
inference(clausify,[status(thm)],[f_3072_2]) ).
fof(f_3073_1,plain,
! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__image__set__diff]) ).
fof(f_3073_2,plain,
! [U_11572,U_11571,U_11570,U_11569,U_11568,U_11567] :
( hAPP(c_Set_Oimage(U_11567,U_11568,U_11569),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11567,tc_HOL_Obool)),U_11571),U_11572)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11568,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11567,U_11568,U_11569),U_11571)),hAPP(c_Set_Oimage(U_11567,U_11568,U_11569),U_11572))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11567,tc_HOL_Obool)),U_11572),U_11570))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11567,tc_HOL_Obool)),U_11571),U_11570))
| ~ c_Fun_Oinj__on(U_11567,U_11568,U_11569,U_11570) ),
inference(variable_rename,[status(thm)],[f_3073_1]) ).
cnf(f_3073_3,plain,
( hAPP(c_Set_Oimage(U_11567,U_11568,U_11569),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11567,tc_HOL_Obool)),U_11571),U_11572)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11568,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11567,U_11568,U_11569),U_11571)),hAPP(c_Set_Oimage(U_11567,U_11568,U_11569),U_11572))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11567,tc_HOL_Obool)),U_11572),U_11570))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11567,tc_HOL_Obool)),U_11571),U_11570))
| ~ c_Fun_Oinj__on(U_11567,U_11568,U_11569,U_11570) ),
inference(clausify,[status(thm)],[f_3073_2]) ).
fof(f_3074_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_pigeonhole]) ).
fof(f_3074_2,plain,
! [U_11576,U_11575,U_11574,U_11573] :
( ~ c_Fun_Oinj__on(U_11574,U_11573,U_11575,U_11576)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11573),hAPP(c_Set_Oimage(U_11574,U_11573,U_11575),U_11576))),hAPP(c_Finite__Set_Ocard(U_11574),U_11576))) ),
inference(variable_rename,[status(thm)],[f_3074_1]) ).
cnf(f_3074_3,plain,
( ~ c_Fun_Oinj__on(U_11574,U_11573,U_11575,U_11576)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11573),hAPP(c_Set_Oimage(U_11574,U_11573,U_11575),U_11576))),hAPP(c_Finite__Set_Ocard(U_11574),U_11576))) ),
inference(clausify,[status(thm)],[f_3074_2]) ).
fof(f_3075_1,plain,
! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__fun__updI]) ).
fof(f_3075_2,plain,
! [U_11582,U_11581,U_11580,U_11579,U_11578,U_11577] :
( c_Fun_Oinj__on(U_11577,U_11578,c_Fun_Ofun__upd(U_11577,U_11578,U_11579,U_11582,U_11581),U_11580)
| hBOOL(hAPP(hAPP(c_member(U_11578),U_11581),hAPP(c_Set_Oimage(U_11577,U_11578,U_11579),U_11580)))
| ~ c_Fun_Oinj__on(U_11577,U_11578,U_11579,U_11580) ),
inference(variable_rename,[status(thm)],[f_3075_1]) ).
cnf(f_3075_3,plain,
( c_Fun_Oinj__on(U_11577,U_11578,c_Fun_Ofun__upd(U_11577,U_11578,U_11579,U_11582,U_11581),U_11580)
| hBOOL(hAPP(hAPP(c_member(U_11578),U_11581),hAPP(c_Set_Oimage(U_11577,U_11578,U_11579),U_11580)))
| ~ c_Fun_Oinj__on(U_11577,U_11578,U_11579,U_11580) ),
inference(clausify,[status(thm)],[f_3075_2]) ).
fof(f_3076_1,plain,
! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2))
| ~ c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_card__bij__eq]) ).
fof(f_3076_2,plain,
! [U_11588,U_11587,U_11586,U_11585,U_11584,U_11583] :
( hAPP(c_Finite__Set_Ocard(U_11583),U_11586) = hAPP(c_Finite__Set_Ocard(U_11584),U_11587)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11584),U_11587))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11583),U_11586))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11583,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11584,U_11583,U_11588),U_11587)),U_11586))
| ~ c_Fun_Oinj__on(U_11584,U_11583,U_11588,U_11587)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11584,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11583,U_11584,U_11585),U_11586)),U_11587))
| ~ c_Fun_Oinj__on(U_11583,U_11584,U_11585,U_11586) ),
inference(variable_rename,[status(thm)],[f_3076_1]) ).
cnf(f_3076_3,plain,
( hAPP(c_Finite__Set_Ocard(U_11583),U_11586) = hAPP(c_Finite__Set_Ocard(U_11584),U_11587)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11584),U_11587))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11583),U_11586))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11583,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11584,U_11583,U_11588),U_11587)),U_11586))
| ~ c_Fun_Oinj__on(U_11584,U_11583,U_11588,U_11587)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11584,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11583,U_11584,U_11585),U_11586)),U_11587))
| ~ c_Fun_Oinj__on(U_11583,U_11584,U_11585,U_11586) ),
inference(clausify,[status(thm)],[f_3076_2]) ).
fof(f_3077_1,plain,
! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
( ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
| hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
& c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) )
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__insert]) ).
fof(f_3077_2,plain,
! [U_11593,U_11592,U_11591,U_11590,U_11589] :
( ( c_Fun_Oinj__on(U_11589,U_11590,U_11591,hAPP(hAPP(c_Set_Oinsert(U_11589),U_11592),U_11593))
| hBOOL(hAPP(hAPP(c_member(U_11590),hAPP(U_11591,U_11592)),hAPP(c_Set_Oimage(U_11589,U_11590,U_11591),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11589,tc_HOL_Obool)),U_11593),hAPP(hAPP(c_Set_Oinsert(U_11589),U_11592),c_Orderings_Obot__class_Obot(tc_fun(U_11589,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(U_11589,U_11590,U_11591,U_11593) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(U_11590),hAPP(U_11591,U_11592)),hAPP(c_Set_Oimage(U_11589,U_11590,U_11591),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11589,tc_HOL_Obool)),U_11593),hAPP(hAPP(c_Set_Oinsert(U_11589),U_11592),c_Orderings_Obot__class_Obot(tc_fun(U_11589,tc_HOL_Obool)))))))
& c_Fun_Oinj__on(U_11589,U_11590,U_11591,U_11593) )
| ~ c_Fun_Oinj__on(U_11589,U_11590,U_11591,hAPP(hAPP(c_Set_Oinsert(U_11589),U_11592),U_11593)) ) ),
inference(variable_rename,[status(thm)],[f_3077_1]) ).
fof(f_3077_3,plain,
( ! [U_11603,U_11601,U_11599,U_11597,U_11595] :
( c_Fun_Oinj__on(U_11595,U_11597,U_11599,hAPP(hAPP(c_Set_Oinsert(U_11595),U_11601),U_11603))
| hBOOL(hAPP(hAPP(c_member(U_11597),hAPP(U_11599,U_11601)),hAPP(c_Set_Oimage(U_11595,U_11597,U_11599),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11595,tc_HOL_Obool)),U_11603),hAPP(hAPP(c_Set_Oinsert(U_11595),U_11601),c_Orderings_Obot__class_Obot(tc_fun(U_11595,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(U_11595,U_11597,U_11599,U_11603) )
& ! [U_11602,U_11600,U_11598,U_11596,U_11594] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_11596),hAPP(U_11598,U_11600)),hAPP(c_Set_Oimage(U_11594,U_11596,U_11598),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11594,tc_HOL_Obool)),U_11602),hAPP(hAPP(c_Set_Oinsert(U_11594),U_11600),c_Orderings_Obot__class_Obot(tc_fun(U_11594,tc_HOL_Obool)))))))
& c_Fun_Oinj__on(U_11594,U_11596,U_11598,U_11602) )
| ~ c_Fun_Oinj__on(U_11594,U_11596,U_11598,hAPP(hAPP(c_Set_Oinsert(U_11594),U_11600),U_11602)) ) ),
inference(miniscope,[status(thm)],[f_3077_2]) ).
cnf(f_3077_4,plain,
( c_Fun_Oinj__on(U_11594,U_11596,U_11598,U_11602)
| ~ c_Fun_Oinj__on(U_11594,U_11596,U_11598,hAPP(hAPP(c_Set_Oinsert(U_11594),U_11600),U_11602)) ),
inference(clausify,[status(thm)],[f_3077_3]) ).
cnf(f_3077_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_11596),hAPP(U_11598,U_11600)),hAPP(c_Set_Oimage(U_11594,U_11596,U_11598),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11594,tc_HOL_Obool)),U_11602),hAPP(hAPP(c_Set_Oinsert(U_11594),U_11600),c_Orderings_Obot__class_Obot(tc_fun(U_11594,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(U_11594,U_11596,U_11598,hAPP(hAPP(c_Set_Oinsert(U_11594),U_11600),U_11602)) ),
inference(clausify,[status(thm)],[f_3077_3]) ).
cnf(f_3077_6,plain,
( c_Fun_Oinj__on(U_11595,U_11597,U_11599,hAPP(hAPP(c_Set_Oinsert(U_11595),U_11601),U_11603))
| hBOOL(hAPP(hAPP(c_member(U_11597),hAPP(U_11599,U_11601)),hAPP(c_Set_Oimage(U_11595,U_11597,U_11599),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11595,tc_HOL_Obool)),U_11603),hAPP(hAPP(c_Set_Oinsert(U_11595),U_11601),c_Orderings_Obot__class_Obot(tc_fun(U_11595,tc_HOL_Obool)))))))
| ~ c_Fun_Oinj__on(U_11595,U_11597,U_11599,U_11603) ),
inference(clausify,[status(thm)],[f_3077_3]) ).
fof(f_3078_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) )
& ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
& c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
& c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) )
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__Un]) ).
fof(f_3078_2,plain,
! [U_11608,U_11607,U_11606,U_11605,U_11604] :
( ( c_Fun_Oinj__on(U_11604,U_11605,U_11606,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11604,tc_HOL_Obool)),U_11607),U_11608))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11605,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11604,U_11605,U_11606),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11604,tc_HOL_Obool)),U_11607),U_11608))),hAPP(c_Set_Oimage(U_11604,U_11605,U_11606),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11604,tc_HOL_Obool)),U_11608),U_11607))) != c_Orderings_Obot__class_Obot(tc_fun(U_11605,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(U_11604,U_11605,U_11606,U_11608)
| ~ c_Fun_Oinj__on(U_11604,U_11605,U_11606,U_11607) )
& ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11605,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11604,U_11605,U_11606),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11604,tc_HOL_Obool)),U_11607),U_11608))),hAPP(c_Set_Oimage(U_11604,U_11605,U_11606),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11604,tc_HOL_Obool)),U_11608),U_11607))) = c_Orderings_Obot__class_Obot(tc_fun(U_11605,tc_HOL_Obool))
& c_Fun_Oinj__on(U_11604,U_11605,U_11606,U_11608)
& c_Fun_Oinj__on(U_11604,U_11605,U_11606,U_11607) )
| ~ c_Fun_Oinj__on(U_11604,U_11605,U_11606,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11604,tc_HOL_Obool)),U_11607),U_11608)) ) ),
inference(variable_rename,[status(thm)],[f_3078_1]) ).
fof(f_3078_3,plain,
( ! [U_11618,U_11616,U_11614,U_11612,U_11610] :
( c_Fun_Oinj__on(U_11610,U_11612,U_11614,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11610,tc_HOL_Obool)),U_11616),U_11618))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11612,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11610,U_11612,U_11614),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11610,tc_HOL_Obool)),U_11616),U_11618))),hAPP(c_Set_Oimage(U_11610,U_11612,U_11614),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11610,tc_HOL_Obool)),U_11618),U_11616))) != c_Orderings_Obot__class_Obot(tc_fun(U_11612,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(U_11610,U_11612,U_11614,U_11618)
| ~ c_Fun_Oinj__on(U_11610,U_11612,U_11614,U_11616) )
& ! [U_11617,U_11615,U_11613,U_11611,U_11609] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11611,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11609,U_11611,U_11613),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11609,tc_HOL_Obool)),U_11615),U_11617))),hAPP(c_Set_Oimage(U_11609,U_11611,U_11613),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11609,tc_HOL_Obool)),U_11617),U_11615))) = c_Orderings_Obot__class_Obot(tc_fun(U_11611,tc_HOL_Obool))
& c_Fun_Oinj__on(U_11609,U_11611,U_11613,U_11617)
& c_Fun_Oinj__on(U_11609,U_11611,U_11613,U_11615) )
| ~ c_Fun_Oinj__on(U_11609,U_11611,U_11613,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11609,tc_HOL_Obool)),U_11615),U_11617)) ) ),
inference(miniscope,[status(thm)],[f_3078_2]) ).
cnf(f_3078_4,plain,
( c_Fun_Oinj__on(U_11609,U_11611,U_11613,U_11615)
| ~ c_Fun_Oinj__on(U_11609,U_11611,U_11613,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11609,tc_HOL_Obool)),U_11615),U_11617)) ),
inference(clausify,[status(thm)],[f_3078_3]) ).
cnf(f_3078_5,plain,
( c_Fun_Oinj__on(U_11609,U_11611,U_11613,U_11617)
| ~ c_Fun_Oinj__on(U_11609,U_11611,U_11613,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11609,tc_HOL_Obool)),U_11615),U_11617)) ),
inference(clausify,[status(thm)],[f_3078_3]) ).
cnf(f_3078_6,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11611,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11609,U_11611,U_11613),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11609,tc_HOL_Obool)),U_11615),U_11617))),hAPP(c_Set_Oimage(U_11609,U_11611,U_11613),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11609,tc_HOL_Obool)),U_11617),U_11615))) = c_Orderings_Obot__class_Obot(tc_fun(U_11611,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(U_11609,U_11611,U_11613,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11609,tc_HOL_Obool)),U_11615),U_11617)) ),
inference(clausify,[status(thm)],[f_3078_3]) ).
cnf(f_3078_7,plain,
( c_Fun_Oinj__on(U_11610,U_11612,U_11614,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11610,tc_HOL_Obool)),U_11616),U_11618))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11612,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11610,U_11612,U_11614),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11610,tc_HOL_Obool)),U_11616),U_11618))),hAPP(c_Set_Oimage(U_11610,U_11612,U_11614),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11610,tc_HOL_Obool)),U_11618),U_11616))) != c_Orderings_Obot__class_Obot(tc_fun(U_11612,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(U_11610,U_11612,U_11614,U_11618)
| ~ c_Fun_Oinj__on(U_11610,U_11612,U_11614,U_11616) ),
inference(clausify,[status(thm)],[f_3078_3]) ).
fof(f_3079_1,plain,
! [V_B_2,T_c,V_A_2,T_b] :
( ( ( ? [B_f] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_B_2))
& c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)))
| ! [B_f] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_B_2))
| ~ c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) ) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__iff__card__le]) ).
fof(f_3079_2,plain,
! [U_11624,U_11623,U_11622,U_11621] :
( ( ( ? [U_11620] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11623,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11621,U_11623,U_11620),U_11622)),U_11624))
& c_Fun_Oinj__on(U_11621,U_11623,U_11620,U_11622) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11621),U_11622)),hAPP(c_Finite__Set_Ocard(U_11623),U_11624))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11621),U_11622)),hAPP(c_Finite__Set_Ocard(U_11623),U_11624)))
| ! [U_11619] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11623,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11621,U_11623,U_11619),U_11622)),U_11624))
| ~ c_Fun_Oinj__on(U_11621,U_11623,U_11619,U_11622) ) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11623),U_11624))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11621),U_11622)) ),
inference(variable_rename,[status(thm)],[f_3079_1]) ).
fof(f_3079_3,plain,
! [U_11624,U_11623,U_11622,U_11621] :
( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11623,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11621,U_11623,sK254(U_11624,U_11623,U_11622,U_11621)),U_11622)),U_11624))
& c_Fun_Oinj__on(U_11621,U_11623,sK254(U_11624,U_11623,U_11622,U_11621),U_11622) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11621),U_11622)),hAPP(c_Finite__Set_Ocard(U_11623),U_11624))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11621),U_11622)),hAPP(c_Finite__Set_Ocard(U_11623),U_11624)))
| ! [U_11619] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11623,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11621,U_11623,U_11619),U_11622)),U_11624))
| ~ c_Fun_Oinj__on(U_11621,U_11623,U_11619,U_11622) ) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11623),U_11624))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11621),U_11622)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK254]),skolemize(U_11620,sK254(U_11624,U_11623,U_11622,U_11621))],[f_3079_2]) ).
cnf(f_3079_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11621),U_11622)),hAPP(c_Finite__Set_Ocard(U_11623),U_11624)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11623,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11621,U_11623,U_11619),U_11622)),U_11624))
| ~ c_Fun_Oinj__on(U_11621,U_11623,U_11619,U_11622)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11623),U_11624))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11621),U_11622)) ),
inference(clausify,[status(thm)],[f_3079_3]) ).
cnf(f_3079_5,plain,
( c_Fun_Oinj__on(U_11621,U_11623,sK254(U_11624,U_11623,U_11622,U_11621),U_11622)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11621),U_11622)),hAPP(c_Finite__Set_Ocard(U_11623),U_11624)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11623),U_11624))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11621),U_11622)) ),
inference(clausify,[status(thm)],[f_3079_3]) ).
cnf(f_3079_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11623,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11621,U_11623,sK254(U_11624,U_11623,U_11622,U_11621)),U_11622)),U_11624))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11621),U_11622)),hAPP(c_Finite__Set_Ocard(U_11623),U_11624)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11623),U_11624))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11621),U_11622)) ),
inference(clausify,[status(thm)],[f_3079_3]) ).
fof(f_3080_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_card__inj__on__le]) ).
fof(f_3080_2,plain,
! [U_11629,U_11628,U_11627,U_11626,U_11625] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11625),U_11628)),hAPP(c_Finite__Set_Ocard(U_11626),U_11629)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11626),U_11629))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11626,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11625,U_11626,U_11627),U_11628)),U_11629))
| ~ c_Fun_Oinj__on(U_11625,U_11626,U_11627,U_11628) ),
inference(variable_rename,[status(thm)],[f_3080_1]) ).
cnf(f_3080_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11625),U_11628)),hAPP(c_Finite__Set_Ocard(U_11626),U_11629)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11626),U_11629))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11626,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11625,U_11626,U_11627),U_11628)),U_11629))
| ~ c_Fun_Oinj__on(U_11625,U_11626,U_11627,U_11628) ),
inference(clausify,[status(thm)],[f_3080_2]) ).
fof(f_3081_1,plain,
! [V_a_2,V_A_2,V_r_2,T_b] :
( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2),V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_quotient__diff1]) ).
fof(f_3081_2,plain,
! [U_11633,U_11632,U_11631,U_11630] :
( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11630),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11630,tc_HOL_Obool)),U_11632),hAPP(hAPP(c_Set_Oinsert(U_11630),U_11633),c_Orderings_Obot__class_Obot(tc_fun(U_11630,tc_HOL_Obool))))),U_11631) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_11630,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11630),U_11632),U_11631)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11630),hAPP(hAPP(c_Set_Oinsert(U_11630),U_11633),c_Orderings_Obot__class_Obot(tc_fun(U_11630,tc_HOL_Obool)))),U_11631))
| ~ hBOOL(hAPP(hAPP(c_member(U_11630),U_11633),U_11632))
| ~ c_Fun_Oinj__on(U_11630,tc_fun(tc_fun(U_11630,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11630,tc_fun(tc_prod(U_11630,U_11630),tc_HOL_Obool),tc_fun(tc_fun(U_11630,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11630,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11630,U_11630),tc_HOL_Obool),tc_fun(tc_fun(U_11630,tc_HOL_Obool),tc_HOL_Obool)),U_11630),c_Equiv__Relations_Oquotient(U_11630)),hAPP(hAPP(c_COMBC(U_11630,tc_fun(U_11630,tc_HOL_Obool),tc_fun(U_11630,tc_HOL_Obool)),c_Set_Oinsert(U_11630)),c_Orderings_Obot__class_Obot(tc_fun(U_11630,tc_HOL_Obool))))),U_11631),U_11632) ),
inference(variable_rename,[status(thm)],[f_3081_1]) ).
cnf(f_3081_3,plain,
( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11630),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11630,tc_HOL_Obool)),U_11632),hAPP(hAPP(c_Set_Oinsert(U_11630),U_11633),c_Orderings_Obot__class_Obot(tc_fun(U_11630,tc_HOL_Obool))))),U_11631) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_11630,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11630),U_11632),U_11631)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_11630),hAPP(hAPP(c_Set_Oinsert(U_11630),U_11633),c_Orderings_Obot__class_Obot(tc_fun(U_11630,tc_HOL_Obool)))),U_11631))
| ~ hBOOL(hAPP(hAPP(c_member(U_11630),U_11633),U_11632))
| ~ c_Fun_Oinj__on(U_11630,tc_fun(tc_fun(U_11630,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_11630,tc_fun(tc_prod(U_11630,U_11630),tc_HOL_Obool),tc_fun(tc_fun(U_11630,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11630,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_11630,U_11630),tc_HOL_Obool),tc_fun(tc_fun(U_11630,tc_HOL_Obool),tc_HOL_Obool)),U_11630),c_Equiv__Relations_Oquotient(U_11630)),hAPP(hAPP(c_COMBC(U_11630,tc_fun(U_11630,tc_HOL_Obool),tc_fun(U_11630,tc_HOL_Obool)),c_Set_Oinsert(U_11630)),c_Orderings_Obot__class_Obot(tc_fun(U_11630,tc_HOL_Obool))))),U_11631),U_11632) ),
inference(clausify,[status(thm)],[f_3081_2]) ).
fof(f_3082_1,plain,
! [V_A_H_2,T_c,T_b,V_A_2] :
( ( ( ? [B_f] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_A_H_2))
& c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) )
| ! [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) != V_A_2 )
& ( ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2
| ! [B_f] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_A_H_2))
| ~ c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2) ) ) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__iff__surj]) ).
fof(f_3082_2,plain,
! [U_11641,U_11640,U_11639,U_11638] :
( ( ( ? [U_11637] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11640,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11639,U_11640,U_11637),U_11638)),U_11641))
& c_Fun_Oinj__on(U_11639,U_11640,U_11637,U_11638) )
| ! [U_11636] : hAPP(c_Set_Oimage(U_11640,U_11639,U_11636),U_11641) != U_11638 )
& ( ? [U_11635] : hAPP(c_Set_Oimage(U_11640,U_11639,U_11635),U_11641) = U_11638
| ! [U_11634] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11640,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11639,U_11640,U_11634),U_11638)),U_11641))
| ~ c_Fun_Oinj__on(U_11639,U_11640,U_11634,U_11638) ) ) )
| U_11638 = c_Orderings_Obot__class_Obot(tc_fun(U_11639,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_3082_1]) ).
fof(f_3082_3,plain,
! [U_11641,U_11640,U_11639,U_11638] :
( ( ( ? [U_11637] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11640,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11639,U_11640,U_11637),U_11638)),U_11641))
& c_Fun_Oinj__on(U_11639,U_11640,U_11637,U_11638) )
| ! [U_11636] : hAPP(c_Set_Oimage(U_11640,U_11639,U_11636),U_11641) != U_11638 )
& ( hAPP(c_Set_Oimage(U_11640,U_11639,sK255(U_11641,U_11640,U_11639,U_11638)),U_11641) = U_11638
| ! [U_11634] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11640,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11639,U_11640,U_11634),U_11638)),U_11641))
| ~ c_Fun_Oinj__on(U_11639,U_11640,U_11634,U_11638) ) ) )
| U_11638 = c_Orderings_Obot__class_Obot(tc_fun(U_11639,tc_HOL_Obool)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK255]),skolemize(U_11635,sK255(U_11641,U_11640,U_11639,U_11638))],[f_3082_2]) ).
fof(f_3082_4,plain,
! [U_11641,U_11640,U_11639,U_11638] :
( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11640,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11639,U_11640,sK256(U_11641,U_11640,U_11639,U_11638)),U_11638)),U_11641))
& c_Fun_Oinj__on(U_11639,U_11640,sK256(U_11641,U_11640,U_11639,U_11638),U_11638) )
| ! [U_11636] : hAPP(c_Set_Oimage(U_11640,U_11639,U_11636),U_11641) != U_11638 )
& ( hAPP(c_Set_Oimage(U_11640,U_11639,sK255(U_11641,U_11640,U_11639,U_11638)),U_11641) = U_11638
| ! [U_11634] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11640,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11639,U_11640,U_11634),U_11638)),U_11641))
| ~ c_Fun_Oinj__on(U_11639,U_11640,U_11634,U_11638) ) ) )
| U_11638 = c_Orderings_Obot__class_Obot(tc_fun(U_11639,tc_HOL_Obool)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK256]),skolemize(U_11637,sK256(U_11641,U_11640,U_11639,U_11638))],[f_3082_3]) ).
cnf(f_3082_5,plain,
( hAPP(c_Set_Oimage(U_11640,U_11639,sK255(U_11641,U_11640,U_11639,U_11638)),U_11641) = U_11638
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11640,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11639,U_11640,U_11634),U_11638)),U_11641))
| ~ c_Fun_Oinj__on(U_11639,U_11640,U_11634,U_11638)
| U_11638 = c_Orderings_Obot__class_Obot(tc_fun(U_11639,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3082_4]) ).
cnf(f_3082_6,plain,
( c_Fun_Oinj__on(U_11639,U_11640,sK256(U_11641,U_11640,U_11639,U_11638),U_11638)
| hAPP(c_Set_Oimage(U_11640,U_11639,U_11636),U_11641) != U_11638
| U_11638 = c_Orderings_Obot__class_Obot(tc_fun(U_11639,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3082_4]) ).
cnf(f_3082_7,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11640,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11639,U_11640,sK256(U_11641,U_11640,U_11639,U_11638)),U_11638)),U_11641))
| hAPP(c_Set_Oimage(U_11640,U_11639,U_11636),U_11641) != U_11638
| U_11638 = c_Orderings_Obot__class_Obot(tc_fun(U_11639,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3082_4]) ).
fof(f_3083_1,plain,
! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2))
& hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2)) )
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2) ),
inference(fof_nnf,[status(thm)],[fact_image__INT]) ).
fof(f_3083_2,plain,
! [U_11650,U_11649,U_11648,U_11647,U_11646,U_11645,U_11644,U_11643] :
( hAPP(c_Set_Oimage(U_11643,U_11644,U_11645),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11647,tc_fun(U_11643,tc_HOL_Obool)),U_11648),U_11649)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11647,tc_fun(U_11644,tc_HOL_Obool)),U_11648),hAPP(hAPP(c_COMBB(tc_fun(U_11643,tc_HOL_Obool),tc_fun(U_11644,tc_HOL_Obool),U_11647),c_Set_Oimage(U_11643,U_11644,U_11645)),U_11649))
| ~ hBOOL(hAPP(hAPP(c_member(U_11647),U_11650),U_11648))
| ? [U_11642] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11643,tc_HOL_Obool)),hAPP(U_11649,U_11642)),U_11646))
& hBOOL(hAPP(hAPP(c_member(U_11647),U_11642),U_11648)) )
| ~ c_Fun_Oinj__on(U_11643,U_11644,U_11645,U_11646) ),
inference(variable_rename,[status(thm)],[f_3083_1]) ).
fof(f_3083_3,plain,
! [U_11650,U_11649,U_11648,U_11647,U_11646,U_11645,U_11644,U_11643] :
( hAPP(c_Set_Oimage(U_11643,U_11644,U_11645),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11647,tc_fun(U_11643,tc_HOL_Obool)),U_11648),U_11649)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11647,tc_fun(U_11644,tc_HOL_Obool)),U_11648),hAPP(hAPP(c_COMBB(tc_fun(U_11643,tc_HOL_Obool),tc_fun(U_11644,tc_HOL_Obool),U_11647),c_Set_Oimage(U_11643,U_11644,U_11645)),U_11649))
| ~ hBOOL(hAPP(hAPP(c_member(U_11647),U_11650),U_11648))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11643,tc_HOL_Obool)),hAPP(U_11649,sK257(U_11650,U_11649,U_11648,U_11647,U_11646,U_11645,U_11644,U_11643))),U_11646))
& hBOOL(hAPP(hAPP(c_member(U_11647),sK257(U_11650,U_11649,U_11648,U_11647,U_11646,U_11645,U_11644,U_11643)),U_11648)) )
| ~ c_Fun_Oinj__on(U_11643,U_11644,U_11645,U_11646) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK257]),skolemize(U_11642,sK257(U_11650,U_11649,U_11648,U_11647,U_11646,U_11645,U_11644,U_11643))],[f_3083_2]) ).
cnf(f_3083_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11647),sK257(U_11650,U_11649,U_11648,U_11647,U_11646,U_11645,U_11644,U_11643)),U_11648))
| hAPP(c_Set_Oimage(U_11643,U_11644,U_11645),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11647,tc_fun(U_11643,tc_HOL_Obool)),U_11648),U_11649)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11647,tc_fun(U_11644,tc_HOL_Obool)),U_11648),hAPP(hAPP(c_COMBB(tc_fun(U_11643,tc_HOL_Obool),tc_fun(U_11644,tc_HOL_Obool),U_11647),c_Set_Oimage(U_11643,U_11644,U_11645)),U_11649))
| ~ hBOOL(hAPP(hAPP(c_member(U_11647),U_11650),U_11648))
| ~ c_Fun_Oinj__on(U_11643,U_11644,U_11645,U_11646) ),
inference(clausify,[status(thm)],[f_3083_3]) ).
cnf(f_3083_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11643,tc_HOL_Obool)),hAPP(U_11649,sK257(U_11650,U_11649,U_11648,U_11647,U_11646,U_11645,U_11644,U_11643))),U_11646))
| hAPP(c_Set_Oimage(U_11643,U_11644,U_11645),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11647,tc_fun(U_11643,tc_HOL_Obool)),U_11648),U_11649)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11647,tc_fun(U_11644,tc_HOL_Obool)),U_11648),hAPP(hAPP(c_COMBB(tc_fun(U_11643,tc_HOL_Obool),tc_fun(U_11644,tc_HOL_Obool),U_11647),c_Set_Oimage(U_11643,U_11644,U_11645)),U_11649))
| ~ hBOOL(hAPP(hAPP(c_member(U_11647),U_11650),U_11648))
| ~ c_Fun_Oinj__on(U_11643,U_11644,U_11645,U_11646) ),
inference(clausify,[status(thm)],[f_3083_3]) ).
fof(f_3084_1,plain,
! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2)),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_the__inv__into__into]) ).
fof(f_3084_2,plain,
! [U_11656,U_11655,U_11654,U_11653,U_11652,U_11651] :
( hBOOL(hAPP(hAPP(c_member(U_11651),hAPP(c_Fun_Othe__inv__into(U_11651,U_11652,U_11654,U_11653),U_11655)),U_11656))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11651,tc_HOL_Obool)),U_11654),U_11656))
| ~ hBOOL(hAPP(hAPP(c_member(U_11652),U_11655),hAPP(c_Set_Oimage(U_11651,U_11652,U_11653),U_11654)))
| ~ c_Fun_Oinj__on(U_11651,U_11652,U_11653,U_11654) ),
inference(variable_rename,[status(thm)],[f_3084_1]) ).
cnf(f_3084_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_11651),hAPP(c_Fun_Othe__inv__into(U_11651,U_11652,U_11654,U_11653),U_11655)),U_11656))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11651,tc_HOL_Obool)),U_11654),U_11656))
| ~ hBOOL(hAPP(hAPP(c_member(U_11652),U_11655),hAPP(c_Set_Oimage(U_11651,U_11652,U_11653),U_11654)))
| ~ c_Fun_Oinj__on(U_11651,U_11652,U_11653,U_11654) ),
inference(clausify,[status(thm)],[f_3084_2]) ).
fof(f_3085_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_3085_2,plain,
! [U_11657] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_11657),
inference(variable_rename,[status(thm)],[f_3085_1]) ).
cnf(f_3085_3,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_11657),
inference(clausify,[status(thm)],[f_3085_2]) ).
fof(f_3086_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_3086_2,plain,
! [U_11659,U_11658] : 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_11658),U_11659),
inference(variable_rename,[status(thm)],[f_3086_1]) ).
cnf(f_3086_3,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_11658),U_11659),
inference(clausify,[status(thm)],[f_3086_2]) ).
fof(f_3087_1,plain,
! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(tc_prod(T_b,T_c),tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_c,T_b)),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))),V_A_2),
inference(fof_nnf,[status(thm)],[fact_swap__inj__on]) ).
fof(f_3087_2,plain,
! [U_11662,U_11661,U_11660] : c_Fun_Oinj__on(tc_prod(U_11660,U_11661),tc_prod(U_11661,U_11660),hAPP(c_Product__Type_Oprod_Oprod__case(U_11660,U_11661,tc_prod(U_11661,U_11660)),hAPP(c_COMBC(U_11661,U_11660,tc_prod(U_11661,U_11660)),c_Product__Type_OPair(U_11661,U_11660))),U_11662),
inference(variable_rename,[status(thm)],[f_3087_1]) ).
cnf(f_3087_3,plain,
c_Fun_Oinj__on(tc_prod(U_11660,U_11661),tc_prod(U_11661,U_11660),hAPP(c_Product__Type_Oprod_Oprod__case(U_11660,U_11661,tc_prod(U_11661,U_11660)),hAPP(c_COMBC(U_11661,U_11660,tc_prod(U_11661,U_11660)),c_Product__Type_OPair(U_11661,U_11660))),U_11662),
inference(clausify,[status(thm)],[f_3087_2]) ).
fof(f_3088_1,plain,
! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| hAPP(V_f_2,V_x_2) != V_y_2
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__eq]) ).
fof(f_3088_2,plain,
! [U_11668,U_11667,U_11666,U_11665,U_11664,U_11663] :
( hAPP(c_Fun_Othe__inv__into(U_11663,U_11664,U_11666,U_11665),U_11668) = U_11667
| ~ hBOOL(hAPP(hAPP(c_member(U_11663),U_11667),U_11666))
| hAPP(U_11665,U_11667) != U_11668
| ~ c_Fun_Oinj__on(U_11663,U_11664,U_11665,U_11666) ),
inference(variable_rename,[status(thm)],[f_3088_1]) ).
cnf(f_3088_3,plain,
( hAPP(c_Fun_Othe__inv__into(U_11663,U_11664,U_11666,U_11665),U_11668) = U_11667
| ~ hBOOL(hAPP(hAPP(c_member(U_11663),U_11667),U_11666))
| hAPP(U_11665,U_11667) != U_11668
| ~ c_Fun_Oinj__on(U_11663,U_11664,U_11665,U_11666) ),
inference(clausify,[status(thm)],[f_3088_2]) ).
fof(f_3089_1,plain,
! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
( hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__f]) ).
fof(f_3089_2,plain,
! [U_11673,U_11672,U_11671,U_11670,U_11669] :
( hAPP(c_Fun_Othe__inv__into(U_11669,U_11670,U_11672,U_11671),hAPP(U_11671,U_11673)) = U_11673
| ~ hBOOL(hAPP(hAPP(c_member(U_11669),U_11673),U_11672))
| ~ c_Fun_Oinj__on(U_11669,U_11670,U_11671,U_11672) ),
inference(variable_rename,[status(thm)],[f_3089_1]) ).
cnf(f_3089_3,plain,
( hAPP(c_Fun_Othe__inv__into(U_11669,U_11670,U_11672,U_11671),hAPP(U_11671,U_11673)) = U_11673
| ~ hBOOL(hAPP(hAPP(c_member(U_11669),U_11673),U_11672))
| ~ c_Fun_Oinj__on(U_11669,U_11670,U_11671,U_11672) ),
inference(clausify,[status(thm)],[f_3089_2]) ).
fof(f_3090_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__the__inv__into]) ).
fof(f_3090_2,plain,
! [U_11677,U_11676,U_11675,U_11674] :
( c_Fun_Oinj__on(U_11675,U_11674,c_Fun_Othe__inv__into(U_11674,U_11675,U_11677,U_11676),hAPP(c_Set_Oimage(U_11674,U_11675,U_11676),U_11677))
| ~ c_Fun_Oinj__on(U_11674,U_11675,U_11676,U_11677) ),
inference(variable_rename,[status(thm)],[f_3090_1]) ).
cnf(f_3090_3,plain,
( c_Fun_Oinj__on(U_11675,U_11674,c_Fun_Othe__inv__into(U_11674,U_11675,U_11677,U_11676),hAPP(c_Set_Oimage(U_11674,U_11675,U_11676),U_11677))
| ~ c_Fun_Oinj__on(U_11674,U_11675,U_11676,U_11677) ),
inference(clausify,[status(thm)],[f_3090_2]) ).
fof(f_3091_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( hAPP(c_Set_Oimage(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_the__inv__into__onto]) ).
fof(f_3091_2,plain,
! [U_11681,U_11680,U_11679,U_11678] :
( hAPP(c_Set_Oimage(U_11679,U_11678,c_Fun_Othe__inv__into(U_11678,U_11679,U_11681,U_11680)),hAPP(c_Set_Oimage(U_11678,U_11679,U_11680),U_11681)) = U_11681
| ~ c_Fun_Oinj__on(U_11678,U_11679,U_11680,U_11681) ),
inference(variable_rename,[status(thm)],[f_3091_1]) ).
cnf(f_3091_3,plain,
( hAPP(c_Set_Oimage(U_11679,U_11678,c_Fun_Othe__inv__into(U_11678,U_11679,U_11681,U_11680)),hAPP(c_Set_Oimage(U_11678,U_11679,U_11680),U_11681)) = U_11681
| ~ c_Fun_Oinj__on(U_11678,U_11679,U_11680,U_11681) ),
inference(clausify,[status(thm)],[f_3091_2]) ).
fof(f_3092_1,plain,
! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))),
inference(fof_nnf,[status(thm)],[fact_the__inv__into__def]) ).
fof(f_3092_2,plain,
! [U_11686,U_11685,U_11684,U_11683,U_11682] : hAPP(c_Fun_Othe__inv__into(U_11682,U_11683,U_11684,U_11685),U_11686) = c_HOL_OThe(U_11682,hAPP(hAPP(c_COMBS(U_11682,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11682),c_fconj),hAPP(hAPP(c_COMBC(U_11682,tc_fun(U_11682,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11682)),U_11684))),hAPP(hAPP(c_COMBC(U_11682,U_11683,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_11683,tc_fun(U_11683,tc_HOL_Obool),U_11682),c_fequal),U_11685)),U_11686))),
inference(variable_rename,[status(thm)],[f_3092_1]) ).
cnf(f_3092_3,plain,
hAPP(c_Fun_Othe__inv__into(U_11682,U_11683,U_11684,U_11685),U_11686) = c_HOL_OThe(U_11682,hAPP(hAPP(c_COMBS(U_11682,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11682),c_fconj),hAPP(hAPP(c_COMBC(U_11682,tc_fun(U_11682,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11682)),U_11684))),hAPP(hAPP(c_COMBC(U_11682,U_11683,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_11683,tc_fun(U_11683,tc_HOL_Obool),U_11682),c_fequal),U_11685)),U_11686))),
inference(clausify,[status(thm)],[f_3092_2]) ).
fof(f_3093_1,plain,
! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
( hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)) = V_y_2
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_f__the__inv__into__f]) ).
fof(f_3093_2,plain,
! [U_11691,U_11690,U_11689,U_11688,U_11687] :
( hAPP(U_11689,hAPP(c_Fun_Othe__inv__into(U_11687,U_11688,U_11690,U_11689),U_11691)) = U_11691
| ~ hBOOL(hAPP(hAPP(c_member(U_11688),U_11691),hAPP(c_Set_Oimage(U_11687,U_11688,U_11689),U_11690)))
| ~ c_Fun_Oinj__on(U_11687,U_11688,U_11689,U_11690) ),
inference(variable_rename,[status(thm)],[f_3093_1]) ).
cnf(f_3093_3,plain,
( hAPP(U_11689,hAPP(c_Fun_Othe__inv__into(U_11687,U_11688,U_11690,U_11689),U_11691)) = U_11691
| ~ hBOOL(hAPP(hAPP(c_member(U_11688),U_11691),hAPP(c_Set_Oimage(U_11687,U_11688,U_11689),U_11690)))
| ~ c_Fun_Oinj__on(U_11687,U_11688,U_11689,U_11690) ),
inference(clausify,[status(thm)],[f_3093_2]) ).
fof(f_3094_1,plain,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold__Un__disjoint]) ).
fof(f_3094_2,plain,
! [U_11696,U_11695,U_11694,U_11693,U_11692] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11692,U_11693,c_Groups_Otimes__class_Otimes(U_11692)),U_11696),c_Groups_Oone__class_Oone(U_11692)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11693,tc_HOL_Obool)),U_11694),U_11695)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11692),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11692,U_11693,c_Groups_Otimes__class_Otimes(U_11692)),U_11696),c_Groups_Oone__class_Oone(U_11692)),U_11694)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11692,U_11693,c_Groups_Otimes__class_Otimes(U_11692)),U_11696),c_Groups_Oone__class_Oone(U_11692)),U_11695))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11693,tc_HOL_Obool)),U_11694),U_11695) != c_Orderings_Obot__class_Obot(tc_fun(U_11693,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11693),U_11695))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11693),U_11694))
| ~ class_Groups_Ocomm__monoid__mult(U_11692) ),
inference(variable_rename,[status(thm)],[f_3094_1]) ).
cnf(f_3094_3,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11692,U_11693,c_Groups_Otimes__class_Otimes(U_11692)),U_11696),c_Groups_Oone__class_Oone(U_11692)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11693,tc_HOL_Obool)),U_11694),U_11695)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11692),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11692,U_11693,c_Groups_Otimes__class_Otimes(U_11692)),U_11696),c_Groups_Oone__class_Oone(U_11692)),U_11694)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11692,U_11693,c_Groups_Otimes__class_Otimes(U_11692)),U_11696),c_Groups_Oone__class_Oone(U_11692)),U_11695))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11693,tc_HOL_Obool)),U_11694),U_11695) != c_Orderings_Obot__class_Obot(tc_fun(U_11693,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11693),U_11695))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11693),U_11694))
| ~ class_Groups_Ocomm__monoid__mult(U_11692) ),
inference(clausify,[status(thm)],[f_3094_2]) ).
fof(f_3095_1,plain,
! [V_N_2,V_h_2,T_b] :
( hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ohom__commute]) ).
fof(f_3095_2,plain,
! [U_11701,U_11700,U_11699] :
( hAPP(U_11700,c_Big__Operators_Olattice__class_OInf__fin(U_11699,U_11701)) = c_Big__Operators_Olattice__class_OInf__fin(U_11699,hAPP(c_Set_Oimage(U_11699,U_11699,U_11700),U_11701))
| U_11701 = c_Orderings_Obot__class_Obot(tc_fun(U_11699,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11699),U_11701))
| ? [U_11698,U_11697] : hAPP(U_11700,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11699),U_11698),U_11697)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11699),hAPP(U_11700,U_11698)),hAPP(U_11700,U_11697))
| ~ class_Lattices_Olattice(U_11699) ),
inference(variable_rename,[status(thm)],[f_3095_1]) ).
fof(f_3095_3,plain,
! [U_11701,U_11700,U_11699] :
( hAPP(U_11700,c_Big__Operators_Olattice__class_OInf__fin(U_11699,U_11701)) = c_Big__Operators_Olattice__class_OInf__fin(U_11699,hAPP(c_Set_Oimage(U_11699,U_11699,U_11700),U_11701))
| U_11701 = c_Orderings_Obot__class_Obot(tc_fun(U_11699,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11699),U_11701))
| ? [U_11697] : hAPP(U_11700,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11699),sK258(U_11701,U_11700,U_11699)),U_11697)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11699),hAPP(U_11700,sK258(U_11701,U_11700,U_11699))),hAPP(U_11700,U_11697))
| ~ class_Lattices_Olattice(U_11699) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK258]),skolemize(U_11698,sK258(U_11701,U_11700,U_11699))],[f_3095_2]) ).
fof(f_3095_4,plain,
! [U_11701,U_11700,U_11699] :
( hAPP(U_11700,c_Big__Operators_Olattice__class_OInf__fin(U_11699,U_11701)) = c_Big__Operators_Olattice__class_OInf__fin(U_11699,hAPP(c_Set_Oimage(U_11699,U_11699,U_11700),U_11701))
| U_11701 = c_Orderings_Obot__class_Obot(tc_fun(U_11699,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11699),U_11701))
| hAPP(U_11700,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11699),sK258(U_11701,U_11700,U_11699)),sK259(U_11701,U_11700,U_11699))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11699),hAPP(U_11700,sK258(U_11701,U_11700,U_11699))),hAPP(U_11700,sK259(U_11701,U_11700,U_11699)))
| ~ class_Lattices_Olattice(U_11699) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK259]),skolemize(U_11697,sK259(U_11701,U_11700,U_11699))],[f_3095_3]) ).
cnf(f_3095_5,plain,
( hAPP(U_11700,c_Big__Operators_Olattice__class_OInf__fin(U_11699,U_11701)) = c_Big__Operators_Olattice__class_OInf__fin(U_11699,hAPP(c_Set_Oimage(U_11699,U_11699,U_11700),U_11701))
| U_11701 = c_Orderings_Obot__class_Obot(tc_fun(U_11699,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11699),U_11701))
| hAPP(U_11700,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11699),sK258(U_11701,U_11700,U_11699)),sK259(U_11701,U_11700,U_11699))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11699),hAPP(U_11700,sK258(U_11701,U_11700,U_11699))),hAPP(U_11700,sK259(U_11701,U_11700,U_11699)))
| ~ class_Lattices_Olattice(U_11699) ),
inference(clausify,[status(thm)],[f_3095_4]) ).
fof(f_3096_1,plain,
! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_g_2),V_B_2)
| ? [B_x] :
( hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) )
| ~ c_Nat__Transfer_Onat__set(V_B_2)
| V_A_2 != V_B_2
| ~ class_Groups_Ocomm__monoid__mult(T_b)
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod__cong_I2_J]) ).
fof(f_3096_2,plain,
! [U_11707,U_11706,U_11705,U_11704,U_11703] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11703),U_11706),U_11704) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11703),U_11707),U_11705)
| ? [U_11702] :
( hAPP(U_11706,U_11702) != hAPP(U_11707,U_11702)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11702)) )
| ~ c_Nat__Transfer_Onat__set(U_11705)
| U_11704 != U_11705
| ~ class_Groups_Ocomm__monoid__mult(U_11703)
| ~ class_Groups_Ocomm__monoid__add(U_11703) ),
inference(variable_rename,[status(thm)],[f_3096_1]) ).
fof(f_3096_3,plain,
! [U_11707,U_11706,U_11705,U_11704,U_11703] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11703),U_11706),U_11704) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11703),U_11707),U_11705)
| ( hAPP(U_11706,sK260(U_11707,U_11706,U_11705,U_11704,U_11703)) != hAPP(U_11707,sK260(U_11707,U_11706,U_11705,U_11704,U_11703))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK260(U_11707,U_11706,U_11705,U_11704,U_11703))) )
| ~ c_Nat__Transfer_Onat__set(U_11705)
| U_11704 != U_11705
| ~ class_Groups_Ocomm__monoid__mult(U_11703)
| ~ class_Groups_Ocomm__monoid__add(U_11703) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK260]),skolemize(U_11702,sK260(U_11707,U_11706,U_11705,U_11704,U_11703))],[f_3096_2]) ).
cnf(f_3096_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK260(U_11707,U_11706,U_11705,U_11704,U_11703)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11703),U_11706),U_11704) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11703),U_11707),U_11705)
| ~ c_Nat__Transfer_Onat__set(U_11705)
| U_11704 != U_11705
| ~ class_Groups_Ocomm__monoid__mult(U_11703)
| ~ class_Groups_Ocomm__monoid__add(U_11703) ),
inference(clausify,[status(thm)],[f_3096_3]) ).
cnf(f_3096_5,plain,
( hAPP(U_11706,sK260(U_11707,U_11706,U_11705,U_11704,U_11703)) != hAPP(U_11707,sK260(U_11707,U_11706,U_11705,U_11704,U_11703))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11703),U_11706),U_11704) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_11703),U_11707),U_11705)
| ~ c_Nat__Transfer_Onat__set(U_11705)
| U_11704 != U_11705
| ~ class_Groups_Ocomm__monoid__mult(U_11703)
| ~ class_Groups_Ocomm__monoid__add(U_11703) ),
inference(clausify,[status(thm)],[f_3096_3]) ).
fof(f_3097_1,plain,
! [V_z_2,V_g_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2,
inference(fof_nnf,[status(thm)],[fact_fold__image__empty]) ).
fof(f_3097_2,plain,
! [U_11712,U_11711,U_11710,U_11709,U_11708] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11708,U_11709,U_11710),U_11711),U_11712),c_Orderings_Obot__class_Obot(tc_fun(U_11709,tc_HOL_Obool))) = U_11712,
inference(variable_rename,[status(thm)],[f_3097_1]) ).
cnf(f_3097_3,plain,
hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11708,U_11709,U_11710),U_11711),U_11712),c_Orderings_Obot__class_Obot(tc_fun(U_11709,tc_HOL_Obool))) = U_11712,
inference(clausify,[status(thm)],[f_3097_2]) ).
fof(f_3098_1,plain,
! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oeq__fold__g]) ).
fof(f_3098_2,plain,
! [U_11719,U_11718,U_11717,U_11716,U_11715,U_11714,U_11713] :
( hAPP(U_11718,U_11719) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11713,U_11714,U_11715),U_11717),U_11716),U_11719)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11714),U_11719))
| ~ c_Finite__Set_Ofolding__image__simple(U_11713,U_11714,U_11715,U_11716,U_11717,U_11718) ),
inference(variable_rename,[status(thm)],[f_3098_1]) ).
cnf(f_3098_3,plain,
( hAPP(U_11718,U_11719) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11713,U_11714,U_11715),U_11717),U_11716),U_11719)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11714),U_11719))
| ~ c_Finite__Set_Ofolding__image__simple(U_11713,U_11714,U_11715,U_11716,U_11717,U_11718) ),
inference(clausify,[status(thm)],[f_3098_2]) ).
fof(f_3099_1,plain,
! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),c_Groups_Oone__class_Oone(T_c)),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold__image__distrib]) ).
fof(f_3099_2,plain,
! [U_11724,U_11723,U_11722,U_11721,U_11720] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11720,U_11721,c_Groups_Otimes__class_Otimes(U_11720)),hAPP(hAPP(c_COMBS(U_11721,U_11720,U_11720),hAPP(hAPP(c_COMBB(U_11720,tc_fun(U_11720,U_11720),U_11721),c_Groups_Otimes__class_Otimes(U_11720)),U_11723)),U_11724)),c_Groups_Oone__class_Oone(U_11720)),U_11722) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11720),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11720,U_11721,c_Groups_Otimes__class_Otimes(U_11720)),U_11723),c_Groups_Oone__class_Oone(U_11720)),U_11722)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11720,U_11721,c_Groups_Otimes__class_Otimes(U_11720)),U_11724),c_Groups_Oone__class_Oone(U_11720)),U_11722))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11721),U_11722))
| ~ class_Groups_Ocomm__monoid__mult(U_11720) ),
inference(variable_rename,[status(thm)],[f_3099_1]) ).
cnf(f_3099_3,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11720,U_11721,c_Groups_Otimes__class_Otimes(U_11720)),hAPP(hAPP(c_COMBS(U_11721,U_11720,U_11720),hAPP(hAPP(c_COMBB(U_11720,tc_fun(U_11720,U_11720),U_11721),c_Groups_Otimes__class_Otimes(U_11720)),U_11723)),U_11724)),c_Groups_Oone__class_Oone(U_11720)),U_11722) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11720),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11720,U_11721,c_Groups_Otimes__class_Otimes(U_11720)),U_11723),c_Groups_Oone__class_Oone(U_11720)),U_11722)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11720,U_11721,c_Groups_Otimes__class_Otimes(U_11720)),U_11724),c_Groups_Oone__class_Oone(U_11720)),U_11722))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11721),U_11722))
| ~ class_Groups_Ocomm__monoid__mult(U_11720) ),
inference(clausify,[status(thm)],[f_3099_2]) ).
fof(f_3100_1,plain,
! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Oab__semigroup__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold__image__insert]) ).
fof(f_3100_2,plain,
! [U_11730,U_11729,U_11728,U_11727,U_11726,U_11725] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11725,U_11726,c_Groups_Otimes__class_Otimes(U_11725)),U_11729),U_11730),hAPP(hAPP(c_Set_Oinsert(U_11726),U_11728),U_11727)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11725),hAPP(U_11729,U_11728)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11725,U_11726,c_Groups_Otimes__class_Otimes(U_11725)),U_11729),U_11730),U_11727))
| hBOOL(hAPP(hAPP(c_member(U_11726),U_11728),U_11727))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11726),U_11727))
| ~ class_Groups_Oab__semigroup__mult(U_11725) ),
inference(variable_rename,[status(thm)],[f_3100_1]) ).
cnf(f_3100_3,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11725,U_11726,c_Groups_Otimes__class_Otimes(U_11725)),U_11729),U_11730),hAPP(hAPP(c_Set_Oinsert(U_11726),U_11728),U_11727)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11725),hAPP(U_11729,U_11728)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11725,U_11726,c_Groups_Otimes__class_Otimes(U_11725)),U_11729),U_11730),U_11727))
| hBOOL(hAPP(hAPP(c_member(U_11726),U_11728),U_11727))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11726),U_11727))
| ~ class_Groups_Oab__semigroup__mult(U_11725) ),
inference(clausify,[status(thm)],[f_3100_2]) ).
fof(f_3101_1,plain,
! [V_g_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Oeq__fold]) ).
fof(f_3101_2,plain,
! [U_11734,U_11733,U_11732,U_11731] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11732,U_11731),U_11734),U_11733) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11731,U_11732,c_Groups_Oplus__class_Oplus(U_11731)),U_11734),c_Groups_Ozero__class_Ozero(U_11731)),U_11733)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11732),U_11733))
| ~ class_Groups_Ocomm__monoid__add(U_11731) ),
inference(variable_rename,[status(thm)],[f_3101_1]) ).
cnf(f_3101_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11732,U_11731),U_11734),U_11733) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11731,U_11732,c_Groups_Oplus__class_Oplus(U_11731)),U_11734),c_Groups_Ozero__class_Ozero(U_11731)),U_11733)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11732),U_11733))
| ~ class_Groups_Ocomm__monoid__add(U_11731) ),
inference(clausify,[status(thm)],[f_3101_2]) ).
fof(f_3102_1,plain,
! [V_g_2,V_A_2,T_b,T_c] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) )
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum_OF__eq]) ).
fof(f_3102_2,plain,
! [U_11738,U_11737,U_11736,U_11735] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11736,U_11735),U_11738),U_11737) = c_Groups_Ozero__class_Ozero(U_11735)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_11736),U_11737)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11736,U_11735),U_11738),U_11737) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11735,U_11736,c_Groups_Oplus__class_Oplus(U_11735)),U_11738),c_Groups_Ozero__class_Ozero(U_11735)),U_11737)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11736),U_11737)) ) )
| ~ class_Groups_Ocomm__monoid__add(U_11735) ),
inference(variable_rename,[status(thm)],[f_3102_1]) ).
cnf(f_3102_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11736,U_11735),U_11738),U_11737) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11735,U_11736,c_Groups_Oplus__class_Oplus(U_11735)),U_11738),c_Groups_Ozero__class_Ozero(U_11735)),U_11737)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11736),U_11737))
| ~ class_Groups_Ocomm__monoid__add(U_11735) ),
inference(clausify,[status(thm)],[f_3102_2]) ).
cnf(f_3102_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_11736,U_11735),U_11738),U_11737) = c_Groups_Ozero__class_Ozero(U_11735)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_11736),U_11737))
| ~ class_Groups_Ocomm__monoid__add(U_11735) ),
inference(clausify,[status(thm)],[f_3102_2]) ).
fof(f_3103_1,plain,
! [V_g_2,V_A_2,T_b,T_c] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) )
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_OF__eq]) ).
fof(f_3103_2,plain,
! [U_11742,U_11741,U_11740,U_11739] :
( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11740,U_11739),U_11742),U_11741) = c_Groups_Oone__class_Oone(U_11739)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_11740),U_11741)) )
& ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11740,U_11739),U_11742),U_11741) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11739,U_11740,c_Groups_Otimes__class_Otimes(U_11739)),U_11742),c_Groups_Oone__class_Oone(U_11739)),U_11741)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11740),U_11741)) ) )
| ~ class_Groups_Ocomm__monoid__mult(U_11739) ),
inference(variable_rename,[status(thm)],[f_3103_1]) ).
cnf(f_3103_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11740,U_11739),U_11742),U_11741) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11739,U_11740,c_Groups_Otimes__class_Otimes(U_11739)),U_11742),c_Groups_Oone__class_Oone(U_11739)),U_11741)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11740),U_11741))
| ~ class_Groups_Ocomm__monoid__mult(U_11739) ),
inference(clausify,[status(thm)],[f_3103_2]) ).
cnf(f_3103_4,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11740,U_11739),U_11742),U_11741) = c_Groups_Oone__class_Oone(U_11739)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_11740),U_11741))
| ~ class_Groups_Ocomm__monoid__mult(U_11739) ),
inference(clausify,[status(thm)],[f_3103_2]) ).
fof(f_3104_1,plain,
! [V_g_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Oeq__fold]) ).
fof(f_3104_2,plain,
! [U_11746,U_11745,U_11744,U_11743] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11744,U_11743),U_11746),U_11745) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11743,U_11744,c_Groups_Otimes__class_Otimes(U_11743)),U_11746),c_Groups_Oone__class_Oone(U_11743)),U_11745)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11744),U_11745))
| ~ class_Groups_Ocomm__monoid__mult(U_11743) ),
inference(variable_rename,[status(thm)],[f_3104_1]) ).
cnf(f_3104_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11744,U_11743),U_11746),U_11745) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11743,U_11744,c_Groups_Otimes__class_Otimes(U_11743)),U_11746),c_Groups_Oone__class_Oone(U_11743)),U_11745)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11744),U_11745))
| ~ class_Groups_Ocomm__monoid__mult(U_11743) ),
inference(clausify,[status(thm)],[f_3104_2]) ).
fof(f_3105_1,plain,
! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold__image__Un__Int]) ).
fof(f_3105_2,plain,
! [U_11751,U_11750,U_11749,U_11748,U_11747] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11747),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11747,U_11748,c_Groups_Otimes__class_Otimes(U_11747)),U_11751),c_Groups_Oone__class_Oone(U_11747)),U_11749)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11747,U_11748,c_Groups_Otimes__class_Otimes(U_11747)),U_11751),c_Groups_Oone__class_Oone(U_11747)),U_11750)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11747),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11747,U_11748,c_Groups_Otimes__class_Otimes(U_11747)),U_11751),c_Groups_Oone__class_Oone(U_11747)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11748,tc_HOL_Obool)),U_11749),U_11750))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11747,U_11748,c_Groups_Otimes__class_Otimes(U_11747)),U_11751),c_Groups_Oone__class_Oone(U_11747)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11748,tc_HOL_Obool)),U_11749),U_11750)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11748),U_11750))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11748),U_11749))
| ~ class_Groups_Ocomm__monoid__mult(U_11747) ),
inference(variable_rename,[status(thm)],[f_3105_1]) ).
cnf(f_3105_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11747),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11747,U_11748,c_Groups_Otimes__class_Otimes(U_11747)),U_11751),c_Groups_Oone__class_Oone(U_11747)),U_11749)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11747,U_11748,c_Groups_Otimes__class_Otimes(U_11747)),U_11751),c_Groups_Oone__class_Oone(U_11747)),U_11750)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11747),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11747,U_11748,c_Groups_Otimes__class_Otimes(U_11747)),U_11751),c_Groups_Oone__class_Oone(U_11747)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11748,tc_HOL_Obool)),U_11749),U_11750))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11747,U_11748,c_Groups_Otimes__class_Otimes(U_11747)),U_11751),c_Groups_Oone__class_Oone(U_11747)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11748,tc_HOL_Obool)),U_11749),U_11750)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11748),U_11750))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11748),U_11749))
| ~ class_Groups_Ocomm__monoid__mult(U_11747) ),
inference(clausify,[status(thm)],[f_3105_2]) ).
fof(f_3106_1,plain,
! [V_f_2,T_c,V_A_2,T_b] :
( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_c,tc_HOL_Obool),T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_image__eq__fold__image]) ).
fof(f_3106_2,plain,
! [U_11755,U_11754,U_11753,U_11752] :
( hAPP(c_Set_Oimage(U_11752,U_11754,U_11755),U_11753) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_11754,tc_HOL_Obool),U_11752,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11754,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11752,tc_fun(U_11754,tc_HOL_Obool),tc_fun(U_11754,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_11754,tc_fun(tc_fun(U_11754,tc_HOL_Obool),tc_fun(U_11754,tc_HOL_Obool)),U_11752),c_Set_Oinsert(U_11754)),U_11755)),c_Orderings_Obot__class_Obot(tc_fun(U_11754,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_11754,tc_HOL_Obool))),U_11753)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11752),U_11753)) ),
inference(variable_rename,[status(thm)],[f_3106_1]) ).
cnf(f_3106_3,plain,
( hAPP(c_Set_Oimage(U_11752,U_11754,U_11755),U_11753) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_11754,tc_HOL_Obool),U_11752,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11754,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11752,tc_fun(U_11754,tc_HOL_Obool),tc_fun(U_11754,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_11754,tc_fun(tc_fun(U_11754,tc_HOL_Obool),tc_fun(U_11754,tc_HOL_Obool)),U_11752),c_Set_Oinsert(U_11754)),U_11755)),c_Orderings_Obot__class_Obot(tc_fun(U_11754,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_11754,tc_HOL_Obool))),U_11753)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11752),U_11753)) ),
inference(clausify,[status(thm)],[f_3106_2]) ).
fof(f_3107_1,plain,
! [V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card_Oeq__fold__g]) ).
fof(f_3107_2,plain,
! [U_11757,U_11756] :
( hAPP(c_Finite__Set_Ocard(U_11756),U_11757) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_11756,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_11756),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11757)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11756),U_11757)) ),
inference(variable_rename,[status(thm)],[f_3107_1]) ).
cnf(f_3107_3,plain,
( hAPP(c_Finite__Set_Ocard(U_11756),U_11757) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_11756,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_11756),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11757)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11756),U_11757)) ),
inference(clausify,[status(thm)],[f_3107_2]) ).
fof(f_3108_1,plain,
! [V_A_2,T_b] :
( ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
& ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_card__def]) ).
fof(f_3108_2,plain,
! [U_11759,U_11758] :
( ( hAPP(c_Finite__Set_Ocard(U_11758),U_11759) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_11758),U_11759)) )
& ( hAPP(c_Finite__Set_Ocard(U_11758),U_11759) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_11758,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_11758),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11759)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11758),U_11759)) ) ),
inference(variable_rename,[status(thm)],[f_3108_1]) ).
fof(f_3108_3,plain,
( ! [U_11763,U_11761] :
( hAPP(c_Finite__Set_Ocard(U_11761),U_11763) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_11761),U_11763)) )
& ! [U_11762,U_11760] :
( hAPP(c_Finite__Set_Ocard(U_11760),U_11762) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_11760,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_11760),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11762)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11760),U_11762)) ) ),
inference(miniscope,[status(thm)],[f_3108_2]) ).
cnf(f_3108_4,plain,
( hAPP(c_Finite__Set_Ocard(U_11760),U_11762) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_11760,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_11760),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11762)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11760),U_11762)) ),
inference(clausify,[status(thm)],[f_3108_3]) ).
cnf(f_3108_5,plain,
( hAPP(c_Finite__Set_Ocard(U_11761),U_11763) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_11761),U_11763)) ),
inference(clausify,[status(thm)],[f_3108_3]) ).
fof(f_3109_1,plain,
! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( ( ( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) )
& ( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) )
| ~ c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_comm__monoid__big_OF__eq]) ).
fof(f_3109_2,plain,
! [U_11770,U_11769,U_11768,U_11767,U_11766,U_11765,U_11764] :
( ( ( hAPP(hAPP(U_11768,U_11770),U_11769) = U_11767
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_11765),U_11769)) )
& ( hAPP(hAPP(U_11768,U_11770),U_11769) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11764,U_11765,U_11766),U_11770),U_11767),U_11769)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11765),U_11769)) ) )
| ~ c_Big__Operators_Ocomm__monoid__big(U_11764,U_11765,U_11766,U_11767,U_11768) ),
inference(variable_rename,[status(thm)],[f_3109_1]) ).
cnf(f_3109_3,plain,
( hAPP(hAPP(U_11768,U_11770),U_11769) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11764,U_11765,U_11766),U_11770),U_11767),U_11769)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11765),U_11769))
| ~ c_Big__Operators_Ocomm__monoid__big(U_11764,U_11765,U_11766,U_11767,U_11768) ),
inference(clausify,[status(thm)],[f_3109_2]) ).
cnf(f_3109_4,plain,
( hAPP(hAPP(U_11768,U_11770),U_11769) = U_11767
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_11765),U_11769))
| ~ c_Big__Operators_Ocomm__monoid__big(U_11764,U_11765,U_11766,U_11767,U_11768) ),
inference(clausify,[status(thm)],[f_3109_2]) ).
fof(f_3110_1,plain,
! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_T_2))
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_c)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold__image__Un__one]) ).
fof(f_3110_2,plain,
! [U_11776,U_11775,U_11774,U_11773,U_11772] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11772,U_11773,c_Groups_Otimes__class_Otimes(U_11772)),U_11776),c_Groups_Oone__class_Oone(U_11772)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11773,tc_HOL_Obool)),U_11774),U_11775)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11772),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11772,U_11773,c_Groups_Otimes__class_Otimes(U_11772)),U_11776),c_Groups_Oone__class_Oone(U_11772)),U_11774)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11772,U_11773,c_Groups_Otimes__class_Otimes(U_11772)),U_11776),c_Groups_Oone__class_Oone(U_11772)),U_11775))
| ? [U_11771] :
( hAPP(U_11776,U_11771) != c_Groups_Oone__class_Oone(U_11772)
& hBOOL(hAPP(hAPP(c_member(U_11773),U_11771),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11773,tc_HOL_Obool)),U_11774),U_11775))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11773),U_11775))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11773),U_11774))
| ~ class_Groups_Ocomm__monoid__mult(U_11772) ),
inference(variable_rename,[status(thm)],[f_3110_1]) ).
fof(f_3110_3,plain,
! [U_11776,U_11775,U_11774,U_11773,U_11772] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11772,U_11773,c_Groups_Otimes__class_Otimes(U_11772)),U_11776),c_Groups_Oone__class_Oone(U_11772)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11773,tc_HOL_Obool)),U_11774),U_11775)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11772),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11772,U_11773,c_Groups_Otimes__class_Otimes(U_11772)),U_11776),c_Groups_Oone__class_Oone(U_11772)),U_11774)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11772,U_11773,c_Groups_Otimes__class_Otimes(U_11772)),U_11776),c_Groups_Oone__class_Oone(U_11772)),U_11775))
| ( hAPP(U_11776,sK261(U_11776,U_11775,U_11774,U_11773,U_11772)) != c_Groups_Oone__class_Oone(U_11772)
& hBOOL(hAPP(hAPP(c_member(U_11773),sK261(U_11776,U_11775,U_11774,U_11773,U_11772)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11773,tc_HOL_Obool)),U_11774),U_11775))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11773),U_11775))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11773),U_11774))
| ~ class_Groups_Ocomm__monoid__mult(U_11772) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK261]),skolemize(U_11771,sK261(U_11776,U_11775,U_11774,U_11773,U_11772))],[f_3110_2]) ).
cnf(f_3110_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11773),sK261(U_11776,U_11775,U_11774,U_11773,U_11772)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11773,tc_HOL_Obool)),U_11774),U_11775)))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11772,U_11773,c_Groups_Otimes__class_Otimes(U_11772)),U_11776),c_Groups_Oone__class_Oone(U_11772)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11773,tc_HOL_Obool)),U_11774),U_11775)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11772),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11772,U_11773,c_Groups_Otimes__class_Otimes(U_11772)),U_11776),c_Groups_Oone__class_Oone(U_11772)),U_11774)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11772,U_11773,c_Groups_Otimes__class_Otimes(U_11772)),U_11776),c_Groups_Oone__class_Oone(U_11772)),U_11775))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11773),U_11775))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11773),U_11774))
| ~ class_Groups_Ocomm__monoid__mult(U_11772) ),
inference(clausify,[status(thm)],[f_3110_3]) ).
cnf(f_3110_5,plain,
( hAPP(U_11776,sK261(U_11776,U_11775,U_11774,U_11773,U_11772)) != c_Groups_Oone__class_Oone(U_11772)
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11772,U_11773,c_Groups_Otimes__class_Otimes(U_11772)),U_11776),c_Groups_Oone__class_Oone(U_11772)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11773,tc_HOL_Obool)),U_11774),U_11775)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11772),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11772,U_11773,c_Groups_Otimes__class_Otimes(U_11772)),U_11776),c_Groups_Oone__class_Oone(U_11772)),U_11774)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11772,U_11773,c_Groups_Otimes__class_Otimes(U_11772)),U_11776),c_Groups_Oone__class_Oone(U_11772)),U_11775))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11773),U_11775))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11773),U_11774))
| ~ class_Groups_Ocomm__monoid__mult(U_11772) ),
inference(clausify,[status(thm)],[f_3110_3]) ).
fof(f_3111_1,plain,
! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_x_2))
| ~ class_Groups_Oab__semigroup__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold__graph__permute__diff]) ).
fof(f_3111_2,plain,
! [U_11781,U_11780,U_11779,U_11778,U_11777] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11777,U_11777,c_Groups_Otimes__class_Otimes(U_11777),U_11781,hAPP(hAPP(c_Set_Oinsert(U_11777),U_11778),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11777,tc_HOL_Obool)),U_11779),hAPP(hAPP(c_Set_Oinsert(U_11777),U_11781),c_Orderings_Obot__class_Obot(tc_fun(U_11777,tc_HOL_Obool)))))),U_11780))
| hBOOL(hAPP(hAPP(c_member(U_11777),U_11778),U_11779))
| ~ hBOOL(hAPP(hAPP(c_member(U_11777),U_11781),U_11779))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11777,U_11777,c_Groups_Otimes__class_Otimes(U_11777),U_11778,U_11779),U_11780))
| ~ class_Groups_Oab__semigroup__mult(U_11777) ),
inference(variable_rename,[status(thm)],[f_3111_1]) ).
cnf(f_3111_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11777,U_11777,c_Groups_Otimes__class_Otimes(U_11777),U_11781,hAPP(hAPP(c_Set_Oinsert(U_11777),U_11778),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11777,tc_HOL_Obool)),U_11779),hAPP(hAPP(c_Set_Oinsert(U_11777),U_11781),c_Orderings_Obot__class_Obot(tc_fun(U_11777,tc_HOL_Obool)))))),U_11780))
| hBOOL(hAPP(hAPP(c_member(U_11777),U_11778),U_11779))
| ~ hBOOL(hAPP(hAPP(c_member(U_11777),U_11781),U_11779))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11777,U_11777,c_Groups_Otimes__class_Otimes(U_11777),U_11778,U_11779),U_11780))
| ~ class_Groups_Oab__semigroup__mult(U_11777) ),
inference(clausify,[status(thm)],[f_3111_2]) ).
fof(f_3112_1,plain,
! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_fold__graph__imp__finite]) ).
fof(f_3112_2,plain,
! [U_11787,U_11786,U_11785,U_11784,U_11783,U_11782] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11782),U_11786))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11782,U_11783,U_11784,U_11785,U_11786),U_11787)) ),
inference(variable_rename,[status(thm)],[f_3112_1]) ).
cnf(f_3112_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11782),U_11786))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11782,U_11783,U_11784,U_11785,U_11786),U_11787)) ),
inference(clausify,[status(thm)],[f_3112_2]) ).
fof(f_3113_1,plain,
! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)),
inference(fof_nnf,[status(thm)],[fact_fold__graph_Oequations_I1_J]) ).
fof(f_3113_2,plain,
! [U_11791,U_11790,U_11789,U_11788] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11788,U_11789,U_11790,U_11791,c_Orderings_Obot__class_Obot(tc_fun(U_11788,tc_HOL_Obool))),U_11791)),
inference(variable_rename,[status(thm)],[f_3113_1]) ).
cnf(f_3113_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11788,U_11789,U_11790,U_11791,c_Orderings_Obot__class_Obot(tc_fun(U_11788,tc_HOL_Obool))),U_11791)),
inference(clausify,[status(thm)],[f_3113_2]) ).
fof(f_3114_1,plain,
! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)),
inference(fof_nnf,[status(thm)],[fact_fold__graph_OemptyI]) ).
fof(f_3114_2,plain,
! [U_11795,U_11794,U_11793,U_11792] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11792,U_11793,U_11794,U_11795,c_Orderings_Obot__class_Obot(tc_fun(U_11792,tc_HOL_Obool))),U_11795)),
inference(variable_rename,[status(thm)],[f_3114_1]) ).
cnf(f_3114_3,plain,
hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11792,U_11793,U_11794,U_11795,c_Orderings_Obot__class_Obot(tc_fun(U_11792,tc_HOL_Obool))),U_11795)),
inference(clausify,[status(thm)],[f_3114_2]) ).
fof(f_3115_1,plain,
! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
( V_x_2 = V_z_2
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_empty__fold__graphE]) ).
fof(f_3115_2,plain,
! [U_11800,U_11799,U_11798,U_11797,U_11796] :
( U_11800 = U_11799
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11796,U_11797,U_11798,U_11799,c_Orderings_Obot__class_Obot(tc_fun(U_11796,tc_HOL_Obool))),U_11800)) ),
inference(variable_rename,[status(thm)],[f_3115_1]) ).
fof(f_3115_3,plain,
! [U_11800,U_11799] :
( ! [U_11798,U_11797,U_11796] : ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11796,U_11797,U_11798,U_11799,c_Orderings_Obot__class_Obot(tc_fun(U_11796,tc_HOL_Obool))),U_11800))
| U_11800 = U_11799 ),
inference(miniscope,[status(thm)],[f_3115_2]) ).
cnf(f_3115_4,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11796,U_11797,U_11798,U_11799,c_Orderings_Obot__class_Obot(tc_fun(U_11796,tc_HOL_Obool))),U_11800))
| U_11800 = U_11799 ),
inference(clausify,[status(thm)],[f_3115_3]) ).
fof(f_3116_1,plain,
! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_fold__graph_OinsertI]) ).
fof(f_3116_2,plain,
! [U_11807,U_11806,U_11805,U_11804,U_11803,U_11802,U_11801] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11801,U_11804,U_11805,U_11806,hAPP(hAPP(c_Set_Oinsert(U_11801),U_11802),U_11803)),hAPP(hAPP(U_11805,U_11802),U_11807)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11801,U_11804,U_11805,U_11806,U_11803),U_11807))
| hBOOL(hAPP(hAPP(c_member(U_11801),U_11802),U_11803)) ),
inference(variable_rename,[status(thm)],[f_3116_1]) ).
cnf(f_3116_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11801,U_11804,U_11805,U_11806,hAPP(hAPP(c_Set_Oinsert(U_11801),U_11802),U_11803)),hAPP(hAPP(U_11805,U_11802),U_11807)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11801,U_11804,U_11805,U_11806,U_11803),U_11807))
| hBOOL(hAPP(hAPP(c_member(U_11801),U_11802),U_11803)) ),
inference(clausify,[status(thm)],[f_3116_2]) ).
fof(f_3117_1,plain,
! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2)))
| hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_y_2))
| ~ class_Groups_Oab__semigroup__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold__graph__insert__swap]) ).
fof(f_3117_2,plain,
! [U_11812,U_11811,U_11810,U_11809,U_11808] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11808,U_11808,c_Groups_Otimes__class_Otimes(U_11808),U_11812,hAPP(hAPP(c_Set_Oinsert(U_11808),U_11809),U_11810)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11808),U_11812),U_11811)))
| hBOOL(hAPP(hAPP(c_member(U_11808),U_11809),U_11810))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11808,U_11808,c_Groups_Otimes__class_Otimes(U_11808),U_11809,U_11810),U_11811))
| ~ class_Groups_Oab__semigroup__mult(U_11808) ),
inference(variable_rename,[status(thm)],[f_3117_1]) ).
cnf(f_3117_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11808,U_11808,c_Groups_Otimes__class_Otimes(U_11808),U_11812,hAPP(hAPP(c_Set_Oinsert(U_11808),U_11809),U_11810)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11808),U_11812),U_11811)))
| hBOOL(hAPP(hAPP(c_member(U_11808),U_11809),U_11810))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11808,U_11808,c_Groups_Otimes__class_Otimes(U_11808),U_11809,U_11810),U_11811))
| ~ class_Groups_Oab__semigroup__mult(U_11808) ),
inference(clausify,[status(thm)],[f_3117_2]) ).
fof(f_3118_1,plain,
! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_comm__monoid__big_Oinfinite]) ).
fof(f_3118_2,plain,
! [U_11819,U_11818,U_11817,U_11816,U_11815,U_11814,U_11813] :
( hAPP(hAPP(U_11817,U_11819),U_11818) = U_11816
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_11814),U_11818))
| ~ c_Big__Operators_Ocomm__monoid__big(U_11813,U_11814,U_11815,U_11816,U_11817) ),
inference(variable_rename,[status(thm)],[f_3118_1]) ).
fof(f_3118_3,plain,
! [U_11819,U_11818,U_11817,U_11816,U_11815,U_11814] :
( ! [U_11813] : ~ c_Big__Operators_Ocomm__monoid__big(U_11813,U_11814,U_11815,U_11816,U_11817)
| hAPP(hAPP(U_11817,U_11819),U_11818) = U_11816
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_11814),U_11818)) ),
inference(miniscope,[status(thm)],[f_3118_2]) ).
cnf(f_3118_4,plain,
( ~ c_Big__Operators_Ocomm__monoid__big(U_11813,U_11814,U_11815,U_11816,U_11817)
| hAPP(hAPP(U_11817,U_11819),U_11818) = U_11816
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_11814),U_11818)) ),
inference(clausify,[status(thm)],[f_3118_3]) ).
fof(f_3119_1,plain,
! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_y_2)) ),
inference(fof_nnf,[status(thm)],[fact_Diff1__fold__graph]) ).
fof(f_3119_2,plain,
! [U_11826,U_11825,U_11824,U_11823,U_11822,U_11821,U_11820] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11820,U_11821,U_11822,U_11823,U_11824),hAPP(hAPP(U_11822,U_11825),U_11826)))
| ~ hBOOL(hAPP(hAPP(c_member(U_11820),U_11825),U_11824))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11820,U_11821,U_11822,U_11823,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11820,tc_HOL_Obool)),U_11824),hAPP(hAPP(c_Set_Oinsert(U_11820),U_11825),c_Orderings_Obot__class_Obot(tc_fun(U_11820,tc_HOL_Obool))))),U_11826)) ),
inference(variable_rename,[status(thm)],[f_3119_1]) ).
cnf(f_3119_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11820,U_11821,U_11822,U_11823,U_11824),hAPP(hAPP(U_11822,U_11825),U_11826)))
| ~ hBOOL(hAPP(hAPP(c_member(U_11820),U_11825),U_11824))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11820,U_11821,U_11822,U_11823,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11820,tc_HOL_Obool)),U_11824),hAPP(hAPP(c_Set_Oinsert(U_11820),U_11825),c_Orderings_Obot__class_Obot(tc_fun(U_11820,tc_HOL_Obool))))),U_11826)) ),
inference(clausify,[status(thm)],[f_3119_2]) ).
fof(f_3120_1,plain,
! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_x_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_fold1Set_Ointros]) ).
fof(f_3120_2,plain,
! [U_11831,U_11830,U_11829,U_11828,U_11827] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_11827,U_11828,hAPP(hAPP(c_Set_Oinsert(U_11827),U_11829),U_11830)),U_11831))
| hBOOL(hAPP(hAPP(c_member(U_11827),U_11829),U_11830))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11827,U_11827,U_11828,U_11829,U_11830),U_11831)) ),
inference(variable_rename,[status(thm)],[f_3120_1]) ).
cnf(f_3120_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_11827,U_11828,hAPP(hAPP(c_Set_Oinsert(U_11827),U_11829),U_11830)),U_11831))
| hBOOL(hAPP(hAPP(c_member(U_11827),U_11829),U_11830))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_11827,U_11827,U_11828,U_11829,U_11830),U_11831)) ),
inference(clausify,[status(thm)],[f_3120_2]) ).
fof(f_3121_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_3121_2,plain,
! [U_11834,U_11833,U_11832] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_11832),U_11833) = U_11834
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11832),U_11833),U_11834) != c_Orderings_Otop__class_Otop(U_11832)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11832),U_11833),U_11834) != c_Orderings_Obot__class_Obot(U_11832)
| ~ class_Lattices_Oboolean__algebra(U_11832) ),
inference(variable_rename,[status(thm)],[f_3121_1]) ).
cnf(f_3121_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_11832),U_11833) = U_11834
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11832),U_11833),U_11834) != c_Orderings_Otop__class_Otop(U_11832)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11832),U_11833),U_11834) != c_Orderings_Obot__class_Obot(U_11832)
| ~ class_Lattices_Oboolean__algebra(U_11832) ),
inference(clausify,[status(thm)],[f_3121_2]) ).
fof(f_3122_1,plain,
! [V_x_2,V_r_2,T_b] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_accp__acc__eq]) ).
fof(f_3122_2,plain,
! [U_11837,U_11836,U_11835] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11835,hAPP(hAPP(c_COMBC(U_11835,tc_fun(tc_prod(U_11835,U_11835),tc_HOL_Obool),tc_fun(U_11835,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11835,tc_fun(tc_fun(tc_prod(U_11835,U_11835),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11835,U_11835),tc_HOL_Obool),tc_fun(U_11835,tc_HOL_Obool)),U_11835),c_COMBC(U_11835,tc_fun(tc_prod(U_11835,U_11835),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11835,tc_prod(U_11835,U_11835)),tc_fun(U_11835,tc_fun(tc_fun(tc_prod(U_11835,U_11835),tc_HOL_Obool),tc_HOL_Obool)),U_11835),hAPP(c_COMBB(tc_prod(U_11835,U_11835),tc_fun(tc_fun(tc_prod(U_11835,U_11835),tc_HOL_Obool),tc_HOL_Obool),U_11835),c_member(tc_prod(U_11835,U_11835)))),c_Product__Type_OPair(U_11835,U_11835)))),U_11836)),U_11837))
| ~ hBOOL(hAPP(hAPP(c_member(U_11835),U_11837),c_Wellfounded_Oacc(U_11835,U_11836))) )
& ( hBOOL(hAPP(hAPP(c_member(U_11835),U_11837),c_Wellfounded_Oacc(U_11835,U_11836)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11835,hAPP(hAPP(c_COMBC(U_11835,tc_fun(tc_prod(U_11835,U_11835),tc_HOL_Obool),tc_fun(U_11835,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11835,tc_fun(tc_fun(tc_prod(U_11835,U_11835),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11835,U_11835),tc_HOL_Obool),tc_fun(U_11835,tc_HOL_Obool)),U_11835),c_COMBC(U_11835,tc_fun(tc_prod(U_11835,U_11835),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11835,tc_prod(U_11835,U_11835)),tc_fun(U_11835,tc_fun(tc_fun(tc_prod(U_11835,U_11835),tc_HOL_Obool),tc_HOL_Obool)),U_11835),hAPP(c_COMBB(tc_prod(U_11835,U_11835),tc_fun(tc_fun(tc_prod(U_11835,U_11835),tc_HOL_Obool),tc_HOL_Obool),U_11835),c_member(tc_prod(U_11835,U_11835)))),c_Product__Type_OPair(U_11835,U_11835)))),U_11836)),U_11837)) ) ),
inference(variable_rename,[status(thm)],[f_3122_1]) ).
fof(f_3122_3,plain,
( ! [U_11843,U_11841,U_11839] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11839,hAPP(hAPP(c_COMBC(U_11839,tc_fun(tc_prod(U_11839,U_11839),tc_HOL_Obool),tc_fun(U_11839,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11839,tc_fun(tc_fun(tc_prod(U_11839,U_11839),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11839,U_11839),tc_HOL_Obool),tc_fun(U_11839,tc_HOL_Obool)),U_11839),c_COMBC(U_11839,tc_fun(tc_prod(U_11839,U_11839),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11839,tc_prod(U_11839,U_11839)),tc_fun(U_11839,tc_fun(tc_fun(tc_prod(U_11839,U_11839),tc_HOL_Obool),tc_HOL_Obool)),U_11839),hAPP(c_COMBB(tc_prod(U_11839,U_11839),tc_fun(tc_fun(tc_prod(U_11839,U_11839),tc_HOL_Obool),tc_HOL_Obool),U_11839),c_member(tc_prod(U_11839,U_11839)))),c_Product__Type_OPair(U_11839,U_11839)))),U_11841)),U_11843))
| ~ hBOOL(hAPP(hAPP(c_member(U_11839),U_11843),c_Wellfounded_Oacc(U_11839,U_11841))) )
& ! [U_11842,U_11840,U_11838] :
( hBOOL(hAPP(hAPP(c_member(U_11838),U_11842),c_Wellfounded_Oacc(U_11838,U_11840)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11838,hAPP(hAPP(c_COMBC(U_11838,tc_fun(tc_prod(U_11838,U_11838),tc_HOL_Obool),tc_fun(U_11838,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11838,tc_fun(tc_fun(tc_prod(U_11838,U_11838),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11838,U_11838),tc_HOL_Obool),tc_fun(U_11838,tc_HOL_Obool)),U_11838),c_COMBC(U_11838,tc_fun(tc_prod(U_11838,U_11838),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11838,tc_prod(U_11838,U_11838)),tc_fun(U_11838,tc_fun(tc_fun(tc_prod(U_11838,U_11838),tc_HOL_Obool),tc_HOL_Obool)),U_11838),hAPP(c_COMBB(tc_prod(U_11838,U_11838),tc_fun(tc_fun(tc_prod(U_11838,U_11838),tc_HOL_Obool),tc_HOL_Obool),U_11838),c_member(tc_prod(U_11838,U_11838)))),c_Product__Type_OPair(U_11838,U_11838)))),U_11840)),U_11842)) ) ),
inference(miniscope,[status(thm)],[f_3122_2]) ).
cnf(f_3122_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11838),U_11842),c_Wellfounded_Oacc(U_11838,U_11840)))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_11838,hAPP(hAPP(c_COMBC(U_11838,tc_fun(tc_prod(U_11838,U_11838),tc_HOL_Obool),tc_fun(U_11838,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11838,tc_fun(tc_fun(tc_prod(U_11838,U_11838),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11838,U_11838),tc_HOL_Obool),tc_fun(U_11838,tc_HOL_Obool)),U_11838),c_COMBC(U_11838,tc_fun(tc_prod(U_11838,U_11838),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11838,tc_prod(U_11838,U_11838)),tc_fun(U_11838,tc_fun(tc_fun(tc_prod(U_11838,U_11838),tc_HOL_Obool),tc_HOL_Obool)),U_11838),hAPP(c_COMBB(tc_prod(U_11838,U_11838),tc_fun(tc_fun(tc_prod(U_11838,U_11838),tc_HOL_Obool),tc_HOL_Obool),U_11838),c_member(tc_prod(U_11838,U_11838)))),c_Product__Type_OPair(U_11838,U_11838)))),U_11840)),U_11842)) ),
inference(clausify,[status(thm)],[f_3122_3]) ).
cnf(f_3122_5,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_11839,hAPP(hAPP(c_COMBC(U_11839,tc_fun(tc_prod(U_11839,U_11839),tc_HOL_Obool),tc_fun(U_11839,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11839,tc_fun(tc_fun(tc_prod(U_11839,U_11839),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11839,U_11839),tc_HOL_Obool),tc_fun(U_11839,tc_HOL_Obool)),U_11839),c_COMBC(U_11839,tc_fun(tc_prod(U_11839,U_11839),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11839,tc_prod(U_11839,U_11839)),tc_fun(U_11839,tc_fun(tc_fun(tc_prod(U_11839,U_11839),tc_HOL_Obool),tc_HOL_Obool)),U_11839),hAPP(c_COMBB(tc_prod(U_11839,U_11839),tc_fun(tc_fun(tc_prod(U_11839,U_11839),tc_HOL_Obool),tc_HOL_Obool),U_11839),c_member(tc_prod(U_11839,U_11839)))),c_Product__Type_OPair(U_11839,U_11839)))),U_11841)),U_11843))
| ~ hBOOL(hAPP(hAPP(c_member(U_11839),U_11843),c_Wellfounded_Oacc(U_11839,U_11841))) ),
inference(clausify,[status(thm)],[f_3122_3]) ).
fof(f_3123_1,plain,
! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_UNIV__I]) ).
fof(f_3123_2,plain,
! [U_11845,U_11844] : hBOOL(hAPP(hAPP(c_member(U_11844),U_11845),c_Orderings_Otop__class_Otop(tc_fun(U_11844,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_3123_1]) ).
cnf(f_3123_3,plain,
hBOOL(hAPP(hAPP(c_member(U_11844),U_11845),c_Orderings_Otop__class_Otop(tc_fun(U_11844,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_3123_2]) ).
fof(f_3124_1,plain,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Int__UNIV__right]) ).
fof(f_3124_2,plain,
! [U_11847,U_11846] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11846,tc_HOL_Obool)),U_11847),c_Orderings_Otop__class_Otop(tc_fun(U_11846,tc_HOL_Obool))) = U_11847,
inference(variable_rename,[status(thm)],[f_3124_1]) ).
cnf(f_3124_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11846,tc_HOL_Obool)),U_11847),c_Orderings_Otop__class_Otop(tc_fun(U_11846,tc_HOL_Obool))) = U_11847,
inference(clausify,[status(thm)],[f_3124_2]) ).
fof(f_3125_1,plain,
! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2,
inference(fof_nnf,[status(thm)],[fact_Int__UNIV__left]) ).
fof(f_3125_2,plain,
! [U_11849,U_11848] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11848,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11848,tc_HOL_Obool))),U_11849) = U_11849,
inference(variable_rename,[status(thm)],[f_3125_1]) ).
cnf(f_3125_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11848,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11848,tc_HOL_Obool))),U_11849) = U_11849,
inference(clausify,[status(thm)],[f_3125_2]) ).
fof(f_3126_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_3126_2,plain,
! [U_11851,U_11850] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11850),c_Orderings_Otop__class_Otop(U_11850)),U_11851) = U_11851
| ~ class_Lattices_Obounded__lattice__top(U_11850) ),
inference(variable_rename,[status(thm)],[f_3126_1]) ).
cnf(f_3126_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11850),c_Orderings_Otop__class_Otop(U_11850)),U_11851) = U_11851
| ~ class_Lattices_Obounded__lattice__top(U_11850) ),
inference(clausify,[status(thm)],[f_3126_2]) ).
fof(f_3127_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_3127_2,plain,
! [U_11853,U_11852] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11852),U_11853),c_Orderings_Otop__class_Otop(U_11852)) = U_11853
| ~ class_Lattices_Obounded__lattice__top(U_11852) ),
inference(variable_rename,[status(thm)],[f_3127_1]) ).
cnf(f_3127_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11852),U_11853),c_Orderings_Otop__class_Otop(U_11852)) = U_11853
| ~ class_Lattices_Obounded__lattice__top(U_11852) ),
inference(clausify,[status(thm)],[f_3127_2]) ).
fof(f_3128_1,plain,
! [V_y_2,V_x_2,T_b] :
( ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
| V_y_2 != c_Orderings_Otop__class_Otop(T_b)
| V_x_2 != c_Orderings_Otop__class_Otop(T_b) )
& ( ( V_y_2 = c_Orderings_Otop__class_Otop(T_b)
& V_x_2 = c_Orderings_Otop__class_Otop(T_b) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) != c_Orderings_Otop__class_Otop(T_b) ) )
| ~ class_Lattices_Obounded__lattice__top(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__eq__top__iff]) ).
fof(f_3128_2,plain,
! [U_11856,U_11855,U_11854] :
( ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11854),U_11855),U_11856) = c_Orderings_Otop__class_Otop(U_11854)
| U_11856 != c_Orderings_Otop__class_Otop(U_11854)
| U_11855 != c_Orderings_Otop__class_Otop(U_11854) )
& ( ( U_11856 = c_Orderings_Otop__class_Otop(U_11854)
& U_11855 = c_Orderings_Otop__class_Otop(U_11854) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11854),U_11855),U_11856) != c_Orderings_Otop__class_Otop(U_11854) ) )
| ~ class_Lattices_Obounded__lattice__top(U_11854) ),
inference(variable_rename,[status(thm)],[f_3128_1]) ).
cnf(f_3128_3,plain,
( U_11855 = c_Orderings_Otop__class_Otop(U_11854)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11854),U_11855),U_11856) != c_Orderings_Otop__class_Otop(U_11854)
| ~ class_Lattices_Obounded__lattice__top(U_11854) ),
inference(clausify,[status(thm)],[f_3128_2]) ).
cnf(f_3128_4,plain,
( U_11856 = c_Orderings_Otop__class_Otop(U_11854)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11854),U_11855),U_11856) != c_Orderings_Otop__class_Otop(U_11854)
| ~ class_Lattices_Obounded__lattice__top(U_11854) ),
inference(clausify,[status(thm)],[f_3128_2]) ).
cnf(f_3128_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11854),U_11855),U_11856) = c_Orderings_Otop__class_Otop(U_11854)
| U_11856 != c_Orderings_Otop__class_Otop(U_11854)
| U_11855 != c_Orderings_Otop__class_Otop(U_11854)
| ~ class_Lattices_Obounded__lattice__top(U_11854) ),
inference(clausify,[status(thm)],[f_3128_2]) ).
fof(f_3129_1,plain,
! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_UNIV__not__empty]) ).
fof(f_3129_2,plain,
! [U_11857] : c_Orderings_Otop__class_Otop(tc_fun(U_11857,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_11857,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3129_1]) ).
cnf(f_3129_3,plain,
c_Orderings_Otop__class_Otop(tc_fun(U_11857,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_11857,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3129_2]) ).
fof(f_3130_1,plain,
! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Un__UNIV__left]) ).
fof(f_3130_2,plain,
! [U_11859,U_11858] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11858,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11858,tc_HOL_Obool))),U_11859) = c_Orderings_Otop__class_Otop(tc_fun(U_11858,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3130_1]) ).
cnf(f_3130_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11858,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11858,tc_HOL_Obool))),U_11859) = c_Orderings_Otop__class_Otop(tc_fun(U_11858,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3130_2]) ).
fof(f_3131_1,plain,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Un__UNIV__right]) ).
fof(f_3131_2,plain,
! [U_11861,U_11860] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11860,tc_HOL_Obool)),U_11861),c_Orderings_Otop__class_Otop(tc_fun(U_11860,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_11860,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3131_1]) ).
cnf(f_3131_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11860,tc_HOL_Obool)),U_11861),c_Orderings_Otop__class_Otop(tc_fun(U_11860,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_11860,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3131_2]) ).
fof(f_3132_1,plain,
! [V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBB(T_d,T_b,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_range__composition]) ).
fof(f_3132_2,plain,
! [U_11866,U_11865,U_11864,U_11863,U_11862] : hAPP(c_Set_Oimage(U_11862,U_11863,hAPP(hAPP(c_COMBB(U_11864,U_11863,U_11862),U_11865),U_11866)),c_Orderings_Otop__class_Otop(tc_fun(U_11862,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_11864,U_11863,U_11865),hAPP(c_Set_Oimage(U_11862,U_11864,U_11866),c_Orderings_Otop__class_Otop(tc_fun(U_11862,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_3132_1]) ).
cnf(f_3132_3,plain,
hAPP(c_Set_Oimage(U_11862,U_11863,hAPP(hAPP(c_COMBB(U_11864,U_11863,U_11862),U_11865),U_11866)),c_Orderings_Otop__class_Otop(tc_fun(U_11862,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_11864,U_11863,U_11865),hAPP(c_Set_Oimage(U_11862,U_11864,U_11866),c_Orderings_Otop__class_Otop(tc_fun(U_11862,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_3132_2]) ).
fof(f_3133_1,plain,
! [V_B_2,V_A_2,T_c,T_b] :
( ( c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
| ? [B_x] :
( hAPP(V_B_2,B_x) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ),
inference(fof_nnf,[status(thm)],[fact_INTER__UNIV__conv_I1_J]) ).
fof(f_3133_2,plain,
! [U_11872,U_11871,U_11870,U_11869] :
( ( c_Orderings_Otop__class_Otop(tc_fun(U_11869,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11870,tc_fun(U_11869,tc_HOL_Obool)),U_11871),U_11872)
| ? [U_11868] :
( hAPP(U_11872,U_11868) != c_Orderings_Otop__class_Otop(tc_fun(U_11869,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_11870),U_11868),U_11871)) ) )
& ( ! [U_11867] :
( hAPP(U_11872,U_11867) = c_Orderings_Otop__class_Otop(tc_fun(U_11869,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_11870),U_11867),U_11871)) )
| c_Orderings_Otop__class_Otop(tc_fun(U_11869,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11870,tc_fun(U_11869,tc_HOL_Obool)),U_11871),U_11872) ) ),
inference(variable_rename,[status(thm)],[f_3133_1]) ).
fof(f_3133_3,plain,
( ! [U_11880,U_11878,U_11876,U_11874] :
( c_Orderings_Otop__class_Otop(tc_fun(U_11874,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11876,tc_fun(U_11874,tc_HOL_Obool)),U_11878),U_11880)
| ? [U_11868] :
( hAPP(U_11880,U_11868) != c_Orderings_Otop__class_Otop(tc_fun(U_11874,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_11876),U_11868),U_11878)) ) )
& ! [U_11879,U_11877,U_11875,U_11873] :
( ! [U_11867] :
( hAPP(U_11879,U_11867) = c_Orderings_Otop__class_Otop(tc_fun(U_11873,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_11875),U_11867),U_11877)) )
| c_Orderings_Otop__class_Otop(tc_fun(U_11873,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11875,tc_fun(U_11873,tc_HOL_Obool)),U_11877),U_11879) ) ),
inference(miniscope,[status(thm)],[f_3133_2]) ).
fof(f_3133_4,plain,
( ! [U_11880,U_11878,U_11876,U_11874] :
( c_Orderings_Otop__class_Otop(tc_fun(U_11874,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11876,tc_fun(U_11874,tc_HOL_Obool)),U_11878),U_11880)
| ( hAPP(U_11880,sK262(U_11880,U_11878,U_11876,U_11874)) != c_Orderings_Otop__class_Otop(tc_fun(U_11874,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_11876),sK262(U_11880,U_11878,U_11876,U_11874)),U_11878)) ) )
& ! [U_11879,U_11877,U_11875,U_11873] :
( ! [U_11867] :
( hAPP(U_11879,U_11867) = c_Orderings_Otop__class_Otop(tc_fun(U_11873,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_11875),U_11867),U_11877)) )
| c_Orderings_Otop__class_Otop(tc_fun(U_11873,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11875,tc_fun(U_11873,tc_HOL_Obool)),U_11877),U_11879) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK262]),skolemize(U_11868,sK262(U_11880,U_11878,U_11876,U_11874))],[f_3133_3]) ).
cnf(f_3133_5,plain,
( hAPP(U_11879,U_11867) = c_Orderings_Otop__class_Otop(tc_fun(U_11873,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_11875),U_11867),U_11877))
| c_Orderings_Otop__class_Otop(tc_fun(U_11873,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11875,tc_fun(U_11873,tc_HOL_Obool)),U_11877),U_11879) ),
inference(clausify,[status(thm)],[f_3133_4]) ).
cnf(f_3133_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_11876),sK262(U_11880,U_11878,U_11876,U_11874)),U_11878))
| c_Orderings_Otop__class_Otop(tc_fun(U_11874,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11876,tc_fun(U_11874,tc_HOL_Obool)),U_11878),U_11880) ),
inference(clausify,[status(thm)],[f_3133_4]) ).
cnf(f_3133_7,plain,
( hAPP(U_11880,sK262(U_11880,U_11878,U_11876,U_11874)) != c_Orderings_Otop__class_Otop(tc_fun(U_11874,tc_HOL_Obool))
| c_Orderings_Otop__class_Otop(tc_fun(U_11874,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11876,tc_fun(U_11874,tc_HOL_Obool)),U_11878),U_11880) ),
inference(clausify,[status(thm)],[f_3133_4]) ).
fof(f_3134_1,plain,
! [V_B_2,V_A_2,T_b,T_c] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
| ? [B_x] :
( hAPP(V_B_2,B_x) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INTER__UNIV__conv_I2_J]) ).
fof(f_3134_2,plain,
! [U_11886,U_11885,U_11884,U_11883] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11883,tc_fun(U_11884,tc_HOL_Obool)),U_11885),U_11886) = c_Orderings_Otop__class_Otop(tc_fun(U_11884,tc_HOL_Obool))
| ? [U_11882] :
( hAPP(U_11886,U_11882) != c_Orderings_Otop__class_Otop(tc_fun(U_11884,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_11883),U_11882),U_11885)) ) )
& ( ! [U_11881] :
( hAPP(U_11886,U_11881) = c_Orderings_Otop__class_Otop(tc_fun(U_11884,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_11883),U_11881),U_11885)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11883,tc_fun(U_11884,tc_HOL_Obool)),U_11885),U_11886) != c_Orderings_Otop__class_Otop(tc_fun(U_11884,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3134_1]) ).
fof(f_3134_3,plain,
( ! [U_11894,U_11892,U_11890,U_11888] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11888,tc_fun(U_11890,tc_HOL_Obool)),U_11892),U_11894) = c_Orderings_Otop__class_Otop(tc_fun(U_11890,tc_HOL_Obool))
| ? [U_11882] :
( hAPP(U_11894,U_11882) != c_Orderings_Otop__class_Otop(tc_fun(U_11890,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_11888),U_11882),U_11892)) ) )
& ! [U_11893,U_11891,U_11889,U_11887] :
( ! [U_11881] :
( hAPP(U_11893,U_11881) = c_Orderings_Otop__class_Otop(tc_fun(U_11889,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_11887),U_11881),U_11891)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11887,tc_fun(U_11889,tc_HOL_Obool)),U_11891),U_11893) != c_Orderings_Otop__class_Otop(tc_fun(U_11889,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_3134_2]) ).
fof(f_3134_4,plain,
( ! [U_11894,U_11892,U_11890,U_11888] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11888,tc_fun(U_11890,tc_HOL_Obool)),U_11892),U_11894) = c_Orderings_Otop__class_Otop(tc_fun(U_11890,tc_HOL_Obool))
| ( hAPP(U_11894,sK263(U_11894,U_11892,U_11890,U_11888)) != c_Orderings_Otop__class_Otop(tc_fun(U_11890,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(U_11888),sK263(U_11894,U_11892,U_11890,U_11888)),U_11892)) ) )
& ! [U_11893,U_11891,U_11889,U_11887] :
( ! [U_11881] :
( hAPP(U_11893,U_11881) = c_Orderings_Otop__class_Otop(tc_fun(U_11889,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_11887),U_11881),U_11891)) )
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11887,tc_fun(U_11889,tc_HOL_Obool)),U_11891),U_11893) != c_Orderings_Otop__class_Otop(tc_fun(U_11889,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK263]),skolemize(U_11882,sK263(U_11894,U_11892,U_11890,U_11888))],[f_3134_3]) ).
cnf(f_3134_5,plain,
( hAPP(U_11893,U_11881) = c_Orderings_Otop__class_Otop(tc_fun(U_11889,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_11887),U_11881),U_11891))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11887,tc_fun(U_11889,tc_HOL_Obool)),U_11891),U_11893) != c_Orderings_Otop__class_Otop(tc_fun(U_11889,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3134_4]) ).
cnf(f_3134_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_11888),sK263(U_11894,U_11892,U_11890,U_11888)),U_11892))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11888,tc_fun(U_11890,tc_HOL_Obool)),U_11892),U_11894) = c_Orderings_Otop__class_Otop(tc_fun(U_11890,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3134_4]) ).
cnf(f_3134_7,plain,
( hAPP(U_11894,sK263(U_11894,U_11892,U_11890,U_11888)) != c_Orderings_Otop__class_Otop(tc_fun(U_11890,tc_HOL_Obool))
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11888,tc_fun(U_11890,tc_HOL_Obool)),U_11892),U_11894) = c_Orderings_Otop__class_Otop(tc_fun(U_11890,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3134_4]) ).
fof(f_3135_1,plain,
! [T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV]) ).
fof(f_3135_2,plain,
! [U_11896,U_11895] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_11895,U_11896)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_11895,U_11896),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11896),c_Orderings_Otop__class_Otop(tc_fun(U_11896,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11895),c_Orderings_Otop__class_Otop(tc_fun(U_11895,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_3135_1]) ).
cnf(f_3135_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_11895,U_11896)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_11895,U_11896),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11896),c_Orderings_Otop__class_Otop(tc_fun(U_11896,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11895),c_Orderings_Otop__class_Otop(tc_fun(U_11895,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_3135_2]) ).
fof(f_3136_1,plain,
! [T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2]) ).
fof(f_3136_2,plain,
! [U_11898,U_11897] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11898),c_Orderings_Otop__class_Otop(tc_fun(U_11898,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11897,U_11898)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_11897,U_11898),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_3136_1]) ).
fof(f_3136_3,plain,
! [U_11898] :
( ! [U_11897] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11897,U_11898)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_11897,U_11898),tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_11898),c_Orderings_Otop__class_Otop(tc_fun(U_11898,tc_HOL_Obool)))) ),
inference(miniscope,[status(thm)],[f_3136_2]) ).
cnf(f_3136_4,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11897,U_11898)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_11897,U_11898),tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_11898),c_Orderings_Otop__class_Otop(tc_fun(U_11898,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_3136_3]) ).
fof(f_3137_1,plain,
! [T_c,T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Plus__UNIV__iff]) ).
fof(f_3137_2,plain,
! [U_11900,U_11899] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_11899,U_11900)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_11899,U_11900),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11900),c_Orderings_Otop__class_Otop(tc_fun(U_11900,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11899),c_Orderings_Otop__class_Otop(tc_fun(U_11899,tc_HOL_Obool)))) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11900),c_Orderings_Otop__class_Otop(tc_fun(U_11900,tc_HOL_Obool))))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_11899),c_Orderings_Otop__class_Otop(tc_fun(U_11899,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_11899,U_11900)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_11899,U_11900),tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[f_3137_1]) ).
fof(f_3137_3,plain,
( ! [U_11904,U_11902] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_11902,U_11904)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_11902,U_11904),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11904),c_Orderings_Otop__class_Otop(tc_fun(U_11904,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11902),c_Orderings_Otop__class_Otop(tc_fun(U_11902,tc_HOL_Obool)))) )
& ! [U_11903,U_11901] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11903),c_Orderings_Otop__class_Otop(tc_fun(U_11903,tc_HOL_Obool))))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_11901),c_Orderings_Otop__class_Otop(tc_fun(U_11901,tc_HOL_Obool)))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_11901,U_11903)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_11901,U_11903),tc_HOL_Obool)))) ) ),
inference(miniscope,[status(thm)],[f_3137_2]) ).
cnf(f_3137_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11901),c_Orderings_Otop__class_Otop(tc_fun(U_11901,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_11901,U_11903)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_11901,U_11903),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_3137_3]) ).
cnf(f_3137_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11903),c_Orderings_Otop__class_Otop(tc_fun(U_11903,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_11901,U_11903)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_11901,U_11903),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_3137_3]) ).
cnf(f_3137_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_11902,U_11904)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_11902,U_11904),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11904),c_Orderings_Otop__class_Otop(tc_fun(U_11904,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11902),c_Orderings_Otop__class_Otop(tc_fun(U_11902,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_3137_3]) ).
fof(f_3138_1,plain,
! [T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool)))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV]) ).
fof(f_3138_2,plain,
! [U_11905] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_11905)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_11905),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11905),c_Orderings_Otop__class_Otop(tc_fun(U_11905,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11905),c_Orderings_Otop__class_Otop(tc_fun(U_11905,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_11905)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_11905),tc_HOL_Obool)))) ) ),
inference(variable_rename,[status(thm)],[f_3138_1]) ).
fof(f_3138_3,plain,
( ! [U_11907] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_11907)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_11907),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11907),c_Orderings_Otop__class_Otop(tc_fun(U_11907,tc_HOL_Obool)))) )
& ! [U_11906] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11906),c_Orderings_Otop__class_Otop(tc_fun(U_11906,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_11906)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_11906),tc_HOL_Obool)))) ) ),
inference(miniscope,[status(thm)],[f_3138_2]) ).
cnf(f_3138_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11906),c_Orderings_Otop__class_Otop(tc_fun(U_11906,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_11906)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_11906),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_3138_3]) ).
cnf(f_3138_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_11907)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_11907),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11907),c_Orderings_Otop__class_Otop(tc_fun(U_11907,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_3138_3]) ).
fof(f_3139_1,plain,
! [T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
| ~ class_Finite__Set_Ofinite(T_b) ),
inference(fof_nnf,[status(thm)],[fact_finite__UNIV]) ).
fof(f_3139_2,plain,
! [U_11908] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11908),c_Orderings_Otop__class_Otop(tc_fun(U_11908,tc_HOL_Obool))))
| ~ class_Finite__Set_Ofinite(U_11908) ),
inference(variable_rename,[status(thm)],[f_3139_1]) ).
cnf(f_3139_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11908),c_Orderings_Otop__class_Otop(tc_fun(U_11908,tc_HOL_Obool))))
| ~ class_Finite__Set_Ofinite(U_11908) ),
inference(clausify,[status(thm)],[f_3139_2]) ).
fof(f_3140_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]) ).
cnf(f_3140_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(clausify,[status(thm)],[f_3140_1]) ).
fof(f_3141_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]) ).
cnf(f_3141_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(clausify,[status(thm)],[f_3141_1]) ).
fof(f_3142_1,plain,
! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_subset__UNIV]) ).
fof(f_3142_2,plain,
! [U_11910,U_11909] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11909,tc_HOL_Obool)),U_11910),c_Orderings_Otop__class_Otop(tc_fun(U_11909,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_3142_1]) ).
cnf(f_3142_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11909,tc_HOL_Obool)),U_11910),c_Orderings_Otop__class_Otop(tc_fun(U_11909,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_3142_2]) ).
fof(f_3143_1,plain,
! [T_c,T_b] : c_Sum__Type_OPlus(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_UNIV__Plus__UNIV]) ).
fof(f_3143_2,plain,
! [U_11912,U_11911] : c_Sum__Type_OPlus(U_11911,U_11912,c_Orderings_Otop__class_Otop(tc_fun(U_11911,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11912,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_11911,U_11912),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3143_1]) ).
cnf(f_3143_3,plain,
c_Sum__Type_OPlus(U_11911,U_11912,c_Orderings_Otop__class_Otop(tc_fun(U_11911,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11912,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_11911,U_11912),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3143_2]) ).
fof(f_3144_1,plain,
! [V_x_2,T_c,T_b] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b)
| ~ class_Orderings_Otop(T_b) ),
inference(fof_nnf,[status(thm)],[fact_top__apply]) ).
fof(f_3144_2,plain,
! [U_11915,U_11914,U_11913] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_11914,U_11913)),U_11915) = c_Orderings_Otop__class_Otop(U_11913)
| ~ class_Orderings_Otop(U_11913) ),
inference(variable_rename,[status(thm)],[f_3144_1]) ).
cnf(f_3144_3,plain,
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_11914,U_11913)),U_11915) = c_Orderings_Otop__class_Otop(U_11913)
| ~ class_Orderings_Otop(U_11913) ),
inference(clausify,[status(thm)],[f_3144_2]) ).
fof(f_3145_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_3145_2,plain,
! [U_11917,U_11916] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11916),U_11917),c_Orderings_Otop__class_Otop(U_11916)))
| ~ class_Orderings_Otop(U_11916) ),
inference(variable_rename,[status(thm)],[f_3145_1]) ).
cnf(f_3145_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11916),U_11917),c_Orderings_Otop__class_Otop(U_11916)))
| ~ class_Orderings_Otop(U_11916) ),
inference(clausify,[status(thm)],[f_3145_2]) ).
fof(f_3146_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]) ).
cnf(f_3146_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(clausify,[status(thm)],[f_3146_1]) ).
fof(f_3147_1,plain,
! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Pow__UNIV]) ).
fof(f_3147_2,plain,
! [U_11918] : hAPP(c_Set_OPow(U_11918),c_Orderings_Otop__class_Otop(tc_fun(U_11918,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_11918,tc_HOL_Obool),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3147_1]) ).
cnf(f_3147_3,plain,
hAPP(c_Set_OPow(U_11918),c_Orderings_Otop__class_Otop(tc_fun(U_11918,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_11918,tc_HOL_Obool),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3147_2]) ).
fof(f_3148_1,plain,
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),
inference(fof_nnf,[status(thm)],[fact_equiv__intrel]) ).
cnf(f_3148_2,plain,
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),
inference(clausify,[status(thm)],[f_3148_1]) ).
fof(f_3149_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]) ).
cnf(f_3149_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(clausify,[status(thm)],[f_3149_1]) ).
fof(f_3150_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_3150_2,plain,
! [U_11920,U_11919] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11919),U_11920),c_Orderings_Otop__class_Otop(U_11919)) = c_Orderings_Otop__class_Otop(U_11919)
| ~ class_Lattices_Obounded__lattice__top(U_11919) ),
inference(variable_rename,[status(thm)],[f_3150_1]) ).
cnf(f_3150_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11919),U_11920),c_Orderings_Otop__class_Otop(U_11919)) = c_Orderings_Otop__class_Otop(U_11919)
| ~ class_Lattices_Obounded__lattice__top(U_11919) ),
inference(clausify,[status(thm)],[f_3150_2]) ).
fof(f_3151_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_3151_2,plain,
! [U_11922,U_11921] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11921),c_Orderings_Otop__class_Otop(U_11921)),U_11922) = c_Orderings_Otop__class_Otop(U_11921)
| ~ class_Lattices_Obounded__lattice__top(U_11921) ),
inference(variable_rename,[status(thm)],[f_3151_1]) ).
cnf(f_3151_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11921),c_Orderings_Otop__class_Otop(U_11921)),U_11922) = c_Orderings_Otop__class_Otop(U_11921)
| ~ class_Lattices_Obounded__lattice__top(U_11921) ),
inference(clausify,[status(thm)],[f_3151_2]) ).
fof(f_3152_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]) ).
cnf(f_3152_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(clausify,[status(thm)],[f_3152_1]) ).
fof(f_3153_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]) ).
cnf(f_3153_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(clausify,[status(thm)],[f_3153_1]) ).
fof(f_3154_1,plain,
! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
( 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_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_injD]) ).
fof(f_3154_2,plain,
! [U_11927,U_11926,U_11925,U_11924,U_11923] :
( U_11926 = U_11927
| hAPP(U_11925,U_11926) != hAPP(U_11925,U_11927)
| ~ c_Fun_Oinj__on(U_11923,U_11924,U_11925,c_Orderings_Otop__class_Otop(tc_fun(U_11923,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_3154_1]) ).
fof(f_3154_3,plain,
! [U_11927,U_11926,U_11925] :
( ! [U_11924,U_11923] : ~ c_Fun_Oinj__on(U_11923,U_11924,U_11925,c_Orderings_Otop__class_Otop(tc_fun(U_11923,tc_HOL_Obool)))
| U_11926 = U_11927
| hAPP(U_11925,U_11926) != hAPP(U_11925,U_11927) ),
inference(miniscope,[status(thm)],[f_3154_2]) ).
cnf(f_3154_4,plain,
( ~ c_Fun_Oinj__on(U_11923,U_11924,U_11925,c_Orderings_Otop__class_Otop(tc_fun(U_11923,tc_HOL_Obool)))
| U_11926 = U_11927
| hAPP(U_11925,U_11926) != hAPP(U_11925,U_11927) ),
inference(clausify,[status(thm)],[f_3154_3]) ).
fof(f_3155_1,plain,
! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
( ( ( 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_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_inj__eq]) ).
fof(f_3155_2,plain,
! [U_11932,U_11931,U_11930,U_11929,U_11928] :
( ( ( hAPP(U_11930,U_11931) = hAPP(U_11930,U_11932)
| U_11931 != U_11932 )
& ( U_11931 = U_11932
| hAPP(U_11930,U_11931) != hAPP(U_11930,U_11932) ) )
| ~ c_Fun_Oinj__on(U_11928,U_11929,U_11930,c_Orderings_Otop__class_Otop(tc_fun(U_11928,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_3155_1]) ).
fof(f_3155_3,plain,
! [U_11932,U_11931,U_11930] :
( ! [U_11929,U_11928] : ~ c_Fun_Oinj__on(U_11928,U_11929,U_11930,c_Orderings_Otop__class_Otop(tc_fun(U_11928,tc_HOL_Obool)))
| ( ( hAPP(U_11930,U_11931) = hAPP(U_11930,U_11932)
| U_11931 != U_11932 )
& ( U_11931 = U_11932
| hAPP(U_11930,U_11931) != hAPP(U_11930,U_11932) ) ) ),
inference(miniscope,[status(thm)],[f_3155_2]) ).
cnf(f_3155_4,plain,
( U_11931 = U_11932
| hAPP(U_11930,U_11931) != hAPP(U_11930,U_11932)
| ~ c_Fun_Oinj__on(U_11928,U_11929,U_11930,c_Orderings_Otop__class_Otop(tc_fun(U_11928,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3155_3]) ).
cnf(f_3155_5,plain,
( hAPP(U_11930,U_11931) = hAPP(U_11930,U_11932)
| U_11931 != U_11932
| ~ c_Fun_Oinj__on(U_11928,U_11929,U_11930,c_Orderings_Otop__class_Otop(tc_fun(U_11928,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3155_3]) ).
fof(f_3156_1,plain,
! [V_x_2,V_f_2,T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)),
inference(fof_nnf,[status(thm)],[fact_empty__fold1SetE]) ).
fof(f_3156_2,plain,
! [U_11935,U_11934,U_11933] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_11933,U_11934,c_Orderings_Obot__class_Obot(tc_fun(U_11933,tc_HOL_Obool))),U_11935)),
inference(variable_rename,[status(thm)],[f_3156_1]) ).
cnf(f_3156_3,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_11933,U_11934,c_Orderings_Obot__class_Obot(tc_fun(U_11933,tc_HOL_Obool))),U_11935)),
inference(clausify,[status(thm)],[f_3156_2]) ).
fof(f_3157_1,plain,
! [V_x_2,V_A_2,V_f_2,T_b] :
( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_fold1Set__nonempty]) ).
fof(f_3157_2,plain,
! [U_11939,U_11938,U_11937,U_11936] :
( U_11938 != c_Orderings_Obot__class_Obot(tc_fun(U_11936,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_11936,U_11937,U_11938),U_11939)) ),
inference(variable_rename,[status(thm)],[f_3157_1]) ).
cnf(f_3157_3,plain,
( U_11938 != c_Orderings_Obot__class_Obot(tc_fun(U_11936,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_11936,U_11937,U_11938),U_11939)) ),
inference(clausify,[status(thm)],[f_3157_2]) ).
fof(f_3158_1,plain,
! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
| V_b_2 != hAPP(V_f_2,V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_range__eqI]) ).
fof(f_3158_2,plain,
! [U_11944,U_11943,U_11942,U_11941,U_11940] :
( hBOOL(hAPP(hAPP(c_member(U_11943),U_11940),hAPP(c_Set_Oimage(U_11944,U_11943,U_11941),c_Orderings_Otop__class_Otop(tc_fun(U_11944,tc_HOL_Obool)))))
| U_11940 != hAPP(U_11941,U_11942) ),
inference(variable_rename,[status(thm)],[f_3158_1]) ).
cnf(f_3158_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_11943),U_11940),hAPP(c_Set_Oimage(U_11944,U_11943,U_11941),c_Orderings_Otop__class_Otop(tc_fun(U_11944,tc_HOL_Obool)))))
| U_11940 != hAPP(U_11941,U_11942) ),
inference(clausify,[status(thm)],[f_3158_2]) ).
fof(f_3159_1,plain,
! [T_c,V_x_2,V_f_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))),
inference(fof_nnf,[status(thm)],[fact_rangeI]) ).
fof(f_3159_2,plain,
! [U_11948,U_11947,U_11946,U_11945] : hBOOL(hAPP(hAPP(c_member(U_11945),hAPP(U_11946,U_11947)),hAPP(c_Set_Oimage(U_11948,U_11945,U_11946),c_Orderings_Otop__class_Otop(tc_fun(U_11948,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_3159_1]) ).
cnf(f_3159_3,plain,
hBOOL(hAPP(hAPP(c_member(U_11945),hAPP(U_11946,U_11947)),hAPP(c_Set_Oimage(U_11948,U_11945,U_11946),c_Orderings_Otop__class_Otop(tc_fun(U_11948,tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_3159_2]) ).
fof(f_3160_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]) ).
cnf(f_3160_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(clausify,[status(thm)],[f_3160_1]) ).
fof(f_3161_1,plain,
! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Diff__UNIV]) ).
fof(f_3161_2,plain,
! [U_11950,U_11949] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11949,tc_HOL_Obool)),U_11950),c_Orderings_Otop__class_Otop(tc_fun(U_11949,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_11949,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3161_1]) ).
cnf(f_3161_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11949,tc_HOL_Obool)),U_11950),c_Orderings_Otop__class_Otop(tc_fun(U_11949,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_11949,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3161_2]) ).
fof(f_3162_1,plain,
! [V_A_2,T_b] :
( V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(T_b),V_A_2) != hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV]) ).
fof(f_3162_2,plain,
! [U_11952,U_11951] :
( U_11952 = c_Orderings_Otop__class_Otop(tc_fun(U_11951,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_11951),U_11952) != hAPP(c_Finite__Set_Ocard(U_11951),c_Orderings_Otop__class_Otop(tc_fun(U_11951,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11951),c_Orderings_Otop__class_Otop(tc_fun(U_11951,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_3162_1]) ).
cnf(f_3162_3,plain,
( U_11952 = c_Orderings_Otop__class_Otop(tc_fun(U_11951,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(U_11951),U_11952) != hAPP(c_Finite__Set_Ocard(U_11951),c_Orderings_Otop__class_Otop(tc_fun(U_11951,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11951),c_Orderings_Otop__class_Otop(tc_fun(U_11951,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_3162_2]) ).
fof(f_3163_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( ( ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
| V_A_2 != V_B_2 )
& ( V_A_2 = V_B_2
| hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) != hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) ) )
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_inj__image__eq__iff]) ).
fof(f_3163_2,plain,
! [U_11957,U_11956,U_11955,U_11954,U_11953] :
( ( ( hAPP(c_Set_Oimage(U_11953,U_11954,U_11955),U_11956) = hAPP(c_Set_Oimage(U_11953,U_11954,U_11955),U_11957)
| U_11956 != U_11957 )
& ( U_11956 = U_11957
| hAPP(c_Set_Oimage(U_11953,U_11954,U_11955),U_11956) != hAPP(c_Set_Oimage(U_11953,U_11954,U_11955),U_11957) ) )
| ~ c_Fun_Oinj__on(U_11953,U_11954,U_11955,c_Orderings_Otop__class_Otop(tc_fun(U_11953,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_3163_1]) ).
cnf(f_3163_3,plain,
( U_11956 = U_11957
| hAPP(c_Set_Oimage(U_11953,U_11954,U_11955),U_11956) != hAPP(c_Set_Oimage(U_11953,U_11954,U_11955),U_11957)
| ~ c_Fun_Oinj__on(U_11953,U_11954,U_11955,c_Orderings_Otop__class_Otop(tc_fun(U_11953,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3163_2]) ).
cnf(f_3163_4,plain,
( hAPP(c_Set_Oimage(U_11953,U_11954,U_11955),U_11956) = hAPP(c_Set_Oimage(U_11953,U_11954,U_11955),U_11957)
| U_11956 != U_11957
| ~ c_Fun_Oinj__on(U_11953,U_11954,U_11955,c_Orderings_Otop__class_Otop(tc_fun(U_11953,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3163_2]) ).
fof(f_3164_1,plain,
! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Compl__UNIV__eq]) ).
fof(f_3164_2,plain,
! [U_11958] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11958,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11958,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_11958,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3164_1]) ).
cnf(f_3164_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11958,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11958,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_11958,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3164_2]) ).
fof(f_3165_1,plain,
! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Compl__empty__eq]) ).
fof(f_3165_2,plain,
! [U_11959] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11959,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_11959,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_11959,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3165_1]) ).
cnf(f_3165_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11959,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_11959,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_11959,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3165_2]) ).
fof(f_3166_1,plain,
! [V_A_2,T_b] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__compl]) ).
fof(f_3166_2,plain,
! [U_11961,U_11960] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11960),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11960,tc_HOL_Obool)),U_11961)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11960),c_Orderings_Otop__class_Otop(tc_fun(U_11960,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11960),c_Orderings_Otop__class_Otop(tc_fun(U_11960,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11960),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11960,tc_HOL_Obool)),U_11961))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11960),U_11961)) ),
inference(variable_rename,[status(thm)],[f_3166_1]) ).
cnf(f_3166_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11960),c_Orderings_Otop__class_Otop(tc_fun(U_11960,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11960),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11960,tc_HOL_Obool)),U_11961)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11960),U_11961)) ),
inference(clausify,[status(thm)],[f_3166_2]) ).
cnf(f_3166_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11960),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11960,tc_HOL_Obool)),U_11961)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11960),c_Orderings_Otop__class_Otop(tc_fun(U_11960,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11960),U_11961)) ),
inference(clausify,[status(thm)],[f_3166_2]) ).
fof(f_3167_1,plain,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Compl__partition2]) ).
fof(f_3167_2,plain,
! [U_11963,U_11962] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11962,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11962,tc_HOL_Obool)),U_11963)),U_11963) = c_Orderings_Otop__class_Otop(tc_fun(U_11962,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3167_1]) ).
cnf(f_3167_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11962,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11962,tc_HOL_Obool)),U_11963)),U_11963) = c_Orderings_Otop__class_Otop(tc_fun(U_11962,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3167_2]) ).
fof(f_3168_1,plain,
! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Compl__partition]) ).
fof(f_3168_2,plain,
! [U_11965,U_11964] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11964,tc_HOL_Obool)),U_11965),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11964,tc_HOL_Obool)),U_11965)) = c_Orderings_Otop__class_Otop(tc_fun(U_11964,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3168_1]) ).
cnf(f_3168_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11964,tc_HOL_Obool)),U_11965),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11964,tc_HOL_Obool)),U_11965)) = c_Orderings_Otop__class_Otop(tc_fun(U_11964,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3168_2]) ).
fof(f_3169_1,plain,
! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_A_2),
inference(fof_nnf,[status(thm)],[fact_Compl__eq__Diff__UNIV]) ).
fof(f_3169_2,plain,
! [U_11967,U_11966] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11966,tc_HOL_Obool)),U_11967) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11966,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11966,tc_HOL_Obool))),U_11967),
inference(variable_rename,[status(thm)],[f_3169_1]) ).
cnf(f_3169_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11966,tc_HOL_Obool)),U_11967) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11966,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11966,tc_HOL_Obool))),U_11967),
inference(clausify,[status(thm)],[f_3169_2]) ).
fof(f_3170_1,plain,
! [V_y_2,V_x_2] :
( ( ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(c_Code__Numeral_Oof__nat,V_x_2) != hAPP(c_Code__Numeral_Oof__nat,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))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_code__numeral_Oof__nat__inject]) ).
fof(f_3170_2,plain,
! [U_11969,U_11968] :
( ( ( hAPP(c_Code__Numeral_Oof__nat,U_11968) = hAPP(c_Code__Numeral_Oof__nat,U_11969)
| U_11968 != U_11969 )
& ( U_11968 = U_11969
| hAPP(c_Code__Numeral_Oof__nat,U_11968) != hAPP(c_Code__Numeral_Oof__nat,U_11969) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11969),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11968),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_3170_1]) ).
cnf(f_3170_3,plain,
( U_11968 = U_11969
| hAPP(c_Code__Numeral_Oof__nat,U_11968) != hAPP(c_Code__Numeral_Oof__nat,U_11969)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11969),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11968),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_3170_2]) ).
cnf(f_3170_4,plain,
( hAPP(c_Code__Numeral_Oof__nat,U_11968) = hAPP(c_Code__Numeral_Oof__nat,U_11969)
| U_11968 != U_11969
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11969),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11968),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_3170_2]) ).
fof(f_3171_1,plain,
! [V_x_2,V_r_2,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq]) ).
fof(f_3171_2,plain,
! [U_11973,U_11972,U_11971,U_11970] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11970,tc_fun(U_11971,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11970,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11971,tc_HOL_Obool),tc_fun(U_11971,tc_HOL_Obool),U_11970),hAPP(c_COMBC(U_11971,tc_fun(U_11971,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11971))),U_11972)),U_11973))
| ~ hBOOL(hAPP(hAPP(c_member(U_11971),U_11973),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11970,tc_fun(U_11971,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11970,tc_HOL_Obool))),U_11972))) )
& ( hBOOL(hAPP(hAPP(c_member(U_11971),U_11973),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11970,tc_fun(U_11971,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11970,tc_HOL_Obool))),U_11972)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11970,tc_fun(U_11971,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11970,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11971,tc_HOL_Obool),tc_fun(U_11971,tc_HOL_Obool),U_11970),hAPP(c_COMBC(U_11971,tc_fun(U_11971,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11971))),U_11972)),U_11973)) ) ),
inference(variable_rename,[status(thm)],[f_3171_1]) ).
fof(f_3171_3,plain,
( ! [U_11981,U_11979,U_11977,U_11975] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11975,tc_fun(U_11977,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11975,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11977,tc_HOL_Obool),tc_fun(U_11977,tc_HOL_Obool),U_11975),hAPP(c_COMBC(U_11977,tc_fun(U_11977,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11977))),U_11979)),U_11981))
| ~ hBOOL(hAPP(hAPP(c_member(U_11977),U_11981),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11975,tc_fun(U_11977,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11975,tc_HOL_Obool))),U_11979))) )
& ! [U_11980,U_11978,U_11976,U_11974] :
( hBOOL(hAPP(hAPP(c_member(U_11976),U_11980),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11974,tc_fun(U_11976,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11974,tc_HOL_Obool))),U_11978)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11974,tc_fun(U_11976,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11974,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11976,tc_HOL_Obool),tc_fun(U_11976,tc_HOL_Obool),U_11974),hAPP(c_COMBC(U_11976,tc_fun(U_11976,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11976))),U_11978)),U_11980)) ) ),
inference(miniscope,[status(thm)],[f_3171_2]) ).
cnf(f_3171_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11976),U_11980),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11974,tc_fun(U_11976,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11974,tc_HOL_Obool))),U_11978)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11974,tc_fun(U_11976,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11974,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11976,tc_HOL_Obool),tc_fun(U_11976,tc_HOL_Obool),U_11974),hAPP(c_COMBC(U_11976,tc_fun(U_11976,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11976))),U_11978)),U_11980)) ),
inference(clausify,[status(thm)],[f_3171_3]) ).
cnf(f_3171_5,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11975,tc_fun(U_11977,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11975,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11977,tc_HOL_Obool),tc_fun(U_11977,tc_HOL_Obool),U_11975),hAPP(c_COMBC(U_11977,tc_fun(U_11977,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11977))),U_11979)),U_11981))
| ~ hBOOL(hAPP(hAPP(c_member(U_11977),U_11981),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_11975,tc_fun(U_11977,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11975,tc_HOL_Obool))),U_11979))) ),
inference(clausify,[status(thm)],[f_3171_3]) ).
fof(f_3172_1,plain,
! [V_f_2,T_d,V_g_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,hAPP(hAPP(c_COMBB(T_b,T_d,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ),
inference(fof_nnf,[status(thm)],[fact_finite__range__imageI]) ).
fof(f_3172_2,plain,
! [U_11986,U_11985,U_11984,U_11983,U_11982] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11985),hAPP(c_Set_Oimage(U_11983,U_11985,hAPP(hAPP(c_COMBB(U_11982,U_11985,U_11983),U_11986),U_11984)),c_Orderings_Otop__class_Otop(tc_fun(U_11983,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11982),hAPP(c_Set_Oimage(U_11983,U_11982,U_11984),c_Orderings_Otop__class_Otop(tc_fun(U_11983,tc_HOL_Obool))))) ),
inference(variable_rename,[status(thm)],[f_3172_1]) ).
cnf(f_3172_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11985),hAPP(c_Set_Oimage(U_11983,U_11985,hAPP(hAPP(c_COMBB(U_11982,U_11985,U_11983),U_11986),U_11984)),c_Orderings_Otop__class_Otop(tc_fun(U_11983,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11982),hAPP(c_Set_Oimage(U_11983,U_11982,U_11984),c_Orderings_Otop__class_Otop(tc_fun(U_11983,tc_HOL_Obool))))) ),
inference(clausify,[status(thm)],[f_3172_2]) ).
fof(f_3173_1,plain,
! [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)))),
inference(fof_nnf,[status(thm)],[fact_nat__of]) ).
fof(f_3173_2,plain,
! [U_11987] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_11987)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_3173_1]) ).
cnf(f_3173_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_11987)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_3173_2]) ).
fof(f_3174_1,plain,
! [V_x_2,V_f_2,T_c,T_b] :
( hAPP(c_Fun_Othe__inv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_the__inv__f__f]) ).
fof(f_3174_2,plain,
! [U_11991,U_11990,U_11989,U_11988] :
( hAPP(c_Fun_Othe__inv__into(U_11988,U_11989,c_Orderings_Otop__class_Otop(tc_fun(U_11988,tc_HOL_Obool)),U_11990),hAPP(U_11990,U_11991)) = U_11991
| ~ c_Fun_Oinj__on(U_11988,U_11989,U_11990,c_Orderings_Otop__class_Otop(tc_fun(U_11988,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_3174_1]) ).
cnf(f_3174_3,plain,
( hAPP(c_Fun_Othe__inv__into(U_11988,U_11989,c_Orderings_Otop__class_Otop(tc_fun(U_11988,tc_HOL_Obool)),U_11990),hAPP(U_11990,U_11991)) = U_11991
| ~ c_Fun_Oinj__on(U_11988,U_11989,U_11990,c_Orderings_Otop__class_Otop(tc_fun(U_11988,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3174_2]) ).
fof(f_3175_1,plain,
! [V_x_2,V_r_2,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_INF__INT__eq]) ).
fof(f_3175_2,plain,
! [U_11995,U_11994,U_11993,U_11992] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11992,tc_fun(U_11993,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11992,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11993,tc_HOL_Obool),tc_fun(U_11993,tc_HOL_Obool),U_11992),hAPP(c_COMBC(U_11993,tc_fun(U_11993,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11993))),U_11994)),U_11995))
| ~ hBOOL(hAPP(hAPP(c_member(U_11993),U_11995),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11992,tc_fun(U_11993,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11992,tc_HOL_Obool))),U_11994))) )
& ( hBOOL(hAPP(hAPP(c_member(U_11993),U_11995),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11992,tc_fun(U_11993,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11992,tc_HOL_Obool))),U_11994)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11992,tc_fun(U_11993,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11992,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11993,tc_HOL_Obool),tc_fun(U_11993,tc_HOL_Obool),U_11992),hAPP(c_COMBC(U_11993,tc_fun(U_11993,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11993))),U_11994)),U_11995)) ) ),
inference(variable_rename,[status(thm)],[f_3175_1]) ).
fof(f_3175_3,plain,
( ! [U_12003,U_12001,U_11999,U_11997] :
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11997,tc_fun(U_11999,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11997,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11999,tc_HOL_Obool),tc_fun(U_11999,tc_HOL_Obool),U_11997),hAPP(c_COMBC(U_11999,tc_fun(U_11999,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11999))),U_12001)),U_12003))
| ~ hBOOL(hAPP(hAPP(c_member(U_11999),U_12003),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11997,tc_fun(U_11999,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11997,tc_HOL_Obool))),U_12001))) )
& ! [U_12002,U_12000,U_11998,U_11996] :
( hBOOL(hAPP(hAPP(c_member(U_11998),U_12002),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11996,tc_fun(U_11998,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11996,tc_HOL_Obool))),U_12000)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11996,tc_fun(U_11998,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11996,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11998,tc_HOL_Obool),tc_fun(U_11998,tc_HOL_Obool),U_11996),hAPP(c_COMBC(U_11998,tc_fun(U_11998,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11998))),U_12000)),U_12002)) ) ),
inference(miniscope,[status(thm)],[f_3175_2]) ).
cnf(f_3175_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_11998),U_12002),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11996,tc_fun(U_11998,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11996,tc_HOL_Obool))),U_12000)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11996,tc_fun(U_11998,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11996,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11998,tc_HOL_Obool),tc_fun(U_11998,tc_HOL_Obool),U_11996),hAPP(c_COMBC(U_11998,tc_fun(U_11998,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11998))),U_12000)),U_12002)) ),
inference(clausify,[status(thm)],[f_3175_3]) ).
cnf(f_3175_5,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11997,tc_fun(U_11999,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11997,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11999,tc_HOL_Obool),tc_fun(U_11999,tc_HOL_Obool),U_11997),hAPP(c_COMBC(U_11999,tc_fun(U_11999,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11999))),U_12001)),U_12003))
| ~ hBOOL(hAPP(hAPP(c_member(U_11999),U_12003),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_11997,tc_fun(U_11999,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_11997,tc_HOL_Obool))),U_12001))) ),
inference(clausify,[status(thm)],[f_3175_3]) ).
fof(f_3176_1,plain,
! [V_B_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_INT__empty]) ).
fof(f_3176_2,plain,
! [U_12006,U_12005,U_12004] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12004,tc_fun(U_12005,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_12004,tc_HOL_Obool))),U_12006) = c_Orderings_Otop__class_Otop(tc_fun(U_12005,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3176_1]) ).
cnf(f_3176_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12004,tc_fun(U_12005,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_12004,tc_HOL_Obool))),U_12006) = c_Orderings_Otop__class_Otop(tc_fun(U_12005,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3176_2]) ).
fof(f_3177_1,plain,
! [V_c_2,T_c,T_b,V_A_2] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__constant]) ).
fof(f_3177_2,plain,
! [U_12010,U_12009,U_12008,U_12007] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12008,tc_fun(U_12009,tc_HOL_Obool)),U_12007),hAPP(c_COMBK(tc_fun(U_12009,tc_HOL_Obool),U_12008),U_12010)) = U_12010
| U_12007 = c_Orderings_Obot__class_Obot(tc_fun(U_12008,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12008,tc_fun(U_12009,tc_HOL_Obool)),U_12007),hAPP(c_COMBK(tc_fun(U_12009,tc_HOL_Obool),U_12008),U_12010)) = c_Orderings_Otop__class_Otop(tc_fun(U_12009,tc_HOL_Obool))
| U_12007 != c_Orderings_Obot__class_Obot(tc_fun(U_12008,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3177_1]) ).
fof(f_3177_3,plain,
( ! [U_12018,U_12016,U_12014,U_12012] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12014,tc_fun(U_12016,tc_HOL_Obool)),U_12012),hAPP(c_COMBK(tc_fun(U_12016,tc_HOL_Obool),U_12014),U_12018)) = U_12018
| U_12012 = c_Orderings_Obot__class_Obot(tc_fun(U_12014,tc_HOL_Obool)) )
& ! [U_12017,U_12015,U_12013,U_12011] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12013,tc_fun(U_12015,tc_HOL_Obool)),U_12011),hAPP(c_COMBK(tc_fun(U_12015,tc_HOL_Obool),U_12013),U_12017)) = c_Orderings_Otop__class_Otop(tc_fun(U_12015,tc_HOL_Obool))
| U_12011 != c_Orderings_Obot__class_Obot(tc_fun(U_12013,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_3177_2]) ).
cnf(f_3177_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12013,tc_fun(U_12015,tc_HOL_Obool)),U_12011),hAPP(c_COMBK(tc_fun(U_12015,tc_HOL_Obool),U_12013),U_12017)) = c_Orderings_Otop__class_Otop(tc_fun(U_12015,tc_HOL_Obool))
| U_12011 != c_Orderings_Obot__class_Obot(tc_fun(U_12013,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3177_3]) ).
cnf(f_3177_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12014,tc_fun(U_12016,tc_HOL_Obool)),U_12012),hAPP(c_COMBK(tc_fun(U_12016,tc_HOL_Obool),U_12014),U_12018)) = U_12018
| U_12012 = c_Orderings_Obot__class_Obot(tc_fun(U_12014,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3177_3]) ).
fof(f_3178_1,plain,
! [T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
| hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1]) ).
fof(f_3178_2,plain,
! [U_12020,U_12019] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12019),c_Orderings_Otop__class_Otop(tc_fun(U_12019,tc_HOL_Obool))))
| hAPP(c_Finite__Set_Ocard(U_12020),c_Orderings_Otop__class_Otop(tc_fun(U_12020,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_12019,U_12020)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_12019,U_12020),tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_3178_1]) ).
cnf(f_3178_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12019),c_Orderings_Otop__class_Otop(tc_fun(U_12019,tc_HOL_Obool))))
| hAPP(c_Finite__Set_Ocard(U_12020),c_Orderings_Otop__class_Otop(tc_fun(U_12020,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_12019,U_12020)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_12019,U_12020),tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_3178_2]) ).
fof(f_3179_1,plain,
! [T_b] :
( c_Fun_Oinj__on(tc_Nat_Onat,T_b,c_Nat_Osemiring__1__class_Oof__nat(T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| ~ class_Nat_Osemiring__char__0(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inj__of__nat]) ).
fof(f_3179_2,plain,
! [U_12021] :
( c_Fun_Oinj__on(tc_Nat_Onat,U_12021,c_Nat_Osemiring__1__class_Oof__nat(U_12021),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| ~ class_Nat_Osemiring__char__0(U_12021) ),
inference(variable_rename,[status(thm)],[f_3179_1]) ).
cnf(f_3179_3,plain,
( c_Fun_Oinj__on(tc_Nat_Onat,U_12021,c_Nat_Osemiring__1__class_Oof__nat(U_12021),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| ~ class_Nat_Osemiring__char__0(U_12021) ),
inference(clausify,[status(thm)],[f_3179_2]) ).
fof(f_3180_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]) ).
cnf(f_3180_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(clausify,[status(thm)],[f_3180_1]) ).
fof(f_3181_1,plain,
! [V_R2_2,V_R1_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oacc(T_b,V_R2_2)),c_Wellfounded_Oacc(T_b,V_R1_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R1_2),V_R2_2)) ),
inference(fof_nnf,[status(thm)],[fact_acc__subset]) ).
fof(f_3181_2,plain,
! [U_12024,U_12023,U_12022] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12022,tc_HOL_Obool)),c_Wellfounded_Oacc(U_12022,U_12024)),c_Wellfounded_Oacc(U_12022,U_12023)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12022,U_12022),tc_HOL_Obool)),U_12023),U_12024)) ),
inference(variable_rename,[status(thm)],[f_3181_1]) ).
cnf(f_3181_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12022,tc_HOL_Obool)),c_Wellfounded_Oacc(U_12022,U_12024)),c_Wellfounded_Oacc(U_12022,U_12023)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12022,U_12022),tc_HOL_Obool)),U_12023),U_12024)) ),
inference(clausify,[status(thm)],[f_3181_2]) ).
fof(f_3182_1,plain,
! [T_d,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,tc_fun(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_c),T_b),c_COMBK(T_c,T_d)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_inj__fun]) ).
fof(f_3182_2,plain,
! [U_12028,U_12027,U_12026,U_12025] :
( c_Fun_Oinj__on(U_12025,tc_fun(U_12028,U_12026),hAPP(hAPP(c_COMBB(U_12026,tc_fun(U_12028,U_12026),U_12025),c_COMBK(U_12026,U_12028)),U_12027),c_Orderings_Otop__class_Otop(tc_fun(U_12025,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(U_12025,U_12026,U_12027,c_Orderings_Otop__class_Otop(tc_fun(U_12025,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_3182_1]) ).
cnf(f_3182_3,plain,
( c_Fun_Oinj__on(U_12025,tc_fun(U_12028,U_12026),hAPP(hAPP(c_COMBB(U_12026,tc_fun(U_12028,U_12026),U_12025),c_COMBK(U_12026,U_12028)),U_12027),c_Orderings_Otop__class_Otop(tc_fun(U_12025,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(U_12025,U_12026,U_12027,c_Orderings_Otop__class_Otop(tc_fun(U_12025,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3182_2]) ).
fof(f_3183_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_3183_2,plain,
! [U_12029] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_12029),c_Orderings_Otop__class_Otop(U_12029)) = c_Orderings_Obot__class_Obot(U_12029)
| ~ class_Lattices_Oboolean__algebra(U_12029) ),
inference(variable_rename,[status(thm)],[f_3183_1]) ).
cnf(f_3183_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_12029),c_Orderings_Otop__class_Otop(U_12029)) = c_Orderings_Obot__class_Obot(U_12029)
| ~ class_Lattices_Oboolean__algebra(U_12029) ),
inference(clausify,[status(thm)],[f_3183_2]) ).
fof(f_3184_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_3184_2,plain,
! [U_12030] :
( hAPP(c_Groups_Ouminus__class_Ouminus(U_12030),c_Orderings_Obot__class_Obot(U_12030)) = c_Orderings_Otop__class_Otop(U_12030)
| ~ class_Lattices_Oboolean__algebra(U_12030) ),
inference(variable_rename,[status(thm)],[f_3184_1]) ).
cnf(f_3184_3,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(U_12030),c_Orderings_Obot__class_Obot(U_12030)) = c_Orderings_Otop__class_Otop(U_12030)
| ~ class_Lattices_Oboolean__algebra(U_12030) ),
inference(clausify,[status(thm)],[f_3184_2]) ).
fof(f_3185_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_3185_2,plain,
! [U_12032,U_12031] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12031),U_12032),hAPP(c_Groups_Ouminus__class_Ouminus(U_12031),U_12032)) = c_Orderings_Otop__class_Otop(U_12031)
| ~ class_Lattices_Oboolean__algebra(U_12031) ),
inference(variable_rename,[status(thm)],[f_3185_1]) ).
cnf(f_3185_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12031),U_12032),hAPP(c_Groups_Ouminus__class_Ouminus(U_12031),U_12032)) = c_Orderings_Otop__class_Otop(U_12031)
| ~ class_Lattices_Oboolean__algebra(U_12031) ),
inference(clausify,[status(thm)],[f_3185_2]) ).
fof(f_3186_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_3186_2,plain,
! [U_12034,U_12033] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12033),hAPP(c_Groups_Ouminus__class_Ouminus(U_12033),U_12034)),U_12034) = c_Orderings_Otop__class_Otop(U_12033)
| ~ class_Lattices_Oboolean__algebra(U_12033) ),
inference(variable_rename,[status(thm)],[f_3186_1]) ).
cnf(f_3186_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_12033),hAPP(c_Groups_Ouminus__class_Ouminus(U_12033),U_12034)),U_12034) = c_Orderings_Otop__class_Otop(U_12033)
| ~ class_Lattices_Oboolean__algebra(U_12033) ),
inference(clausify,[status(thm)],[f_3186_2]) ).
fof(f_3187_1,plain,
! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) )
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_inj__image__mem__iff]) ).
fof(f_3187_2,plain,
! [U_12039,U_12038,U_12037,U_12036,U_12035] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_12036),hAPP(U_12037,U_12038)),hAPP(c_Set_Oimage(U_12035,U_12036,U_12037),U_12039)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12035),U_12038),U_12039)) )
& ( hBOOL(hAPP(hAPP(c_member(U_12035),U_12038),U_12039))
| ~ hBOOL(hAPP(hAPP(c_member(U_12036),hAPP(U_12037,U_12038)),hAPP(c_Set_Oimage(U_12035,U_12036,U_12037),U_12039))) ) )
| ~ c_Fun_Oinj__on(U_12035,U_12036,U_12037,c_Orderings_Otop__class_Otop(tc_fun(U_12035,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_3187_1]) ).
cnf(f_3187_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_12035),U_12038),U_12039))
| ~ hBOOL(hAPP(hAPP(c_member(U_12036),hAPP(U_12037,U_12038)),hAPP(c_Set_Oimage(U_12035,U_12036,U_12037),U_12039)))
| ~ c_Fun_Oinj__on(U_12035,U_12036,U_12037,c_Orderings_Otop__class_Otop(tc_fun(U_12035,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3187_2]) ).
cnf(f_3187_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12036),hAPP(U_12037,U_12038)),hAPP(c_Set_Oimage(U_12035,U_12036,U_12037),U_12039)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12035),U_12038),U_12039))
| ~ c_Fun_Oinj__on(U_12035,U_12036,U_12037,c_Orderings_Otop__class_Otop(tc_fun(U_12035,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3187_2]) ).
fof(f_3188_1,plain,
! [V_b_2,V_f_2,T_c,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
| ! [B_x] :
( ? [B_y] :
( 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_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) )
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_range__ex1__eq]) ).
fof(f_3188_2,plain,
! [U_12047,U_12046,U_12045,U_12044] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_12045),U_12047),hAPP(c_Set_Oimage(U_12044,U_12045,U_12046),c_Orderings_Otop__class_Otop(tc_fun(U_12044,tc_HOL_Obool)))))
| ! [U_12043] :
( ? [U_12042] :
( U_12042 != U_12043
& U_12047 = hAPP(U_12046,U_12042) )
| U_12047 != hAPP(U_12046,U_12043) ) )
& ( ? [U_12041] :
( ! [U_12040] :
( U_12040 = U_12041
| U_12047 != hAPP(U_12046,U_12040) )
& U_12047 = hAPP(U_12046,U_12041) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12045),U_12047),hAPP(c_Set_Oimage(U_12044,U_12045,U_12046),c_Orderings_Otop__class_Otop(tc_fun(U_12044,tc_HOL_Obool))))) ) )
| ~ c_Fun_Oinj__on(U_12044,U_12045,U_12046,c_Orderings_Otop__class_Otop(tc_fun(U_12044,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_3188_1]) ).
fof(f_3188_3,plain,
! [U_12047,U_12046,U_12045,U_12044] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_12045),U_12047),hAPP(c_Set_Oimage(U_12044,U_12045,U_12046),c_Orderings_Otop__class_Otop(tc_fun(U_12044,tc_HOL_Obool)))))
| ! [U_12043] :
( ? [U_12042] :
( U_12042 != U_12043
& U_12047 = hAPP(U_12046,U_12042) )
| U_12047 != hAPP(U_12046,U_12043) ) )
& ( ( ! [U_12040] :
( U_12040 = sK264(U_12047,U_12046,U_12045,U_12044)
| U_12047 != hAPP(U_12046,U_12040) )
& U_12047 = hAPP(U_12046,sK264(U_12047,U_12046,U_12045,U_12044)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12045),U_12047),hAPP(c_Set_Oimage(U_12044,U_12045,U_12046),c_Orderings_Otop__class_Otop(tc_fun(U_12044,tc_HOL_Obool))))) ) )
| ~ c_Fun_Oinj__on(U_12044,U_12045,U_12046,c_Orderings_Otop__class_Otop(tc_fun(U_12044,tc_HOL_Obool))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK264]),skolemize(U_12041,sK264(U_12047,U_12046,U_12045,U_12044))],[f_3188_2]) ).
fof(f_3188_4,plain,
! [U_12047,U_12046,U_12045,U_12044] :
( ( ( hBOOL(hAPP(hAPP(c_member(U_12045),U_12047),hAPP(c_Set_Oimage(U_12044,U_12045,U_12046),c_Orderings_Otop__class_Otop(tc_fun(U_12044,tc_HOL_Obool)))))
| ! [U_12043] :
( ( sK265(U_12047,U_12046,U_12045,U_12044,U_12043) != U_12043
& U_12047 = hAPP(U_12046,sK265(U_12047,U_12046,U_12045,U_12044,U_12043)) )
| U_12047 != hAPP(U_12046,U_12043) ) )
& ( ( ! [U_12040] :
( U_12040 = sK264(U_12047,U_12046,U_12045,U_12044)
| U_12047 != hAPP(U_12046,U_12040) )
& U_12047 = hAPP(U_12046,sK264(U_12047,U_12046,U_12045,U_12044)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12045),U_12047),hAPP(c_Set_Oimage(U_12044,U_12045,U_12046),c_Orderings_Otop__class_Otop(tc_fun(U_12044,tc_HOL_Obool))))) ) )
| ~ c_Fun_Oinj__on(U_12044,U_12045,U_12046,c_Orderings_Otop__class_Otop(tc_fun(U_12044,tc_HOL_Obool))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK265]),skolemize(U_12042,sK265(U_12047,U_12046,U_12045,U_12044,U_12043))],[f_3188_3]) ).
cnf(f_3188_5,plain,
( U_12047 = hAPP(U_12046,sK264(U_12047,U_12046,U_12045,U_12044))
| ~ hBOOL(hAPP(hAPP(c_member(U_12045),U_12047),hAPP(c_Set_Oimage(U_12044,U_12045,U_12046),c_Orderings_Otop__class_Otop(tc_fun(U_12044,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(U_12044,U_12045,U_12046,c_Orderings_Otop__class_Otop(tc_fun(U_12044,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3188_4]) ).
cnf(f_3188_6,plain,
( U_12040 = sK264(U_12047,U_12046,U_12045,U_12044)
| U_12047 != hAPP(U_12046,U_12040)
| ~ hBOOL(hAPP(hAPP(c_member(U_12045),U_12047),hAPP(c_Set_Oimage(U_12044,U_12045,U_12046),c_Orderings_Otop__class_Otop(tc_fun(U_12044,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(U_12044,U_12045,U_12046,c_Orderings_Otop__class_Otop(tc_fun(U_12044,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3188_4]) ).
cnf(f_3188_7,plain,
( U_12047 = hAPP(U_12046,sK265(U_12047,U_12046,U_12045,U_12044,U_12043))
| U_12047 != hAPP(U_12046,U_12043)
| hBOOL(hAPP(hAPP(c_member(U_12045),U_12047),hAPP(c_Set_Oimage(U_12044,U_12045,U_12046),c_Orderings_Otop__class_Otop(tc_fun(U_12044,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(U_12044,U_12045,U_12046,c_Orderings_Otop__class_Otop(tc_fun(U_12044,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3188_4]) ).
cnf(f_3188_8,plain,
( sK265(U_12047,U_12046,U_12045,U_12044,U_12043) != U_12043
| U_12047 != hAPP(U_12046,U_12043)
| hBOOL(hAPP(hAPP(c_member(U_12045),U_12047),hAPP(c_Set_Oimage(U_12044,U_12045,U_12046),c_Orderings_Otop__class_Otop(tc_fun(U_12044,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(U_12044,U_12045,U_12046,c_Orderings_Otop__class_Otop(tc_fun(U_12044,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3188_4]) ).
fof(f_3189_1,plain,
! [V_f_2,T_b] :
( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
| hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_finite__UNIV__surj__inj]) ).
fof(f_3189_2,plain,
! [U_12049,U_12048] :
( c_Fun_Oinj__on(U_12048,U_12048,U_12049,c_Orderings_Otop__class_Otop(tc_fun(U_12048,tc_HOL_Obool)))
| hAPP(c_Set_Oimage(U_12048,U_12048,U_12049),c_Orderings_Otop__class_Otop(tc_fun(U_12048,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12048,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12048),c_Orderings_Otop__class_Otop(tc_fun(U_12048,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_3189_1]) ).
cnf(f_3189_3,plain,
( c_Fun_Oinj__on(U_12048,U_12048,U_12049,c_Orderings_Otop__class_Otop(tc_fun(U_12048,tc_HOL_Obool)))
| hAPP(c_Set_Oimage(U_12048,U_12048,U_12049),c_Orderings_Otop__class_Otop(tc_fun(U_12048,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12048,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12048),c_Orderings_Otop__class_Otop(tc_fun(U_12048,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_3189_2]) ).
fof(f_3190_1,plain,
! [V_f_2,T_b] :
( hAPP(c_Set_Oimage(T_b,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj]) ).
fof(f_3190_2,plain,
! [U_12051,U_12050] :
( hAPP(c_Set_Oimage(U_12050,U_12050,U_12051),c_Orderings_Otop__class_Otop(tc_fun(U_12050,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_12050,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(U_12050,U_12050,U_12051,c_Orderings_Otop__class_Otop(tc_fun(U_12050,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12050),c_Orderings_Otop__class_Otop(tc_fun(U_12050,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_3190_1]) ).
cnf(f_3190_3,plain,
( hAPP(c_Set_Oimage(U_12050,U_12050,U_12051),c_Orderings_Otop__class_Otop(tc_fun(U_12050,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_12050,tc_HOL_Obool))
| ~ c_Fun_Oinj__on(U_12050,U_12050,U_12051,c_Orderings_Otop__class_Otop(tc_fun(U_12050,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12050),c_Orderings_Otop__class_Otop(tc_fun(U_12050,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_3190_2]) ).
fof(f_3191_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) )
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_inj__image__subset__iff]) ).
fof(f_3191_2,plain,
! [U_12056,U_12055,U_12054,U_12053,U_12052] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12053,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12052,U_12053,U_12054),U_12055)),hAPP(c_Set_Oimage(U_12052,U_12053,U_12054),U_12056)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12052,tc_HOL_Obool)),U_12055),U_12056)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12052,tc_HOL_Obool)),U_12055),U_12056))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12053,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12052,U_12053,U_12054),U_12055)),hAPP(c_Set_Oimage(U_12052,U_12053,U_12054),U_12056))) ) )
| ~ c_Fun_Oinj__on(U_12052,U_12053,U_12054,c_Orderings_Otop__class_Otop(tc_fun(U_12052,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_3191_1]) ).
cnf(f_3191_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12052,tc_HOL_Obool)),U_12055),U_12056))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12053,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12052,U_12053,U_12054),U_12055)),hAPP(c_Set_Oimage(U_12052,U_12053,U_12054),U_12056)))
| ~ c_Fun_Oinj__on(U_12052,U_12053,U_12054,c_Orderings_Otop__class_Otop(tc_fun(U_12052,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3191_2]) ).
cnf(f_3191_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12053,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12052,U_12053,U_12054),U_12055)),hAPP(c_Set_Oimage(U_12052,U_12053,U_12054),U_12056)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12052,tc_HOL_Obool)),U_12055),U_12056))
| ~ c_Fun_Oinj__on(U_12052,U_12053,U_12054,c_Orderings_Otop__class_Otop(tc_fun(U_12052,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3191_2]) ).
fof(f_3192_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_image__Int]) ).
fof(f_3192_2,plain,
! [U_12061,U_12060,U_12059,U_12058,U_12057] :
( hAPP(c_Set_Oimage(U_12057,U_12058,U_12059),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12057,tc_HOL_Obool)),U_12060),U_12061)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12058,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12057,U_12058,U_12059),U_12060)),hAPP(c_Set_Oimage(U_12057,U_12058,U_12059),U_12061))
| ~ c_Fun_Oinj__on(U_12057,U_12058,U_12059,c_Orderings_Otop__class_Otop(tc_fun(U_12057,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_3192_1]) ).
cnf(f_3192_3,plain,
( hAPP(c_Set_Oimage(U_12057,U_12058,U_12059),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12057,tc_HOL_Obool)),U_12060),U_12061)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12058,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12057,U_12058,U_12059),U_12060)),hAPP(c_Set_Oimage(U_12057,U_12058,U_12059),U_12061))
| ~ c_Fun_Oinj__on(U_12057,U_12058,U_12059,c_Orderings_Otop__class_Otop(tc_fun(U_12057,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3192_2]) ).
fof(f_3193_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_image__set__diff]) ).
fof(f_3193_2,plain,
! [U_12066,U_12065,U_12064,U_12063,U_12062] :
( hAPP(c_Set_Oimage(U_12062,U_12063,U_12064),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12062,tc_HOL_Obool)),U_12065),U_12066)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12063,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12062,U_12063,U_12064),U_12065)),hAPP(c_Set_Oimage(U_12062,U_12063,U_12064),U_12066))
| ~ c_Fun_Oinj__on(U_12062,U_12063,U_12064,c_Orderings_Otop__class_Otop(tc_fun(U_12062,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_3193_1]) ).
cnf(f_3193_3,plain,
( hAPP(c_Set_Oimage(U_12062,U_12063,U_12064),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12062,tc_HOL_Obool)),U_12065),U_12066)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12063,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12062,U_12063,U_12064),U_12065)),hAPP(c_Set_Oimage(U_12062,U_12063,U_12064),U_12066))
| ~ c_Fun_Oinj__on(U_12062,U_12063,U_12064,c_Orderings_Otop__class_Otop(tc_fun(U_12062,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3193_2]) ).
fof(f_3194_1,plain,
! [V_A_2,V_f_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))))
| hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_surj__Compl__image__subset]) ).
fof(f_3194_2,plain,
! [U_12070,U_12069,U_12068,U_12067] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12068,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12068,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12067,U_12068,U_12069),U_12070))),hAPP(c_Set_Oimage(U_12067,U_12068,U_12069),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12067,tc_HOL_Obool)),U_12070))))
| hAPP(c_Set_Oimage(U_12067,U_12068,U_12069),c_Orderings_Otop__class_Otop(tc_fun(U_12067,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12068,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_3194_1]) ).
cnf(f_3194_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12068,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12068,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12067,U_12068,U_12069),U_12070))),hAPP(c_Set_Oimage(U_12067,U_12068,U_12069),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12067,tc_HOL_Obool)),U_12070))))
| hAPP(c_Set_Oimage(U_12067,U_12068,U_12069),c_Orderings_Otop__class_Otop(tc_fun(U_12067,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12068,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3194_2]) ).
fof(f_3195_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]) ).
cnf(f_3195_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(clausify,[status(thm)],[f_3195_1]) ).
fof(f_3196_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I1_J]) ).
fof(f_3196_2,plain,
! [U_12075,U_12074,U_12073,U_12072,U_12071] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12072,tc_fun(U_12073,tc_HOL_Obool)),U_12071),hAPP(hAPP(c_COMBC(U_12072,tc_fun(U_12073,tc_HOL_Obool),tc_fun(U_12073,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12073,tc_HOL_Obool),tc_fun(tc_fun(U_12073,tc_HOL_Obool),tc_fun(U_12073,tc_HOL_Obool)),U_12072),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12073,tc_HOL_Obool))),U_12074)),U_12075)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12073,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12072,tc_fun(U_12073,tc_HOL_Obool)),U_12071),U_12074)),U_12075)
| U_12071 = c_Orderings_Obot__class_Obot(tc_fun(U_12072,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12072,tc_fun(U_12073,tc_HOL_Obool)),U_12071),hAPP(hAPP(c_COMBC(U_12072,tc_fun(U_12073,tc_HOL_Obool),tc_fun(U_12073,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12073,tc_HOL_Obool),tc_fun(tc_fun(U_12073,tc_HOL_Obool),tc_fun(U_12073,tc_HOL_Obool)),U_12072),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12073,tc_HOL_Obool))),U_12074)),U_12075)) = c_Orderings_Otop__class_Otop(tc_fun(U_12073,tc_HOL_Obool))
| U_12071 != c_Orderings_Obot__class_Obot(tc_fun(U_12072,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3196_1]) ).
fof(f_3196_3,plain,
( ! [U_12085,U_12083,U_12081,U_12079,U_12077] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12079,tc_fun(U_12081,tc_HOL_Obool)),U_12077),hAPP(hAPP(c_COMBC(U_12079,tc_fun(U_12081,tc_HOL_Obool),tc_fun(U_12081,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12081,tc_HOL_Obool),tc_fun(tc_fun(U_12081,tc_HOL_Obool),tc_fun(U_12081,tc_HOL_Obool)),U_12079),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12081,tc_HOL_Obool))),U_12083)),U_12085)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12081,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12079,tc_fun(U_12081,tc_HOL_Obool)),U_12077),U_12083)),U_12085)
| U_12077 = c_Orderings_Obot__class_Obot(tc_fun(U_12079,tc_HOL_Obool)) )
& ! [U_12084,U_12082,U_12080,U_12078,U_12076] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12078,tc_fun(U_12080,tc_HOL_Obool)),U_12076),hAPP(hAPP(c_COMBC(U_12078,tc_fun(U_12080,tc_HOL_Obool),tc_fun(U_12080,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12080,tc_HOL_Obool),tc_fun(tc_fun(U_12080,tc_HOL_Obool),tc_fun(U_12080,tc_HOL_Obool)),U_12078),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12080,tc_HOL_Obool))),U_12082)),U_12084)) = c_Orderings_Otop__class_Otop(tc_fun(U_12080,tc_HOL_Obool))
| U_12076 != c_Orderings_Obot__class_Obot(tc_fun(U_12078,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_3196_2]) ).
cnf(f_3196_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12078,tc_fun(U_12080,tc_HOL_Obool)),U_12076),hAPP(hAPP(c_COMBC(U_12078,tc_fun(U_12080,tc_HOL_Obool),tc_fun(U_12080,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12080,tc_HOL_Obool),tc_fun(tc_fun(U_12080,tc_HOL_Obool),tc_fun(U_12080,tc_HOL_Obool)),U_12078),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12080,tc_HOL_Obool))),U_12082)),U_12084)) = c_Orderings_Otop__class_Otop(tc_fun(U_12080,tc_HOL_Obool))
| U_12076 != c_Orderings_Obot__class_Obot(tc_fun(U_12078,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3196_3]) ).
cnf(f_3196_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12079,tc_fun(U_12081,tc_HOL_Obool)),U_12077),hAPP(hAPP(c_COMBC(U_12079,tc_fun(U_12081,tc_HOL_Obool),tc_fun(U_12081,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12081,tc_HOL_Obool),tc_fun(tc_fun(U_12081,tc_HOL_Obool),tc_fun(U_12081,tc_HOL_Obool)),U_12079),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12081,tc_HOL_Obool))),U_12083)),U_12085)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12081,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12079,tc_fun(U_12081,tc_HOL_Obool)),U_12077),U_12083)),U_12085)
| U_12077 = c_Orderings_Obot__class_Obot(tc_fun(U_12079,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3196_3]) ).
fof(f_3197_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I2_J]) ).
fof(f_3197_2,plain,
! [U_12090,U_12089,U_12088,U_12087,U_12086] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12087,tc_fun(U_12088,tc_HOL_Obool)),U_12086),hAPP(hAPP(c_COMBB(tc_fun(U_12088,tc_HOL_Obool),tc_fun(U_12088,tc_HOL_Obool),U_12087),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12088,tc_HOL_Obool)),U_12089)),U_12090)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12088,tc_HOL_Obool)),U_12089),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12087,tc_fun(U_12088,tc_HOL_Obool)),U_12086),U_12090))
| U_12086 = c_Orderings_Obot__class_Obot(tc_fun(U_12087,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12087,tc_fun(U_12088,tc_HOL_Obool)),U_12086),hAPP(hAPP(c_COMBB(tc_fun(U_12088,tc_HOL_Obool),tc_fun(U_12088,tc_HOL_Obool),U_12087),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12088,tc_HOL_Obool)),U_12089)),U_12090)) = c_Orderings_Otop__class_Otop(tc_fun(U_12088,tc_HOL_Obool))
| U_12086 != c_Orderings_Obot__class_Obot(tc_fun(U_12087,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3197_1]) ).
fof(f_3197_3,plain,
( ! [U_12100,U_12098,U_12096,U_12094,U_12092] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12094,tc_fun(U_12096,tc_HOL_Obool)),U_12092),hAPP(hAPP(c_COMBB(tc_fun(U_12096,tc_HOL_Obool),tc_fun(U_12096,tc_HOL_Obool),U_12094),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12096,tc_HOL_Obool)),U_12098)),U_12100)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12096,tc_HOL_Obool)),U_12098),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12094,tc_fun(U_12096,tc_HOL_Obool)),U_12092),U_12100))
| U_12092 = c_Orderings_Obot__class_Obot(tc_fun(U_12094,tc_HOL_Obool)) )
& ! [U_12099,U_12097,U_12095,U_12093,U_12091] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12093,tc_fun(U_12095,tc_HOL_Obool)),U_12091),hAPP(hAPP(c_COMBB(tc_fun(U_12095,tc_HOL_Obool),tc_fun(U_12095,tc_HOL_Obool),U_12093),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12095,tc_HOL_Obool)),U_12097)),U_12099)) = c_Orderings_Otop__class_Otop(tc_fun(U_12095,tc_HOL_Obool))
| U_12091 != c_Orderings_Obot__class_Obot(tc_fun(U_12093,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_3197_2]) ).
cnf(f_3197_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12093,tc_fun(U_12095,tc_HOL_Obool)),U_12091),hAPP(hAPP(c_COMBB(tc_fun(U_12095,tc_HOL_Obool),tc_fun(U_12095,tc_HOL_Obool),U_12093),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12095,tc_HOL_Obool)),U_12097)),U_12099)) = c_Orderings_Otop__class_Otop(tc_fun(U_12095,tc_HOL_Obool))
| U_12091 != c_Orderings_Obot__class_Obot(tc_fun(U_12093,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3197_3]) ).
cnf(f_3197_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12094,tc_fun(U_12096,tc_HOL_Obool)),U_12092),hAPP(hAPP(c_COMBB(tc_fun(U_12096,tc_HOL_Obool),tc_fun(U_12096,tc_HOL_Obool),U_12094),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12096,tc_HOL_Obool)),U_12098)),U_12100)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12096,tc_HOL_Obool)),U_12098),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12094,tc_fun(U_12096,tc_HOL_Obool)),U_12092),U_12100))
| U_12092 = c_Orderings_Obot__class_Obot(tc_fun(U_12094,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3197_3]) ).
fof(f_3198_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2)
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I3_J]) ).
fof(f_3198_2,plain,
! [U_12105,U_12104,U_12103,U_12102,U_12101] :
( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12103,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12102,tc_fun(U_12103,tc_HOL_Obool)),U_12101),U_12104)),U_12105) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12102,tc_fun(U_12103,tc_HOL_Obool)),U_12101),hAPP(hAPP(c_COMBC(U_12102,tc_fun(U_12103,tc_HOL_Obool),tc_fun(U_12103,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12103,tc_HOL_Obool),tc_fun(tc_fun(U_12103,tc_HOL_Obool),tc_fun(U_12103,tc_HOL_Obool)),U_12102),c_Groups_Ominus__class_Ominus(tc_fun(U_12103,tc_HOL_Obool))),U_12104)),U_12105))
| U_12101 = c_Orderings_Obot__class_Obot(tc_fun(U_12102,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12103,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12102,tc_fun(U_12103,tc_HOL_Obool)),U_12101),U_12104)),U_12105) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12103,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12103,tc_HOL_Obool))),U_12105)
| U_12101 != c_Orderings_Obot__class_Obot(tc_fun(U_12102,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3198_1]) ).
fof(f_3198_3,plain,
( ! [U_12115,U_12113,U_12111,U_12109,U_12107] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12111,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12109,tc_fun(U_12111,tc_HOL_Obool)),U_12107),U_12113)),U_12115) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12109,tc_fun(U_12111,tc_HOL_Obool)),U_12107),hAPP(hAPP(c_COMBC(U_12109,tc_fun(U_12111,tc_HOL_Obool),tc_fun(U_12111,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12111,tc_HOL_Obool),tc_fun(tc_fun(U_12111,tc_HOL_Obool),tc_fun(U_12111,tc_HOL_Obool)),U_12109),c_Groups_Ominus__class_Ominus(tc_fun(U_12111,tc_HOL_Obool))),U_12113)),U_12115))
| U_12107 = c_Orderings_Obot__class_Obot(tc_fun(U_12109,tc_HOL_Obool)) )
& ! [U_12114,U_12112,U_12110,U_12108,U_12106] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12110,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12108,tc_fun(U_12110,tc_HOL_Obool)),U_12106),U_12112)),U_12114) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12110,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12110,tc_HOL_Obool))),U_12114)
| U_12106 != c_Orderings_Obot__class_Obot(tc_fun(U_12108,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_3198_2]) ).
cnf(f_3198_4,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12110,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12108,tc_fun(U_12110,tc_HOL_Obool)),U_12106),U_12112)),U_12114) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12110,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12110,tc_HOL_Obool))),U_12114)
| U_12106 != c_Orderings_Obot__class_Obot(tc_fun(U_12108,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3198_3]) ).
cnf(f_3198_5,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12111,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12109,tc_fun(U_12111,tc_HOL_Obool)),U_12107),U_12113)),U_12115) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12109,tc_fun(U_12111,tc_HOL_Obool)),U_12107),hAPP(hAPP(c_COMBC(U_12109,tc_fun(U_12111,tc_HOL_Obool),tc_fun(U_12111,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12111,tc_HOL_Obool),tc_fun(tc_fun(U_12111,tc_HOL_Obool),tc_fun(U_12111,tc_HOL_Obool)),U_12109),c_Groups_Ominus__class_Ominus(tc_fun(U_12111,tc_HOL_Obool))),U_12113)),U_12115))
| U_12107 = c_Orderings_Obot__class_Obot(tc_fun(U_12109,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3198_3]) ).
fof(f_3199_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2)
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I3_J]) ).
fof(f_3199_2,plain,
! [U_12120,U_12119,U_12118,U_12117,U_12116] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12117,tc_fun(U_12118,tc_HOL_Obool)),U_12116),hAPP(hAPP(c_COMBC(U_12117,tc_fun(U_12118,tc_HOL_Obool),tc_fun(U_12118,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12118,tc_HOL_Obool),tc_fun(tc_fun(U_12118,tc_HOL_Obool),tc_fun(U_12118,tc_HOL_Obool)),U_12117),c_Groups_Ominus__class_Ominus(tc_fun(U_12118,tc_HOL_Obool))),U_12119)),U_12120)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12118,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12117,tc_fun(U_12118,tc_HOL_Obool)),U_12116),U_12119)),U_12120)
| U_12116 = c_Orderings_Obot__class_Obot(tc_fun(U_12117,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12117,tc_fun(U_12118,tc_HOL_Obool)),U_12116),hAPP(hAPP(c_COMBC(U_12117,tc_fun(U_12118,tc_HOL_Obool),tc_fun(U_12118,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12118,tc_HOL_Obool),tc_fun(tc_fun(U_12118,tc_HOL_Obool),tc_fun(U_12118,tc_HOL_Obool)),U_12117),c_Groups_Ominus__class_Ominus(tc_fun(U_12118,tc_HOL_Obool))),U_12119)),U_12120)) = c_Orderings_Otop__class_Otop(tc_fun(U_12118,tc_HOL_Obool))
| U_12116 != c_Orderings_Obot__class_Obot(tc_fun(U_12117,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3199_1]) ).
fof(f_3199_3,plain,
( ! [U_12130,U_12128,U_12126,U_12124,U_12122] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12124,tc_fun(U_12126,tc_HOL_Obool)),U_12122),hAPP(hAPP(c_COMBC(U_12124,tc_fun(U_12126,tc_HOL_Obool),tc_fun(U_12126,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12126,tc_HOL_Obool),tc_fun(tc_fun(U_12126,tc_HOL_Obool),tc_fun(U_12126,tc_HOL_Obool)),U_12124),c_Groups_Ominus__class_Ominus(tc_fun(U_12126,tc_HOL_Obool))),U_12128)),U_12130)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12126,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12124,tc_fun(U_12126,tc_HOL_Obool)),U_12122),U_12128)),U_12130)
| U_12122 = c_Orderings_Obot__class_Obot(tc_fun(U_12124,tc_HOL_Obool)) )
& ! [U_12129,U_12127,U_12125,U_12123,U_12121] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12123,tc_fun(U_12125,tc_HOL_Obool)),U_12121),hAPP(hAPP(c_COMBC(U_12123,tc_fun(U_12125,tc_HOL_Obool),tc_fun(U_12125,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12125,tc_HOL_Obool),tc_fun(tc_fun(U_12125,tc_HOL_Obool),tc_fun(U_12125,tc_HOL_Obool)),U_12123),c_Groups_Ominus__class_Ominus(tc_fun(U_12125,tc_HOL_Obool))),U_12127)),U_12129)) = c_Orderings_Otop__class_Otop(tc_fun(U_12125,tc_HOL_Obool))
| U_12121 != c_Orderings_Obot__class_Obot(tc_fun(U_12123,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_3199_2]) ).
cnf(f_3199_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12123,tc_fun(U_12125,tc_HOL_Obool)),U_12121),hAPP(hAPP(c_COMBC(U_12123,tc_fun(U_12125,tc_HOL_Obool),tc_fun(U_12125,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12125,tc_HOL_Obool),tc_fun(tc_fun(U_12125,tc_HOL_Obool),tc_fun(U_12125,tc_HOL_Obool)),U_12123),c_Groups_Ominus__class_Ominus(tc_fun(U_12125,tc_HOL_Obool))),U_12127)),U_12129)) = c_Orderings_Otop__class_Otop(tc_fun(U_12125,tc_HOL_Obool))
| U_12121 != c_Orderings_Obot__class_Obot(tc_fun(U_12123,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3199_3]) ).
cnf(f_3199_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12124,tc_fun(U_12126,tc_HOL_Obool)),U_12122),hAPP(hAPP(c_COMBC(U_12124,tc_fun(U_12126,tc_HOL_Obool),tc_fun(U_12126,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12126,tc_HOL_Obool),tc_fun(tc_fun(U_12126,tc_HOL_Obool),tc_fun(U_12126,tc_HOL_Obool)),U_12124),c_Groups_Ominus__class_Ominus(tc_fun(U_12126,tc_HOL_Obool))),U_12128)),U_12130)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12126,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12124,tc_fun(U_12126,tc_HOL_Obool)),U_12122),U_12128)),U_12130)
| U_12122 = c_Orderings_Obot__class_Obot(tc_fun(U_12124,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3199_3]) ).
fof(f_3200_1,plain,
! [V_y_2] :
( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_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)))) ),
inference(fof_nnf,[status(thm)],[fact_of__nat__inverse]) ).
fof(f_3200_2,plain,
! [U_12131] :
( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_12131)) = U_12131
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_12131),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_3200_1]) ).
cnf(f_3200_3,plain,
( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_12131)) = U_12131
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_12131),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_3200_2]) ).
fof(f_3201_1,plain,
! [V_b_2,V_a_2,V_f_2,T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_b_2))
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_b_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_fold1Set__sing]) ).
fof(f_3201_2,plain,
! [U_12135,U_12134,U_12133,U_12132] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12132,U_12133,hAPP(hAPP(c_Set_Oinsert(U_12132),U_12134),c_Orderings_Obot__class_Obot(tc_fun(U_12132,tc_HOL_Obool)))),U_12135))
| U_12134 != U_12135 )
& ( U_12134 = U_12135
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12132,U_12133,hAPP(hAPP(c_Set_Oinsert(U_12132),U_12134),c_Orderings_Obot__class_Obot(tc_fun(U_12132,tc_HOL_Obool)))),U_12135)) ) ),
inference(variable_rename,[status(thm)],[f_3201_1]) ).
fof(f_3201_3,plain,
( ! [U_12143,U_12141] :
( ! [U_12139,U_12137] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12137,U_12139,hAPP(hAPP(c_Set_Oinsert(U_12137),U_12141),c_Orderings_Obot__class_Obot(tc_fun(U_12137,tc_HOL_Obool)))),U_12143))
| U_12141 != U_12143 )
& ! [U_12142,U_12140] :
( ! [U_12138,U_12136] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12136,U_12138,hAPP(hAPP(c_Set_Oinsert(U_12136),U_12140),c_Orderings_Obot__class_Obot(tc_fun(U_12136,tc_HOL_Obool)))),U_12142))
| U_12140 = U_12142 ) ),
inference(miniscope,[status(thm)],[f_3201_2]) ).
cnf(f_3201_4,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12136,U_12138,hAPP(hAPP(c_Set_Oinsert(U_12136),U_12140),c_Orderings_Obot__class_Obot(tc_fun(U_12136,tc_HOL_Obool)))),U_12142))
| U_12140 = U_12142 ),
inference(clausify,[status(thm)],[f_3201_3]) ).
cnf(f_3201_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12137,U_12139,hAPP(hAPP(c_Set_Oinsert(U_12137),U_12141),c_Orderings_Obot__class_Obot(tc_fun(U_12137,tc_HOL_Obool)))),U_12143))
| U_12141 != U_12143 ),
inference(clausify,[status(thm)],[f_3201_3]) ).
fof(f_3202_1,plain,
! [V_a_2,V_r_2,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_acc__downward]) ).
fof(f_3202_2,plain,
! [U_12147,U_12146,U_12145,U_12144] :
( hBOOL(hAPP(hAPP(c_member(U_12144),U_12147),c_Wellfounded_Oacc(U_12144,U_12146)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12144,U_12144)),hAPP(hAPP(c_Product__Type_OPair(U_12144,U_12144),U_12147),U_12145)),U_12146))
| ~ hBOOL(hAPP(hAPP(c_member(U_12144),U_12145),c_Wellfounded_Oacc(U_12144,U_12146))) ),
inference(variable_rename,[status(thm)],[f_3202_1]) ).
cnf(f_3202_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_12144),U_12147),c_Wellfounded_Oacc(U_12144,U_12146)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12144,U_12144)),hAPP(hAPP(c_Product__Type_OPair(U_12144,U_12144),U_12147),U_12145)),U_12146))
| ~ hBOOL(hAPP(hAPP(c_member(U_12144),U_12145),c_Wellfounded_Oacc(U_12144,U_12146))) ),
inference(clausify,[status(thm)],[f_3202_2]) ).
fof(f_3203_1,plain,
! [V_r_2,V_a_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_acc_Osimps]) ).
fof(f_3203_2,plain,
! [U_12152,U_12151,U_12150] :
( ( hBOOL(hAPP(hAPP(c_member(U_12150),U_12151),c_Wellfounded_Oacc(U_12150,U_12152)))
| ? [U_12149] :
( ~ hBOOL(hAPP(hAPP(c_member(U_12150),U_12149),c_Wellfounded_Oacc(U_12150,U_12152)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_12150,U_12150)),hAPP(hAPP(c_Product__Type_OPair(U_12150,U_12150),U_12149),U_12151)),U_12152)) ) )
& ( ! [U_12148] :
( hBOOL(hAPP(hAPP(c_member(U_12150),U_12148),c_Wellfounded_Oacc(U_12150,U_12152)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12150,U_12150)),hAPP(hAPP(c_Product__Type_OPair(U_12150,U_12150),U_12148),U_12151)),U_12152)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12150),U_12151),c_Wellfounded_Oacc(U_12150,U_12152))) ) ),
inference(variable_rename,[status(thm)],[f_3203_1]) ).
fof(f_3203_3,plain,
( ! [U_12158,U_12156,U_12154] :
( hBOOL(hAPP(hAPP(c_member(U_12154),U_12156),c_Wellfounded_Oacc(U_12154,U_12158)))
| ? [U_12149] :
( ~ hBOOL(hAPP(hAPP(c_member(U_12154),U_12149),c_Wellfounded_Oacc(U_12154,U_12158)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_12154,U_12154)),hAPP(hAPP(c_Product__Type_OPair(U_12154,U_12154),U_12149),U_12156)),U_12158)) ) )
& ! [U_12157,U_12155,U_12153] :
( ! [U_12148] :
( hBOOL(hAPP(hAPP(c_member(U_12153),U_12148),c_Wellfounded_Oacc(U_12153,U_12157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12153,U_12153)),hAPP(hAPP(c_Product__Type_OPair(U_12153,U_12153),U_12148),U_12155)),U_12157)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12153),U_12155),c_Wellfounded_Oacc(U_12153,U_12157))) ) ),
inference(miniscope,[status(thm)],[f_3203_2]) ).
fof(f_3203_4,plain,
( ! [U_12158,U_12156,U_12154] :
( hBOOL(hAPP(hAPP(c_member(U_12154),U_12156),c_Wellfounded_Oacc(U_12154,U_12158)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_12154),sK266(U_12158,U_12156,U_12154)),c_Wellfounded_Oacc(U_12154,U_12158)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_12154,U_12154)),hAPP(hAPP(c_Product__Type_OPair(U_12154,U_12154),sK266(U_12158,U_12156,U_12154)),U_12156)),U_12158)) ) )
& ! [U_12157,U_12155,U_12153] :
( ! [U_12148] :
( hBOOL(hAPP(hAPP(c_member(U_12153),U_12148),c_Wellfounded_Oacc(U_12153,U_12157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12153,U_12153)),hAPP(hAPP(c_Product__Type_OPair(U_12153,U_12153),U_12148),U_12155)),U_12157)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12153),U_12155),c_Wellfounded_Oacc(U_12153,U_12157))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK266]),skolemize(U_12149,sK266(U_12158,U_12156,U_12154))],[f_3203_3]) ).
cnf(f_3203_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_12153),U_12148),c_Wellfounded_Oacc(U_12153,U_12157)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12153,U_12153)),hAPP(hAPP(c_Product__Type_OPair(U_12153,U_12153),U_12148),U_12155)),U_12157))
| ~ hBOOL(hAPP(hAPP(c_member(U_12153),U_12155),c_Wellfounded_Oacc(U_12153,U_12157))) ),
inference(clausify,[status(thm)],[f_3203_4]) ).
cnf(f_3203_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12154,U_12154)),hAPP(hAPP(c_Product__Type_OPair(U_12154,U_12154),sK266(U_12158,U_12156,U_12154)),U_12156)),U_12158))
| hBOOL(hAPP(hAPP(c_member(U_12154),U_12156),c_Wellfounded_Oacc(U_12154,U_12158))) ),
inference(clausify,[status(thm)],[f_3203_4]) ).
cnf(f_3203_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_12154),sK266(U_12158,U_12156,U_12154)),c_Wellfounded_Oacc(U_12154,U_12158)))
| hBOOL(hAPP(hAPP(c_member(U_12154),U_12156),c_Wellfounded_Oacc(U_12154,U_12158))) ),
inference(clausify,[status(thm)],[f_3203_4]) ).
fof(f_3204_1,plain,
! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2),
inference(fof_nnf,[status(thm)],[fact_UN__UN__finite__eq]) ).
fof(f_3204_2,plain,
! [U_12160,U_12159] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12159,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_12159,tc_HOL_Obool)),tc_fun(U_12159,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_12159,tc_HOL_Obool)),tc_fun(U_12159,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12159,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_12160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12159,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12160),
inference(variable_rename,[status(thm)],[f_3204_1]) ).
cnf(f_3204_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12159,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_12159,tc_HOL_Obool)),tc_fun(U_12159,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_12159,tc_HOL_Obool)),tc_fun(U_12159,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12159,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_12160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12159,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12160),
inference(clausify,[status(thm)],[f_3204_2]) ).
fof(f_3205_1,plain,
! [T_b] : c_Fun_Oinj__on(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_inj__singleton]) ).
fof(f_3205_2,plain,
! [U_12161] : c_Fun_Oinj__on(U_12161,tc_fun(U_12161,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12161,tc_fun(U_12161,tc_HOL_Obool),tc_fun(U_12161,tc_HOL_Obool)),c_Set_Oinsert(U_12161)),c_Orderings_Obot__class_Obot(tc_fun(U_12161,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12161,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_3205_1]) ).
cnf(f_3205_3,plain,
c_Fun_Oinj__on(U_12161,tc_fun(U_12161,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_12161,tc_fun(U_12161,tc_HOL_Obool),tc_fun(U_12161,tc_HOL_Obool)),c_Set_Oinsert(U_12161)),c_Orderings_Obot__class_Obot(tc_fun(U_12161,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12161,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_3205_2]) ).
fof(f_3206_1,plain,
! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_INF__INT__eq2]) ).
fof(f_3206_2,plain,
! [U_12167,U_12166,U_12165,U_12164,U_12163,U_12162] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12162,tc_fun(U_12163,tc_fun(U_12164,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12162,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12163,U_12164),tc_HOL_Obool),tc_fun(U_12163,tc_fun(U_12164,tc_HOL_Obool)),U_12162),hAPP(c_COMBC(U_12163,tc_fun(tc_prod(U_12163,U_12164),tc_HOL_Obool),tc_fun(U_12164,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12164,tc_fun(tc_fun(tc_prod(U_12163,U_12164),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12163,U_12164),tc_HOL_Obool),tc_fun(U_12164,tc_HOL_Obool)),U_12163),c_COMBC(U_12164,tc_fun(tc_prod(U_12163,U_12164),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12164,tc_prod(U_12163,U_12164)),tc_fun(U_12164,tc_fun(tc_fun(tc_prod(U_12163,U_12164),tc_HOL_Obool),tc_HOL_Obool)),U_12163),hAPP(c_COMBB(tc_prod(U_12163,U_12164),tc_fun(tc_fun(tc_prod(U_12163,U_12164),tc_HOL_Obool),tc_HOL_Obool),U_12164),c_member(tc_prod(U_12163,U_12164)))),c_Product__Type_OPair(U_12163,U_12164))))),U_12165)),U_12166),U_12167))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12163,U_12164)),hAPP(hAPP(c_Product__Type_OPair(U_12163,U_12164),U_12166),U_12167)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12162,tc_fun(tc_prod(U_12163,U_12164),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12162,tc_HOL_Obool))),U_12165))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12163,U_12164)),hAPP(hAPP(c_Product__Type_OPair(U_12163,U_12164),U_12166),U_12167)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12162,tc_fun(tc_prod(U_12163,U_12164),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12162,tc_HOL_Obool))),U_12165)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12162,tc_fun(U_12163,tc_fun(U_12164,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12162,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12163,U_12164),tc_HOL_Obool),tc_fun(U_12163,tc_fun(U_12164,tc_HOL_Obool)),U_12162),hAPP(c_COMBC(U_12163,tc_fun(tc_prod(U_12163,U_12164),tc_HOL_Obool),tc_fun(U_12164,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12164,tc_fun(tc_fun(tc_prod(U_12163,U_12164),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12163,U_12164),tc_HOL_Obool),tc_fun(U_12164,tc_HOL_Obool)),U_12163),c_COMBC(U_12164,tc_fun(tc_prod(U_12163,U_12164),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12164,tc_prod(U_12163,U_12164)),tc_fun(U_12164,tc_fun(tc_fun(tc_prod(U_12163,U_12164),tc_HOL_Obool),tc_HOL_Obool)),U_12163),hAPP(c_COMBB(tc_prod(U_12163,U_12164),tc_fun(tc_fun(tc_prod(U_12163,U_12164),tc_HOL_Obool),tc_HOL_Obool),U_12164),c_member(tc_prod(U_12163,U_12164)))),c_Product__Type_OPair(U_12163,U_12164))))),U_12165)),U_12166),U_12167)) ) ),
inference(variable_rename,[status(thm)],[f_3206_1]) ).
fof(f_3206_3,plain,
( ! [U_12179,U_12177,U_12175,U_12173,U_12171,U_12169] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12169,tc_fun(U_12171,tc_fun(U_12173,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12169,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12171,U_12173),tc_HOL_Obool),tc_fun(U_12171,tc_fun(U_12173,tc_HOL_Obool)),U_12169),hAPP(c_COMBC(U_12171,tc_fun(tc_prod(U_12171,U_12173),tc_HOL_Obool),tc_fun(U_12173,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12173,tc_fun(tc_fun(tc_prod(U_12171,U_12173),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12171,U_12173),tc_HOL_Obool),tc_fun(U_12173,tc_HOL_Obool)),U_12171),c_COMBC(U_12173,tc_fun(tc_prod(U_12171,U_12173),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12173,tc_prod(U_12171,U_12173)),tc_fun(U_12173,tc_fun(tc_fun(tc_prod(U_12171,U_12173),tc_HOL_Obool),tc_HOL_Obool)),U_12171),hAPP(c_COMBB(tc_prod(U_12171,U_12173),tc_fun(tc_fun(tc_prod(U_12171,U_12173),tc_HOL_Obool),tc_HOL_Obool),U_12173),c_member(tc_prod(U_12171,U_12173)))),c_Product__Type_OPair(U_12171,U_12173))))),U_12175)),U_12177),U_12179))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12171,U_12173)),hAPP(hAPP(c_Product__Type_OPair(U_12171,U_12173),U_12177),U_12179)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12169,tc_fun(tc_prod(U_12171,U_12173),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12169,tc_HOL_Obool))),U_12175))) )
& ! [U_12178,U_12176,U_12174,U_12172,U_12170,U_12168] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12170,U_12172)),hAPP(hAPP(c_Product__Type_OPair(U_12170,U_12172),U_12176),U_12178)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12168,tc_fun(tc_prod(U_12170,U_12172),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12168,tc_HOL_Obool))),U_12174)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12168,tc_fun(U_12170,tc_fun(U_12172,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12168,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12170,U_12172),tc_HOL_Obool),tc_fun(U_12170,tc_fun(U_12172,tc_HOL_Obool)),U_12168),hAPP(c_COMBC(U_12170,tc_fun(tc_prod(U_12170,U_12172),tc_HOL_Obool),tc_fun(U_12172,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12172,tc_fun(tc_fun(tc_prod(U_12170,U_12172),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12170,U_12172),tc_HOL_Obool),tc_fun(U_12172,tc_HOL_Obool)),U_12170),c_COMBC(U_12172,tc_fun(tc_prod(U_12170,U_12172),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12172,tc_prod(U_12170,U_12172)),tc_fun(U_12172,tc_fun(tc_fun(tc_prod(U_12170,U_12172),tc_HOL_Obool),tc_HOL_Obool)),U_12170),hAPP(c_COMBB(tc_prod(U_12170,U_12172),tc_fun(tc_fun(tc_prod(U_12170,U_12172),tc_HOL_Obool),tc_HOL_Obool),U_12172),c_member(tc_prod(U_12170,U_12172)))),c_Product__Type_OPair(U_12170,U_12172))))),U_12174)),U_12176),U_12178)) ) ),
inference(miniscope,[status(thm)],[f_3206_2]) ).
cnf(f_3206_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12170,U_12172)),hAPP(hAPP(c_Product__Type_OPair(U_12170,U_12172),U_12176),U_12178)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12168,tc_fun(tc_prod(U_12170,U_12172),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12168,tc_HOL_Obool))),U_12174)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12168,tc_fun(U_12170,tc_fun(U_12172,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12168,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12170,U_12172),tc_HOL_Obool),tc_fun(U_12170,tc_fun(U_12172,tc_HOL_Obool)),U_12168),hAPP(c_COMBC(U_12170,tc_fun(tc_prod(U_12170,U_12172),tc_HOL_Obool),tc_fun(U_12172,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12172,tc_fun(tc_fun(tc_prod(U_12170,U_12172),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12170,U_12172),tc_HOL_Obool),tc_fun(U_12172,tc_HOL_Obool)),U_12170),c_COMBC(U_12172,tc_fun(tc_prod(U_12170,U_12172),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12172,tc_prod(U_12170,U_12172)),tc_fun(U_12172,tc_fun(tc_fun(tc_prod(U_12170,U_12172),tc_HOL_Obool),tc_HOL_Obool)),U_12170),hAPP(c_COMBB(tc_prod(U_12170,U_12172),tc_fun(tc_fun(tc_prod(U_12170,U_12172),tc_HOL_Obool),tc_HOL_Obool),U_12172),c_member(tc_prod(U_12170,U_12172)))),c_Product__Type_OPair(U_12170,U_12172))))),U_12174)),U_12176),U_12178)) ),
inference(clausify,[status(thm)],[f_3206_3]) ).
cnf(f_3206_5,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12169,tc_fun(U_12171,tc_fun(U_12173,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12169,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12171,U_12173),tc_HOL_Obool),tc_fun(U_12171,tc_fun(U_12173,tc_HOL_Obool)),U_12169),hAPP(c_COMBC(U_12171,tc_fun(tc_prod(U_12171,U_12173),tc_HOL_Obool),tc_fun(U_12173,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12173,tc_fun(tc_fun(tc_prod(U_12171,U_12173),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12171,U_12173),tc_HOL_Obool),tc_fun(U_12173,tc_HOL_Obool)),U_12171),c_COMBC(U_12173,tc_fun(tc_prod(U_12171,U_12173),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12173,tc_prod(U_12171,U_12173)),tc_fun(U_12173,tc_fun(tc_fun(tc_prod(U_12171,U_12173),tc_HOL_Obool),tc_HOL_Obool)),U_12171),hAPP(c_COMBB(tc_prod(U_12171,U_12173),tc_fun(tc_fun(tc_prod(U_12171,U_12173),tc_HOL_Obool),tc_HOL_Obool),U_12173),c_member(tc_prod(U_12171,U_12173)))),c_Product__Type_OPair(U_12171,U_12173))))),U_12175)),U_12177),U_12179))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12171,U_12173)),hAPP(hAPP(c_Product__Type_OPair(U_12171,U_12173),U_12177),U_12179)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12169,tc_fun(tc_prod(U_12171,U_12173),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12169,tc_HOL_Obool))),U_12175))) ),
inference(clausify,[status(thm)],[f_3206_3]) ).
fof(f_3207_1,plain,
! [T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ),
inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0]) ).
fof(f_3207_2,plain,
! [U_12180] :
( 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_12180),c_Orderings_Otop__class_Otop(tc_fun(U_12180,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12180),c_Orderings_Otop__class_Otop(tc_fun(U_12180,tc_HOL_Obool)))) ),
inference(variable_rename,[status(thm)],[f_3207_1]) ).
cnf(f_3207_3,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_12180),c_Orderings_Otop__class_Otop(tc_fun(U_12180,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12180),c_Orderings_Otop__class_Otop(tc_fun(U_12180,tc_HOL_Obool)))) ),
inference(clausify,[status(thm)],[f_3207_2]) ).
fof(f_3208_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]) ).
cnf(f_3208_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(clausify,[status(thm)],[f_3208_1]) ).
fof(f_3209_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_inj__image__Compl__subset]) ).
fof(f_3209_2,plain,
! [U_12184,U_12183,U_12182,U_12181] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12182,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12181,U_12182,U_12183),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12181,tc_HOL_Obool)),U_12184))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12182,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12181,U_12182,U_12183),U_12184))))
| ~ c_Fun_Oinj__on(U_12181,U_12182,U_12183,c_Orderings_Otop__class_Otop(tc_fun(U_12181,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_3209_1]) ).
cnf(f_3209_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12182,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12181,U_12182,U_12183),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12181,tc_HOL_Obool)),U_12184))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12182,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12181,U_12182,U_12183),U_12184))))
| ~ c_Fun_Oinj__on(U_12181,U_12182,U_12183,c_Orderings_Otop__class_Otop(tc_fun(U_12181,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3209_2]) ).
fof(f_3210_1,plain,
! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2))
| V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
| V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I4_J]) ).
fof(f_3210_2,plain,
! [U_12189,U_12188,U_12187,U_12186,U_12185] :
( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12186,tc_fun(U_12187,tc_HOL_Obool)),U_12185),hAPP(hAPP(c_COMBB(tc_fun(U_12187,tc_HOL_Obool),tc_fun(U_12187,tc_HOL_Obool),U_12186),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12187,tc_HOL_Obool)),U_12188)),U_12189)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12187,tc_HOL_Obool)),U_12188),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12186,tc_fun(U_12187,tc_HOL_Obool)),U_12185),U_12189))
| U_12185 = c_Orderings_Obot__class_Obot(tc_fun(U_12186,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12186,tc_fun(U_12187,tc_HOL_Obool)),U_12185),hAPP(hAPP(c_COMBB(tc_fun(U_12187,tc_HOL_Obool),tc_fun(U_12187,tc_HOL_Obool),U_12186),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12187,tc_HOL_Obool)),U_12188)),U_12189)) = c_Orderings_Otop__class_Otop(tc_fun(U_12187,tc_HOL_Obool))
| U_12185 != c_Orderings_Obot__class_Obot(tc_fun(U_12186,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3210_1]) ).
fof(f_3210_3,plain,
( ! [U_12199,U_12197,U_12195,U_12193,U_12191] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12193,tc_fun(U_12195,tc_HOL_Obool)),U_12191),hAPP(hAPP(c_COMBB(tc_fun(U_12195,tc_HOL_Obool),tc_fun(U_12195,tc_HOL_Obool),U_12193),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12195,tc_HOL_Obool)),U_12197)),U_12199)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12195,tc_HOL_Obool)),U_12197),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12193,tc_fun(U_12195,tc_HOL_Obool)),U_12191),U_12199))
| U_12191 = c_Orderings_Obot__class_Obot(tc_fun(U_12193,tc_HOL_Obool)) )
& ! [U_12198,U_12196,U_12194,U_12192,U_12190] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12192,tc_fun(U_12194,tc_HOL_Obool)),U_12190),hAPP(hAPP(c_COMBB(tc_fun(U_12194,tc_HOL_Obool),tc_fun(U_12194,tc_HOL_Obool),U_12192),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12194,tc_HOL_Obool)),U_12196)),U_12198)) = c_Orderings_Otop__class_Otop(tc_fun(U_12194,tc_HOL_Obool))
| U_12190 != c_Orderings_Obot__class_Obot(tc_fun(U_12192,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_3210_2]) ).
cnf(f_3210_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12192,tc_fun(U_12194,tc_HOL_Obool)),U_12190),hAPP(hAPP(c_COMBB(tc_fun(U_12194,tc_HOL_Obool),tc_fun(U_12194,tc_HOL_Obool),U_12192),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12194,tc_HOL_Obool)),U_12196)),U_12198)) = c_Orderings_Otop__class_Otop(tc_fun(U_12194,tc_HOL_Obool))
| U_12190 != c_Orderings_Obot__class_Obot(tc_fun(U_12192,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3210_3]) ).
cnf(f_3210_5,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12193,tc_fun(U_12195,tc_HOL_Obool)),U_12191),hAPP(hAPP(c_COMBB(tc_fun(U_12195,tc_HOL_Obool),tc_fun(U_12195,tc_HOL_Obool),U_12193),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12195,tc_HOL_Obool)),U_12197)),U_12199)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12195,tc_HOL_Obool)),U_12197),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12193,tc_fun(U_12195,tc_HOL_Obool)),U_12191),U_12199))
| U_12191 = c_Orderings_Obot__class_Obot(tc_fun(U_12193,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3210_3]) ).
fof(f_3211_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]) ).
cnf(f_3211_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(clausify,[status(thm)],[f_3211_1]) ).
fof(f_3212_1,plain,
! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq2]) ).
fof(f_3212_2,plain,
! [U_12205,U_12204,U_12203,U_12202,U_12201,U_12200] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12200,tc_fun(U_12201,tc_fun(U_12202,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12200,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12201,U_12202),tc_HOL_Obool),tc_fun(U_12201,tc_fun(U_12202,tc_HOL_Obool)),U_12200),hAPP(c_COMBC(U_12201,tc_fun(tc_prod(U_12201,U_12202),tc_HOL_Obool),tc_fun(U_12202,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12202,tc_fun(tc_fun(tc_prod(U_12201,U_12202),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12201,U_12202),tc_HOL_Obool),tc_fun(U_12202,tc_HOL_Obool)),U_12201),c_COMBC(U_12202,tc_fun(tc_prod(U_12201,U_12202),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12202,tc_prod(U_12201,U_12202)),tc_fun(U_12202,tc_fun(tc_fun(tc_prod(U_12201,U_12202),tc_HOL_Obool),tc_HOL_Obool)),U_12201),hAPP(c_COMBB(tc_prod(U_12201,U_12202),tc_fun(tc_fun(tc_prod(U_12201,U_12202),tc_HOL_Obool),tc_HOL_Obool),U_12202),c_member(tc_prod(U_12201,U_12202)))),c_Product__Type_OPair(U_12201,U_12202))))),U_12203)),U_12204),U_12205))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12201,U_12202)),hAPP(hAPP(c_Product__Type_OPair(U_12201,U_12202),U_12204),U_12205)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12200,tc_fun(tc_prod(U_12201,U_12202),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12200,tc_HOL_Obool))),U_12203))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12201,U_12202)),hAPP(hAPP(c_Product__Type_OPair(U_12201,U_12202),U_12204),U_12205)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12200,tc_fun(tc_prod(U_12201,U_12202),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12200,tc_HOL_Obool))),U_12203)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12200,tc_fun(U_12201,tc_fun(U_12202,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12200,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12201,U_12202),tc_HOL_Obool),tc_fun(U_12201,tc_fun(U_12202,tc_HOL_Obool)),U_12200),hAPP(c_COMBC(U_12201,tc_fun(tc_prod(U_12201,U_12202),tc_HOL_Obool),tc_fun(U_12202,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12202,tc_fun(tc_fun(tc_prod(U_12201,U_12202),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12201,U_12202),tc_HOL_Obool),tc_fun(U_12202,tc_HOL_Obool)),U_12201),c_COMBC(U_12202,tc_fun(tc_prod(U_12201,U_12202),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12202,tc_prod(U_12201,U_12202)),tc_fun(U_12202,tc_fun(tc_fun(tc_prod(U_12201,U_12202),tc_HOL_Obool),tc_HOL_Obool)),U_12201),hAPP(c_COMBB(tc_prod(U_12201,U_12202),tc_fun(tc_fun(tc_prod(U_12201,U_12202),tc_HOL_Obool),tc_HOL_Obool),U_12202),c_member(tc_prod(U_12201,U_12202)))),c_Product__Type_OPair(U_12201,U_12202))))),U_12203)),U_12204),U_12205)) ) ),
inference(variable_rename,[status(thm)],[f_3212_1]) ).
fof(f_3212_3,plain,
( ! [U_12217,U_12215,U_12213,U_12211,U_12209,U_12207] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12207,tc_fun(U_12209,tc_fun(U_12211,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12207,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12209,U_12211),tc_HOL_Obool),tc_fun(U_12209,tc_fun(U_12211,tc_HOL_Obool)),U_12207),hAPP(c_COMBC(U_12209,tc_fun(tc_prod(U_12209,U_12211),tc_HOL_Obool),tc_fun(U_12211,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12211,tc_fun(tc_fun(tc_prod(U_12209,U_12211),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12209,U_12211),tc_HOL_Obool),tc_fun(U_12211,tc_HOL_Obool)),U_12209),c_COMBC(U_12211,tc_fun(tc_prod(U_12209,U_12211),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12211,tc_prod(U_12209,U_12211)),tc_fun(U_12211,tc_fun(tc_fun(tc_prod(U_12209,U_12211),tc_HOL_Obool),tc_HOL_Obool)),U_12209),hAPP(c_COMBB(tc_prod(U_12209,U_12211),tc_fun(tc_fun(tc_prod(U_12209,U_12211),tc_HOL_Obool),tc_HOL_Obool),U_12211),c_member(tc_prod(U_12209,U_12211)))),c_Product__Type_OPair(U_12209,U_12211))))),U_12213)),U_12215),U_12217))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12209,U_12211)),hAPP(hAPP(c_Product__Type_OPair(U_12209,U_12211),U_12215),U_12217)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12207,tc_fun(tc_prod(U_12209,U_12211),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12207,tc_HOL_Obool))),U_12213))) )
& ! [U_12216,U_12214,U_12212,U_12210,U_12208,U_12206] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12208,U_12210)),hAPP(hAPP(c_Product__Type_OPair(U_12208,U_12210),U_12214),U_12216)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12206,tc_fun(tc_prod(U_12208,U_12210),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12206,tc_HOL_Obool))),U_12212)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12206,tc_fun(U_12208,tc_fun(U_12210,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12206,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12208,U_12210),tc_HOL_Obool),tc_fun(U_12208,tc_fun(U_12210,tc_HOL_Obool)),U_12206),hAPP(c_COMBC(U_12208,tc_fun(tc_prod(U_12208,U_12210),tc_HOL_Obool),tc_fun(U_12210,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12210,tc_fun(tc_fun(tc_prod(U_12208,U_12210),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12208,U_12210),tc_HOL_Obool),tc_fun(U_12210,tc_HOL_Obool)),U_12208),c_COMBC(U_12210,tc_fun(tc_prod(U_12208,U_12210),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12210,tc_prod(U_12208,U_12210)),tc_fun(U_12210,tc_fun(tc_fun(tc_prod(U_12208,U_12210),tc_HOL_Obool),tc_HOL_Obool)),U_12208),hAPP(c_COMBB(tc_prod(U_12208,U_12210),tc_fun(tc_fun(tc_prod(U_12208,U_12210),tc_HOL_Obool),tc_HOL_Obool),U_12210),c_member(tc_prod(U_12208,U_12210)))),c_Product__Type_OPair(U_12208,U_12210))))),U_12212)),U_12214),U_12216)) ) ),
inference(miniscope,[status(thm)],[f_3212_2]) ).
cnf(f_3212_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12208,U_12210)),hAPP(hAPP(c_Product__Type_OPair(U_12208,U_12210),U_12214),U_12216)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12206,tc_fun(tc_prod(U_12208,U_12210),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12206,tc_HOL_Obool))),U_12212)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12206,tc_fun(U_12208,tc_fun(U_12210,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12206,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12208,U_12210),tc_HOL_Obool),tc_fun(U_12208,tc_fun(U_12210,tc_HOL_Obool)),U_12206),hAPP(c_COMBC(U_12208,tc_fun(tc_prod(U_12208,U_12210),tc_HOL_Obool),tc_fun(U_12210,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12210,tc_fun(tc_fun(tc_prod(U_12208,U_12210),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12208,U_12210),tc_HOL_Obool),tc_fun(U_12210,tc_HOL_Obool)),U_12208),c_COMBC(U_12210,tc_fun(tc_prod(U_12208,U_12210),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12210,tc_prod(U_12208,U_12210)),tc_fun(U_12210,tc_fun(tc_fun(tc_prod(U_12208,U_12210),tc_HOL_Obool),tc_HOL_Obool)),U_12208),hAPP(c_COMBB(tc_prod(U_12208,U_12210),tc_fun(tc_fun(tc_prod(U_12208,U_12210),tc_HOL_Obool),tc_HOL_Obool),U_12210),c_member(tc_prod(U_12208,U_12210)))),c_Product__Type_OPair(U_12208,U_12210))))),U_12212)),U_12214),U_12216)) ),
inference(clausify,[status(thm)],[f_3212_3]) ).
cnf(f_3212_5,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12207,tc_fun(U_12209,tc_fun(U_12211,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_12207,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_12209,U_12211),tc_HOL_Obool),tc_fun(U_12209,tc_fun(U_12211,tc_HOL_Obool)),U_12207),hAPP(c_COMBC(U_12209,tc_fun(tc_prod(U_12209,U_12211),tc_HOL_Obool),tc_fun(U_12211,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12211,tc_fun(tc_fun(tc_prod(U_12209,U_12211),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12209,U_12211),tc_HOL_Obool),tc_fun(U_12211,tc_HOL_Obool)),U_12209),c_COMBC(U_12211,tc_fun(tc_prod(U_12209,U_12211),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12211,tc_prod(U_12209,U_12211)),tc_fun(U_12211,tc_fun(tc_fun(tc_prod(U_12209,U_12211),tc_HOL_Obool),tc_HOL_Obool)),U_12209),hAPP(c_COMBB(tc_prod(U_12209,U_12211),tc_fun(tc_fun(tc_prod(U_12209,U_12211),tc_HOL_Obool),tc_HOL_Obool),U_12211),c_member(tc_prod(U_12209,U_12211)))),c_Product__Type_OPair(U_12209,U_12211))))),U_12213)),U_12215),U_12217))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12209,U_12211)),hAPP(hAPP(c_Product__Type_OPair(U_12209,U_12211),U_12215),U_12217)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12207,tc_fun(tc_prod(U_12209,U_12211),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_12207,tc_HOL_Obool))),U_12213))) ),
inference(clausify,[status(thm)],[f_3212_3]) ).
fof(f_3213_1,plain,
! [V_B_2,V_k_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2)))
| ? [B_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_UN__finite2__subset]) ).
fof(f_3213_2,plain,
! [U_12222,U_12221,U_12220,U_12219] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12219,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12219,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12220)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12219,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12222)))
| ? [U_12218] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12219,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12219,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12218)),U_12220)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12219,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_12218),U_12221))),U_12222))) ),
inference(variable_rename,[status(thm)],[f_3213_1]) ).
fof(f_3213_3,plain,
! [U_12222,U_12221,U_12220,U_12219] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12219,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12219,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12220)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12219,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12222)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12219,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12219,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK267(U_12222,U_12221,U_12220,U_12219))),U_12220)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12219,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),sK267(U_12222,U_12221,U_12220,U_12219)),U_12221))),U_12222))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK267]),skolemize(U_12218,sK267(U_12222,U_12221,U_12220,U_12219))],[f_3213_2]) ).
cnf(f_3213_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12219,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12219,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12220)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12219,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12222)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12219,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12219,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK267(U_12222,U_12221,U_12220,U_12219))),U_12220)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12219,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),sK267(U_12222,U_12221,U_12220,U_12219)),U_12221))),U_12222))) ),
inference(clausify,[status(thm)],[f_3213_3]) ).
fof(f_3214_1,plain,
! [V_B_2,V_k_2,V_A_2,T_b] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2)
| ? [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_n),V_k_2))),V_B_2) ),
inference(fof_nnf,[status(thm)],[fact_UN__finite2__eq]) ).
fof(f_3214_2,plain,
! [U_12227,U_12226,U_12225,U_12224] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12224,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12225) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12224,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12227)
| ? [U_12223] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12224,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12223)),U_12225) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12224,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_12223),U_12226))),U_12227) ),
inference(variable_rename,[status(thm)],[f_3214_1]) ).
fof(f_3214_3,plain,
! [U_12227,U_12226,U_12225,U_12224] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12224,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12225) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12224,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12227)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12224,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK268(U_12227,U_12226,U_12225,U_12224))),U_12225) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12224,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),sK268(U_12227,U_12226,U_12225,U_12224)),U_12226))),U_12227) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK268]),skolemize(U_12223,sK268(U_12227,U_12226,U_12225,U_12224))],[f_3214_2]) ).
cnf(f_3214_4,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12224,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12225) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12224,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12227)
| hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12224,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK268(U_12227,U_12226,U_12225,U_12224))),U_12225) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12224,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),sK268(U_12227,U_12226,U_12225,U_12224)),U_12226))),U_12227) ),
inference(clausify,[status(thm)],[f_3214_3]) ).
fof(f_3215_1,plain,
! [V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2))
| ? [B_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)),V_A_2)),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_UN__finite__subset]) ).
fof(f_3215_2,plain,
! [U_12231,U_12230,U_12229] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12229,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12229,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12230)),U_12231))
| ? [U_12228] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12229,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12229,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12228)),U_12230)),U_12231)) ),
inference(variable_rename,[status(thm)],[f_3215_1]) ).
fof(f_3215_3,plain,
! [U_12231,U_12230,U_12229] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12229,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12229,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12230)),U_12231))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12229,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12229,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK269(U_12231,U_12230,U_12229))),U_12230)),U_12231)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK269]),skolemize(U_12228,sK269(U_12231,U_12230,U_12229))],[f_3215_2]) ).
cnf(f_3215_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12229,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12229,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_12230)),U_12231))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12229,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_12229,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK269(U_12231,U_12230,U_12229))),U_12230)),U_12231)) ),
inference(clausify,[status(thm)],[f_3215_3]) ).
fof(f_3216_1,plain,
! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)),
inference(fof_nnf,[status(thm)],[fact_top1I]) ).
fof(f_3216_2,plain,
! [U_12233,U_12232] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_12232,tc_HOL_Obool)),U_12233)),
inference(variable_rename,[status(thm)],[f_3216_1]) ).
cnf(f_3216_3,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_12232,tc_HOL_Obool)),U_12233)),
inference(clausify,[status(thm)],[f_3216_2]) ).
fof(f_3217_1,plain,
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),
inference(fof_nnf,[status(thm)],[fact_Integ__def]) ).
cnf(f_3217_2,plain,
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),
inference(clausify,[status(thm)],[f_3217_1]) ).
fof(f_3218_1,plain,
! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_iso__tuple__UNIV__I]) ).
fof(f_3218_2,plain,
! [U_12235,U_12234] : hBOOL(hAPP(hAPP(c_member(U_12234),U_12235),c_Orderings_Otop__class_Otop(tc_fun(U_12234,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_3218_1]) ).
cnf(f_3218_3,plain,
hBOOL(hAPP(hAPP(c_member(U_12234),U_12235),c_Orderings_Otop__class_Otop(tc_fun(U_12234,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_3218_2]) ).
fof(f_3219_1,plain,
! [V_A_2,T_b] :
( ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
| ~ c_Equiv__Relations_Oequivp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_A_2)) )
& ( c_Equiv__Relations_Oequivp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_A_2))
| ~ c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2) ) ),
inference(fof_nnf,[status(thm)],[fact_equivp__equiv]) ).
fof(f_3219_2,plain,
! [U_12237,U_12236] :
( ( c_Equiv__Relations_Oequiv(U_12236,c_Orderings_Otop__class_Otop(tc_fun(U_12236,tc_HOL_Obool)),U_12237)
| ~ c_Equiv__Relations_Oequivp(U_12236,hAPP(hAPP(c_COMBC(U_12236,tc_fun(tc_prod(U_12236,U_12236),tc_HOL_Obool),tc_fun(U_12236,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12236,tc_fun(tc_fun(tc_prod(U_12236,U_12236),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12236,U_12236),tc_HOL_Obool),tc_fun(U_12236,tc_HOL_Obool)),U_12236),c_COMBC(U_12236,tc_fun(tc_prod(U_12236,U_12236),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12236,tc_prod(U_12236,U_12236)),tc_fun(U_12236,tc_fun(tc_fun(tc_prod(U_12236,U_12236),tc_HOL_Obool),tc_HOL_Obool)),U_12236),hAPP(c_COMBB(tc_prod(U_12236,U_12236),tc_fun(tc_fun(tc_prod(U_12236,U_12236),tc_HOL_Obool),tc_HOL_Obool),U_12236),c_member(tc_prod(U_12236,U_12236)))),c_Product__Type_OPair(U_12236,U_12236)))),U_12237)) )
& ( c_Equiv__Relations_Oequivp(U_12236,hAPP(hAPP(c_COMBC(U_12236,tc_fun(tc_prod(U_12236,U_12236),tc_HOL_Obool),tc_fun(U_12236,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12236,tc_fun(tc_fun(tc_prod(U_12236,U_12236),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12236,U_12236),tc_HOL_Obool),tc_fun(U_12236,tc_HOL_Obool)),U_12236),c_COMBC(U_12236,tc_fun(tc_prod(U_12236,U_12236),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12236,tc_prod(U_12236,U_12236)),tc_fun(U_12236,tc_fun(tc_fun(tc_prod(U_12236,U_12236),tc_HOL_Obool),tc_HOL_Obool)),U_12236),hAPP(c_COMBB(tc_prod(U_12236,U_12236),tc_fun(tc_fun(tc_prod(U_12236,U_12236),tc_HOL_Obool),tc_HOL_Obool),U_12236),c_member(tc_prod(U_12236,U_12236)))),c_Product__Type_OPair(U_12236,U_12236)))),U_12237))
| ~ c_Equiv__Relations_Oequiv(U_12236,c_Orderings_Otop__class_Otop(tc_fun(U_12236,tc_HOL_Obool)),U_12237) ) ),
inference(variable_rename,[status(thm)],[f_3219_1]) ).
fof(f_3219_3,plain,
( ! [U_12241,U_12239] :
( c_Equiv__Relations_Oequiv(U_12239,c_Orderings_Otop__class_Otop(tc_fun(U_12239,tc_HOL_Obool)),U_12241)
| ~ c_Equiv__Relations_Oequivp(U_12239,hAPP(hAPP(c_COMBC(U_12239,tc_fun(tc_prod(U_12239,U_12239),tc_HOL_Obool),tc_fun(U_12239,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12239,tc_fun(tc_fun(tc_prod(U_12239,U_12239),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12239,U_12239),tc_HOL_Obool),tc_fun(U_12239,tc_HOL_Obool)),U_12239),c_COMBC(U_12239,tc_fun(tc_prod(U_12239,U_12239),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12239,tc_prod(U_12239,U_12239)),tc_fun(U_12239,tc_fun(tc_fun(tc_prod(U_12239,U_12239),tc_HOL_Obool),tc_HOL_Obool)),U_12239),hAPP(c_COMBB(tc_prod(U_12239,U_12239),tc_fun(tc_fun(tc_prod(U_12239,U_12239),tc_HOL_Obool),tc_HOL_Obool),U_12239),c_member(tc_prod(U_12239,U_12239)))),c_Product__Type_OPair(U_12239,U_12239)))),U_12241)) )
& ! [U_12240,U_12238] :
( c_Equiv__Relations_Oequivp(U_12238,hAPP(hAPP(c_COMBC(U_12238,tc_fun(tc_prod(U_12238,U_12238),tc_HOL_Obool),tc_fun(U_12238,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12238,tc_fun(tc_fun(tc_prod(U_12238,U_12238),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12238,U_12238),tc_HOL_Obool),tc_fun(U_12238,tc_HOL_Obool)),U_12238),c_COMBC(U_12238,tc_fun(tc_prod(U_12238,U_12238),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12238,tc_prod(U_12238,U_12238)),tc_fun(U_12238,tc_fun(tc_fun(tc_prod(U_12238,U_12238),tc_HOL_Obool),tc_HOL_Obool)),U_12238),hAPP(c_COMBB(tc_prod(U_12238,U_12238),tc_fun(tc_fun(tc_prod(U_12238,U_12238),tc_HOL_Obool),tc_HOL_Obool),U_12238),c_member(tc_prod(U_12238,U_12238)))),c_Product__Type_OPair(U_12238,U_12238)))),U_12240))
| ~ c_Equiv__Relations_Oequiv(U_12238,c_Orderings_Otop__class_Otop(tc_fun(U_12238,tc_HOL_Obool)),U_12240) ) ),
inference(miniscope,[status(thm)],[f_3219_2]) ).
cnf(f_3219_4,plain,
( c_Equiv__Relations_Oequivp(U_12238,hAPP(hAPP(c_COMBC(U_12238,tc_fun(tc_prod(U_12238,U_12238),tc_HOL_Obool),tc_fun(U_12238,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12238,tc_fun(tc_fun(tc_prod(U_12238,U_12238),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12238,U_12238),tc_HOL_Obool),tc_fun(U_12238,tc_HOL_Obool)),U_12238),c_COMBC(U_12238,tc_fun(tc_prod(U_12238,U_12238),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12238,tc_prod(U_12238,U_12238)),tc_fun(U_12238,tc_fun(tc_fun(tc_prod(U_12238,U_12238),tc_HOL_Obool),tc_HOL_Obool)),U_12238),hAPP(c_COMBB(tc_prod(U_12238,U_12238),tc_fun(tc_fun(tc_prod(U_12238,U_12238),tc_HOL_Obool),tc_HOL_Obool),U_12238),c_member(tc_prod(U_12238,U_12238)))),c_Product__Type_OPair(U_12238,U_12238)))),U_12240))
| ~ c_Equiv__Relations_Oequiv(U_12238,c_Orderings_Otop__class_Otop(tc_fun(U_12238,tc_HOL_Obool)),U_12240) ),
inference(clausify,[status(thm)],[f_3219_3]) ).
cnf(f_3219_5,plain,
( c_Equiv__Relations_Oequiv(U_12239,c_Orderings_Otop__class_Otop(tc_fun(U_12239,tc_HOL_Obool)),U_12241)
| ~ c_Equiv__Relations_Oequivp(U_12239,hAPP(hAPP(c_COMBC(U_12239,tc_fun(tc_prod(U_12239,U_12239),tc_HOL_Obool),tc_fun(U_12239,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12239,tc_fun(tc_fun(tc_prod(U_12239,U_12239),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_12239,U_12239),tc_HOL_Obool),tc_fun(U_12239,tc_HOL_Obool)),U_12239),c_COMBC(U_12239,tc_fun(tc_prod(U_12239,U_12239),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12239,tc_prod(U_12239,U_12239)),tc_fun(U_12239,tc_fun(tc_fun(tc_prod(U_12239,U_12239),tc_HOL_Obool),tc_HOL_Obool)),U_12239),hAPP(c_COMBB(tc_prod(U_12239,U_12239),tc_fun(tc_fun(tc_prod(U_12239,U_12239),tc_HOL_Obool),tc_HOL_Obool),U_12239),c_member(tc_prod(U_12239,U_12239)))),c_Product__Type_OPair(U_12239,U_12239)))),U_12241)) ),
inference(clausify,[status(thm)],[f_3219_3]) ).
fof(f_3220_1,plain,
! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal),
inference(fof_nnf,[status(thm)],[fact_identity__equivp]) ).
fof(f_3220_2,plain,
! [U_12242] : c_Equiv__Relations_Oequivp(U_12242,c_fequal),
inference(variable_rename,[status(thm)],[f_3220_1]) ).
cnf(f_3220_3,plain,
c_Equiv__Relations_Oequivp(U_12242,c_fequal),
inference(clausify,[status(thm)],[f_3220_2]) ).
fof(f_3221_1,plain,
! [V_R_2,T_b] :
( ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
| ? [B_x,B_y] :
( ( ~ hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
& hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) )
| ( hAPP(V_R_2,B_x) != hAPP(V_R_2,B_y)
& hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) ) ) )
& ( ! [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) )
& ( hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y)
| ~ hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) ) )
| ~ c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ),
inference(fof_nnf,[status(thm)],[fact_equivp__def]) ).
fof(f_3221_2,plain,
! [U_12248,U_12247] :
( ( c_Equiv__Relations_Oequivp(U_12247,U_12248)
| ? [U_12246,U_12245] :
( ( ~ hBOOL(hAPP(hAPP(U_12248,U_12246),U_12245))
& hAPP(U_12248,U_12246) = hAPP(U_12248,U_12245) )
| ( hAPP(U_12248,U_12246) != hAPP(U_12248,U_12245)
& hBOOL(hAPP(hAPP(U_12248,U_12246),U_12245)) ) ) )
& ( ! [U_12244,U_12243] :
( ( hBOOL(hAPP(hAPP(U_12248,U_12244),U_12243))
| hAPP(U_12248,U_12244) != hAPP(U_12248,U_12243) )
& ( hAPP(U_12248,U_12244) = hAPP(U_12248,U_12243)
| ~ hBOOL(hAPP(hAPP(U_12248,U_12244),U_12243)) ) )
| ~ c_Equiv__Relations_Oequivp(U_12247,U_12248) ) ),
inference(variable_rename,[status(thm)],[f_3221_1]) ).
fof(f_3221_3,plain,
( ! [U_12260] :
( ! [U_12258] : c_Equiv__Relations_Oequivp(U_12258,U_12260)
| ? [U_12256,U_12254] :
( ~ hBOOL(hAPP(hAPP(U_12260,U_12256),U_12254))
& hAPP(U_12260,U_12256) = hAPP(U_12260,U_12254) )
| ? [U_12255,U_12253] :
( hAPP(U_12260,U_12255) != hAPP(U_12260,U_12253)
& hBOOL(hAPP(hAPP(U_12260,U_12255),U_12253)) ) )
& ! [U_12259] :
( ! [U_12257] : ~ c_Equiv__Relations_Oequivp(U_12257,U_12259)
| ( ! [U_12252,U_12250] :
( hBOOL(hAPP(hAPP(U_12259,U_12252),U_12250))
| hAPP(U_12259,U_12252) != hAPP(U_12259,U_12250) )
& ! [U_12251,U_12249] :
( hAPP(U_12259,U_12251) = hAPP(U_12259,U_12249)
| ~ hBOOL(hAPP(hAPP(U_12259,U_12251),U_12249)) ) ) ) ),
inference(miniscope,[status(thm)],[f_3221_2]) ).
fof(f_3221_4,plain,
( ! [U_12260] :
( ! [U_12258] : c_Equiv__Relations_Oequivp(U_12258,U_12260)
| ? [U_12256,U_12254] :
( ~ hBOOL(hAPP(hAPP(U_12260,U_12256),U_12254))
& hAPP(U_12260,U_12256) = hAPP(U_12260,U_12254) )
| ? [U_12253] :
( hAPP(U_12260,sK270(U_12260)) != hAPP(U_12260,U_12253)
& hBOOL(hAPP(hAPP(U_12260,sK270(U_12260)),U_12253)) ) )
& ! [U_12259] :
( ! [U_12257] : ~ c_Equiv__Relations_Oequivp(U_12257,U_12259)
| ( ! [U_12252,U_12250] :
( hBOOL(hAPP(hAPP(U_12259,U_12252),U_12250))
| hAPP(U_12259,U_12252) != hAPP(U_12259,U_12250) )
& ! [U_12251,U_12249] :
( hAPP(U_12259,U_12251) = hAPP(U_12259,U_12249)
| ~ hBOOL(hAPP(hAPP(U_12259,U_12251),U_12249)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK270]),skolemize(U_12255,sK270(U_12260))],[f_3221_3]) ).
fof(f_3221_5,plain,
( ! [U_12260] :
( ! [U_12258] : c_Equiv__Relations_Oequivp(U_12258,U_12260)
| ? [U_12256,U_12254] :
( ~ hBOOL(hAPP(hAPP(U_12260,U_12256),U_12254))
& hAPP(U_12260,U_12256) = hAPP(U_12260,U_12254) )
| ( hAPP(U_12260,sK270(U_12260)) != hAPP(U_12260,sK271(U_12260))
& hBOOL(hAPP(hAPP(U_12260,sK270(U_12260)),sK271(U_12260))) ) )
& ! [U_12259] :
( ! [U_12257] : ~ c_Equiv__Relations_Oequivp(U_12257,U_12259)
| ( ! [U_12252,U_12250] :
( hBOOL(hAPP(hAPP(U_12259,U_12252),U_12250))
| hAPP(U_12259,U_12252) != hAPP(U_12259,U_12250) )
& ! [U_12251,U_12249] :
( hAPP(U_12259,U_12251) = hAPP(U_12259,U_12249)
| ~ hBOOL(hAPP(hAPP(U_12259,U_12251),U_12249)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK271]),skolemize(U_12253,sK271(U_12260))],[f_3221_4]) ).
fof(f_3221_6,plain,
( ! [U_12260] :
( ! [U_12258] : c_Equiv__Relations_Oequivp(U_12258,U_12260)
| ? [U_12254] :
( ~ hBOOL(hAPP(hAPP(U_12260,sK272(U_12260)),U_12254))
& hAPP(U_12260,sK272(U_12260)) = hAPP(U_12260,U_12254) )
| ( hAPP(U_12260,sK270(U_12260)) != hAPP(U_12260,sK271(U_12260))
& hBOOL(hAPP(hAPP(U_12260,sK270(U_12260)),sK271(U_12260))) ) )
& ! [U_12259] :
( ! [U_12257] : ~ c_Equiv__Relations_Oequivp(U_12257,U_12259)
| ( ! [U_12252,U_12250] :
( hBOOL(hAPP(hAPP(U_12259,U_12252),U_12250))
| hAPP(U_12259,U_12252) != hAPP(U_12259,U_12250) )
& ! [U_12251,U_12249] :
( hAPP(U_12259,U_12251) = hAPP(U_12259,U_12249)
| ~ hBOOL(hAPP(hAPP(U_12259,U_12251),U_12249)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK272]),skolemize(U_12256,sK272(U_12260))],[f_3221_5]) ).
fof(f_3221_7,plain,
( ! [U_12260] :
( ! [U_12258] : c_Equiv__Relations_Oequivp(U_12258,U_12260)
| ( ~ hBOOL(hAPP(hAPP(U_12260,sK272(U_12260)),sK273(U_12260)))
& hAPP(U_12260,sK272(U_12260)) = hAPP(U_12260,sK273(U_12260)) )
| ( hAPP(U_12260,sK270(U_12260)) != hAPP(U_12260,sK271(U_12260))
& hBOOL(hAPP(hAPP(U_12260,sK270(U_12260)),sK271(U_12260))) ) )
& ! [U_12259] :
( ! [U_12257] : ~ c_Equiv__Relations_Oequivp(U_12257,U_12259)
| ( ! [U_12252,U_12250] :
( hBOOL(hAPP(hAPP(U_12259,U_12252),U_12250))
| hAPP(U_12259,U_12252) != hAPP(U_12259,U_12250) )
& ! [U_12251,U_12249] :
( hAPP(U_12259,U_12251) = hAPP(U_12259,U_12249)
| ~ hBOOL(hAPP(hAPP(U_12259,U_12251),U_12249)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK273]),skolemize(U_12254,sK273(U_12260))],[f_3221_6]) ).
cnf(f_3221_8,plain,
( hAPP(U_12259,U_12251) = hAPP(U_12259,U_12249)
| ~ hBOOL(hAPP(hAPP(U_12259,U_12251),U_12249))
| ~ c_Equiv__Relations_Oequivp(U_12257,U_12259) ),
inference(clausify,[status(thm)],[f_3221_7]) ).
cnf(f_3221_9,plain,
( hBOOL(hAPP(hAPP(U_12259,U_12252),U_12250))
| hAPP(U_12259,U_12252) != hAPP(U_12259,U_12250)
| ~ c_Equiv__Relations_Oequivp(U_12257,U_12259) ),
inference(clausify,[status(thm)],[f_3221_7]) ).
cnf(f_3221_10,plain,
( hAPP(U_12260,sK272(U_12260)) = hAPP(U_12260,sK273(U_12260))
| hBOOL(hAPP(hAPP(U_12260,sK270(U_12260)),sK271(U_12260)))
| c_Equiv__Relations_Oequivp(U_12258,U_12260) ),
inference(clausify,[status(thm)],[f_3221_7]) ).
cnf(f_3221_11,plain,
( ~ hBOOL(hAPP(hAPP(U_12260,sK272(U_12260)),sK273(U_12260)))
| hBOOL(hAPP(hAPP(U_12260,sK270(U_12260)),sK271(U_12260)))
| c_Equiv__Relations_Oequivp(U_12258,U_12260) ),
inference(clausify,[status(thm)],[f_3221_7]) ).
cnf(f_3221_12,plain,
( hAPP(U_12260,sK272(U_12260)) = hAPP(U_12260,sK273(U_12260))
| hAPP(U_12260,sK270(U_12260)) != hAPP(U_12260,sK271(U_12260))
| c_Equiv__Relations_Oequivp(U_12258,U_12260) ),
inference(clausify,[status(thm)],[f_3221_7]) ).
cnf(f_3221_13,plain,
( ~ hBOOL(hAPP(hAPP(U_12260,sK272(U_12260)),sK273(U_12260)))
| hAPP(U_12260,sK270(U_12260)) != hAPP(U_12260,sK271(U_12260))
| c_Equiv__Relations_Oequivp(U_12258,U_12260) ),
inference(clausify,[status(thm)],[f_3221_7]) ).
fof(f_3222_1,plain,
! [V_x_2,V_R_2,T_b] :
( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2))
| ~ c_Equiv__Relations_Oequivp(T_b,V_R_2) ),
inference(fof_nnf,[status(thm)],[fact_equivp__reflp]) ).
fof(f_3222_2,plain,
! [U_12263,U_12262,U_12261] :
( hBOOL(hAPP(hAPP(U_12262,U_12263),U_12263))
| ~ c_Equiv__Relations_Oequivp(U_12261,U_12262) ),
inference(variable_rename,[status(thm)],[f_3222_1]) ).
fof(f_3222_3,plain,
! [U_12263,U_12262] :
( ! [U_12261] : ~ c_Equiv__Relations_Oequivp(U_12261,U_12262)
| hBOOL(hAPP(hAPP(U_12262,U_12263),U_12263)) ),
inference(miniscope,[status(thm)],[f_3222_2]) ).
cnf(f_3222_4,plain,
( ~ c_Equiv__Relations_Oequivp(U_12261,U_12262)
| hBOOL(hAPP(hAPP(U_12262,U_12263),U_12263)) ),
inference(clausify,[status(thm)],[f_3222_3]) ).
fof(f_3223_1,plain,
! [V_y_2,V_x_2,V_R_2,T_b] :
( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2))
| ~ hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
| ~ c_Equiv__Relations_Oequivp(T_b,V_R_2) ),
inference(fof_nnf,[status(thm)],[fact_equivp__symp]) ).
fof(f_3223_2,plain,
! [U_12267,U_12266,U_12265,U_12264] :
( hBOOL(hAPP(hAPP(U_12265,U_12267),U_12266))
| ~ hBOOL(hAPP(hAPP(U_12265,U_12266),U_12267))
| ~ c_Equiv__Relations_Oequivp(U_12264,U_12265) ),
inference(variable_rename,[status(thm)],[f_3223_1]) ).
fof(f_3223_3,plain,
! [U_12267,U_12266,U_12265] :
( ! [U_12264] : ~ c_Equiv__Relations_Oequivp(U_12264,U_12265)
| hBOOL(hAPP(hAPP(U_12265,U_12267),U_12266))
| ~ hBOOL(hAPP(hAPP(U_12265,U_12266),U_12267)) ),
inference(miniscope,[status(thm)],[f_3223_2]) ).
cnf(f_3223_4,plain,
( ~ c_Equiv__Relations_Oequivp(U_12264,U_12265)
| hBOOL(hAPP(hAPP(U_12265,U_12267),U_12266))
| ~ hBOOL(hAPP(hAPP(U_12265,U_12266),U_12267)) ),
inference(clausify,[status(thm)],[f_3223_3]) ).
fof(f_3224_1,plain,
! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
| ~ hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
| ~ c_Equiv__Relations_Oequivp(T_b,V_R_2) ),
inference(fof_nnf,[status(thm)],[fact_equivp__transp]) ).
fof(f_3224_2,plain,
! [U_12272,U_12271,U_12270,U_12269,U_12268] :
( hBOOL(hAPP(hAPP(U_12269,U_12270),U_12272))
| ~ hBOOL(hAPP(hAPP(U_12269,U_12271),U_12272))
| ~ hBOOL(hAPP(hAPP(U_12269,U_12270),U_12271))
| ~ c_Equiv__Relations_Oequivp(U_12268,U_12269) ),
inference(variable_rename,[status(thm)],[f_3224_1]) ).
fof(f_3224_3,plain,
! [U_12272,U_12271,U_12270,U_12269] :
( ! [U_12268] : ~ c_Equiv__Relations_Oequivp(U_12268,U_12269)
| hBOOL(hAPP(hAPP(U_12269,U_12270),U_12272))
| ~ hBOOL(hAPP(hAPP(U_12269,U_12271),U_12272))
| ~ hBOOL(hAPP(hAPP(U_12269,U_12270),U_12271)) ),
inference(miniscope,[status(thm)],[f_3224_2]) ).
cnf(f_3224_4,plain,
( ~ c_Equiv__Relations_Oequivp(U_12268,U_12269)
| hBOOL(hAPP(hAPP(U_12269,U_12270),U_12272))
| ~ hBOOL(hAPP(hAPP(U_12269,U_12271),U_12272))
| ~ hBOOL(hAPP(hAPP(U_12269,U_12270),U_12271)) ),
inference(clausify,[status(thm)],[f_3224_3]) ).
fof(f_3225_1,plain,
! [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)),
inference(fof_nnf,[status(thm)],[fact_Rep__Integ]) ).
fof(f_3225_2,plain,
! [U_12273] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_12273)),c_Int_OInteg)),
inference(variable_rename,[status(thm)],[f_3225_1]) ).
cnf(f_3225_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_12273)),c_Int_OInteg)),
inference(clausify,[status(thm)],[f_3225_2]) ).
fof(f_3226_1,plain,
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),
inference(fof_nnf,[status(thm)],[fact_type__definition__Integ]) ).
cnf(f_3226_2,plain,
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),
inference(clausify,[status(thm)],[f_3226_1]) ).
fof(f_3227_1,plain,
! [V_a_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_inj__vimage__singleton]) ).
fof(f_3227_2,plain,
! [U_12277,U_12276,U_12275,U_12274] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12274,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12274,U_12275,U_12276),hAPP(hAPP(c_Set_Oinsert(U_12275),U_12277),c_Orderings_Obot__class_Obot(tc_fun(U_12275,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_12274),c_HOL_OThe(U_12274,hAPP(hAPP(c_COMBC(U_12274,U_12275,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12275,tc_fun(U_12275,tc_HOL_Obool),U_12274),c_fequal),U_12276)),U_12277))),c_Orderings_Obot__class_Obot(tc_fun(U_12274,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(U_12274,U_12275,U_12276,c_Orderings_Otop__class_Otop(tc_fun(U_12274,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_3227_1]) ).
cnf(f_3227_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12274,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12274,U_12275,U_12276),hAPP(hAPP(c_Set_Oinsert(U_12275),U_12277),c_Orderings_Obot__class_Obot(tc_fun(U_12275,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_12274),c_HOL_OThe(U_12274,hAPP(hAPP(c_COMBC(U_12274,U_12275,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12275,tc_fun(U_12275,tc_HOL_Obool),U_12274),c_fequal),U_12276)),U_12277))),c_Orderings_Obot__class_Obot(tc_fun(U_12274,tc_HOL_Obool)))))
| ~ c_Fun_Oinj__on(U_12274,U_12275,U_12276,c_Orderings_Otop__class_Otop(tc_fun(U_12274,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3227_2]) ).
fof(f_3228_1,plain,
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))),
inference(fof_nnf,[status(thm)],[fact_type__definition__code__numeral]) ).
cnf(f_3228_2,plain,
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))),
inference(clausify,[status(thm)],[f_3228_1]) ).
fof(f_3229_1,plain,
! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),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_3229_2,plain,
! [U_12283,U_12282,U_12281,U_12280,U_12279,U_12278] :
( hBOOL(hAPP(hAPP(c_member(U_12283),U_12279),hAPP(c_Set_Ovimage(U_12283,U_12281,U_12278),U_12282)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12281),U_12280),U_12282))
| hAPP(U_12278,U_12279) != U_12280 ),
inference(variable_rename,[status(thm)],[f_3229_1]) ).
cnf(f_3229_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_12283),U_12279),hAPP(c_Set_Ovimage(U_12283,U_12281,U_12278),U_12282)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12281),U_12280),U_12282))
| hAPP(U_12278,U_12279) != U_12280 ),
inference(clausify,[status(thm)],[f_3229_2]) ).
fof(f_3230_1,plain,
! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
| ~ hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) )
& ( hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2)))
| ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_vimage__code]) ).
fof(f_3230_2,plain,
! [U_12288,U_12287,U_12286,U_12285,U_12284] :
( ( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12284,U_12285,U_12286),U_12287),U_12288))
| ~ hBOOL(hAPP(U_12287,hAPP(U_12286,U_12288))) )
& ( hBOOL(hAPP(U_12287,hAPP(U_12286,U_12288)))
| ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12284,U_12285,U_12286),U_12287),U_12288)) ) ),
inference(variable_rename,[status(thm)],[f_3230_1]) ).
fof(f_3230_3,plain,
( ! [U_12298,U_12296,U_12294] :
( ! [U_12292,U_12290] : hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12290,U_12292,U_12294),U_12296),U_12298))
| ~ hBOOL(hAPP(U_12296,hAPP(U_12294,U_12298))) )
& ! [U_12297,U_12295,U_12293] :
( ! [U_12291,U_12289] : ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12289,U_12291,U_12293),U_12295),U_12297))
| hBOOL(hAPP(U_12295,hAPP(U_12293,U_12297))) ) ),
inference(miniscope,[status(thm)],[f_3230_2]) ).
cnf(f_3230_4,plain,
( ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12289,U_12291,U_12293),U_12295),U_12297))
| hBOOL(hAPP(U_12295,hAPP(U_12293,U_12297))) ),
inference(clausify,[status(thm)],[f_3230_3]) ).
cnf(f_3230_5,plain,
( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_12290,U_12292,U_12294),U_12296),U_12298))
| ~ hBOOL(hAPP(U_12296,hAPP(U_12294,U_12298))) ),
inference(clausify,[status(thm)],[f_3230_3]) ).
fof(f_3231_1,plain,
! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__Compl]) ).
fof(f_3231_2,plain,
! [U_12302,U_12301,U_12300,U_12299] : hAPP(c_Set_Ovimage(U_12299,U_12300,U_12301),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12300,tc_HOL_Obool)),U_12302)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12299,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12299,U_12300,U_12301),U_12302)),
inference(variable_rename,[status(thm)],[f_3231_1]) ).
cnf(f_3231_3,plain,
hAPP(c_Set_Ovimage(U_12299,U_12300,U_12301),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12300,tc_HOL_Obool)),U_12302)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12299,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12299,U_12300,U_12301),U_12302)),
inference(clausify,[status(thm)],[f_3231_2]) ).
fof(f_3232_1,plain,
! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2,
inference(fof_nnf,[status(thm)],[fact_vimage__ident]) ).
fof(f_3232_2,plain,
! [U_12304,U_12303] : hAPP(c_Set_Ovimage(U_12303,U_12303,c_COMBI(U_12303)),U_12304) = U_12304,
inference(variable_rename,[status(thm)],[f_3232_1]) ).
cnf(f_3232_3,plain,
hAPP(c_Set_Ovimage(U_12303,U_12303,c_COMBI(U_12303)),U_12304) = U_12304,
inference(clausify,[status(thm)],[f_3232_2]) ).
fof(f_3233_1,plain,
! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_vimage__mono]) ).
fof(f_3233_2,plain,
! [U_12309,U_12308,U_12307,U_12306,U_12305] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12308,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12308,U_12305,U_12309),U_12306)),hAPP(c_Set_Ovimage(U_12308,U_12305,U_12309),U_12307)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12305,tc_HOL_Obool)),U_12306),U_12307)) ),
inference(variable_rename,[status(thm)],[f_3233_1]) ).
cnf(f_3233_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12308,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12308,U_12305,U_12309),U_12306)),hAPP(c_Set_Ovimage(U_12308,U_12305,U_12309),U_12307)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12305,tc_HOL_Obool)),U_12306),U_12307)) ),
inference(clausify,[status(thm)],[f_3233_2]) ).
fof(f_3234_1,plain,
! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_vimageI2]) ).
fof(f_3234_2,plain,
! [U_12314,U_12313,U_12312,U_12311,U_12310] :
( hBOOL(hAPP(hAPP(c_member(U_12314),U_12312),hAPP(c_Set_Ovimage(U_12314,U_12310,U_12311),U_12313)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12310),hAPP(U_12311,U_12312)),U_12313)) ),
inference(variable_rename,[status(thm)],[f_3234_1]) ).
cnf(f_3234_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_12314),U_12312),hAPP(c_Set_Ovimage(U_12314,U_12310,U_12311),U_12313)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12310),hAPP(U_12311,U_12312)),U_12313)) ),
inference(clausify,[status(thm)],[f_3234_2]) ).
fof(f_3235_1,plain,
! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_vimageD]) ).
fof(f_3235_2,plain,
! [U_12319,U_12318,U_12317,U_12316,U_12315] :
( hBOOL(hAPP(hAPP(c_member(U_12317),hAPP(U_12318,U_12316)),U_12319))
| ~ hBOOL(hAPP(hAPP(c_member(U_12315),U_12316),hAPP(c_Set_Ovimage(U_12315,U_12317,U_12318),U_12319))) ),
inference(variable_rename,[status(thm)],[f_3235_1]) ).
fof(f_3235_3,plain,
! [U_12319,U_12318,U_12317,U_12316] :
( ! [U_12315] : ~ hBOOL(hAPP(hAPP(c_member(U_12315),U_12316),hAPP(c_Set_Ovimage(U_12315,U_12317,U_12318),U_12319)))
| hBOOL(hAPP(hAPP(c_member(U_12317),hAPP(U_12318,U_12316)),U_12319)) ),
inference(miniscope,[status(thm)],[f_3235_2]) ).
cnf(f_3235_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_12315),U_12316),hAPP(c_Set_Ovimage(U_12315,U_12317,U_12318),U_12319)))
| hBOOL(hAPP(hAPP(c_member(U_12317),hAPP(U_12318,U_12316)),U_12319)) ),
inference(clausify,[status(thm)],[f_3235_3]) ).
fof(f_3236_1,plain,
! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_vimage__eq]) ).
fof(f_3236_2,plain,
! [U_12324,U_12323,U_12322,U_12321,U_12320] :
( ( hBOOL(hAPP(hAPP(c_member(U_12320),U_12321),hAPP(c_Set_Ovimage(U_12320,U_12322,U_12323),U_12324)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12322),hAPP(U_12323,U_12321)),U_12324)) )
& ( hBOOL(hAPP(hAPP(c_member(U_12322),hAPP(U_12323,U_12321)),U_12324))
| ~ hBOOL(hAPP(hAPP(c_member(U_12320),U_12321),hAPP(c_Set_Ovimage(U_12320,U_12322,U_12323),U_12324))) ) ),
inference(variable_rename,[status(thm)],[f_3236_1]) ).
fof(f_3236_3,plain,
( ! [U_12334,U_12332,U_12330,U_12328] :
( ! [U_12326] : hBOOL(hAPP(hAPP(c_member(U_12326),U_12328),hAPP(c_Set_Ovimage(U_12326,U_12330,U_12332),U_12334)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12330),hAPP(U_12332,U_12328)),U_12334)) )
& ! [U_12333,U_12331,U_12329,U_12327] :
( ! [U_12325] : ~ hBOOL(hAPP(hAPP(c_member(U_12325),U_12327),hAPP(c_Set_Ovimage(U_12325,U_12329,U_12331),U_12333)))
| hBOOL(hAPP(hAPP(c_member(U_12329),hAPP(U_12331,U_12327)),U_12333)) ) ),
inference(miniscope,[status(thm)],[f_3236_2]) ).
cnf(f_3236_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_12325),U_12327),hAPP(c_Set_Ovimage(U_12325,U_12329,U_12331),U_12333)))
| hBOOL(hAPP(hAPP(c_member(U_12329),hAPP(U_12331,U_12327)),U_12333)) ),
inference(clausify,[status(thm)],[f_3236_3]) ).
cnf(f_3236_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_12326),U_12328),hAPP(c_Set_Ovimage(U_12326,U_12330,U_12332),U_12334)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12330),hAPP(U_12332,U_12328)),U_12334)) ),
inference(clausify,[status(thm)],[f_3236_3]) ).
fof(f_3237_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__Un]) ).
fof(f_3237_2,plain,
! [U_12339,U_12338,U_12337,U_12336,U_12335] : hAPP(c_Set_Ovimage(U_12335,U_12336,U_12337),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12336,tc_HOL_Obool)),U_12338),U_12339)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12335,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12335,U_12336,U_12337),U_12338)),hAPP(c_Set_Ovimage(U_12335,U_12336,U_12337),U_12339)),
inference(variable_rename,[status(thm)],[f_3237_1]) ).
cnf(f_3237_3,plain,
hAPP(c_Set_Ovimage(U_12335,U_12336,U_12337),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12336,tc_HOL_Obool)),U_12338),U_12339)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12335,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12335,U_12336,U_12337),U_12338)),hAPP(c_Set_Ovimage(U_12335,U_12336,U_12337),U_12339)),
inference(clausify,[status(thm)],[f_3237_2]) ).
fof(f_3238_1,plain,
! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_vimage__empty]) ).
fof(f_3238_2,plain,
! [U_12342,U_12341,U_12340] : hAPP(c_Set_Ovimage(U_12340,U_12341,U_12342),c_Orderings_Obot__class_Obot(tc_fun(U_12341,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12340,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3238_1]) ).
cnf(f_3238_3,plain,
hAPP(c_Set_Ovimage(U_12340,U_12341,U_12342),c_Orderings_Obot__class_Obot(tc_fun(U_12341,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12340,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3238_2]) ).
fof(f_3239_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__Int]) ).
fof(f_3239_2,plain,
! [U_12347,U_12346,U_12345,U_12344,U_12343] : hAPP(c_Set_Ovimage(U_12343,U_12344,U_12345),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12344,tc_HOL_Obool)),U_12346),U_12347)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12343,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12343,U_12344,U_12345),U_12346)),hAPP(c_Set_Ovimage(U_12343,U_12344,U_12345),U_12347)),
inference(variable_rename,[status(thm)],[f_3239_1]) ).
cnf(f_3239_3,plain,
hAPP(c_Set_Ovimage(U_12343,U_12344,U_12345),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12344,tc_HOL_Obool)),U_12346),U_12347)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12343,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12343,U_12344,U_12345),U_12346)),hAPP(c_Set_Ovimage(U_12343,U_12344,U_12345),U_12347)),
inference(clausify,[status(thm)],[f_3239_2]) ).
fof(f_3240_1,plain,
! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__Diff]) ).
fof(f_3240_2,plain,
! [U_12352,U_12351,U_12350,U_12349,U_12348] : hAPP(c_Set_Ovimage(U_12348,U_12349,U_12350),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12349,tc_HOL_Obool)),U_12351),U_12352)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12348,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12348,U_12349,U_12350),U_12351)),hAPP(c_Set_Ovimage(U_12348,U_12349,U_12350),U_12352)),
inference(variable_rename,[status(thm)],[f_3240_1]) ).
cnf(f_3240_3,plain,
hAPP(c_Set_Ovimage(U_12348,U_12349,U_12350),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12349,tc_HOL_Obool)),U_12351),U_12352)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12348,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12348,U_12349,U_12350),U_12351)),hAPP(c_Set_Ovimage(U_12348,U_12349,U_12350),U_12352)),
inference(clausify,[status(thm)],[f_3240_2]) ).
fof(f_3241_1,plain,
! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__INT]) ).
fof(f_3241_2,plain,
! [U_12358,U_12357,U_12356,U_12355,U_12354,U_12353] : hAPP(c_Set_Ovimage(U_12353,U_12354,U_12355),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12356,tc_fun(U_12354,tc_HOL_Obool)),U_12357),U_12358)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12356,tc_fun(U_12353,tc_HOL_Obool)),U_12357),hAPP(hAPP(c_COMBB(tc_fun(U_12354,tc_HOL_Obool),tc_fun(U_12353,tc_HOL_Obool),U_12356),c_Set_Ovimage(U_12353,U_12354,U_12355)),U_12358)),
inference(variable_rename,[status(thm)],[f_3241_1]) ).
cnf(f_3241_3,plain,
hAPP(c_Set_Ovimage(U_12353,U_12354,U_12355),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12356,tc_fun(U_12354,tc_HOL_Obool)),U_12357),U_12358)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_12356,tc_fun(U_12353,tc_HOL_Obool)),U_12357),hAPP(hAPP(c_COMBB(tc_fun(U_12354,tc_HOL_Obool),tc_fun(U_12353,tc_HOL_Obool),U_12356),c_Set_Ovimage(U_12353,U_12354,U_12355)),U_12358)),
inference(clausify,[status(thm)],[f_3241_2]) ).
fof(f_3242_1,plain,
! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__UN]) ).
fof(f_3242_2,plain,
! [U_12364,U_12363,U_12362,U_12361,U_12360,U_12359] : hAPP(c_Set_Ovimage(U_12359,U_12360,U_12361),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12362,tc_fun(U_12360,tc_HOL_Obool)),U_12363),U_12364)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12362,tc_fun(U_12359,tc_HOL_Obool)),U_12363),hAPP(hAPP(c_COMBB(tc_fun(U_12360,tc_HOL_Obool),tc_fun(U_12359,tc_HOL_Obool),U_12362),c_Set_Ovimage(U_12359,U_12360,U_12361)),U_12364)),
inference(variable_rename,[status(thm)],[f_3242_1]) ).
cnf(f_3242_3,plain,
hAPP(c_Set_Ovimage(U_12359,U_12360,U_12361),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12362,tc_fun(U_12360,tc_HOL_Obool)),U_12363),U_12364)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12362,tc_fun(U_12359,tc_HOL_Obool)),U_12363),hAPP(hAPP(c_COMBB(tc_fun(U_12360,tc_HOL_Obool),tc_fun(U_12359,tc_HOL_Obool),U_12362),c_Set_Ovimage(U_12359,U_12360,U_12361)),U_12364)),
inference(clausify,[status(thm)],[f_3242_2]) ).
fof(f_3243_1,plain,
! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_vimage__UNIV]) ).
fof(f_3243_2,plain,
! [U_12367,U_12366,U_12365] : hAPP(c_Set_Ovimage(U_12365,U_12366,U_12367),c_Orderings_Otop__class_Otop(tc_fun(U_12366,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_12365,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3243_1]) ).
cnf(f_3243_3,plain,
hAPP(c_Set_Ovimage(U_12365,U_12366,U_12367),c_Orderings_Otop__class_Otop(tc_fun(U_12366,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_12365,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3243_2]) ).
fof(f_3244_1,plain,
! [V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_image__vimage__subset]) ).
fof(f_3244_2,plain,
! [U_12371,U_12370,U_12369,U_12368] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12368,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12369,U_12368,U_12370),hAPP(c_Set_Ovimage(U_12369,U_12368,U_12370),U_12371))),U_12371)),
inference(variable_rename,[status(thm)],[f_3244_1]) ).
cnf(f_3244_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12368,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12369,U_12368,U_12370),hAPP(c_Set_Ovimage(U_12369,U_12368,U_12370),U_12371))),U_12371)),
inference(clausify,[status(thm)],[f_3244_2]) ).
fof(f_3245_1,plain,
! [V_A_2,V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = V_A_2
| hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_surj__image__vimage__eq]) ).
fof(f_3245_2,plain,
! [U_12375,U_12374,U_12373,U_12372] :
( hAPP(c_Set_Oimage(U_12372,U_12373,U_12374),hAPP(c_Set_Ovimage(U_12372,U_12373,U_12374),U_12375)) = U_12375
| hAPP(c_Set_Oimage(U_12372,U_12373,U_12374),c_Orderings_Otop__class_Otop(tc_fun(U_12372,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12373,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_3245_1]) ).
cnf(f_3245_3,plain,
( hAPP(c_Set_Oimage(U_12372,U_12373,U_12374),hAPP(c_Set_Ovimage(U_12372,U_12373,U_12374),U_12375)) = U_12375
| hAPP(c_Set_Oimage(U_12372,U_12373,U_12374),c_Orderings_Otop__class_Otop(tc_fun(U_12372,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12373,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3245_2]) ).
fof(f_3246_1,plain,
! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
| hAPP(V_f_2,V_a_2) != V_b_2 )
& ( hAPP(V_f_2,V_a_2) = V_b_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ),
inference(fof_nnf,[status(thm)],[fact_vimage__singleton__eq]) ).
fof(f_3246_2,plain,
! [U_12380,U_12379,U_12378,U_12377,U_12376] :
( ( hBOOL(hAPP(hAPP(c_member(U_12376),U_12377),hAPP(c_Set_Ovimage(U_12376,U_12378,U_12379),hAPP(hAPP(c_Set_Oinsert(U_12378),U_12380),c_Orderings_Obot__class_Obot(tc_fun(U_12378,tc_HOL_Obool))))))
| hAPP(U_12379,U_12377) != U_12380 )
& ( hAPP(U_12379,U_12377) = U_12380
| ~ hBOOL(hAPP(hAPP(c_member(U_12376),U_12377),hAPP(c_Set_Ovimage(U_12376,U_12378,U_12379),hAPP(hAPP(c_Set_Oinsert(U_12378),U_12380),c_Orderings_Obot__class_Obot(tc_fun(U_12378,tc_HOL_Obool)))))) ) ),
inference(variable_rename,[status(thm)],[f_3246_1]) ).
fof(f_3246_3,plain,
( ! [U_12390,U_12388,U_12386,U_12384] :
( ! [U_12382] : hBOOL(hAPP(hAPP(c_member(U_12382),U_12384),hAPP(c_Set_Ovimage(U_12382,U_12386,U_12388),hAPP(hAPP(c_Set_Oinsert(U_12386),U_12390),c_Orderings_Obot__class_Obot(tc_fun(U_12386,tc_HOL_Obool))))))
| hAPP(U_12388,U_12384) != U_12390 )
& ! [U_12389,U_12387,U_12385,U_12383] :
( ! [U_12381] : ~ hBOOL(hAPP(hAPP(c_member(U_12381),U_12383),hAPP(c_Set_Ovimage(U_12381,U_12385,U_12387),hAPP(hAPP(c_Set_Oinsert(U_12385),U_12389),c_Orderings_Obot__class_Obot(tc_fun(U_12385,tc_HOL_Obool))))))
| hAPP(U_12387,U_12383) = U_12389 ) ),
inference(miniscope,[status(thm)],[f_3246_2]) ).
cnf(f_3246_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_12381),U_12383),hAPP(c_Set_Ovimage(U_12381,U_12385,U_12387),hAPP(hAPP(c_Set_Oinsert(U_12385),U_12389),c_Orderings_Obot__class_Obot(tc_fun(U_12385,tc_HOL_Obool))))))
| hAPP(U_12387,U_12383) = U_12389 ),
inference(clausify,[status(thm)],[f_3246_3]) ).
cnf(f_3246_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_12382),U_12384),hAPP(c_Set_Ovimage(U_12382,U_12386,U_12388),hAPP(hAPP(c_Set_Oinsert(U_12386),U_12390),c_Orderings_Obot__class_Obot(tc_fun(U_12386,tc_HOL_Obool))))))
| hAPP(U_12388,U_12384) != U_12390 ),
inference(clausify,[status(thm)],[f_3246_3]) ).
fof(f_3247_1,plain,
! [V_B_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__insert]) ).
fof(f_3247_2,plain,
! [U_12395,U_12394,U_12393,U_12392,U_12391] : hAPP(c_Set_Ovimage(U_12391,U_12392,U_12393),hAPP(hAPP(c_Set_Oinsert(U_12392),U_12394),U_12395)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12391,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12391,U_12392,U_12393),hAPP(hAPP(c_Set_Oinsert(U_12392),U_12394),c_Orderings_Obot__class_Obot(tc_fun(U_12392,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_12391,U_12392,U_12393),U_12395)),
inference(variable_rename,[status(thm)],[f_3247_1]) ).
cnf(f_3247_3,plain,
hAPP(c_Set_Ovimage(U_12391,U_12392,U_12393),hAPP(hAPP(c_Set_Oinsert(U_12392),U_12394),U_12395)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12391,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12391,U_12392,U_12393),hAPP(hAPP(c_Set_Oinsert(U_12392),U_12394),c_Orderings_Obot__class_Obot(tc_fun(U_12392,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_12391,U_12392,U_12393),U_12395)),
inference(clausify,[status(thm)],[f_3247_2]) ).
fof(f_3248_1,plain,
! [V_F_2,V_h_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2))
| hAPP(c_Set_Oimage(T_b,T_c,V_h_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__vimageD]) ).
fof(f_3248_2,plain,
! [U_12399,U_12398,U_12397,U_12396] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12397),U_12399))
| hAPP(c_Set_Oimage(U_12396,U_12397,U_12398),c_Orderings_Otop__class_Otop(tc_fun(U_12396,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12397,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12396),hAPP(c_Set_Ovimage(U_12396,U_12397,U_12398),U_12399))) ),
inference(variable_rename,[status(thm)],[f_3248_1]) ).
cnf(f_3248_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12397),U_12399))
| hAPP(c_Set_Oimage(U_12396,U_12397,U_12398),c_Orderings_Otop__class_Otop(tc_fun(U_12396,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12397,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12396),hAPP(c_Set_Ovimage(U_12396,U_12397,U_12398),U_12399))) ),
inference(clausify,[status(thm)],[f_3248_2]) ).
fof(f_3249_1,plain,
! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)),V_A_2))
| hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_vimage__subsetD]) ).
fof(f_3249_2,plain,
! [U_12404,U_12403,U_12402,U_12401,U_12400] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12401,tc_HOL_Obool)),U_12403),hAPP(c_Set_Oimage(U_12400,U_12401,U_12402),U_12404)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12400,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12400,U_12401,U_12402),U_12403)),U_12404))
| hAPP(c_Set_Oimage(U_12400,U_12401,U_12402),c_Orderings_Otop__class_Otop(tc_fun(U_12400,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12401,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_3249_1]) ).
cnf(f_3249_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12401,tc_HOL_Obool)),U_12403),hAPP(c_Set_Oimage(U_12400,U_12401,U_12402),U_12404)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12400,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12400,U_12401,U_12402),U_12403)),U_12404))
| hAPP(c_Set_Oimage(U_12400,U_12401,U_12402),c_Orderings_Otop__class_Otop(tc_fun(U_12400,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12401,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3249_2]) ).
fof(f_3250_1,plain,
! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_image__vimage__eq]) ).
fof(f_3250_2,plain,
! [U_12408,U_12407,U_12406,U_12405] : hAPP(c_Set_Oimage(U_12405,U_12406,U_12407),hAPP(c_Set_Ovimage(U_12405,U_12406,U_12407),U_12408)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12406,tc_HOL_Obool)),U_12408),hAPP(c_Set_Oimage(U_12405,U_12406,U_12407),c_Orderings_Otop__class_Otop(tc_fun(U_12405,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_3250_1]) ).
cnf(f_3250_3,plain,
hAPP(c_Set_Oimage(U_12405,U_12406,U_12407),hAPP(c_Set_Ovimage(U_12405,U_12406,U_12407),U_12408)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12406,tc_HOL_Obool)),U_12408),hAPP(c_Set_Oimage(U_12405,U_12406,U_12407),c_Orderings_Otop__class_Otop(tc_fun(U_12405,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_3250_2]) ).
fof(f_3251_1,plain,
! [V_h_2,T_c,V_F_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2)))
| ~ c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__vimageI]) ).
fof(f_3251_2,plain,
! [U_12412,U_12411,U_12410,U_12409] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12411),hAPP(c_Set_Ovimage(U_12411,U_12409,U_12412),U_12410)))
| ~ c_Fun_Oinj__on(U_12411,U_12409,U_12412,c_Orderings_Otop__class_Otop(tc_fun(U_12411,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12409),U_12410)) ),
inference(variable_rename,[status(thm)],[f_3251_1]) ).
cnf(f_3251_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12411),hAPP(c_Set_Ovimage(U_12411,U_12409,U_12412),U_12410)))
| ~ c_Fun_Oinj__on(U_12411,U_12409,U_12412,c_Orderings_Otop__class_Otop(tc_fun(U_12411,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12409),U_12410)) ),
inference(clausify,[status(thm)],[f_3251_2]) ).
fof(f_3252_1,plain,
! [V_A_2,V_f_2,T_c,T_b] :
( hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_inj__vimage__image__eq]) ).
fof(f_3252_2,plain,
! [U_12416,U_12415,U_12414,U_12413] :
( hAPP(c_Set_Ovimage(U_12413,U_12414,U_12415),hAPP(c_Set_Oimage(U_12413,U_12414,U_12415),U_12416)) = U_12416
| ~ c_Fun_Oinj__on(U_12413,U_12414,U_12415,c_Orderings_Otop__class_Otop(tc_fun(U_12413,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_3252_1]) ).
cnf(f_3252_3,plain,
( hAPP(c_Set_Ovimage(U_12413,U_12414,U_12415),hAPP(c_Set_Oimage(U_12413,U_12414,U_12415),U_12416)) = U_12416
| ~ c_Fun_Oinj__on(U_12413,U_12414,U_12415,c_Orderings_Otop__class_Otop(tc_fun(U_12413,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3252_2]) ).
fof(f_3253_1,plain,
! [T_c,V_A_2,V_c_2,T_b] :
( ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
& ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_vimage__const]) ).
fof(f_3253_2,plain,
! [U_12420,U_12419,U_12418,U_12417] :
( ( hAPP(c_Set_Ovimage(U_12420,U_12417,hAPP(c_COMBK(U_12417,U_12420),U_12418)),U_12419) = c_Orderings_Obot__class_Obot(tc_fun(U_12420,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_12417),U_12418),U_12419)) )
& ( hAPP(c_Set_Ovimage(U_12420,U_12417,hAPP(c_COMBK(U_12417,U_12420),U_12418)),U_12419) = c_Orderings_Otop__class_Otop(tc_fun(U_12420,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_12417),U_12418),U_12419)) ) ),
inference(variable_rename,[status(thm)],[f_3253_1]) ).
fof(f_3253_3,plain,
( ! [U_12428,U_12426,U_12424,U_12422] :
( hAPP(c_Set_Ovimage(U_12428,U_12422,hAPP(c_COMBK(U_12422,U_12428),U_12424)),U_12426) = c_Orderings_Obot__class_Obot(tc_fun(U_12428,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_12422),U_12424),U_12426)) )
& ! [U_12427,U_12425,U_12423,U_12421] :
( hAPP(c_Set_Ovimage(U_12427,U_12421,hAPP(c_COMBK(U_12421,U_12427),U_12423)),U_12425) = c_Orderings_Otop__class_Otop(tc_fun(U_12427,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_12421),U_12423),U_12425)) ) ),
inference(miniscope,[status(thm)],[f_3253_2]) ).
cnf(f_3253_4,plain,
( hAPP(c_Set_Ovimage(U_12427,U_12421,hAPP(c_COMBK(U_12421,U_12427),U_12423)),U_12425) = c_Orderings_Otop__class_Otop(tc_fun(U_12427,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_12421),U_12423),U_12425)) ),
inference(clausify,[status(thm)],[f_3253_3]) ).
cnf(f_3253_5,plain,
( hAPP(c_Set_Ovimage(U_12428,U_12422,hAPP(c_COMBK(U_12422,U_12428),U_12424)),U_12426) = c_Orderings_Obot__class_Obot(tc_fun(U_12428,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_12422),U_12424),U_12426)) ),
inference(clausify,[status(thm)],[f_3253_3]) ).
fof(f_3254_1,plain,
! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Ovimage(T_b,T_c,V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),
inference(fof_nnf,[status(thm)],[fact_vimage__eq__UN]) ).
fof(f_3254_2,plain,
! [U_12432,U_12431,U_12430,U_12429] : hAPP(c_Set_Ovimage(U_12429,U_12430,U_12431),U_12432) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12430,tc_fun(U_12429,tc_HOL_Obool)),U_12432),hAPP(hAPP(c_COMBB(tc_fun(U_12430,tc_HOL_Obool),tc_fun(U_12429,tc_HOL_Obool),U_12430),c_Set_Ovimage(U_12429,U_12430,U_12431)),hAPP(hAPP(c_COMBC(U_12430,tc_fun(U_12430,tc_HOL_Obool),tc_fun(U_12430,tc_HOL_Obool)),c_Set_Oinsert(U_12430)),c_Orderings_Obot__class_Obot(tc_fun(U_12430,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_3254_1]) ).
cnf(f_3254_3,plain,
hAPP(c_Set_Ovimage(U_12429,U_12430,U_12431),U_12432) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12430,tc_fun(U_12429,tc_HOL_Obool)),U_12432),hAPP(hAPP(c_COMBB(tc_fun(U_12430,tc_HOL_Obool),tc_fun(U_12429,tc_HOL_Obool),U_12430),c_Set_Ovimage(U_12429,U_12430,U_12431)),hAPP(hAPP(c_COMBC(U_12430,tc_fun(U_12430,tc_HOL_Obool),tc_fun(U_12430,tc_HOL_Obool)),c_Set_Oinsert(U_12430)),c_Orderings_Obot__class_Obot(tc_fun(U_12430,tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_3254_2]) ).
fof(f_3255_1,plain,
! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_vimage__subsetI]) ).
fof(f_3255_2,plain,
! [U_12437,U_12436,U_12435,U_12434,U_12433] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12433,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12433,U_12434,U_12435),U_12436)),U_12437))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12434,tc_HOL_Obool)),U_12436),hAPP(c_Set_Oimage(U_12433,U_12434,U_12435),U_12437)))
| ~ c_Fun_Oinj__on(U_12433,U_12434,U_12435,c_Orderings_Otop__class_Otop(tc_fun(U_12433,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_3255_1]) ).
cnf(f_3255_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12433,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_12433,U_12434,U_12435),U_12436)),U_12437))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12434,tc_HOL_Obool)),U_12436),hAPP(c_Set_Oimage(U_12433,U_12434,U_12435),U_12437)))
| ~ c_Fun_Oinj__on(U_12433,U_12434,U_12435,c_Orderings_Otop__class_Otop(tc_fun(U_12433,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3255_2]) ).
fof(f_3256_1,plain,
! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] :
( ( ( ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) )
& ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) ) )
| hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
& ( ( ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2
| hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) )
& ( hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_vimage__if]) ).
fof(f_3256_2,plain,
! [U_12443,U_12442,U_12441,U_12440,U_12439,U_12438] :
( ( ( ( hAPP(c_Set_Ovimage(U_12442,U_12438,hAPP(hAPP(c_COMBC(U_12442,U_12438,U_12438),hAPP(hAPP(c_COMBC(U_12442,U_12438,tc_fun(U_12438,U_12438)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12438,tc_fun(U_12438,U_12438)),U_12442),c_If(U_12438)),hAPP(hAPP(c_COMBC(U_12442,tc_fun(U_12442,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12442)),U_12443))),U_12439)),U_12441)),U_12440) = c_Orderings_Obot__class_Obot(tc_fun(U_12442,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_12438),U_12441),U_12440)) )
& ( hAPP(c_Set_Ovimage(U_12442,U_12438,hAPP(hAPP(c_COMBC(U_12442,U_12438,U_12438),hAPP(hAPP(c_COMBC(U_12442,U_12438,tc_fun(U_12438,U_12438)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12438,tc_fun(U_12438,U_12438)),U_12442),c_If(U_12438)),hAPP(hAPP(c_COMBC(U_12442,tc_fun(U_12442,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12442)),U_12443))),U_12439)),U_12441)),U_12440) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12442,tc_HOL_Obool)),U_12443)
| ~ hBOOL(hAPP(hAPP(c_member(U_12438),U_12441),U_12440)) ) )
| hBOOL(hAPP(hAPP(c_member(U_12438),U_12439),U_12440)) )
& ( ( ( hAPP(c_Set_Ovimage(U_12442,U_12438,hAPP(hAPP(c_COMBC(U_12442,U_12438,U_12438),hAPP(hAPP(c_COMBC(U_12442,U_12438,tc_fun(U_12438,U_12438)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12438,tc_fun(U_12438,U_12438)),U_12442),c_If(U_12438)),hAPP(hAPP(c_COMBC(U_12442,tc_fun(U_12442,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12442)),U_12443))),U_12439)),U_12441)),U_12440) = U_12443
| hBOOL(hAPP(hAPP(c_member(U_12438),U_12441),U_12440)) )
& ( hAPP(c_Set_Ovimage(U_12442,U_12438,hAPP(hAPP(c_COMBC(U_12442,U_12438,U_12438),hAPP(hAPP(c_COMBC(U_12442,U_12438,tc_fun(U_12438,U_12438)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12438,tc_fun(U_12438,U_12438)),U_12442),c_If(U_12438)),hAPP(hAPP(c_COMBC(U_12442,tc_fun(U_12442,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12442)),U_12443))),U_12439)),U_12441)),U_12440) = c_Orderings_Otop__class_Otop(tc_fun(U_12442,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_12438),U_12441),U_12440)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12438),U_12439),U_12440)) ) ),
inference(variable_rename,[status(thm)],[f_3256_1]) ).
fof(f_3256_3,plain,
( ! [U_12455,U_12453,U_12451,U_12449,U_12447,U_12445] :
( ( ( hAPP(c_Set_Ovimage(U_12453,U_12445,hAPP(hAPP(c_COMBC(U_12453,U_12445,U_12445),hAPP(hAPP(c_COMBC(U_12453,U_12445,tc_fun(U_12445,U_12445)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12445,tc_fun(U_12445,U_12445)),U_12453),c_If(U_12445)),hAPP(hAPP(c_COMBC(U_12453,tc_fun(U_12453,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12453)),U_12455))),U_12447)),U_12451)),U_12449) = c_Orderings_Obot__class_Obot(tc_fun(U_12453,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_12445),U_12451),U_12449)) )
& ( hAPP(c_Set_Ovimage(U_12453,U_12445,hAPP(hAPP(c_COMBC(U_12453,U_12445,U_12445),hAPP(hAPP(c_COMBC(U_12453,U_12445,tc_fun(U_12445,U_12445)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12445,tc_fun(U_12445,U_12445)),U_12453),c_If(U_12445)),hAPP(hAPP(c_COMBC(U_12453,tc_fun(U_12453,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12453)),U_12455))),U_12447)),U_12451)),U_12449) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12453,tc_HOL_Obool)),U_12455)
| ~ hBOOL(hAPP(hAPP(c_member(U_12445),U_12451),U_12449)) ) )
| hBOOL(hAPP(hAPP(c_member(U_12445),U_12447),U_12449)) )
& ! [U_12454,U_12452,U_12450,U_12448,U_12446,U_12444] :
( ( ( hAPP(c_Set_Ovimage(U_12452,U_12444,hAPP(hAPP(c_COMBC(U_12452,U_12444,U_12444),hAPP(hAPP(c_COMBC(U_12452,U_12444,tc_fun(U_12444,U_12444)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12444,tc_fun(U_12444,U_12444)),U_12452),c_If(U_12444)),hAPP(hAPP(c_COMBC(U_12452,tc_fun(U_12452,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12452)),U_12454))),U_12446)),U_12450)),U_12448) = U_12454
| hBOOL(hAPP(hAPP(c_member(U_12444),U_12450),U_12448)) )
& ( hAPP(c_Set_Ovimage(U_12452,U_12444,hAPP(hAPP(c_COMBC(U_12452,U_12444,U_12444),hAPP(hAPP(c_COMBC(U_12452,U_12444,tc_fun(U_12444,U_12444)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12444,tc_fun(U_12444,U_12444)),U_12452),c_If(U_12444)),hAPP(hAPP(c_COMBC(U_12452,tc_fun(U_12452,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12452)),U_12454))),U_12446)),U_12450)),U_12448) = c_Orderings_Otop__class_Otop(tc_fun(U_12452,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_12444),U_12450),U_12448)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12444),U_12446),U_12448)) ) ),
inference(miniscope,[status(thm)],[f_3256_2]) ).
cnf(f_3256_4,plain,
( hAPP(c_Set_Ovimage(U_12452,U_12444,hAPP(hAPP(c_COMBC(U_12452,U_12444,U_12444),hAPP(hAPP(c_COMBC(U_12452,U_12444,tc_fun(U_12444,U_12444)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12444,tc_fun(U_12444,U_12444)),U_12452),c_If(U_12444)),hAPP(hAPP(c_COMBC(U_12452,tc_fun(U_12452,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12452)),U_12454))),U_12446)),U_12450)),U_12448) = c_Orderings_Otop__class_Otop(tc_fun(U_12452,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(U_12444),U_12450),U_12448))
| ~ hBOOL(hAPP(hAPP(c_member(U_12444),U_12446),U_12448)) ),
inference(clausify,[status(thm)],[f_3256_3]) ).
cnf(f_3256_5,plain,
( hAPP(c_Set_Ovimage(U_12452,U_12444,hAPP(hAPP(c_COMBC(U_12452,U_12444,U_12444),hAPP(hAPP(c_COMBC(U_12452,U_12444,tc_fun(U_12444,U_12444)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12444,tc_fun(U_12444,U_12444)),U_12452),c_If(U_12444)),hAPP(hAPP(c_COMBC(U_12452,tc_fun(U_12452,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12452)),U_12454))),U_12446)),U_12450)),U_12448) = U_12454
| hBOOL(hAPP(hAPP(c_member(U_12444),U_12450),U_12448))
| ~ hBOOL(hAPP(hAPP(c_member(U_12444),U_12446),U_12448)) ),
inference(clausify,[status(thm)],[f_3256_3]) ).
cnf(f_3256_6,plain,
( hAPP(c_Set_Ovimage(U_12453,U_12445,hAPP(hAPP(c_COMBC(U_12453,U_12445,U_12445),hAPP(hAPP(c_COMBC(U_12453,U_12445,tc_fun(U_12445,U_12445)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12445,tc_fun(U_12445,U_12445)),U_12453),c_If(U_12445)),hAPP(hAPP(c_COMBC(U_12453,tc_fun(U_12453,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12453)),U_12455))),U_12447)),U_12451)),U_12449) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12453,tc_HOL_Obool)),U_12455)
| ~ hBOOL(hAPP(hAPP(c_member(U_12445),U_12451),U_12449))
| hBOOL(hAPP(hAPP(c_member(U_12445),U_12447),U_12449)) ),
inference(clausify,[status(thm)],[f_3256_3]) ).
cnf(f_3256_7,plain,
( hAPP(c_Set_Ovimage(U_12453,U_12445,hAPP(hAPP(c_COMBC(U_12453,U_12445,U_12445),hAPP(hAPP(c_COMBC(U_12453,U_12445,tc_fun(U_12445,U_12445)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12445,tc_fun(U_12445,U_12445)),U_12453),c_If(U_12445)),hAPP(hAPP(c_COMBC(U_12453,tc_fun(U_12453,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12453)),U_12455))),U_12447)),U_12451)),U_12449) = c_Orderings_Obot__class_Obot(tc_fun(U_12453,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(U_12445),U_12451),U_12449))
| hBOOL(hAPP(hAPP(c_member(U_12445),U_12447),U_12449)) ),
inference(clausify,[status(thm)],[f_3256_3]) ).
fof(f_3257_1,plain,
! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( hAPP(c_Set_Oimage(T_b,T_c,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2
| ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__range]) ).
fof(f_3257_2,plain,
! [U_12460,U_12459,U_12458,U_12457,U_12456] :
( hAPP(c_Set_Oimage(U_12456,U_12457,U_12458),c_Orderings_Otop__class_Otop(tc_fun(U_12456,tc_HOL_Obool))) = U_12460
| ~ c_Typedef_Otype__definition(U_12456,U_12457,U_12458,U_12459,U_12460) ),
inference(variable_rename,[status(thm)],[f_3257_1]) ).
cnf(f_3257_3,plain,
( hAPP(c_Set_Oimage(U_12456,U_12457,U_12458),c_Orderings_Otop__class_Otop(tc_fun(U_12456,tc_HOL_Obool))) = U_12460
| ~ c_Typedef_Otype__definition(U_12456,U_12457,U_12458,U_12459,U_12460) ),
inference(clausify,[status(thm)],[f_3257_2]) ).
fof(f_3258_1,plain,
! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( hAPP(c_Set_Oimage(T_c,T_b,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
| ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__image]) ).
fof(f_3258_2,plain,
! [U_12465,U_12464,U_12463,U_12462,U_12461] :
( hAPP(c_Set_Oimage(U_12462,U_12461,U_12464),U_12465) = c_Orderings_Otop__class_Otop(tc_fun(U_12461,tc_HOL_Obool))
| ~ c_Typedef_Otype__definition(U_12461,U_12462,U_12463,U_12464,U_12465) ),
inference(variable_rename,[status(thm)],[f_3258_1]) ).
cnf(f_3258_3,plain,
( hAPP(c_Set_Oimage(U_12462,U_12461,U_12464),U_12465) = c_Orderings_Otop__class_Otop(tc_fun(U_12461,tc_HOL_Obool))
| ~ c_Typedef_Otype__definition(U_12461,U_12462,U_12463,U_12464,U_12465) ),
inference(clausify,[status(thm)],[f_3258_2]) ).
fof(f_3259_1,plain,
! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2))
| ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_type__definition_ORep]) ).
fof(f_3259_2,plain,
! [U_12471,U_12470,U_12469,U_12468,U_12467,U_12466] :
( hBOOL(hAPP(hAPP(c_member(U_12467),hAPP(U_12468,U_12471)),U_12470))
| ~ c_Typedef_Otype__definition(U_12466,U_12467,U_12468,U_12469,U_12470) ),
inference(variable_rename,[status(thm)],[f_3259_1]) ).
fof(f_3259_3,plain,
! [U_12471,U_12470,U_12469,U_12468,U_12467] :
( ! [U_12466] : ~ c_Typedef_Otype__definition(U_12466,U_12467,U_12468,U_12469,U_12470)
| hBOOL(hAPP(hAPP(c_member(U_12467),hAPP(U_12468,U_12471)),U_12470)) ),
inference(miniscope,[status(thm)],[f_3259_2]) ).
cnf(f_3259_4,plain,
( ~ c_Typedef_Otype__definition(U_12466,U_12467,U_12468,U_12469,U_12470)
| hBOOL(hAPP(hAPP(c_member(U_12467),hAPP(U_12468,U_12471)),U_12470)) ),
inference(clausify,[status(thm)],[f_3259_3]) ).
fof(f_3260_1,plain,
! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( ( ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(V_Rep_2,V_x_2) != hAPP(V_Rep_2,V_y_2) ) )
| ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inject]) ).
fof(f_3260_2,plain,
! [U_12478,U_12477,U_12476,U_12475,U_12474,U_12473,U_12472] :
( ( ( hAPP(U_12474,U_12477) = hAPP(U_12474,U_12478)
| U_12477 != U_12478 )
& ( U_12477 = U_12478
| hAPP(U_12474,U_12477) != hAPP(U_12474,U_12478) ) )
| ~ c_Typedef_Otype__definition(U_12472,U_12473,U_12474,U_12475,U_12476) ),
inference(variable_rename,[status(thm)],[f_3260_1]) ).
fof(f_3260_3,plain,
! [U_12478,U_12477,U_12476,U_12475,U_12474] :
( ! [U_12473,U_12472] : ~ c_Typedef_Otype__definition(U_12472,U_12473,U_12474,U_12475,U_12476)
| ( ( hAPP(U_12474,U_12477) = hAPP(U_12474,U_12478)
| U_12477 != U_12478 )
& ( U_12477 = U_12478
| hAPP(U_12474,U_12477) != hAPP(U_12474,U_12478) ) ) ),
inference(miniscope,[status(thm)],[f_3260_2]) ).
cnf(f_3260_4,plain,
( U_12477 = U_12478
| hAPP(U_12474,U_12477) != hAPP(U_12474,U_12478)
| ~ c_Typedef_Otype__definition(U_12472,U_12473,U_12474,U_12475,U_12476) ),
inference(clausify,[status(thm)],[f_3260_3]) ).
cnf(f_3260_5,plain,
( hAPP(U_12474,U_12477) = hAPP(U_12474,U_12478)
| U_12477 != U_12478
| ~ c_Typedef_Otype__definition(U_12472,U_12473,U_12474,U_12475,U_12476) ),
inference(clausify,[status(thm)],[f_3260_3]) ).
fof(f_3261_1,plain,
! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2
| ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inverse]) ).
fof(f_3261_2,plain,
! [U_12484,U_12483,U_12482,U_12481,U_12480,U_12479] :
( hAPP(U_12482,hAPP(U_12481,U_12484)) = U_12484
| ~ c_Typedef_Otype__definition(U_12479,U_12480,U_12481,U_12482,U_12483) ),
inference(variable_rename,[status(thm)],[f_3261_1]) ).
fof(f_3261_3,plain,
! [U_12484,U_12483,U_12482,U_12481] :
( ! [U_12480,U_12479] : ~ c_Typedef_Otype__definition(U_12479,U_12480,U_12481,U_12482,U_12483)
| hAPP(U_12482,hAPP(U_12481,U_12484)) = U_12484 ),
inference(miniscope,[status(thm)],[f_3261_2]) ).
cnf(f_3261_4,plain,
( ~ c_Typedef_Otype__definition(U_12479,U_12480,U_12481,U_12482,U_12483)
| hAPP(U_12482,hAPP(U_12481,U_12484)) = U_12484 ),
inference(clausify,[status(thm)],[f_3261_3]) ).
fof(f_3262_1,plain,
! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( ( ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| hAPP(V_Abs_2,V_x_2) != hAPP(V_Abs_2,V_y_2) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inject]) ).
fof(f_3262_2,plain,
! [U_12491,U_12490,U_12489,U_12488,U_12487,U_12486,U_12485] :
( ( ( hAPP(U_12488,U_12490) = hAPP(U_12488,U_12491)
| U_12490 != U_12491 )
& ( U_12490 = U_12491
| hAPP(U_12488,U_12490) != hAPP(U_12488,U_12491) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12486),U_12491),U_12489))
| ~ hBOOL(hAPP(hAPP(c_member(U_12486),U_12490),U_12489))
| ~ c_Typedef_Otype__definition(U_12485,U_12486,U_12487,U_12488,U_12489) ),
inference(variable_rename,[status(thm)],[f_3262_1]) ).
fof(f_3262_3,plain,
! [U_12491,U_12490,U_12489,U_12488,U_12487,U_12486] :
( ! [U_12485] : ~ c_Typedef_Otype__definition(U_12485,U_12486,U_12487,U_12488,U_12489)
| ( ( hAPP(U_12488,U_12490) = hAPP(U_12488,U_12491)
| U_12490 != U_12491 )
& ( U_12490 = U_12491
| hAPP(U_12488,U_12490) != hAPP(U_12488,U_12491) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12486),U_12491),U_12489))
| ~ hBOOL(hAPP(hAPP(c_member(U_12486),U_12490),U_12489)) ),
inference(miniscope,[status(thm)],[f_3262_2]) ).
cnf(f_3262_4,plain,
( U_12490 = U_12491
| hAPP(U_12488,U_12490) != hAPP(U_12488,U_12491)
| ~ hBOOL(hAPP(hAPP(c_member(U_12486),U_12491),U_12489))
| ~ hBOOL(hAPP(hAPP(c_member(U_12486),U_12490),U_12489))
| ~ c_Typedef_Otype__definition(U_12485,U_12486,U_12487,U_12488,U_12489) ),
inference(clausify,[status(thm)],[f_3262_3]) ).
cnf(f_3262_5,plain,
( hAPP(U_12488,U_12490) = hAPP(U_12488,U_12491)
| U_12490 != U_12491
| ~ hBOOL(hAPP(hAPP(c_member(U_12486),U_12491),U_12489))
| ~ hBOOL(hAPP(hAPP(c_member(U_12486),U_12490),U_12489))
| ~ c_Typedef_Otype__definition(U_12485,U_12486,U_12487,U_12488,U_12489) ),
inference(clausify,[status(thm)],[f_3262_3]) ).
fof(f_3263_1,plain,
! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
( hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
| ~ c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inverse]) ).
fof(f_3263_2,plain,
! [U_12497,U_12496,U_12495,U_12494,U_12493,U_12492] :
( hAPP(U_12494,hAPP(U_12495,U_12497)) = U_12497
| ~ hBOOL(hAPP(hAPP(c_member(U_12493),U_12497),U_12496))
| ~ c_Typedef_Otype__definition(U_12492,U_12493,U_12494,U_12495,U_12496) ),
inference(variable_rename,[status(thm)],[f_3263_1]) ).
fof(f_3263_3,plain,
! [U_12497,U_12496,U_12495,U_12494,U_12493] :
( ! [U_12492] : ~ c_Typedef_Otype__definition(U_12492,U_12493,U_12494,U_12495,U_12496)
| hAPP(U_12494,hAPP(U_12495,U_12497)) = U_12497
| ~ hBOOL(hAPP(hAPP(c_member(U_12493),U_12497),U_12496)) ),
inference(miniscope,[status(thm)],[f_3263_2]) ).
cnf(f_3263_4,plain,
( ~ c_Typedef_Otype__definition(U_12492,U_12493,U_12494,U_12495,U_12496)
| hAPP(U_12494,hAPP(U_12495,U_12497)) = U_12497
| ~ hBOOL(hAPP(hAPP(c_member(U_12493),U_12497),U_12496)) ),
inference(clausify,[status(thm)],[f_3263_3]) ).
fof(f_3264_1,plain,
! [V_a2_2,V_a1_2,V_R_2,T_b] :
( ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
| ? [B_x] :
( ! [B_xa] :
( ~ hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) )
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) )
| V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) )
& ( ( ! [B_x] :
( ? [B_xa] :
( hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa))
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) )
& V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) )
| ~ c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2) ) ),
inference(fof_nnf,[status(thm)],[fact_max__extp_Oequations]) ).
fof(f_3264_2,plain,
! [U_12505,U_12504,U_12503,U_12502] :
( ( c_Wellfounded_Omax__extp(U_12502,U_12503,U_12504,U_12505)
| ? [U_12501] :
( ! [U_12500] :
( ~ hBOOL(hAPP(hAPP(U_12503,U_12501),U_12500))
| ~ hBOOL(hAPP(hAPP(c_member(U_12502),U_12500),U_12505)) )
& hBOOL(hAPP(hAPP(c_member(U_12502),U_12501),U_12504)) )
| U_12505 = c_Orderings_Obot__class_Obot(tc_fun(U_12502,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12502),U_12505))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12502),U_12504)) )
& ( ( ! [U_12499] :
( ? [U_12498] :
( hBOOL(hAPP(hAPP(U_12503,U_12499),U_12498))
& hBOOL(hAPP(hAPP(c_member(U_12502),U_12498),U_12505)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12502),U_12499),U_12504)) )
& U_12505 != c_Orderings_Obot__class_Obot(tc_fun(U_12502,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_12502),U_12505))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_12502),U_12504)) )
| ~ c_Wellfounded_Omax__extp(U_12502,U_12503,U_12504,U_12505) ) ),
inference(variable_rename,[status(thm)],[f_3264_1]) ).
fof(f_3264_3,plain,
( ! [U_12513,U_12511,U_12509,U_12507] :
( c_Wellfounded_Omax__extp(U_12507,U_12509,U_12511,U_12513)
| ? [U_12501] :
( ! [U_12500] :
( ~ hBOOL(hAPP(hAPP(U_12509,U_12501),U_12500))
| ~ hBOOL(hAPP(hAPP(c_member(U_12507),U_12500),U_12513)) )
& hBOOL(hAPP(hAPP(c_member(U_12507),U_12501),U_12511)) )
| U_12513 = c_Orderings_Obot__class_Obot(tc_fun(U_12507,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12507),U_12513))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12507),U_12511)) )
& ! [U_12512,U_12510,U_12508,U_12506] :
( ( ! [U_12499] :
( ? [U_12498] :
( hBOOL(hAPP(hAPP(U_12508,U_12499),U_12498))
& hBOOL(hAPP(hAPP(c_member(U_12506),U_12498),U_12512)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12506),U_12499),U_12510)) )
& U_12512 != c_Orderings_Obot__class_Obot(tc_fun(U_12506,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_12506),U_12512))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_12506),U_12510)) )
| ~ c_Wellfounded_Omax__extp(U_12506,U_12508,U_12510,U_12512) ) ),
inference(miniscope,[status(thm)],[f_3264_2]) ).
fof(f_3264_4,plain,
( ! [U_12513,U_12511,U_12509,U_12507] :
( c_Wellfounded_Omax__extp(U_12507,U_12509,U_12511,U_12513)
| ? [U_12501] :
( ! [U_12500] :
( ~ hBOOL(hAPP(hAPP(U_12509,U_12501),U_12500))
| ~ hBOOL(hAPP(hAPP(c_member(U_12507),U_12500),U_12513)) )
& hBOOL(hAPP(hAPP(c_member(U_12507),U_12501),U_12511)) )
| U_12513 = c_Orderings_Obot__class_Obot(tc_fun(U_12507,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12507),U_12513))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12507),U_12511)) )
& ! [U_12512,U_12510,U_12508,U_12506] :
( ( ! [U_12499] :
( ( hBOOL(hAPP(hAPP(U_12508,U_12499),sK274(U_12512,U_12510,U_12508,U_12506,U_12499)))
& hBOOL(hAPP(hAPP(c_member(U_12506),sK274(U_12512,U_12510,U_12508,U_12506,U_12499)),U_12512)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12506),U_12499),U_12510)) )
& U_12512 != c_Orderings_Obot__class_Obot(tc_fun(U_12506,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_12506),U_12512))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_12506),U_12510)) )
| ~ c_Wellfounded_Omax__extp(U_12506,U_12508,U_12510,U_12512) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK274]),skolemize(U_12498,sK274(U_12512,U_12510,U_12508,U_12506,U_12499))],[f_3264_3]) ).
fof(f_3264_5,plain,
( ! [U_12513,U_12511,U_12509,U_12507] :
( c_Wellfounded_Omax__extp(U_12507,U_12509,U_12511,U_12513)
| ( ! [U_12500] :
( ~ hBOOL(hAPP(hAPP(U_12509,sK275(U_12513,U_12511,U_12509,U_12507)),U_12500))
| ~ hBOOL(hAPP(hAPP(c_member(U_12507),U_12500),U_12513)) )
& hBOOL(hAPP(hAPP(c_member(U_12507),sK275(U_12513,U_12511,U_12509,U_12507)),U_12511)) )
| U_12513 = c_Orderings_Obot__class_Obot(tc_fun(U_12507,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12507),U_12513))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12507),U_12511)) )
& ! [U_12512,U_12510,U_12508,U_12506] :
( ( ! [U_12499] :
( ( hBOOL(hAPP(hAPP(U_12508,U_12499),sK274(U_12512,U_12510,U_12508,U_12506,U_12499)))
& hBOOL(hAPP(hAPP(c_member(U_12506),sK274(U_12512,U_12510,U_12508,U_12506,U_12499)),U_12512)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12506),U_12499),U_12510)) )
& U_12512 != c_Orderings_Obot__class_Obot(tc_fun(U_12506,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_12506),U_12512))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_12506),U_12510)) )
| ~ c_Wellfounded_Omax__extp(U_12506,U_12508,U_12510,U_12512) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK275]),skolemize(U_12501,sK275(U_12513,U_12511,U_12509,U_12507))],[f_3264_4]) ).
cnf(f_3264_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12506),U_12510))
| ~ c_Wellfounded_Omax__extp(U_12506,U_12508,U_12510,U_12512) ),
inference(clausify,[status(thm)],[f_3264_5]) ).
cnf(f_3264_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12506),U_12512))
| ~ c_Wellfounded_Omax__extp(U_12506,U_12508,U_12510,U_12512) ),
inference(clausify,[status(thm)],[f_3264_5]) ).
cnf(f_3264_8,plain,
( U_12512 != c_Orderings_Obot__class_Obot(tc_fun(U_12506,tc_HOL_Obool))
| ~ c_Wellfounded_Omax__extp(U_12506,U_12508,U_12510,U_12512) ),
inference(clausify,[status(thm)],[f_3264_5]) ).
cnf(f_3264_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_12506),sK274(U_12512,U_12510,U_12508,U_12506,U_12499)),U_12512))
| ~ hBOOL(hAPP(hAPP(c_member(U_12506),U_12499),U_12510))
| ~ c_Wellfounded_Omax__extp(U_12506,U_12508,U_12510,U_12512) ),
inference(clausify,[status(thm)],[f_3264_5]) ).
cnf(f_3264_10,plain,
( hBOOL(hAPP(hAPP(U_12508,U_12499),sK274(U_12512,U_12510,U_12508,U_12506,U_12499)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12506),U_12499),U_12510))
| ~ c_Wellfounded_Omax__extp(U_12506,U_12508,U_12510,U_12512) ),
inference(clausify,[status(thm)],[f_3264_5]) ).
cnf(f_3264_11,plain,
( hBOOL(hAPP(hAPP(c_member(U_12507),sK275(U_12513,U_12511,U_12509,U_12507)),U_12511))
| U_12513 = c_Orderings_Obot__class_Obot(tc_fun(U_12507,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12507),U_12513))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12507),U_12511))
| c_Wellfounded_Omax__extp(U_12507,U_12509,U_12511,U_12513) ),
inference(clausify,[status(thm)],[f_3264_5]) ).
cnf(f_3264_12,plain,
( ~ hBOOL(hAPP(hAPP(U_12509,sK275(U_12513,U_12511,U_12509,U_12507)),U_12500))
| ~ hBOOL(hAPP(hAPP(c_member(U_12507),U_12500),U_12513))
| U_12513 = c_Orderings_Obot__class_Obot(tc_fun(U_12507,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12507),U_12513))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12507),U_12511))
| c_Wellfounded_Omax__extp(U_12507,U_12509,U_12511,U_12513) ),
inference(clausify,[status(thm)],[f_3264_5]) ).
fof(f_3265_1,plain,
! [V_R_2,V_Y_2,V_X_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
| ? [B_x] :
( ! [B_xa] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2)) )
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2)) )
| V_Y_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ),
inference(fof_nnf,[status(thm)],[fact_max__ext_Ointros]) ).
fof(f_3265_2,plain,
! [U_12519,U_12518,U_12517,U_12516] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_12516,tc_HOL_Obool),tc_fun(U_12516,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_12516,tc_HOL_Obool),tc_fun(U_12516,tc_HOL_Obool)),U_12517),U_12518)),c_Wellfounded_Omax__ext(U_12516,U_12519)))
| ? [U_12515] :
( ! [U_12514] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12516,U_12516)),hAPP(hAPP(c_Product__Type_OPair(U_12516,U_12516),U_12515),U_12514)),U_12519))
| ~ hBOOL(hAPP(hAPP(c_member(U_12516),U_12514),U_12518)) )
& hBOOL(hAPP(hAPP(c_member(U_12516),U_12515),U_12517)) )
| U_12518 = c_Orderings_Obot__class_Obot(tc_fun(U_12516,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12516),U_12518))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12516),U_12517)) ),
inference(variable_rename,[status(thm)],[f_3265_1]) ).
fof(f_3265_3,plain,
! [U_12519,U_12518,U_12517,U_12516] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_12516,tc_HOL_Obool),tc_fun(U_12516,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_12516,tc_HOL_Obool),tc_fun(U_12516,tc_HOL_Obool)),U_12517),U_12518)),c_Wellfounded_Omax__ext(U_12516,U_12519)))
| ( ! [U_12514] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12516,U_12516)),hAPP(hAPP(c_Product__Type_OPair(U_12516,U_12516),sK276(U_12519,U_12518,U_12517,U_12516)),U_12514)),U_12519))
| ~ hBOOL(hAPP(hAPP(c_member(U_12516),U_12514),U_12518)) )
& hBOOL(hAPP(hAPP(c_member(U_12516),sK276(U_12519,U_12518,U_12517,U_12516)),U_12517)) )
| U_12518 = c_Orderings_Obot__class_Obot(tc_fun(U_12516,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12516),U_12518))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12516),U_12517)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK276]),skolemize(U_12515,sK276(U_12519,U_12518,U_12517,U_12516))],[f_3265_2]) ).
cnf(f_3265_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12516),sK276(U_12519,U_12518,U_12517,U_12516)),U_12517))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_12516,tc_HOL_Obool),tc_fun(U_12516,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_12516,tc_HOL_Obool),tc_fun(U_12516,tc_HOL_Obool)),U_12517),U_12518)),c_Wellfounded_Omax__ext(U_12516,U_12519)))
| U_12518 = c_Orderings_Obot__class_Obot(tc_fun(U_12516,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12516),U_12518))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12516),U_12517)) ),
inference(clausify,[status(thm)],[f_3265_3]) ).
cnf(f_3265_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12516,U_12516)),hAPP(hAPP(c_Product__Type_OPair(U_12516,U_12516),sK276(U_12519,U_12518,U_12517,U_12516)),U_12514)),U_12519))
| ~ hBOOL(hAPP(hAPP(c_member(U_12516),U_12514),U_12518))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_12516,tc_HOL_Obool),tc_fun(U_12516,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_12516,tc_HOL_Obool),tc_fun(U_12516,tc_HOL_Obool)),U_12517),U_12518)),c_Wellfounded_Omax__ext(U_12516,U_12519)))
| U_12518 = c_Orderings_Obot__class_Obot(tc_fun(U_12516,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12516),U_12518))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12516),U_12517)) ),
inference(clausify,[status(thm)],[f_3265_3]) ).
fof(f_3266_1,plain,
! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2)),V_a3_2))
| ! [B_a,B_A] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
| hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) != hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) ) )
& ( ? [B_a,B_A] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
& hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2)),V_a3_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_fold1Set_Oequations]) ).
fof(f_3266_2,plain,
! [U_12528,U_12527,U_12526,U_12525,U_12524] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12524,U_12525,hAPP(hAPP(c_Set_Oinsert(U_12524),U_12526),U_12527)),U_12528))
| ! [U_12523,U_12522] :
( hBOOL(hAPP(hAPP(c_member(U_12524),U_12523),U_12522))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12524,U_12524,U_12525,U_12523,U_12522),U_12528))
| hAPP(hAPP(c_Set_Oinsert(U_12524),U_12526),U_12527) != hAPP(hAPP(c_Set_Oinsert(U_12524),U_12523),U_12522) ) )
& ( ? [U_12521,U_12520] :
( ~ hBOOL(hAPP(hAPP(c_member(U_12524),U_12521),U_12520))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12524,U_12524,U_12525,U_12521,U_12520),U_12528))
& hAPP(hAPP(c_Set_Oinsert(U_12524),U_12526),U_12527) = hAPP(hAPP(c_Set_Oinsert(U_12524),U_12521),U_12520) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12524,U_12525,hAPP(hAPP(c_Set_Oinsert(U_12524),U_12526),U_12527)),U_12528)) ) ),
inference(variable_rename,[status(thm)],[f_3266_1]) ).
fof(f_3266_3,plain,
( ! [U_12538,U_12536,U_12534,U_12532,U_12530] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12530,U_12532,hAPP(hAPP(c_Set_Oinsert(U_12530),U_12534),U_12536)),U_12538))
| ! [U_12523,U_12522] :
( hBOOL(hAPP(hAPP(c_member(U_12530),U_12523),U_12522))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12530,U_12530,U_12532,U_12523,U_12522),U_12538))
| hAPP(hAPP(c_Set_Oinsert(U_12530),U_12534),U_12536) != hAPP(hAPP(c_Set_Oinsert(U_12530),U_12523),U_12522) ) )
& ! [U_12537,U_12535,U_12533,U_12531,U_12529] :
( ? [U_12521,U_12520] :
( ~ hBOOL(hAPP(hAPP(c_member(U_12529),U_12521),U_12520))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12529,U_12529,U_12531,U_12521,U_12520),U_12537))
& hAPP(hAPP(c_Set_Oinsert(U_12529),U_12533),U_12535) = hAPP(hAPP(c_Set_Oinsert(U_12529),U_12521),U_12520) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12529,U_12531,hAPP(hAPP(c_Set_Oinsert(U_12529),U_12533),U_12535)),U_12537)) ) ),
inference(miniscope,[status(thm)],[f_3266_2]) ).
fof(f_3266_4,plain,
( ! [U_12538,U_12536,U_12534,U_12532,U_12530] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12530,U_12532,hAPP(hAPP(c_Set_Oinsert(U_12530),U_12534),U_12536)),U_12538))
| ! [U_12523,U_12522] :
( hBOOL(hAPP(hAPP(c_member(U_12530),U_12523),U_12522))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12530,U_12530,U_12532,U_12523,U_12522),U_12538))
| hAPP(hAPP(c_Set_Oinsert(U_12530),U_12534),U_12536) != hAPP(hAPP(c_Set_Oinsert(U_12530),U_12523),U_12522) ) )
& ! [U_12537,U_12535,U_12533,U_12531,U_12529] :
( ? [U_12520] :
( ~ hBOOL(hAPP(hAPP(c_member(U_12529),sK277(U_12537,U_12535,U_12533,U_12531,U_12529)),U_12520))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12529,U_12529,U_12531,sK277(U_12537,U_12535,U_12533,U_12531,U_12529),U_12520),U_12537))
& hAPP(hAPP(c_Set_Oinsert(U_12529),U_12533),U_12535) = hAPP(hAPP(c_Set_Oinsert(U_12529),sK277(U_12537,U_12535,U_12533,U_12531,U_12529)),U_12520) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12529,U_12531,hAPP(hAPP(c_Set_Oinsert(U_12529),U_12533),U_12535)),U_12537)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK277]),skolemize(U_12521,sK277(U_12537,U_12535,U_12533,U_12531,U_12529))],[f_3266_3]) ).
fof(f_3266_5,plain,
( ! [U_12538,U_12536,U_12534,U_12532,U_12530] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12530,U_12532,hAPP(hAPP(c_Set_Oinsert(U_12530),U_12534),U_12536)),U_12538))
| ! [U_12523,U_12522] :
( hBOOL(hAPP(hAPP(c_member(U_12530),U_12523),U_12522))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12530,U_12530,U_12532,U_12523,U_12522),U_12538))
| hAPP(hAPP(c_Set_Oinsert(U_12530),U_12534),U_12536) != hAPP(hAPP(c_Set_Oinsert(U_12530),U_12523),U_12522) ) )
& ! [U_12537,U_12535,U_12533,U_12531,U_12529] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_12529),sK277(U_12537,U_12535,U_12533,U_12531,U_12529)),sK278(U_12537,U_12535,U_12533,U_12531,U_12529)))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12529,U_12529,U_12531,sK277(U_12537,U_12535,U_12533,U_12531,U_12529),sK278(U_12537,U_12535,U_12533,U_12531,U_12529)),U_12537))
& hAPP(hAPP(c_Set_Oinsert(U_12529),U_12533),U_12535) = hAPP(hAPP(c_Set_Oinsert(U_12529),sK277(U_12537,U_12535,U_12533,U_12531,U_12529)),sK278(U_12537,U_12535,U_12533,U_12531,U_12529)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12529,U_12531,hAPP(hAPP(c_Set_Oinsert(U_12529),U_12533),U_12535)),U_12537)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK278]),skolemize(U_12520,sK278(U_12537,U_12535,U_12533,U_12531,U_12529))],[f_3266_4]) ).
cnf(f_3266_6,plain,
( hAPP(hAPP(c_Set_Oinsert(U_12529),U_12533),U_12535) = hAPP(hAPP(c_Set_Oinsert(U_12529),sK277(U_12537,U_12535,U_12533,U_12531,U_12529)),sK278(U_12537,U_12535,U_12533,U_12531,U_12529))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12529,U_12531,hAPP(hAPP(c_Set_Oinsert(U_12529),U_12533),U_12535)),U_12537)) ),
inference(clausify,[status(thm)],[f_3266_5]) ).
cnf(f_3266_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12529,U_12529,U_12531,sK277(U_12537,U_12535,U_12533,U_12531,U_12529),sK278(U_12537,U_12535,U_12533,U_12531,U_12529)),U_12537))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12529,U_12531,hAPP(hAPP(c_Set_Oinsert(U_12529),U_12533),U_12535)),U_12537)) ),
inference(clausify,[status(thm)],[f_3266_5]) ).
cnf(f_3266_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_12529),sK277(U_12537,U_12535,U_12533,U_12531,U_12529)),sK278(U_12537,U_12535,U_12533,U_12531,U_12529)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12529,U_12531,hAPP(hAPP(c_Set_Oinsert(U_12529),U_12533),U_12535)),U_12537)) ),
inference(clausify,[status(thm)],[f_3266_5]) ).
cnf(f_3266_9,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12530,U_12532,hAPP(hAPP(c_Set_Oinsert(U_12530),U_12534),U_12536)),U_12538))
| hBOOL(hAPP(hAPP(c_member(U_12530),U_12523),U_12522))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12530,U_12530,U_12532,U_12523,U_12522),U_12538))
| hAPP(hAPP(c_Set_Oinsert(U_12530),U_12534),U_12536) != hAPP(hAPP(c_Set_Oinsert(U_12530),U_12523),U_12522) ),
inference(clausify,[status(thm)],[f_3266_5]) ).
fof(f_3267_1,plain,
! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
( ? [B_a,B_A] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
& hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2)),V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__fold1SetE]) ).
fof(f_3267_2,plain,
! [U_12545,U_12544,U_12543,U_12542,U_12541] :
( ? [U_12540,U_12539] :
( ~ hBOOL(hAPP(hAPP(c_member(U_12541),U_12540),U_12539))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12541,U_12541,U_12542,U_12540,U_12539),U_12545))
& hAPP(hAPP(c_Set_Oinsert(U_12541),U_12543),U_12544) = hAPP(hAPP(c_Set_Oinsert(U_12541),U_12540),U_12539) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12541,U_12542,hAPP(hAPP(c_Set_Oinsert(U_12541),U_12543),U_12544)),U_12545)) ),
inference(variable_rename,[status(thm)],[f_3267_1]) ).
fof(f_3267_3,plain,
! [U_12545,U_12544,U_12543,U_12542,U_12541] :
( ? [U_12539] :
( ~ hBOOL(hAPP(hAPP(c_member(U_12541),sK279(U_12545,U_12544,U_12543,U_12542,U_12541)),U_12539))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12541,U_12541,U_12542,sK279(U_12545,U_12544,U_12543,U_12542,U_12541),U_12539),U_12545))
& hAPP(hAPP(c_Set_Oinsert(U_12541),U_12543),U_12544) = hAPP(hAPP(c_Set_Oinsert(U_12541),sK279(U_12545,U_12544,U_12543,U_12542,U_12541)),U_12539) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12541,U_12542,hAPP(hAPP(c_Set_Oinsert(U_12541),U_12543),U_12544)),U_12545)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK279]),skolemize(U_12540,sK279(U_12545,U_12544,U_12543,U_12542,U_12541))],[f_3267_2]) ).
fof(f_3267_4,plain,
! [U_12545,U_12544,U_12543,U_12542,U_12541] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_12541),sK279(U_12545,U_12544,U_12543,U_12542,U_12541)),sK280(U_12545,U_12544,U_12543,U_12542,U_12541)))
& hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12541,U_12541,U_12542,sK279(U_12545,U_12544,U_12543,U_12542,U_12541),sK280(U_12545,U_12544,U_12543,U_12542,U_12541)),U_12545))
& hAPP(hAPP(c_Set_Oinsert(U_12541),U_12543),U_12544) = hAPP(hAPP(c_Set_Oinsert(U_12541),sK279(U_12545,U_12544,U_12543,U_12542,U_12541)),sK280(U_12545,U_12544,U_12543,U_12542,U_12541)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12541,U_12542,hAPP(hAPP(c_Set_Oinsert(U_12541),U_12543),U_12544)),U_12545)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK280]),skolemize(U_12539,sK280(U_12545,U_12544,U_12543,U_12542,U_12541))],[f_3267_3]) ).
cnf(f_3267_5,plain,
( hAPP(hAPP(c_Set_Oinsert(U_12541),U_12543),U_12544) = hAPP(hAPP(c_Set_Oinsert(U_12541),sK279(U_12545,U_12544,U_12543,U_12542,U_12541)),sK280(U_12545,U_12544,U_12543,U_12542,U_12541))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12541,U_12542,hAPP(hAPP(c_Set_Oinsert(U_12541),U_12543),U_12544)),U_12545)) ),
inference(clausify,[status(thm)],[f_3267_4]) ).
cnf(f_3267_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_12541,U_12541,U_12542,sK279(U_12545,U_12544,U_12543,U_12542,U_12541),sK280(U_12545,U_12544,U_12543,U_12542,U_12541)),U_12545))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12541,U_12542,hAPP(hAPP(c_Set_Oinsert(U_12541),U_12543),U_12544)),U_12545)) ),
inference(clausify,[status(thm)],[f_3267_4]) ).
cnf(f_3267_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_12541),sK279(U_12545,U_12544,U_12543,U_12542,U_12541)),sK280(U_12545,U_12544,U_12543,U_12542,U_12541)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_12541,U_12542,hAPP(hAPP(c_Set_Oinsert(U_12541),U_12543),U_12544)),U_12545)) ),
inference(clausify,[status(thm)],[f_3267_4]) ).
fof(f_3268_1,plain,
! [V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Set_Oimage(T_d,tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_Oimage(T_d,T_c,V_g_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_b),c_Set_Ovimage(T_d,T_b,V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_A_2))),
inference(fof_nnf,[status(thm)],[fact_image__split__eq__Sigma]) ).
fof(f_3268_2,plain,
! [U_12551,U_12550,U_12549,U_12548,U_12547,U_12546] : hAPP(c_Set_Oimage(U_12546,tc_prod(U_12547,U_12548),hAPP(hAPP(c_COMBS(U_12546,U_12548,tc_prod(U_12547,U_12548)),hAPP(hAPP(c_COMBB(U_12547,tc_fun(U_12548,tc_prod(U_12547,U_12548)),U_12546),c_Product__Type_OPair(U_12547,U_12548)),U_12549)),U_12550)),U_12551) = hAPP(hAPP(c_Product__Type_OSigma(U_12547,U_12548),hAPP(c_Set_Oimage(U_12546,U_12547,U_12549),U_12551)),hAPP(hAPP(c_COMBB(tc_fun(U_12546,tc_HOL_Obool),tc_fun(U_12548,tc_HOL_Obool),U_12547),c_Set_Oimage(U_12546,U_12548,U_12550)),hAPP(hAPP(c_COMBC(U_12547,tc_fun(U_12546,tc_HOL_Obool),tc_fun(U_12546,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12546,tc_HOL_Obool),tc_fun(tc_fun(U_12546,tc_HOL_Obool),tc_fun(U_12546,tc_HOL_Obool)),U_12547),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12546,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12547,tc_HOL_Obool),tc_fun(U_12546,tc_HOL_Obool),U_12547),c_Set_Ovimage(U_12546,U_12547,U_12549)),hAPP(hAPP(c_COMBC(U_12547,tc_fun(U_12547,tc_HOL_Obool),tc_fun(U_12547,tc_HOL_Obool)),c_Set_Oinsert(U_12547)),c_Orderings_Obot__class_Obot(tc_fun(U_12547,tc_HOL_Obool)))))),U_12551))),
inference(variable_rename,[status(thm)],[f_3268_1]) ).
cnf(f_3268_3,plain,
hAPP(c_Set_Oimage(U_12546,tc_prod(U_12547,U_12548),hAPP(hAPP(c_COMBS(U_12546,U_12548,tc_prod(U_12547,U_12548)),hAPP(hAPP(c_COMBB(U_12547,tc_fun(U_12548,tc_prod(U_12547,U_12548)),U_12546),c_Product__Type_OPair(U_12547,U_12548)),U_12549)),U_12550)),U_12551) = hAPP(hAPP(c_Product__Type_OSigma(U_12547,U_12548),hAPP(c_Set_Oimage(U_12546,U_12547,U_12549),U_12551)),hAPP(hAPP(c_COMBB(tc_fun(U_12546,tc_HOL_Obool),tc_fun(U_12548,tc_HOL_Obool),U_12547),c_Set_Oimage(U_12546,U_12548,U_12550)),hAPP(hAPP(c_COMBC(U_12547,tc_fun(U_12546,tc_HOL_Obool),tc_fun(U_12546,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12546,tc_HOL_Obool),tc_fun(tc_fun(U_12546,tc_HOL_Obool),tc_fun(U_12546,tc_HOL_Obool)),U_12547),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12546,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12547,tc_HOL_Obool),tc_fun(U_12546,tc_HOL_Obool),U_12547),c_Set_Ovimage(U_12546,U_12547,U_12549)),hAPP(hAPP(c_COMBC(U_12547,tc_fun(U_12547,tc_HOL_Obool),tc_fun(U_12547,tc_HOL_Obool)),c_Set_Oinsert(U_12547)),c_Orderings_Obot__class_Obot(tc_fun(U_12547,tc_HOL_Obool)))))),U_12551))),
inference(clausify,[status(thm)],[f_3268_2]) ).
fof(f_3269_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Oab__semigroup__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__Un]) ).
fof(f_3269_2,plain,
! [U_12554,U_12553,U_12552] :
( hAPP(c_Finite__Set_Ofold1(U_12552,c_Groups_Otimes__class_Otimes(U_12552)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12552,tc_HOL_Obool)),U_12553),U_12554)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12552),hAPP(c_Finite__Set_Ofold1(U_12552,c_Groups_Otimes__class_Otimes(U_12552)),U_12553)),hAPP(c_Finite__Set_Ofold1(U_12552,c_Groups_Otimes__class_Otimes(U_12552)),U_12554))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12552,tc_HOL_Obool)),U_12553),U_12554) != c_Orderings_Obot__class_Obot(tc_fun(U_12552,tc_HOL_Obool))
| U_12554 = c_Orderings_Obot__class_Obot(tc_fun(U_12552,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12552),U_12554))
| U_12553 = c_Orderings_Obot__class_Obot(tc_fun(U_12552,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12552),U_12553))
| ~ class_Groups_Oab__semigroup__mult(U_12552) ),
inference(variable_rename,[status(thm)],[f_3269_1]) ).
cnf(f_3269_3,plain,
( hAPP(c_Finite__Set_Ofold1(U_12552,c_Groups_Otimes__class_Otimes(U_12552)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12552,tc_HOL_Obool)),U_12553),U_12554)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12552),hAPP(c_Finite__Set_Ofold1(U_12552,c_Groups_Otimes__class_Otimes(U_12552)),U_12553)),hAPP(c_Finite__Set_Ofold1(U_12552,c_Groups_Otimes__class_Otimes(U_12552)),U_12554))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12552,tc_HOL_Obool)),U_12553),U_12554) != c_Orderings_Obot__class_Obot(tc_fun(U_12552,tc_HOL_Obool))
| U_12554 = c_Orderings_Obot__class_Obot(tc_fun(U_12552,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12552),U_12554))
| U_12553 = c_Orderings_Obot__class_Obot(tc_fun(U_12552,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12552),U_12553))
| ~ class_Groups_Oab__semigroup__mult(U_12552) ),
inference(clausify,[status(thm)],[f_3269_2]) ).
fof(f_3270_1,plain,
! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_SigmaI]) ).
fof(f_3270_2,plain,
! [U_12560,U_12559,U_12558,U_12557,U_12556,U_12555] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12555,U_12558)),hAPP(hAPP(c_Product__Type_OPair(U_12555,U_12558),U_12556),U_12559)),hAPP(hAPP(c_Product__Type_OSigma(U_12555,U_12558),U_12557),U_12560)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12558),U_12559),hAPP(U_12560,U_12556)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12555),U_12556),U_12557)) ),
inference(variable_rename,[status(thm)],[f_3270_1]) ).
cnf(f_3270_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12555,U_12558)),hAPP(hAPP(c_Product__Type_OPair(U_12555,U_12558),U_12556),U_12559)),hAPP(hAPP(c_Product__Type_OSigma(U_12555,U_12558),U_12557),U_12560)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12558),U_12559),hAPP(U_12560,U_12556)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12555),U_12556),U_12557)) ),
inference(clausify,[status(thm)],[f_3270_2]) ).
fof(f_3271_1,plain,
! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
( ( ( hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))
| V_A_2 != V_B_2 )
& ( V_A_2 = V_B_2
| hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) != hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Times__eq__cancel2]) ).
fof(f_3271_2,plain,
! [U_12566,U_12565,U_12564,U_12563,U_12562,U_12561] :
( ( ( hAPP(hAPP(c_Product__Type_OSigma(U_12564,U_12561),U_12565),hAPP(c_COMBK(tc_fun(U_12561,tc_HOL_Obool),U_12564),U_12563)) = hAPP(hAPP(c_Product__Type_OSigma(U_12564,U_12561),U_12566),hAPP(c_COMBK(tc_fun(U_12561,tc_HOL_Obool),U_12564),U_12563))
| U_12565 != U_12566 )
& ( U_12565 = U_12566
| hAPP(hAPP(c_Product__Type_OSigma(U_12564,U_12561),U_12565),hAPP(c_COMBK(tc_fun(U_12561,tc_HOL_Obool),U_12564),U_12563)) != hAPP(hAPP(c_Product__Type_OSigma(U_12564,U_12561),U_12566),hAPP(c_COMBK(tc_fun(U_12561,tc_HOL_Obool),U_12564),U_12563)) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12561),U_12562),U_12563)) ),
inference(variable_rename,[status(thm)],[f_3271_1]) ).
cnf(f_3271_3,plain,
( U_12565 = U_12566
| hAPP(hAPP(c_Product__Type_OSigma(U_12564,U_12561),U_12565),hAPP(c_COMBK(tc_fun(U_12561,tc_HOL_Obool),U_12564),U_12563)) != hAPP(hAPP(c_Product__Type_OSigma(U_12564,U_12561),U_12566),hAPP(c_COMBK(tc_fun(U_12561,tc_HOL_Obool),U_12564),U_12563))
| ~ hBOOL(hAPP(hAPP(c_member(U_12561),U_12562),U_12563)) ),
inference(clausify,[status(thm)],[f_3271_2]) ).
cnf(f_3271_4,plain,
( hAPP(hAPP(c_Product__Type_OSigma(U_12564,U_12561),U_12565),hAPP(c_COMBK(tc_fun(U_12561,tc_HOL_Obool),U_12564),U_12563)) = hAPP(hAPP(c_Product__Type_OSigma(U_12564,U_12561),U_12566),hAPP(c_COMBK(tc_fun(U_12561,tc_HOL_Obool),U_12564),U_12563))
| U_12565 != U_12566
| ~ hBOOL(hAPP(hAPP(c_member(U_12561),U_12562),U_12563)) ),
inference(clausify,[status(thm)],[f_3271_2]) ).
fof(f_3272_1,plain,
! [V_B_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Sigma__empty1]) ).
fof(f_3272_2,plain,
! [U_12569,U_12568,U_12567] : hAPP(hAPP(c_Product__Type_OSigma(U_12567,U_12568),c_Orderings_Obot__class_Obot(tc_fun(U_12567,tc_HOL_Obool))),U_12569) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12567,U_12568),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3272_1]) ).
cnf(f_3272_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12567,U_12568),c_Orderings_Obot__class_Obot(tc_fun(U_12567,tc_HOL_Obool))),U_12569) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12567,U_12568),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3272_2]) ).
fof(f_3273_1,plain,
! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Sigma__Diff__distrib1]) ).
fof(f_3273_2,plain,
! [U_12574,U_12573,U_12572,U_12571,U_12570] : hAPP(hAPP(c_Product__Type_OSigma(U_12570,U_12571),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12570,tc_HOL_Obool)),U_12572),U_12573)),U_12574) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12570,U_12571),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12570,U_12571),U_12572),U_12574)),hAPP(hAPP(c_Product__Type_OSigma(U_12570,U_12571),U_12573),U_12574)),
inference(variable_rename,[status(thm)],[f_3273_1]) ).
cnf(f_3273_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12570,U_12571),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12570,tc_HOL_Obool)),U_12572),U_12573)),U_12574) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12570,U_12571),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12570,U_12571),U_12572),U_12574)),hAPP(hAPP(c_Product__Type_OSigma(U_12570,U_12571),U_12573),U_12574)),
inference(clausify,[status(thm)],[f_3273_2]) ).
fof(f_3274_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
inference(fof_nnf,[status(thm)],[fact_Times__Diff__distrib1]) ).
fof(f_3274_2,plain,
! [U_12579,U_12578,U_12577,U_12576,U_12575] : hAPP(hAPP(c_Product__Type_OSigma(U_12575,U_12576),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12575,tc_HOL_Obool)),U_12577),U_12578)),hAPP(c_COMBK(tc_fun(U_12576,tc_HOL_Obool),U_12575),U_12579)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12575,U_12576),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12575,U_12576),U_12577),hAPP(c_COMBK(tc_fun(U_12576,tc_HOL_Obool),U_12575),U_12579))),hAPP(hAPP(c_Product__Type_OSigma(U_12575,U_12576),U_12578),hAPP(c_COMBK(tc_fun(U_12576,tc_HOL_Obool),U_12575),U_12579))),
inference(variable_rename,[status(thm)],[f_3274_1]) ).
cnf(f_3274_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12575,U_12576),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12575,tc_HOL_Obool)),U_12577),U_12578)),hAPP(c_COMBK(tc_fun(U_12576,tc_HOL_Obool),U_12575),U_12579)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12575,U_12576),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12575,U_12576),U_12577),hAPP(c_COMBK(tc_fun(U_12576,tc_HOL_Obool),U_12575),U_12579))),hAPP(hAPP(c_Product__Type_OSigma(U_12575,U_12576),U_12578),hAPP(c_COMBK(tc_fun(U_12576,tc_HOL_Obool),U_12575),U_12579))),
inference(clausify,[status(thm)],[f_3274_2]) ).
fof(f_3275_1,plain,
! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Sigma__Diff__distrib2]) ).
fof(f_3275_2,plain,
! [U_12584,U_12583,U_12582,U_12581,U_12580] : hAPP(hAPP(c_Product__Type_OSigma(U_12580,U_12581),U_12582),hAPP(hAPP(c_COMBS(U_12580,tc_fun(U_12581,tc_HOL_Obool),tc_fun(U_12581,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12581,tc_HOL_Obool),tc_fun(tc_fun(U_12581,tc_HOL_Obool),tc_fun(U_12581,tc_HOL_Obool)),U_12580),c_Groups_Ominus__class_Ominus(tc_fun(U_12581,tc_HOL_Obool))),U_12583)),U_12584)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12580,U_12581),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12580,U_12581),U_12582),U_12583)),hAPP(hAPP(c_Product__Type_OSigma(U_12580,U_12581),U_12582),U_12584)),
inference(variable_rename,[status(thm)],[f_3275_1]) ).
cnf(f_3275_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12580,U_12581),U_12582),hAPP(hAPP(c_COMBS(U_12580,tc_fun(U_12581,tc_HOL_Obool),tc_fun(U_12581,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12581,tc_HOL_Obool),tc_fun(tc_fun(U_12581,tc_HOL_Obool),tc_fun(U_12581,tc_HOL_Obool)),U_12580),c_Groups_Ominus__class_Ominus(tc_fun(U_12581,tc_HOL_Obool))),U_12583)),U_12584)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_12580,U_12581),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12580,U_12581),U_12582),U_12583)),hAPP(hAPP(c_Product__Type_OSigma(U_12580,U_12581),U_12582),U_12584)),
inference(clausify,[status(thm)],[f_3275_2]) ).
fof(f_3276_1,plain,
! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_card__cartesian__product]) ).
fof(f_3276_2,plain,
! [U_12588,U_12587,U_12586,U_12585] : hAPP(c_Finite__Set_Ocard(tc_prod(U_12585,U_12586)),hAPP(hAPP(c_Product__Type_OSigma(U_12585,U_12586),U_12587),hAPP(c_COMBK(tc_fun(U_12586,tc_HOL_Obool),U_12585),U_12588))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_12585),U_12587)),hAPP(c_Finite__Set_Ocard(U_12586),U_12588)),
inference(variable_rename,[status(thm)],[f_3276_1]) ).
cnf(f_3276_3,plain,
hAPP(c_Finite__Set_Ocard(tc_prod(U_12585,U_12586)),hAPP(hAPP(c_Product__Type_OSigma(U_12585,U_12586),U_12587),hAPP(c_COMBK(tc_fun(U_12586,tc_HOL_Obool),U_12585),U_12588))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_12585),U_12587)),hAPP(c_Finite__Set_Ocard(U_12586),U_12588)),
inference(clausify,[status(thm)],[f_3276_2]) ).
fof(f_3277_1,plain,
! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2)))
| ~ class_Groups_Ocomm__monoid__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setsum__cartesian__product]) ).
fof(f_3277_2,plain,
! [U_12594,U_12593,U_12592,U_12591,U_12590,U_12589] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12590,U_12589),hAPP(hAPP(c_COMBC(U_12590,tc_fun(U_12591,tc_HOL_Obool),U_12589),hAPP(hAPP(c_COMBB(tc_fun(U_12591,U_12589),tc_fun(tc_fun(U_12591,tc_HOL_Obool),U_12589),U_12590),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12591,U_12589)),U_12592)),U_12593)),U_12594) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12590,U_12591),U_12589),hAPP(c_Product__Type_Oprod_Oprod__case(U_12590,U_12591,U_12589),U_12592)),hAPP(hAPP(c_Product__Type_OSigma(U_12590,U_12591),U_12594),hAPP(c_COMBK(tc_fun(U_12591,tc_HOL_Obool),U_12590),U_12593)))
| ~ class_Groups_Ocomm__monoid__add(U_12589) ),
inference(variable_rename,[status(thm)],[f_3277_1]) ).
cnf(f_3277_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12590,U_12589),hAPP(hAPP(c_COMBC(U_12590,tc_fun(U_12591,tc_HOL_Obool),U_12589),hAPP(hAPP(c_COMBB(tc_fun(U_12591,U_12589),tc_fun(tc_fun(U_12591,tc_HOL_Obool),U_12589),U_12590),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12591,U_12589)),U_12592)),U_12593)),U_12594) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12590,U_12591),U_12589),hAPP(c_Product__Type_Oprod_Oprod__case(U_12590,U_12591,U_12589),U_12592)),hAPP(hAPP(c_Product__Type_OSigma(U_12590,U_12591),U_12594),hAPP(c_COMBK(tc_fun(U_12591,tc_HOL_Obool),U_12590),U_12593)))
| ~ class_Groups_Ocomm__monoid__add(U_12589) ),
inference(clausify,[status(thm)],[f_3277_2]) ).
fof(f_3278_1,plain,
! [V_B_2,V_A_2,T_c,T_b] :
( ( hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))
| ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
& V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) )
& ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_Times__empty]) ).
fof(f_3278_2,plain,
! [U_12598,U_12597,U_12596,U_12595] :
( ( hAPP(hAPP(c_Product__Type_OSigma(U_12595,U_12596),U_12597),hAPP(c_COMBK(tc_fun(U_12596,tc_HOL_Obool),U_12595),U_12598)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12595,U_12596),tc_HOL_Obool))
| ( U_12598 != c_Orderings_Obot__class_Obot(tc_fun(U_12596,tc_HOL_Obool))
& U_12597 != c_Orderings_Obot__class_Obot(tc_fun(U_12595,tc_HOL_Obool)) ) )
& ( U_12598 = c_Orderings_Obot__class_Obot(tc_fun(U_12596,tc_HOL_Obool))
| U_12597 = c_Orderings_Obot__class_Obot(tc_fun(U_12595,tc_HOL_Obool))
| hAPP(hAPP(c_Product__Type_OSigma(U_12595,U_12596),U_12597),hAPP(c_COMBK(tc_fun(U_12596,tc_HOL_Obool),U_12595),U_12598)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12595,U_12596),tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3278_1]) ).
fof(f_3278_3,plain,
( ! [U_12606,U_12604,U_12602,U_12600] :
( hAPP(hAPP(c_Product__Type_OSigma(U_12600,U_12602),U_12604),hAPP(c_COMBK(tc_fun(U_12602,tc_HOL_Obool),U_12600),U_12606)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12600,U_12602),tc_HOL_Obool))
| ( U_12606 != c_Orderings_Obot__class_Obot(tc_fun(U_12602,tc_HOL_Obool))
& U_12604 != c_Orderings_Obot__class_Obot(tc_fun(U_12600,tc_HOL_Obool)) ) )
& ! [U_12605,U_12603,U_12601,U_12599] :
( U_12605 = c_Orderings_Obot__class_Obot(tc_fun(U_12601,tc_HOL_Obool))
| U_12603 = c_Orderings_Obot__class_Obot(tc_fun(U_12599,tc_HOL_Obool))
| hAPP(hAPP(c_Product__Type_OSigma(U_12599,U_12601),U_12603),hAPP(c_COMBK(tc_fun(U_12601,tc_HOL_Obool),U_12599),U_12605)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12599,U_12601),tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_3278_2]) ).
cnf(f_3278_4,plain,
( U_12605 = c_Orderings_Obot__class_Obot(tc_fun(U_12601,tc_HOL_Obool))
| U_12603 = c_Orderings_Obot__class_Obot(tc_fun(U_12599,tc_HOL_Obool))
| hAPP(hAPP(c_Product__Type_OSigma(U_12599,U_12601),U_12603),hAPP(c_COMBK(tc_fun(U_12601,tc_HOL_Obool),U_12599),U_12605)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12599,U_12601),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3278_3]) ).
cnf(f_3278_5,plain,
( U_12604 != c_Orderings_Obot__class_Obot(tc_fun(U_12600,tc_HOL_Obool))
| hAPP(hAPP(c_Product__Type_OSigma(U_12600,U_12602),U_12604),hAPP(c_COMBK(tc_fun(U_12602,tc_HOL_Obool),U_12600),U_12606)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12600,U_12602),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3278_3]) ).
cnf(f_3278_6,plain,
( U_12606 != c_Orderings_Obot__class_Obot(tc_fun(U_12602,tc_HOL_Obool))
| hAPP(hAPP(c_Product__Type_OSigma(U_12600,U_12602),U_12604),hAPP(c_COMBK(tc_fun(U_12602,tc_HOL_Obool),U_12600),U_12606)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12600,U_12602),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3278_3]) ).
fof(f_3279_1,plain,
! [V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Sigma__empty2]) ).
fof(f_3279_2,plain,
! [U_12609,U_12608,U_12607] : hAPP(hAPP(c_Product__Type_OSigma(U_12607,U_12608),U_12609),hAPP(c_COMBK(tc_fun(U_12608,tc_HOL_Obool),U_12607),c_Orderings_Obot__class_Obot(tc_fun(U_12608,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12607,U_12608),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3279_1]) ).
cnf(f_3279_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12607,U_12608),U_12609),hAPP(c_COMBK(tc_fun(U_12608,tc_HOL_Obool),U_12607),c_Orderings_Obot__class_Obot(tc_fun(U_12608,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12607,U_12608),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3279_2]) ).
fof(f_3280_1,plain,
! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))),
inference(fof_nnf,[status(thm)],[fact_Compl__Times__UNIV1]) ).
fof(f_3280_2,plain,
! [U_12612,U_12611,U_12610] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_12610,U_12611),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12610,U_12611),c_Orderings_Otop__class_Otop(tc_fun(U_12610,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12611,tc_HOL_Obool),U_12610),U_12612))) = hAPP(hAPP(c_Product__Type_OSigma(U_12610,U_12611),c_Orderings_Otop__class_Otop(tc_fun(U_12610,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12611,tc_HOL_Obool),U_12610),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12611,tc_HOL_Obool)),U_12612))),
inference(variable_rename,[status(thm)],[f_3280_1]) ).
cnf(f_3280_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_12610,U_12611),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12610,U_12611),c_Orderings_Otop__class_Otop(tc_fun(U_12610,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12611,tc_HOL_Obool),U_12610),U_12612))) = hAPP(hAPP(c_Product__Type_OSigma(U_12610,U_12611),c_Orderings_Otop__class_Otop(tc_fun(U_12610,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12611,tc_HOL_Obool),U_12610),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12611,tc_HOL_Obool)),U_12612))),
inference(clausify,[status(thm)],[f_3280_2]) ).
fof(f_3281_1,plain,
! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))),
inference(fof_nnf,[status(thm)],[fact_Compl__Times__UNIV2]) ).
fof(f_3281_2,plain,
! [U_12615,U_12614,U_12613] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_12613,U_12614),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12613,U_12614),U_12615),hAPP(c_COMBK(tc_fun(U_12614,tc_HOL_Obool),U_12613),c_Orderings_Otop__class_Otop(tc_fun(U_12614,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(U_12613,U_12614),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12613,tc_HOL_Obool)),U_12615)),hAPP(c_COMBK(tc_fun(U_12614,tc_HOL_Obool),U_12613),c_Orderings_Otop__class_Otop(tc_fun(U_12614,tc_HOL_Obool)))),
inference(variable_rename,[status(thm)],[f_3281_1]) ).
cnf(f_3281_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_12613,U_12614),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12613,U_12614),U_12615),hAPP(c_COMBK(tc_fun(U_12614,tc_HOL_Obool),U_12613),c_Orderings_Otop__class_Otop(tc_fun(U_12614,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(U_12613,U_12614),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12613,tc_HOL_Obool)),U_12615)),hAPP(c_COMBK(tc_fun(U_12614,tc_HOL_Obool),U_12613),c_Orderings_Otop__class_Otop(tc_fun(U_12614,tc_HOL_Obool)))),
inference(clausify,[status(thm)],[f_3281_2]) ).
fof(f_3282_1,plain,
! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2)))
| ~ class_Groups_Ocomm__monoid__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_setprod__cartesian__product]) ).
fof(f_3282_2,plain,
! [U_12621,U_12620,U_12619,U_12618,U_12617,U_12616] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12617,U_12616),hAPP(hAPP(c_COMBC(U_12617,tc_fun(U_12618,tc_HOL_Obool),U_12616),hAPP(hAPP(c_COMBB(tc_fun(U_12618,U_12616),tc_fun(tc_fun(U_12618,tc_HOL_Obool),U_12616),U_12617),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12618,U_12616)),U_12619)),U_12620)),U_12621) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12617,U_12618),U_12616),hAPP(c_Product__Type_Oprod_Oprod__case(U_12617,U_12618,U_12616),U_12619)),hAPP(hAPP(c_Product__Type_OSigma(U_12617,U_12618),U_12621),hAPP(c_COMBK(tc_fun(U_12618,tc_HOL_Obool),U_12617),U_12620)))
| ~ class_Groups_Ocomm__monoid__mult(U_12616) ),
inference(variable_rename,[status(thm)],[f_3282_1]) ).
cnf(f_3282_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12617,U_12616),hAPP(hAPP(c_COMBC(U_12617,tc_fun(U_12618,tc_HOL_Obool),U_12616),hAPP(hAPP(c_COMBB(tc_fun(U_12618,U_12616),tc_fun(tc_fun(U_12618,tc_HOL_Obool),U_12616),U_12617),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12618,U_12616)),U_12619)),U_12620)),U_12621) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12617,U_12618),U_12616),hAPP(c_Product__Type_Oprod_Oprod__case(U_12617,U_12618,U_12616),U_12619)),hAPP(hAPP(c_Product__Type_OSigma(U_12617,U_12618),U_12621),hAPP(c_COMBK(tc_fun(U_12618,tc_HOL_Obool),U_12617),U_12620)))
| ~ class_Groups_Ocomm__monoid__mult(U_12616) ),
inference(clausify,[status(thm)],[f_3282_2]) ).
fof(f_3283_1,plain,
! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Sigma__Un__distrib1]) ).
fof(f_3283_2,plain,
! [U_12626,U_12625,U_12624,U_12623,U_12622] : hAPP(hAPP(c_Product__Type_OSigma(U_12622,U_12623),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12622,tc_HOL_Obool)),U_12624),U_12625)),U_12626) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12622,U_12623),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12622,U_12623),U_12624),U_12626)),hAPP(hAPP(c_Product__Type_OSigma(U_12622,U_12623),U_12625),U_12626)),
inference(variable_rename,[status(thm)],[f_3283_1]) ).
cnf(f_3283_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12622,U_12623),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12622,tc_HOL_Obool)),U_12624),U_12625)),U_12626) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12622,U_12623),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12622,U_12623),U_12624),U_12626)),hAPP(hAPP(c_Product__Type_OSigma(U_12622,U_12623),U_12625),U_12626)),
inference(clausify,[status(thm)],[f_3283_2]) ).
fof(f_3284_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
inference(fof_nnf,[status(thm)],[fact_Times__Un__distrib1]) ).
fof(f_3284_2,plain,
! [U_12631,U_12630,U_12629,U_12628,U_12627] : hAPP(hAPP(c_Product__Type_OSigma(U_12627,U_12628),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12627,tc_HOL_Obool)),U_12629),U_12630)),hAPP(c_COMBK(tc_fun(U_12628,tc_HOL_Obool),U_12627),U_12631)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12627,U_12628),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12627,U_12628),U_12629),hAPP(c_COMBK(tc_fun(U_12628,tc_HOL_Obool),U_12627),U_12631))),hAPP(hAPP(c_Product__Type_OSigma(U_12627,U_12628),U_12630),hAPP(c_COMBK(tc_fun(U_12628,tc_HOL_Obool),U_12627),U_12631))),
inference(variable_rename,[status(thm)],[f_3284_1]) ).
cnf(f_3284_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12627,U_12628),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12627,tc_HOL_Obool)),U_12629),U_12630)),hAPP(c_COMBK(tc_fun(U_12628,tc_HOL_Obool),U_12627),U_12631)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12627,U_12628),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12627,U_12628),U_12629),hAPP(c_COMBK(tc_fun(U_12628,tc_HOL_Obool),U_12627),U_12631))),hAPP(hAPP(c_Product__Type_OSigma(U_12627,U_12628),U_12630),hAPP(c_COMBK(tc_fun(U_12628,tc_HOL_Obool),U_12627),U_12631))),
inference(clausify,[status(thm)],[f_3284_2]) ).
fof(f_3285_1,plain,
! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Sigma__Un__distrib2]) ).
fof(f_3285_2,plain,
! [U_12636,U_12635,U_12634,U_12633,U_12632] : hAPP(hAPP(c_Product__Type_OSigma(U_12632,U_12633),U_12634),hAPP(hAPP(c_COMBS(U_12632,tc_fun(U_12633,tc_HOL_Obool),tc_fun(U_12633,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12633,tc_HOL_Obool),tc_fun(tc_fun(U_12633,tc_HOL_Obool),tc_fun(U_12633,tc_HOL_Obool)),U_12632),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12633,tc_HOL_Obool))),U_12635)),U_12636)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12632,U_12633),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12632,U_12633),U_12634),U_12635)),hAPP(hAPP(c_Product__Type_OSigma(U_12632,U_12633),U_12634),U_12636)),
inference(variable_rename,[status(thm)],[f_3285_1]) ).
cnf(f_3285_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12632,U_12633),U_12634),hAPP(hAPP(c_COMBS(U_12632,tc_fun(U_12633,tc_HOL_Obool),tc_fun(U_12633,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12633,tc_HOL_Obool),tc_fun(tc_fun(U_12633,tc_HOL_Obool),tc_fun(U_12633,tc_HOL_Obool)),U_12632),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12633,tc_HOL_Obool))),U_12635)),U_12636)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12632,U_12633),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12632,U_12633),U_12634),U_12635)),hAPP(hAPP(c_Product__Type_OSigma(U_12632,U_12633),U_12634),U_12636)),
inference(clausify,[status(thm)],[f_3285_2]) ).
fof(f_3286_1,plain,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_b,T_c)),hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_swap__product]) ).
fof(f_3286_2,plain,
! [U_12640,U_12639,U_12638,U_12637] : hAPP(c_Set_Oimage(tc_prod(U_12637,U_12638),tc_prod(U_12638,U_12637),hAPP(c_Product__Type_Oprod_Oprod__case(U_12637,U_12638,tc_prod(U_12638,U_12637)),hAPP(c_COMBC(U_12638,U_12637,tc_prod(U_12638,U_12637)),c_Product__Type_OPair(U_12638,U_12637)))),hAPP(hAPP(c_Product__Type_OSigma(U_12637,U_12638),U_12639),hAPP(c_COMBK(tc_fun(U_12638,tc_HOL_Obool),U_12637),U_12640))) = hAPP(hAPP(c_Product__Type_OSigma(U_12638,U_12637),U_12640),hAPP(c_COMBK(tc_fun(U_12637,tc_HOL_Obool),U_12638),U_12639)),
inference(variable_rename,[status(thm)],[f_3286_1]) ).
cnf(f_3286_3,plain,
hAPP(c_Set_Oimage(tc_prod(U_12637,U_12638),tc_prod(U_12638,U_12637),hAPP(c_Product__Type_Oprod_Oprod__case(U_12637,U_12638,tc_prod(U_12638,U_12637)),hAPP(c_COMBC(U_12638,U_12637,tc_prod(U_12638,U_12637)),c_Product__Type_OPair(U_12638,U_12637)))),hAPP(hAPP(c_Product__Type_OSigma(U_12637,U_12638),U_12639),hAPP(c_COMBK(tc_fun(U_12638,tc_HOL_Obool),U_12637),U_12640))) = hAPP(hAPP(c_Product__Type_OSigma(U_12638,U_12637),U_12640),hAPP(c_COMBK(tc_fun(U_12637,tc_HOL_Obool),U_12638),U_12639)),
inference(clausify,[status(thm)],[f_3286_2]) ).
fof(f_3287_1,plain,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__cartesian__product]) ).
fof(f_3287_2,plain,
! [U_12644,U_12643,U_12642,U_12641] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12641,U_12643)),hAPP(hAPP(c_Product__Type_OSigma(U_12641,U_12643),U_12642),hAPP(c_COMBK(tc_fun(U_12643,tc_HOL_Obool),U_12641),U_12644))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12643),U_12644))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12641),U_12642)) ),
inference(variable_rename,[status(thm)],[f_3287_1]) ).
cnf(f_3287_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12641,U_12643)),hAPP(hAPP(c_Product__Type_OSigma(U_12641,U_12643),U_12642),hAPP(c_COMBK(tc_fun(U_12643,tc_HOL_Obool),U_12641),U_12644))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12643),U_12644))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12641),U_12642)) ),
inference(clausify,[status(thm)],[f_3287_2]) ).
fof(f_3288_1,plain,
! [V_a_2,V_f_2,T_b,V_g_2] :
( hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2
| V_g_2 != c_Finite__Set_Ofold1(T_b,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fold1__singleton__def]) ).
fof(f_3288_2,plain,
! [U_12648,U_12647,U_12646,U_12645] :
( hAPP(U_12645,hAPP(hAPP(c_Set_Oinsert(U_12646),U_12648),c_Orderings_Obot__class_Obot(tc_fun(U_12646,tc_HOL_Obool)))) = U_12648
| U_12645 != c_Finite__Set_Ofold1(U_12646,U_12647) ),
inference(variable_rename,[status(thm)],[f_3288_1]) ).
cnf(f_3288_3,plain,
( hAPP(U_12645,hAPP(hAPP(c_Set_Oinsert(U_12646),U_12648),c_Orderings_Obot__class_Obot(tc_fun(U_12646,tc_HOL_Obool)))) = U_12648
| U_12645 != c_Finite__Set_Ofold1(U_12646,U_12647) ),
inference(clausify,[status(thm)],[f_3288_2]) ).
fof(f_3289_1,plain,
! [V_a_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2,
inference(fof_nnf,[status(thm)],[fact_fold1__singleton]) ).
fof(f_3289_2,plain,
! [U_12651,U_12650,U_12649] : hAPP(c_Finite__Set_Ofold1(U_12649,U_12650),hAPP(hAPP(c_Set_Oinsert(U_12649),U_12651),c_Orderings_Obot__class_Obot(tc_fun(U_12649,tc_HOL_Obool)))) = U_12651,
inference(variable_rename,[status(thm)],[f_3289_1]) ).
cnf(f_3289_3,plain,
hAPP(c_Finite__Set_Ofold1(U_12649,U_12650),hAPP(hAPP(c_Set_Oinsert(U_12649),U_12651),c_Orderings_Obot__class_Obot(tc_fun(U_12649,tc_HOL_Obool)))) = U_12651,
inference(clausify,[status(thm)],[f_3289_2]) ).
fof(f_3290_1,plain,
! [V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
| ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_equiv__type]) ).
fof(f_3290_2,plain,
! [U_12654,U_12653,U_12652] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12652,U_12652),tc_HOL_Obool)),U_12654),hAPP(hAPP(c_Product__Type_OSigma(U_12652,U_12652),U_12653),hAPP(c_COMBK(tc_fun(U_12652,tc_HOL_Obool),U_12652),U_12653))))
| ~ c_Equiv__Relations_Oequiv(U_12652,U_12653,U_12654) ),
inference(variable_rename,[status(thm)],[f_3290_1]) ).
cnf(f_3290_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12652,U_12652),tc_HOL_Obool)),U_12654),hAPP(hAPP(c_Product__Type_OSigma(U_12652,U_12652),U_12653),hAPP(c_COMBK(tc_fun(U_12652,tc_HOL_Obool),U_12652),U_12653))))
| ~ c_Equiv__Relations_Oequiv(U_12652,U_12653,U_12654) ),
inference(clausify,[status(thm)],[f_3290_2]) ).
fof(f_3291_1,plain,
! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Sigma__Int__distrib2]) ).
fof(f_3291_2,plain,
! [U_12659,U_12658,U_12657,U_12656,U_12655] : hAPP(hAPP(c_Product__Type_OSigma(U_12655,U_12656),U_12657),hAPP(hAPP(c_COMBS(U_12655,tc_fun(U_12656,tc_HOL_Obool),tc_fun(U_12656,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12656,tc_HOL_Obool),tc_fun(tc_fun(U_12656,tc_HOL_Obool),tc_fun(U_12656,tc_HOL_Obool)),U_12655),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12656,tc_HOL_Obool))),U_12658)),U_12659)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12655,U_12656),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12655,U_12656),U_12657),U_12658)),hAPP(hAPP(c_Product__Type_OSigma(U_12655,U_12656),U_12657),U_12659)),
inference(variable_rename,[status(thm)],[f_3291_1]) ).
cnf(f_3291_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12655,U_12656),U_12657),hAPP(hAPP(c_COMBS(U_12655,tc_fun(U_12656,tc_HOL_Obool),tc_fun(U_12656,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12656,tc_HOL_Obool),tc_fun(tc_fun(U_12656,tc_HOL_Obool),tc_fun(U_12656,tc_HOL_Obool)),U_12655),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12656,tc_HOL_Obool))),U_12658)),U_12659)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12655,U_12656),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12655,U_12656),U_12657),U_12658)),hAPP(hAPP(c_Product__Type_OSigma(U_12655,U_12656),U_12657),U_12659)),
inference(clausify,[status(thm)],[f_3291_2]) ).
fof(f_3292_1,plain,
! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
inference(fof_nnf,[status(thm)],[fact_Times__Int__distrib1]) ).
fof(f_3292_2,plain,
! [U_12664,U_12663,U_12662,U_12661,U_12660] : hAPP(hAPP(c_Product__Type_OSigma(U_12660,U_12661),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12660,tc_HOL_Obool)),U_12662),U_12663)),hAPP(c_COMBK(tc_fun(U_12661,tc_HOL_Obool),U_12660),U_12664)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12660,U_12661),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12660,U_12661),U_12662),hAPP(c_COMBK(tc_fun(U_12661,tc_HOL_Obool),U_12660),U_12664))),hAPP(hAPP(c_Product__Type_OSigma(U_12660,U_12661),U_12663),hAPP(c_COMBK(tc_fun(U_12661,tc_HOL_Obool),U_12660),U_12664))),
inference(variable_rename,[status(thm)],[f_3292_1]) ).
cnf(f_3292_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12660,U_12661),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12660,tc_HOL_Obool)),U_12662),U_12663)),hAPP(c_COMBK(tc_fun(U_12661,tc_HOL_Obool),U_12660),U_12664)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12660,U_12661),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12660,U_12661),U_12662),hAPP(c_COMBK(tc_fun(U_12661,tc_HOL_Obool),U_12660),U_12664))),hAPP(hAPP(c_Product__Type_OSigma(U_12660,U_12661),U_12663),hAPP(c_COMBK(tc_fun(U_12661,tc_HOL_Obool),U_12660),U_12664))),
inference(clausify,[status(thm)],[f_3292_2]) ).
fof(f_3293_1,plain,
! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
inference(fof_nnf,[status(thm)],[fact_Sigma__Int__distrib1]) ).
fof(f_3293_2,plain,
! [U_12669,U_12668,U_12667,U_12666,U_12665] : hAPP(hAPP(c_Product__Type_OSigma(U_12665,U_12666),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12665,tc_HOL_Obool)),U_12667),U_12668)),U_12669) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12665,U_12666),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12665,U_12666),U_12667),U_12669)),hAPP(hAPP(c_Product__Type_OSigma(U_12665,U_12666),U_12668),U_12669)),
inference(variable_rename,[status(thm)],[f_3293_1]) ).
cnf(f_3293_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12665,U_12666),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12665,tc_HOL_Obool)),U_12667),U_12668)),U_12669) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_12665,U_12666),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12665,U_12666),U_12667),U_12669)),hAPP(hAPP(c_Product__Type_OSigma(U_12665,U_12666),U_12668),U_12669)),
inference(clausify,[status(thm)],[f_3293_2]) ).
fof(f_3294_1,plain,
! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId__on(T_b,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))),
inference(fof_nnf,[status(thm)],[fact_Id__on__subset__Times]) ).
fof(f_3294_2,plain,
! [U_12671,U_12670] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12670,U_12670),tc_HOL_Obool)),c_Relation_OId__on(U_12670,U_12671)),hAPP(hAPP(c_Product__Type_OSigma(U_12670,U_12670),U_12671),hAPP(c_COMBK(tc_fun(U_12670,tc_HOL_Obool),U_12670),U_12671)))),
inference(variable_rename,[status(thm)],[f_3294_1]) ).
cnf(f_3294_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12670,U_12670),tc_HOL_Obool)),c_Relation_OId__on(U_12670,U_12671)),hAPP(hAPP(c_Product__Type_OSigma(U_12670,U_12670),U_12671),hAPP(c_COMBK(tc_fun(U_12670,tc_HOL_Obool),U_12670),U_12671)))),
inference(clausify,[status(thm)],[f_3294_2]) ).
fof(f_3295_1,plain,
! [T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_UNIV__Times__UNIV]) ).
fof(f_3295_2,plain,
! [U_12673,U_12672] : hAPP(hAPP(c_Product__Type_OSigma(U_12672,U_12673),c_Orderings_Otop__class_Otop(tc_fun(U_12672,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12673,tc_HOL_Obool),U_12672),c_Orderings_Otop__class_Otop(tc_fun(U_12673,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12672,U_12673),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3295_1]) ).
cnf(f_3295_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12672,U_12673),c_Orderings_Otop__class_Otop(tc_fun(U_12672,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_12673,tc_HOL_Obool),U_12672),c_Orderings_Otop__class_Otop(tc_fun(U_12673,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12672,U_12673),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3295_2]) ).
fof(f_3296_1,plain,
! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
& hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_SigmaE2]) ).
fof(f_3296_2,plain,
! [U_12679,U_12678,U_12677,U_12676,U_12675,U_12674] :
( ( hBOOL(hAPP(hAPP(c_member(U_12675),U_12677),hAPP(U_12679,U_12676)))
& hBOOL(hAPP(hAPP(c_member(U_12674),U_12676),U_12678)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12674,U_12675)),hAPP(hAPP(c_Product__Type_OPair(U_12674,U_12675),U_12676),U_12677)),hAPP(hAPP(c_Product__Type_OSigma(U_12674,U_12675),U_12678),U_12679))) ),
inference(variable_rename,[status(thm)],[f_3296_1]) ).
cnf(f_3296_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_12674),U_12676),U_12678))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12674,U_12675)),hAPP(hAPP(c_Product__Type_OPair(U_12674,U_12675),U_12676),U_12677)),hAPP(hAPP(c_Product__Type_OSigma(U_12674,U_12675),U_12678),U_12679))) ),
inference(clausify,[status(thm)],[f_3296_2]) ).
cnf(f_3296_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12675),U_12677),hAPP(U_12679,U_12676)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12674,U_12675)),hAPP(hAPP(c_Product__Type_OPair(U_12674,U_12675),U_12676),U_12677)),hAPP(hAPP(c_Product__Type_OSigma(U_12674,U_12675),U_12678),U_12679))) ),
inference(clausify,[status(thm)],[f_3296_2]) ).
fof(f_3297_1,plain,
! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_SigmaD2]) ).
fof(f_3297_2,plain,
! [U_12685,U_12684,U_12683,U_12682,U_12681,U_12680] :
( hBOOL(hAPP(hAPP(c_member(U_12681),U_12683),hAPP(U_12685,U_12682)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12680,U_12681)),hAPP(hAPP(c_Product__Type_OPair(U_12680,U_12681),U_12682),U_12683)),hAPP(hAPP(c_Product__Type_OSigma(U_12680,U_12681),U_12684),U_12685))) ),
inference(variable_rename,[status(thm)],[f_3297_1]) ).
fof(f_3297_3,plain,
! [U_12685,U_12684,U_12683,U_12682,U_12681] :
( ! [U_12680] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12680,U_12681)),hAPP(hAPP(c_Product__Type_OPair(U_12680,U_12681),U_12682),U_12683)),hAPP(hAPP(c_Product__Type_OSigma(U_12680,U_12681),U_12684),U_12685)))
| hBOOL(hAPP(hAPP(c_member(U_12681),U_12683),hAPP(U_12685,U_12682))) ),
inference(miniscope,[status(thm)],[f_3297_2]) ).
cnf(f_3297_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12680,U_12681)),hAPP(hAPP(c_Product__Type_OPair(U_12680,U_12681),U_12682),U_12683)),hAPP(hAPP(c_Product__Type_OSigma(U_12680,U_12681),U_12684),U_12685)))
| hBOOL(hAPP(hAPP(c_member(U_12681),U_12683),hAPP(U_12685,U_12682))) ),
inference(clausify,[status(thm)],[f_3297_3]) ).
fof(f_3298_1,plain,
! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_SigmaD1]) ).
fof(f_3298_2,plain,
! [U_12691,U_12690,U_12689,U_12688,U_12687,U_12686] :
( hBOOL(hAPP(hAPP(c_member(U_12686),U_12688),U_12690))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12686,U_12687)),hAPP(hAPP(c_Product__Type_OPair(U_12686,U_12687),U_12688),U_12689)),hAPP(hAPP(c_Product__Type_OSigma(U_12686,U_12687),U_12690),U_12691))) ),
inference(variable_rename,[status(thm)],[f_3298_1]) ).
cnf(f_3298_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_12686),U_12688),U_12690))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12686,U_12687)),hAPP(hAPP(c_Product__Type_OPair(U_12686,U_12687),U_12688),U_12689)),hAPP(hAPP(c_Product__Type_OSigma(U_12686,U_12687),U_12690),U_12691))) ),
inference(clausify,[status(thm)],[f_3298_2]) ).
fof(f_3299_1,plain,
! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
& ( ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
& hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_mem__Sigma__iff]) ).
fof(f_3299_2,plain,
! [U_12697,U_12696,U_12695,U_12694,U_12693,U_12692] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12692,U_12693)),hAPP(hAPP(c_Product__Type_OPair(U_12692,U_12693),U_12694),U_12695)),hAPP(hAPP(c_Product__Type_OSigma(U_12692,U_12693),U_12696),U_12697)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12693),U_12695),hAPP(U_12697,U_12694)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12692),U_12694),U_12696)) )
& ( ( hBOOL(hAPP(hAPP(c_member(U_12693),U_12695),hAPP(U_12697,U_12694)))
& hBOOL(hAPP(hAPP(c_member(U_12692),U_12694),U_12696)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12692,U_12693)),hAPP(hAPP(c_Product__Type_OPair(U_12692,U_12693),U_12694),U_12695)),hAPP(hAPP(c_Product__Type_OSigma(U_12692,U_12693),U_12696),U_12697))) ) ),
inference(variable_rename,[status(thm)],[f_3299_1]) ).
fof(f_3299_3,plain,
( ! [U_12709,U_12707,U_12705,U_12703,U_12701,U_12699] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12699,U_12701)),hAPP(hAPP(c_Product__Type_OPair(U_12699,U_12701),U_12703),U_12705)),hAPP(hAPP(c_Product__Type_OSigma(U_12699,U_12701),U_12707),U_12709)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12701),U_12705),hAPP(U_12709,U_12703)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12699),U_12703),U_12707)) )
& ! [U_12708,U_12706,U_12704,U_12702,U_12700,U_12698] :
( ( hBOOL(hAPP(hAPP(c_member(U_12700),U_12704),hAPP(U_12708,U_12702)))
& hBOOL(hAPP(hAPP(c_member(U_12698),U_12702),U_12706)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12698,U_12700)),hAPP(hAPP(c_Product__Type_OPair(U_12698,U_12700),U_12702),U_12704)),hAPP(hAPP(c_Product__Type_OSigma(U_12698,U_12700),U_12706),U_12708))) ) ),
inference(miniscope,[status(thm)],[f_3299_2]) ).
cnf(f_3299_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12698),U_12702),U_12706))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12698,U_12700)),hAPP(hAPP(c_Product__Type_OPair(U_12698,U_12700),U_12702),U_12704)),hAPP(hAPP(c_Product__Type_OSigma(U_12698,U_12700),U_12706),U_12708))) ),
inference(clausify,[status(thm)],[f_3299_3]) ).
cnf(f_3299_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_12700),U_12704),hAPP(U_12708,U_12702)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12698,U_12700)),hAPP(hAPP(c_Product__Type_OPair(U_12698,U_12700),U_12702),U_12704)),hAPP(hAPP(c_Product__Type_OSigma(U_12698,U_12700),U_12706),U_12708))) ),
inference(clausify,[status(thm)],[f_3299_3]) ).
cnf(f_3299_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12699,U_12701)),hAPP(hAPP(c_Product__Type_OPair(U_12699,U_12701),U_12703),U_12705)),hAPP(hAPP(c_Product__Type_OSigma(U_12699,U_12701),U_12707),U_12709)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12701),U_12705),hAPP(U_12709,U_12703)))
| ~ hBOOL(hAPP(hAPP(c_member(U_12699),U_12703),U_12707)) ),
inference(clausify,[status(thm)],[f_3299_3]) ).
fof(f_3300_1,plain,
! [V_A_2,V_F_2,V_f_2,T_b] :
( hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Oeq__fold]) ).
fof(f_3300_2,plain,
! [U_12713,U_12712,U_12711,U_12710] :
( hAPP(U_12712,U_12713) = hAPP(c_Finite__Set_Ofold1(U_12710,U_12711),U_12713)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12710),U_12713))
| ~ c_Finite__Set_Ofolding__one(U_12710,U_12711,U_12712) ),
inference(variable_rename,[status(thm)],[f_3300_1]) ).
cnf(f_3300_3,plain,
( hAPP(U_12712,U_12713) = hAPP(c_Finite__Set_Ofold1(U_12710,U_12711),U_12713)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12710),U_12713))
| ~ c_Finite__Set_Ofolding__one(U_12710,U_12711,U_12712) ),
inference(clausify,[status(thm)],[f_3300_2]) ).
fof(f_3301_1,plain,
! [V_A_2,V_x_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2),
inference(fof_nnf,[status(thm)],[fact_card__cartesian__product__singleton]) ).
fof(f_3301_2,plain,
! [U_12717,U_12716,U_12715,U_12714] : hAPP(c_Finite__Set_Ocard(tc_prod(U_12714,U_12715)),hAPP(hAPP(c_Product__Type_OSigma(U_12714,U_12715),hAPP(hAPP(c_Set_Oinsert(U_12714),U_12716),c_Orderings_Obot__class_Obot(tc_fun(U_12714,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(U_12715,tc_HOL_Obool),U_12714),U_12717))) = hAPP(c_Finite__Set_Ocard(U_12715),U_12717),
inference(variable_rename,[status(thm)],[f_3301_1]) ).
cnf(f_3301_3,plain,
hAPP(c_Finite__Set_Ocard(tc_prod(U_12714,U_12715)),hAPP(hAPP(c_Product__Type_OSigma(U_12714,U_12715),hAPP(hAPP(c_Set_Oinsert(U_12714),U_12716),c_Orderings_Obot__class_Obot(tc_fun(U_12714,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(U_12715,tc_HOL_Obool),U_12714),U_12717))) = hAPP(c_Finite__Set_Ocard(U_12715),U_12717),
inference(clausify,[status(thm)],[f_3301_2]) ).
fof(f_3302_1,plain,
! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) )
& ( 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_prod(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Times__subset__cancel2]) ).
fof(f_3302_2,plain,
! [U_12723,U_12722,U_12721,U_12720,U_12719,U_12718] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12721,U_12718),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12721,U_12718),U_12722),hAPP(c_COMBK(tc_fun(U_12718,tc_HOL_Obool),U_12721),U_12720))),hAPP(hAPP(c_Product__Type_OSigma(U_12721,U_12718),U_12723),hAPP(c_COMBK(tc_fun(U_12718,tc_HOL_Obool),U_12721),U_12720))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12721,tc_HOL_Obool)),U_12722),U_12723)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12721,tc_HOL_Obool)),U_12722),U_12723))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12721,U_12718),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12721,U_12718),U_12722),hAPP(c_COMBK(tc_fun(U_12718,tc_HOL_Obool),U_12721),U_12720))),hAPP(hAPP(c_Product__Type_OSigma(U_12721,U_12718),U_12723),hAPP(c_COMBK(tc_fun(U_12718,tc_HOL_Obool),U_12721),U_12720)))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(U_12718),U_12719),U_12720)) ),
inference(variable_rename,[status(thm)],[f_3302_1]) ).
cnf(f_3302_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12721,tc_HOL_Obool)),U_12722),U_12723))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12721,U_12718),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12721,U_12718),U_12722),hAPP(c_COMBK(tc_fun(U_12718,tc_HOL_Obool),U_12721),U_12720))),hAPP(hAPP(c_Product__Type_OSigma(U_12721,U_12718),U_12723),hAPP(c_COMBK(tc_fun(U_12718,tc_HOL_Obool),U_12721),U_12720))))
| ~ hBOOL(hAPP(hAPP(c_member(U_12718),U_12719),U_12720)) ),
inference(clausify,[status(thm)],[f_3302_2]) ).
cnf(f_3302_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12721,U_12718),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12721,U_12718),U_12722),hAPP(c_COMBK(tc_fun(U_12718,tc_HOL_Obool),U_12721),U_12720))),hAPP(hAPP(c_Product__Type_OSigma(U_12721,U_12718),U_12723),hAPP(c_COMBK(tc_fun(U_12718,tc_HOL_Obool),U_12721),U_12720))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12721,tc_HOL_Obool)),U_12722),U_12723))
| ~ hBOOL(hAPP(hAPP(c_member(U_12718),U_12719),U_12720)) ),
inference(clausify,[status(thm)],[f_3302_2]) ).
fof(f_3303_1,plain,
! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_C_2)),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ),
inference(fof_nnf,[status(thm)],[fact_Image__subset]) ).
fof(f_3303_2,plain,
! [U_12729,U_12728,U_12727,U_12726,U_12725,U_12724] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12725,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12724,U_12725,U_12726),U_12729)),U_12728))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12724,U_12725),tc_HOL_Obool)),U_12726),hAPP(hAPP(c_Product__Type_OSigma(U_12724,U_12725),U_12727),hAPP(c_COMBK(tc_fun(U_12725,tc_HOL_Obool),U_12724),U_12728)))) ),
inference(variable_rename,[status(thm)],[f_3303_1]) ).
cnf(f_3303_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12725,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12724,U_12725,U_12726),U_12729)),U_12728))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12724,U_12725),tc_HOL_Obool)),U_12726),hAPP(hAPP(c_Product__Type_OSigma(U_12724,U_12725),U_12727),hAPP(c_COMBK(tc_fun(U_12725,tc_HOL_Obool),U_12724),U_12728)))) ),
inference(clausify,[status(thm)],[f_3303_2]) ).
fof(f_3304_1,plain,
! [V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ),
inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD1]) ).
fof(f_3304_2,plain,
! [U_12733,U_12732,U_12731,U_12730] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12730),U_12732))
| U_12733 = c_Orderings_Obot__class_Obot(tc_fun(U_12731,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12730,U_12731)),hAPP(hAPP(c_Product__Type_OSigma(U_12730,U_12731),U_12732),hAPP(c_COMBK(tc_fun(U_12731,tc_HOL_Obool),U_12730),U_12733)))) ),
inference(variable_rename,[status(thm)],[f_3304_1]) ).
cnf(f_3304_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12730),U_12732))
| U_12733 = c_Orderings_Obot__class_Obot(tc_fun(U_12731,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12730,U_12731)),hAPP(hAPP(c_Product__Type_OSigma(U_12730,U_12731),U_12732),hAPP(c_COMBK(tc_fun(U_12731,tc_HOL_Obool),U_12730),U_12733)))) ),
inference(clausify,[status(thm)],[f_3304_2]) ).
fof(f_3305_1,plain,
! [V_B_2,V_A_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ),
inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD2]) ).
fof(f_3305_2,plain,
! [U_12737,U_12736,U_12735,U_12734] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12735),U_12737))
| U_12736 = c_Orderings_Obot__class_Obot(tc_fun(U_12734,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12734,U_12735)),hAPP(hAPP(c_Product__Type_OSigma(U_12734,U_12735),U_12736),hAPP(c_COMBK(tc_fun(U_12735,tc_HOL_Obool),U_12734),U_12737)))) ),
inference(variable_rename,[status(thm)],[f_3305_1]) ).
cnf(f_3305_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12735),U_12737))
| U_12736 = c_Orderings_Obot__class_Obot(tc_fun(U_12734,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12734,U_12735)),hAPP(hAPP(c_Product__Type_OSigma(U_12734,U_12735),U_12736),hAPP(c_COMBK(tc_fun(U_12735,tc_HOL_Obool),U_12734),U_12737)))) ),
inference(clausify,[status(thm)],[f_3305_2]) ).
fof(f_3306_1,plain,
! [V_A_2,T_c,T_b,V_B_2] :
( ( hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = V_A_2
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_fst__image__times]) ).
fof(f_3306_2,plain,
! [U_12741,U_12740,U_12739,U_12738] :
( ( hAPP(c_Set_Oimage(tc_prod(U_12740,U_12739),U_12740,c_Product__Type_Ofst(U_12740,U_12739)),hAPP(hAPP(c_Product__Type_OSigma(U_12740,U_12739),U_12741),hAPP(c_COMBK(tc_fun(U_12739,tc_HOL_Obool),U_12740),U_12738))) = U_12741
| U_12738 = c_Orderings_Obot__class_Obot(tc_fun(U_12739,tc_HOL_Obool)) )
& ( hAPP(c_Set_Oimage(tc_prod(U_12740,U_12739),U_12740,c_Product__Type_Ofst(U_12740,U_12739)),hAPP(hAPP(c_Product__Type_OSigma(U_12740,U_12739),U_12741),hAPP(c_COMBK(tc_fun(U_12739,tc_HOL_Obool),U_12740),U_12738))) = c_Orderings_Obot__class_Obot(tc_fun(U_12740,tc_HOL_Obool))
| U_12738 != c_Orderings_Obot__class_Obot(tc_fun(U_12739,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3306_1]) ).
fof(f_3306_3,plain,
( ! [U_12749,U_12747,U_12745,U_12743] :
( hAPP(c_Set_Oimage(tc_prod(U_12747,U_12745),U_12747,c_Product__Type_Ofst(U_12747,U_12745)),hAPP(hAPP(c_Product__Type_OSigma(U_12747,U_12745),U_12749),hAPP(c_COMBK(tc_fun(U_12745,tc_HOL_Obool),U_12747),U_12743))) = U_12749
| U_12743 = c_Orderings_Obot__class_Obot(tc_fun(U_12745,tc_HOL_Obool)) )
& ! [U_12748,U_12746,U_12744,U_12742] :
( hAPP(c_Set_Oimage(tc_prod(U_12746,U_12744),U_12746,c_Product__Type_Ofst(U_12746,U_12744)),hAPP(hAPP(c_Product__Type_OSigma(U_12746,U_12744),U_12748),hAPP(c_COMBK(tc_fun(U_12744,tc_HOL_Obool),U_12746),U_12742))) = c_Orderings_Obot__class_Obot(tc_fun(U_12746,tc_HOL_Obool))
| U_12742 != c_Orderings_Obot__class_Obot(tc_fun(U_12744,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_3306_2]) ).
cnf(f_3306_4,plain,
( hAPP(c_Set_Oimage(tc_prod(U_12746,U_12744),U_12746,c_Product__Type_Ofst(U_12746,U_12744)),hAPP(hAPP(c_Product__Type_OSigma(U_12746,U_12744),U_12748),hAPP(c_COMBK(tc_fun(U_12744,tc_HOL_Obool),U_12746),U_12742))) = c_Orderings_Obot__class_Obot(tc_fun(U_12746,tc_HOL_Obool))
| U_12742 != c_Orderings_Obot__class_Obot(tc_fun(U_12744,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3306_3]) ).
cnf(f_3306_5,plain,
( hAPP(c_Set_Oimage(tc_prod(U_12747,U_12745),U_12747,c_Product__Type_Ofst(U_12747,U_12745)),hAPP(hAPP(c_Product__Type_OSigma(U_12747,U_12745),U_12749),hAPP(c_COMBK(tc_fun(U_12745,tc_HOL_Obool),U_12747),U_12743))) = U_12749
| U_12743 = c_Orderings_Obot__class_Obot(tc_fun(U_12745,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3306_3]) ).
fof(f_3307_1,plain,
! [V_B_2,T_c,T_b,V_A_2] :
( ( hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = V_B_2
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
| V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_snd__image__times]) ).
fof(f_3307_2,plain,
! [U_12753,U_12752,U_12751,U_12750] :
( ( hAPP(c_Set_Oimage(tc_prod(U_12751,U_12752),U_12752,c_Product__Type_Osnd(U_12751,U_12752)),hAPP(hAPP(c_Product__Type_OSigma(U_12751,U_12752),U_12750),hAPP(c_COMBK(tc_fun(U_12752,tc_HOL_Obool),U_12751),U_12753))) = U_12753
| U_12750 = c_Orderings_Obot__class_Obot(tc_fun(U_12751,tc_HOL_Obool)) )
& ( hAPP(c_Set_Oimage(tc_prod(U_12751,U_12752),U_12752,c_Product__Type_Osnd(U_12751,U_12752)),hAPP(hAPP(c_Product__Type_OSigma(U_12751,U_12752),U_12750),hAPP(c_COMBK(tc_fun(U_12752,tc_HOL_Obool),U_12751),U_12753))) = c_Orderings_Obot__class_Obot(tc_fun(U_12752,tc_HOL_Obool))
| U_12750 != c_Orderings_Obot__class_Obot(tc_fun(U_12751,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3307_1]) ).
fof(f_3307_3,plain,
( ! [U_12761,U_12759,U_12757,U_12755] :
( hAPP(c_Set_Oimage(tc_prod(U_12757,U_12759),U_12759,c_Product__Type_Osnd(U_12757,U_12759)),hAPP(hAPP(c_Product__Type_OSigma(U_12757,U_12759),U_12755),hAPP(c_COMBK(tc_fun(U_12759,tc_HOL_Obool),U_12757),U_12761))) = U_12761
| U_12755 = c_Orderings_Obot__class_Obot(tc_fun(U_12757,tc_HOL_Obool)) )
& ! [U_12760,U_12758,U_12756,U_12754] :
( hAPP(c_Set_Oimage(tc_prod(U_12756,U_12758),U_12758,c_Product__Type_Osnd(U_12756,U_12758)),hAPP(hAPP(c_Product__Type_OSigma(U_12756,U_12758),U_12754),hAPP(c_COMBK(tc_fun(U_12758,tc_HOL_Obool),U_12756),U_12760))) = c_Orderings_Obot__class_Obot(tc_fun(U_12758,tc_HOL_Obool))
| U_12754 != c_Orderings_Obot__class_Obot(tc_fun(U_12756,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_3307_2]) ).
cnf(f_3307_4,plain,
( hAPP(c_Set_Oimage(tc_prod(U_12756,U_12758),U_12758,c_Product__Type_Osnd(U_12756,U_12758)),hAPP(hAPP(c_Product__Type_OSigma(U_12756,U_12758),U_12754),hAPP(c_COMBK(tc_fun(U_12758,tc_HOL_Obool),U_12756),U_12760))) = c_Orderings_Obot__class_Obot(tc_fun(U_12758,tc_HOL_Obool))
| U_12754 != c_Orderings_Obot__class_Obot(tc_fun(U_12756,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3307_3]) ).
cnf(f_3307_5,plain,
( hAPP(c_Set_Oimage(tc_prod(U_12757,U_12759),U_12759,c_Product__Type_Osnd(U_12757,U_12759)),hAPP(hAPP(c_Product__Type_OSigma(U_12757,U_12759),U_12755),hAPP(c_COMBK(tc_fun(U_12759,tc_HOL_Obool),U_12757),U_12761))) = U_12761
| U_12755 = c_Orderings_Obot__class_Obot(tc_fun(U_12757,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3307_3]) ).
fof(f_3308_1,plain,
! [V_A_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2)),
inference(fof_nnf,[status(thm)],[fact_fold1__def]) ).
fof(f_3308_2,plain,
! [U_12764,U_12763,U_12762] : hAPP(c_Finite__Set_Ofold1(U_12762,U_12763),U_12764) = c_HOL_OThe(U_12762,c_Finite__Set_Ofold1Set(U_12762,U_12763,U_12764)),
inference(variable_rename,[status(thm)],[f_3308_1]) ).
cnf(f_3308_3,plain,
hAPP(c_Finite__Set_Ofold1(U_12762,U_12763),U_12764) = c_HOL_OThe(U_12762,c_Finite__Set_Ofold1Set(U_12762,U_12763,U_12764)),
inference(clausify,[status(thm)],[f_3308_2]) ).
fof(f_3309_1,plain,
! [V_A_2,T_b] :
( c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_OF__eq]) ).
fof(f_3309_2,plain,
! [U_12766,U_12765] :
( c_Big__Operators_Olattice__class_OSup__fin(U_12765,U_12766) = hAPP(c_Finite__Set_Ofold1(U_12765,c_Lattices_Osemilattice__sup__class_Osup(U_12765)),U_12766)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12765),U_12766))
| ~ class_Lattices_Olattice(U_12765) ),
inference(variable_rename,[status(thm)],[f_3309_1]) ).
cnf(f_3309_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_12765,U_12766) = hAPP(c_Finite__Set_Ofold1(U_12765,c_Lattices_Osemilattice__sup__class_Osup(U_12765)),U_12766)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12765),U_12766))
| ~ class_Lattices_Olattice(U_12765) ),
inference(clausify,[status(thm)],[f_3309_2]) ).
fof(f_3310_1,plain,
! [V_A_2,T_b] :
( c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_OF__eq]) ).
fof(f_3310_2,plain,
! [U_12768,U_12767] :
( c_Big__Operators_Olattice__class_OInf__fin(U_12767,U_12768) = hAPP(c_Finite__Set_Ofold1(U_12767,c_Lattices_Osemilattice__inf__class_Oinf(U_12767)),U_12768)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12767),U_12768))
| ~ class_Lattices_Olattice(U_12767) ),
inference(variable_rename,[status(thm)],[f_3310_1]) ).
cnf(f_3310_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_12767,U_12768) = hAPP(c_Finite__Set_Ofold1(U_12767,c_Lattices_Osemilattice__inf__class_Oinf(U_12767)),U_12768)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12767),U_12768))
| ~ class_Lattices_Olattice(U_12767) ),
inference(clausify,[status(thm)],[f_3310_2]) ).
fof(f_3311_1,plain,
! [V_A_2,T_b] :
( c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_OF__eq]) ).
fof(f_3311_2,plain,
! [U_12770,U_12769] :
( c_Big__Operators_Olinorder__class_OMin(U_12769,U_12770) = hAPP(c_Finite__Set_Ofold1(U_12769,c_Orderings_Oord__class_Omin(U_12769)),U_12770)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12769),U_12770))
| ~ class_Orderings_Olinorder(U_12769) ),
inference(variable_rename,[status(thm)],[f_3311_1]) ).
cnf(f_3311_3,plain,
( c_Big__Operators_Olinorder__class_OMin(U_12769,U_12770) = hAPP(c_Finite__Set_Ofold1(U_12769,c_Orderings_Oord__class_Omin(U_12769)),U_12770)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12769),U_12770))
| ~ class_Orderings_Olinorder(U_12769) ),
inference(clausify,[status(thm)],[f_3311_2]) ).
fof(f_3312_1,plain,
! [V_A_2,T_b] :
( c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_OF__eq]) ).
fof(f_3312_2,plain,
! [U_12772,U_12771] :
( c_Big__Operators_Olinorder__class_OMax(U_12771,U_12772) = hAPP(c_Finite__Set_Ofold1(U_12771,c_Orderings_Oord__class_Omax(U_12771)),U_12772)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12771),U_12772))
| ~ class_Orderings_Olinorder(U_12771) ),
inference(variable_rename,[status(thm)],[f_3312_1]) ).
cnf(f_3312_3,plain,
( c_Big__Operators_Olinorder__class_OMax(U_12771,U_12772) = hAPP(c_Finite__Set_Ofold1(U_12771,c_Orderings_Oord__class_Omax(U_12771)),U_12772)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12771),U_12772))
| ~ class_Orderings_Olinorder(U_12771) ),
inference(clausify,[status(thm)],[f_3312_2]) ).
fof(f_3313_1,plain,
! [V_A_2,T_b] :
( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_OF__eq]) ).
fof(f_3313_2,plain,
! [U_12774,U_12773] :
( c_Big__Operators_Olattice_OInf__fin(U_12773,c_Orderings_Oord__class_Omin(U_12773),U_12774) = hAPP(c_Finite__Set_Ofold1(U_12773,c_Orderings_Oord__class_Omin(U_12773)),U_12774)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12773),U_12774))
| ~ class_Orderings_Olinorder(U_12773) ),
inference(variable_rename,[status(thm)],[f_3313_1]) ).
cnf(f_3313_3,plain,
( c_Big__Operators_Olattice_OInf__fin(U_12773,c_Orderings_Oord__class_Omin(U_12773),U_12774) = hAPP(c_Finite__Set_Ofold1(U_12773,c_Orderings_Oord__class_Omin(U_12773)),U_12774)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12773),U_12774))
| ~ class_Orderings_Olinorder(U_12773) ),
inference(clausify,[status(thm)],[f_3313_2]) ).
fof(f_3314_1,plain,
! [V_A_2,T_b] :
( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_OF__eq]) ).
fof(f_3314_2,plain,
! [U_12776,U_12775] :
( c_Big__Operators_Olattice_OSup__fin(U_12775,c_Orderings_Oord__class_Omax(U_12775),U_12776) = hAPP(c_Finite__Set_Ofold1(U_12775,c_Orderings_Oord__class_Omax(U_12775)),U_12776)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12775),U_12776))
| ~ class_Orderings_Olinorder(U_12775) ),
inference(variable_rename,[status(thm)],[f_3314_1]) ).
cnf(f_3314_3,plain,
( c_Big__Operators_Olattice_OSup__fin(U_12775,c_Orderings_Oord__class_Omax(U_12775),U_12776) = hAPP(c_Finite__Set_Ofold1(U_12775,c_Orderings_Oord__class_Omax(U_12775)),U_12776)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12775),U_12776))
| ~ class_Orderings_Olinorder(U_12775) ),
inference(clausify,[status(thm)],[f_3314_2]) ).
fof(f_3315_1,plain,
! [V_r_2,V_A_2,T_b] :
( ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) )
& ( ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) )
| ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_refl__on__def]) ).
fof(f_3315_2,plain,
! [U_12781,U_12780,U_12779] :
( ( c_Relation_Orefl__on(U_12779,U_12780,U_12781)
| ? [U_12778] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12779,U_12779)),hAPP(hAPP(c_Product__Type_OPair(U_12779,U_12779),U_12778),U_12778)),U_12781))
& hBOOL(hAPP(hAPP(c_member(U_12779),U_12778),U_12780)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12779,U_12779),tc_HOL_Obool)),U_12781),hAPP(hAPP(c_Product__Type_OSigma(U_12779,U_12779),U_12780),hAPP(c_COMBK(tc_fun(U_12779,tc_HOL_Obool),U_12779),U_12780)))) )
& ( ( ! [U_12777] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12779,U_12779)),hAPP(hAPP(c_Product__Type_OPair(U_12779,U_12779),U_12777),U_12777)),U_12781))
| ~ hBOOL(hAPP(hAPP(c_member(U_12779),U_12777),U_12780)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12779,U_12779),tc_HOL_Obool)),U_12781),hAPP(hAPP(c_Product__Type_OSigma(U_12779,U_12779),U_12780),hAPP(c_COMBK(tc_fun(U_12779,tc_HOL_Obool),U_12779),U_12780)))) )
| ~ c_Relation_Orefl__on(U_12779,U_12780,U_12781) ) ),
inference(variable_rename,[status(thm)],[f_3315_1]) ).
fof(f_3315_3,plain,
( ! [U_12787,U_12785,U_12783] :
( c_Relation_Orefl__on(U_12783,U_12785,U_12787)
| ? [U_12778] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12783,U_12783)),hAPP(hAPP(c_Product__Type_OPair(U_12783,U_12783),U_12778),U_12778)),U_12787))
& hBOOL(hAPP(hAPP(c_member(U_12783),U_12778),U_12785)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12783,U_12783),tc_HOL_Obool)),U_12787),hAPP(hAPP(c_Product__Type_OSigma(U_12783,U_12783),U_12785),hAPP(c_COMBK(tc_fun(U_12783,tc_HOL_Obool),U_12783),U_12785)))) )
& ! [U_12786,U_12784,U_12782] :
( ( ! [U_12777] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12782,U_12782)),hAPP(hAPP(c_Product__Type_OPair(U_12782,U_12782),U_12777),U_12777)),U_12786))
| ~ hBOOL(hAPP(hAPP(c_member(U_12782),U_12777),U_12784)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12782,U_12782),tc_HOL_Obool)),U_12786),hAPP(hAPP(c_Product__Type_OSigma(U_12782,U_12782),U_12784),hAPP(c_COMBK(tc_fun(U_12782,tc_HOL_Obool),U_12782),U_12784)))) )
| ~ c_Relation_Orefl__on(U_12782,U_12784,U_12786) ) ),
inference(miniscope,[status(thm)],[f_3315_2]) ).
fof(f_3315_4,plain,
( ! [U_12787,U_12785,U_12783] :
( c_Relation_Orefl__on(U_12783,U_12785,U_12787)
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12783,U_12783)),hAPP(hAPP(c_Product__Type_OPair(U_12783,U_12783),sK281(U_12787,U_12785,U_12783)),sK281(U_12787,U_12785,U_12783))),U_12787))
& hBOOL(hAPP(hAPP(c_member(U_12783),sK281(U_12787,U_12785,U_12783)),U_12785)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12783,U_12783),tc_HOL_Obool)),U_12787),hAPP(hAPP(c_Product__Type_OSigma(U_12783,U_12783),U_12785),hAPP(c_COMBK(tc_fun(U_12783,tc_HOL_Obool),U_12783),U_12785)))) )
& ! [U_12786,U_12784,U_12782] :
( ( ! [U_12777] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12782,U_12782)),hAPP(hAPP(c_Product__Type_OPair(U_12782,U_12782),U_12777),U_12777)),U_12786))
| ~ hBOOL(hAPP(hAPP(c_member(U_12782),U_12777),U_12784)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12782,U_12782),tc_HOL_Obool)),U_12786),hAPP(hAPP(c_Product__Type_OSigma(U_12782,U_12782),U_12784),hAPP(c_COMBK(tc_fun(U_12782,tc_HOL_Obool),U_12782),U_12784)))) )
| ~ c_Relation_Orefl__on(U_12782,U_12784,U_12786) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK281]),skolemize(U_12778,sK281(U_12787,U_12785,U_12783))],[f_3315_3]) ).
cnf(f_3315_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12782,U_12782),tc_HOL_Obool)),U_12786),hAPP(hAPP(c_Product__Type_OSigma(U_12782,U_12782),U_12784),hAPP(c_COMBK(tc_fun(U_12782,tc_HOL_Obool),U_12782),U_12784))))
| ~ c_Relation_Orefl__on(U_12782,U_12784,U_12786) ),
inference(clausify,[status(thm)],[f_3315_4]) ).
cnf(f_3315_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12782,U_12782)),hAPP(hAPP(c_Product__Type_OPair(U_12782,U_12782),U_12777),U_12777)),U_12786))
| ~ hBOOL(hAPP(hAPP(c_member(U_12782),U_12777),U_12784))
| ~ c_Relation_Orefl__on(U_12782,U_12784,U_12786) ),
inference(clausify,[status(thm)],[f_3315_4]) ).
cnf(f_3315_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_12783),sK281(U_12787,U_12785,U_12783)),U_12785))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12783,U_12783),tc_HOL_Obool)),U_12787),hAPP(hAPP(c_Product__Type_OSigma(U_12783,U_12783),U_12785),hAPP(c_COMBK(tc_fun(U_12783,tc_HOL_Obool),U_12783),U_12785))))
| c_Relation_Orefl__on(U_12783,U_12785,U_12787) ),
inference(clausify,[status(thm)],[f_3315_4]) ).
cnf(f_3315_8,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12783,U_12783)),hAPP(hAPP(c_Product__Type_OPair(U_12783,U_12783),sK281(U_12787,U_12785,U_12783)),sK281(U_12787,U_12785,U_12783))),U_12787))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12783,U_12783),tc_HOL_Obool)),U_12787),hAPP(hAPP(c_Product__Type_OSigma(U_12783,U_12783),U_12785),hAPP(c_COMBK(tc_fun(U_12783,tc_HOL_Obool),U_12783),U_12785))))
| c_Relation_Orefl__on(U_12783,U_12785,U_12787) ),
inference(clausify,[status(thm)],[f_3315_4]) ).
fof(f_3316_1,plain,
! [V_B_2,V_b_2,V_A_2,V_a_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_insert__times__insert]) ).
fof(f_3316_2,plain,
! [U_12793,U_12792,U_12791,U_12790,U_12789,U_12788] : hAPP(hAPP(c_Product__Type_OSigma(U_12788,U_12789),hAPP(hAPP(c_Set_Oinsert(U_12788),U_12790),U_12791)),hAPP(c_COMBK(tc_fun(U_12789,tc_HOL_Obool),U_12788),hAPP(hAPP(c_Set_Oinsert(U_12789),U_12792),U_12793))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(U_12788,U_12789)),hAPP(hAPP(c_Product__Type_OPair(U_12788,U_12789),U_12790),U_12792)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12788,U_12789),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12788,U_12789),U_12791),hAPP(c_COMBK(tc_fun(U_12789,tc_HOL_Obool),U_12788),hAPP(hAPP(c_Set_Oinsert(U_12789),U_12792),U_12793)))),hAPP(hAPP(c_Product__Type_OSigma(U_12788,U_12789),hAPP(hAPP(c_Set_Oinsert(U_12788),U_12790),U_12791)),hAPP(c_COMBK(tc_fun(U_12789,tc_HOL_Obool),U_12788),U_12793)))),
inference(variable_rename,[status(thm)],[f_3316_1]) ).
cnf(f_3316_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12788,U_12789),hAPP(hAPP(c_Set_Oinsert(U_12788),U_12790),U_12791)),hAPP(c_COMBK(tc_fun(U_12789,tc_HOL_Obool),U_12788),hAPP(hAPP(c_Set_Oinsert(U_12789),U_12792),U_12793))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(U_12788,U_12789)),hAPP(hAPP(c_Product__Type_OPair(U_12788,U_12789),U_12790),U_12792)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12788,U_12789),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12788,U_12789),U_12791),hAPP(c_COMBK(tc_fun(U_12789,tc_HOL_Obool),U_12788),hAPP(hAPP(c_Set_Oinsert(U_12789),U_12792),U_12793)))),hAPP(hAPP(c_Product__Type_OSigma(U_12788,U_12789),hAPP(hAPP(c_Set_Oinsert(U_12788),U_12790),U_12791)),hAPP(c_COMBK(tc_fun(U_12789,tc_HOL_Obool),U_12788),U_12793)))),
inference(clausify,[status(thm)],[f_3316_2]) ).
fof(f_3317_1,plain,
! [V_X_2,V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__equiv__class]) ).
fof(f_3317_2,plain,
! [U_12797,U_12796,U_12795,U_12794] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12794),U_12797))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12794,tc_HOL_Obool)),U_12797),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12794),U_12795),U_12796)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12794,U_12794),tc_HOL_Obool)),U_12796),hAPP(hAPP(c_Product__Type_OSigma(U_12794,U_12794),U_12795),hAPP(c_COMBK(tc_fun(U_12794,tc_HOL_Obool),U_12794),U_12795))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12794),U_12795)) ),
inference(variable_rename,[status(thm)],[f_3317_1]) ).
cnf(f_3317_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12794),U_12797))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_12794,tc_HOL_Obool)),U_12797),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12794),U_12795),U_12796)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12794,U_12794),tc_HOL_Obool)),U_12796),hAPP(hAPP(c_Product__Type_OSigma(U_12794,U_12794),U_12795),hAPP(c_COMBK(tc_fun(U_12794,tc_HOL_Obool),U_12794),U_12795))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12794),U_12795)) ),
inference(clausify,[status(thm)],[f_3317_2]) ).
fof(f_3318_1,plain,
! [V_F_2,V_E_2,V_B_2,V_A_2,T_c,T_b,T_e,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_d,T_e),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_d),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_d),c_Product__Type_OSigma(T_b,T_c)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_e),c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_F_2))),
inference(fof_nnf,[status(thm)],[fact_UN__Times__distrib]) ).
fof(f_3318_2,plain,
! [U_12805,U_12804,U_12803,U_12802,U_12801,U_12800,U_12799,U_12798] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(U_12798,U_12799),tc_fun(tc_prod(U_12800,U_12801),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12798,U_12799),U_12802),hAPP(c_COMBK(tc_fun(U_12799,tc_HOL_Obool),U_12798),U_12803))),hAPP(c_Product__Type_Oprod_Oprod__case(U_12798,U_12799,tc_fun(tc_prod(U_12800,U_12801),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_12798,tc_fun(U_12799,tc_fun(U_12800,tc_fun(U_12801,tc_HOL_Obool))),tc_fun(U_12799,tc_fun(tc_prod(U_12800,U_12801),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12800,tc_fun(U_12801,tc_HOL_Obool)),tc_fun(tc_prod(U_12800,U_12801),tc_HOL_Obool)),tc_fun(tc_fun(U_12799,tc_fun(U_12800,tc_fun(U_12801,tc_HOL_Obool))),tc_fun(U_12799,tc_fun(tc_prod(U_12800,U_12801),tc_HOL_Obool))),U_12798),c_COMBB(tc_fun(U_12800,tc_fun(U_12801,tc_HOL_Obool)),tc_fun(tc_prod(U_12800,U_12801),tc_HOL_Obool),U_12799)),hAPP(hAPP(c_COMBB(tc_fun(U_12800,tc_HOL_Obool),tc_fun(tc_fun(U_12800,tc_fun(U_12801,tc_HOL_Obool)),tc_fun(tc_prod(U_12800,U_12801),tc_HOL_Obool)),U_12798),c_Product__Type_OSigma(U_12800,U_12801)),U_12804))),hAPP(hAPP(c_COMBB(tc_fun(U_12801,tc_HOL_Obool),tc_fun(U_12800,tc_fun(U_12801,tc_HOL_Obool)),U_12799),c_COMBK(tc_fun(U_12801,tc_HOL_Obool),U_12800)),U_12805)))) = hAPP(hAPP(c_Product__Type_OSigma(U_12800,U_12801),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12798,tc_fun(U_12800,tc_HOL_Obool)),U_12802),U_12804)),hAPP(c_COMBK(tc_fun(U_12801,tc_HOL_Obool),U_12800),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12799,tc_fun(U_12801,tc_HOL_Obool)),U_12803),U_12805))),
inference(variable_rename,[status(thm)],[f_3318_1]) ).
cnf(f_3318_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(U_12798,U_12799),tc_fun(tc_prod(U_12800,U_12801),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_12798,U_12799),U_12802),hAPP(c_COMBK(tc_fun(U_12799,tc_HOL_Obool),U_12798),U_12803))),hAPP(c_Product__Type_Oprod_Oprod__case(U_12798,U_12799,tc_fun(tc_prod(U_12800,U_12801),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_12798,tc_fun(U_12799,tc_fun(U_12800,tc_fun(U_12801,tc_HOL_Obool))),tc_fun(U_12799,tc_fun(tc_prod(U_12800,U_12801),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_12800,tc_fun(U_12801,tc_HOL_Obool)),tc_fun(tc_prod(U_12800,U_12801),tc_HOL_Obool)),tc_fun(tc_fun(U_12799,tc_fun(U_12800,tc_fun(U_12801,tc_HOL_Obool))),tc_fun(U_12799,tc_fun(tc_prod(U_12800,U_12801),tc_HOL_Obool))),U_12798),c_COMBB(tc_fun(U_12800,tc_fun(U_12801,tc_HOL_Obool)),tc_fun(tc_prod(U_12800,U_12801),tc_HOL_Obool),U_12799)),hAPP(hAPP(c_COMBB(tc_fun(U_12800,tc_HOL_Obool),tc_fun(tc_fun(U_12800,tc_fun(U_12801,tc_HOL_Obool)),tc_fun(tc_prod(U_12800,U_12801),tc_HOL_Obool)),U_12798),c_Product__Type_OSigma(U_12800,U_12801)),U_12804))),hAPP(hAPP(c_COMBB(tc_fun(U_12801,tc_HOL_Obool),tc_fun(U_12800,tc_fun(U_12801,tc_HOL_Obool)),U_12799),c_COMBK(tc_fun(U_12801,tc_HOL_Obool),U_12800)),U_12805)))) = hAPP(hAPP(c_Product__Type_OSigma(U_12800,U_12801),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12798,tc_fun(U_12800,tc_HOL_Obool)),U_12802),U_12804)),hAPP(c_COMBK(tc_fun(U_12801,tc_HOL_Obool),U_12800),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12799,tc_fun(U_12801,tc_HOL_Obool)),U_12803),U_12805))),
inference(clausify,[status(thm)],[f_3318_2]) ).
fof(f_3319_1,plain,
! [V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))),
inference(fof_nnf,[status(thm)],[fact_Sigma__def]) ).
fof(f_3319_2,plain,
! [U_12809,U_12808,U_12807,U_12806] : hAPP(hAPP(c_Product__Type_OSigma(U_12806,U_12807),U_12808),U_12809) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12806,tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool)),U_12808),hAPP(hAPP(c_COMBS(U_12806,tc_fun(U_12807,tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool)),tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12807,tc_HOL_Obool),tc_fun(tc_fun(U_12807,tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool)),tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool)),U_12806),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12807,tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool))),U_12809)),hAPP(hAPP(c_COMBC(U_12806,tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool),tc_fun(U_12807,tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12807,tc_fun(tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool),tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool),tc_fun(U_12807,tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool))),U_12806),c_COMBC(U_12807,tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool),tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12807,tc_prod(U_12806,U_12807)),tc_fun(U_12807,tc_fun(tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool),tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool))),U_12806),hAPP(c_COMBB(tc_prod(U_12806,U_12807),tc_fun(tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool),tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool)),U_12807),c_Set_Oinsert(tc_prod(U_12806,U_12807)))),c_Product__Type_OPair(U_12806,U_12807)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_3319_1]) ).
cnf(f_3319_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_12806,U_12807),U_12808),U_12809) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12806,tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool)),U_12808),hAPP(hAPP(c_COMBS(U_12806,tc_fun(U_12807,tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool)),tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_12807,tc_HOL_Obool),tc_fun(tc_fun(U_12807,tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool)),tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool)),U_12806),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12807,tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool))),U_12809)),hAPP(hAPP(c_COMBC(U_12806,tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool),tc_fun(U_12807,tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12807,tc_fun(tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool),tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool),tc_fun(U_12807,tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool))),U_12806),c_COMBC(U_12807,tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool),tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_12807,tc_prod(U_12806,U_12807)),tc_fun(U_12807,tc_fun(tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool),tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool))),U_12806),hAPP(c_COMBB(tc_prod(U_12806,U_12807),tc_fun(tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool),tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool)),U_12807),c_Set_Oinsert(tc_prod(U_12806,U_12807)))),c_Product__Type_OPair(U_12806,U_12807)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_12806,U_12807),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_3319_2]) ).
fof(f_3320_1,plain,
! [V_a_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Osemilattice__inf(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__belowI]) ).
fof(f_3320_2,plain,
! [U_12812,U_12811,U_12810] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12810),hAPP(c_Finite__Set_Ofold1(U_12810,c_Lattices_Osemilattice__inf__class_Oinf(U_12810)),U_12811)),U_12812))
| ~ hBOOL(hAPP(hAPP(c_member(U_12810),U_12812),U_12811))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12810),U_12811))
| ~ class_Lattices_Osemilattice__inf(U_12810) ),
inference(variable_rename,[status(thm)],[f_3320_1]) ).
cnf(f_3320_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12810),hAPP(c_Finite__Set_Ofold1(U_12810,c_Lattices_Osemilattice__inf__class_Oinf(U_12810)),U_12811)),U_12812))
| ~ hBOOL(hAPP(hAPP(c_member(U_12810),U_12812),U_12811))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12810),U_12811))
| ~ class_Lattices_Osemilattice__inf(U_12810) ),
inference(clausify,[status(thm)],[f_3320_2]) ).
fof(f_3321_1,plain,
! [V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__quotient]) ).
fof(f_3321_2,plain,
! [U_12815,U_12814,U_12813] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_12813,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12813),U_12814),U_12815)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12813,U_12813),tc_HOL_Obool)),U_12815),hAPP(hAPP(c_Product__Type_OSigma(U_12813,U_12813),U_12814),hAPP(c_COMBK(tc_fun(U_12813,tc_HOL_Obool),U_12813),U_12814))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12813),U_12814)) ),
inference(variable_rename,[status(thm)],[f_3321_1]) ).
cnf(f_3321_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_12813,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12813),U_12814),U_12815)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12813,U_12813),tc_HOL_Obool)),U_12815),hAPP(hAPP(c_Product__Type_OSigma(U_12813,U_12813),U_12814),hAPP(c_COMBK(tc_fun(U_12813,tc_HOL_Obool),U_12813),U_12814))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12813),U_12814)) ),
inference(clausify,[status(thm)],[f_3321_2]) ).
fof(f_3322_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2))) ) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Osemilattice__inf(T_b) ),
inference(fof_nnf,[status(thm)],[fact_below__fold1__iff]) ).
fof(f_3322_2,plain,
! [U_12820,U_12819,U_12818] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12818),U_12820),hAPP(c_Finite__Set_Ofold1(U_12818,c_Lattices_Osemilattice__inf__class_Oinf(U_12818)),U_12819)))
| ? [U_12817] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12818),U_12820),U_12817))
& hBOOL(hAPP(hAPP(c_member(U_12818),U_12817),U_12819)) ) )
& ( ! [U_12816] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12818),U_12820),U_12816))
| ~ hBOOL(hAPP(hAPP(c_member(U_12818),U_12816),U_12819)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12818),U_12820),hAPP(c_Finite__Set_Ofold1(U_12818,c_Lattices_Osemilattice__inf__class_Oinf(U_12818)),U_12819))) ) )
| U_12819 = c_Orderings_Obot__class_Obot(tc_fun(U_12818,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12818),U_12819))
| ~ class_Lattices_Osemilattice__inf(U_12818) ),
inference(variable_rename,[status(thm)],[f_3322_1]) ).
fof(f_3322_3,plain,
! [U_12820,U_12819,U_12818] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12818),U_12820),hAPP(c_Finite__Set_Ofold1(U_12818,c_Lattices_Osemilattice__inf__class_Oinf(U_12818)),U_12819)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12818),U_12820),sK282(U_12820,U_12819,U_12818)))
& hBOOL(hAPP(hAPP(c_member(U_12818),sK282(U_12820,U_12819,U_12818)),U_12819)) ) )
& ( ! [U_12816] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12818),U_12820),U_12816))
| ~ hBOOL(hAPP(hAPP(c_member(U_12818),U_12816),U_12819)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12818),U_12820),hAPP(c_Finite__Set_Ofold1(U_12818,c_Lattices_Osemilattice__inf__class_Oinf(U_12818)),U_12819))) ) )
| U_12819 = c_Orderings_Obot__class_Obot(tc_fun(U_12818,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12818),U_12819))
| ~ class_Lattices_Osemilattice__inf(U_12818) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK282]),skolemize(U_12817,sK282(U_12820,U_12819,U_12818))],[f_3322_2]) ).
cnf(f_3322_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12818),U_12820),U_12816))
| ~ hBOOL(hAPP(hAPP(c_member(U_12818),U_12816),U_12819))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12818),U_12820),hAPP(c_Finite__Set_Ofold1(U_12818,c_Lattices_Osemilattice__inf__class_Oinf(U_12818)),U_12819)))
| U_12819 = c_Orderings_Obot__class_Obot(tc_fun(U_12818,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12818),U_12819))
| ~ class_Lattices_Osemilattice__inf(U_12818) ),
inference(clausify,[status(thm)],[f_3322_3]) ).
cnf(f_3322_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_12818),sK282(U_12820,U_12819,U_12818)),U_12819))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12818),U_12820),hAPP(c_Finite__Set_Ofold1(U_12818,c_Lattices_Osemilattice__inf__class_Oinf(U_12818)),U_12819)))
| U_12819 = c_Orderings_Obot__class_Obot(tc_fun(U_12818,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12818),U_12819))
| ~ class_Lattices_Osemilattice__inf(U_12818) ),
inference(clausify,[status(thm)],[f_3322_3]) ).
cnf(f_3322_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12818),U_12820),sK282(U_12820,U_12819,U_12818)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12818),U_12820),hAPP(c_Finite__Set_Ofold1(U_12818,c_Lattices_Osemilattice__inf__class_Oinf(U_12818)),U_12819)))
| U_12819 = c_Orderings_Obot__class_Obot(tc_fun(U_12818,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12818),U_12819))
| ~ class_Lattices_Osemilattice__inf(U_12818) ),
inference(clausify,[status(thm)],[f_3322_3]) ).
fof(f_3323_1,plain,
! [V_a_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofold1__belowI]) ).
fof(f_3323_2,plain,
! [U_12823,U_12822,U_12821] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12821),hAPP(c_Finite__Set_Ofold1(U_12821,c_Orderings_Oord__class_Omin(U_12821)),U_12822)),U_12823))
| ~ hBOOL(hAPP(hAPP(c_member(U_12821),U_12823),U_12822))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12821),U_12822))
| ~ class_Orderings_Olinorder(U_12821) ),
inference(variable_rename,[status(thm)],[f_3323_1]) ).
cnf(f_3323_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12821),hAPP(c_Finite__Set_Ofold1(U_12821,c_Orderings_Oord__class_Omin(U_12821)),U_12822)),U_12823))
| ~ hBOOL(hAPP(hAPP(c_member(U_12821),U_12823),U_12822))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12821),U_12822))
| ~ class_Orderings_Olinorder(U_12821) ),
inference(clausify,[status(thm)],[f_3323_2]) ).
fof(f_3324_1,plain,
! [V_x_2,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__insert__idem]) ).
fof(f_3324_2,plain,
! [U_12826,U_12825,U_12824] :
( hAPP(c_Finite__Set_Ofold1(U_12824,c_Groups_Otimes__class_Otimes(U_12824)),hAPP(hAPP(c_Set_Oinsert(U_12824),U_12826),U_12825)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12824),U_12826),hAPP(c_Finite__Set_Ofold1(U_12824,c_Groups_Otimes__class_Otimes(U_12824)),U_12825))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12824),U_12825))
| U_12825 = c_Orderings_Obot__class_Obot(tc_fun(U_12824,tc_HOL_Obool))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_12824) ),
inference(variable_rename,[status(thm)],[f_3324_1]) ).
cnf(f_3324_3,plain,
( hAPP(c_Finite__Set_Ofold1(U_12824,c_Groups_Otimes__class_Otimes(U_12824)),hAPP(hAPP(c_Set_Oinsert(U_12824),U_12826),U_12825)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12824),U_12826),hAPP(c_Finite__Set_Ofold1(U_12824,c_Groups_Otimes__class_Otimes(U_12824)),U_12825))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12824),U_12825))
| U_12825 = c_Orderings_Obot__class_Obot(tc_fun(U_12824,tc_HOL_Obool))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_12824) ),
inference(clausify,[status(thm)],[f_3324_2]) ).
fof(f_3325_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2)) ) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__below__iff]) ).
fof(f_3325_2,plain,
! [U_12831,U_12830,U_12829] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12829),hAPP(c_Finite__Set_Ofold1(U_12829,c_Orderings_Oord__class_Omin(U_12829)),U_12830)),U_12831))
| ! [U_12828] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12829),U_12828),U_12831))
| ~ hBOOL(hAPP(hAPP(c_member(U_12829),U_12828),U_12830)) ) )
& ( ? [U_12827] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12829),U_12827),U_12831))
& hBOOL(hAPP(hAPP(c_member(U_12829),U_12827),U_12830)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12829),hAPP(c_Finite__Set_Ofold1(U_12829,c_Orderings_Oord__class_Omin(U_12829)),U_12830)),U_12831)) ) )
| U_12830 = c_Orderings_Obot__class_Obot(tc_fun(U_12829,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12829),U_12830))
| ~ class_Orderings_Olinorder(U_12829) ),
inference(variable_rename,[status(thm)],[f_3325_1]) ).
fof(f_3325_3,plain,
! [U_12831,U_12830,U_12829] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12829),hAPP(c_Finite__Set_Ofold1(U_12829,c_Orderings_Oord__class_Omin(U_12829)),U_12830)),U_12831))
| ! [U_12828] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12829),U_12828),U_12831))
| ~ hBOOL(hAPP(hAPP(c_member(U_12829),U_12828),U_12830)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12829),sK283(U_12831,U_12830,U_12829)),U_12831))
& hBOOL(hAPP(hAPP(c_member(U_12829),sK283(U_12831,U_12830,U_12829)),U_12830)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12829),hAPP(c_Finite__Set_Ofold1(U_12829,c_Orderings_Oord__class_Omin(U_12829)),U_12830)),U_12831)) ) )
| U_12830 = c_Orderings_Obot__class_Obot(tc_fun(U_12829,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12829),U_12830))
| ~ class_Orderings_Olinorder(U_12829) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK283]),skolemize(U_12827,sK283(U_12831,U_12830,U_12829))],[f_3325_2]) ).
cnf(f_3325_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12829),sK283(U_12831,U_12830,U_12829)),U_12830))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12829),hAPP(c_Finite__Set_Ofold1(U_12829,c_Orderings_Oord__class_Omin(U_12829)),U_12830)),U_12831))
| U_12830 = c_Orderings_Obot__class_Obot(tc_fun(U_12829,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12829),U_12830))
| ~ class_Orderings_Olinorder(U_12829) ),
inference(clausify,[status(thm)],[f_3325_3]) ).
cnf(f_3325_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12829),sK283(U_12831,U_12830,U_12829)),U_12831))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12829),hAPP(c_Finite__Set_Ofold1(U_12829,c_Orderings_Oord__class_Omin(U_12829)),U_12830)),U_12831))
| U_12830 = c_Orderings_Obot__class_Obot(tc_fun(U_12829,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12829),U_12830))
| ~ class_Orderings_Olinorder(U_12829) ),
inference(clausify,[status(thm)],[f_3325_3]) ).
cnf(f_3325_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12829),hAPP(c_Finite__Set_Ofold1(U_12829,c_Orderings_Oord__class_Omin(U_12829)),U_12830)),U_12831))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12829),U_12828),U_12831))
| ~ hBOOL(hAPP(hAPP(c_member(U_12829),U_12828),U_12830))
| U_12830 = c_Orderings_Obot__class_Obot(tc_fun(U_12829,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12829),U_12830))
| ~ class_Orderings_Olinorder(U_12829) ),
inference(clausify,[status(thm)],[f_3325_3]) ).
fof(f_3326_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) ) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Obelow__fold1__iff]) ).
fof(f_3326_2,plain,
! [U_12836,U_12835,U_12834] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12834),U_12836),hAPP(c_Finite__Set_Ofold1(U_12834,c_Orderings_Oord__class_Omin(U_12834)),U_12835)))
| ? [U_12833] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12834),U_12836),U_12833))
& hBOOL(hAPP(hAPP(c_member(U_12834),U_12833),U_12835)) ) )
& ( ! [U_12832] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12834),U_12836),U_12832))
| ~ hBOOL(hAPP(hAPP(c_member(U_12834),U_12832),U_12835)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12834),U_12836),hAPP(c_Finite__Set_Ofold1(U_12834,c_Orderings_Oord__class_Omin(U_12834)),U_12835))) ) )
| U_12835 = c_Orderings_Obot__class_Obot(tc_fun(U_12834,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12834),U_12835))
| ~ class_Orderings_Olinorder(U_12834) ),
inference(variable_rename,[status(thm)],[f_3326_1]) ).
fof(f_3326_3,plain,
! [U_12836,U_12835,U_12834] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12834),U_12836),hAPP(c_Finite__Set_Ofold1(U_12834,c_Orderings_Oord__class_Omin(U_12834)),U_12835)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12834),U_12836),sK284(U_12836,U_12835,U_12834)))
& hBOOL(hAPP(hAPP(c_member(U_12834),sK284(U_12836,U_12835,U_12834)),U_12835)) ) )
& ( ! [U_12832] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12834),U_12836),U_12832))
| ~ hBOOL(hAPP(hAPP(c_member(U_12834),U_12832),U_12835)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12834),U_12836),hAPP(c_Finite__Set_Ofold1(U_12834,c_Orderings_Oord__class_Omin(U_12834)),U_12835))) ) )
| U_12835 = c_Orderings_Obot__class_Obot(tc_fun(U_12834,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12834),U_12835))
| ~ class_Orderings_Olinorder(U_12834) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK284]),skolemize(U_12833,sK284(U_12836,U_12835,U_12834))],[f_3326_2]) ).
cnf(f_3326_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12834),U_12836),U_12832))
| ~ hBOOL(hAPP(hAPP(c_member(U_12834),U_12832),U_12835))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12834),U_12836),hAPP(c_Finite__Set_Ofold1(U_12834,c_Orderings_Oord__class_Omin(U_12834)),U_12835)))
| U_12835 = c_Orderings_Obot__class_Obot(tc_fun(U_12834,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12834),U_12835))
| ~ class_Orderings_Olinorder(U_12834) ),
inference(clausify,[status(thm)],[f_3326_3]) ).
cnf(f_3326_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_12834),sK284(U_12836,U_12835,U_12834)),U_12835))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12834),U_12836),hAPP(c_Finite__Set_Ofold1(U_12834,c_Orderings_Oord__class_Omin(U_12834)),U_12835)))
| U_12835 = c_Orderings_Obot__class_Obot(tc_fun(U_12834,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12834),U_12835))
| ~ class_Orderings_Olinorder(U_12834) ),
inference(clausify,[status(thm)],[f_3326_3]) ).
cnf(f_3326_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12834),U_12836),sK284(U_12836,U_12835,U_12834)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12834),U_12836),hAPP(c_Finite__Set_Ofold1(U_12834,c_Orderings_Oord__class_Omin(U_12834)),U_12835)))
| U_12835 = c_Orderings_Obot__class_Obot(tc_fun(U_12834,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12834),U_12835))
| ~ class_Orderings_Olinorder(U_12834) ),
inference(clausify,[status(thm)],[f_3326_3]) ).
fof(f_3327_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__Un2]) ).
fof(f_3327_2,plain,
! [U_12839,U_12838,U_12837] :
( hAPP(c_Finite__Set_Ofold1(U_12837,c_Groups_Otimes__class_Otimes(U_12837)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12837,tc_HOL_Obool)),U_12838),U_12839)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12837),hAPP(c_Finite__Set_Ofold1(U_12837,c_Groups_Otimes__class_Otimes(U_12837)),U_12838)),hAPP(c_Finite__Set_Ofold1(U_12837,c_Groups_Otimes__class_Otimes(U_12837)),U_12839))
| U_12839 = c_Orderings_Obot__class_Obot(tc_fun(U_12837,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12837),U_12839))
| U_12838 = c_Orderings_Obot__class_Obot(tc_fun(U_12837,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12837),U_12838))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_12837) ),
inference(variable_rename,[status(thm)],[f_3327_1]) ).
cnf(f_3327_3,plain,
( hAPP(c_Finite__Set_Ofold1(U_12837,c_Groups_Otimes__class_Otimes(U_12837)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12837,tc_HOL_Obool)),U_12838),U_12839)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12837),hAPP(c_Finite__Set_Ofold1(U_12837,c_Groups_Otimes__class_Otimes(U_12837)),U_12838)),hAPP(c_Finite__Set_Ofold1(U_12837,c_Groups_Otimes__class_Otimes(U_12837)),U_12839))
| U_12839 = c_Orderings_Obot__class_Obot(tc_fun(U_12837,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12837),U_12839))
| U_12838 = c_Orderings_Obot__class_Obot(tc_fun(U_12837,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12837),U_12838))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_12837) ),
inference(clausify,[status(thm)],[f_3327_2]) ).
fof(f_3328_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) ) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_strict__below__fold1__iff]) ).
fof(f_3328_2,plain,
! [U_12844,U_12843,U_12842] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12842),U_12844),hAPP(c_Finite__Set_Ofold1(U_12842,c_Orderings_Oord__class_Omin(U_12842)),U_12843)))
| ? [U_12841] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12842),U_12844),U_12841))
& hBOOL(hAPP(hAPP(c_member(U_12842),U_12841),U_12843)) ) )
& ( ! [U_12840] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12842),U_12844),U_12840))
| ~ hBOOL(hAPP(hAPP(c_member(U_12842),U_12840),U_12843)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12842),U_12844),hAPP(c_Finite__Set_Ofold1(U_12842,c_Orderings_Oord__class_Omin(U_12842)),U_12843))) ) )
| U_12843 = c_Orderings_Obot__class_Obot(tc_fun(U_12842,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12842),U_12843))
| ~ class_Orderings_Olinorder(U_12842) ),
inference(variable_rename,[status(thm)],[f_3328_1]) ).
fof(f_3328_3,plain,
! [U_12844,U_12843,U_12842] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12842),U_12844),hAPP(c_Finite__Set_Ofold1(U_12842,c_Orderings_Oord__class_Omin(U_12842)),U_12843)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12842),U_12844),sK285(U_12844,U_12843,U_12842)))
& hBOOL(hAPP(hAPP(c_member(U_12842),sK285(U_12844,U_12843,U_12842)),U_12843)) ) )
& ( ! [U_12840] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12842),U_12844),U_12840))
| ~ hBOOL(hAPP(hAPP(c_member(U_12842),U_12840),U_12843)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12842),U_12844),hAPP(c_Finite__Set_Ofold1(U_12842,c_Orderings_Oord__class_Omin(U_12842)),U_12843))) ) )
| U_12843 = c_Orderings_Obot__class_Obot(tc_fun(U_12842,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12842),U_12843))
| ~ class_Orderings_Olinorder(U_12842) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK285]),skolemize(U_12841,sK285(U_12844,U_12843,U_12842))],[f_3328_2]) ).
cnf(f_3328_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12842),U_12844),U_12840))
| ~ hBOOL(hAPP(hAPP(c_member(U_12842),U_12840),U_12843))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12842),U_12844),hAPP(c_Finite__Set_Ofold1(U_12842,c_Orderings_Oord__class_Omin(U_12842)),U_12843)))
| U_12843 = c_Orderings_Obot__class_Obot(tc_fun(U_12842,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12842),U_12843))
| ~ class_Orderings_Olinorder(U_12842) ),
inference(clausify,[status(thm)],[f_3328_3]) ).
cnf(f_3328_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_12842),sK285(U_12844,U_12843,U_12842)),U_12843))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12842),U_12844),hAPP(c_Finite__Set_Ofold1(U_12842,c_Orderings_Oord__class_Omin(U_12842)),U_12843)))
| U_12843 = c_Orderings_Obot__class_Obot(tc_fun(U_12842,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12842),U_12843))
| ~ class_Orderings_Olinorder(U_12842) ),
inference(clausify,[status(thm)],[f_3328_3]) ).
cnf(f_3328_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12842),U_12844),sK285(U_12844,U_12843,U_12842)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12842),U_12844),hAPP(c_Finite__Set_Ofold1(U_12842,c_Orderings_Oord__class_Omin(U_12842)),U_12843)))
| U_12843 = c_Orderings_Obot__class_Obot(tc_fun(U_12842,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12842),U_12843))
| ~ class_Orderings_Olinorder(U_12842) ),
inference(clausify,[status(thm)],[f_3328_3]) ).
fof(f_3329_1,plain,
! [V_x_2,V_A_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2)) ) )
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__strict__below__iff]) ).
fof(f_3329_2,plain,
! [U_12849,U_12848,U_12847] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12847),hAPP(c_Finite__Set_Ofold1(U_12847,c_Orderings_Oord__class_Omin(U_12847)),U_12848)),U_12849))
| ! [U_12846] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12847),U_12846),U_12849))
| ~ hBOOL(hAPP(hAPP(c_member(U_12847),U_12846),U_12848)) ) )
& ( ? [U_12845] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12847),U_12845),U_12849))
& hBOOL(hAPP(hAPP(c_member(U_12847),U_12845),U_12848)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12847),hAPP(c_Finite__Set_Ofold1(U_12847,c_Orderings_Oord__class_Omin(U_12847)),U_12848)),U_12849)) ) )
| U_12848 = c_Orderings_Obot__class_Obot(tc_fun(U_12847,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12847),U_12848))
| ~ class_Orderings_Olinorder(U_12847) ),
inference(variable_rename,[status(thm)],[f_3329_1]) ).
fof(f_3329_3,plain,
! [U_12849,U_12848,U_12847] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12847),hAPP(c_Finite__Set_Ofold1(U_12847,c_Orderings_Oord__class_Omin(U_12847)),U_12848)),U_12849))
| ! [U_12846] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12847),U_12846),U_12849))
| ~ hBOOL(hAPP(hAPP(c_member(U_12847),U_12846),U_12848)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12847),sK286(U_12849,U_12848,U_12847)),U_12849))
& hBOOL(hAPP(hAPP(c_member(U_12847),sK286(U_12849,U_12848,U_12847)),U_12848)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12847),hAPP(c_Finite__Set_Ofold1(U_12847,c_Orderings_Oord__class_Omin(U_12847)),U_12848)),U_12849)) ) )
| U_12848 = c_Orderings_Obot__class_Obot(tc_fun(U_12847,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12847),U_12848))
| ~ class_Orderings_Olinorder(U_12847) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK286]),skolemize(U_12845,sK286(U_12849,U_12848,U_12847))],[f_3329_2]) ).
cnf(f_3329_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12847),sK286(U_12849,U_12848,U_12847)),U_12848))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12847),hAPP(c_Finite__Set_Ofold1(U_12847,c_Orderings_Oord__class_Omin(U_12847)),U_12848)),U_12849))
| U_12848 = c_Orderings_Obot__class_Obot(tc_fun(U_12847,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12847),U_12848))
| ~ class_Orderings_Olinorder(U_12847) ),
inference(clausify,[status(thm)],[f_3329_3]) ).
cnf(f_3329_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12847),sK286(U_12849,U_12848,U_12847)),U_12849))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12847),hAPP(c_Finite__Set_Ofold1(U_12847,c_Orderings_Oord__class_Omin(U_12847)),U_12848)),U_12849))
| U_12848 = c_Orderings_Obot__class_Obot(tc_fun(U_12847,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12847),U_12848))
| ~ class_Orderings_Olinorder(U_12847) ),
inference(clausify,[status(thm)],[f_3329_3]) ).
cnf(f_3329_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12847),hAPP(c_Finite__Set_Ofold1(U_12847,c_Orderings_Oord__class_Omin(U_12847)),U_12848)),U_12849))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12847),U_12846),U_12849))
| ~ hBOOL(hAPP(hAPP(c_member(U_12847),U_12846),U_12848))
| U_12848 = c_Orderings_Obot__class_Obot(tc_fun(U_12847,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12847),U_12848))
| ~ class_Orderings_Olinorder(U_12847) ),
inference(clausify,[status(thm)],[f_3329_3]) ).
fof(f_3330_1,plain,
! [V_x_2,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Groups_Oab__semigroup__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__insert]) ).
fof(f_3330_2,plain,
! [U_12852,U_12851,U_12850] :
( hAPP(c_Finite__Set_Ofold1(U_12850,c_Groups_Otimes__class_Otimes(U_12850)),hAPP(hAPP(c_Set_Oinsert(U_12850),U_12852),U_12851)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12850),U_12852),hAPP(c_Finite__Set_Ofold1(U_12850,c_Groups_Otimes__class_Otimes(U_12850)),U_12851))
| hBOOL(hAPP(hAPP(c_member(U_12850),U_12852),U_12851))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12850),U_12851))
| U_12851 = c_Orderings_Obot__class_Obot(tc_fun(U_12850,tc_HOL_Obool))
| ~ class_Groups_Oab__semigroup__mult(U_12850) ),
inference(variable_rename,[status(thm)],[f_3330_1]) ).
cnf(f_3330_3,plain,
( hAPP(c_Finite__Set_Ofold1(U_12850,c_Groups_Otimes__class_Otimes(U_12850)),hAPP(hAPP(c_Set_Oinsert(U_12850),U_12852),U_12851)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12850),U_12852),hAPP(c_Finite__Set_Ofold1(U_12850,c_Groups_Otimes__class_Otimes(U_12850)),U_12851))
| hBOOL(hAPP(hAPP(c_member(U_12850),U_12852),U_12851))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12850),U_12851))
| U_12851 = c_Orderings_Obot__class_Obot(tc_fun(U_12850,tc_HOL_Obool))
| ~ class_Groups_Oab__semigroup__mult(U_12850) ),
inference(clausify,[status(thm)],[f_3330_2]) ).
fof(f_3331_1,plain,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__antimono]) ).
fof(f_3331_2,plain,
! [U_12855,U_12854,U_12853] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12853),hAPP(c_Finite__Set_Ofold1(U_12853,c_Orderings_Oord__class_Omin(U_12853)),U_12855)),hAPP(c_Finite__Set_Ofold1(U_12853,c_Orderings_Oord__class_Omin(U_12853)),U_12854)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12853),U_12855))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12853,tc_HOL_Obool)),U_12854),U_12855))
| U_12854 = c_Orderings_Obot__class_Obot(tc_fun(U_12853,tc_HOL_Obool))
| ~ class_Orderings_Olinorder(U_12853) ),
inference(variable_rename,[status(thm)],[f_3331_1]) ).
cnf(f_3331_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12853),hAPP(c_Finite__Set_Ofold1(U_12853,c_Orderings_Oord__class_Omin(U_12853)),U_12855)),hAPP(c_Finite__Set_Ofold1(U_12853,c_Orderings_Oord__class_Omin(U_12853)),U_12854)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12853),U_12855))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12853,tc_HOL_Obool)),U_12854),U_12855))
| U_12854 = c_Orderings_Obot__class_Obot(tc_fun(U_12853,tc_HOL_Obool))
| ~ class_Orderings_Olinorder(U_12853) ),
inference(clausify,[status(thm)],[f_3331_2]) ).
fof(f_3332_1,plain,
! [V_A_2,V_F_2,V_f_2,T_b] :
( hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_semilattice__big_OF__eq]) ).
fof(f_3332_2,plain,
! [U_12859,U_12858,U_12857,U_12856] :
( hAPP(U_12858,U_12859) = hAPP(c_Finite__Set_Ofold1(U_12856,U_12857),U_12859)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12856),U_12859))
| ~ c_Big__Operators_Osemilattice__big(U_12856,U_12857,U_12858) ),
inference(variable_rename,[status(thm)],[f_3332_1]) ).
cnf(f_3332_3,plain,
( hAPP(U_12858,U_12859) = hAPP(c_Finite__Set_Ofold1(U_12856,U_12857),U_12859)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12856),U_12859))
| ~ c_Big__Operators_Osemilattice__big(U_12856,U_12857,U_12858) ),
inference(clausify,[status(thm)],[f_3332_2]) ).
fof(f_3333_1,plain,
! [V_A_2,V_I_2,T_c,T_b] :
? [B_f] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_prod(T_c,T_b),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_I_2),V_A_2)))
& c_Fun_Oinj__on(T_b,tc_prod(T_c,T_b),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Ex__inj__on__UNION__Sigma]) ).
fof(f_3333_2,plain,
! [U_12864,U_12863,U_12862,U_12861] :
? [U_12860] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12862,U_12861),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12861,tc_prod(U_12862,U_12861),U_12860),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12862,tc_fun(U_12861,tc_HOL_Obool)),U_12863),U_12864))),hAPP(hAPP(c_Product__Type_OSigma(U_12862,U_12861),U_12863),U_12864)))
& c_Fun_Oinj__on(U_12861,tc_prod(U_12862,U_12861),U_12860,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12862,tc_fun(U_12861,tc_HOL_Obool)),U_12863),U_12864)) ),
inference(variable_rename,[status(thm)],[f_3333_1]) ).
fof(f_3333_3,plain,
! [U_12864,U_12863,U_12862,U_12861] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12862,U_12861),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12861,tc_prod(U_12862,U_12861),sK287(U_12864,U_12863,U_12862,U_12861)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12862,tc_fun(U_12861,tc_HOL_Obool)),U_12863),U_12864))),hAPP(hAPP(c_Product__Type_OSigma(U_12862,U_12861),U_12863),U_12864)))
& c_Fun_Oinj__on(U_12861,tc_prod(U_12862,U_12861),sK287(U_12864,U_12863,U_12862,U_12861),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12862,tc_fun(U_12861,tc_HOL_Obool)),U_12863),U_12864)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK287]),skolemize(U_12860,sK287(U_12864,U_12863,U_12862,U_12861))],[f_3333_2]) ).
cnf(f_3333_4,plain,
c_Fun_Oinj__on(U_12861,tc_prod(U_12862,U_12861),sK287(U_12864,U_12863,U_12862,U_12861),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12862,tc_fun(U_12861,tc_HOL_Obool)),U_12863),U_12864)),
inference(clausify,[status(thm)],[f_3333_3]) ).
cnf(f_3333_5,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12862,U_12861),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_12861,tc_prod(U_12862,U_12861),sK287(U_12864,U_12863,U_12862,U_12861)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_12862,tc_fun(U_12861,tc_HOL_Obool)),U_12863),U_12864))),hAPP(hAPP(c_Product__Type_OSigma(U_12862,U_12861),U_12863),U_12864))),
inference(clausify,[status(thm)],[f_3333_3]) ).
fof(f_3334_1,plain,
! [V_A_2,V_r_2,T_b] :
( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ),
inference(fof_nnf,[status(thm)],[fact_refl__onI]) ).
fof(f_3334_2,plain,
! [U_12868,U_12867,U_12866] :
( c_Relation_Orefl__on(U_12866,U_12868,U_12867)
| ? [U_12865] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12866,U_12866)),hAPP(hAPP(c_Product__Type_OPair(U_12866,U_12866),U_12865),U_12865)),U_12867))
& hBOOL(hAPP(hAPP(c_member(U_12866),U_12865),U_12868)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12866,U_12866),tc_HOL_Obool)),U_12867),hAPP(hAPP(c_Product__Type_OSigma(U_12866,U_12866),U_12868),hAPP(c_COMBK(tc_fun(U_12866,tc_HOL_Obool),U_12866),U_12868)))) ),
inference(variable_rename,[status(thm)],[f_3334_1]) ).
fof(f_3334_3,plain,
! [U_12868,U_12867,U_12866] :
( c_Relation_Orefl__on(U_12866,U_12868,U_12867)
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12866,U_12866)),hAPP(hAPP(c_Product__Type_OPair(U_12866,U_12866),sK288(U_12868,U_12867,U_12866)),sK288(U_12868,U_12867,U_12866))),U_12867))
& hBOOL(hAPP(hAPP(c_member(U_12866),sK288(U_12868,U_12867,U_12866)),U_12868)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12866,U_12866),tc_HOL_Obool)),U_12867),hAPP(hAPP(c_Product__Type_OSigma(U_12866,U_12866),U_12868),hAPP(c_COMBK(tc_fun(U_12866,tc_HOL_Obool),U_12866),U_12868)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK288]),skolemize(U_12865,sK288(U_12868,U_12867,U_12866))],[f_3334_2]) ).
cnf(f_3334_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12866),sK288(U_12868,U_12867,U_12866)),U_12868))
| c_Relation_Orefl__on(U_12866,U_12868,U_12867)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12866,U_12866),tc_HOL_Obool)),U_12867),hAPP(hAPP(c_Product__Type_OSigma(U_12866,U_12866),U_12868),hAPP(c_COMBK(tc_fun(U_12866,tc_HOL_Obool),U_12866),U_12868)))) ),
inference(clausify,[status(thm)],[f_3334_3]) ).
cnf(f_3334_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12866,U_12866)),hAPP(hAPP(c_Product__Type_OPair(U_12866,U_12866),sK288(U_12868,U_12867,U_12866)),sK288(U_12868,U_12867,U_12866))),U_12867))
| c_Relation_Orefl__on(U_12866,U_12868,U_12867)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12866,U_12866),tc_HOL_Obool)),U_12867),hAPP(hAPP(c_Product__Type_OSigma(U_12866,U_12866),U_12868),hAPP(c_COMBK(tc_fun(U_12866,tc_HOL_Obool),U_12866),U_12868)))) ),
inference(clausify,[status(thm)],[f_3334_3]) ).
fof(f_3335_1,plain,
! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))
| ? [B_x] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod__Sigma]) ).
fof(f_3335_2,plain,
! [U_12875,U_12874,U_12873,U_12872,U_12871,U_12870] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12871,U_12870),hAPP(hAPP(c_COMBS(U_12871,tc_fun(U_12873,tc_HOL_Obool),U_12870),hAPP(hAPP(c_COMBB(tc_fun(U_12873,U_12870),tc_fun(tc_fun(U_12873,tc_HOL_Obool),U_12870),U_12871),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12873,U_12870)),U_12875)),U_12874)),U_12872) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12871,U_12873),U_12870),hAPP(c_Product__Type_Oprod_Oprod__case(U_12871,U_12873,U_12870),U_12875)),hAPP(hAPP(c_Product__Type_OSigma(U_12871,U_12873),U_12872),U_12874))
| ? [U_12869] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12873),hAPP(U_12874,U_12869)))
& hBOOL(hAPP(hAPP(c_member(U_12871),U_12869),U_12872)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12871),U_12872))
| ~ class_Groups_Ocomm__monoid__mult(U_12870) ),
inference(variable_rename,[status(thm)],[f_3335_1]) ).
fof(f_3335_3,plain,
! [U_12875,U_12874,U_12873,U_12872,U_12871,U_12870] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12871,U_12870),hAPP(hAPP(c_COMBS(U_12871,tc_fun(U_12873,tc_HOL_Obool),U_12870),hAPP(hAPP(c_COMBB(tc_fun(U_12873,U_12870),tc_fun(tc_fun(U_12873,tc_HOL_Obool),U_12870),U_12871),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12873,U_12870)),U_12875)),U_12874)),U_12872) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12871,U_12873),U_12870),hAPP(c_Product__Type_Oprod_Oprod__case(U_12871,U_12873,U_12870),U_12875)),hAPP(hAPP(c_Product__Type_OSigma(U_12871,U_12873),U_12872),U_12874))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12873),hAPP(U_12874,sK289(U_12875,U_12874,U_12873,U_12872,U_12871,U_12870))))
& hBOOL(hAPP(hAPP(c_member(U_12871),sK289(U_12875,U_12874,U_12873,U_12872,U_12871,U_12870)),U_12872)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12871),U_12872))
| ~ class_Groups_Ocomm__monoid__mult(U_12870) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK289]),skolemize(U_12869,sK289(U_12875,U_12874,U_12873,U_12872,U_12871,U_12870))],[f_3335_2]) ).
cnf(f_3335_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12871),sK289(U_12875,U_12874,U_12873,U_12872,U_12871,U_12870)),U_12872))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12871,U_12870),hAPP(hAPP(c_COMBS(U_12871,tc_fun(U_12873,tc_HOL_Obool),U_12870),hAPP(hAPP(c_COMBB(tc_fun(U_12873,U_12870),tc_fun(tc_fun(U_12873,tc_HOL_Obool),U_12870),U_12871),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12873,U_12870)),U_12875)),U_12874)),U_12872) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12871,U_12873),U_12870),hAPP(c_Product__Type_Oprod_Oprod__case(U_12871,U_12873,U_12870),U_12875)),hAPP(hAPP(c_Product__Type_OSigma(U_12871,U_12873),U_12872),U_12874))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12871),U_12872))
| ~ class_Groups_Ocomm__monoid__mult(U_12870) ),
inference(clausify,[status(thm)],[f_3335_3]) ).
cnf(f_3335_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12873),hAPP(U_12874,sK289(U_12875,U_12874,U_12873,U_12872,U_12871,U_12870))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12871,U_12870),hAPP(hAPP(c_COMBS(U_12871,tc_fun(U_12873,tc_HOL_Obool),U_12870),hAPP(hAPP(c_COMBB(tc_fun(U_12873,U_12870),tc_fun(tc_fun(U_12873,tc_HOL_Obool),U_12870),U_12871),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_12873,U_12870)),U_12875)),U_12874)),U_12872) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_12871,U_12873),U_12870),hAPP(c_Product__Type_Oprod_Oprod__case(U_12871,U_12873,U_12870),U_12875)),hAPP(hAPP(c_Product__Type_OSigma(U_12871,U_12873),U_12872),U_12874))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12871),U_12872))
| ~ class_Groups_Ocomm__monoid__mult(U_12870) ),
inference(clausify,[status(thm)],[f_3335_3]) ).
fof(f_3336_1,plain,
! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_b,T_c),T_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))
| ? [B_x] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__Sigma]) ).
fof(f_3336_2,plain,
! [U_12882,U_12881,U_12880,U_12879,U_12878,U_12877] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12878,U_12877),hAPP(hAPP(c_COMBS(U_12878,tc_fun(U_12880,tc_HOL_Obool),U_12877),hAPP(hAPP(c_COMBB(tc_fun(U_12880,U_12877),tc_fun(tc_fun(U_12880,tc_HOL_Obool),U_12877),U_12878),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12880,U_12877)),U_12882)),U_12881)),U_12879) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12878,U_12880),U_12877),hAPP(c_Product__Type_Oprod_Oprod__case(U_12878,U_12880,U_12877),U_12882)),hAPP(hAPP(c_Product__Type_OSigma(U_12878,U_12880),U_12879),U_12881))
| ? [U_12876] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12880),hAPP(U_12881,U_12876)))
& hBOOL(hAPP(hAPP(c_member(U_12878),U_12876),U_12879)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12878),U_12879))
| ~ class_Groups_Ocomm__monoid__add(U_12877) ),
inference(variable_rename,[status(thm)],[f_3336_1]) ).
fof(f_3336_3,plain,
! [U_12882,U_12881,U_12880,U_12879,U_12878,U_12877] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12878,U_12877),hAPP(hAPP(c_COMBS(U_12878,tc_fun(U_12880,tc_HOL_Obool),U_12877),hAPP(hAPP(c_COMBB(tc_fun(U_12880,U_12877),tc_fun(tc_fun(U_12880,tc_HOL_Obool),U_12877),U_12878),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12880,U_12877)),U_12882)),U_12881)),U_12879) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12878,U_12880),U_12877),hAPP(c_Product__Type_Oprod_Oprod__case(U_12878,U_12880,U_12877),U_12882)),hAPP(hAPP(c_Product__Type_OSigma(U_12878,U_12880),U_12879),U_12881))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12880),hAPP(U_12881,sK290(U_12882,U_12881,U_12880,U_12879,U_12878,U_12877))))
& hBOOL(hAPP(hAPP(c_member(U_12878),sK290(U_12882,U_12881,U_12880,U_12879,U_12878,U_12877)),U_12879)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12878),U_12879))
| ~ class_Groups_Ocomm__monoid__add(U_12877) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK290]),skolemize(U_12876,sK290(U_12882,U_12881,U_12880,U_12879,U_12878,U_12877))],[f_3336_2]) ).
cnf(f_3336_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12878),sK290(U_12882,U_12881,U_12880,U_12879,U_12878,U_12877)),U_12879))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12878,U_12877),hAPP(hAPP(c_COMBS(U_12878,tc_fun(U_12880,tc_HOL_Obool),U_12877),hAPP(hAPP(c_COMBB(tc_fun(U_12880,U_12877),tc_fun(tc_fun(U_12880,tc_HOL_Obool),U_12877),U_12878),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12880,U_12877)),U_12882)),U_12881)),U_12879) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12878,U_12880),U_12877),hAPP(c_Product__Type_Oprod_Oprod__case(U_12878,U_12880,U_12877),U_12882)),hAPP(hAPP(c_Product__Type_OSigma(U_12878,U_12880),U_12879),U_12881))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12878),U_12879))
| ~ class_Groups_Ocomm__monoid__add(U_12877) ),
inference(clausify,[status(thm)],[f_3336_3]) ).
cnf(f_3336_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12880),hAPP(U_12881,sK290(U_12882,U_12881,U_12880,U_12879,U_12878,U_12877))))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12878,U_12877),hAPP(hAPP(c_COMBS(U_12878,tc_fun(U_12880,tc_HOL_Obool),U_12877),hAPP(hAPP(c_COMBB(tc_fun(U_12880,U_12877),tc_fun(tc_fun(U_12880,tc_HOL_Obool),U_12877),U_12878),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12880,U_12877)),U_12882)),U_12881)),U_12879) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_12878,U_12880),U_12877),hAPP(c_Product__Type_Oprod_Oprod__case(U_12878,U_12880,U_12877),U_12882)),hAPP(hAPP(c_Product__Type_OSigma(U_12878,U_12880),U_12879),U_12881))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12878),U_12879))
| ~ class_Groups_Ocomm__monoid__add(U_12877) ),
inference(clausify,[status(thm)],[f_3336_3]) ).
fof(f_3337_1,plain,
! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBC(T_b,T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),T_b),c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d))),V_g_2)),c_Groups_Oone__class_Oone(T_d))),V_B_2)),c_Groups_Oone__class_Oone(T_d)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,tc_prod(T_b,T_c),c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_g_2)),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))
| ? [B_x] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_fold__image__Sigma]) ).
fof(f_3337_2,plain,
! [U_12889,U_12888,U_12887,U_12886,U_12885,U_12884] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12884,U_12885,c_Groups_Otimes__class_Otimes(U_12884)),hAPP(hAPP(c_COMBS(U_12885,tc_fun(U_12887,tc_HOL_Obool),U_12884),hAPP(hAPP(c_COMBC(U_12885,U_12884,tc_fun(tc_fun(U_12887,tc_HOL_Obool),U_12884)),hAPP(hAPP(c_COMBB(tc_fun(U_12887,U_12884),tc_fun(U_12884,tc_fun(tc_fun(U_12887,tc_HOL_Obool),U_12884)),U_12885),c_Finite__Set_Ofold__image(U_12884,U_12887,c_Groups_Otimes__class_Otimes(U_12884))),U_12889)),c_Groups_Oone__class_Oone(U_12884))),U_12888)),c_Groups_Oone__class_Oone(U_12884)),U_12886) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12884,tc_prod(U_12885,U_12887),c_Groups_Otimes__class_Otimes(U_12884)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12885,U_12887,U_12884),U_12889)),c_Groups_Oone__class_Oone(U_12884)),hAPP(hAPP(c_Product__Type_OSigma(U_12885,U_12887),U_12886),U_12888))
| ? [U_12883] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12887),hAPP(U_12888,U_12883)))
& hBOOL(hAPP(hAPP(c_member(U_12885),U_12883),U_12886)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12885),U_12886))
| ~ class_Groups_Ocomm__monoid__mult(U_12884) ),
inference(variable_rename,[status(thm)],[f_3337_1]) ).
fof(f_3337_3,plain,
! [U_12889,U_12888,U_12887,U_12886,U_12885,U_12884] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12884,U_12885,c_Groups_Otimes__class_Otimes(U_12884)),hAPP(hAPP(c_COMBS(U_12885,tc_fun(U_12887,tc_HOL_Obool),U_12884),hAPP(hAPP(c_COMBC(U_12885,U_12884,tc_fun(tc_fun(U_12887,tc_HOL_Obool),U_12884)),hAPP(hAPP(c_COMBB(tc_fun(U_12887,U_12884),tc_fun(U_12884,tc_fun(tc_fun(U_12887,tc_HOL_Obool),U_12884)),U_12885),c_Finite__Set_Ofold__image(U_12884,U_12887,c_Groups_Otimes__class_Otimes(U_12884))),U_12889)),c_Groups_Oone__class_Oone(U_12884))),U_12888)),c_Groups_Oone__class_Oone(U_12884)),U_12886) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12884,tc_prod(U_12885,U_12887),c_Groups_Otimes__class_Otimes(U_12884)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12885,U_12887,U_12884),U_12889)),c_Groups_Oone__class_Oone(U_12884)),hAPP(hAPP(c_Product__Type_OSigma(U_12885,U_12887),U_12886),U_12888))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12887),hAPP(U_12888,sK291(U_12889,U_12888,U_12887,U_12886,U_12885,U_12884))))
& hBOOL(hAPP(hAPP(c_member(U_12885),sK291(U_12889,U_12888,U_12887,U_12886,U_12885,U_12884)),U_12886)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12885),U_12886))
| ~ class_Groups_Ocomm__monoid__mult(U_12884) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK291]),skolemize(U_12883,sK291(U_12889,U_12888,U_12887,U_12886,U_12885,U_12884))],[f_3337_2]) ).
cnf(f_3337_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12885),sK291(U_12889,U_12888,U_12887,U_12886,U_12885,U_12884)),U_12886))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12884,U_12885,c_Groups_Otimes__class_Otimes(U_12884)),hAPP(hAPP(c_COMBS(U_12885,tc_fun(U_12887,tc_HOL_Obool),U_12884),hAPP(hAPP(c_COMBC(U_12885,U_12884,tc_fun(tc_fun(U_12887,tc_HOL_Obool),U_12884)),hAPP(hAPP(c_COMBB(tc_fun(U_12887,U_12884),tc_fun(U_12884,tc_fun(tc_fun(U_12887,tc_HOL_Obool),U_12884)),U_12885),c_Finite__Set_Ofold__image(U_12884,U_12887,c_Groups_Otimes__class_Otimes(U_12884))),U_12889)),c_Groups_Oone__class_Oone(U_12884))),U_12888)),c_Groups_Oone__class_Oone(U_12884)),U_12886) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12884,tc_prod(U_12885,U_12887),c_Groups_Otimes__class_Otimes(U_12884)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12885,U_12887,U_12884),U_12889)),c_Groups_Oone__class_Oone(U_12884)),hAPP(hAPP(c_Product__Type_OSigma(U_12885,U_12887),U_12886),U_12888))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12885),U_12886))
| ~ class_Groups_Ocomm__monoid__mult(U_12884) ),
inference(clausify,[status(thm)],[f_3337_3]) ).
cnf(f_3337_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12887),hAPP(U_12888,sK291(U_12889,U_12888,U_12887,U_12886,U_12885,U_12884))))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12884,U_12885,c_Groups_Otimes__class_Otimes(U_12884)),hAPP(hAPP(c_COMBS(U_12885,tc_fun(U_12887,tc_HOL_Obool),U_12884),hAPP(hAPP(c_COMBC(U_12885,U_12884,tc_fun(tc_fun(U_12887,tc_HOL_Obool),U_12884)),hAPP(hAPP(c_COMBB(tc_fun(U_12887,U_12884),tc_fun(U_12884,tc_fun(tc_fun(U_12887,tc_HOL_Obool),U_12884)),U_12885),c_Finite__Set_Ofold__image(U_12884,U_12887,c_Groups_Otimes__class_Otimes(U_12884))),U_12889)),c_Groups_Oone__class_Oone(U_12884))),U_12888)),c_Groups_Oone__class_Oone(U_12884)),U_12886) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12884,tc_prod(U_12885,U_12887),c_Groups_Otimes__class_Otimes(U_12884)),hAPP(c_Product__Type_Oprod_Oprod__case(U_12885,U_12887,U_12884),U_12889)),c_Groups_Oone__class_Oone(U_12884)),hAPP(hAPP(c_Product__Type_OSigma(U_12885,U_12887),U_12886),U_12888))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12885),U_12886))
| ~ class_Groups_Ocomm__monoid__mult(U_12884) ),
inference(clausify,[status(thm)],[f_3337_3]) ).
fof(f_3338_1,plain,
! [V_B_2,T_c,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),V_B_2)),V_A_2)
| ? [B_x] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__SigmaI]) ).
fof(f_3338_2,plain,
! [U_12894,U_12893,U_12892,U_12891] :
( hAPP(c_Finite__Set_Ocard(tc_prod(U_12891,U_12893)),hAPP(hAPP(c_Product__Type_OSigma(U_12891,U_12893),U_12892),U_12894)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12891,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12893,tc_HOL_Obool),tc_Nat_Onat,U_12891),c_Finite__Set_Ocard(U_12893)),U_12894)),U_12892)
| ? [U_12890] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12893),hAPP(U_12894,U_12890)))
& hBOOL(hAPP(hAPP(c_member(U_12891),U_12890),U_12892)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12891),U_12892)) ),
inference(variable_rename,[status(thm)],[f_3338_1]) ).
fof(f_3338_3,plain,
! [U_12894,U_12893,U_12892,U_12891] :
( hAPP(c_Finite__Set_Ocard(tc_prod(U_12891,U_12893)),hAPP(hAPP(c_Product__Type_OSigma(U_12891,U_12893),U_12892),U_12894)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12891,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12893,tc_HOL_Obool),tc_Nat_Onat,U_12891),c_Finite__Set_Ocard(U_12893)),U_12894)),U_12892)
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12893),hAPP(U_12894,sK292(U_12894,U_12893,U_12892,U_12891))))
& hBOOL(hAPP(hAPP(c_member(U_12891),sK292(U_12894,U_12893,U_12892,U_12891)),U_12892)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12891),U_12892)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK292]),skolemize(U_12890,sK292(U_12894,U_12893,U_12892,U_12891))],[f_3338_2]) ).
cnf(f_3338_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12891),sK292(U_12894,U_12893,U_12892,U_12891)),U_12892))
| hAPP(c_Finite__Set_Ocard(tc_prod(U_12891,U_12893)),hAPP(hAPP(c_Product__Type_OSigma(U_12891,U_12893),U_12892),U_12894)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12891,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12893,tc_HOL_Obool),tc_Nat_Onat,U_12891),c_Finite__Set_Ocard(U_12893)),U_12894)),U_12892)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12891),U_12892)) ),
inference(clausify,[status(thm)],[f_3338_3]) ).
cnf(f_3338_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12893),hAPP(U_12894,sK292(U_12894,U_12893,U_12892,U_12891))))
| hAPP(c_Finite__Set_Ocard(tc_prod(U_12891,U_12893)),hAPP(hAPP(c_Product__Type_OSigma(U_12891,U_12893),U_12892),U_12894)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12891,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12893,tc_HOL_Obool),tc_Nat_Onat,U_12891),c_Finite__Set_Ocard(U_12893)),U_12894)),U_12892)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12891),U_12892)) ),
inference(clausify,[status(thm)],[f_3338_3]) ).
fof(f_3339_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),V_A_2))
| ? [B_x,B_y] : ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Oab__semigroup__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__in]) ).
fof(f_3339_2,plain,
! [U_12898,U_12897] :
( hBOOL(hAPP(hAPP(c_member(U_12897),hAPP(c_Finite__Set_Ofold1(U_12897,c_Groups_Otimes__class_Otimes(U_12897)),U_12898)),U_12898))
| ? [U_12896,U_12895] : ~ hBOOL(hAPP(hAPP(c_member(U_12897),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12897),U_12896),U_12895)),hAPP(hAPP(c_Set_Oinsert(U_12897),U_12896),hAPP(hAPP(c_Set_Oinsert(U_12897),U_12895),c_Orderings_Obot__class_Obot(tc_fun(U_12897,tc_HOL_Obool))))))
| U_12898 = c_Orderings_Obot__class_Obot(tc_fun(U_12897,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12897),U_12898))
| ~ class_Groups_Oab__semigroup__mult(U_12897) ),
inference(variable_rename,[status(thm)],[f_3339_1]) ).
fof(f_3339_3,plain,
! [U_12898,U_12897] :
( hBOOL(hAPP(hAPP(c_member(U_12897),hAPP(c_Finite__Set_Ofold1(U_12897,c_Groups_Otimes__class_Otimes(U_12897)),U_12898)),U_12898))
| ? [U_12895] : ~ hBOOL(hAPP(hAPP(c_member(U_12897),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12897),sK293(U_12898,U_12897)),U_12895)),hAPP(hAPP(c_Set_Oinsert(U_12897),sK293(U_12898,U_12897)),hAPP(hAPP(c_Set_Oinsert(U_12897),U_12895),c_Orderings_Obot__class_Obot(tc_fun(U_12897,tc_HOL_Obool))))))
| U_12898 = c_Orderings_Obot__class_Obot(tc_fun(U_12897,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12897),U_12898))
| ~ class_Groups_Oab__semigroup__mult(U_12897) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK293]),skolemize(U_12896,sK293(U_12898,U_12897))],[f_3339_2]) ).
fof(f_3339_4,plain,
! [U_12898,U_12897] :
( hBOOL(hAPP(hAPP(c_member(U_12897),hAPP(c_Finite__Set_Ofold1(U_12897,c_Groups_Otimes__class_Otimes(U_12897)),U_12898)),U_12898))
| ~ hBOOL(hAPP(hAPP(c_member(U_12897),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12897),sK293(U_12898,U_12897)),sK294(U_12898,U_12897))),hAPP(hAPP(c_Set_Oinsert(U_12897),sK293(U_12898,U_12897)),hAPP(hAPP(c_Set_Oinsert(U_12897),sK294(U_12898,U_12897)),c_Orderings_Obot__class_Obot(tc_fun(U_12897,tc_HOL_Obool))))))
| U_12898 = c_Orderings_Obot__class_Obot(tc_fun(U_12897,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12897),U_12898))
| ~ class_Groups_Oab__semigroup__mult(U_12897) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK294]),skolemize(U_12895,sK294(U_12898,U_12897))],[f_3339_3]) ).
cnf(f_3339_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_12897),hAPP(c_Finite__Set_Ofold1(U_12897,c_Groups_Otimes__class_Otimes(U_12897)),U_12898)),U_12898))
| ~ hBOOL(hAPP(hAPP(c_member(U_12897),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12897),sK293(U_12898,U_12897)),sK294(U_12898,U_12897))),hAPP(hAPP(c_Set_Oinsert(U_12897),sK293(U_12898,U_12897)),hAPP(hAPP(c_Set_Oinsert(U_12897),sK294(U_12898,U_12897)),c_Orderings_Obot__class_Obot(tc_fun(U_12897,tc_HOL_Obool))))))
| U_12898 = c_Orderings_Obot__class_Obot(tc_fun(U_12897,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12897),U_12898))
| ~ class_Groups_Oab__semigroup__mult(U_12897) ),
inference(clausify,[status(thm)],[f_3339_4]) ).
fof(f_3340_1,plain,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
| ? [B_a] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__SigmaI]) ).
fof(f_3340_2,plain,
! [U_12903,U_12902,U_12901,U_12900] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12900,U_12902)),hAPP(hAPP(c_Product__Type_OSigma(U_12900,U_12902),U_12901),U_12903)))
| ? [U_12899] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12902),hAPP(U_12903,U_12899)))
& hBOOL(hAPP(hAPP(c_member(U_12900),U_12899),U_12901)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12900),U_12901)) ),
inference(variable_rename,[status(thm)],[f_3340_1]) ).
fof(f_3340_3,plain,
! [U_12903,U_12902,U_12901,U_12900] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12900,U_12902)),hAPP(hAPP(c_Product__Type_OSigma(U_12900,U_12902),U_12901),U_12903)))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12902),hAPP(U_12903,sK295(U_12903,U_12902,U_12901,U_12900))))
& hBOOL(hAPP(hAPP(c_member(U_12900),sK295(U_12903,U_12902,U_12901,U_12900)),U_12901)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12900),U_12901)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK295]),skolemize(U_12899,sK295(U_12903,U_12902,U_12901,U_12900))],[f_3340_2]) ).
cnf(f_3340_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12900),sK295(U_12903,U_12902,U_12901,U_12900)),U_12901))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12900,U_12902)),hAPP(hAPP(c_Product__Type_OSigma(U_12900,U_12902),U_12901),U_12903)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12900),U_12901)) ),
inference(clausify,[status(thm)],[f_3340_3]) ).
cnf(f_3340_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12902),hAPP(U_12903,sK295(U_12903,U_12902,U_12901,U_12900))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_12900,U_12902)),hAPP(hAPP(c_Product__Type_OSigma(U_12900,U_12902),U_12901),U_12903)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12900),U_12901)) ),
inference(clausify,[status(thm)],[f_3340_3]) ).
fof(f_3341_1,plain,
! [V_N_2,V_h_2,T_b] :
( hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
| ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_hom__fold1__commute]) ).
fof(f_3341_2,plain,
! [U_12908,U_12907,U_12906] :
( hAPP(U_12907,hAPP(c_Finite__Set_Ofold1(U_12906,c_Groups_Otimes__class_Otimes(U_12906)),U_12908)) = hAPP(c_Finite__Set_Ofold1(U_12906,c_Groups_Otimes__class_Otimes(U_12906)),hAPP(c_Set_Oimage(U_12906,U_12906,U_12907),U_12908))
| U_12908 = c_Orderings_Obot__class_Obot(tc_fun(U_12906,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12906),U_12908))
| ? [U_12905,U_12904] : hAPP(U_12907,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12906),U_12905),U_12904)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12906),hAPP(U_12907,U_12905)),hAPP(U_12907,U_12904))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_12906) ),
inference(variable_rename,[status(thm)],[f_3341_1]) ).
fof(f_3341_3,plain,
! [U_12908,U_12907,U_12906] :
( hAPP(U_12907,hAPP(c_Finite__Set_Ofold1(U_12906,c_Groups_Otimes__class_Otimes(U_12906)),U_12908)) = hAPP(c_Finite__Set_Ofold1(U_12906,c_Groups_Otimes__class_Otimes(U_12906)),hAPP(c_Set_Oimage(U_12906,U_12906,U_12907),U_12908))
| U_12908 = c_Orderings_Obot__class_Obot(tc_fun(U_12906,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12906),U_12908))
| ? [U_12904] : hAPP(U_12907,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12906),sK296(U_12908,U_12907,U_12906)),U_12904)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12906),hAPP(U_12907,sK296(U_12908,U_12907,U_12906))),hAPP(U_12907,U_12904))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_12906) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK296]),skolemize(U_12905,sK296(U_12908,U_12907,U_12906))],[f_3341_2]) ).
fof(f_3341_4,plain,
! [U_12908,U_12907,U_12906] :
( hAPP(U_12907,hAPP(c_Finite__Set_Ofold1(U_12906,c_Groups_Otimes__class_Otimes(U_12906)),U_12908)) = hAPP(c_Finite__Set_Ofold1(U_12906,c_Groups_Otimes__class_Otimes(U_12906)),hAPP(c_Set_Oimage(U_12906,U_12906,U_12907),U_12908))
| U_12908 = c_Orderings_Obot__class_Obot(tc_fun(U_12906,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12906),U_12908))
| hAPP(U_12907,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12906),sK296(U_12908,U_12907,U_12906)),sK297(U_12908,U_12907,U_12906))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12906),hAPP(U_12907,sK296(U_12908,U_12907,U_12906))),hAPP(U_12907,sK297(U_12908,U_12907,U_12906)))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_12906) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK297]),skolemize(U_12904,sK297(U_12908,U_12907,U_12906))],[f_3341_3]) ).
cnf(f_3341_5,plain,
( hAPP(U_12907,hAPP(c_Finite__Set_Ofold1(U_12906,c_Groups_Otimes__class_Otimes(U_12906)),U_12908)) = hAPP(c_Finite__Set_Ofold1(U_12906,c_Groups_Otimes__class_Otimes(U_12906)),hAPP(c_Set_Oimage(U_12906,U_12906,U_12907),U_12908))
| U_12908 = c_Orderings_Obot__class_Obot(tc_fun(U_12906,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12906),U_12908))
| hAPP(U_12907,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12906),sK296(U_12908,U_12907,U_12906)),sK297(U_12908,U_12907,U_12906))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12906),hAPP(U_12907,sK296(U_12908,U_12907,U_12906))),hAPP(U_12907,sK297(U_12908,U_12907,U_12906)))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_12906) ),
inference(clausify,[status(thm)],[f_3341_4]) ).
fof(f_3342_1,plain,
! [V_B_2,V_A_2,V_c_2,T_c,T_b] :
( ? [B_x] :
( ? [B_y] :
( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)
& hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x))) )
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ),
inference(fof_nnf,[status(thm)],[fact_SigmaE]) ).
fof(f_3342_2,plain,
! [U_12915,U_12914,U_12913,U_12912,U_12911] :
( ? [U_12910] :
( ? [U_12909] :
( U_12913 = hAPP(hAPP(c_Product__Type_OPair(U_12911,U_12912),U_12910),U_12909)
& hBOOL(hAPP(hAPP(c_member(U_12912),U_12909),hAPP(U_12915,U_12910))) )
& hBOOL(hAPP(hAPP(c_member(U_12911),U_12910),U_12914)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12911,U_12912)),U_12913),hAPP(hAPP(c_Product__Type_OSigma(U_12911,U_12912),U_12914),U_12915))) ),
inference(variable_rename,[status(thm)],[f_3342_1]) ).
fof(f_3342_3,plain,
! [U_12915,U_12914,U_12913,U_12912,U_12911] :
( ( ? [U_12909] :
( U_12913 = hAPP(hAPP(c_Product__Type_OPair(U_12911,U_12912),sK298(U_12915,U_12914,U_12913,U_12912,U_12911)),U_12909)
& hBOOL(hAPP(hAPP(c_member(U_12912),U_12909),hAPP(U_12915,sK298(U_12915,U_12914,U_12913,U_12912,U_12911)))) )
& hBOOL(hAPP(hAPP(c_member(U_12911),sK298(U_12915,U_12914,U_12913,U_12912,U_12911)),U_12914)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12911,U_12912)),U_12913),hAPP(hAPP(c_Product__Type_OSigma(U_12911,U_12912),U_12914),U_12915))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK298]),skolemize(U_12910,sK298(U_12915,U_12914,U_12913,U_12912,U_12911))],[f_3342_2]) ).
fof(f_3342_4,plain,
! [U_12915,U_12914,U_12913,U_12912,U_12911] :
( ( U_12913 = hAPP(hAPP(c_Product__Type_OPair(U_12911,U_12912),sK298(U_12915,U_12914,U_12913,U_12912,U_12911)),sK299(U_12915,U_12914,U_12913,U_12912,U_12911))
& hBOOL(hAPP(hAPP(c_member(U_12912),sK299(U_12915,U_12914,U_12913,U_12912,U_12911)),hAPP(U_12915,sK298(U_12915,U_12914,U_12913,U_12912,U_12911))))
& hBOOL(hAPP(hAPP(c_member(U_12911),sK298(U_12915,U_12914,U_12913,U_12912,U_12911)),U_12914)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12911,U_12912)),U_12913),hAPP(hAPP(c_Product__Type_OSigma(U_12911,U_12912),U_12914),U_12915))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK299]),skolemize(U_12909,sK299(U_12915,U_12914,U_12913,U_12912,U_12911))],[f_3342_3]) ).
cnf(f_3342_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_12911),sK298(U_12915,U_12914,U_12913,U_12912,U_12911)),U_12914))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12911,U_12912)),U_12913),hAPP(hAPP(c_Product__Type_OSigma(U_12911,U_12912),U_12914),U_12915))) ),
inference(clausify,[status(thm)],[f_3342_4]) ).
cnf(f_3342_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_12912),sK299(U_12915,U_12914,U_12913,U_12912,U_12911)),hAPP(U_12915,sK298(U_12915,U_12914,U_12913,U_12912,U_12911))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12911,U_12912)),U_12913),hAPP(hAPP(c_Product__Type_OSigma(U_12911,U_12912),U_12914),U_12915))) ),
inference(clausify,[status(thm)],[f_3342_4]) ).
cnf(f_3342_7,plain,
( U_12913 = hAPP(hAPP(c_Product__Type_OPair(U_12911,U_12912),sK298(U_12915,U_12914,U_12913,U_12912,U_12911)),sK299(U_12915,U_12914,U_12913,U_12912,U_12911))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12911,U_12912)),U_12913),hAPP(hAPP(c_Product__Type_OSigma(U_12911,U_12912),U_12914),U_12915))) ),
inference(clausify,[status(thm)],[f_3342_4]) ).
fof(f_3343_1,plain,
! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))
| hAPP(c_Set_Oimage(T_e,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
| hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_map__pair__surj]) ).
fof(f_3343_2,plain,
! [U_12921,U_12920,U_12919,U_12918,U_12917,U_12916] :
( hAPP(c_Set_Oimage(tc_prod(U_12916,U_12919),tc_prod(U_12917,U_12920),c_Product__Type_Omap__pair(U_12916,U_12917,U_12919,U_12920,U_12918,U_12921)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12916,U_12919),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12917,U_12920),tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_12919,U_12920,U_12921),c_Orderings_Otop__class_Otop(tc_fun(U_12919,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12920,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_12916,U_12917,U_12918),c_Orderings_Otop__class_Otop(tc_fun(U_12916,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12917,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_3343_1]) ).
cnf(f_3343_3,plain,
( hAPP(c_Set_Oimage(tc_prod(U_12916,U_12919),tc_prod(U_12917,U_12920),c_Product__Type_Omap__pair(U_12916,U_12917,U_12919,U_12920,U_12918,U_12921)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12916,U_12919),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_12917,U_12920),tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_12919,U_12920,U_12921),c_Orderings_Otop__class_Otop(tc_fun(U_12919,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12920,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_12916,U_12917,U_12918),c_Orderings_Otop__class_Otop(tc_fun(U_12916,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_12917,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3343_2]) ).
fof(f_3344_1,plain,
! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),tc_prod(T_d,T_e),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)),V_R_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_R_2)) ),
inference(fof_nnf,[status(thm)],[fact_map__pair__imageI]) ).
fof(f_3344_2,plain,
! [U_12930,U_12929,U_12928,U_12927,U_12926,U_12925,U_12924,U_12923,U_12922] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12927,U_12928)),hAPP(hAPP(c_Product__Type_OPair(U_12927,U_12928),hAPP(U_12929,U_12924)),hAPP(U_12930,U_12925))),hAPP(c_Set_Oimage(tc_prod(U_12922,U_12923),tc_prod(U_12927,U_12928),c_Product__Type_Omap__pair(U_12922,U_12927,U_12923,U_12928,U_12929,U_12930)),U_12926)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12922,U_12923)),hAPP(hAPP(c_Product__Type_OPair(U_12922,U_12923),U_12924),U_12925)),U_12926)) ),
inference(variable_rename,[status(thm)],[f_3344_1]) ).
cnf(f_3344_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12927,U_12928)),hAPP(hAPP(c_Product__Type_OPair(U_12927,U_12928),hAPP(U_12929,U_12924)),hAPP(U_12930,U_12925))),hAPP(c_Set_Oimage(tc_prod(U_12922,U_12923),tc_prod(U_12927,U_12928),c_Product__Type_Omap__pair(U_12922,U_12927,U_12923,U_12928,U_12929,U_12930)),U_12926)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12922,U_12923)),hAPP(hAPP(c_Product__Type_OPair(U_12922,U_12923),U_12924),U_12925)),U_12926)) ),
inference(clausify,[status(thm)],[f_3344_2]) ).
fof(f_3345_1,plain,
! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2)),
inference(fof_nnf,[status(thm)],[fact_fst__map__pair]) ).
fof(f_3345_2,plain,
! [U_12937,U_12936,U_12935,U_12934,U_12933,U_12932,U_12931] : hAPP(c_Product__Type_Ofst(U_12931,U_12932),hAPP(c_Product__Type_Omap__pair(U_12933,U_12931,U_12934,U_12932,U_12935,U_12936),U_12937)) = hAPP(U_12935,hAPP(c_Product__Type_Ofst(U_12933,U_12934),U_12937)),
inference(variable_rename,[status(thm)],[f_3345_1]) ).
cnf(f_3345_3,plain,
hAPP(c_Product__Type_Ofst(U_12931,U_12932),hAPP(c_Product__Type_Omap__pair(U_12933,U_12931,U_12934,U_12932,U_12935,U_12936),U_12937)) = hAPP(U_12935,hAPP(c_Product__Type_Ofst(U_12933,U_12934),U_12937)),
inference(clausify,[status(thm)],[f_3345_2]) ).
fof(f_3346_1,plain,
! [V_z_2,T_c,T_b] : hAPP(c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)),V_z_2) = V_z_2,
inference(fof_nnf,[status(thm)],[fact_map__pair__ident]) ).
fof(f_3346_2,plain,
! [U_12940,U_12939,U_12938] : hAPP(c_Product__Type_Omap__pair(U_12938,U_12938,U_12939,U_12939,c_COMBI(U_12938),c_COMBI(U_12939)),U_12940) = U_12940,
inference(variable_rename,[status(thm)],[f_3346_1]) ).
cnf(f_3346_3,plain,
hAPP(c_Product__Type_Omap__pair(U_12938,U_12938,U_12939,U_12939,c_COMBI(U_12938),c_COMBI(U_12939)),U_12940) = U_12940,
inference(clausify,[status(thm)],[f_3346_2]) ).
fof(f_3347_1,plain,
! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Omap__pair(T_d,T_c,T_e,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)),
inference(fof_nnf,[status(thm)],[fact_snd__prod__fun]) ).
fof(f_3347_2,plain,
! [U_12947,U_12946,U_12945,U_12944,U_12943,U_12942,U_12941] : hAPP(c_Product__Type_Osnd(U_12941,U_12942),hAPP(c_Product__Type_Omap__pair(U_12943,U_12941,U_12944,U_12942,U_12945,U_12946),U_12947)) = hAPP(U_12946,hAPP(c_Product__Type_Osnd(U_12943,U_12944),U_12947)),
inference(variable_rename,[status(thm)],[f_3347_1]) ).
cnf(f_3347_3,plain,
hAPP(c_Product__Type_Osnd(U_12941,U_12942),hAPP(c_Product__Type_Omap__pair(U_12943,U_12941,U_12944,U_12942,U_12945,U_12946),U_12947)) = hAPP(U_12946,hAPP(c_Product__Type_Osnd(U_12943,U_12944),U_12947)),
inference(clausify,[status(thm)],[f_3347_2]) ).
fof(f_3348_1,plain,
! [V_b_2,V_a_2,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)),
inference(fof_nnf,[status(thm)],[fact_map__pair__simp]) ).
fof(f_3348_2,plain,
! [U_12955,U_12954,U_12953,U_12952,U_12951,U_12950,U_12949,U_12948] : hAPP(c_Product__Type_Omap__pair(U_12948,U_12949,U_12950,U_12951,U_12952,U_12953),hAPP(hAPP(c_Product__Type_OPair(U_12948,U_12950),U_12954),U_12955)) = hAPP(hAPP(c_Product__Type_OPair(U_12949,U_12951),hAPP(U_12952,U_12954)),hAPP(U_12953,U_12955)),
inference(variable_rename,[status(thm)],[f_3348_1]) ).
cnf(f_3348_3,plain,
hAPP(c_Product__Type_Omap__pair(U_12948,U_12949,U_12950,U_12951,U_12952,U_12953),hAPP(hAPP(c_Product__Type_OPair(U_12948,U_12950),U_12954),U_12955)) = hAPP(hAPP(c_Product__Type_OPair(U_12949,U_12951),hAPP(U_12952,U_12954)),hAPP(U_12953,U_12955)),
inference(clausify,[status(thm)],[f_3348_2]) ).
fof(f_3349_1,plain,
! [V_g_2,V_f_2,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_d,T_e)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),T_b),c_COMBB(T_e,tc_prod(T_d,T_e),T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_e,tc_prod(T_d,T_e)),T_b),c_Product__Type_OPair(T_d,T_e)),V_f_2))),V_g_2)),
inference(fof_nnf,[status(thm)],[fact_map__pair__def]) ).
fof(f_3349_2,plain,
! [U_12961,U_12960,U_12959,U_12958,U_12957,U_12956] : c_Product__Type_Omap__pair(U_12956,U_12957,U_12958,U_12959,U_12960,U_12961) = hAPP(c_Product__Type_Oprod_Oprod__case(U_12956,U_12958,tc_prod(U_12957,U_12959)),hAPP(hAPP(c_COMBC(U_12956,tc_fun(U_12958,U_12959),tc_fun(U_12958,tc_prod(U_12957,U_12959))),hAPP(hAPP(c_COMBB(tc_fun(U_12959,tc_prod(U_12957,U_12959)),tc_fun(tc_fun(U_12958,U_12959),tc_fun(U_12958,tc_prod(U_12957,U_12959))),U_12956),c_COMBB(U_12959,tc_prod(U_12957,U_12959),U_12958)),hAPP(hAPP(c_COMBB(U_12957,tc_fun(U_12959,tc_prod(U_12957,U_12959)),U_12956),c_Product__Type_OPair(U_12957,U_12959)),U_12960))),U_12961)),
inference(variable_rename,[status(thm)],[f_3349_1]) ).
cnf(f_3349_3,plain,
c_Product__Type_Omap__pair(U_12956,U_12957,U_12958,U_12959,U_12960,U_12961) = hAPP(c_Product__Type_Oprod_Oprod__case(U_12956,U_12958,tc_prod(U_12957,U_12959)),hAPP(hAPP(c_COMBC(U_12956,tc_fun(U_12958,U_12959),tc_fun(U_12958,tc_prod(U_12957,U_12959))),hAPP(hAPP(c_COMBB(tc_fun(U_12959,tc_prod(U_12957,U_12959)),tc_fun(tc_fun(U_12958,U_12959),tc_fun(U_12958,tc_prod(U_12957,U_12959))),U_12956),c_COMBB(U_12959,tc_prod(U_12957,U_12959),U_12958)),hAPP(hAPP(c_COMBB(U_12957,tc_fun(U_12959,tc_prod(U_12957,U_12959)),U_12956),c_Product__Type_OPair(U_12957,U_12959)),U_12960))),U_12961)),
inference(clausify,[status(thm)],[f_3349_2]) ).
fof(f_3350_1,plain,
! [V_B_H_2,V_B_2,V_g_2,T_d,T_e,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_H_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_H_2))
| hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) != V_B_H_2
| hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) != V_A_H_2 ),
inference(fof_nnf,[status(thm)],[fact_map__pair__surj__on]) ).
fof(f_3350_2,plain,
! [U_12971,U_12970,U_12969,U_12968,U_12967,U_12966,U_12965,U_12964,U_12963,U_12962] :
( hAPP(c_Set_Oimage(tc_prod(U_12962,U_12967),tc_prod(U_12963,U_12968),c_Product__Type_Omap__pair(U_12962,U_12963,U_12967,U_12968,U_12964,U_12969)),hAPP(hAPP(c_Product__Type_OSigma(U_12962,U_12967),U_12965),hAPP(c_COMBK(tc_fun(U_12967,tc_HOL_Obool),U_12962),U_12970))) = hAPP(hAPP(c_Product__Type_OSigma(U_12963,U_12968),U_12966),hAPP(c_COMBK(tc_fun(U_12968,tc_HOL_Obool),U_12963),U_12971))
| hAPP(c_Set_Oimage(U_12967,U_12968,U_12969),U_12970) != U_12971
| hAPP(c_Set_Oimage(U_12962,U_12963,U_12964),U_12965) != U_12966 ),
inference(variable_rename,[status(thm)],[f_3350_1]) ).
cnf(f_3350_3,plain,
( hAPP(c_Set_Oimage(tc_prod(U_12962,U_12967),tc_prod(U_12963,U_12968),c_Product__Type_Omap__pair(U_12962,U_12963,U_12967,U_12968,U_12964,U_12969)),hAPP(hAPP(c_Product__Type_OSigma(U_12962,U_12967),U_12965),hAPP(c_COMBK(tc_fun(U_12967,tc_HOL_Obool),U_12962),U_12970))) = hAPP(hAPP(c_Product__Type_OSigma(U_12963,U_12968),U_12966),hAPP(c_COMBK(tc_fun(U_12968,tc_HOL_Obool),U_12963),U_12971))
| hAPP(c_Set_Oimage(U_12967,U_12968,U_12969),U_12970) != U_12971
| hAPP(c_Set_Oimage(U_12962,U_12963,U_12964),U_12965) != U_12966 ),
inference(clausify,[status(thm)],[f_3350_2]) ).
fof(f_3351_1,plain,
! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(tc_prod(T_b,T_d),tc_prod(T_c,T_e),c_Product__Type_Omap__pair(T_b,T_c,T_d,T_e,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_2)))
| ~ c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_map__pair__inj__on]) ).
fof(f_3351_2,plain,
! [U_12979,U_12978,U_12977,U_12976,U_12975,U_12974,U_12973,U_12972] :
( c_Fun_Oinj__on(tc_prod(U_12972,U_12976),tc_prod(U_12973,U_12977),c_Product__Type_Omap__pair(U_12972,U_12973,U_12976,U_12977,U_12974,U_12978),hAPP(hAPP(c_Product__Type_OSigma(U_12972,U_12976),U_12975),hAPP(c_COMBK(tc_fun(U_12976,tc_HOL_Obool),U_12972),U_12979)))
| ~ c_Fun_Oinj__on(U_12976,U_12977,U_12978,U_12979)
| ~ c_Fun_Oinj__on(U_12972,U_12973,U_12974,U_12975) ),
inference(variable_rename,[status(thm)],[f_3351_1]) ).
cnf(f_3351_3,plain,
( c_Fun_Oinj__on(tc_prod(U_12972,U_12976),tc_prod(U_12973,U_12977),c_Product__Type_Omap__pair(U_12972,U_12973,U_12976,U_12977,U_12974,U_12978),hAPP(hAPP(c_Product__Type_OSigma(U_12972,U_12976),U_12975),hAPP(c_COMBK(tc_fun(U_12976,tc_HOL_Obool),U_12972),U_12979)))
| ~ c_Fun_Oinj__on(U_12976,U_12977,U_12978,U_12979)
| ~ c_Fun_Oinj__on(U_12972,U_12973,U_12974,U_12975) ),
inference(clausify,[status(thm)],[f_3351_2]) ).
fof(f_3352_1,plain,
! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
( ? [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),B_x),B_y)),V_R_2))
& V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_prod__fun__imageE]) ).
fof(f_3352_2,plain,
! [U_12989,U_12988,U_12987,U_12986,U_12985,U_12984,U_12983,U_12982] :
( ? [U_12981,U_12980] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12985,U_12986)),hAPP(hAPP(c_Product__Type_OPair(U_12985,U_12986),U_12981),U_12980)),U_12989))
& U_12984 = hAPP(hAPP(c_Product__Type_OPair(U_12982,U_12983),hAPP(U_12987,U_12981)),hAPP(U_12988,U_12980)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12982,U_12983)),U_12984),hAPP(c_Set_Oimage(tc_prod(U_12985,U_12986),tc_prod(U_12982,U_12983),c_Product__Type_Omap__pair(U_12985,U_12982,U_12986,U_12983,U_12987,U_12988)),U_12989))) ),
inference(variable_rename,[status(thm)],[f_3352_1]) ).
fof(f_3352_3,plain,
! [U_12989,U_12988,U_12987,U_12986,U_12985,U_12984,U_12983,U_12982] :
( ? [U_12980] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12985,U_12986)),hAPP(hAPP(c_Product__Type_OPair(U_12985,U_12986),sK300(U_12989,U_12988,U_12987,U_12986,U_12985,U_12984,U_12983,U_12982)),U_12980)),U_12989))
& U_12984 = hAPP(hAPP(c_Product__Type_OPair(U_12982,U_12983),hAPP(U_12987,sK300(U_12989,U_12988,U_12987,U_12986,U_12985,U_12984,U_12983,U_12982))),hAPP(U_12988,U_12980)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12982,U_12983)),U_12984),hAPP(c_Set_Oimage(tc_prod(U_12985,U_12986),tc_prod(U_12982,U_12983),c_Product__Type_Omap__pair(U_12985,U_12982,U_12986,U_12983,U_12987,U_12988)),U_12989))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK300]),skolemize(U_12981,sK300(U_12989,U_12988,U_12987,U_12986,U_12985,U_12984,U_12983,U_12982))],[f_3352_2]) ).
fof(f_3352_4,plain,
! [U_12989,U_12988,U_12987,U_12986,U_12985,U_12984,U_12983,U_12982] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12985,U_12986)),hAPP(hAPP(c_Product__Type_OPair(U_12985,U_12986),sK300(U_12989,U_12988,U_12987,U_12986,U_12985,U_12984,U_12983,U_12982)),sK301(U_12989,U_12988,U_12987,U_12986,U_12985,U_12984,U_12983,U_12982))),U_12989))
& U_12984 = hAPP(hAPP(c_Product__Type_OPair(U_12982,U_12983),hAPP(U_12987,sK300(U_12989,U_12988,U_12987,U_12986,U_12985,U_12984,U_12983,U_12982))),hAPP(U_12988,sK301(U_12989,U_12988,U_12987,U_12986,U_12985,U_12984,U_12983,U_12982))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12982,U_12983)),U_12984),hAPP(c_Set_Oimage(tc_prod(U_12985,U_12986),tc_prod(U_12982,U_12983),c_Product__Type_Omap__pair(U_12985,U_12982,U_12986,U_12983,U_12987,U_12988)),U_12989))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK301]),skolemize(U_12980,sK301(U_12989,U_12988,U_12987,U_12986,U_12985,U_12984,U_12983,U_12982))],[f_3352_3]) ).
cnf(f_3352_5,plain,
( U_12984 = hAPP(hAPP(c_Product__Type_OPair(U_12982,U_12983),hAPP(U_12987,sK300(U_12989,U_12988,U_12987,U_12986,U_12985,U_12984,U_12983,U_12982))),hAPP(U_12988,sK301(U_12989,U_12988,U_12987,U_12986,U_12985,U_12984,U_12983,U_12982)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12982,U_12983)),U_12984),hAPP(c_Set_Oimage(tc_prod(U_12985,U_12986),tc_prod(U_12982,U_12983),c_Product__Type_Omap__pair(U_12985,U_12982,U_12986,U_12983,U_12987,U_12988)),U_12989))) ),
inference(clausify,[status(thm)],[f_3352_4]) ).
cnf(f_3352_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12985,U_12986)),hAPP(hAPP(c_Product__Type_OPair(U_12985,U_12986),sK300(U_12989,U_12988,U_12987,U_12986,U_12985,U_12984,U_12983,U_12982)),sK301(U_12989,U_12988,U_12987,U_12986,U_12985,U_12984,U_12983,U_12982))),U_12989))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12982,U_12983)),U_12984),hAPP(c_Set_Oimage(tc_prod(U_12985,U_12986),tc_prod(U_12982,U_12983),c_Product__Type_Omap__pair(U_12985,U_12982,U_12986,U_12983,U_12987,U_12988)),U_12989))) ),
inference(clausify,[status(thm)],[f_3352_4]) ).
fof(f_3353_1,plain,
! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
( hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| ? [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(V_f_2,B_x),B_y)) != hAPP(hAPP(V_f_2,hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
| ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ohom__commute]) ).
fof(f_3353_2,plain,
! [U_12996,U_12995,U_12994,U_12993,U_12992] :
( hAPP(U_12995,hAPP(U_12994,U_12996)) = hAPP(U_12994,hAPP(c_Set_Oimage(U_12992,U_12992,U_12995),U_12996))
| U_12996 = c_Orderings_Obot__class_Obot(tc_fun(U_12992,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12992),U_12996))
| ? [U_12991,U_12990] : hAPP(U_12995,hAPP(hAPP(U_12993,U_12991),U_12990)) != hAPP(hAPP(U_12993,hAPP(U_12995,U_12991)),hAPP(U_12995,U_12990))
| ~ c_Finite__Set_Ofolding__one__idem(U_12992,U_12993,U_12994) ),
inference(variable_rename,[status(thm)],[f_3353_1]) ).
fof(f_3353_3,plain,
! [U_12996,U_12995,U_12994,U_12993,U_12992] :
( hAPP(U_12995,hAPP(U_12994,U_12996)) = hAPP(U_12994,hAPP(c_Set_Oimage(U_12992,U_12992,U_12995),U_12996))
| U_12996 = c_Orderings_Obot__class_Obot(tc_fun(U_12992,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12992),U_12996))
| ? [U_12990] : hAPP(U_12995,hAPP(hAPP(U_12993,sK302(U_12996,U_12995,U_12994,U_12993,U_12992)),U_12990)) != hAPP(hAPP(U_12993,hAPP(U_12995,sK302(U_12996,U_12995,U_12994,U_12993,U_12992))),hAPP(U_12995,U_12990))
| ~ c_Finite__Set_Ofolding__one__idem(U_12992,U_12993,U_12994) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK302]),skolemize(U_12991,sK302(U_12996,U_12995,U_12994,U_12993,U_12992))],[f_3353_2]) ).
fof(f_3353_4,plain,
! [U_12996,U_12995,U_12994,U_12993,U_12992] :
( hAPP(U_12995,hAPP(U_12994,U_12996)) = hAPP(U_12994,hAPP(c_Set_Oimage(U_12992,U_12992,U_12995),U_12996))
| U_12996 = c_Orderings_Obot__class_Obot(tc_fun(U_12992,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12992),U_12996))
| hAPP(U_12995,hAPP(hAPP(U_12993,sK302(U_12996,U_12995,U_12994,U_12993,U_12992)),sK303(U_12996,U_12995,U_12994,U_12993,U_12992))) != hAPP(hAPP(U_12993,hAPP(U_12995,sK302(U_12996,U_12995,U_12994,U_12993,U_12992))),hAPP(U_12995,sK303(U_12996,U_12995,U_12994,U_12993,U_12992)))
| ~ c_Finite__Set_Ofolding__one__idem(U_12992,U_12993,U_12994) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK303]),skolemize(U_12990,sK303(U_12996,U_12995,U_12994,U_12993,U_12992))],[f_3353_3]) ).
cnf(f_3353_5,plain,
( hAPP(U_12995,hAPP(U_12994,U_12996)) = hAPP(U_12994,hAPP(c_Set_Oimage(U_12992,U_12992,U_12995),U_12996))
| U_12996 = c_Orderings_Obot__class_Obot(tc_fun(U_12992,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12992),U_12996))
| hAPP(U_12995,hAPP(hAPP(U_12993,sK302(U_12996,U_12995,U_12994,U_12993,U_12992)),sK303(U_12996,U_12995,U_12994,U_12993,U_12992))) != hAPP(hAPP(U_12993,hAPP(U_12995,sK302(U_12996,U_12995,U_12994,U_12993,U_12992))),hAPP(U_12995,sK303(U_12996,U_12995,U_12994,U_12993,U_12992)))
| ~ c_Finite__Set_Ofolding__one__idem(U_12992,U_12993,U_12994) ),
inference(clausify,[status(thm)],[f_3353_4]) ).
fof(f_3354_1,plain,
! [V_f_2,V_S_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_S_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) ),
inference(fof_nnf,[status(thm)],[fact_setprod__pos__nat]) ).
fof(f_3354_2,plain,
! [U_13000,U_12999,U_12998] :
( 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_12998,tc_Nat_Onat),U_13000),U_12999)))
| ? [U_12997] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_13000,U_12997)))
& hBOOL(hAPP(hAPP(c_member(U_12998),U_12997),U_12999)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12998),U_12999)) ),
inference(variable_rename,[status(thm)],[f_3354_1]) ).
fof(f_3354_3,plain,
! [U_13000,U_12999,U_12998] :
( 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_12998,tc_Nat_Onat),U_13000),U_12999)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_13000,sK304(U_13000,U_12999,U_12998))))
& hBOOL(hAPP(hAPP(c_member(U_12998),sK304(U_13000,U_12999,U_12998)),U_12999)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12998),U_12999)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK304]),skolemize(U_12997,sK304(U_13000,U_12999,U_12998))],[f_3354_2]) ).
cnf(f_3354_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_12998),sK304(U_13000,U_12999,U_12998)),U_12999))
| 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_12998,tc_Nat_Onat),U_13000),U_12999)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12998),U_12999)) ),
inference(clausify,[status(thm)],[f_3354_3]) ).
cnf(f_3354_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_13000,sK304(U_13000,U_12999,U_12998))))
| 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_12998,tc_Nat_Onat),U_13000),U_12999)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12998),U_12999)) ),
inference(clausify,[status(thm)],[f_3354_3]) ).
fof(f_3355_1,plain,
! [V_y_2] :
( ? [B_x] : V_y_2 = hAPP(c_Int_ORep__Integ,B_x)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) ),
inference(fof_nnf,[status(thm)],[fact_Rep__Integ__cases]) ).
fof(f_3355_2,plain,
! [U_13002] :
( ? [U_13001] : U_13002 = hAPP(c_Int_ORep__Integ,U_13001)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13002),c_Int_OInteg)) ),
inference(variable_rename,[status(thm)],[f_3355_1]) ).
fof(f_3355_3,plain,
! [U_13002] :
( U_13002 = hAPP(c_Int_ORep__Integ,sK305(U_13002))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13002),c_Int_OInteg)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK305]),skolemize(U_13001,sK305(U_13002))],[f_3355_2]) ).
cnf(f_3355_4,plain,
( U_13002 = hAPP(c_Int_ORep__Integ,sK305(U_13002))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13002),c_Int_OInteg)) ),
inference(clausify,[status(thm)],[f_3355_3]) ).
fof(f_3356_1,plain,
! [V_P_2,V_y_2] :
( hBOOL(hAPP(V_P_2,V_y_2))
| ? [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) ),
inference(fof_nnf,[status(thm)],[fact_Rep__Integ__induct]) ).
fof(f_3356_2,plain,
! [U_13005,U_13004] :
( hBOOL(hAPP(U_13005,U_13004))
| ? [U_13003] : ~ hBOOL(hAPP(U_13005,hAPP(c_Int_ORep__Integ,U_13003)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13004),c_Int_OInteg)) ),
inference(variable_rename,[status(thm)],[f_3356_1]) ).
fof(f_3356_3,plain,
! [U_13005,U_13004] :
( hBOOL(hAPP(U_13005,U_13004))
| ~ hBOOL(hAPP(U_13005,hAPP(c_Int_ORep__Integ,sK306(U_13005,U_13004))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13004),c_Int_OInteg)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK306]),skolemize(U_13003,sK306(U_13005,U_13004))],[f_3356_2]) ).
cnf(f_3356_4,plain,
( hBOOL(hAPP(U_13005,U_13004))
| ~ hBOOL(hAPP(U_13005,hAPP(c_Int_ORep__Integ,sK306(U_13005,U_13004))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13004),c_Int_OInteg)) ),
inference(clausify,[status(thm)],[f_3356_3]) ).
fof(f_3357_1,plain,
! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__remove]) ).
fof(f_3357_2,plain,
! [U_13006] : c_Finite__Set_Ofun__left__comm__idem(U_13006,tc_fun(U_13006,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13006,tc_HOL_Obool),tc_fun(tc_fun(U_13006,tc_HOL_Obool),tc_fun(U_13006,tc_HOL_Obool)),U_13006),hAPP(c_COMBC(tc_fun(U_13006,tc_HOL_Obool),tc_fun(U_13006,tc_HOL_Obool),tc_fun(U_13006,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_13006,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_13006,tc_fun(U_13006,tc_HOL_Obool),tc_fun(U_13006,tc_HOL_Obool)),c_Set_Oinsert(U_13006)),c_Orderings_Obot__class_Obot(tc_fun(U_13006,tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_3357_1]) ).
cnf(f_3357_3,plain,
c_Finite__Set_Ofun__left__comm__idem(U_13006,tc_fun(U_13006,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13006,tc_HOL_Obool),tc_fun(tc_fun(U_13006,tc_HOL_Obool),tc_fun(U_13006,tc_HOL_Obool)),U_13006),hAPP(c_COMBC(tc_fun(U_13006,tc_HOL_Obool),tc_fun(U_13006,tc_HOL_Obool),tc_fun(U_13006,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_13006,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_13006,tc_fun(U_13006,tc_HOL_Obool),tc_fun(U_13006,tc_HOL_Obool)),c_Set_Oinsert(U_13006)),c_Orderings_Obot__class_Obot(tc_fun(U_13006,tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_3357_2]) ).
fof(f_3358_1,plain,
! [T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b))
| ~ class_Lattices_Osemilattice__sup(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__sup]) ).
fof(f_3358_2,plain,
! [U_13007] :
( c_Finite__Set_Ofun__left__comm__idem(U_13007,U_13007,c_Lattices_Osemilattice__sup__class_Osup(U_13007))
| ~ class_Lattices_Osemilattice__sup(U_13007) ),
inference(variable_rename,[status(thm)],[f_3358_1]) ).
cnf(f_3358_3,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_13007,U_13007,c_Lattices_Osemilattice__sup__class_Osup(U_13007))
| ~ class_Lattices_Osemilattice__sup(U_13007) ),
inference(clausify,[status(thm)],[f_3358_2]) ).
fof(f_3359_1,plain,
! [T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b))
| ~ class_Lattices_Osemilattice__inf(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__inf]) ).
fof(f_3359_2,plain,
! [U_13008] :
( c_Finite__Set_Ofun__left__comm__idem(U_13008,U_13008,c_Lattices_Osemilattice__inf__class_Oinf(U_13008))
| ~ class_Lattices_Osemilattice__inf(U_13008) ),
inference(variable_rename,[status(thm)],[f_3359_1]) ).
cnf(f_3359_3,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_13008,U_13008,c_Lattices_Osemilattice__inf__class_Oinf(U_13008))
| ~ class_Lattices_Osemilattice__inf(U_13008) ),
inference(clausify,[status(thm)],[f_3359_2]) ).
fof(f_3360_1,plain,
! [T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b))
| ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem]) ).
fof(f_3360_2,plain,
! [U_13009] :
( c_Finite__Set_Ofun__left__comm__idem(U_13009,U_13009,c_Groups_Otimes__class_Otimes(U_13009))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_13009) ),
inference(variable_rename,[status(thm)],[f_3360_1]) ).
cnf(f_3360_3,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_13009,U_13009,c_Groups_Otimes__class_Otimes(U_13009))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_13009) ),
inference(clausify,[status(thm)],[f_3360_2]) ).
fof(f_3361_1,plain,
! [V_g_2,T_d,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2))
| ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__comm__idem__apply]) ).
fof(f_3361_2,plain,
! [U_13014,U_13013,U_13012,U_13011,U_13010] :
( c_Finite__Set_Ofun__left__comm__idem(U_13013,U_13011,hAPP(hAPP(c_COMBB(U_13010,tc_fun(U_13011,U_13011),U_13013),U_13012),U_13014))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_13010,U_13011,U_13012) ),
inference(variable_rename,[status(thm)],[f_3361_1]) ).
cnf(f_3361_3,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_13013,U_13011,hAPP(hAPP(c_COMBB(U_13010,tc_fun(U_13011,U_13011),U_13013),U_13012),U_13014))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_13010,U_13011,U_13012) ),
inference(clausify,[status(thm)],[f_3361_2]) ).
fof(f_3362_1,plain,
! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) = hAPP(hAPP(V_f_2,V_x_2),V_z_2)
| ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__idem]) ).
fof(f_3362_2,plain,
! [U_13019,U_13018,U_13017,U_13016,U_13015] :
( hAPP(hAPP(U_13017,U_13018),hAPP(hAPP(U_13017,U_13018),U_13019)) = hAPP(hAPP(U_13017,U_13018),U_13019)
| ~ c_Finite__Set_Ofun__left__comm__idem(U_13015,U_13016,U_13017) ),
inference(variable_rename,[status(thm)],[f_3362_1]) ).
fof(f_3362_3,plain,
! [U_13019,U_13018,U_13017] :
( ! [U_13016,U_13015] : ~ c_Finite__Set_Ofun__left__comm__idem(U_13015,U_13016,U_13017)
| hAPP(hAPP(U_13017,U_13018),hAPP(hAPP(U_13017,U_13018),U_13019)) = hAPP(hAPP(U_13017,U_13018),U_13019) ),
inference(miniscope,[status(thm)],[f_3362_2]) ).
cnf(f_3362_4,plain,
( ~ c_Finite__Set_Ofun__left__comm__idem(U_13015,U_13016,U_13017)
| hAPP(hAPP(U_13017,U_13018),hAPP(hAPP(U_13017,U_13018),U_13019)) = hAPP(hAPP(U_13017,U_13018),U_13019) ),
inference(clausify,[status(thm)],[f_3362_3]) ).
fof(f_3363_1,plain,
! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__insert]) ).
fof(f_3363_2,plain,
! [U_13020] : c_Finite__Set_Ofun__left__comm__idem(U_13020,tc_fun(U_13020,tc_HOL_Obool),c_Set_Oinsert(U_13020)),
inference(variable_rename,[status(thm)],[f_3363_1]) ).
cnf(f_3363_3,plain,
c_Finite__Set_Ofun__left__comm__idem(U_13020,tc_fun(U_13020,tc_HOL_Obool),c_Set_Oinsert(U_13020)),
inference(clausify,[status(thm)],[f_3363_2]) ).
fof(f_3364_1,plain,
! [T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__inf]) ).
fof(f_3364_2,plain,
! [U_13021] :
( c_Finite__Set_Ofun__left__comm__idem(U_13021,U_13021,c_Orderings_Oord__class_Omin(U_13021))
| ~ class_Orderings_Olinorder(U_13021) ),
inference(variable_rename,[status(thm)],[f_3364_1]) ).
cnf(f_3364_3,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_13021,U_13021,c_Orderings_Oord__class_Omin(U_13021))
| ~ class_Orderings_Olinorder(U_13021) ),
inference(clausify,[status(thm)],[f_3364_2]) ).
fof(f_3365_1,plain,
! [T_b] :
( c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__sup]) ).
fof(f_3365_2,plain,
! [U_13022] :
( c_Finite__Set_Ofun__left__comm__idem(U_13022,U_13022,c_Orderings_Oord__class_Omax(U_13022))
| ~ class_Orderings_Olinorder(U_13022) ),
inference(variable_rename,[status(thm)],[f_3365_1]) ).
cnf(f_3365_3,plain,
( c_Finite__Set_Ofun__left__comm__idem(U_13022,U_13022,c_Orderings_Oord__class_Omax(U_13022))
| ~ class_Orderings_Olinorder(U_13022) ),
inference(clausify,[status(thm)],[f_3365_2]) ).
fof(f_3366_1,plain,
! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
( c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))
| ? [B_i] :
( ~ c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i))
& hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2)) )
| V_I_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__INTER]) ).
fof(f_3366_2,plain,
! [U_13029,U_13028,U_13027,U_13026,U_13025,U_13024] :
( c_Fun_Oinj__on(U_13026,U_13027,U_13028,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13025,tc_fun(U_13026,tc_HOL_Obool)),U_13024),U_13029))
| ? [U_13023] :
( ~ c_Fun_Oinj__on(U_13026,U_13027,U_13028,hAPP(U_13029,U_13023))
& hBOOL(hAPP(hAPP(c_member(U_13025),U_13023),U_13024)) )
| U_13024 = c_Orderings_Obot__class_Obot(tc_fun(U_13025,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_3366_1]) ).
fof(f_3366_3,plain,
! [U_13029,U_13028,U_13027,U_13026,U_13025,U_13024] :
( c_Fun_Oinj__on(U_13026,U_13027,U_13028,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13025,tc_fun(U_13026,tc_HOL_Obool)),U_13024),U_13029))
| ( ~ c_Fun_Oinj__on(U_13026,U_13027,U_13028,hAPP(U_13029,sK307(U_13029,U_13028,U_13027,U_13026,U_13025,U_13024)))
& hBOOL(hAPP(hAPP(c_member(U_13025),sK307(U_13029,U_13028,U_13027,U_13026,U_13025,U_13024)),U_13024)) )
| U_13024 = c_Orderings_Obot__class_Obot(tc_fun(U_13025,tc_HOL_Obool)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK307]),skolemize(U_13023,sK307(U_13029,U_13028,U_13027,U_13026,U_13025,U_13024))],[f_3366_2]) ).
cnf(f_3366_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_13025),sK307(U_13029,U_13028,U_13027,U_13026,U_13025,U_13024)),U_13024))
| c_Fun_Oinj__on(U_13026,U_13027,U_13028,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13025,tc_fun(U_13026,tc_HOL_Obool)),U_13024),U_13029))
| U_13024 = c_Orderings_Obot__class_Obot(tc_fun(U_13025,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3366_3]) ).
cnf(f_3366_5,plain,
( ~ c_Fun_Oinj__on(U_13026,U_13027,U_13028,hAPP(U_13029,sK307(U_13029,U_13028,U_13027,U_13026,U_13025,U_13024)))
| c_Fun_Oinj__on(U_13026,U_13027,U_13028,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13025,tc_fun(U_13026,tc_HOL_Obool)),U_13024),U_13029))
| U_13024 = c_Orderings_Obot__class_Obot(tc_fun(U_13025,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3366_3]) ).
fof(f_3367_1,plain,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
| ? [B_x] :
( hAPP(V_g_2,B_x) != V_z_2
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__inter__neutral]) ).
fof(f_3367_2,plain,
! [U_13038,U_13037,U_13036,U_13035,U_13034,U_13033,U_13032,U_13031] :
( hAPP(U_13036,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13032,tc_HOL_Obool)),U_13037),U_13038)) = hAPP(hAPP(U_13033,hAPP(U_13036,U_13037)),hAPP(U_13036,U_13038))
| ? [U_13030] :
( hAPP(U_13035,U_13030) != U_13034
& hBOOL(hAPP(hAPP(c_member(U_13032),U_13030),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13032,tc_HOL_Obool)),U_13037),U_13038))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13032),U_13038))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13032),U_13037))
| ~ c_Finite__Set_Ofolding__image__simple(U_13031,U_13032,U_13033,U_13034,U_13035,U_13036) ),
inference(variable_rename,[status(thm)],[f_3367_1]) ).
fof(f_3367_3,plain,
! [U_13038,U_13037,U_13036,U_13035,U_13034,U_13033,U_13032] :
( ! [U_13031] : ~ c_Finite__Set_Ofolding__image__simple(U_13031,U_13032,U_13033,U_13034,U_13035,U_13036)
| hAPP(U_13036,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13032,tc_HOL_Obool)),U_13037),U_13038)) = hAPP(hAPP(U_13033,hAPP(U_13036,U_13037)),hAPP(U_13036,U_13038))
| ? [U_13030] :
( hAPP(U_13035,U_13030) != U_13034
& hBOOL(hAPP(hAPP(c_member(U_13032),U_13030),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13032,tc_HOL_Obool)),U_13037),U_13038))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13032),U_13038))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13032),U_13037)) ),
inference(miniscope,[status(thm)],[f_3367_2]) ).
fof(f_3367_4,plain,
! [U_13038,U_13037,U_13036,U_13035,U_13034,U_13033,U_13032] :
( ! [U_13031] : ~ c_Finite__Set_Ofolding__image__simple(U_13031,U_13032,U_13033,U_13034,U_13035,U_13036)
| hAPP(U_13036,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13032,tc_HOL_Obool)),U_13037),U_13038)) = hAPP(hAPP(U_13033,hAPP(U_13036,U_13037)),hAPP(U_13036,U_13038))
| ( hAPP(U_13035,sK308(U_13038,U_13037,U_13036,U_13035,U_13034,U_13033,U_13032)) != U_13034
& hBOOL(hAPP(hAPP(c_member(U_13032),sK308(U_13038,U_13037,U_13036,U_13035,U_13034,U_13033,U_13032)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13032,tc_HOL_Obool)),U_13037),U_13038))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13032),U_13038))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13032),U_13037)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK308]),skolemize(U_13030,sK308(U_13038,U_13037,U_13036,U_13035,U_13034,U_13033,U_13032))],[f_3367_3]) ).
cnf(f_3367_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_13032),sK308(U_13038,U_13037,U_13036,U_13035,U_13034,U_13033,U_13032)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13032,tc_HOL_Obool)),U_13037),U_13038)))
| hAPP(U_13036,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13032,tc_HOL_Obool)),U_13037),U_13038)) = hAPP(hAPP(U_13033,hAPP(U_13036,U_13037)),hAPP(U_13036,U_13038))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13032),U_13038))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13032),U_13037))
| ~ c_Finite__Set_Ofolding__image__simple(U_13031,U_13032,U_13033,U_13034,U_13035,U_13036) ),
inference(clausify,[status(thm)],[f_3367_4]) ).
cnf(f_3367_6,plain,
( hAPP(U_13035,sK308(U_13038,U_13037,U_13036,U_13035,U_13034,U_13033,U_13032)) != U_13034
| hAPP(U_13036,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13032,tc_HOL_Obool)),U_13037),U_13038)) = hAPP(hAPP(U_13033,hAPP(U_13036,U_13037)),hAPP(U_13036,U_13038))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13032),U_13038))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13032),U_13037))
| ~ c_Finite__Set_Ofolding__image__simple(U_13031,U_13032,U_13033,U_13034,U_13035,U_13036) ),
inference(clausify,[status(thm)],[f_3367_4]) ).
fof(f_3368_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_3368_2,plain,
! [U_13040,U_13039] :
( 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_13039))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13040))))) = 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_13039))),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_13040)))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13039)) ),
inference(variable_rename,[status(thm)],[f_3368_1]) ).
cnf(f_3368_3,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_13039))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13040))))) = 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_13039))),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_13040)))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13039)) ),
inference(clausify,[status(thm)],[f_3368_2]) ).
fof(f_3369_1,plain,
! [T_b,V_a_2,V_P_2] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
| ~ hBOOL(hAPP(V_P_2,V_a_2)) ),
inference(fof_nnf,[status(thm)],[fact_CollectI]) ).
fof(f_3369_2,plain,
! [U_13043,U_13042,U_13041] :
( hBOOL(hAPP(hAPP(c_member(U_13043),U_13042),hAPP(c_Set_OCollect(U_13043),U_13041)))
| ~ hBOOL(hAPP(U_13041,U_13042)) ),
inference(variable_rename,[status(thm)],[f_3369_1]) ).
cnf(f_3369_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_13043),U_13042),hAPP(c_Set_OCollect(U_13043),U_13041)))
| ~ hBOOL(hAPP(U_13041,U_13042)) ),
inference(clausify,[status(thm)],[f_3369_2]) ).
fof(f_3370_1,plain,
! [V_Q_2,V_P_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2))))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2)))
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__conjI]) ).
fof(f_3370_2,plain,
! [U_13046,U_13045,U_13044] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13044),hAPP(c_Set_OCollect(U_13044),hAPP(hAPP(c_COMBS(U_13044,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13044),c_fconj),U_13045)),U_13046))))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13044),hAPP(c_Set_OCollect(U_13044),U_13046)))
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13044),hAPP(c_Set_OCollect(U_13044),U_13045))) ) ),
inference(variable_rename,[status(thm)],[f_3370_1]) ).
cnf(f_3370_3,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13044),hAPP(c_Set_OCollect(U_13044),U_13045)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_13044),hAPP(c_Set_OCollect(U_13044),hAPP(hAPP(c_COMBS(U_13044,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13044),c_fconj),U_13045)),U_13046)))) ),
inference(clausify,[status(thm)],[f_3370_2]) ).
cnf(f_3370_4,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13044),hAPP(c_Set_OCollect(U_13044),U_13046)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_13044),hAPP(c_Set_OCollect(U_13044),hAPP(hAPP(c_COMBS(U_13044,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13044),c_fconj),U_13045)),U_13046)))) ),
inference(clausify,[status(thm)],[f_3370_2]) ).
fof(f_3371_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_3371_2,plain,
! [U_13047] : 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_13047)))),
inference(variable_rename,[status(thm)],[f_3371_1]) ).
cnf(f_3371_3,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_13047)))),
inference(clausify,[status(thm)],[f_3371_2]) ).
fof(f_3372_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_3372_2,plain,
! [U_13048] : 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_13048)))),
inference(variable_rename,[status(thm)],[f_3372_1]) ).
cnf(f_3372_3,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_13048)))),
inference(clausify,[status(thm)],[f_3372_2]) ).
fof(f_3373_1,plain,
! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),V_P_2) = V_P_2,
inference(fof_nnf,[status(thm)],[fact_Collect__def]) ).
fof(f_3373_2,plain,
! [U_13050,U_13049] : hAPP(c_Set_OCollect(U_13049),U_13050) = U_13050,
inference(variable_rename,[status(thm)],[f_3373_1]) ).
cnf(f_3373_3,plain,
hAPP(c_Set_OCollect(U_13049),U_13050) = U_13050,
inference(clausify,[status(thm)],[f_3373_2]) ).
fof(f_3374_1,plain,
! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)),
inference(fof_nnf,[status(thm)],[fact_Collect__disj__eq]) ).
fof(f_3374_2,plain,
! [U_13053,U_13052,U_13051] : hAPP(c_Set_OCollect(U_13051),hAPP(hAPP(c_COMBS(U_13051,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13051),c_fdisj),U_13052)),U_13053)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13051,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13051),U_13052)),hAPP(c_Set_OCollect(U_13051),U_13053)),
inference(variable_rename,[status(thm)],[f_3374_1]) ).
cnf(f_3374_3,plain,
hAPP(c_Set_OCollect(U_13051),hAPP(hAPP(c_COMBS(U_13051,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13051),c_fdisj),U_13052)),U_13053)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13051,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13051),U_13052)),hAPP(c_Set_OCollect(U_13051),U_13053)),
inference(clausify,[status(thm)],[f_3374_2]) ).
fof(f_3375_1,plain,
! [V_P_2,T_b] :
( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_P_2)
| ? [B_x] : hBOOL(hAPP(V_P_2,B_x)) )
& ( ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x))
| c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(c_Set_OCollect(T_b),V_P_2) ) ),
inference(fof_nnf,[status(thm)],[fact_empty__Collect__eq]) ).
fof(f_3375_2,plain,
! [U_13057,U_13056] :
( ( c_Orderings_Obot__class_Obot(tc_fun(U_13056,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13056),U_13057)
| ? [U_13055] : hBOOL(hAPP(U_13057,U_13055)) )
& ( ! [U_13054] : ~ hBOOL(hAPP(U_13057,U_13054))
| c_Orderings_Obot__class_Obot(tc_fun(U_13056,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_13056),U_13057) ) ),
inference(variable_rename,[status(thm)],[f_3375_1]) ).
fof(f_3375_3,plain,
( ! [U_13061] :
( ! [U_13059] : c_Orderings_Obot__class_Obot(tc_fun(U_13059,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13059),U_13061)
| ? [U_13055] : hBOOL(hAPP(U_13061,U_13055)) )
& ! [U_13060] :
( ! [U_13058] : c_Orderings_Obot__class_Obot(tc_fun(U_13058,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_13058),U_13060)
| ! [U_13054] : ~ hBOOL(hAPP(U_13060,U_13054)) ) ),
inference(miniscope,[status(thm)],[f_3375_2]) ).
fof(f_3375_4,plain,
( ! [U_13061] :
( ! [U_13059] : c_Orderings_Obot__class_Obot(tc_fun(U_13059,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13059),U_13061)
| hBOOL(hAPP(U_13061,sK309(U_13061))) )
& ! [U_13060] :
( ! [U_13058] : c_Orderings_Obot__class_Obot(tc_fun(U_13058,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_13058),U_13060)
| ! [U_13054] : ~ hBOOL(hAPP(U_13060,U_13054)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK309]),skolemize(U_13055,sK309(U_13061))],[f_3375_3]) ).
cnf(f_3375_5,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_13058,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_13058),U_13060)
| ~ hBOOL(hAPP(U_13060,U_13054)) ),
inference(clausify,[status(thm)],[f_3375_4]) ).
cnf(f_3375_6,plain,
( c_Orderings_Obot__class_Obot(tc_fun(U_13059,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13059),U_13061)
| hBOOL(hAPP(U_13061,sK309(U_13061))) ),
inference(clausify,[status(thm)],[f_3375_4]) ).
fof(f_3376_1,plain,
! [V_P_2,T_b] :
( ( hAPP(c_Set_OCollect(T_b),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ? [B_x] : hBOOL(hAPP(V_P_2,B_x)) )
& ( ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x))
| hAPP(c_Set_OCollect(T_b),V_P_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_Collect__empty__eq]) ).
fof(f_3376_2,plain,
! [U_13065,U_13064] :
( ( hAPP(c_Set_OCollect(U_13064),U_13065) = c_Orderings_Obot__class_Obot(tc_fun(U_13064,tc_HOL_Obool))
| ? [U_13063] : hBOOL(hAPP(U_13065,U_13063)) )
& ( ! [U_13062] : ~ hBOOL(hAPP(U_13065,U_13062))
| hAPP(c_Set_OCollect(U_13064),U_13065) != c_Orderings_Obot__class_Obot(tc_fun(U_13064,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3376_1]) ).
fof(f_3376_3,plain,
( ! [U_13069] :
( ! [U_13067] : hAPP(c_Set_OCollect(U_13067),U_13069) = c_Orderings_Obot__class_Obot(tc_fun(U_13067,tc_HOL_Obool))
| ? [U_13063] : hBOOL(hAPP(U_13069,U_13063)) )
& ! [U_13068] :
( ! [U_13066] : hAPP(c_Set_OCollect(U_13066),U_13068) != c_Orderings_Obot__class_Obot(tc_fun(U_13066,tc_HOL_Obool))
| ! [U_13062] : ~ hBOOL(hAPP(U_13068,U_13062)) ) ),
inference(miniscope,[status(thm)],[f_3376_2]) ).
fof(f_3376_4,plain,
( ! [U_13069] :
( ! [U_13067] : hAPP(c_Set_OCollect(U_13067),U_13069) = c_Orderings_Obot__class_Obot(tc_fun(U_13067,tc_HOL_Obool))
| hBOOL(hAPP(U_13069,sK310(U_13069))) )
& ! [U_13068] :
( ! [U_13066] : hAPP(c_Set_OCollect(U_13066),U_13068) != c_Orderings_Obot__class_Obot(tc_fun(U_13066,tc_HOL_Obool))
| ! [U_13062] : ~ hBOOL(hAPP(U_13068,U_13062)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK310]),skolemize(U_13063,sK310(U_13069))],[f_3376_3]) ).
cnf(f_3376_5,plain,
( hAPP(c_Set_OCollect(U_13066),U_13068) != c_Orderings_Obot__class_Obot(tc_fun(U_13066,tc_HOL_Obool))
| ~ hBOOL(hAPP(U_13068,U_13062)) ),
inference(clausify,[status(thm)],[f_3376_4]) ).
cnf(f_3376_6,plain,
( hAPP(c_Set_OCollect(U_13067),U_13069) = c_Orderings_Obot__class_Obot(tc_fun(U_13067,tc_HOL_Obool))
| hBOOL(hAPP(U_13069,sK310(U_13069))) ),
inference(clausify,[status(thm)],[f_3376_4]) ).
fof(f_3377_1,plain,
! [T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse)),
inference(fof_nnf,[status(thm)],[fact_empty__def]) ).
fof(f_3377_2,plain,
! [U_13070] : c_Orderings_Obot__class_Obot(tc_fun(U_13070,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13070),hAPP(c_COMBK(tc_HOL_Obool,U_13070),c_fFalse)),
inference(variable_rename,[status(thm)],[f_3377_1]) ).
cnf(f_3377_3,plain,
c_Orderings_Obot__class_Obot(tc_fun(U_13070,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13070),hAPP(c_COMBK(tc_HOL_Obool,U_13070),c_fFalse)),
inference(clausify,[status(thm)],[f_3377_2]) ).
fof(f_3378_1,plain,
! [V_P_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_P_2)),
inference(fof_nnf,[status(thm)],[fact_insert__Collect]) ).
fof(f_3378_2,plain,
! [U_13073,U_13072,U_13071] : hAPP(hAPP(c_Set_Oinsert(U_13071),U_13072),hAPP(c_Set_OCollect(U_13071),U_13073)) = hAPP(c_Set_OCollect(U_13071),hAPP(hAPP(c_COMBS(U_13071,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13071),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13071),c_fNot),hAPP(hAPP(c_COMBC(U_13071,U_13071,tc_HOL_Obool),c_fequal),U_13072)))),U_13073)),
inference(variable_rename,[status(thm)],[f_3378_1]) ).
cnf(f_3378_3,plain,
hAPP(hAPP(c_Set_Oinsert(U_13071),U_13072),hAPP(c_Set_OCollect(U_13071),U_13073)) = hAPP(c_Set_OCollect(U_13071),hAPP(hAPP(c_COMBS(U_13071,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13071),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13071),c_fNot),hAPP(hAPP(c_COMBC(U_13071,U_13071,tc_HOL_Obool),c_fequal),U_13072)))),U_13073)),
inference(clausify,[status(thm)],[f_3378_2]) ).
fof(f_3379_1,plain,
! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)),
inference(fof_nnf,[status(thm)],[fact_Collect__conj__eq]) ).
fof(f_3379_2,plain,
! [U_13076,U_13075,U_13074] : hAPP(c_Set_OCollect(U_13074),hAPP(hAPP(c_COMBS(U_13074,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13074),c_fconj),U_13075)),U_13076)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13074,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13074),U_13075)),hAPP(c_Set_OCollect(U_13074),U_13076)),
inference(variable_rename,[status(thm)],[f_3379_1]) ).
cnf(f_3379_3,plain,
hAPP(c_Set_OCollect(U_13074),hAPP(hAPP(c_COMBS(U_13074,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13074),c_fconj),U_13075)),U_13076)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13074,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13074),U_13075)),hAPP(c_Set_OCollect(U_13074),U_13076)),
inference(clausify,[status(thm)],[f_3379_2]) ).
fof(f_3380_1,plain,
! [V_Q_2,V_P_2,T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),V_P_2)),V_Q_2)))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__disjI]) ).
fof(f_3380_2,plain,
! [U_13079,U_13078,U_13077] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13077),hAPP(c_Set_OCollect(U_13077),hAPP(hAPP(c_COMBS(U_13077,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13077),c_fdisj),U_13078)),U_13079))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13077),hAPP(c_Set_OCollect(U_13077),U_13079)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13077),hAPP(c_Set_OCollect(U_13077),U_13078))) )
& ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13077),hAPP(c_Set_OCollect(U_13077),U_13079)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_13077),hAPP(c_Set_OCollect(U_13077),U_13078))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13077),hAPP(c_Set_OCollect(U_13077),hAPP(hAPP(c_COMBS(U_13077,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13077),c_fdisj),U_13078)),U_13079)))) ) ),
inference(variable_rename,[status(thm)],[f_3380_1]) ).
fof(f_3380_3,plain,
( ! [U_13085,U_13083,U_13081] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13081),hAPP(c_Set_OCollect(U_13081),hAPP(hAPP(c_COMBS(U_13081,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13081),c_fdisj),U_13083)),U_13085))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13081),hAPP(c_Set_OCollect(U_13081),U_13085)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13081),hAPP(c_Set_OCollect(U_13081),U_13083))) )
& ! [U_13084,U_13082,U_13080] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13080),hAPP(c_Set_OCollect(U_13080),U_13084)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_13080),hAPP(c_Set_OCollect(U_13080),U_13082))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13080),hAPP(c_Set_OCollect(U_13080),hAPP(hAPP(c_COMBS(U_13080,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13080),c_fdisj),U_13082)),U_13084)))) ) ),
inference(miniscope,[status(thm)],[f_3380_2]) ).
cnf(f_3380_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13080),hAPP(c_Set_OCollect(U_13080),U_13082)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13080),hAPP(c_Set_OCollect(U_13080),hAPP(hAPP(c_COMBS(U_13080,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13080),c_fdisj),U_13082)),U_13084)))) ),
inference(clausify,[status(thm)],[f_3380_3]) ).
cnf(f_3380_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13080),hAPP(c_Set_OCollect(U_13080),U_13084)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13080),hAPP(c_Set_OCollect(U_13080),hAPP(hAPP(c_COMBS(U_13080,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13080),c_fdisj),U_13082)),U_13084)))) ),
inference(clausify,[status(thm)],[f_3380_3]) ).
cnf(f_3380_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13081),hAPP(c_Set_OCollect(U_13081),hAPP(hAPP(c_COMBS(U_13081,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13081),c_fdisj),U_13083)),U_13085))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13081),hAPP(c_Set_OCollect(U_13081),U_13085)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13081),hAPP(c_Set_OCollect(U_13081),U_13083))) ),
inference(clausify,[status(thm)],[f_3380_3]) ).
fof(f_3381_1,plain,
! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fTrue)),
inference(fof_nnf,[status(thm)],[fact_UNIV__def]) ).
fof(f_3381_2,plain,
! [U_13086] : c_Orderings_Otop__class_Otop(tc_fun(U_13086,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13086),hAPP(c_COMBK(tc_HOL_Obool,U_13086),c_fTrue)),
inference(variable_rename,[status(thm)],[f_3381_1]) ).
cnf(f_3381_3,plain,
c_Orderings_Otop__class_Otop(tc_fun(U_13086,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13086),hAPP(c_COMBK(tc_HOL_Obool,U_13086),c_fTrue)),
inference(clausify,[status(thm)],[f_3381_2]) ).
fof(f_3382_1,plain,
! [V_A_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Collect__mem__eq]) ).
fof(f_3382_2,plain,
! [U_13088,U_13087] : hAPP(c_Set_OCollect(U_13087),hAPP(hAPP(c_COMBC(U_13087,tc_fun(U_13087,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13087)),U_13088)) = U_13088,
inference(variable_rename,[status(thm)],[f_3382_1]) ).
cnf(f_3382_3,plain,
hAPP(c_Set_OCollect(U_13087),hAPP(hAPP(c_COMBC(U_13087,tc_fun(U_13087,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13087)),U_13088)) = U_13088,
inference(clausify,[status(thm)],[f_3382_2]) ).
fof(f_3383_1,plain,
! [V_P_2,V_a_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
| ~ hBOOL(hAPP(V_P_2,V_a_2)) )
& ( hBOOL(hAPP(V_P_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_mem__Collect__eq]) ).
fof(f_3383_2,plain,
! [U_13091,U_13090,U_13089] :
( ( hBOOL(hAPP(hAPP(c_member(U_13089),U_13090),hAPP(c_Set_OCollect(U_13089),U_13091)))
| ~ hBOOL(hAPP(U_13091,U_13090)) )
& ( hBOOL(hAPP(U_13091,U_13090))
| ~ hBOOL(hAPP(hAPP(c_member(U_13089),U_13090),hAPP(c_Set_OCollect(U_13089),U_13091))) ) ),
inference(variable_rename,[status(thm)],[f_3383_1]) ).
fof(f_3383_3,plain,
( ! [U_13097,U_13095] :
( ! [U_13093] : hBOOL(hAPP(hAPP(c_member(U_13093),U_13095),hAPP(c_Set_OCollect(U_13093),U_13097)))
| ~ hBOOL(hAPP(U_13097,U_13095)) )
& ! [U_13096,U_13094] :
( ! [U_13092] : ~ hBOOL(hAPP(hAPP(c_member(U_13092),U_13094),hAPP(c_Set_OCollect(U_13092),U_13096)))
| hBOOL(hAPP(U_13096,U_13094)) ) ),
inference(miniscope,[status(thm)],[f_3383_2]) ).
cnf(f_3383_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_13092),U_13094),hAPP(c_Set_OCollect(U_13092),U_13096)))
| hBOOL(hAPP(U_13096,U_13094)) ),
inference(clausify,[status(thm)],[f_3383_3]) ).
cnf(f_3383_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_13093),U_13095),hAPP(c_Set_OCollect(U_13093),U_13097)))
| ~ hBOOL(hAPP(U_13097,U_13095)) ),
inference(clausify,[status(thm)],[f_3383_3]) ).
fof(f_3384_1,plain,
! [V_P_2,V_a_2,T_b] :
( hBOOL(hAPP(V_P_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
inference(fof_nnf,[status(thm)],[fact_CollectD]) ).
fof(f_3384_2,plain,
! [U_13100,U_13099,U_13098] :
( hBOOL(hAPP(U_13100,U_13099))
| ~ hBOOL(hAPP(hAPP(c_member(U_13098),U_13099),hAPP(c_Set_OCollect(U_13098),U_13100))) ),
inference(variable_rename,[status(thm)],[f_3384_1]) ).
fof(f_3384_3,plain,
! [U_13100,U_13099] :
( ! [U_13098] : ~ hBOOL(hAPP(hAPP(c_member(U_13098),U_13099),hAPP(c_Set_OCollect(U_13098),U_13100)))
| hBOOL(hAPP(U_13100,U_13099)) ),
inference(miniscope,[status(thm)],[f_3384_2]) ).
cnf(f_3384_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_13098),U_13099),hAPP(c_Set_OCollect(U_13098),U_13100)))
| hBOOL(hAPP(U_13100,U_13099)) ),
inference(clausify,[status(thm)],[f_3384_3]) ).
fof(f_3385_1,plain,
! [V_P_2,V_a_2,T_b] :
( hBOOL(hAPP(V_P_2,V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
inference(fof_nnf,[status(thm)],[fact_CollectE]) ).
fof(f_3385_2,plain,
! [U_13103,U_13102,U_13101] :
( hBOOL(hAPP(U_13103,U_13102))
| ~ hBOOL(hAPP(hAPP(c_member(U_13101),U_13102),hAPP(c_Set_OCollect(U_13101),U_13103))) ),
inference(variable_rename,[status(thm)],[f_3385_1]) ).
fof(f_3385_3,plain,
! [U_13103,U_13102] :
( ! [U_13101] : ~ hBOOL(hAPP(hAPP(c_member(U_13101),U_13102),hAPP(c_Set_OCollect(U_13101),U_13103)))
| hBOOL(hAPP(U_13103,U_13102)) ),
inference(miniscope,[status(thm)],[f_3385_2]) ).
cnf(f_3385_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_13101),U_13102),hAPP(c_Set_OCollect(U_13101),U_13103)))
| hBOOL(hAPP(U_13103,U_13102)) ),
inference(clausify,[status(thm)],[f_3385_3]) ).
fof(f_3386_1,plain,
! [V_P_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_P_2),V_f_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__Collect__eq]) ).
fof(f_3386_2,plain,
! [U_13107,U_13106,U_13105,U_13104] : hAPP(c_Set_Ovimage(U_13104,U_13105,U_13106),hAPP(c_Set_OCollect(U_13105),U_13107)) = hAPP(c_Set_OCollect(U_13104),hAPP(hAPP(c_COMBB(U_13105,tc_HOL_Obool,U_13104),U_13107),U_13106)),
inference(variable_rename,[status(thm)],[f_3386_1]) ).
cnf(f_3386_3,plain,
hAPP(c_Set_Ovimage(U_13104,U_13105,U_13106),hAPP(c_Set_OCollect(U_13105),U_13107)) = hAPP(c_Set_OCollect(U_13104),hAPP(hAPP(c_COMBB(U_13105,tc_HOL_Obool,U_13104),U_13107),U_13106)),
inference(clausify,[status(thm)],[f_3386_2]) ).
fof(f_3387_1,plain,
! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),
inference(fof_nnf,[status(thm)],[fact_Collect__neg__eq]) ).
fof(f_3387_2,plain,
! [U_13109,U_13108] : hAPP(c_Set_OCollect(U_13108),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13108),c_fNot),U_13109)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13108,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13108),U_13109)),
inference(variable_rename,[status(thm)],[f_3387_1]) ).
cnf(f_3387_3,plain,
hAPP(c_Set_OCollect(U_13108),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13108),c_fNot),U_13109)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13108,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13108),U_13109)),
inference(clausify,[status(thm)],[f_3387_2]) ).
fof(f_3388_1,plain,
! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Q_2)),
inference(fof_nnf,[status(thm)],[fact_SetCompr__Sigma__eq]) ).
fof(f_3388_2,plain,
! [U_13113,U_13112,U_13111,U_13110] : hAPP(c_Set_OCollect(tc_prod(U_13110,U_13111)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13110,U_13111,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_13110,tc_fun(U_13111,tc_HOL_Obool),tc_fun(U_13111,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13111,tc_HOL_Obool),tc_fun(U_13111,tc_HOL_Obool)),U_13110),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13111)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13110),c_fconj),U_13112))),U_13113))) = hAPP(hAPP(c_Product__Type_OSigma(U_13110,U_13111),hAPP(c_Set_OCollect(U_13110),U_13112)),hAPP(hAPP(c_COMBB(tc_fun(U_13111,tc_HOL_Obool),tc_fun(U_13111,tc_HOL_Obool),U_13110),c_Set_OCollect(U_13111)),U_13113)),
inference(variable_rename,[status(thm)],[f_3388_1]) ).
cnf(f_3388_3,plain,
hAPP(c_Set_OCollect(tc_prod(U_13110,U_13111)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13110,U_13111,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_13110,tc_fun(U_13111,tc_HOL_Obool),tc_fun(U_13111,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13111,tc_HOL_Obool),tc_fun(U_13111,tc_HOL_Obool)),U_13110),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13111)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13110),c_fconj),U_13112))),U_13113))) = hAPP(hAPP(c_Product__Type_OSigma(U_13110,U_13111),hAPP(c_Set_OCollect(U_13110),U_13112)),hAPP(hAPP(c_COMBB(tc_fun(U_13111,tc_HOL_Obool),tc_fun(U_13111,tc_HOL_Obool),U_13110),c_Set_OCollect(U_13111)),U_13113)),
inference(clausify,[status(thm)],[f_3388_2]) ).
fof(f_3389_1,plain,
! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Q_2))),
inference(fof_nnf,[status(thm)],[fact_Collect__split]) ).
fof(f_3389_2,plain,
! [U_13117,U_13116,U_13115,U_13114] : hAPP(c_Set_OCollect(tc_prod(U_13114,U_13115)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13114,U_13115,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13114,tc_fun(U_13115,tc_HOL_Obool),tc_fun(U_13115,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13115,tc_HOL_Obool),tc_fun(U_13115,tc_HOL_Obool)),U_13114),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13115)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13114),c_fconj),U_13116))),U_13117))) = hAPP(hAPP(c_Product__Type_OSigma(U_13114,U_13115),hAPP(c_Set_OCollect(U_13114),U_13116)),hAPP(c_COMBK(tc_fun(U_13115,tc_HOL_Obool),U_13114),hAPP(c_Set_OCollect(U_13115),U_13117))),
inference(variable_rename,[status(thm)],[f_3389_1]) ).
cnf(f_3389_3,plain,
hAPP(c_Set_OCollect(tc_prod(U_13114,U_13115)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13114,U_13115,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13114,tc_fun(U_13115,tc_HOL_Obool),tc_fun(U_13115,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13115,tc_HOL_Obool),tc_fun(U_13115,tc_HOL_Obool)),U_13114),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13115)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13114),c_fconj),U_13116))),U_13117))) = hAPP(hAPP(c_Product__Type_OSigma(U_13114,U_13115),hAPP(c_Set_OCollect(U_13114),U_13116)),hAPP(c_COMBK(tc_fun(U_13115,tc_HOL_Obool),U_13114),hAPP(c_Set_OCollect(U_13115),U_13117))),
inference(clausify,[status(thm)],[f_3389_2]) ).
fof(f_3390_1,plain,
! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
inference(fof_nnf,[status(thm)],[fact_insert__compr]) ).
fof(f_3390_2,plain,
! [U_13120,U_13119,U_13118] : hAPP(hAPP(c_Set_Oinsert(U_13118),U_13119),U_13120) = hAPP(c_Set_OCollect(U_13118),hAPP(hAPP(c_COMBS(U_13118,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13118),c_fdisj),hAPP(hAPP(c_COMBC(U_13118,U_13118,tc_HOL_Obool),c_fequal),U_13119))),hAPP(hAPP(c_COMBC(U_13118,tc_fun(U_13118,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13118)),U_13120))),
inference(variable_rename,[status(thm)],[f_3390_1]) ).
cnf(f_3390_3,plain,
hAPP(hAPP(c_Set_Oinsert(U_13118),U_13119),U_13120) = hAPP(c_Set_OCollect(U_13118),hAPP(hAPP(c_COMBS(U_13118,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13118),c_fdisj),hAPP(hAPP(c_COMBC(U_13118,U_13118,tc_HOL_Obool),c_fequal),U_13119))),hAPP(hAPP(c_COMBC(U_13118,tc_fun(U_13118,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13118)),U_13120))),
inference(clausify,[status(thm)],[f_3390_2]) ).
fof(f_3391_1,plain,
! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
inference(fof_nnf,[status(thm)],[fact_insert__compr__raw]) ).
fof(f_3391_2,plain,
! [U_13123,U_13122,U_13121] : hAPP(hAPP(c_Set_Oinsert(U_13121),U_13122),U_13123) = hAPP(c_Set_OCollect(U_13121),hAPP(hAPP(c_COMBS(U_13121,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13121),c_fdisj),hAPP(hAPP(c_COMBC(U_13121,U_13121,tc_HOL_Obool),c_fequal),U_13122))),hAPP(hAPP(c_COMBC(U_13121,tc_fun(U_13121,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13121)),U_13123))),
inference(variable_rename,[status(thm)],[f_3391_1]) ).
cnf(f_3391_3,plain,
hAPP(hAPP(c_Set_Oinsert(U_13121),U_13122),U_13123) = hAPP(c_Set_OCollect(U_13121),hAPP(hAPP(c_COMBS(U_13121,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13121),c_fdisj),hAPP(hAPP(c_COMBC(U_13121,U_13121,tc_HOL_Obool),c_fequal),U_13122))),hAPP(hAPP(c_COMBC(U_13121,tc_fun(U_13121,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13121)),U_13123))),
inference(clausify,[status(thm)],[f_3391_2]) ).
fof(f_3392_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fdisj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
inference(fof_nnf,[status(thm)],[fact_Un__def]) ).
fof(f_3392_2,plain,
! [U_13126,U_13125,U_13124] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13124,tc_HOL_Obool)),U_13125),U_13126) = hAPP(c_Set_OCollect(U_13124),hAPP(hAPP(c_COMBS(U_13124,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13124),c_fdisj),hAPP(hAPP(c_COMBC(U_13124,tc_fun(U_13124,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13124)),U_13125))),hAPP(hAPP(c_COMBC(U_13124,tc_fun(U_13124,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13124)),U_13126))),
inference(variable_rename,[status(thm)],[f_3392_1]) ).
cnf(f_3392_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13124,tc_HOL_Obool)),U_13125),U_13126) = hAPP(c_Set_OCollect(U_13124),hAPP(hAPP(c_COMBS(U_13124,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13124),c_fdisj),hAPP(hAPP(c_COMBC(U_13124,tc_fun(U_13124,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13124)),U_13125))),hAPP(hAPP(c_COMBC(U_13124,tc_fun(U_13124,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13124)),U_13126))),
inference(clausify,[status(thm)],[f_3392_2]) ).
fof(f_3393_1,plain,
! [V_P_2,V_A_2,V_x_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))))
| ~ hBOOL(hAPP(V_P_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
& ( ( hBOOL(hAPP(V_P_2,V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2)))) ) ),
inference(fof_nnf,[status(thm)],[fact_Int__Collect]) ).
fof(f_3393_2,plain,
! [U_13130,U_13129,U_13128,U_13127] :
( ( hBOOL(hAPP(hAPP(c_member(U_13127),U_13128),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13127,tc_HOL_Obool)),U_13129),hAPP(c_Set_OCollect(U_13127),U_13130))))
| ~ hBOOL(hAPP(U_13130,U_13128))
| ~ hBOOL(hAPP(hAPP(c_member(U_13127),U_13128),U_13129)) )
& ( ( hBOOL(hAPP(U_13130,U_13128))
& hBOOL(hAPP(hAPP(c_member(U_13127),U_13128),U_13129)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_13127),U_13128),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13127,tc_HOL_Obool)),U_13129),hAPP(c_Set_OCollect(U_13127),U_13130)))) ) ),
inference(variable_rename,[status(thm)],[f_3393_1]) ).
fof(f_3393_3,plain,
( ! [U_13138,U_13136,U_13134,U_13132] :
( hBOOL(hAPP(hAPP(c_member(U_13132),U_13134),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13132,tc_HOL_Obool)),U_13136),hAPP(c_Set_OCollect(U_13132),U_13138))))
| ~ hBOOL(hAPP(U_13138,U_13134))
| ~ hBOOL(hAPP(hAPP(c_member(U_13132),U_13134),U_13136)) )
& ! [U_13137,U_13135,U_13133,U_13131] :
( ( hBOOL(hAPP(U_13137,U_13133))
& hBOOL(hAPP(hAPP(c_member(U_13131),U_13133),U_13135)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_13131),U_13133),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13131,tc_HOL_Obool)),U_13135),hAPP(c_Set_OCollect(U_13131),U_13137)))) ) ),
inference(miniscope,[status(thm)],[f_3393_2]) ).
cnf(f_3393_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_13131),U_13133),U_13135))
| ~ hBOOL(hAPP(hAPP(c_member(U_13131),U_13133),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13131,tc_HOL_Obool)),U_13135),hAPP(c_Set_OCollect(U_13131),U_13137)))) ),
inference(clausify,[status(thm)],[f_3393_3]) ).
cnf(f_3393_5,plain,
( hBOOL(hAPP(U_13137,U_13133))
| ~ hBOOL(hAPP(hAPP(c_member(U_13131),U_13133),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13131,tc_HOL_Obool)),U_13135),hAPP(c_Set_OCollect(U_13131),U_13137)))) ),
inference(clausify,[status(thm)],[f_3393_3]) ).
cnf(f_3393_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_13132),U_13134),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13132,tc_HOL_Obool)),U_13136),hAPP(c_Set_OCollect(U_13132),U_13138))))
| ~ hBOOL(hAPP(U_13138,U_13134))
| ~ hBOOL(hAPP(hAPP(c_member(U_13132),U_13134),U_13136)) ),
inference(clausify,[status(thm)],[f_3393_3]) ).
fof(f_3394_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),
inference(fof_nnf,[status(thm)],[fact_Int__def]) ).
fof(f_3394_2,plain,
! [U_13141,U_13140,U_13139] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13139,tc_HOL_Obool)),U_13140),U_13141) = hAPP(c_Set_OCollect(U_13139),hAPP(hAPP(c_COMBS(U_13139,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13139),c_fconj),hAPP(hAPP(c_COMBC(U_13139,tc_fun(U_13139,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13139)),U_13140))),hAPP(hAPP(c_COMBC(U_13139,tc_fun(U_13139,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13139)),U_13141))),
inference(variable_rename,[status(thm)],[f_3394_1]) ).
cnf(f_3394_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13139,tc_HOL_Obool)),U_13140),U_13141) = hAPP(c_Set_OCollect(U_13139),hAPP(hAPP(c_COMBS(U_13139,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13139),c_fconj),hAPP(hAPP(c_COMBC(U_13139,tc_fun(U_13139,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13139)),U_13140))),hAPP(hAPP(c_COMBC(U_13139,tc_fun(U_13139,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13139)),U_13141))),
inference(clausify,[status(thm)],[f_3394_2]) ).
fof(f_3395_1,plain,
! [T_b,V_a_2,V_P_2] :
( ( hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(V_P_2,V_a_2)) )
& ( hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
| ~ hBOOL(hAPP(V_P_2,V_a_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Collect__conv__if]) ).
fof(f_3395_2,plain,
! [U_13144,U_13143,U_13142] :
( ( hAPP(c_Set_OCollect(U_13144),hAPP(hAPP(c_COMBS(U_13144,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13144),c_fconj),hAPP(hAPP(c_COMBC(U_13144,U_13144,tc_HOL_Obool),c_fequal),U_13143))),U_13142)) = c_Orderings_Obot__class_Obot(tc_fun(U_13144,tc_HOL_Obool))
| hBOOL(hAPP(U_13142,U_13143)) )
& ( hAPP(c_Set_OCollect(U_13144),hAPP(hAPP(c_COMBS(U_13144,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13144),c_fconj),hAPP(hAPP(c_COMBC(U_13144,U_13144,tc_HOL_Obool),c_fequal),U_13143))),U_13142)) = hAPP(hAPP(c_Set_Oinsert(U_13144),U_13143),c_Orderings_Obot__class_Obot(tc_fun(U_13144,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_13142,U_13143)) ) ),
inference(variable_rename,[status(thm)],[f_3395_1]) ).
fof(f_3395_3,plain,
( ! [U_13150,U_13148,U_13146] :
( hAPP(c_Set_OCollect(U_13150),hAPP(hAPP(c_COMBS(U_13150,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13150),c_fconj),hAPP(hAPP(c_COMBC(U_13150,U_13150,tc_HOL_Obool),c_fequal),U_13148))),U_13146)) = c_Orderings_Obot__class_Obot(tc_fun(U_13150,tc_HOL_Obool))
| hBOOL(hAPP(U_13146,U_13148)) )
& ! [U_13149,U_13147,U_13145] :
( hAPP(c_Set_OCollect(U_13149),hAPP(hAPP(c_COMBS(U_13149,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13149),c_fconj),hAPP(hAPP(c_COMBC(U_13149,U_13149,tc_HOL_Obool),c_fequal),U_13147))),U_13145)) = hAPP(hAPP(c_Set_Oinsert(U_13149),U_13147),c_Orderings_Obot__class_Obot(tc_fun(U_13149,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_13145,U_13147)) ) ),
inference(miniscope,[status(thm)],[f_3395_2]) ).
cnf(f_3395_4,plain,
( hAPP(c_Set_OCollect(U_13149),hAPP(hAPP(c_COMBS(U_13149,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13149),c_fconj),hAPP(hAPP(c_COMBC(U_13149,U_13149,tc_HOL_Obool),c_fequal),U_13147))),U_13145)) = hAPP(hAPP(c_Set_Oinsert(U_13149),U_13147),c_Orderings_Obot__class_Obot(tc_fun(U_13149,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_13145,U_13147)) ),
inference(clausify,[status(thm)],[f_3395_3]) ).
cnf(f_3395_5,plain,
( hAPP(c_Set_OCollect(U_13150),hAPP(hAPP(c_COMBS(U_13150,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13150),c_fconj),hAPP(hAPP(c_COMBC(U_13150,U_13150,tc_HOL_Obool),c_fequal),U_13148))),U_13146)) = c_Orderings_Obot__class_Obot(tc_fun(U_13150,tc_HOL_Obool))
| hBOOL(hAPP(U_13146,U_13148)) ),
inference(clausify,[status(thm)],[f_3395_3]) ).
fof(f_3396_1,plain,
! [T_b,V_a_2,V_P_2] :
( ( hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| hBOOL(hAPP(V_P_2,V_a_2)) )
& ( hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
| ~ hBOOL(hAPP(V_P_2,V_a_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Collect__conv__if2]) ).
fof(f_3396_2,plain,
! [U_13153,U_13152,U_13151] :
( ( hAPP(c_Set_OCollect(U_13153),hAPP(hAPP(c_COMBS(U_13153,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13153),c_fconj),hAPP(c_fequal,U_13152))),U_13151)) = c_Orderings_Obot__class_Obot(tc_fun(U_13153,tc_HOL_Obool))
| hBOOL(hAPP(U_13151,U_13152)) )
& ( hAPP(c_Set_OCollect(U_13153),hAPP(hAPP(c_COMBS(U_13153,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13153),c_fconj),hAPP(c_fequal,U_13152))),U_13151)) = hAPP(hAPP(c_Set_Oinsert(U_13153),U_13152),c_Orderings_Obot__class_Obot(tc_fun(U_13153,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_13151,U_13152)) ) ),
inference(variable_rename,[status(thm)],[f_3396_1]) ).
fof(f_3396_3,plain,
( ! [U_13159,U_13157,U_13155] :
( hAPP(c_Set_OCollect(U_13159),hAPP(hAPP(c_COMBS(U_13159,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13159),c_fconj),hAPP(c_fequal,U_13157))),U_13155)) = c_Orderings_Obot__class_Obot(tc_fun(U_13159,tc_HOL_Obool))
| hBOOL(hAPP(U_13155,U_13157)) )
& ! [U_13158,U_13156,U_13154] :
( hAPP(c_Set_OCollect(U_13158),hAPP(hAPP(c_COMBS(U_13158,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13158),c_fconj),hAPP(c_fequal,U_13156))),U_13154)) = hAPP(hAPP(c_Set_Oinsert(U_13158),U_13156),c_Orderings_Obot__class_Obot(tc_fun(U_13158,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_13154,U_13156)) ) ),
inference(miniscope,[status(thm)],[f_3396_2]) ).
cnf(f_3396_4,plain,
( hAPP(c_Set_OCollect(U_13158),hAPP(hAPP(c_COMBS(U_13158,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13158),c_fconj),hAPP(c_fequal,U_13156))),U_13154)) = hAPP(hAPP(c_Set_Oinsert(U_13158),U_13156),c_Orderings_Obot__class_Obot(tc_fun(U_13158,tc_HOL_Obool)))
| ~ hBOOL(hAPP(U_13154,U_13156)) ),
inference(clausify,[status(thm)],[f_3396_3]) ).
cnf(f_3396_5,plain,
( hAPP(c_Set_OCollect(U_13159),hAPP(hAPP(c_COMBS(U_13159,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13159),c_fconj),hAPP(c_fequal,U_13157))),U_13155)) = c_Orderings_Obot__class_Obot(tc_fun(U_13159,tc_HOL_Obool))
| hBOOL(hAPP(U_13155,U_13157)) ),
inference(clausify,[status(thm)],[f_3396_3]) ).
fof(f_3397_1,plain,
! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_singleton__conv]) ).
fof(f_3397_2,plain,
! [U_13161,U_13160] : hAPP(c_Set_OCollect(U_13160),hAPP(hAPP(c_COMBC(U_13160,U_13160,tc_HOL_Obool),c_fequal),U_13161)) = hAPP(hAPP(c_Set_Oinsert(U_13160),U_13161),c_Orderings_Obot__class_Obot(tc_fun(U_13160,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_3397_1]) ).
cnf(f_3397_3,plain,
hAPP(c_Set_OCollect(U_13160),hAPP(hAPP(c_COMBC(U_13160,U_13160,tc_HOL_Obool),c_fequal),U_13161)) = hAPP(hAPP(c_Set_Oinsert(U_13160),U_13161),c_Orderings_Obot__class_Obot(tc_fun(U_13160,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_3397_2]) ).
fof(f_3398_1,plain,
! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_singleton__conv2]) ).
fof(f_3398_2,plain,
! [U_13163,U_13162] : hAPP(c_Set_OCollect(U_13162),hAPP(c_fequal,U_13163)) = hAPP(hAPP(c_Set_Oinsert(U_13162),U_13163),c_Orderings_Obot__class_Obot(tc_fun(U_13162,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_3398_1]) ).
cnf(f_3398_3,plain,
hAPP(c_Set_OCollect(U_13162),hAPP(c_fequal,U_13163)) = hAPP(hAPP(c_Set_Oinsert(U_13162),U_13163),c_Orderings_Obot__class_Obot(tc_fun(U_13162,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_3398_2]) ).
fof(f_3399_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_set__diff__eq]) ).
fof(f_3399_2,plain,
! [U_13166,U_13165,U_13164] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13164,tc_HOL_Obool)),U_13165),U_13166) = hAPP(c_Set_OCollect(U_13164),hAPP(hAPP(c_COMBS(U_13164,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13164),c_fconj),hAPP(hAPP(c_COMBC(U_13164,tc_fun(U_13164,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13164)),U_13165))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13164),c_fNot),hAPP(hAPP(c_COMBC(U_13164,tc_fun(U_13164,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13164)),U_13166)))),
inference(variable_rename,[status(thm)],[f_3399_1]) ).
cnf(f_3399_3,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13164,tc_HOL_Obool)),U_13165),U_13166) = hAPP(c_Set_OCollect(U_13164),hAPP(hAPP(c_COMBS(U_13164,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13164),c_fconj),hAPP(hAPP(c_COMBC(U_13164,tc_fun(U_13164,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13164)),U_13165))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13164),c_fNot),hAPP(hAPP(c_COMBC(U_13164,tc_fun(U_13164,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13164)),U_13166)))),
inference(clausify,[status(thm)],[f_3399_2]) ).
fof(f_3400_1,plain,
! [V_P_2,T_b] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__not]) ).
fof(f_3400_2,plain,
! [U_13168,U_13167] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13167),hAPP(c_Set_OCollect(U_13167),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13167),c_fNot),U_13168))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13167),c_Orderings_Otop__class_Otop(tc_fun(U_13167,tc_HOL_Obool)))) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13167),c_Orderings_Otop__class_Otop(tc_fun(U_13167,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13167),hAPP(c_Set_OCollect(U_13167),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13167),c_fNot),U_13168)))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13167),hAPP(c_Set_OCollect(U_13167),U_13168))) ),
inference(variable_rename,[status(thm)],[f_3400_1]) ).
cnf(f_3400_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13167),c_Orderings_Otop__class_Otop(tc_fun(U_13167,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13167),hAPP(c_Set_OCollect(U_13167),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13167),c_fNot),U_13168))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13167),hAPP(c_Set_OCollect(U_13167),U_13168))) ),
inference(clausify,[status(thm)],[f_3400_2]) ).
cnf(f_3400_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13167),hAPP(c_Set_OCollect(U_13167),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13167),c_fNot),U_13168))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13167),c_Orderings_Otop__class_Otop(tc_fun(U_13167,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13167),hAPP(c_Set_OCollect(U_13167),U_13168))) ),
inference(clausify,[status(thm)],[f_3400_2]) ).
fof(f_3401_1,plain,
! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2),
inference(fof_nnf,[status(thm)],[fact_insert__def]) ).
fof(f_3401_2,plain,
! [U_13171,U_13170,U_13169] : hAPP(hAPP(c_Set_Oinsert(U_13169),U_13170),U_13171) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13169,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13169),hAPP(hAPP(c_COMBC(U_13169,U_13169,tc_HOL_Obool),c_fequal),U_13170))),U_13171),
inference(variable_rename,[status(thm)],[f_3401_1]) ).
cnf(f_3401_3,plain,
hAPP(hAPP(c_Set_Oinsert(U_13169),U_13170),U_13171) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13169,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13169),hAPP(hAPP(c_COMBC(U_13169,U_13169,tc_HOL_Obool),c_fequal),U_13170))),U_13171),
inference(clausify,[status(thm)],[f_3401_2]) ).
fof(f_3402_1,plain,
! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),
inference(fof_nnf,[status(thm)],[fact_Compl__eq]) ).
fof(f_3402_2,plain,
! [U_13173,U_13172] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13172,tc_HOL_Obool)),U_13173) = hAPP(c_Set_OCollect(U_13172),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13172),c_fNot),hAPP(hAPP(c_COMBC(U_13172,tc_fun(U_13172,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13172)),U_13173))),
inference(variable_rename,[status(thm)],[f_3402_1]) ).
cnf(f_3402_3,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13172,tc_HOL_Obool)),U_13173) = hAPP(c_Set_OCollect(U_13172),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13172),c_fNot),hAPP(hAPP(c_COMBC(U_13172,tc_fun(U_13172,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13172)),U_13173))),
inference(clausify,[status(thm)],[f_3402_2]) ).
fof(f_3403_1,plain,
! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(T_c)),V_f_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__def]) ).
fof(f_3403_2,plain,
! [U_13177,U_13176,U_13175,U_13174] : hAPP(c_Set_Ovimage(U_13174,U_13175,U_13176),U_13177) = hAPP(c_Set_OCollect(U_13174),hAPP(hAPP(c_COMBC(U_13174,tc_fun(U_13175,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13175,tc_fun(tc_fun(U_13175,tc_HOL_Obool),tc_HOL_Obool),U_13174),c_member(U_13175)),U_13176)),U_13177)),
inference(variable_rename,[status(thm)],[f_3403_1]) ).
cnf(f_3403_3,plain,
hAPP(c_Set_Ovimage(U_13174,U_13175,U_13176),U_13177) = hAPP(c_Set_OCollect(U_13174),hAPP(hAPP(c_COMBC(U_13174,tc_fun(U_13175,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13175,tc_fun(tc_fun(U_13175,tc_HOL_Obool),tc_HOL_Obool),U_13174),c_member(U_13175)),U_13176)),U_13177)),
inference(clausify,[status(thm)],[f_3403_2]) ).
fof(f_3404_1,plain,
! [V_P_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_P_2))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_P_2))),
inference(fof_nnf,[status(thm)],[fact_Collect__ball__eq]) ).
fof(f_3404_2,plain,
! [U_13181,U_13180,U_13179,U_13178] : hAPP(c_Set_OCollect(U_13178),hAPP(hAPP(c_COMBB(tc_fun(U_13179,tc_HOL_Obool),tc_HOL_Obool,U_13178),c_HOL_OAll(U_13179)),hAPP(hAPP(c_COMBB(tc_fun(U_13179,tc_HOL_Obool),tc_fun(U_13179,tc_HOL_Obool),U_13178),hAPP(c_COMBS(U_13179,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13179),c_fimplies),hAPP(hAPP(c_COMBC(U_13179,tc_fun(U_13179,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13179)),U_13180)))),U_13181))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13179,tc_fun(U_13178,tc_HOL_Obool)),U_13180),hAPP(hAPP(c_COMBB(tc_fun(U_13178,tc_HOL_Obool),tc_fun(U_13178,tc_HOL_Obool),U_13179),c_Set_OCollect(U_13178)),hAPP(c_COMBC(U_13178,U_13179,tc_HOL_Obool),U_13181))),
inference(variable_rename,[status(thm)],[f_3404_1]) ).
cnf(f_3404_3,plain,
hAPP(c_Set_OCollect(U_13178),hAPP(hAPP(c_COMBB(tc_fun(U_13179,tc_HOL_Obool),tc_HOL_Obool,U_13178),c_HOL_OAll(U_13179)),hAPP(hAPP(c_COMBB(tc_fun(U_13179,tc_HOL_Obool),tc_fun(U_13179,tc_HOL_Obool),U_13178),hAPP(c_COMBS(U_13179,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13179),c_fimplies),hAPP(hAPP(c_COMBC(U_13179,tc_fun(U_13179,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13179)),U_13180)))),U_13181))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13179,tc_fun(U_13178,tc_HOL_Obool)),U_13180),hAPP(hAPP(c_COMBB(tc_fun(U_13178,tc_HOL_Obool),tc_fun(U_13178,tc_HOL_Obool),U_13179),c_Set_OCollect(U_13178)),hAPP(c_COMBC(U_13178,U_13179,tc_HOL_Obool),U_13181))),
inference(clausify,[status(thm)],[f_3404_2]) ).
fof(f_3405_1,plain,
! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(c_Set_OCollect(T_b),V_Q_2)),
inference(fof_nnf,[status(thm)],[fact_Collect__imp__eq]) ).
fof(f_3405_2,plain,
! [U_13184,U_13183,U_13182] : hAPP(c_Set_OCollect(U_13182),hAPP(hAPP(c_COMBS(U_13182,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13182),c_fimplies),U_13183)),U_13184)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13182,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13182,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13182),U_13183))),hAPP(c_Set_OCollect(U_13182),U_13184)),
inference(variable_rename,[status(thm)],[f_3405_1]) ).
cnf(f_3405_3,plain,
hAPP(c_Set_OCollect(U_13182),hAPP(hAPP(c_COMBS(U_13182,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13182),c_fimplies),U_13183)),U_13184)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13182,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13182,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13182),U_13183))),hAPP(c_Set_OCollect(U_13182),U_13184)),
inference(clausify,[status(thm)],[f_3405_2]) ).
fof(f_3406_1,plain,
! [V_i_2,V_P_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_P_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_3406_2,plain,
! [U_13186,U_13185] : 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_13185)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13186))))),
inference(variable_rename,[status(thm)],[f_3406_1]) ).
cnf(f_3406_3,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_13185)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13186))))),
inference(clausify,[status(thm)],[f_3406_2]) ).
fof(f_3407_1,plain,
! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_d),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_d),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d)),hAPP(c_COMBC(T_b,T_c,T_d),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2))))),V_T_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__setsum__restrict]) ).
fof(f_3407_2,plain,
! [U_13193,U_13192,U_13191,U_13190,U_13189,U_13188,U_13187] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13188,U_13187),hAPP(hAPP(c_COMBS(U_13188,tc_fun(U_13190,tc_HOL_Obool),U_13187),hAPP(hAPP(c_COMBB(tc_fun(U_13190,U_13187),tc_fun(tc_fun(U_13190,tc_HOL_Obool),U_13187),U_13188),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13190,U_13187)),U_13192)),hAPP(hAPP(c_COMBB(tc_fun(U_13190,tc_HOL_Obool),tc_fun(U_13190,tc_HOL_Obool),U_13188),c_Set_OCollect(U_13190)),hAPP(hAPP(c_COMBB(tc_fun(U_13190,tc_HOL_Obool),tc_fun(U_13190,tc_HOL_Obool),U_13188),hAPP(c_COMBS(U_13190,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13190),c_fconj),hAPP(hAPP(c_COMBC(U_13190,tc_fun(U_13190,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13190)),U_13191)))),U_13193)))),U_13189) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13190,U_13187),hAPP(hAPP(c_COMBS(U_13190,tc_fun(U_13188,tc_HOL_Obool),U_13187),hAPP(hAPP(c_COMBB(tc_fun(U_13188,U_13187),tc_fun(tc_fun(U_13188,tc_HOL_Obool),U_13187),U_13190),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13188,U_13187)),hAPP(c_COMBC(U_13188,U_13190,U_13187),U_13192))),hAPP(hAPP(c_COMBB(tc_fun(U_13188,tc_HOL_Obool),tc_fun(U_13188,tc_HOL_Obool),U_13190),c_Set_OCollect(U_13188)),hAPP(hAPP(c_COMBB(tc_fun(U_13188,tc_HOL_Obool),tc_fun(U_13188,tc_HOL_Obool),U_13190),hAPP(c_COMBS(U_13188,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13188),c_fconj),hAPP(hAPP(c_COMBC(U_13188,tc_fun(U_13188,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13188)),U_13189)))),hAPP(c_COMBC(U_13188,U_13190,tc_HOL_Obool),U_13193))))),U_13191)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13190),U_13191))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13188),U_13189))
| ~ class_Groups_Ocomm__monoid__add(U_13187) ),
inference(variable_rename,[status(thm)],[f_3407_1]) ).
cnf(f_3407_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13188,U_13187),hAPP(hAPP(c_COMBS(U_13188,tc_fun(U_13190,tc_HOL_Obool),U_13187),hAPP(hAPP(c_COMBB(tc_fun(U_13190,U_13187),tc_fun(tc_fun(U_13190,tc_HOL_Obool),U_13187),U_13188),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13190,U_13187)),U_13192)),hAPP(hAPP(c_COMBB(tc_fun(U_13190,tc_HOL_Obool),tc_fun(U_13190,tc_HOL_Obool),U_13188),c_Set_OCollect(U_13190)),hAPP(hAPP(c_COMBB(tc_fun(U_13190,tc_HOL_Obool),tc_fun(U_13190,tc_HOL_Obool),U_13188),hAPP(c_COMBS(U_13190,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13190),c_fconj),hAPP(hAPP(c_COMBC(U_13190,tc_fun(U_13190,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13190)),U_13191)))),U_13193)))),U_13189) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13190,U_13187),hAPP(hAPP(c_COMBS(U_13190,tc_fun(U_13188,tc_HOL_Obool),U_13187),hAPP(hAPP(c_COMBB(tc_fun(U_13188,U_13187),tc_fun(tc_fun(U_13188,tc_HOL_Obool),U_13187),U_13190),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13188,U_13187)),hAPP(c_COMBC(U_13188,U_13190,U_13187),U_13192))),hAPP(hAPP(c_COMBB(tc_fun(U_13188,tc_HOL_Obool),tc_fun(U_13188,tc_HOL_Obool),U_13190),c_Set_OCollect(U_13188)),hAPP(hAPP(c_COMBB(tc_fun(U_13188,tc_HOL_Obool),tc_fun(U_13188,tc_HOL_Obool),U_13190),hAPP(c_COMBS(U_13188,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13188),c_fconj),hAPP(hAPP(c_COMBC(U_13188,tc_fun(U_13188,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13188)),U_13189)))),hAPP(c_COMBC(U_13188,U_13190,tc_HOL_Obool),U_13193))))),U_13191)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13190),U_13191))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13188),U_13189))
| ~ class_Groups_Ocomm__monoid__add(U_13187) ),
inference(clausify,[status(thm)],[f_3407_2]) ).
fof(f_3408_1,plain,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_member(T_b))),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_INTER__def]) ).
fof(f_3408_2,plain,
! [U_13197,U_13196,U_13195,U_13194] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13194,tc_fun(U_13195,tc_HOL_Obool)),U_13196),U_13197) = hAPP(c_Set_OCollect(U_13195),hAPP(hAPP(c_COMBB(tc_fun(U_13194,tc_HOL_Obool),tc_HOL_Obool,U_13195),c_HOL_OAll(U_13194)),hAPP(hAPP(c_COMBB(tc_fun(U_13194,tc_HOL_Obool),tc_fun(U_13194,tc_HOL_Obool),U_13195),hAPP(c_COMBS(U_13194,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13194),c_fimplies),hAPP(hAPP(c_COMBC(U_13194,tc_fun(U_13194,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13194)),U_13196)))),hAPP(hAPP(c_COMBC(U_13195,tc_fun(U_13194,tc_fun(U_13195,tc_HOL_Obool)),tc_fun(U_13194,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13195,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13194,tc_fun(U_13195,tc_HOL_Obool)),tc_fun(U_13194,tc_HOL_Obool)),U_13195),c_COMBB(tc_fun(U_13195,tc_HOL_Obool),tc_HOL_Obool,U_13194)),c_member(U_13195))),U_13197)))),
inference(variable_rename,[status(thm)],[f_3408_1]) ).
cnf(f_3408_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_13194,tc_fun(U_13195,tc_HOL_Obool)),U_13196),U_13197) = hAPP(c_Set_OCollect(U_13195),hAPP(hAPP(c_COMBB(tc_fun(U_13194,tc_HOL_Obool),tc_HOL_Obool,U_13195),c_HOL_OAll(U_13194)),hAPP(hAPP(c_COMBB(tc_fun(U_13194,tc_HOL_Obool),tc_fun(U_13194,tc_HOL_Obool),U_13195),hAPP(c_COMBS(U_13194,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13194),c_fimplies),hAPP(hAPP(c_COMBC(U_13194,tc_fun(U_13194,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13194)),U_13196)))),hAPP(hAPP(c_COMBC(U_13195,tc_fun(U_13194,tc_fun(U_13195,tc_HOL_Obool)),tc_fun(U_13194,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13195,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13194,tc_fun(U_13195,tc_HOL_Obool)),tc_fun(U_13194,tc_HOL_Obool)),U_13195),c_COMBB(tc_fun(U_13195,tc_HOL_Obool),tc_HOL_Obool,U_13194)),c_member(U_13195))),U_13197)))),
inference(clausify,[status(thm)],[f_3408_2]) ).
fof(f_3409_1,plain,
! [V_S_2,V_g_2,V_f_2,V_P_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_c),c_If(T_b)),V_P_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_P_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_P_2))))),
inference(fof_nnf,[status(thm)],[fact_if__image__distrib]) ).
fof(f_3409_2,plain,
! [U_13203,U_13202,U_13201,U_13200,U_13199,U_13198] : hAPP(c_Set_Oimage(U_13198,U_13199,hAPP(hAPP(c_COMBS(U_13198,U_13199,U_13199),hAPP(hAPP(c_COMBS(U_13198,U_13199,tc_fun(U_13199,U_13199)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13199,tc_fun(U_13199,U_13199)),U_13198),c_If(U_13199)),U_13200)),U_13201)),U_13202)),U_13203) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13199,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13198,U_13199,U_13201),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13198,tc_HOL_Obool)),U_13203),hAPP(c_Set_OCollect(U_13198),U_13200)))),hAPP(c_Set_Oimage(U_13198,U_13199,U_13202),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13198,tc_HOL_Obool)),U_13203),hAPP(c_Set_OCollect(U_13198),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13198),c_fNot),U_13200))))),
inference(variable_rename,[status(thm)],[f_3409_1]) ).
cnf(f_3409_3,plain,
hAPP(c_Set_Oimage(U_13198,U_13199,hAPP(hAPP(c_COMBS(U_13198,U_13199,U_13199),hAPP(hAPP(c_COMBS(U_13198,U_13199,tc_fun(U_13199,U_13199)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13199,tc_fun(U_13199,U_13199)),U_13198),c_If(U_13199)),U_13200)),U_13201)),U_13202)),U_13203) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13199,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13198,U_13199,U_13201),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13198,tc_HOL_Obool)),U_13203),hAPP(c_Set_OCollect(U_13198),U_13200)))),hAPP(c_Set_Oimage(U_13198,U_13199,U_13202),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13198,tc_HOL_Obool)),U_13203),hAPP(c_Set_OCollect(U_13198),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13198),c_fNot),U_13200))))),
inference(clausify,[status(thm)],[f_3409_2]) ).
fof(f_3410_1,plain,
! [V_na_2,V_f_2,T_b,V_A_2] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| V_A_2 != hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,V_f_2),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_na_2))) ),
inference(fof_nnf,[status(thm)],[fact_nat__seg__image__imp__finite]) ).
fof(f_3410_2,plain,
! [U_13207,U_13206,U_13205,U_13204] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13205),U_13204))
| U_13204 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13205,U_13206),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_13207))) ),
inference(variable_rename,[status(thm)],[f_3410_1]) ).
cnf(f_3410_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13205),U_13204))
| U_13204 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13205,U_13206),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_13207))) ),
inference(clausify,[status(thm)],[f_3410_2]) ).
fof(f_3411_1,plain,
! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set_H]) ).
fof(f_3411_2,plain,
! [U_13212,U_13211,U_13210,U_13209,U_13208] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13209,U_13208),U_13211),hAPP(c_Set_OCollect(U_13209),hAPP(hAPP(c_COMBS(U_13209,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13209),c_fconj),hAPP(hAPP(c_COMBC(U_13209,tc_fun(U_13209,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13209)),U_13210))),hAPP(hAPP(c_COMBC(U_13209,tc_fun(U_13209,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13209)),U_13212)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13209,U_13208),hAPP(hAPP(c_COMBC(U_13209,U_13208,U_13208),hAPP(hAPP(c_COMBS(U_13209,U_13208,tc_fun(U_13208,U_13208)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13208,tc_fun(U_13208,U_13208)),U_13209),c_If(U_13208)),hAPP(hAPP(c_COMBC(U_13209,tc_fun(U_13209,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13209)),U_13212))),U_13211)),c_Groups_Ozero__class_Ozero(U_13208))),U_13210)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13209),U_13210))
| ~ class_Groups_Ocomm__monoid__add(U_13208) ),
inference(variable_rename,[status(thm)],[f_3411_1]) ).
cnf(f_3411_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13209,U_13208),U_13211),hAPP(c_Set_OCollect(U_13209),hAPP(hAPP(c_COMBS(U_13209,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13209),c_fconj),hAPP(hAPP(c_COMBC(U_13209,tc_fun(U_13209,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13209)),U_13210))),hAPP(hAPP(c_COMBC(U_13209,tc_fun(U_13209,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13209)),U_13212)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13209,U_13208),hAPP(hAPP(c_COMBC(U_13209,U_13208,U_13208),hAPP(hAPP(c_COMBS(U_13209,U_13208,tc_fun(U_13208,U_13208)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13208,tc_fun(U_13208,U_13208)),U_13209),c_If(U_13208)),hAPP(hAPP(c_COMBC(U_13209,tc_fun(U_13209,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13209)),U_13212))),U_13211)),c_Groups_Ozero__class_Ozero(U_13208))),U_13210)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13209),U_13210))
| ~ class_Groups_Ocomm__monoid__add(U_13208) ),
inference(clausify,[status(thm)],[f_3411_2]) ).
fof(f_3412_1,plain,
! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),T_c,T_d),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))),hAPP(c_COMBC(T_b,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_b),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_S_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__image__gen]) ).
fof(f_3412_2,plain,
! [U_13218,U_13217,U_13216,U_13215,U_13214,U_13213] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13214,U_13213),U_13216),U_13215) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13217,U_13213),hAPP(hAPP(c_COMBB(tc_fun(U_13214,tc_HOL_Obool),U_13213,U_13217),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13214,U_13213),U_13216)),hAPP(hAPP(c_COMBB(tc_fun(U_13214,tc_HOL_Obool),tc_fun(U_13214,tc_HOL_Obool),U_13217),c_Set_OCollect(U_13214)),hAPP(hAPP(c_COMBB(tc_fun(U_13214,tc_HOL_Obool),tc_fun(U_13214,tc_HOL_Obool),U_13217),hAPP(c_COMBS(U_13214,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13214),c_fconj),hAPP(hAPP(c_COMBC(U_13214,tc_fun(U_13214,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13214)),U_13215)))),hAPP(c_COMBC(U_13214,U_13217,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13217,tc_fun(U_13217,tc_HOL_Obool),U_13214),c_fequal),U_13218)))))),hAPP(c_Set_Oimage(U_13214,U_13217,U_13218),U_13215))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13214),U_13215))
| ~ class_Groups_Ocomm__monoid__add(U_13213) ),
inference(variable_rename,[status(thm)],[f_3412_1]) ).
cnf(f_3412_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13214,U_13213),U_13216),U_13215) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13217,U_13213),hAPP(hAPP(c_COMBB(tc_fun(U_13214,tc_HOL_Obool),U_13213,U_13217),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13214,U_13213),U_13216)),hAPP(hAPP(c_COMBB(tc_fun(U_13214,tc_HOL_Obool),tc_fun(U_13214,tc_HOL_Obool),U_13217),c_Set_OCollect(U_13214)),hAPP(hAPP(c_COMBB(tc_fun(U_13214,tc_HOL_Obool),tc_fun(U_13214,tc_HOL_Obool),U_13217),hAPP(c_COMBS(U_13214,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13214),c_fconj),hAPP(hAPP(c_COMBC(U_13214,tc_fun(U_13214,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13214)),U_13215)))),hAPP(c_COMBC(U_13214,U_13217,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13217,tc_fun(U_13217,tc_HOL_Obool),U_13214),c_fequal),U_13218)))))),hAPP(c_Set_Oimage(U_13214,U_13217,U_13218),U_13215))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13214),U_13215))
| ~ class_Groups_Ocomm__monoid__add(U_13213) ),
inference(clausify,[status(thm)],[f_3412_2]) ).
fof(f_3413_1,plain,
! [V_a_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_b))),hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2))),V_r_2)),
inference(fof_nnf,[status(thm)],[fact_Image__singleton]) ).
fof(f_3413_2,plain,
! [U_13222,U_13221,U_13220,U_13219] : hAPP(c_Relation_OImage(U_13219,U_13220,U_13221),hAPP(hAPP(c_Set_Oinsert(U_13219),U_13222),c_Orderings_Obot__class_Obot(tc_fun(U_13219,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_13220),hAPP(hAPP(c_COMBC(U_13220,tc_fun(tc_prod(U_13219,U_13220),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_13219,U_13220),tc_fun(tc_fun(tc_prod(U_13219,U_13220),tc_HOL_Obool),tc_HOL_Obool),U_13220),c_member(tc_prod(U_13219,U_13220))),hAPP(c_Product__Type_OPair(U_13219,U_13220),U_13222))),U_13221)),
inference(variable_rename,[status(thm)],[f_3413_1]) ).
cnf(f_3413_3,plain,
hAPP(c_Relation_OImage(U_13219,U_13220,U_13221),hAPP(hAPP(c_Set_Oinsert(U_13219),U_13222),c_Orderings_Obot__class_Obot(tc_fun(U_13219,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_13220),hAPP(hAPP(c_COMBC(U_13220,tc_fun(tc_prod(U_13219,U_13220),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_13219,U_13220),tc_fun(tc_fun(tc_prod(U_13219,U_13220),tc_HOL_Obool),tc_HOL_Obool),U_13220),c_member(tc_prod(U_13219,U_13220))),hAPP(c_Product__Type_OPair(U_13219,U_13220),U_13222))),U_13221)),
inference(clausify,[status(thm)],[f_3413_2]) ).
fof(f_3414_1,plain,
! [V_g_2,V_f_2,V_P_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_P_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__cases]) ).
fof(f_3414_2,plain,
! [U_13228,U_13227,U_13226,U_13225,U_13224,U_13223] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13224,U_13223),hAPP(hAPP(c_COMBS(U_13224,U_13223,U_13223),hAPP(hAPP(c_COMBS(U_13224,U_13223,tc_fun(U_13223,U_13223)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13223,tc_fun(U_13223,U_13223)),U_13224),c_If(U_13223)),U_13226)),U_13227)),U_13228)),U_13225) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13223),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13224,U_13223),U_13227),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13224,tc_HOL_Obool)),U_13225),hAPP(c_Set_OCollect(U_13224),U_13226)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13224,U_13223),U_13228),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13224,tc_HOL_Obool)),U_13225),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13224,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13224),U_13226)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13224),U_13225))
| ~ class_Groups_Ocomm__monoid__add(U_13223) ),
inference(variable_rename,[status(thm)],[f_3414_1]) ).
cnf(f_3414_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13224,U_13223),hAPP(hAPP(c_COMBS(U_13224,U_13223,U_13223),hAPP(hAPP(c_COMBS(U_13224,U_13223,tc_fun(U_13223,U_13223)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_13223,tc_fun(U_13223,U_13223)),U_13224),c_If(U_13223)),U_13226)),U_13227)),U_13228)),U_13225) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13223),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13224,U_13223),U_13227),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13224,tc_HOL_Obool)),U_13225),hAPP(c_Set_OCollect(U_13224),U_13226)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13224,U_13223),U_13228),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13224,tc_HOL_Obool)),U_13225),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13224,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_13224),U_13226)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13224),U_13225))
| ~ class_Groups_Ocomm__monoid__add(U_13223) ),
inference(clausify,[status(thm)],[f_3414_2]) ).
fof(f_3415_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_3415_2,plain,
! [U_13230,U_13229] :
( 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_13229))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13230)))) = 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_13229))),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_13230)))))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13229)) ),
inference(variable_rename,[status(thm)],[f_3415_1]) ).
cnf(f_3415_3,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_13229))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_13230)))) = 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_13229))),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_13230)))))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_13229)) ),
inference(clausify,[status(thm)],[f_3415_2]) ).
fof(f_3416_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_3416_2,plain,
! [U_13232,U_13231] :
( 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_13231))),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_13232))))) != 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_13231)) ),
inference(variable_rename,[status(thm)],[f_3416_1]) ).
cnf(f_3416_3,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_13231))),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_13232))))) != 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_13231)) ),
inference(clausify,[status(thm)],[f_3416_2]) ).
fof(f_3417_1,plain,
! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(T_c),V_T_2))
| ? [B_x] :
( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) != V_k_2
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__multicount]) ).
fof(f_3417_2,plain,
! [U_13239,U_13238,U_13237,U_13236,U_13235,U_13234] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13234,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13236,tc_HOL_Obool),tc_Nat_Onat,U_13234),c_Finite__Set_Ocard(U_13236)),hAPP(hAPP(c_COMBB(tc_fun(U_13236,tc_HOL_Obool),tc_fun(U_13236,tc_HOL_Obool),U_13234),c_Set_OCollect(U_13236)),hAPP(hAPP(c_COMBB(tc_fun(U_13236,tc_HOL_Obool),tc_fun(U_13236,tc_HOL_Obool),U_13234),hAPP(c_COMBS(U_13236,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13236),c_fconj),hAPP(hAPP(c_COMBC(U_13236,tc_fun(U_13236,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13236)),U_13237)))),U_13238)))),U_13235) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13239),hAPP(c_Finite__Set_Ocard(U_13236),U_13237))
| ? [U_13233] :
( hAPP(c_Finite__Set_Ocard(U_13234),hAPP(c_Set_OCollect(U_13234),hAPP(hAPP(c_COMBS(U_13234,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13234),c_fconj),hAPP(hAPP(c_COMBC(U_13234,tc_fun(U_13234,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13234)),U_13235))),hAPP(hAPP(c_COMBC(U_13234,U_13236,tc_HOL_Obool),U_13238),U_13233)))) != U_13239
& hBOOL(hAPP(hAPP(c_member(U_13236),U_13233),U_13237)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13236),U_13237))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13234),U_13235)) ),
inference(variable_rename,[status(thm)],[f_3417_1]) ).
fof(f_3417_3,plain,
! [U_13239,U_13238,U_13237,U_13236,U_13235,U_13234] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13234,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13236,tc_HOL_Obool),tc_Nat_Onat,U_13234),c_Finite__Set_Ocard(U_13236)),hAPP(hAPP(c_COMBB(tc_fun(U_13236,tc_HOL_Obool),tc_fun(U_13236,tc_HOL_Obool),U_13234),c_Set_OCollect(U_13236)),hAPP(hAPP(c_COMBB(tc_fun(U_13236,tc_HOL_Obool),tc_fun(U_13236,tc_HOL_Obool),U_13234),hAPP(c_COMBS(U_13236,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13236),c_fconj),hAPP(hAPP(c_COMBC(U_13236,tc_fun(U_13236,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13236)),U_13237)))),U_13238)))),U_13235) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13239),hAPP(c_Finite__Set_Ocard(U_13236),U_13237))
| ( hAPP(c_Finite__Set_Ocard(U_13234),hAPP(c_Set_OCollect(U_13234),hAPP(hAPP(c_COMBS(U_13234,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13234),c_fconj),hAPP(hAPP(c_COMBC(U_13234,tc_fun(U_13234,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13234)),U_13235))),hAPP(hAPP(c_COMBC(U_13234,U_13236,tc_HOL_Obool),U_13238),sK311(U_13239,U_13238,U_13237,U_13236,U_13235,U_13234))))) != U_13239
& hBOOL(hAPP(hAPP(c_member(U_13236),sK311(U_13239,U_13238,U_13237,U_13236,U_13235,U_13234)),U_13237)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13236),U_13237))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13234),U_13235)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK311]),skolemize(U_13233,sK311(U_13239,U_13238,U_13237,U_13236,U_13235,U_13234))],[f_3417_2]) ).
cnf(f_3417_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_13236),sK311(U_13239,U_13238,U_13237,U_13236,U_13235,U_13234)),U_13237))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13234,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13236,tc_HOL_Obool),tc_Nat_Onat,U_13234),c_Finite__Set_Ocard(U_13236)),hAPP(hAPP(c_COMBB(tc_fun(U_13236,tc_HOL_Obool),tc_fun(U_13236,tc_HOL_Obool),U_13234),c_Set_OCollect(U_13236)),hAPP(hAPP(c_COMBB(tc_fun(U_13236,tc_HOL_Obool),tc_fun(U_13236,tc_HOL_Obool),U_13234),hAPP(c_COMBS(U_13236,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13236),c_fconj),hAPP(hAPP(c_COMBC(U_13236,tc_fun(U_13236,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13236)),U_13237)))),U_13238)))),U_13235) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13239),hAPP(c_Finite__Set_Ocard(U_13236),U_13237))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13236),U_13237))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13234),U_13235)) ),
inference(clausify,[status(thm)],[f_3417_3]) ).
cnf(f_3417_5,plain,
( hAPP(c_Finite__Set_Ocard(U_13234),hAPP(c_Set_OCollect(U_13234),hAPP(hAPP(c_COMBS(U_13234,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13234),c_fconj),hAPP(hAPP(c_COMBC(U_13234,tc_fun(U_13234,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13234)),U_13235))),hAPP(hAPP(c_COMBC(U_13234,U_13236,tc_HOL_Obool),U_13238),sK311(U_13239,U_13238,U_13237,U_13236,U_13235,U_13234))))) != U_13239
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13234,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13236,tc_HOL_Obool),tc_Nat_Onat,U_13234),c_Finite__Set_Ocard(U_13236)),hAPP(hAPP(c_COMBB(tc_fun(U_13236,tc_HOL_Obool),tc_fun(U_13236,tc_HOL_Obool),U_13234),c_Set_OCollect(U_13236)),hAPP(hAPP(c_COMBB(tc_fun(U_13236,tc_HOL_Obool),tc_fun(U_13236,tc_HOL_Obool),U_13234),hAPP(c_COMBS(U_13236,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13236),c_fconj),hAPP(hAPP(c_COMBC(U_13236,tc_fun(U_13236,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13236)),U_13237)))),U_13238)))),U_13235) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_13239),hAPP(c_Finite__Set_Ocard(U_13236),U_13237))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13236),U_13237))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13234),U_13235)) ),
inference(clausify,[status(thm)],[f_3417_3]) ).
fof(f_3418_1,plain,
! [V_x_2,V_A_2,T_b] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf1__distrib]) ).
fof(f_3418_2,plain,
! [U_13242,U_13241,U_13240] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_13240),U_13242),c_Big__Operators_Olattice_OInf__fin(U_13240,c_Orderings_Oord__class_Omin(U_13240),U_13241)) = c_Big__Operators_Olattice_OInf__fin(U_13240,c_Orderings_Oord__class_Omin(U_13240),hAPP(c_Set_OCollect(U_13240),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_HOL_Obool),tc_HOL_Obool,U_13240),c_HOL_OEx(U_13240)),hAPP(hAPP(c_COMBC(U_13240,tc_fun(U_13240,tc_HOL_Obool),tc_fun(U_13240,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13240,tc_HOL_Obool),tc_fun(U_13240,tc_HOL_Obool)),U_13240),c_COMBS(U_13240,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_HOL_Obool),tc_fun(U_13240,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13240),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13240),c_fconj)),hAPP(hAPP(c_COMBC(U_13240,tc_fun(U_13240,U_13240),tc_fun(U_13240,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_HOL_Obool),tc_fun(tc_fun(U_13240,U_13240),tc_fun(U_13240,tc_HOL_Obool)),U_13240),c_COMBB(U_13240,tc_HOL_Obool,U_13240)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_13240),U_13242))))),hAPP(hAPP(c_COMBC(U_13240,tc_fun(U_13240,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13240)),U_13241)))))
| U_13241 = c_Orderings_Obot__class_Obot(tc_fun(U_13240,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13240),U_13241))
| ~ class_Orderings_Olinorder(U_13240) ),
inference(variable_rename,[status(thm)],[f_3418_1]) ).
cnf(f_3418_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_13240),U_13242),c_Big__Operators_Olattice_OInf__fin(U_13240,c_Orderings_Oord__class_Omin(U_13240),U_13241)) = c_Big__Operators_Olattice_OInf__fin(U_13240,c_Orderings_Oord__class_Omin(U_13240),hAPP(c_Set_OCollect(U_13240),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_HOL_Obool),tc_HOL_Obool,U_13240),c_HOL_OEx(U_13240)),hAPP(hAPP(c_COMBC(U_13240,tc_fun(U_13240,tc_HOL_Obool),tc_fun(U_13240,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13240,tc_HOL_Obool),tc_fun(U_13240,tc_HOL_Obool)),U_13240),c_COMBS(U_13240,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_HOL_Obool),tc_fun(U_13240,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13240),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13240),c_fconj)),hAPP(hAPP(c_COMBC(U_13240,tc_fun(U_13240,U_13240),tc_fun(U_13240,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13240,tc_HOL_Obool),tc_fun(tc_fun(U_13240,U_13240),tc_fun(U_13240,tc_HOL_Obool)),U_13240),c_COMBB(U_13240,tc_HOL_Obool,U_13240)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_13240),U_13242))))),hAPP(hAPP(c_COMBC(U_13240,tc_fun(U_13240,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13240)),U_13241)))))
| U_13241 = c_Orderings_Obot__class_Obot(tc_fun(U_13240,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13240),U_13241))
| ~ class_Orderings_Olinorder(U_13240) ),
inference(clausify,[status(thm)],[f_3418_2]) ).
fof(f_3419_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omax(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))))))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf2__distrib]) ).
fof(f_3419_2,plain,
! [U_13245,U_13244,U_13243] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_13243),c_Big__Operators_Olattice_OInf__fin(U_13243,c_Orderings_Oord__class_Omin(U_13243),U_13244)),c_Big__Operators_Olattice_OInf__fin(U_13243,c_Orderings_Oord__class_Omin(U_13243),U_13245)) = c_Big__Operators_Olattice_OInf__fin(U_13243,c_Orderings_Oord__class_Omin(U_13243),hAPP(c_Set_OCollect(U_13243),hAPP(hAPP(c_COMBB(tc_fun(U_13243,tc_HOL_Obool),tc_HOL_Obool,U_13243),c_HOL_OEx(U_13243)),hAPP(hAPP(c_COMBB(tc_fun(U_13243,tc_fun(U_13243,tc_HOL_Obool)),tc_fun(U_13243,tc_HOL_Obool),U_13243),hAPP(c_COMBB(tc_fun(U_13243,tc_HOL_Obool),tc_HOL_Obool,U_13243),c_HOL_OEx(U_13243))),hAPP(hAPP(c_COMBC(U_13243,tc_fun(U_13243,tc_fun(U_13243,tc_HOL_Obool)),tc_fun(U_13243,tc_fun(U_13243,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13243,tc_fun(tc_fun(U_13243,tc_HOL_Obool),tc_fun(U_13243,tc_HOL_Obool))),tc_fun(tc_fun(U_13243,tc_fun(U_13243,tc_HOL_Obool)),tc_fun(U_13243,tc_fun(U_13243,tc_HOL_Obool))),U_13243),c_COMBS(U_13243,tc_fun(U_13243,tc_HOL_Obool),tc_fun(U_13243,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13243,tc_fun(U_13243,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13243,tc_fun(tc_fun(U_13243,tc_HOL_Obool),tc_fun(U_13243,tc_HOL_Obool))),U_13243),hAPP(c_COMBB(tc_fun(U_13243,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13243,tc_HOL_Obool),tc_fun(U_13243,tc_HOL_Obool)),U_13243),c_COMBS(U_13243,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13243,tc_fun(U_13243,tc_HOL_Obool)),tc_fun(U_13243,tc_fun(U_13243,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13243),hAPP(c_COMBB(tc_fun(U_13243,tc_HOL_Obool),tc_fun(U_13243,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13243),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13243),c_fconj))),hAPP(hAPP(c_COMBC(U_13243,tc_fun(U_13243,tc_fun(U_13243,U_13243)),tc_fun(U_13243,tc_fun(U_13243,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13243,U_13243),tc_fun(U_13243,tc_HOL_Obool)),tc_fun(tc_fun(U_13243,tc_fun(U_13243,U_13243)),tc_fun(U_13243,tc_fun(U_13243,tc_HOL_Obool))),U_13243),c_COMBB(tc_fun(U_13243,U_13243),tc_fun(U_13243,tc_HOL_Obool),U_13243)),hAPP(hAPP(c_COMBB(tc_fun(U_13243,tc_HOL_Obool),tc_fun(tc_fun(U_13243,U_13243),tc_fun(U_13243,tc_HOL_Obool)),U_13243),c_COMBB(U_13243,tc_HOL_Obool,U_13243)),c_fequal))),c_Orderings_Oord__class_Omax(U_13243)))))),hAPP(hAPP(c_COMBC(U_13243,tc_fun(U_13243,tc_HOL_Obool),tc_fun(U_13243,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13243,tc_HOL_Obool),tc_fun(U_13243,tc_HOL_Obool)),U_13243),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13243)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13243),c_fconj),hAPP(hAPP(c_COMBC(U_13243,tc_fun(U_13243,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13243)),U_13244)))),hAPP(hAPP(c_COMBC(U_13243,tc_fun(U_13243,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13243)),U_13245)))))))
| U_13245 = c_Orderings_Obot__class_Obot(tc_fun(U_13243,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13243),U_13245))
| U_13244 = c_Orderings_Obot__class_Obot(tc_fun(U_13243,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13243),U_13244))
| ~ class_Orderings_Olinorder(U_13243) ),
inference(variable_rename,[status(thm)],[f_3419_1]) ).
cnf(f_3419_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_13243),c_Big__Operators_Olattice_OInf__fin(U_13243,c_Orderings_Oord__class_Omin(U_13243),U_13244)),c_Big__Operators_Olattice_OInf__fin(U_13243,c_Orderings_Oord__class_Omin(U_13243),U_13245)) = c_Big__Operators_Olattice_OInf__fin(U_13243,c_Orderings_Oord__class_Omin(U_13243),hAPP(c_Set_OCollect(U_13243),hAPP(hAPP(c_COMBB(tc_fun(U_13243,tc_HOL_Obool),tc_HOL_Obool,U_13243),c_HOL_OEx(U_13243)),hAPP(hAPP(c_COMBB(tc_fun(U_13243,tc_fun(U_13243,tc_HOL_Obool)),tc_fun(U_13243,tc_HOL_Obool),U_13243),hAPP(c_COMBB(tc_fun(U_13243,tc_HOL_Obool),tc_HOL_Obool,U_13243),c_HOL_OEx(U_13243))),hAPP(hAPP(c_COMBC(U_13243,tc_fun(U_13243,tc_fun(U_13243,tc_HOL_Obool)),tc_fun(U_13243,tc_fun(U_13243,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13243,tc_fun(tc_fun(U_13243,tc_HOL_Obool),tc_fun(U_13243,tc_HOL_Obool))),tc_fun(tc_fun(U_13243,tc_fun(U_13243,tc_HOL_Obool)),tc_fun(U_13243,tc_fun(U_13243,tc_HOL_Obool))),U_13243),c_COMBS(U_13243,tc_fun(U_13243,tc_HOL_Obool),tc_fun(U_13243,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13243,tc_fun(U_13243,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13243,tc_fun(tc_fun(U_13243,tc_HOL_Obool),tc_fun(U_13243,tc_HOL_Obool))),U_13243),hAPP(c_COMBB(tc_fun(U_13243,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13243,tc_HOL_Obool),tc_fun(U_13243,tc_HOL_Obool)),U_13243),c_COMBS(U_13243,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13243,tc_fun(U_13243,tc_HOL_Obool)),tc_fun(U_13243,tc_fun(U_13243,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13243),hAPP(c_COMBB(tc_fun(U_13243,tc_HOL_Obool),tc_fun(U_13243,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13243),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13243),c_fconj))),hAPP(hAPP(c_COMBC(U_13243,tc_fun(U_13243,tc_fun(U_13243,U_13243)),tc_fun(U_13243,tc_fun(U_13243,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13243,U_13243),tc_fun(U_13243,tc_HOL_Obool)),tc_fun(tc_fun(U_13243,tc_fun(U_13243,U_13243)),tc_fun(U_13243,tc_fun(U_13243,tc_HOL_Obool))),U_13243),c_COMBB(tc_fun(U_13243,U_13243),tc_fun(U_13243,tc_HOL_Obool),U_13243)),hAPP(hAPP(c_COMBB(tc_fun(U_13243,tc_HOL_Obool),tc_fun(tc_fun(U_13243,U_13243),tc_fun(U_13243,tc_HOL_Obool)),U_13243),c_COMBB(U_13243,tc_HOL_Obool,U_13243)),c_fequal))),c_Orderings_Oord__class_Omax(U_13243)))))),hAPP(hAPP(c_COMBC(U_13243,tc_fun(U_13243,tc_HOL_Obool),tc_fun(U_13243,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13243,tc_HOL_Obool),tc_fun(U_13243,tc_HOL_Obool)),U_13243),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13243)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13243),c_fconj),hAPP(hAPP(c_COMBC(U_13243,tc_fun(U_13243,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13243)),U_13244)))),hAPP(hAPP(c_COMBC(U_13243,tc_fun(U_13243,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13243)),U_13245)))))))
| U_13245 = c_Orderings_Obot__class_Obot(tc_fun(U_13243,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13243),U_13245))
| U_13244 = c_Orderings_Obot__class_Obot(tc_fun(U_13243,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13243),U_13244))
| ~ class_Orderings_Olinorder(U_13243) ),
inference(clausify,[status(thm)],[f_3419_2]) ).
fof(f_3420_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__subsets]) ).
fof(f_3420_2,plain,
! [U_13247,U_13246] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13246,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_13246,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_13246,tc_HOL_Obool),tc_fun(U_13246,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_13246,tc_HOL_Obool))),U_13247))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13246),U_13247)) ),
inference(variable_rename,[status(thm)],[f_3420_1]) ).
cnf(f_3420_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13246,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_13246,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_13246,tc_HOL_Obool),tc_fun(U_13246,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_13246,tc_HOL_Obool))),U_13247))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13246),U_13247)) ),
inference(clausify,[status(thm)],[f_3420_2]) ).
fof(f_3421_1,plain,
! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_b))))),
inference(fof_nnf,[status(thm)],[fact_Pow__Compl]) ).
fof(f_3421_2,plain,
! [U_13249,U_13248] : hAPP(c_Set_OPow(U_13248),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13248,tc_HOL_Obool)),U_13249)) = hAPP(c_Set_OCollect(tc_fun(U_13248,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13248,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_13248,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_13248,tc_HOL_Obool),tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13248,tc_HOL_Obool)),c_COMBS(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_13248,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_13248,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_13248,tc_HOL_Obool),tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_fun(U_13248,tc_HOL_Obool)),tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_fun(U_13248,tc_HOL_Obool)),tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13248,tc_HOL_Obool)),c_COMBB(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13248,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_13248,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13248,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_13248,tc_HOL_Obool)),U_13249)),c_Set_OPow(U_13248))))),
inference(variable_rename,[status(thm)],[f_3421_1]) ).
cnf(f_3421_3,plain,
hAPP(c_Set_OPow(U_13248),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13248,tc_HOL_Obool)),U_13249)) = hAPP(c_Set_OCollect(tc_fun(U_13248,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13248,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_13248,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_13248,tc_HOL_Obool),tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13248,tc_HOL_Obool)),c_COMBS(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_13248,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_13248,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_13248,tc_HOL_Obool),tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_fun(U_13248,tc_HOL_Obool)),tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_fun(U_13248,tc_HOL_Obool)),tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13248,tc_HOL_Obool)),c_COMBB(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13248,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_13248,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13248,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_13248,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_13248,tc_HOL_Obool)),U_13249)),c_Set_OPow(U_13248))))),
inference(clausify,[status(thm)],[f_3421_2]) ).
fof(f_3422_1,plain,
! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Pow__def]) ).
fof(f_3422_2,plain,
! [U_13251,U_13250] : hAPP(c_Set_OPow(U_13250),U_13251) = hAPP(c_Set_OCollect(tc_fun(U_13250,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_13250,tc_HOL_Obool),tc_fun(U_13250,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_13250,tc_HOL_Obool))),U_13251)),
inference(variable_rename,[status(thm)],[f_3422_1]) ).
cnf(f_3422_3,plain,
hAPP(c_Set_OPow(U_13250),U_13251) = hAPP(c_Set_OCollect(tc_fun(U_13250,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_13250,tc_HOL_Obool),tc_fun(U_13250,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_13250,tc_HOL_Obool))),U_13251)),
inference(clausify,[status(thm)],[f_3422_2]) ).
fof(f_3423_1,plain,
! [V_f_2,T_c,V_P_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,T_b)),c_fequal)),V_f_2)))),V_P_2)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__image__set]) ).
fof(f_3423_2,plain,
! [U_13255,U_13254,U_13253,U_13252] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13254),hAPP(c_Set_OCollect(U_13254),hAPP(hAPP(c_COMBB(tc_fun(U_13252,tc_HOL_Obool),tc_HOL_Obool,U_13254),c_HOL_OEx(U_13252)),hAPP(hAPP(c_COMBC(U_13254,tc_fun(U_13252,tc_HOL_Obool),tc_fun(U_13252,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13252,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13252,tc_HOL_Obool),tc_fun(U_13252,tc_HOL_Obool)),U_13254),c_COMBS(U_13252,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13252,tc_HOL_Obool),tc_fun(U_13252,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13254),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13252),c_fconj)),hAPP(hAPP(c_COMBC(U_13254,tc_fun(U_13252,U_13254),tc_fun(U_13252,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13254,tc_HOL_Obool),tc_fun(tc_fun(U_13252,U_13254),tc_fun(U_13252,tc_HOL_Obool)),U_13254),c_COMBB(U_13254,tc_HOL_Obool,U_13252)),c_fequal)),U_13255)))),U_13253)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13252),hAPP(c_Set_OCollect(U_13252),U_13253))) ),
inference(variable_rename,[status(thm)],[f_3423_1]) ).
cnf(f_3423_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13254),hAPP(c_Set_OCollect(U_13254),hAPP(hAPP(c_COMBB(tc_fun(U_13252,tc_HOL_Obool),tc_HOL_Obool,U_13254),c_HOL_OEx(U_13252)),hAPP(hAPP(c_COMBC(U_13254,tc_fun(U_13252,tc_HOL_Obool),tc_fun(U_13252,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13252,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13252,tc_HOL_Obool),tc_fun(U_13252,tc_HOL_Obool)),U_13254),c_COMBS(U_13252,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13252,tc_HOL_Obool),tc_fun(U_13252,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13254),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13252),c_fconj)),hAPP(hAPP(c_COMBC(U_13254,tc_fun(U_13252,U_13254),tc_fun(U_13252,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13254,tc_HOL_Obool),tc_fun(tc_fun(U_13252,U_13254),tc_fun(U_13252,tc_HOL_Obool)),U_13254),c_COMBB(U_13254,tc_HOL_Obool,U_13252)),c_fequal)),U_13255)))),U_13253)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13252),hAPP(c_Set_OCollect(U_13252),U_13253))) ),
inference(clausify,[status(thm)],[f_3423_2]) ).
fof(f_3424_1,plain,
! [V_Q_2,T_c,V_P_2,T_b] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2)))))
| ? [B_y] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_y))))
& hBOOL(hAPP(V_P_2,B_y)) ) )
& ( ! [B_y] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_y))))
| ~ hBOOL(hAPP(V_P_2,B_y)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__Collect__bounded__ex]) ).
fof(f_3424_2,plain,
! [U_13261,U_13260,U_13259,U_13258] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13260),hAPP(c_Set_OCollect(U_13260),hAPP(hAPP(c_COMBB(tc_fun(U_13258,tc_HOL_Obool),tc_HOL_Obool,U_13260),c_HOL_OEx(U_13258)),hAPP(hAPP(c_COMBB(tc_fun(U_13258,tc_HOL_Obool),tc_fun(U_13258,tc_HOL_Obool),U_13260),hAPP(c_COMBS(U_13258,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13258),c_fconj),U_13259))),U_13261)))))
| ? [U_13257] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13260),hAPP(c_Set_OCollect(U_13260),hAPP(hAPP(c_COMBC(U_13260,U_13258,tc_HOL_Obool),U_13261),U_13257))))
& hBOOL(hAPP(U_13259,U_13257)) ) )
& ( ! [U_13256] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13260),hAPP(c_Set_OCollect(U_13260),hAPP(hAPP(c_COMBC(U_13260,U_13258,tc_HOL_Obool),U_13261),U_13256))))
| ~ hBOOL(hAPP(U_13259,U_13256)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13260),hAPP(c_Set_OCollect(U_13260),hAPP(hAPP(c_COMBB(tc_fun(U_13258,tc_HOL_Obool),tc_HOL_Obool,U_13260),c_HOL_OEx(U_13258)),hAPP(hAPP(c_COMBB(tc_fun(U_13258,tc_HOL_Obool),tc_fun(U_13258,tc_HOL_Obool),U_13260),hAPP(c_COMBS(U_13258,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13258),c_fconj),U_13259))),U_13261))))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13258),hAPP(c_Set_OCollect(U_13258),U_13259))) ),
inference(variable_rename,[status(thm)],[f_3424_1]) ).
fof(f_3424_3,plain,
! [U_13261,U_13260,U_13259,U_13258] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13260),hAPP(c_Set_OCollect(U_13260),hAPP(hAPP(c_COMBB(tc_fun(U_13258,tc_HOL_Obool),tc_HOL_Obool,U_13260),c_HOL_OEx(U_13258)),hAPP(hAPP(c_COMBB(tc_fun(U_13258,tc_HOL_Obool),tc_fun(U_13258,tc_HOL_Obool),U_13260),hAPP(c_COMBS(U_13258,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13258),c_fconj),U_13259))),U_13261)))))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13260),hAPP(c_Set_OCollect(U_13260),hAPP(hAPP(c_COMBC(U_13260,U_13258,tc_HOL_Obool),U_13261),sK312(U_13261,U_13260,U_13259,U_13258)))))
& hBOOL(hAPP(U_13259,sK312(U_13261,U_13260,U_13259,U_13258))) ) )
& ( ! [U_13256] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13260),hAPP(c_Set_OCollect(U_13260),hAPP(hAPP(c_COMBC(U_13260,U_13258,tc_HOL_Obool),U_13261),U_13256))))
| ~ hBOOL(hAPP(U_13259,U_13256)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13260),hAPP(c_Set_OCollect(U_13260),hAPP(hAPP(c_COMBB(tc_fun(U_13258,tc_HOL_Obool),tc_HOL_Obool,U_13260),c_HOL_OEx(U_13258)),hAPP(hAPP(c_COMBB(tc_fun(U_13258,tc_HOL_Obool),tc_fun(U_13258,tc_HOL_Obool),U_13260),hAPP(c_COMBS(U_13258,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13258),c_fconj),U_13259))),U_13261))))) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13258),hAPP(c_Set_OCollect(U_13258),U_13259))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK312]),skolemize(U_13257,sK312(U_13261,U_13260,U_13259,U_13258))],[f_3424_2]) ).
cnf(f_3424_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13260),hAPP(c_Set_OCollect(U_13260),hAPP(hAPP(c_COMBC(U_13260,U_13258,tc_HOL_Obool),U_13261),U_13256))))
| ~ hBOOL(hAPP(U_13259,U_13256))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13260),hAPP(c_Set_OCollect(U_13260),hAPP(hAPP(c_COMBB(tc_fun(U_13258,tc_HOL_Obool),tc_HOL_Obool,U_13260),c_HOL_OEx(U_13258)),hAPP(hAPP(c_COMBB(tc_fun(U_13258,tc_HOL_Obool),tc_fun(U_13258,tc_HOL_Obool),U_13260),hAPP(c_COMBS(U_13258,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13258),c_fconj),U_13259))),U_13261)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13258),hAPP(c_Set_OCollect(U_13258),U_13259))) ),
inference(clausify,[status(thm)],[f_3424_3]) ).
cnf(f_3424_5,plain,
( hBOOL(hAPP(U_13259,sK312(U_13261,U_13260,U_13259,U_13258)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_13260),hAPP(c_Set_OCollect(U_13260),hAPP(hAPP(c_COMBB(tc_fun(U_13258,tc_HOL_Obool),tc_HOL_Obool,U_13260),c_HOL_OEx(U_13258)),hAPP(hAPP(c_COMBB(tc_fun(U_13258,tc_HOL_Obool),tc_fun(U_13258,tc_HOL_Obool),U_13260),hAPP(c_COMBS(U_13258,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13258),c_fconj),U_13259))),U_13261)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13258),hAPP(c_Set_OCollect(U_13258),U_13259))) ),
inference(clausify,[status(thm)],[f_3424_3]) ).
cnf(f_3424_6,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13260),hAPP(c_Set_OCollect(U_13260),hAPP(hAPP(c_COMBC(U_13260,U_13258,tc_HOL_Obool),U_13261),sK312(U_13261,U_13260,U_13259,U_13258)))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_13260),hAPP(c_Set_OCollect(U_13260),hAPP(hAPP(c_COMBB(tc_fun(U_13258,tc_HOL_Obool),tc_HOL_Obool,U_13260),c_HOL_OEx(U_13258)),hAPP(hAPP(c_COMBB(tc_fun(U_13258,tc_HOL_Obool),tc_fun(U_13258,tc_HOL_Obool),U_13260),hAPP(c_COMBS(U_13258,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13258),c_fconj),U_13259))),U_13261)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13258),hAPP(c_Set_OCollect(U_13258),U_13259))) ),
inference(clausify,[status(thm)],[f_3424_3]) ).
fof(f_3425_1,plain,
! [T_c,T_b] : c_Fun_Oinj__on(tc_fun(T_b,T_c),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Set_OCollect(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool)),hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_inj__graph]) ).
fof(f_3425_2,plain,
! [U_13263,U_13262] : c_Fun_Oinj__on(tc_fun(U_13262,U_13263),tc_fun(tc_prod(U_13262,U_13263),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13262,U_13263),tc_HOL_Obool),tc_fun(tc_prod(U_13262,U_13263),tc_HOL_Obool),tc_fun(U_13262,U_13263)),c_Set_OCollect(tc_prod(U_13262,U_13263))),hAPP(hAPP(c_COMBB(tc_fun(U_13262,tc_fun(U_13263,tc_HOL_Obool)),tc_fun(tc_prod(U_13262,U_13263),tc_HOL_Obool),tc_fun(U_13262,U_13263)),c_Product__Type_Oprod_Oprod__case(U_13262,U_13263,tc_HOL_Obool)),hAPP(c_COMBB(U_13263,tc_fun(U_13263,tc_HOL_Obool),U_13262),hAPP(c_COMBC(U_13263,U_13263,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13262,U_13263),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_3425_1]) ).
cnf(f_3425_3,plain,
c_Fun_Oinj__on(tc_fun(U_13262,U_13263),tc_fun(tc_prod(U_13262,U_13263),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13262,U_13263),tc_HOL_Obool),tc_fun(tc_prod(U_13262,U_13263),tc_HOL_Obool),tc_fun(U_13262,U_13263)),c_Set_OCollect(tc_prod(U_13262,U_13263))),hAPP(hAPP(c_COMBB(tc_fun(U_13262,tc_fun(U_13263,tc_HOL_Obool)),tc_fun(tc_prod(U_13262,U_13263),tc_HOL_Obool),tc_fun(U_13262,U_13263)),c_Product__Type_Oprod_Oprod__case(U_13262,U_13263,tc_HOL_Obool)),hAPP(c_COMBB(U_13263,tc_fun(U_13263,tc_HOL_Obool),U_13262),hAPP(c_COMBC(U_13263,U_13263,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13262,U_13263),tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_3425_2]) ).
fof(f_3426_1,plain,
! [V_P_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_P_2))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J]) ).
fof(f_3426_2,plain,
! [U_13264] : 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_13264))),
inference(variable_rename,[status(thm)],[f_3426_1]) ).
cnf(f_3426_3,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_13264))),
inference(clausify,[status(thm)],[f_3426_2]) ).
fof(f_3427_1,plain,
! [T_b] : c_Wellfounded_Ofinite__psubset(T_b) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_b)))),
inference(fof_nnf,[status(thm)],[fact_finite__psubset__def]) ).
fof(f_3427_2,plain,
! [U_13265] : c_Wellfounded_Ofinite__psubset(U_13265) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_13265,tc_HOL_Obool),tc_fun(U_13265,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_13265,tc_HOL_Obool),tc_fun(U_13265,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_13265,tc_HOL_Obool),tc_fun(tc_fun(U_13265,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13265,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13265,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_13265,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13265,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13265,tc_HOL_Obool)),c_COMBS(tc_fun(U_13265,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13265,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13265,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_13265,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_13265,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_13265,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_13265)))),
inference(variable_rename,[status(thm)],[f_3427_1]) ).
cnf(f_3427_3,plain,
c_Wellfounded_Ofinite__psubset(U_13265) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_13265,tc_HOL_Obool),tc_fun(U_13265,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_13265,tc_HOL_Obool),tc_fun(U_13265,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_13265,tc_HOL_Obool),tc_fun(tc_fun(U_13265,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13265,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13265,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_13265,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13265,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_13265,tc_HOL_Obool)),c_COMBS(tc_fun(U_13265,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13265,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13265,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_13265,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_13265,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_13265,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_13265)))),
inference(clausify,[status(thm)],[f_3427_2]) ).
fof(f_3428_1,plain,
! [V_f_2,V_r_2,T_b,T_c] : hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_c,T_c)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_c),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),T_b),c_COMBB(T_c,tc_prod(T_c,T_c),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_prod(T_c,T_c)),T_b),c_Product__Type_OPair(T_c,T_c)),V_f_2))),V_f_2)))),V_r_2))),
inference(fof_nnf,[status(thm)],[fact_inv__image__def]) ).
fof(f_3428_2,plain,
! [U_13269,U_13268,U_13267,U_13266] : hAPP(hAPP(c_Relation_Oinv__image(U_13266,U_13267),U_13268),U_13269) = hAPP(c_Set_OCollect(tc_prod(U_13267,U_13267)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13267,U_13267,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13267,tc_fun(tc_prod(U_13266,U_13266),tc_HOL_Obool),tc_fun(U_13267,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13267,tc_fun(tc_fun(tc_prod(U_13266,U_13266),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13266,U_13266),tc_HOL_Obool),tc_fun(U_13267,tc_HOL_Obool)),U_13267),c_COMBC(U_13267,tc_fun(tc_prod(U_13266,U_13266),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13267,tc_prod(U_13266,U_13266)),tc_fun(U_13267,tc_fun(tc_fun(tc_prod(U_13266,U_13266),tc_HOL_Obool),tc_HOL_Obool)),U_13267),hAPP(c_COMBB(tc_prod(U_13266,U_13266),tc_fun(tc_fun(tc_prod(U_13266,U_13266),tc_HOL_Obool),tc_HOL_Obool),U_13267),c_member(tc_prod(U_13266,U_13266)))),hAPP(hAPP(c_COMBC(U_13267,tc_fun(U_13267,U_13266),tc_fun(U_13267,tc_prod(U_13266,U_13266))),hAPP(hAPP(c_COMBB(tc_fun(U_13266,tc_prod(U_13266,U_13266)),tc_fun(tc_fun(U_13267,U_13266),tc_fun(U_13267,tc_prod(U_13266,U_13266))),U_13267),c_COMBB(U_13266,tc_prod(U_13266,U_13266),U_13267)),hAPP(hAPP(c_COMBB(U_13266,tc_fun(U_13266,tc_prod(U_13266,U_13266)),U_13267),c_Product__Type_OPair(U_13266,U_13266)),U_13269))),U_13269)))),U_13268))),
inference(variable_rename,[status(thm)],[f_3428_1]) ).
cnf(f_3428_3,plain,
hAPP(hAPP(c_Relation_Oinv__image(U_13266,U_13267),U_13268),U_13269) = hAPP(c_Set_OCollect(tc_prod(U_13267,U_13267)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13267,U_13267,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13267,tc_fun(tc_prod(U_13266,U_13266),tc_HOL_Obool),tc_fun(U_13267,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13267,tc_fun(tc_fun(tc_prod(U_13266,U_13266),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13266,U_13266),tc_HOL_Obool),tc_fun(U_13267,tc_HOL_Obool)),U_13267),c_COMBC(U_13267,tc_fun(tc_prod(U_13266,U_13266),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13267,tc_prod(U_13266,U_13266)),tc_fun(U_13267,tc_fun(tc_fun(tc_prod(U_13266,U_13266),tc_HOL_Obool),tc_HOL_Obool)),U_13267),hAPP(c_COMBB(tc_prod(U_13266,U_13266),tc_fun(tc_fun(tc_prod(U_13266,U_13266),tc_HOL_Obool),tc_HOL_Obool),U_13267),c_member(tc_prod(U_13266,U_13266)))),hAPP(hAPP(c_COMBC(U_13267,tc_fun(U_13267,U_13266),tc_fun(U_13267,tc_prod(U_13266,U_13266))),hAPP(hAPP(c_COMBB(tc_fun(U_13266,tc_prod(U_13266,U_13266)),tc_fun(tc_fun(U_13267,U_13266),tc_fun(U_13267,tc_prod(U_13266,U_13266))),U_13267),c_COMBB(U_13266,tc_prod(U_13266,U_13266),U_13267)),hAPP(hAPP(c_COMBB(U_13266,tc_fun(U_13266,tc_prod(U_13266,U_13266)),U_13267),c_Product__Type_OPair(U_13266,U_13266)),U_13269))),U_13269)))),U_13268))),
inference(clausify,[status(thm)],[f_3428_2]) ).
fof(f_3429_1,plain,
! [V_P_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_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_P_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_3429_2,plain,
! [U_13270] : 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_13270)) = 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_13270),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[f_3429_1]) ).
cnf(f_3429_3,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_13270)) = 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_13270),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
inference(clausify,[status(thm)],[f_3429_2]) ).
fof(f_3430_1,plain,
! [V_P_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_P_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_P_2),c_Int_Onat)))),
inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J]) ).
fof(f_3430_2,plain,
! [U_13271] : hAPP(c_Set_OCollect(tc_Nat_Onat),U_13271) = 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_13271),c_Int_Onat)))),
inference(variable_rename,[status(thm)],[f_3430_1]) ).
cnf(f_3430_3,plain,
hAPP(c_Set_OCollect(tc_Nat_Onat),U_13271) = 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_13271),c_Int_Onat)))),
inference(clausify,[status(thm)],[f_3430_2]) ).
fof(f_3431_1,plain,
! [V_k_2,V_N_2,T_b] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2)))))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| ~ class_Groups_Olinordered__ab__semigroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__Max__commute]) ).
fof(f_3431_2,plain,
! [U_13274,U_13273,U_13272] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13272),U_13274),c_Big__Operators_Olinorder__class_OMax(U_13272,U_13273)) = c_Big__Operators_Olinorder__class_OMax(U_13272,hAPP(c_Set_OCollect(U_13272),hAPP(hAPP(c_COMBB(tc_fun(U_13272,tc_HOL_Obool),tc_HOL_Obool,U_13272),c_HOL_OEx(U_13272)),hAPP(hAPP(c_COMBC(U_13272,tc_fun(U_13272,tc_HOL_Obool),tc_fun(U_13272,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13272,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13272,tc_HOL_Obool),tc_fun(U_13272,tc_HOL_Obool)),U_13272),c_COMBS(U_13272,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13272,tc_HOL_Obool),tc_fun(U_13272,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13272),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13272),c_fconj)),hAPP(hAPP(c_COMBC(U_13272,tc_fun(U_13272,U_13272),tc_fun(U_13272,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13272,tc_HOL_Obool),tc_fun(tc_fun(U_13272,U_13272),tc_fun(U_13272,tc_HOL_Obool)),U_13272),c_COMBB(U_13272,tc_HOL_Obool,U_13272)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_13272),U_13274))))),hAPP(hAPP(c_COMBC(U_13272,tc_fun(U_13272,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13272)),U_13273)))))
| U_13273 = c_Orderings_Obot__class_Obot(tc_fun(U_13272,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13272),U_13273))
| ~ class_Groups_Olinordered__ab__semigroup__add(U_13272) ),
inference(variable_rename,[status(thm)],[f_3431_1]) ).
cnf(f_3431_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13272),U_13274),c_Big__Operators_Olinorder__class_OMax(U_13272,U_13273)) = c_Big__Operators_Olinorder__class_OMax(U_13272,hAPP(c_Set_OCollect(U_13272),hAPP(hAPP(c_COMBB(tc_fun(U_13272,tc_HOL_Obool),tc_HOL_Obool,U_13272),c_HOL_OEx(U_13272)),hAPP(hAPP(c_COMBC(U_13272,tc_fun(U_13272,tc_HOL_Obool),tc_fun(U_13272,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13272,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13272,tc_HOL_Obool),tc_fun(U_13272,tc_HOL_Obool)),U_13272),c_COMBS(U_13272,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13272,tc_HOL_Obool),tc_fun(U_13272,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13272),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13272),c_fconj)),hAPP(hAPP(c_COMBC(U_13272,tc_fun(U_13272,U_13272),tc_fun(U_13272,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13272,tc_HOL_Obool),tc_fun(tc_fun(U_13272,U_13272),tc_fun(U_13272,tc_HOL_Obool)),U_13272),c_COMBB(U_13272,tc_HOL_Obool,U_13272)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_13272),U_13274))))),hAPP(hAPP(c_COMBC(U_13272,tc_fun(U_13272,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13272)),U_13273)))))
| U_13273 = c_Orderings_Obot__class_Obot(tc_fun(U_13272,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13272),U_13273))
| ~ class_Groups_Olinordered__ab__semigroup__add(U_13272) ),
inference(clausify,[status(thm)],[f_3431_2]) ).
fof(f_3432_1,plain,
! [V_k_2,V_N_2,T_b] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2)))))
| V_N_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
| ~ class_Groups_Olinordered__ab__semigroup__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_add__Min__commute]) ).
fof(f_3432_2,plain,
! [U_13277,U_13276,U_13275] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13275),U_13277),c_Big__Operators_Olinorder__class_OMin(U_13275,U_13276)) = c_Big__Operators_Olinorder__class_OMin(U_13275,hAPP(c_Set_OCollect(U_13275),hAPP(hAPP(c_COMBB(tc_fun(U_13275,tc_HOL_Obool),tc_HOL_Obool,U_13275),c_HOL_OEx(U_13275)),hAPP(hAPP(c_COMBC(U_13275,tc_fun(U_13275,tc_HOL_Obool),tc_fun(U_13275,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13275,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13275,tc_HOL_Obool),tc_fun(U_13275,tc_HOL_Obool)),U_13275),c_COMBS(U_13275,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13275,tc_HOL_Obool),tc_fun(U_13275,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13275),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13275),c_fconj)),hAPP(hAPP(c_COMBC(U_13275,tc_fun(U_13275,U_13275),tc_fun(U_13275,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13275,tc_HOL_Obool),tc_fun(tc_fun(U_13275,U_13275),tc_fun(U_13275,tc_HOL_Obool)),U_13275),c_COMBB(U_13275,tc_HOL_Obool,U_13275)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_13275),U_13277))))),hAPP(hAPP(c_COMBC(U_13275,tc_fun(U_13275,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13275)),U_13276)))))
| U_13276 = c_Orderings_Obot__class_Obot(tc_fun(U_13275,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13275),U_13276))
| ~ class_Groups_Olinordered__ab__semigroup__add(U_13275) ),
inference(variable_rename,[status(thm)],[f_3432_1]) ).
cnf(f_3432_3,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_13275),U_13277),c_Big__Operators_Olinorder__class_OMin(U_13275,U_13276)) = c_Big__Operators_Olinorder__class_OMin(U_13275,hAPP(c_Set_OCollect(U_13275),hAPP(hAPP(c_COMBB(tc_fun(U_13275,tc_HOL_Obool),tc_HOL_Obool,U_13275),c_HOL_OEx(U_13275)),hAPP(hAPP(c_COMBC(U_13275,tc_fun(U_13275,tc_HOL_Obool),tc_fun(U_13275,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13275,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13275,tc_HOL_Obool),tc_fun(U_13275,tc_HOL_Obool)),U_13275),c_COMBS(U_13275,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13275,tc_HOL_Obool),tc_fun(U_13275,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13275),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13275),c_fconj)),hAPP(hAPP(c_COMBC(U_13275,tc_fun(U_13275,U_13275),tc_fun(U_13275,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13275,tc_HOL_Obool),tc_fun(tc_fun(U_13275,U_13275),tc_fun(U_13275,tc_HOL_Obool)),U_13275),c_COMBB(U_13275,tc_HOL_Obool,U_13275)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_13275),U_13277))))),hAPP(hAPP(c_COMBC(U_13275,tc_fun(U_13275,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13275)),U_13276)))))
| U_13276 = c_Orderings_Obot__class_Obot(tc_fun(U_13275,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13275),U_13276))
| ~ class_Groups_Olinordered__ab__semigroup__add(U_13275) ),
inference(clausify,[status(thm)],[f_3432_2]) ).
fof(f_3433_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))))))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Odistrib__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sup__Inf2__distrib]) ).
fof(f_3433_2,plain,
! [U_13280,U_13279,U_13278] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13278),c_Big__Operators_Olattice__class_OInf__fin(U_13278,U_13279)),c_Big__Operators_Olattice__class_OInf__fin(U_13278,U_13280)) = c_Big__Operators_Olattice__class_OInf__fin(U_13278,hAPP(c_Set_OCollect(U_13278),hAPP(hAPP(c_COMBB(tc_fun(U_13278,tc_HOL_Obool),tc_HOL_Obool,U_13278),c_HOL_OEx(U_13278)),hAPP(hAPP(c_COMBB(tc_fun(U_13278,tc_fun(U_13278,tc_HOL_Obool)),tc_fun(U_13278,tc_HOL_Obool),U_13278),hAPP(c_COMBB(tc_fun(U_13278,tc_HOL_Obool),tc_HOL_Obool,U_13278),c_HOL_OEx(U_13278))),hAPP(hAPP(c_COMBC(U_13278,tc_fun(U_13278,tc_fun(U_13278,tc_HOL_Obool)),tc_fun(U_13278,tc_fun(U_13278,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13278,tc_fun(tc_fun(U_13278,tc_HOL_Obool),tc_fun(U_13278,tc_HOL_Obool))),tc_fun(tc_fun(U_13278,tc_fun(U_13278,tc_HOL_Obool)),tc_fun(U_13278,tc_fun(U_13278,tc_HOL_Obool))),U_13278),c_COMBS(U_13278,tc_fun(U_13278,tc_HOL_Obool),tc_fun(U_13278,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13278,tc_fun(U_13278,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13278,tc_fun(tc_fun(U_13278,tc_HOL_Obool),tc_fun(U_13278,tc_HOL_Obool))),U_13278),hAPP(c_COMBB(tc_fun(U_13278,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13278,tc_HOL_Obool),tc_fun(U_13278,tc_HOL_Obool)),U_13278),c_COMBS(U_13278,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13278,tc_fun(U_13278,tc_HOL_Obool)),tc_fun(U_13278,tc_fun(U_13278,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13278),hAPP(c_COMBB(tc_fun(U_13278,tc_HOL_Obool),tc_fun(U_13278,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13278),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13278),c_fconj))),hAPP(hAPP(c_COMBC(U_13278,tc_fun(U_13278,tc_fun(U_13278,U_13278)),tc_fun(U_13278,tc_fun(U_13278,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13278,U_13278),tc_fun(U_13278,tc_HOL_Obool)),tc_fun(tc_fun(U_13278,tc_fun(U_13278,U_13278)),tc_fun(U_13278,tc_fun(U_13278,tc_HOL_Obool))),U_13278),c_COMBB(tc_fun(U_13278,U_13278),tc_fun(U_13278,tc_HOL_Obool),U_13278)),hAPP(hAPP(c_COMBB(tc_fun(U_13278,tc_HOL_Obool),tc_fun(tc_fun(U_13278,U_13278),tc_fun(U_13278,tc_HOL_Obool)),U_13278),c_COMBB(U_13278,tc_HOL_Obool,U_13278)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_13278)))))),hAPP(hAPP(c_COMBC(U_13278,tc_fun(U_13278,tc_HOL_Obool),tc_fun(U_13278,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13278,tc_HOL_Obool),tc_fun(U_13278,tc_HOL_Obool)),U_13278),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13278)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13278),c_fconj),hAPP(hAPP(c_COMBC(U_13278,tc_fun(U_13278,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13278)),U_13279)))),hAPP(hAPP(c_COMBC(U_13278,tc_fun(U_13278,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13278)),U_13280)))))))
| U_13280 = c_Orderings_Obot__class_Obot(tc_fun(U_13278,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13278),U_13280))
| U_13279 = c_Orderings_Obot__class_Obot(tc_fun(U_13278,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13278),U_13279))
| ~ class_Lattices_Odistrib__lattice(U_13278) ),
inference(variable_rename,[status(thm)],[f_3433_1]) ).
cnf(f_3433_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13278),c_Big__Operators_Olattice__class_OInf__fin(U_13278,U_13279)),c_Big__Operators_Olattice__class_OInf__fin(U_13278,U_13280)) = c_Big__Operators_Olattice__class_OInf__fin(U_13278,hAPP(c_Set_OCollect(U_13278),hAPP(hAPP(c_COMBB(tc_fun(U_13278,tc_HOL_Obool),tc_HOL_Obool,U_13278),c_HOL_OEx(U_13278)),hAPP(hAPP(c_COMBB(tc_fun(U_13278,tc_fun(U_13278,tc_HOL_Obool)),tc_fun(U_13278,tc_HOL_Obool),U_13278),hAPP(c_COMBB(tc_fun(U_13278,tc_HOL_Obool),tc_HOL_Obool,U_13278),c_HOL_OEx(U_13278))),hAPP(hAPP(c_COMBC(U_13278,tc_fun(U_13278,tc_fun(U_13278,tc_HOL_Obool)),tc_fun(U_13278,tc_fun(U_13278,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13278,tc_fun(tc_fun(U_13278,tc_HOL_Obool),tc_fun(U_13278,tc_HOL_Obool))),tc_fun(tc_fun(U_13278,tc_fun(U_13278,tc_HOL_Obool)),tc_fun(U_13278,tc_fun(U_13278,tc_HOL_Obool))),U_13278),c_COMBS(U_13278,tc_fun(U_13278,tc_HOL_Obool),tc_fun(U_13278,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13278,tc_fun(U_13278,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13278,tc_fun(tc_fun(U_13278,tc_HOL_Obool),tc_fun(U_13278,tc_HOL_Obool))),U_13278),hAPP(c_COMBB(tc_fun(U_13278,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13278,tc_HOL_Obool),tc_fun(U_13278,tc_HOL_Obool)),U_13278),c_COMBS(U_13278,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13278,tc_fun(U_13278,tc_HOL_Obool)),tc_fun(U_13278,tc_fun(U_13278,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13278),hAPP(c_COMBB(tc_fun(U_13278,tc_HOL_Obool),tc_fun(U_13278,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13278),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13278),c_fconj))),hAPP(hAPP(c_COMBC(U_13278,tc_fun(U_13278,tc_fun(U_13278,U_13278)),tc_fun(U_13278,tc_fun(U_13278,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13278,U_13278),tc_fun(U_13278,tc_HOL_Obool)),tc_fun(tc_fun(U_13278,tc_fun(U_13278,U_13278)),tc_fun(U_13278,tc_fun(U_13278,tc_HOL_Obool))),U_13278),c_COMBB(tc_fun(U_13278,U_13278),tc_fun(U_13278,tc_HOL_Obool),U_13278)),hAPP(hAPP(c_COMBB(tc_fun(U_13278,tc_HOL_Obool),tc_fun(tc_fun(U_13278,U_13278),tc_fun(U_13278,tc_HOL_Obool)),U_13278),c_COMBB(U_13278,tc_HOL_Obool,U_13278)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_13278)))))),hAPP(hAPP(c_COMBC(U_13278,tc_fun(U_13278,tc_HOL_Obool),tc_fun(U_13278,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13278,tc_HOL_Obool),tc_fun(U_13278,tc_HOL_Obool)),U_13278),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13278)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13278),c_fconj),hAPP(hAPP(c_COMBC(U_13278,tc_fun(U_13278,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13278)),U_13279)))),hAPP(hAPP(c_COMBC(U_13278,tc_fun(U_13278,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13278)),U_13280)))))))
| U_13280 = c_Orderings_Obot__class_Obot(tc_fun(U_13278,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13278),U_13280))
| U_13279 = c_Orderings_Obot__class_Obot(tc_fun(U_13278,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13278),U_13279))
| ~ class_Lattices_Odistrib__lattice(U_13278) ),
inference(clausify,[status(thm)],[f_3433_2]) ).
fof(f_3434_1,plain,
! [V_x_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Odistrib__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sup__Inf1__distrib]) ).
fof(f_3434_2,plain,
! [U_13283,U_13282,U_13281] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13281),U_13283),c_Big__Operators_Olattice__class_OInf__fin(U_13281,U_13282)) = c_Big__Operators_Olattice__class_OInf__fin(U_13281,hAPP(c_Set_OCollect(U_13281),hAPP(hAPP(c_COMBB(tc_fun(U_13281,tc_HOL_Obool),tc_HOL_Obool,U_13281),c_HOL_OEx(U_13281)),hAPP(hAPP(c_COMBC(U_13281,tc_fun(U_13281,tc_HOL_Obool),tc_fun(U_13281,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13281,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13281,tc_HOL_Obool),tc_fun(U_13281,tc_HOL_Obool)),U_13281),c_COMBS(U_13281,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13281,tc_HOL_Obool),tc_fun(U_13281,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13281),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13281),c_fconj)),hAPP(hAPP(c_COMBC(U_13281,tc_fun(U_13281,U_13281),tc_fun(U_13281,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13281,tc_HOL_Obool),tc_fun(tc_fun(U_13281,U_13281),tc_fun(U_13281,tc_HOL_Obool)),U_13281),c_COMBB(U_13281,tc_HOL_Obool,U_13281)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13281),U_13283))))),hAPP(hAPP(c_COMBC(U_13281,tc_fun(U_13281,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13281)),U_13282)))))
| U_13282 = c_Orderings_Obot__class_Obot(tc_fun(U_13281,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13281),U_13282))
| ~ class_Lattices_Odistrib__lattice(U_13281) ),
inference(variable_rename,[status(thm)],[f_3434_1]) ).
cnf(f_3434_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13281),U_13283),c_Big__Operators_Olattice__class_OInf__fin(U_13281,U_13282)) = c_Big__Operators_Olattice__class_OInf__fin(U_13281,hAPP(c_Set_OCollect(U_13281),hAPP(hAPP(c_COMBB(tc_fun(U_13281,tc_HOL_Obool),tc_HOL_Obool,U_13281),c_HOL_OEx(U_13281)),hAPP(hAPP(c_COMBC(U_13281,tc_fun(U_13281,tc_HOL_Obool),tc_fun(U_13281,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13281,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13281,tc_HOL_Obool),tc_fun(U_13281,tc_HOL_Obool)),U_13281),c_COMBS(U_13281,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13281,tc_HOL_Obool),tc_fun(U_13281,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13281),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13281),c_fconj)),hAPP(hAPP(c_COMBC(U_13281,tc_fun(U_13281,U_13281),tc_fun(U_13281,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13281,tc_HOL_Obool),tc_fun(tc_fun(U_13281,U_13281),tc_fun(U_13281,tc_HOL_Obool)),U_13281),c_COMBB(U_13281,tc_HOL_Obool,U_13281)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13281),U_13283))))),hAPP(hAPP(c_COMBC(U_13281,tc_fun(U_13281,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13281)),U_13282)))))
| U_13282 = c_Orderings_Obot__class_Obot(tc_fun(U_13281,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13281),U_13282))
| ~ class_Lattices_Odistrib__lattice(U_13281) ),
inference(clausify,[status(thm)],[f_3434_2]) ).
fof(f_3435_1,plain,
! [V_x_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Odistrib__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__Sup1__distrib]) ).
fof(f_3435_2,plain,
! [U_13286,U_13285,U_13284] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13284),U_13286),c_Big__Operators_Olattice__class_OSup__fin(U_13284,U_13285)) = c_Big__Operators_Olattice__class_OSup__fin(U_13284,hAPP(c_Set_OCollect(U_13284),hAPP(hAPP(c_COMBB(tc_fun(U_13284,tc_HOL_Obool),tc_HOL_Obool,U_13284),c_HOL_OEx(U_13284)),hAPP(hAPP(c_COMBC(U_13284,tc_fun(U_13284,tc_HOL_Obool),tc_fun(U_13284,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13284,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13284,tc_HOL_Obool),tc_fun(U_13284,tc_HOL_Obool)),U_13284),c_COMBS(U_13284,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13284,tc_HOL_Obool),tc_fun(U_13284,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13284),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13284),c_fconj)),hAPP(hAPP(c_COMBC(U_13284,tc_fun(U_13284,U_13284),tc_fun(U_13284,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13284,tc_HOL_Obool),tc_fun(tc_fun(U_13284,U_13284),tc_fun(U_13284,tc_HOL_Obool)),U_13284),c_COMBB(U_13284,tc_HOL_Obool,U_13284)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13284),U_13286))))),hAPP(hAPP(c_COMBC(U_13284,tc_fun(U_13284,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13284)),U_13285)))))
| U_13285 = c_Orderings_Obot__class_Obot(tc_fun(U_13284,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13284),U_13285))
| ~ class_Lattices_Odistrib__lattice(U_13284) ),
inference(variable_rename,[status(thm)],[f_3435_1]) ).
cnf(f_3435_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13284),U_13286),c_Big__Operators_Olattice__class_OSup__fin(U_13284,U_13285)) = c_Big__Operators_Olattice__class_OSup__fin(U_13284,hAPP(c_Set_OCollect(U_13284),hAPP(hAPP(c_COMBB(tc_fun(U_13284,tc_HOL_Obool),tc_HOL_Obool,U_13284),c_HOL_OEx(U_13284)),hAPP(hAPP(c_COMBC(U_13284,tc_fun(U_13284,tc_HOL_Obool),tc_fun(U_13284,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13284,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13284,tc_HOL_Obool),tc_fun(U_13284,tc_HOL_Obool)),U_13284),c_COMBS(U_13284,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13284,tc_HOL_Obool),tc_fun(U_13284,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13284),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13284),c_fconj)),hAPP(hAPP(c_COMBC(U_13284,tc_fun(U_13284,U_13284),tc_fun(U_13284,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13284,tc_HOL_Obool),tc_fun(tc_fun(U_13284,U_13284),tc_fun(U_13284,tc_HOL_Obool)),U_13284),c_COMBB(U_13284,tc_HOL_Obool,U_13284)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13284),U_13286))))),hAPP(hAPP(c_COMBC(U_13284,tc_fun(U_13284,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13284)),U_13285)))))
| U_13285 = c_Orderings_Obot__class_Obot(tc_fun(U_13284,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13284),U_13285))
| ~ class_Lattices_Odistrib__lattice(U_13284) ),
inference(clausify,[status(thm)],[f_3435_2]) ).
fof(f_3436_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))))))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Odistrib__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__Sup2__distrib]) ).
fof(f_3436_2,plain,
! [U_13289,U_13288,U_13287] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13287),c_Big__Operators_Olattice__class_OSup__fin(U_13287,U_13288)),c_Big__Operators_Olattice__class_OSup__fin(U_13287,U_13289)) = c_Big__Operators_Olattice__class_OSup__fin(U_13287,hAPP(c_Set_OCollect(U_13287),hAPP(hAPP(c_COMBB(tc_fun(U_13287,tc_HOL_Obool),tc_HOL_Obool,U_13287),c_HOL_OEx(U_13287)),hAPP(hAPP(c_COMBB(tc_fun(U_13287,tc_fun(U_13287,tc_HOL_Obool)),tc_fun(U_13287,tc_HOL_Obool),U_13287),hAPP(c_COMBB(tc_fun(U_13287,tc_HOL_Obool),tc_HOL_Obool,U_13287),c_HOL_OEx(U_13287))),hAPP(hAPP(c_COMBC(U_13287,tc_fun(U_13287,tc_fun(U_13287,tc_HOL_Obool)),tc_fun(U_13287,tc_fun(U_13287,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13287,tc_fun(tc_fun(U_13287,tc_HOL_Obool),tc_fun(U_13287,tc_HOL_Obool))),tc_fun(tc_fun(U_13287,tc_fun(U_13287,tc_HOL_Obool)),tc_fun(U_13287,tc_fun(U_13287,tc_HOL_Obool))),U_13287),c_COMBS(U_13287,tc_fun(U_13287,tc_HOL_Obool),tc_fun(U_13287,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13287,tc_fun(U_13287,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13287,tc_fun(tc_fun(U_13287,tc_HOL_Obool),tc_fun(U_13287,tc_HOL_Obool))),U_13287),hAPP(c_COMBB(tc_fun(U_13287,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13287,tc_HOL_Obool),tc_fun(U_13287,tc_HOL_Obool)),U_13287),c_COMBS(U_13287,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13287,tc_fun(U_13287,tc_HOL_Obool)),tc_fun(U_13287,tc_fun(U_13287,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13287),hAPP(c_COMBB(tc_fun(U_13287,tc_HOL_Obool),tc_fun(U_13287,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13287),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13287),c_fconj))),hAPP(hAPP(c_COMBC(U_13287,tc_fun(U_13287,tc_fun(U_13287,U_13287)),tc_fun(U_13287,tc_fun(U_13287,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13287,U_13287),tc_fun(U_13287,tc_HOL_Obool)),tc_fun(tc_fun(U_13287,tc_fun(U_13287,U_13287)),tc_fun(U_13287,tc_fun(U_13287,tc_HOL_Obool))),U_13287),c_COMBB(tc_fun(U_13287,U_13287),tc_fun(U_13287,tc_HOL_Obool),U_13287)),hAPP(hAPP(c_COMBB(tc_fun(U_13287,tc_HOL_Obool),tc_fun(tc_fun(U_13287,U_13287),tc_fun(U_13287,tc_HOL_Obool)),U_13287),c_COMBB(U_13287,tc_HOL_Obool,U_13287)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_13287)))))),hAPP(hAPP(c_COMBC(U_13287,tc_fun(U_13287,tc_HOL_Obool),tc_fun(U_13287,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13287,tc_HOL_Obool),tc_fun(U_13287,tc_HOL_Obool)),U_13287),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13287)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13287),c_fconj),hAPP(hAPP(c_COMBC(U_13287,tc_fun(U_13287,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13287)),U_13288)))),hAPP(hAPP(c_COMBC(U_13287,tc_fun(U_13287,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13287)),U_13289)))))))
| U_13289 = c_Orderings_Obot__class_Obot(tc_fun(U_13287,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13287),U_13289))
| U_13288 = c_Orderings_Obot__class_Obot(tc_fun(U_13287,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13287),U_13288))
| ~ class_Lattices_Odistrib__lattice(U_13287) ),
inference(variable_rename,[status(thm)],[f_3436_1]) ).
cnf(f_3436_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13287),c_Big__Operators_Olattice__class_OSup__fin(U_13287,U_13288)),c_Big__Operators_Olattice__class_OSup__fin(U_13287,U_13289)) = c_Big__Operators_Olattice__class_OSup__fin(U_13287,hAPP(c_Set_OCollect(U_13287),hAPP(hAPP(c_COMBB(tc_fun(U_13287,tc_HOL_Obool),tc_HOL_Obool,U_13287),c_HOL_OEx(U_13287)),hAPP(hAPP(c_COMBB(tc_fun(U_13287,tc_fun(U_13287,tc_HOL_Obool)),tc_fun(U_13287,tc_HOL_Obool),U_13287),hAPP(c_COMBB(tc_fun(U_13287,tc_HOL_Obool),tc_HOL_Obool,U_13287),c_HOL_OEx(U_13287))),hAPP(hAPP(c_COMBC(U_13287,tc_fun(U_13287,tc_fun(U_13287,tc_HOL_Obool)),tc_fun(U_13287,tc_fun(U_13287,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13287,tc_fun(tc_fun(U_13287,tc_HOL_Obool),tc_fun(U_13287,tc_HOL_Obool))),tc_fun(tc_fun(U_13287,tc_fun(U_13287,tc_HOL_Obool)),tc_fun(U_13287,tc_fun(U_13287,tc_HOL_Obool))),U_13287),c_COMBS(U_13287,tc_fun(U_13287,tc_HOL_Obool),tc_fun(U_13287,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13287,tc_fun(U_13287,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13287,tc_fun(tc_fun(U_13287,tc_HOL_Obool),tc_fun(U_13287,tc_HOL_Obool))),U_13287),hAPP(c_COMBB(tc_fun(U_13287,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13287,tc_HOL_Obool),tc_fun(U_13287,tc_HOL_Obool)),U_13287),c_COMBS(U_13287,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13287,tc_fun(U_13287,tc_HOL_Obool)),tc_fun(U_13287,tc_fun(U_13287,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13287),hAPP(c_COMBB(tc_fun(U_13287,tc_HOL_Obool),tc_fun(U_13287,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13287),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13287),c_fconj))),hAPP(hAPP(c_COMBC(U_13287,tc_fun(U_13287,tc_fun(U_13287,U_13287)),tc_fun(U_13287,tc_fun(U_13287,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13287,U_13287),tc_fun(U_13287,tc_HOL_Obool)),tc_fun(tc_fun(U_13287,tc_fun(U_13287,U_13287)),tc_fun(U_13287,tc_fun(U_13287,tc_HOL_Obool))),U_13287),c_COMBB(tc_fun(U_13287,U_13287),tc_fun(U_13287,tc_HOL_Obool),U_13287)),hAPP(hAPP(c_COMBB(tc_fun(U_13287,tc_HOL_Obool),tc_fun(tc_fun(U_13287,U_13287),tc_fun(U_13287,tc_HOL_Obool)),U_13287),c_COMBB(U_13287,tc_HOL_Obool,U_13287)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_13287)))))),hAPP(hAPP(c_COMBC(U_13287,tc_fun(U_13287,tc_HOL_Obool),tc_fun(U_13287,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13287,tc_HOL_Obool),tc_fun(U_13287,tc_HOL_Obool)),U_13287),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13287)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13287),c_fconj),hAPP(hAPP(c_COMBC(U_13287,tc_fun(U_13287,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13287)),U_13288)))),hAPP(hAPP(c_COMBC(U_13287,tc_fun(U_13287,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13287)),U_13289)))))))
| U_13289 = c_Orderings_Obot__class_Obot(tc_fun(U_13287,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13287),U_13289))
| U_13288 = c_Orderings_Obot__class_Obot(tc_fun(U_13287,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13287),U_13288))
| ~ class_Lattices_Odistrib__lattice(U_13287) ),
inference(clausify,[status(thm)],[f_3436_2]) ).
fof(f_3437_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omin(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))))))
| V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup2__distrib]) ).
fof(f_3437_2,plain,
! [U_13292,U_13291,U_13290] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_13290),c_Big__Operators_Olattice_OSup__fin(U_13290,c_Orderings_Oord__class_Omax(U_13290),U_13291)),c_Big__Operators_Olattice_OSup__fin(U_13290,c_Orderings_Oord__class_Omax(U_13290),U_13292)) = c_Big__Operators_Olattice_OSup__fin(U_13290,c_Orderings_Oord__class_Omax(U_13290),hAPP(c_Set_OCollect(U_13290),hAPP(hAPP(c_COMBB(tc_fun(U_13290,tc_HOL_Obool),tc_HOL_Obool,U_13290),c_HOL_OEx(U_13290)),hAPP(hAPP(c_COMBB(tc_fun(U_13290,tc_fun(U_13290,tc_HOL_Obool)),tc_fun(U_13290,tc_HOL_Obool),U_13290),hAPP(c_COMBB(tc_fun(U_13290,tc_HOL_Obool),tc_HOL_Obool,U_13290),c_HOL_OEx(U_13290))),hAPP(hAPP(c_COMBC(U_13290,tc_fun(U_13290,tc_fun(U_13290,tc_HOL_Obool)),tc_fun(U_13290,tc_fun(U_13290,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13290,tc_fun(tc_fun(U_13290,tc_HOL_Obool),tc_fun(U_13290,tc_HOL_Obool))),tc_fun(tc_fun(U_13290,tc_fun(U_13290,tc_HOL_Obool)),tc_fun(U_13290,tc_fun(U_13290,tc_HOL_Obool))),U_13290),c_COMBS(U_13290,tc_fun(U_13290,tc_HOL_Obool),tc_fun(U_13290,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13290,tc_fun(U_13290,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13290,tc_fun(tc_fun(U_13290,tc_HOL_Obool),tc_fun(U_13290,tc_HOL_Obool))),U_13290),hAPP(c_COMBB(tc_fun(U_13290,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13290,tc_HOL_Obool),tc_fun(U_13290,tc_HOL_Obool)),U_13290),c_COMBS(U_13290,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13290,tc_fun(U_13290,tc_HOL_Obool)),tc_fun(U_13290,tc_fun(U_13290,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13290),hAPP(c_COMBB(tc_fun(U_13290,tc_HOL_Obool),tc_fun(U_13290,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13290),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13290),c_fconj))),hAPP(hAPP(c_COMBC(U_13290,tc_fun(U_13290,tc_fun(U_13290,U_13290)),tc_fun(U_13290,tc_fun(U_13290,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13290,U_13290),tc_fun(U_13290,tc_HOL_Obool)),tc_fun(tc_fun(U_13290,tc_fun(U_13290,U_13290)),tc_fun(U_13290,tc_fun(U_13290,tc_HOL_Obool))),U_13290),c_COMBB(tc_fun(U_13290,U_13290),tc_fun(U_13290,tc_HOL_Obool),U_13290)),hAPP(hAPP(c_COMBB(tc_fun(U_13290,tc_HOL_Obool),tc_fun(tc_fun(U_13290,U_13290),tc_fun(U_13290,tc_HOL_Obool)),U_13290),c_COMBB(U_13290,tc_HOL_Obool,U_13290)),c_fequal))),c_Orderings_Oord__class_Omin(U_13290)))))),hAPP(hAPP(c_COMBC(U_13290,tc_fun(U_13290,tc_HOL_Obool),tc_fun(U_13290,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13290,tc_HOL_Obool),tc_fun(U_13290,tc_HOL_Obool)),U_13290),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13290)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13290),c_fconj),hAPP(hAPP(c_COMBC(U_13290,tc_fun(U_13290,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13290)),U_13291)))),hAPP(hAPP(c_COMBC(U_13290,tc_fun(U_13290,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13290)),U_13292)))))))
| U_13292 = c_Orderings_Obot__class_Obot(tc_fun(U_13290,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13290),U_13292))
| U_13291 = c_Orderings_Obot__class_Obot(tc_fun(U_13290,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13290),U_13291))
| ~ class_Orderings_Olinorder(U_13290) ),
inference(variable_rename,[status(thm)],[f_3437_1]) ).
cnf(f_3437_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_13290),c_Big__Operators_Olattice_OSup__fin(U_13290,c_Orderings_Oord__class_Omax(U_13290),U_13291)),c_Big__Operators_Olattice_OSup__fin(U_13290,c_Orderings_Oord__class_Omax(U_13290),U_13292)) = c_Big__Operators_Olattice_OSup__fin(U_13290,c_Orderings_Oord__class_Omax(U_13290),hAPP(c_Set_OCollect(U_13290),hAPP(hAPP(c_COMBB(tc_fun(U_13290,tc_HOL_Obool),tc_HOL_Obool,U_13290),c_HOL_OEx(U_13290)),hAPP(hAPP(c_COMBB(tc_fun(U_13290,tc_fun(U_13290,tc_HOL_Obool)),tc_fun(U_13290,tc_HOL_Obool),U_13290),hAPP(c_COMBB(tc_fun(U_13290,tc_HOL_Obool),tc_HOL_Obool,U_13290),c_HOL_OEx(U_13290))),hAPP(hAPP(c_COMBC(U_13290,tc_fun(U_13290,tc_fun(U_13290,tc_HOL_Obool)),tc_fun(U_13290,tc_fun(U_13290,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13290,tc_fun(tc_fun(U_13290,tc_HOL_Obool),tc_fun(U_13290,tc_HOL_Obool))),tc_fun(tc_fun(U_13290,tc_fun(U_13290,tc_HOL_Obool)),tc_fun(U_13290,tc_fun(U_13290,tc_HOL_Obool))),U_13290),c_COMBS(U_13290,tc_fun(U_13290,tc_HOL_Obool),tc_fun(U_13290,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13290,tc_fun(U_13290,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13290,tc_fun(tc_fun(U_13290,tc_HOL_Obool),tc_fun(U_13290,tc_HOL_Obool))),U_13290),hAPP(c_COMBB(tc_fun(U_13290,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13290,tc_HOL_Obool),tc_fun(U_13290,tc_HOL_Obool)),U_13290),c_COMBS(U_13290,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13290,tc_fun(U_13290,tc_HOL_Obool)),tc_fun(U_13290,tc_fun(U_13290,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13290),hAPP(c_COMBB(tc_fun(U_13290,tc_HOL_Obool),tc_fun(U_13290,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13290),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13290),c_fconj))),hAPP(hAPP(c_COMBC(U_13290,tc_fun(U_13290,tc_fun(U_13290,U_13290)),tc_fun(U_13290,tc_fun(U_13290,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13290,U_13290),tc_fun(U_13290,tc_HOL_Obool)),tc_fun(tc_fun(U_13290,tc_fun(U_13290,U_13290)),tc_fun(U_13290,tc_fun(U_13290,tc_HOL_Obool))),U_13290),c_COMBB(tc_fun(U_13290,U_13290),tc_fun(U_13290,tc_HOL_Obool),U_13290)),hAPP(hAPP(c_COMBB(tc_fun(U_13290,tc_HOL_Obool),tc_fun(tc_fun(U_13290,U_13290),tc_fun(U_13290,tc_HOL_Obool)),U_13290),c_COMBB(U_13290,tc_HOL_Obool,U_13290)),c_fequal))),c_Orderings_Oord__class_Omin(U_13290)))))),hAPP(hAPP(c_COMBC(U_13290,tc_fun(U_13290,tc_HOL_Obool),tc_fun(U_13290,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13290,tc_HOL_Obool),tc_fun(U_13290,tc_HOL_Obool)),U_13290),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13290)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13290),c_fconj),hAPP(hAPP(c_COMBC(U_13290,tc_fun(U_13290,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13290)),U_13291)))),hAPP(hAPP(c_COMBC(U_13290,tc_fun(U_13290,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13290)),U_13292)))))))
| U_13292 = c_Orderings_Obot__class_Obot(tc_fun(U_13290,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13290),U_13292))
| U_13291 = c_Orderings_Obot__class_Obot(tc_fun(U_13290,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13290),U_13291))
| ~ class_Orderings_Olinorder(U_13290) ),
inference(clausify,[status(thm)],[f_3437_2]) ).
fof(f_3438_1,plain,
! [V_x_2,V_A_2,T_b] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup1__distrib]) ).
fof(f_3438_2,plain,
! [U_13295,U_13294,U_13293] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_13293),U_13295),c_Big__Operators_Olattice_OSup__fin(U_13293,c_Orderings_Oord__class_Omax(U_13293),U_13294)) = c_Big__Operators_Olattice_OSup__fin(U_13293,c_Orderings_Oord__class_Omax(U_13293),hAPP(c_Set_OCollect(U_13293),hAPP(hAPP(c_COMBB(tc_fun(U_13293,tc_HOL_Obool),tc_HOL_Obool,U_13293),c_HOL_OEx(U_13293)),hAPP(hAPP(c_COMBC(U_13293,tc_fun(U_13293,tc_HOL_Obool),tc_fun(U_13293,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13293,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13293,tc_HOL_Obool),tc_fun(U_13293,tc_HOL_Obool)),U_13293),c_COMBS(U_13293,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13293,tc_HOL_Obool),tc_fun(U_13293,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13293),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13293),c_fconj)),hAPP(hAPP(c_COMBC(U_13293,tc_fun(U_13293,U_13293),tc_fun(U_13293,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13293,tc_HOL_Obool),tc_fun(tc_fun(U_13293,U_13293),tc_fun(U_13293,tc_HOL_Obool)),U_13293),c_COMBB(U_13293,tc_HOL_Obool,U_13293)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_13293),U_13295))))),hAPP(hAPP(c_COMBC(U_13293,tc_fun(U_13293,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13293)),U_13294)))))
| U_13294 = c_Orderings_Obot__class_Obot(tc_fun(U_13293,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13293),U_13294))
| ~ class_Orderings_Olinorder(U_13293) ),
inference(variable_rename,[status(thm)],[f_3438_1]) ).
cnf(f_3438_3,plain,
( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_13293),U_13295),c_Big__Operators_Olattice_OSup__fin(U_13293,c_Orderings_Oord__class_Omax(U_13293),U_13294)) = c_Big__Operators_Olattice_OSup__fin(U_13293,c_Orderings_Oord__class_Omax(U_13293),hAPP(c_Set_OCollect(U_13293),hAPP(hAPP(c_COMBB(tc_fun(U_13293,tc_HOL_Obool),tc_HOL_Obool,U_13293),c_HOL_OEx(U_13293)),hAPP(hAPP(c_COMBC(U_13293,tc_fun(U_13293,tc_HOL_Obool),tc_fun(U_13293,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13293,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13293,tc_HOL_Obool),tc_fun(U_13293,tc_HOL_Obool)),U_13293),c_COMBS(U_13293,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13293,tc_HOL_Obool),tc_fun(U_13293,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13293),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13293),c_fconj)),hAPP(hAPP(c_COMBC(U_13293,tc_fun(U_13293,U_13293),tc_fun(U_13293,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13293,tc_HOL_Obool),tc_fun(tc_fun(U_13293,U_13293),tc_fun(U_13293,tc_HOL_Obool)),U_13293),c_COMBB(U_13293,tc_HOL_Obool,U_13293)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_13293),U_13295))))),hAPP(hAPP(c_COMBC(U_13293,tc_fun(U_13293,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13293)),U_13294)))))
| U_13294 = c_Orderings_Obot__class_Obot(tc_fun(U_13293,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13293),U_13294))
| ~ class_Orderings_Olinorder(U_13293) ),
inference(clausify,[status(thm)],[f_3438_2]) ).
fof(f_3439_1,plain,
! [V_B_2,V_A_2,T_c,T_b] : c_Nitpick_Oprod(T_b,T_c,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Oprod__def]) ).
fof(f_3439_2,plain,
! [U_13299,U_13298,U_13297,U_13296] : c_Nitpick_Oprod(U_13296,U_13297,U_13298,U_13299) = hAPP(c_Set_OCollect(tc_prod(U_13296,U_13297)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13296,U_13297,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13296,tc_fun(U_13297,tc_HOL_Obool),tc_fun(U_13297,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13297,tc_HOL_Obool),tc_fun(U_13297,tc_HOL_Obool)),U_13296),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13297)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13296),c_fconj),hAPP(hAPP(c_COMBC(U_13296,tc_fun(U_13296,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13296)),U_13298)))),hAPP(hAPP(c_COMBC(U_13297,tc_fun(U_13297,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13297)),U_13299)))),
inference(variable_rename,[status(thm)],[f_3439_1]) ).
cnf(f_3439_3,plain,
c_Nitpick_Oprod(U_13296,U_13297,U_13298,U_13299) = hAPP(c_Set_OCollect(tc_prod(U_13296,U_13297)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13296,U_13297,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13296,tc_fun(U_13297,tc_HOL_Obool),tc_fun(U_13297,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13297,tc_HOL_Obool),tc_fun(U_13297,tc_HOL_Obool)),U_13296),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13297)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13296),c_fconj),hAPP(hAPP(c_COMBC(U_13296,tc_fun(U_13296,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13296)),U_13298)))),hAPP(hAPP(c_COMBC(U_13297,tc_fun(U_13297,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13297)),U_13299)))),
inference(clausify,[status(thm)],[f_3439_2]) ).
fof(f_3440_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_3440_2,plain,
! [U_13300] : c_Int_Oint__ge__less__than(U_13300) = 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_13300)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[f_3440_1]) ).
cnf(f_3440_3,plain,
c_Int_Oint__ge__less__than(U_13300) = 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_13300)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(clausify,[status(thm)],[f_3440_2]) ).
fof(f_3441_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_3441_2,plain,
! [U_13301] : c_Int_Oint__ge__less__than2(U_13301) = 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_13301)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[f_3441_1]) ).
cnf(f_3441_3,plain,
c_Int_Oint__ge__less__than2(U_13301) = 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_13301)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
inference(clausify,[status(thm)],[f_3441_2]) ).
fof(f_3442_1,plain,
! [V_r_2,T_b] :
( ( c_Predicate_Oreflp(T_b,V_r_2)
| ~ c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) )
& ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2)))
| ~ c_Predicate_Oreflp(T_b,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_reflp__def]) ).
fof(f_3442_2,plain,
! [U_13303,U_13302] :
( ( c_Predicate_Oreflp(U_13302,U_13303)
| ~ c_Relation_Orefl__on(U_13302,c_Orderings_Otop__class_Otop(tc_fun(U_13302,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_13302,U_13302)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13302,U_13302,tc_HOL_Obool),U_13303))) )
& ( c_Relation_Orefl__on(U_13302,c_Orderings_Otop__class_Otop(tc_fun(U_13302,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_13302,U_13302)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13302,U_13302,tc_HOL_Obool),U_13303)))
| ~ c_Predicate_Oreflp(U_13302,U_13303) ) ),
inference(variable_rename,[status(thm)],[f_3442_1]) ).
fof(f_3442_3,plain,
( ! [U_13307,U_13305] :
( c_Predicate_Oreflp(U_13305,U_13307)
| ~ c_Relation_Orefl__on(U_13305,c_Orderings_Otop__class_Otop(tc_fun(U_13305,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_13305,U_13305)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13305,U_13305,tc_HOL_Obool),U_13307))) )
& ! [U_13306,U_13304] :
( c_Relation_Orefl__on(U_13304,c_Orderings_Otop__class_Otop(tc_fun(U_13304,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_13304,U_13304)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13304,U_13304,tc_HOL_Obool),U_13306)))
| ~ c_Predicate_Oreflp(U_13304,U_13306) ) ),
inference(miniscope,[status(thm)],[f_3442_2]) ).
cnf(f_3442_4,plain,
( c_Relation_Orefl__on(U_13304,c_Orderings_Otop__class_Otop(tc_fun(U_13304,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_13304,U_13304)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13304,U_13304,tc_HOL_Obool),U_13306)))
| ~ c_Predicate_Oreflp(U_13304,U_13306) ),
inference(clausify,[status(thm)],[f_3442_3]) ).
cnf(f_3442_5,plain,
( c_Predicate_Oreflp(U_13305,U_13307)
| ~ c_Relation_Orefl__on(U_13305,c_Orderings_Otop__class_Otop(tc_fun(U_13305,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_13305,U_13305)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13305,U_13305,tc_HOL_Obool),U_13307))) ),
inference(clausify,[status(thm)],[f_3442_3]) ).
fof(f_3443_1,plain,
! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_d),c_Fun_Oid(T_d)),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),T_d),c_COMBB(T_d,tc_HOL_Obool,T_c)),c_fequal))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))))))
| ~ c_Fun_Oinj__on(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))
| ~ class_Rings_Osemiring__0(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__mult__setsum__if__inj]) ).
fof(f_3443_2,plain,
! [U_13314,U_13313,U_13312,U_13311,U_13310,U_13309,U_13308] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13308),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13309,U_13308),U_13311),U_13313)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13310,U_13308),U_13312),U_13314)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13308,U_13308),c_Fun_Oid(U_13308)),hAPP(c_Set_OCollect(U_13308),hAPP(hAPP(c_COMBB(tc_fun(U_13309,tc_HOL_Obool),tc_HOL_Obool,U_13308),c_HOL_OEx(U_13309)),hAPP(hAPP(c_COMBB(tc_fun(U_13309,tc_fun(U_13310,tc_HOL_Obool)),tc_fun(U_13309,tc_HOL_Obool),U_13308),hAPP(c_COMBB(tc_fun(U_13310,tc_HOL_Obool),tc_HOL_Obool,U_13309),c_HOL_OEx(U_13310))),hAPP(hAPP(c_COMBC(U_13308,tc_fun(U_13309,tc_fun(U_13310,tc_HOL_Obool)),tc_fun(U_13309,tc_fun(U_13310,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13309,tc_fun(tc_fun(U_13310,tc_HOL_Obool),tc_fun(U_13310,tc_HOL_Obool))),tc_fun(tc_fun(U_13309,tc_fun(U_13310,tc_HOL_Obool)),tc_fun(U_13309,tc_fun(U_13310,tc_HOL_Obool))),U_13308),c_COMBS(U_13309,tc_fun(U_13310,tc_HOL_Obool),tc_fun(U_13310,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13309,tc_fun(U_13310,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13309,tc_fun(tc_fun(U_13310,tc_HOL_Obool),tc_fun(U_13310,tc_HOL_Obool))),U_13308),hAPP(c_COMBB(tc_fun(U_13310,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13310,tc_HOL_Obool),tc_fun(U_13310,tc_HOL_Obool)),U_13309),c_COMBS(U_13310,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13309,tc_fun(U_13310,tc_HOL_Obool)),tc_fun(U_13309,tc_fun(U_13310,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13308),hAPP(c_COMBB(tc_fun(U_13310,tc_HOL_Obool),tc_fun(U_13310,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13309),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13310),c_fconj))),hAPP(hAPP(c_COMBC(U_13308,tc_fun(U_13309,tc_fun(U_13310,U_13308)),tc_fun(U_13309,tc_fun(U_13310,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13310,U_13308),tc_fun(U_13310,tc_HOL_Obool)),tc_fun(tc_fun(U_13309,tc_fun(U_13310,U_13308)),tc_fun(U_13309,tc_fun(U_13310,tc_HOL_Obool))),U_13308),c_COMBB(tc_fun(U_13310,U_13308),tc_fun(U_13310,tc_HOL_Obool),U_13309)),hAPP(hAPP(c_COMBB(tc_fun(U_13308,tc_HOL_Obool),tc_fun(tc_fun(U_13310,U_13308),tc_fun(U_13310,tc_HOL_Obool)),U_13308),c_COMBB(U_13308,tc_HOL_Obool,U_13310)),c_fequal))),hAPP(hAPP(c_COMBC(U_13309,tc_fun(U_13310,U_13308),tc_fun(U_13310,U_13308)),hAPP(hAPP(c_COMBB(tc_fun(U_13308,U_13308),tc_fun(tc_fun(U_13310,U_13308),tc_fun(U_13310,U_13308)),U_13309),c_COMBB(U_13308,U_13308,U_13310)),hAPP(hAPP(c_COMBB(U_13308,tc_fun(U_13308,U_13308),U_13309),c_Groups_Otimes__class_Otimes(U_13308)),U_13311))),U_13312)))))),hAPP(hAPP(c_COMBC(U_13309,tc_fun(U_13310,tc_HOL_Obool),tc_fun(U_13310,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13310,tc_HOL_Obool),tc_fun(U_13310,tc_HOL_Obool)),U_13309),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13310)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13309),c_fconj),hAPP(hAPP(c_COMBC(U_13309,tc_fun(U_13309,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13309)),U_13313)))),hAPP(hAPP(c_COMBC(U_13310,tc_fun(U_13310,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13310)),U_13314)))))))
| ~ c_Fun_Oinj__on(tc_prod(U_13309,U_13310),U_13308,hAPP(c_Product__Type_Oprod_Oprod__case(U_13309,U_13310,U_13308),hAPP(hAPP(c_COMBC(U_13309,tc_fun(U_13310,U_13308),tc_fun(U_13310,U_13308)),hAPP(hAPP(c_COMBB(tc_fun(U_13308,U_13308),tc_fun(tc_fun(U_13310,U_13308),tc_fun(U_13310,U_13308)),U_13309),c_COMBB(U_13308,U_13308,U_13310)),hAPP(hAPP(c_COMBB(U_13308,tc_fun(U_13308,U_13308),U_13309),c_Groups_Otimes__class_Otimes(U_13308)),U_13311))),U_13312)),hAPP(hAPP(c_Product__Type_OSigma(U_13309,U_13310),U_13313),hAPP(c_COMBK(tc_fun(U_13310,tc_HOL_Obool),U_13309),U_13314)))
| ~ class_Rings_Osemiring__0(U_13308) ),
inference(variable_rename,[status(thm)],[f_3443_1]) ).
cnf(f_3443_3,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13308),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13309,U_13308),U_13311),U_13313)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13310,U_13308),U_13312),U_13314)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13308,U_13308),c_Fun_Oid(U_13308)),hAPP(c_Set_OCollect(U_13308),hAPP(hAPP(c_COMBB(tc_fun(U_13309,tc_HOL_Obool),tc_HOL_Obool,U_13308),c_HOL_OEx(U_13309)),hAPP(hAPP(c_COMBB(tc_fun(U_13309,tc_fun(U_13310,tc_HOL_Obool)),tc_fun(U_13309,tc_HOL_Obool),U_13308),hAPP(c_COMBB(tc_fun(U_13310,tc_HOL_Obool),tc_HOL_Obool,U_13309),c_HOL_OEx(U_13310))),hAPP(hAPP(c_COMBC(U_13308,tc_fun(U_13309,tc_fun(U_13310,tc_HOL_Obool)),tc_fun(U_13309,tc_fun(U_13310,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13309,tc_fun(tc_fun(U_13310,tc_HOL_Obool),tc_fun(U_13310,tc_HOL_Obool))),tc_fun(tc_fun(U_13309,tc_fun(U_13310,tc_HOL_Obool)),tc_fun(U_13309,tc_fun(U_13310,tc_HOL_Obool))),U_13308),c_COMBS(U_13309,tc_fun(U_13310,tc_HOL_Obool),tc_fun(U_13310,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13309,tc_fun(U_13310,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_13309,tc_fun(tc_fun(U_13310,tc_HOL_Obool),tc_fun(U_13310,tc_HOL_Obool))),U_13308),hAPP(c_COMBB(tc_fun(U_13310,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13310,tc_HOL_Obool),tc_fun(U_13310,tc_HOL_Obool)),U_13309),c_COMBS(U_13310,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13309,tc_fun(U_13310,tc_HOL_Obool)),tc_fun(U_13309,tc_fun(U_13310,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_13308),hAPP(c_COMBB(tc_fun(U_13310,tc_HOL_Obool),tc_fun(U_13310,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13309),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13310),c_fconj))),hAPP(hAPP(c_COMBC(U_13308,tc_fun(U_13309,tc_fun(U_13310,U_13308)),tc_fun(U_13309,tc_fun(U_13310,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13310,U_13308),tc_fun(U_13310,tc_HOL_Obool)),tc_fun(tc_fun(U_13309,tc_fun(U_13310,U_13308)),tc_fun(U_13309,tc_fun(U_13310,tc_HOL_Obool))),U_13308),c_COMBB(tc_fun(U_13310,U_13308),tc_fun(U_13310,tc_HOL_Obool),U_13309)),hAPP(hAPP(c_COMBB(tc_fun(U_13308,tc_HOL_Obool),tc_fun(tc_fun(U_13310,U_13308),tc_fun(U_13310,tc_HOL_Obool)),U_13308),c_COMBB(U_13308,tc_HOL_Obool,U_13310)),c_fequal))),hAPP(hAPP(c_COMBC(U_13309,tc_fun(U_13310,U_13308),tc_fun(U_13310,U_13308)),hAPP(hAPP(c_COMBB(tc_fun(U_13308,U_13308),tc_fun(tc_fun(U_13310,U_13308),tc_fun(U_13310,U_13308)),U_13309),c_COMBB(U_13308,U_13308,U_13310)),hAPP(hAPP(c_COMBB(U_13308,tc_fun(U_13308,U_13308),U_13309),c_Groups_Otimes__class_Otimes(U_13308)),U_13311))),U_13312)))))),hAPP(hAPP(c_COMBC(U_13309,tc_fun(U_13310,tc_HOL_Obool),tc_fun(U_13310,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_13310,tc_HOL_Obool),tc_fun(U_13310,tc_HOL_Obool)),U_13309),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13310)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13309),c_fconj),hAPP(hAPP(c_COMBC(U_13309,tc_fun(U_13309,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13309)),U_13313)))),hAPP(hAPP(c_COMBC(U_13310,tc_fun(U_13310,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13310)),U_13314)))))))
| ~ c_Fun_Oinj__on(tc_prod(U_13309,U_13310),U_13308,hAPP(c_Product__Type_Oprod_Oprod__case(U_13309,U_13310,U_13308),hAPP(hAPP(c_COMBC(U_13309,tc_fun(U_13310,U_13308),tc_fun(U_13310,U_13308)),hAPP(hAPP(c_COMBB(tc_fun(U_13308,U_13308),tc_fun(tc_fun(U_13310,U_13308),tc_fun(U_13310,U_13308)),U_13309),c_COMBB(U_13308,U_13308,U_13310)),hAPP(hAPP(c_COMBB(U_13308,tc_fun(U_13308,U_13308),U_13309),c_Groups_Otimes__class_Otimes(U_13308)),U_13311))),U_13312)),hAPP(hAPP(c_Product__Type_OSigma(U_13309,U_13310),U_13313),hAPP(c_COMBK(tc_fun(U_13310,tc_HOL_Obool),U_13309),U_13314)))
| ~ class_Rings_Osemiring__0(U_13308) ),
inference(clausify,[status(thm)],[f_3443_2]) ).
fof(f_3444_1,plain,
! [V_P_2,V_a_2,V_f_2,T_b,V_A_2] :
( hBOOL(hAPP(V_P_2,V_a_2))
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))))) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
| V_A_2 != c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_def__lfp__induct__set]) ).
fof(f_3444_2,plain,
! [U_13320,U_13319,U_13318,U_13317,U_13316] :
( hBOOL(hAPP(U_13320,U_13319))
| ? [U_13315] :
( ~ hBOOL(hAPP(U_13320,U_13315))
& hBOOL(hAPP(hAPP(c_member(U_13317),U_13315),hAPP(U_13318,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13317,tc_HOL_Obool)),U_13316),hAPP(c_Set_OCollect(U_13317),U_13320))))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_13317),U_13319),U_13316))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_13317,tc_HOL_Obool),tc_fun(U_13317,tc_HOL_Obool),U_13318)
| U_13316 != c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_13317,tc_HOL_Obool),U_13318) ),
inference(variable_rename,[status(thm)],[f_3444_1]) ).
fof(f_3444_3,plain,
! [U_13320,U_13319,U_13318,U_13317,U_13316] :
( hBOOL(hAPP(U_13320,U_13319))
| ( ~ hBOOL(hAPP(U_13320,sK313(U_13320,U_13319,U_13318,U_13317,U_13316)))
& hBOOL(hAPP(hAPP(c_member(U_13317),sK313(U_13320,U_13319,U_13318,U_13317,U_13316)),hAPP(U_13318,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13317,tc_HOL_Obool)),U_13316),hAPP(c_Set_OCollect(U_13317),U_13320))))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_13317),U_13319),U_13316))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_13317,tc_HOL_Obool),tc_fun(U_13317,tc_HOL_Obool),U_13318)
| U_13316 != c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_13317,tc_HOL_Obool),U_13318) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK313]),skolemize(U_13315,sK313(U_13320,U_13319,U_13318,U_13317,U_13316))],[f_3444_2]) ).
cnf(f_3444_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_13317),sK313(U_13320,U_13319,U_13318,U_13317,U_13316)),hAPP(U_13318,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13317,tc_HOL_Obool)),U_13316),hAPP(c_Set_OCollect(U_13317),U_13320)))))
| hBOOL(hAPP(U_13320,U_13319))
| ~ hBOOL(hAPP(hAPP(c_member(U_13317),U_13319),U_13316))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_13317,tc_HOL_Obool),tc_fun(U_13317,tc_HOL_Obool),U_13318)
| U_13316 != c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_13317,tc_HOL_Obool),U_13318) ),
inference(clausify,[status(thm)],[f_3444_3]) ).
cnf(f_3444_5,plain,
( ~ hBOOL(hAPP(U_13320,sK313(U_13320,U_13319,U_13318,U_13317,U_13316)))
| hBOOL(hAPP(U_13320,U_13319))
| ~ hBOOL(hAPP(hAPP(c_member(U_13317),U_13319),U_13316))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_13317,tc_HOL_Obool),tc_fun(U_13317,tc_HOL_Obool),U_13318)
| U_13316 != c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_13317,tc_HOL_Obool),U_13318) ),
inference(clausify,[status(thm)],[f_3444_3]) ).
fof(f_3445_1,plain,
! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2),
inference(fof_nnf,[status(thm)],[fact_inj__on__id]) ).
fof(f_3445_2,plain,
! [U_13322,U_13321] : c_Fun_Oinj__on(U_13321,U_13321,c_Fun_Oid(U_13321),U_13322),
inference(variable_rename,[status(thm)],[f_3445_1]) ).
cnf(f_3445_3,plain,
c_Fun_Oinj__on(U_13321,U_13321,c_Fun_Oid(U_13321),U_13322),
inference(clausify,[status(thm)],[f_3445_2]) ).
fof(f_3446_1,plain,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_of__int__eq__id]) ).
cnf(f_3446_2,plain,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
inference(clausify,[status(thm)],[f_3446_1]) ).
fof(f_3447_1,plain,
! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_vimage__id]) ).
fof(f_3447_2,plain,
! [U_13324,U_13323] : hAPP(c_Set_Ovimage(U_13323,U_13323,c_Fun_Oid(U_13323)),U_13324) = U_13324,
inference(variable_rename,[status(thm)],[f_3447_1]) ).
cnf(f_3447_3,plain,
hAPP(c_Set_Ovimage(U_13323,U_13323,c_Fun_Oid(U_13323)),U_13324) = U_13324,
inference(clausify,[status(thm)],[f_3447_2]) ).
fof(f_3448_1,plain,
! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1,
inference(fof_nnf,[status(thm)],[fact_id__def]) ).
fof(f_3448_2,plain,
! [U_13326,U_13325] : hAPP(c_Fun_Oid(U_13325),U_13326) = U_13326,
inference(variable_rename,[status(thm)],[f_3448_1]) ).
cnf(f_3448_3,plain,
hAPP(c_Fun_Oid(U_13325),U_13326) = U_13326,
inference(clausify,[status(thm)],[f_3448_2]) ).
fof(f_3449_1,plain,
! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x,
inference(fof_nnf,[status(thm)],[fact_id__apply]) ).
fof(f_3449_2,plain,
! [U_13328,U_13327] : hAPP(c_Fun_Oid(U_13327),U_13328) = U_13328,
inference(variable_rename,[status(thm)],[f_3449_1]) ).
cnf(f_3449_3,plain,
hAPP(c_Fun_Oid(U_13327),U_13328) = U_13328,
inference(clausify,[status(thm)],[f_3449_2]) ).
fof(f_3450_1,plain,
! [T_c,T_b] : c_Product__Type_Oapfst(T_b,T_b,T_c,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_b,T_c)),
inference(fof_nnf,[status(thm)],[fact_apfst__id]) ).
fof(f_3450_2,plain,
! [U_13330,U_13329] : c_Product__Type_Oapfst(U_13329,U_13329,U_13330,c_Fun_Oid(U_13329)) = c_Fun_Oid(tc_prod(U_13329,U_13330)),
inference(variable_rename,[status(thm)],[f_3450_1]) ).
cnf(f_3450_3,plain,
c_Product__Type_Oapfst(U_13329,U_13329,U_13330,c_Fun_Oid(U_13329)) = c_Fun_Oid(tc_prod(U_13329,U_13330)),
inference(clausify,[status(thm)],[f_3450_2]) ).
fof(f_3451_1,plain,
! [T_b,T_c] : c_Product__Type_Oapsnd(T_c,T_c,T_b,c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
inference(fof_nnf,[status(thm)],[fact_apsnd__id]) ).
fof(f_3451_2,plain,
! [U_13332,U_13331] : c_Product__Type_Oapsnd(U_13331,U_13331,U_13332,c_Fun_Oid(U_13331)) = c_Fun_Oid(tc_prod(U_13332,U_13331)),
inference(variable_rename,[status(thm)],[f_3451_1]) ).
cnf(f_3451_3,plain,
c_Product__Type_Oapsnd(U_13331,U_13331,U_13332,c_Fun_Oid(U_13331)) = c_Fun_Oid(tc_prod(U_13332,U_13331)),
inference(clausify,[status(thm)],[f_3451_2]) ).
fof(f_3452_1,plain,
! [V_x_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2))
| ~ c_Predicate_Oreflp(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_reflpE]) ).
fof(f_3452_2,plain,
! [U_13335,U_13334,U_13333] :
( hBOOL(hAPP(hAPP(U_13334,U_13335),U_13335))
| ~ c_Predicate_Oreflp(U_13333,U_13334) ),
inference(variable_rename,[status(thm)],[f_3452_1]) ).
fof(f_3452_3,plain,
! [U_13335,U_13334] :
( ! [U_13333] : ~ c_Predicate_Oreflp(U_13333,U_13334)
| hBOOL(hAPP(hAPP(U_13334,U_13335),U_13335)) ),
inference(miniscope,[status(thm)],[f_3452_2]) ).
cnf(f_3452_4,plain,
( ~ c_Predicate_Oreflp(U_13333,U_13334)
| hBOOL(hAPP(hAPP(U_13334,U_13335),U_13335)) ),
inference(clausify,[status(thm)],[f_3452_3]) ).
fof(f_3453_1,plain,
! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
inference(fof_nnf,[status(thm)],[fact_map__pair_Oidentity]) ).
fof(f_3453_2,plain,
! [U_13337,U_13336] : c_Product__Type_Omap__pair(U_13336,U_13336,U_13337,U_13337,c_COMBI(U_13336),c_COMBI(U_13337)) = c_Fun_Oid(tc_prod(U_13336,U_13337)),
inference(variable_rename,[status(thm)],[f_3453_1]) ).
cnf(f_3453_3,plain,
c_Product__Type_Omap__pair(U_13336,U_13336,U_13337,U_13337,c_COMBI(U_13336),c_COMBI(U_13337)) = c_Fun_Oid(tc_prod(U_13336,U_13337)),
inference(clausify,[status(thm)],[f_3453_2]) ).
fof(f_3454_1,plain,
! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_Fun_Oid(T_b),c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
inference(fof_nnf,[status(thm)],[fact_map__pair_Oid]) ).
fof(f_3454_2,plain,
! [U_13339,U_13338] : c_Product__Type_Omap__pair(U_13338,U_13338,U_13339,U_13339,c_Fun_Oid(U_13338),c_Fun_Oid(U_13339)) = c_Fun_Oid(tc_prod(U_13338,U_13339)),
inference(variable_rename,[status(thm)],[f_3454_1]) ).
cnf(f_3454_3,plain,
c_Product__Type_Omap__pair(U_13338,U_13338,U_13339,U_13339,c_Fun_Oid(U_13338),c_Fun_Oid(U_13339)) = c_Fun_Oid(tc_prod(U_13338,U_13339)),
inference(clausify,[status(thm)],[f_3454_2]) ).
fof(f_3455_1,plain,
! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2,
inference(fof_nnf,[status(thm)],[fact_image__id]) ).
fof(f_3455_2,plain,
! [U_13341,U_13340] : hAPP(c_Set_Oimage(U_13340,U_13340,c_Fun_Oid(U_13340)),U_13341) = U_13341,
inference(variable_rename,[status(thm)],[f_3455_1]) ).
cnf(f_3455_3,plain,
hAPP(c_Set_Oimage(U_13340,U_13340,c_Fun_Oid(U_13340)),U_13341) = U_13341,
inference(clausify,[status(thm)],[f_3455_2]) ).
fof(f_3456_1,plain,
! [T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_surj__id]) ).
fof(f_3456_2,plain,
! [U_13342] : hAPP(c_Set_Oimage(U_13342,U_13342,c_Fun_Oid(U_13342)),c_Orderings_Otop__class_Otop(tc_fun(U_13342,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13342,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3456_1]) ).
cnf(f_3456_3,plain,
hAPP(c_Set_Oimage(U_13342,U_13342,c_Fun_Oid(U_13342)),c_Orderings_Otop__class_Otop(tc_fun(U_13342,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13342,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3456_2]) ).
fof(f_3457_1,plain,
! [V_f_2,T_c,T_d,T_b] : c_Product__Type_Oapfst(T_b,T_d,T_c,V_f_2) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_c,V_f_2,c_Fun_Oid(T_c)),
inference(fof_nnf,[status(thm)],[fact_apfst__def]) ).
fof(f_3457_2,plain,
! [U_13346,U_13345,U_13344,U_13343] : c_Product__Type_Oapfst(U_13343,U_13344,U_13345,U_13346) = c_Product__Type_Omap__pair(U_13343,U_13344,U_13345,U_13345,U_13346,c_Fun_Oid(U_13345)),
inference(variable_rename,[status(thm)],[f_3457_1]) ).
cnf(f_3457_3,plain,
c_Product__Type_Oapfst(U_13343,U_13344,U_13345,U_13346) = c_Product__Type_Omap__pair(U_13343,U_13344,U_13345,U_13345,U_13346,c_Fun_Oid(U_13345)),
inference(clausify,[status(thm)],[f_3457_2]) ).
fof(f_3458_1,plain,
! [V_f_2,T_b,T_d,T_c] : c_Product__Type_Oapsnd(T_c,T_d,T_b,V_f_2) = c_Product__Type_Omap__pair(T_b,T_b,T_c,T_d,c_Fun_Oid(T_b),V_f_2),
inference(fof_nnf,[status(thm)],[fact_apsnd__def]) ).
fof(f_3458_2,plain,
! [U_13350,U_13349,U_13348,U_13347] : c_Product__Type_Oapsnd(U_13347,U_13348,U_13349,U_13350) = c_Product__Type_Omap__pair(U_13349,U_13349,U_13347,U_13348,c_Fun_Oid(U_13349),U_13350),
inference(variable_rename,[status(thm)],[f_3458_1]) ).
cnf(f_3458_3,plain,
c_Product__Type_Oapsnd(U_13347,U_13348,U_13349,U_13350) = c_Product__Type_Omap__pair(U_13349,U_13349,U_13347,U_13348,c_Fun_Oid(U_13349),U_13350),
inference(clausify,[status(thm)],[f_3458_2]) ).
fof(f_3459_1,plain,
! [T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)),
inference(fof_nnf,[status(thm)],[fact_split__Pair]) ).
fof(f_3459_2,plain,
! [U_13352,U_13351] : hAPP(c_Product__Type_Oprod_Oprod__case(U_13351,U_13352,tc_prod(U_13351,U_13352)),c_Product__Type_OPair(U_13351,U_13352)) = c_Fun_Oid(tc_prod(U_13351,U_13352)),
inference(variable_rename,[status(thm)],[f_3459_1]) ).
cnf(f_3459_3,plain,
hAPP(c_Product__Type_Oprod_Oprod__case(U_13351,U_13352,tc_prod(U_13351,U_13352)),c_Product__Type_OPair(U_13351,U_13352)) = c_Fun_Oid(tc_prod(U_13351,U_13352)),
inference(clausify,[status(thm)],[f_3459_2]) ).
fof(f_3460_1,plain,
! [V_B_2,V_f_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum__reindex__id]) ).
fof(f_3460_2,plain,
! [U_13356,U_13355,U_13354,U_13353] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13354,U_13353),U_13355),U_13356) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13353,U_13353),c_Fun_Oid(U_13353)),hAPP(c_Set_Oimage(U_13354,U_13353,U_13355),U_13356))
| ~ c_Fun_Oinj__on(U_13354,U_13353,U_13355,U_13356)
| ~ class_Groups_Ocomm__monoid__add(U_13353) ),
inference(variable_rename,[status(thm)],[f_3460_1]) ).
cnf(f_3460_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13354,U_13353),U_13355),U_13356) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13353,U_13353),c_Fun_Oid(U_13353)),hAPP(c_Set_Oimage(U_13354,U_13353,U_13355),U_13356))
| ~ c_Fun_Oinj__on(U_13354,U_13353,U_13355,U_13356)
| ~ class_Groups_Ocomm__monoid__add(U_13353) ),
inference(clausify,[status(thm)],[f_3460_2]) ).
fof(f_3461_1,plain,
! [V_B_2,V_f_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__reindex__id]) ).
fof(f_3461_2,plain,
! [U_13360,U_13359,U_13358,U_13357] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13358,U_13357),U_13359),U_13360) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13357,U_13357),c_Fun_Oid(U_13357)),hAPP(c_Set_Oimage(U_13358,U_13357,U_13359),U_13360))
| ~ c_Fun_Oinj__on(U_13358,U_13357,U_13359,U_13360)
| ~ class_Groups_Ocomm__monoid__mult(U_13357) ),
inference(variable_rename,[status(thm)],[f_3461_1]) ).
cnf(f_3461_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13358,U_13357),U_13359),U_13360) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_13357,U_13357),c_Fun_Oid(U_13357)),hAPP(c_Set_Oimage(U_13358,U_13357,U_13359),U_13360))
| ~ c_Fun_Oinj__on(U_13358,U_13357,U_13359,U_13360)
| ~ class_Groups_Ocomm__monoid__mult(U_13357) ),
inference(clausify,[status(thm)],[f_3461_2]) ).
fof(f_3462_1,plain,
! [V_P_2,V_f_2,V_a_2,T_b] :
( hBOOL(hAPP(V_P_2,V_a_2))
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)),hAPP(c_Set_OCollect(T_b),V_P_2))))) )
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))) ),
inference(fof_nnf,[status(thm)],[fact_lfp__induct__set]) ).
fof(f_3462_2,plain,
! [U_13365,U_13364,U_13363,U_13362] :
( hBOOL(hAPP(U_13365,U_13363))
| ? [U_13361] :
( ~ hBOOL(hAPP(U_13365,U_13361))
& hBOOL(hAPP(hAPP(c_member(U_13362),U_13361),hAPP(U_13364,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13362,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_13362,tc_HOL_Obool),U_13364)),hAPP(c_Set_OCollect(U_13362),U_13365))))) )
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_13362,tc_HOL_Obool),tc_fun(U_13362,tc_HOL_Obool),U_13364)
| ~ hBOOL(hAPP(hAPP(c_member(U_13362),U_13363),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_13362,tc_HOL_Obool),U_13364))) ),
inference(variable_rename,[status(thm)],[f_3462_1]) ).
fof(f_3462_3,plain,
! [U_13365,U_13364,U_13363,U_13362] :
( hBOOL(hAPP(U_13365,U_13363))
| ( ~ hBOOL(hAPP(U_13365,sK314(U_13365,U_13364,U_13363,U_13362)))
& hBOOL(hAPP(hAPP(c_member(U_13362),sK314(U_13365,U_13364,U_13363,U_13362)),hAPP(U_13364,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13362,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_13362,tc_HOL_Obool),U_13364)),hAPP(c_Set_OCollect(U_13362),U_13365))))) )
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_13362,tc_HOL_Obool),tc_fun(U_13362,tc_HOL_Obool),U_13364)
| ~ hBOOL(hAPP(hAPP(c_member(U_13362),U_13363),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_13362,tc_HOL_Obool),U_13364))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK314]),skolemize(U_13361,sK314(U_13365,U_13364,U_13363,U_13362))],[f_3462_2]) ).
cnf(f_3462_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_13362),sK314(U_13365,U_13364,U_13363,U_13362)),hAPP(U_13364,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13362,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_13362,tc_HOL_Obool),U_13364)),hAPP(c_Set_OCollect(U_13362),U_13365)))))
| hBOOL(hAPP(U_13365,U_13363))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_13362,tc_HOL_Obool),tc_fun(U_13362,tc_HOL_Obool),U_13364)
| ~ hBOOL(hAPP(hAPP(c_member(U_13362),U_13363),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_13362,tc_HOL_Obool),U_13364))) ),
inference(clausify,[status(thm)],[f_3462_3]) ).
cnf(f_3462_5,plain,
( ~ hBOOL(hAPP(U_13365,sK314(U_13365,U_13364,U_13363,U_13362)))
| hBOOL(hAPP(U_13365,U_13363))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_13362,tc_HOL_Obool),tc_fun(U_13362,tc_HOL_Obool),U_13364)
| ~ hBOOL(hAPP(hAPP(c_member(U_13362),U_13363),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(U_13362,tc_HOL_Obool),U_13364))) ),
inference(clausify,[status(thm)],[f_3462_3]) ).
fof(f_3463_1,plain,
! [V_X_2,V_a_2,V_P_2,T_b,V_A_2] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ? [B_z] :
( ~ hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_A_2)),B_z))
& hBOOL(hAPP(hAPP(c_member(T_b),B_z),V_X_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_OCollect(T_b)),V_P_2))
| V_A_2 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_OCollect(T_b)),V_P_2)) ),
inference(fof_nnf,[status(thm)],[fact_def__Collect__coinduct]) ).
fof(f_3463_2,plain,
! [U_13371,U_13370,U_13369,U_13368,U_13367] :
( hBOOL(hAPP(hAPP(c_member(U_13368),U_13370),U_13367))
| ? [U_13366] :
( ~ hBOOL(hAPP(hAPP(U_13369,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13368,tc_HOL_Obool)),U_13371),U_13367)),U_13366))
& hBOOL(hAPP(hAPP(c_member(U_13368),U_13366),U_13371)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_13368),U_13370),U_13371))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_13368,tc_HOL_Obool),tc_fun(U_13368,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13368,tc_HOL_Obool),tc_fun(U_13368,tc_HOL_Obool),tc_fun(U_13368,tc_HOL_Obool)),c_Set_OCollect(U_13368)),U_13369))
| U_13367 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_13368,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13368,tc_HOL_Obool),tc_fun(U_13368,tc_HOL_Obool),tc_fun(U_13368,tc_HOL_Obool)),c_Set_OCollect(U_13368)),U_13369)) ),
inference(variable_rename,[status(thm)],[f_3463_1]) ).
fof(f_3463_3,plain,
! [U_13371,U_13370,U_13369,U_13368,U_13367] :
( hBOOL(hAPP(hAPP(c_member(U_13368),U_13370),U_13367))
| ( ~ hBOOL(hAPP(hAPP(U_13369,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13368,tc_HOL_Obool)),U_13371),U_13367)),sK315(U_13371,U_13370,U_13369,U_13368,U_13367)))
& hBOOL(hAPP(hAPP(c_member(U_13368),sK315(U_13371,U_13370,U_13369,U_13368,U_13367)),U_13371)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_13368),U_13370),U_13371))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_13368,tc_HOL_Obool),tc_fun(U_13368,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13368,tc_HOL_Obool),tc_fun(U_13368,tc_HOL_Obool),tc_fun(U_13368,tc_HOL_Obool)),c_Set_OCollect(U_13368)),U_13369))
| U_13367 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_13368,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13368,tc_HOL_Obool),tc_fun(U_13368,tc_HOL_Obool),tc_fun(U_13368,tc_HOL_Obool)),c_Set_OCollect(U_13368)),U_13369)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK315]),skolemize(U_13366,sK315(U_13371,U_13370,U_13369,U_13368,U_13367))],[f_3463_2]) ).
cnf(f_3463_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_13368),sK315(U_13371,U_13370,U_13369,U_13368,U_13367)),U_13371))
| hBOOL(hAPP(hAPP(c_member(U_13368),U_13370),U_13367))
| ~ hBOOL(hAPP(hAPP(c_member(U_13368),U_13370),U_13371))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_13368,tc_HOL_Obool),tc_fun(U_13368,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13368,tc_HOL_Obool),tc_fun(U_13368,tc_HOL_Obool),tc_fun(U_13368,tc_HOL_Obool)),c_Set_OCollect(U_13368)),U_13369))
| U_13367 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_13368,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13368,tc_HOL_Obool),tc_fun(U_13368,tc_HOL_Obool),tc_fun(U_13368,tc_HOL_Obool)),c_Set_OCollect(U_13368)),U_13369)) ),
inference(clausify,[status(thm)],[f_3463_3]) ).
cnf(f_3463_5,plain,
( ~ hBOOL(hAPP(hAPP(U_13369,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13368,tc_HOL_Obool)),U_13371),U_13367)),sK315(U_13371,U_13370,U_13369,U_13368,U_13367)))
| hBOOL(hAPP(hAPP(c_member(U_13368),U_13370),U_13367))
| ~ hBOOL(hAPP(hAPP(c_member(U_13368),U_13370),U_13371))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(U_13368,tc_HOL_Obool),tc_fun(U_13368,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13368,tc_HOL_Obool),tc_fun(U_13368,tc_HOL_Obool),tc_fun(U_13368,tc_HOL_Obool)),c_Set_OCollect(U_13368)),U_13369))
| U_13367 != c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(U_13368,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13368,tc_HOL_Obool),tc_fun(U_13368,tc_HOL_Obool),tc_fun(U_13368,tc_HOL_Obool)),c_Set_OCollect(U_13368)),U_13369)) ),
inference(clausify,[status(thm)],[f_3463_3]) ).
fof(f_3464_1,plain,
! [V_P_2,V_f_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(V_P_2,V_a_2),V_b_2))
| ? [B_a,B_b] :
( ~ hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)))))) )
| ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2))) ),
inference(fof_nnf,[status(thm)],[fact_lfp__induct2]) ).
fof(f_3464_2,plain,
! [U_13379,U_13378,U_13377,U_13376,U_13375,U_13374] :
( hBOOL(hAPP(hAPP(U_13379,U_13376),U_13377))
| ? [U_13373,U_13372] :
( ~ hBOOL(hAPP(hAPP(U_13379,U_13373),U_13372))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_13374,U_13375)),hAPP(hAPP(c_Product__Type_OPair(U_13374,U_13375),U_13373),U_13372)),hAPP(U_13378,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),U_13378)),hAPP(c_Set_OCollect(tc_prod(U_13374,U_13375)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13374,U_13375,tc_HOL_Obool),U_13379)))))) )
| ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),U_13378)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13374,U_13375)),hAPP(hAPP(c_Product__Type_OPair(U_13374,U_13375),U_13376),U_13377)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),U_13378))) ),
inference(variable_rename,[status(thm)],[f_3464_1]) ).
fof(f_3464_3,plain,
! [U_13379,U_13378,U_13377,U_13376,U_13375,U_13374] :
( hBOOL(hAPP(hAPP(U_13379,U_13376),U_13377))
| ? [U_13372] :
( ~ hBOOL(hAPP(hAPP(U_13379,sK316(U_13379,U_13378,U_13377,U_13376,U_13375,U_13374)),U_13372))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_13374,U_13375)),hAPP(hAPP(c_Product__Type_OPair(U_13374,U_13375),sK316(U_13379,U_13378,U_13377,U_13376,U_13375,U_13374)),U_13372)),hAPP(U_13378,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),U_13378)),hAPP(c_Set_OCollect(tc_prod(U_13374,U_13375)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13374,U_13375,tc_HOL_Obool),U_13379)))))) )
| ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),U_13378)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13374,U_13375)),hAPP(hAPP(c_Product__Type_OPair(U_13374,U_13375),U_13376),U_13377)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),U_13378))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK316]),skolemize(U_13373,sK316(U_13379,U_13378,U_13377,U_13376,U_13375,U_13374))],[f_3464_2]) ).
fof(f_3464_4,plain,
! [U_13379,U_13378,U_13377,U_13376,U_13375,U_13374] :
( hBOOL(hAPP(hAPP(U_13379,U_13376),U_13377))
| ( ~ hBOOL(hAPP(hAPP(U_13379,sK316(U_13379,U_13378,U_13377,U_13376,U_13375,U_13374)),sK317(U_13379,U_13378,U_13377,U_13376,U_13375,U_13374)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_13374,U_13375)),hAPP(hAPP(c_Product__Type_OPair(U_13374,U_13375),sK316(U_13379,U_13378,U_13377,U_13376,U_13375,U_13374)),sK317(U_13379,U_13378,U_13377,U_13376,U_13375,U_13374))),hAPP(U_13378,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),U_13378)),hAPP(c_Set_OCollect(tc_prod(U_13374,U_13375)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13374,U_13375,tc_HOL_Obool),U_13379)))))) )
| ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),U_13378)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13374,U_13375)),hAPP(hAPP(c_Product__Type_OPair(U_13374,U_13375),U_13376),U_13377)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),U_13378))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK317]),skolemize(U_13372,sK317(U_13379,U_13378,U_13377,U_13376,U_13375,U_13374))],[f_3464_3]) ).
cnf(f_3464_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13374,U_13375)),hAPP(hAPP(c_Product__Type_OPair(U_13374,U_13375),sK316(U_13379,U_13378,U_13377,U_13376,U_13375,U_13374)),sK317(U_13379,U_13378,U_13377,U_13376,U_13375,U_13374))),hAPP(U_13378,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),U_13378)),hAPP(c_Set_OCollect(tc_prod(U_13374,U_13375)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13374,U_13375,tc_HOL_Obool),U_13379))))))
| hBOOL(hAPP(hAPP(U_13379,U_13376),U_13377))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),U_13378)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13374,U_13375)),hAPP(hAPP(c_Product__Type_OPair(U_13374,U_13375),U_13376),U_13377)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),U_13378))) ),
inference(clausify,[status(thm)],[f_3464_4]) ).
cnf(f_3464_6,plain,
( ~ hBOOL(hAPP(hAPP(U_13379,sK316(U_13379,U_13378,U_13377,U_13376,U_13375,U_13374)),sK317(U_13379,U_13378,U_13377,U_13376,U_13375,U_13374)))
| hBOOL(hAPP(hAPP(U_13379,U_13376),U_13377))
| ~ c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),U_13378)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13374,U_13375)),hAPP(hAPP(c_Product__Type_OPair(U_13374,U_13375),U_13376),U_13377)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),U_13378))) ),
inference(clausify,[status(thm)],[f_3464_4]) ).
fof(f_3465_1,plain,
! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_k_2),V_t_2)
| ? [B_x] :
( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_s_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) != hAPP(V_k_2,B_x)
& hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2)) ),
inference(fof_nnf,[status(thm)],[fact_setsum__multicount__gen]) ).
fof(f_3465_2,plain,
! [U_13386,U_13385,U_13384,U_13383,U_13382,U_13381] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13381,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13383,tc_HOL_Obool),tc_Nat_Onat,U_13381),c_Finite__Set_Ocard(U_13383)),hAPP(hAPP(c_COMBB(tc_fun(U_13383,tc_HOL_Obool),tc_fun(U_13383,tc_HOL_Obool),U_13381),c_Set_OCollect(U_13383)),hAPP(hAPP(c_COMBB(tc_fun(U_13383,tc_HOL_Obool),tc_fun(U_13383,tc_HOL_Obool),U_13381),hAPP(c_COMBS(U_13383,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13383),c_fconj),hAPP(hAPP(c_COMBC(U_13383,tc_fun(U_13383,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13383)),U_13384)))),U_13385)))),U_13382) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13383,tc_Nat_Onat),U_13386),U_13384)
| ? [U_13380] :
( hAPP(c_Finite__Set_Ocard(U_13381),hAPP(c_Set_OCollect(U_13381),hAPP(hAPP(c_COMBS(U_13381,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13381),c_fconj),hAPP(hAPP(c_COMBC(U_13381,tc_fun(U_13381,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13381)),U_13382))),hAPP(hAPP(c_COMBC(U_13381,U_13383,tc_HOL_Obool),U_13385),U_13380)))) != hAPP(U_13386,U_13380)
& hBOOL(hAPP(hAPP(c_member(U_13383),U_13380),U_13384)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13383),U_13384))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13381),U_13382)) ),
inference(variable_rename,[status(thm)],[f_3465_1]) ).
fof(f_3465_3,plain,
! [U_13386,U_13385,U_13384,U_13383,U_13382,U_13381] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13381,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13383,tc_HOL_Obool),tc_Nat_Onat,U_13381),c_Finite__Set_Ocard(U_13383)),hAPP(hAPP(c_COMBB(tc_fun(U_13383,tc_HOL_Obool),tc_fun(U_13383,tc_HOL_Obool),U_13381),c_Set_OCollect(U_13383)),hAPP(hAPP(c_COMBB(tc_fun(U_13383,tc_HOL_Obool),tc_fun(U_13383,tc_HOL_Obool),U_13381),hAPP(c_COMBS(U_13383,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13383),c_fconj),hAPP(hAPP(c_COMBC(U_13383,tc_fun(U_13383,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13383)),U_13384)))),U_13385)))),U_13382) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13383,tc_Nat_Onat),U_13386),U_13384)
| ( hAPP(c_Finite__Set_Ocard(U_13381),hAPP(c_Set_OCollect(U_13381),hAPP(hAPP(c_COMBS(U_13381,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13381),c_fconj),hAPP(hAPP(c_COMBC(U_13381,tc_fun(U_13381,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13381)),U_13382))),hAPP(hAPP(c_COMBC(U_13381,U_13383,tc_HOL_Obool),U_13385),sK318(U_13386,U_13385,U_13384,U_13383,U_13382,U_13381))))) != hAPP(U_13386,sK318(U_13386,U_13385,U_13384,U_13383,U_13382,U_13381))
& hBOOL(hAPP(hAPP(c_member(U_13383),sK318(U_13386,U_13385,U_13384,U_13383,U_13382,U_13381)),U_13384)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13383),U_13384))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13381),U_13382)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK318]),skolemize(U_13380,sK318(U_13386,U_13385,U_13384,U_13383,U_13382,U_13381))],[f_3465_2]) ).
cnf(f_3465_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_13383),sK318(U_13386,U_13385,U_13384,U_13383,U_13382,U_13381)),U_13384))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13381,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13383,tc_HOL_Obool),tc_Nat_Onat,U_13381),c_Finite__Set_Ocard(U_13383)),hAPP(hAPP(c_COMBB(tc_fun(U_13383,tc_HOL_Obool),tc_fun(U_13383,tc_HOL_Obool),U_13381),c_Set_OCollect(U_13383)),hAPP(hAPP(c_COMBB(tc_fun(U_13383,tc_HOL_Obool),tc_fun(U_13383,tc_HOL_Obool),U_13381),hAPP(c_COMBS(U_13383,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13383),c_fconj),hAPP(hAPP(c_COMBC(U_13383,tc_fun(U_13383,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13383)),U_13384)))),U_13385)))),U_13382) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13383,tc_Nat_Onat),U_13386),U_13384)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13383),U_13384))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13381),U_13382)) ),
inference(clausify,[status(thm)],[f_3465_3]) ).
cnf(f_3465_5,plain,
( hAPP(c_Finite__Set_Ocard(U_13381),hAPP(c_Set_OCollect(U_13381),hAPP(hAPP(c_COMBS(U_13381,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13381),c_fconj),hAPP(hAPP(c_COMBC(U_13381,tc_fun(U_13381,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13381)),U_13382))),hAPP(hAPP(c_COMBC(U_13381,U_13383,tc_HOL_Obool),U_13385),sK318(U_13386,U_13385,U_13384,U_13383,U_13382,U_13381))))) != hAPP(U_13386,sK318(U_13386,U_13385,U_13384,U_13383,U_13382,U_13381))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13381,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_13383,tc_HOL_Obool),tc_Nat_Onat,U_13381),c_Finite__Set_Ocard(U_13383)),hAPP(hAPP(c_COMBB(tc_fun(U_13383,tc_HOL_Obool),tc_fun(U_13383,tc_HOL_Obool),U_13381),c_Set_OCollect(U_13383)),hAPP(hAPP(c_COMBB(tc_fun(U_13383,tc_HOL_Obool),tc_fun(U_13383,tc_HOL_Obool),U_13381),hAPP(c_COMBS(U_13383,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13383),c_fconj),hAPP(hAPP(c_COMBC(U_13383,tc_fun(U_13383,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13383)),U_13384)))),U_13385)))),U_13382) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_13383,tc_Nat_Onat),U_13386),U_13384)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13383),U_13384))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13381),U_13382)) ),
inference(clausify,[status(thm)],[f_3465_3]) ).
fof(f_3466_1,plain,
! [V_A_2,T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ! [B_n,B_f] : V_A_2 != hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n))) )
& ( ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,B_f),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),B_n)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__conv__nat__seg__image]) ).
fof(f_3466_2,plain,
! [U_13392,U_13391] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13391),U_13392))
| ! [U_13390,U_13389] : U_13392 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13391,U_13389),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_13390))) )
& ( ? [U_13388,U_13387] : U_13392 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_13391,U_13387),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_13388)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13391),U_13392)) ) ),
inference(variable_rename,[status(thm)],[f_3466_1]) ).
fof(f_3466_3,plain,
( ! [U_13396,U_13394] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13394),U_13396))
| ! [U_13390,U_13389] : U_13396 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13394,U_13389),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_13390))) )
& ! [U_13395,U_13393] :
( ? [U_13388,U_13387] : U_13395 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_13393,U_13387),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_13388)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13393),U_13395)) ) ),
inference(miniscope,[status(thm)],[f_3466_2]) ).
fof(f_3466_4,plain,
( ! [U_13396,U_13394] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13394),U_13396))
| ! [U_13390,U_13389] : U_13396 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13394,U_13389),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_13390))) )
& ! [U_13395,U_13393] :
( ? [U_13387] : U_13395 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_13393,U_13387),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)),sK319(U_13395,U_13393))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13393),U_13395)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK319]),skolemize(U_13388,sK319(U_13395,U_13393))],[f_3466_3]) ).
fof(f_3466_5,plain,
( ! [U_13396,U_13394] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13394),U_13396))
| ! [U_13390,U_13389] : U_13396 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13394,U_13389),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_13390))) )
& ! [U_13395,U_13393] :
( U_13395 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_13393,sK320(U_13395,U_13393)),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)),sK319(U_13395,U_13393))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13393),U_13395)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK320]),skolemize(U_13387,sK320(U_13395,U_13393))],[f_3466_4]) ).
cnf(f_3466_6,plain,
( U_13395 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_13393,sK320(U_13395,U_13393)),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)),sK319(U_13395,U_13393))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13393),U_13395)) ),
inference(clausify,[status(thm)],[f_3466_5]) ).
cnf(f_3466_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13394),U_13396))
| U_13396 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_13394,U_13389),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_13390))) ),
inference(clausify,[status(thm)],[f_3466_5]) ).
fof(f_3467_1,plain,
! [V_s_2,V_r_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_d),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBC(T_d,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_d),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_b,T_d)))),c_Product__Type_OPair(T_b,T_d)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_d,T_c)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_d,T_c)))),hAPP(c_COMBC(T_d,T_c,tc_prod(T_d,T_c)),c_Product__Type_OPair(T_d,T_c))))),V_s_2))))),
inference(fof_nnf,[status(thm)],[fact_rel__comp__def]) ).
fof(f_3467_2,plain,
! [U_13401,U_13400,U_13399,U_13398,U_13397] : hAPP(hAPP(c_Relation_Orel__comp(U_13397,U_13398,U_13399),U_13400),U_13401) = hAPP(c_Set_OCollect(tc_prod(U_13397,U_13399)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13397,U_13399,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13399,tc_fun(U_13398,tc_HOL_Obool)),tc_fun(U_13399,tc_HOL_Obool),U_13397),hAPP(c_COMBB(tc_fun(U_13398,tc_HOL_Obool),tc_HOL_Obool,U_13399),c_HOL_OEx(U_13398))),hAPP(hAPP(c_COMBC(U_13397,tc_fun(U_13399,tc_fun(U_13398,tc_HOL_Obool)),tc_fun(U_13399,tc_fun(U_13398,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13398,tc_HOL_Obool),tc_fun(U_13398,tc_HOL_Obool)),tc_fun(tc_fun(U_13399,tc_fun(U_13398,tc_HOL_Obool)),tc_fun(U_13399,tc_fun(U_13398,tc_HOL_Obool))),U_13397),c_COMBB(tc_fun(U_13398,tc_HOL_Obool),tc_fun(U_13398,tc_HOL_Obool),U_13399)),hAPP(hAPP(c_COMBB(tc_fun(U_13398,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13398,tc_HOL_Obool),tc_fun(U_13398,tc_HOL_Obool)),U_13397),c_COMBS(U_13398,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13398,tc_HOL_Obool),tc_fun(U_13398,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13397),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13398),c_fconj)),hAPP(hAPP(c_COMBC(U_13397,tc_fun(tc_prod(U_13397,U_13398),tc_HOL_Obool),tc_fun(U_13398,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13398,tc_fun(tc_fun(tc_prod(U_13397,U_13398),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13397,U_13398),tc_HOL_Obool),tc_fun(U_13398,tc_HOL_Obool)),U_13397),c_COMBC(U_13398,tc_fun(tc_prod(U_13397,U_13398),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13398,tc_prod(U_13397,U_13398)),tc_fun(U_13398,tc_fun(tc_fun(tc_prod(U_13397,U_13398),tc_HOL_Obool),tc_HOL_Obool)),U_13397),hAPP(c_COMBB(tc_prod(U_13397,U_13398),tc_fun(tc_fun(tc_prod(U_13397,U_13398),tc_HOL_Obool),tc_HOL_Obool),U_13398),c_member(tc_prod(U_13397,U_13398)))),c_Product__Type_OPair(U_13397,U_13398)))),U_13400))))),hAPP(hAPP(c_COMBC(U_13399,tc_fun(tc_prod(U_13398,U_13399),tc_HOL_Obool),tc_fun(U_13398,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13398,tc_fun(tc_fun(tc_prod(U_13398,U_13399),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13398,U_13399),tc_HOL_Obool),tc_fun(U_13398,tc_HOL_Obool)),U_13399),c_COMBC(U_13398,tc_fun(tc_prod(U_13398,U_13399),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13398,tc_prod(U_13398,U_13399)),tc_fun(U_13398,tc_fun(tc_fun(tc_prod(U_13398,U_13399),tc_HOL_Obool),tc_HOL_Obool)),U_13399),hAPP(c_COMBB(tc_prod(U_13398,U_13399),tc_fun(tc_fun(tc_prod(U_13398,U_13399),tc_HOL_Obool),tc_HOL_Obool),U_13398),c_member(tc_prod(U_13398,U_13399)))),hAPP(c_COMBC(U_13398,U_13399,tc_prod(U_13398,U_13399)),c_Product__Type_OPair(U_13398,U_13399))))),U_13401))))),
inference(variable_rename,[status(thm)],[f_3467_1]) ).
cnf(f_3467_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_13397,U_13398,U_13399),U_13400),U_13401) = hAPP(c_Set_OCollect(tc_prod(U_13397,U_13399)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13397,U_13399,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13399,tc_fun(U_13398,tc_HOL_Obool)),tc_fun(U_13399,tc_HOL_Obool),U_13397),hAPP(c_COMBB(tc_fun(U_13398,tc_HOL_Obool),tc_HOL_Obool,U_13399),c_HOL_OEx(U_13398))),hAPP(hAPP(c_COMBC(U_13397,tc_fun(U_13399,tc_fun(U_13398,tc_HOL_Obool)),tc_fun(U_13399,tc_fun(U_13398,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13398,tc_HOL_Obool),tc_fun(U_13398,tc_HOL_Obool)),tc_fun(tc_fun(U_13399,tc_fun(U_13398,tc_HOL_Obool)),tc_fun(U_13399,tc_fun(U_13398,tc_HOL_Obool))),U_13397),c_COMBB(tc_fun(U_13398,tc_HOL_Obool),tc_fun(U_13398,tc_HOL_Obool),U_13399)),hAPP(hAPP(c_COMBB(tc_fun(U_13398,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_13398,tc_HOL_Obool),tc_fun(U_13398,tc_HOL_Obool)),U_13397),c_COMBS(U_13398,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13398,tc_HOL_Obool),tc_fun(U_13398,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_13397),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13398),c_fconj)),hAPP(hAPP(c_COMBC(U_13397,tc_fun(tc_prod(U_13397,U_13398),tc_HOL_Obool),tc_fun(U_13398,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13398,tc_fun(tc_fun(tc_prod(U_13397,U_13398),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13397,U_13398),tc_HOL_Obool),tc_fun(U_13398,tc_HOL_Obool)),U_13397),c_COMBC(U_13398,tc_fun(tc_prod(U_13397,U_13398),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13398,tc_prod(U_13397,U_13398)),tc_fun(U_13398,tc_fun(tc_fun(tc_prod(U_13397,U_13398),tc_HOL_Obool),tc_HOL_Obool)),U_13397),hAPP(c_COMBB(tc_prod(U_13397,U_13398),tc_fun(tc_fun(tc_prod(U_13397,U_13398),tc_HOL_Obool),tc_HOL_Obool),U_13398),c_member(tc_prod(U_13397,U_13398)))),c_Product__Type_OPair(U_13397,U_13398)))),U_13400))))),hAPP(hAPP(c_COMBC(U_13399,tc_fun(tc_prod(U_13398,U_13399),tc_HOL_Obool),tc_fun(U_13398,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13398,tc_fun(tc_fun(tc_prod(U_13398,U_13399),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13398,U_13399),tc_HOL_Obool),tc_fun(U_13398,tc_HOL_Obool)),U_13399),c_COMBC(U_13398,tc_fun(tc_prod(U_13398,U_13399),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13398,tc_prod(U_13398,U_13399)),tc_fun(U_13398,tc_fun(tc_fun(tc_prod(U_13398,U_13399),tc_HOL_Obool),tc_HOL_Obool)),U_13399),hAPP(c_COMBB(tc_prod(U_13398,U_13399),tc_fun(tc_fun(tc_prod(U_13398,U_13399),tc_HOL_Obool),tc_HOL_Obool),U_13398),c_member(tc_prod(U_13398,U_13399)))),hAPP(c_COMBC(U_13398,U_13399,tc_prod(U_13398,U_13399)),c_Product__Type_OPair(U_13398,U_13399))))),U_13401))))),
inference(clausify,[status(thm)],[f_3467_2]) ).
fof(f_3468_1,plain,
! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_b_2),V_c_2)),V_s_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_rel__compI]) ).
fof(f_3468_2,plain,
! [U_13409,U_13408,U_13407,U_13406,U_13405,U_13404,U_13403,U_13402] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13402,U_13407)),hAPP(hAPP(c_Product__Type_OPair(U_13402,U_13407),U_13404),U_13408)),hAPP(hAPP(c_Relation_Orel__comp(U_13402,U_13403,U_13407),U_13406),U_13409)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13403,U_13407)),hAPP(hAPP(c_Product__Type_OPair(U_13403,U_13407),U_13405),U_13408)),U_13409))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13402,U_13403)),hAPP(hAPP(c_Product__Type_OPair(U_13402,U_13403),U_13404),U_13405)),U_13406)) ),
inference(variable_rename,[status(thm)],[f_3468_1]) ).
cnf(f_3468_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13402,U_13407)),hAPP(hAPP(c_Product__Type_OPair(U_13402,U_13407),U_13404),U_13408)),hAPP(hAPP(c_Relation_Orel__comp(U_13402,U_13403,U_13407),U_13406),U_13409)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13403,U_13407)),hAPP(hAPP(c_Product__Type_OPair(U_13403,U_13407),U_13405),U_13408)),U_13409))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13402,U_13403)),hAPP(hAPP(c_Product__Type_OPair(U_13402,U_13403),U_13404),U_13405)),U_13406)) ),
inference(clausify,[status(thm)],[f_3468_2]) ).
fof(f_3469_1,plain,
! [V_r_2,V_I_2,T_e,V_s_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e),hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2)),V_r_2)),
inference(fof_nnf,[status(thm)],[fact_rel__comp__UNION__distrib]) ).
fof(f_3469_2,plain,
! [U_13416,U_13415,U_13414,U_13413,U_13412,U_13411,U_13410] : hAPP(hAPP(c_Relation_Orel__comp(U_13410,U_13411,U_13412),U_13413),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13414,tc_fun(tc_prod(U_13411,U_13412),tc_HOL_Obool)),U_13415),U_13416)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13414,tc_fun(tc_prod(U_13410,U_13412),tc_HOL_Obool)),U_13415),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13411,U_13412),tc_HOL_Obool),tc_fun(tc_prod(U_13410,U_13412),tc_HOL_Obool),U_13414),hAPP(c_Relation_Orel__comp(U_13410,U_13411,U_13412),U_13413)),U_13416)),
inference(variable_rename,[status(thm)],[f_3469_1]) ).
cnf(f_3469_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_13410,U_13411,U_13412),U_13413),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13414,tc_fun(tc_prod(U_13411,U_13412),tc_HOL_Obool)),U_13415),U_13416)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13414,tc_fun(tc_prod(U_13410,U_13412),tc_HOL_Obool)),U_13415),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13411,U_13412),tc_HOL_Obool),tc_fun(tc_prod(U_13410,U_13412),tc_HOL_Obool),U_13414),hAPP(c_Relation_Orel__comp(U_13410,U_13411,U_13412),U_13413)),U_13416)),
inference(clausify,[status(thm)],[f_3469_2]) ).
fof(f_3470_1,plain,
! [V_s_2,V_r_2,V_I_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_e),c_Relation_Orel__comp(T_b,T_d,T_c)),V_r_2)),V_s_2)),
inference(fof_nnf,[status(thm)],[fact_rel__comp__UNION__distrib2]) ).
fof(f_3470_2,plain,
! [U_13423,U_13422,U_13421,U_13420,U_13419,U_13418,U_13417] : hAPP(hAPP(c_Relation_Orel__comp(U_13417,U_13418,U_13419),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13420,tc_fun(tc_prod(U_13417,U_13418),tc_HOL_Obool)),U_13421),U_13422)),U_13423) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13420,tc_fun(tc_prod(U_13417,U_13419),tc_HOL_Obool)),U_13421),hAPP(hAPP(c_COMBC(U_13420,tc_fun(tc_prod(U_13418,U_13419),tc_HOL_Obool),tc_fun(tc_prod(U_13417,U_13419),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13417,U_13418),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_13418,U_13419),tc_HOL_Obool),tc_fun(tc_prod(U_13417,U_13419),tc_HOL_Obool)),U_13420),c_Relation_Orel__comp(U_13417,U_13418,U_13419)),U_13422)),U_13423)),
inference(variable_rename,[status(thm)],[f_3470_1]) ).
cnf(f_3470_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_13417,U_13418,U_13419),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13420,tc_fun(tc_prod(U_13417,U_13418),tc_HOL_Obool)),U_13421),U_13422)),U_13423) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13420,tc_fun(tc_prod(U_13417,U_13419),tc_HOL_Obool)),U_13421),hAPP(hAPP(c_COMBC(U_13420,tc_fun(tc_prod(U_13418,U_13419),tc_HOL_Obool),tc_fun(tc_prod(U_13417,U_13419),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13417,U_13418),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_13418,U_13419),tc_HOL_Obool),tc_fun(tc_prod(U_13417,U_13419),tc_HOL_Obool)),U_13420),c_Relation_Orel__comp(U_13417,U_13418,U_13419)),U_13422)),U_13423)),
inference(clausify,[status(thm)],[f_3470_2]) ).
fof(f_3471_1,plain,
! [V_T_2,V_S_2,V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_T_2)),
inference(fof_nnf,[status(thm)],[fact_rel__comp__distrib]) ).
fof(f_3471_2,plain,
! [U_13429,U_13428,U_13427,U_13426,U_13425,U_13424] : hAPP(hAPP(c_Relation_Orel__comp(U_13424,U_13425,U_13426),U_13427),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13425,U_13426),tc_HOL_Obool)),U_13428),U_13429)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13424,U_13426),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13424,U_13425,U_13426),U_13427),U_13428)),hAPP(hAPP(c_Relation_Orel__comp(U_13424,U_13425,U_13426),U_13427),U_13429)),
inference(variable_rename,[status(thm)],[f_3471_1]) ).
cnf(f_3471_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_13424,U_13425,U_13426),U_13427),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13425,U_13426),tc_HOL_Obool)),U_13428),U_13429)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13424,U_13426),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13424,U_13425,U_13426),U_13427),U_13428)),hAPP(hAPP(c_Relation_Orel__comp(U_13424,U_13425,U_13426),U_13427),U_13429)),
inference(clausify,[status(thm)],[f_3471_2]) ).
fof(f_3472_1,plain,
! [V_R_2,V_T_2,V_S_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_S_2),V_T_2)),V_R_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_T_2),V_R_2)),
inference(fof_nnf,[status(thm)],[fact_rel__comp__distrib2]) ).
fof(f_3472_2,plain,
! [U_13435,U_13434,U_13433,U_13432,U_13431,U_13430] : hAPP(hAPP(c_Relation_Orel__comp(U_13430,U_13431,U_13432),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13430,U_13431),tc_HOL_Obool)),U_13433),U_13434)),U_13435) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13430,U_13432),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13430,U_13431,U_13432),U_13433),U_13435)),hAPP(hAPP(c_Relation_Orel__comp(U_13430,U_13431,U_13432),U_13434),U_13435)),
inference(variable_rename,[status(thm)],[f_3472_1]) ).
cnf(f_3472_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_13430,U_13431,U_13432),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13430,U_13431),tc_HOL_Obool)),U_13433),U_13434)),U_13435) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13430,U_13432),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13430,U_13431,U_13432),U_13433),U_13435)),hAPP(hAPP(c_Relation_Orel__comp(U_13430,U_13431,U_13432),U_13434),U_13435)),
inference(clausify,[status(thm)],[f_3472_2]) ).
fof(f_3473_1,plain,
! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_rel__comp__empty2]) ).
fof(f_3473_2,plain,
! [U_13439,U_13438,U_13437,U_13436] : hAPP(hAPP(c_Relation_Orel__comp(U_13436,U_13437,U_13438),U_13439),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13437,U_13438),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13436,U_13438),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3473_1]) ).
cnf(f_3473_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_13436,U_13437,U_13438),U_13439),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13437,U_13438),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13436,U_13438),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3473_2]) ).
fof(f_3474_1,plain,
! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_rel__comp__empty1]) ).
fof(f_3474_2,plain,
! [U_13443,U_13442,U_13441,U_13440] : hAPP(hAPP(c_Relation_Orel__comp(U_13440,U_13441,U_13442),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13440,U_13441),tc_HOL_Obool))),U_13443) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13440,U_13442),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3474_1]) ).
cnf(f_3474_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_13440,U_13441,U_13442),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13440,U_13441),tc_HOL_Obool))),U_13443) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13440,U_13442),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3474_2]) ).
fof(f_3475_1,plain,
! [V_T_2,V_S_2,V_R_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_d),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_c),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_e,T_d,T_c),V_S_2),V_T_2)),
inference(fof_nnf,[status(thm)],[fact_O__assoc]) ).
fof(f_3475_2,plain,
! [U_13450,U_13449,U_13448,U_13447,U_13446,U_13445,U_13444] : hAPP(hAPP(c_Relation_Orel__comp(U_13444,U_13445,U_13446),hAPP(hAPP(c_Relation_Orel__comp(U_13444,U_13447,U_13445),U_13448),U_13449)),U_13450) = hAPP(hAPP(c_Relation_Orel__comp(U_13444,U_13447,U_13446),U_13448),hAPP(hAPP(c_Relation_Orel__comp(U_13447,U_13445,U_13446),U_13449),U_13450)),
inference(variable_rename,[status(thm)],[f_3475_1]) ).
cnf(f_3475_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_13444,U_13445,U_13446),hAPP(hAPP(c_Relation_Orel__comp(U_13444,U_13447,U_13445),U_13448),U_13449)),U_13450) = hAPP(hAPP(c_Relation_Orel__comp(U_13444,U_13447,U_13446),U_13448),hAPP(hAPP(c_Relation_Orel__comp(U_13447,U_13445,U_13446),U_13449),U_13450)),
inference(clausify,[status(thm)],[f_3475_2]) ).
fof(f_3476_1,plain,
! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_H_2),V_s_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_rel__comp__mono]) ).
fof(f_3476_2,plain,
! [U_13457,U_13456,U_13455,U_13454,U_13453,U_13452,U_13451] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13451,U_13455),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13451,U_13452,U_13455),U_13453),U_13456)),hAPP(hAPP(c_Relation_Orel__comp(U_13451,U_13452,U_13455),U_13454),U_13457)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13452,U_13455),tc_HOL_Obool)),U_13456),U_13457))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13451,U_13452),tc_HOL_Obool)),U_13453),U_13454)) ),
inference(variable_rename,[status(thm)],[f_3476_1]) ).
cnf(f_3476_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13451,U_13455),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13451,U_13452,U_13455),U_13453),U_13456)),hAPP(hAPP(c_Relation_Orel__comp(U_13451,U_13452,U_13455),U_13454),U_13457)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13452,U_13455),tc_HOL_Obool)),U_13456),U_13457))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13451,U_13452),tc_HOL_Obool)),U_13453),U_13454)) ),
inference(clausify,[status(thm)],[f_3476_2]) ).
fof(f_3477_1,plain,
! [V_C_2,V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_union__comp__emptyR]) ).
fof(f_3477_2,plain,
! [U_13461,U_13460,U_13459,U_13458] :
( hAPP(hAPP(c_Relation_Orel__comp(U_13458,U_13458,U_13458),U_13459),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13458,U_13458),tc_HOL_Obool)),U_13460),U_13461)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13458,U_13458),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(U_13458,U_13458,U_13458),U_13459),U_13461) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13458,U_13458),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(U_13458,U_13458,U_13458),U_13459),U_13460) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13458,U_13458),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_3477_1]) ).
cnf(f_3477_3,plain,
( hAPP(hAPP(c_Relation_Orel__comp(U_13458,U_13458,U_13458),U_13459),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13458,U_13458),tc_HOL_Obool)),U_13460),U_13461)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13458,U_13458),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(U_13458,U_13458,U_13458),U_13459),U_13461) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13458,U_13458),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(U_13458,U_13458,U_13458),U_13459),U_13460) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13458,U_13458),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3477_2]) ).
fof(f_3478_1,plain,
! [V_B_2,V_C_2,V_A_2,T_b] :
( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_B_2),V_C_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_union__comp__emptyL]) ).
fof(f_3478_2,plain,
! [U_13465,U_13464,U_13463,U_13462] :
( hAPP(hAPP(c_Relation_Orel__comp(U_13462,U_13462,U_13462),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13462,U_13462),tc_HOL_Obool)),U_13463),U_13465)),U_13464) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13462,U_13462),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(U_13462,U_13462,U_13462),U_13465),U_13464) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13462,U_13462),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(U_13462,U_13462,U_13462),U_13463),U_13464) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13462,U_13462),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_3478_1]) ).
cnf(f_3478_3,plain,
( hAPP(hAPP(c_Relation_Orel__comp(U_13462,U_13462,U_13462),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13462,U_13462),tc_HOL_Obool)),U_13463),U_13465)),U_13464) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13462,U_13462),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(U_13462,U_13462,U_13462),U_13465),U_13464) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13462,U_13462),tc_HOL_Obool))
| hAPP(hAPP(c_Relation_Orel__comp(U_13462,U_13462,U_13462),U_13463),U_13464) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13462,U_13462),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3478_2]) ).
fof(f_3479_1,plain,
! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_C_2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_B_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ),
inference(fof_nnf,[status(thm)],[fact_rel__comp__subset__Sigma]) ).
fof(f_3479_2,plain,
! [U_13473,U_13472,U_13471,U_13470,U_13469,U_13468,U_13467,U_13466] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13466,U_13471),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13466,U_13467,U_13471),U_13468),U_13472)),hAPP(hAPP(c_Product__Type_OSigma(U_13466,U_13471),U_13469),hAPP(c_COMBK(tc_fun(U_13471,tc_HOL_Obool),U_13466),U_13473))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13467,U_13471),tc_HOL_Obool)),U_13472),hAPP(hAPP(c_Product__Type_OSigma(U_13467,U_13471),U_13470),hAPP(c_COMBK(tc_fun(U_13471,tc_HOL_Obool),U_13467),U_13473))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13466,U_13467),tc_HOL_Obool)),U_13468),hAPP(hAPP(c_Product__Type_OSigma(U_13466,U_13467),U_13469),hAPP(c_COMBK(tc_fun(U_13467,tc_HOL_Obool),U_13466),U_13470)))) ),
inference(variable_rename,[status(thm)],[f_3479_1]) ).
cnf(f_3479_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13466,U_13471),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13466,U_13467,U_13471),U_13468),U_13472)),hAPP(hAPP(c_Product__Type_OSigma(U_13466,U_13471),U_13469),hAPP(c_COMBK(tc_fun(U_13471,tc_HOL_Obool),U_13466),U_13473))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13467,U_13471),tc_HOL_Obool)),U_13472),hAPP(hAPP(c_Product__Type_OSigma(U_13467,U_13471),U_13470),hAPP(c_COMBK(tc_fun(U_13471,tc_HOL_Obool),U_13467),U_13473))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13466,U_13467),tc_HOL_Obool)),U_13468),hAPP(hAPP(c_Product__Type_OSigma(U_13466,U_13467),U_13469),hAPP(c_COMBK(tc_fun(U_13467,tc_HOL_Obool),U_13466),U_13470)))) ),
inference(clausify,[status(thm)],[f_3479_2]) ).
fof(f_3480_1,plain,
! [V_S_2,V_R_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_b,V_R_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) ),
inference(fof_nnf,[status(thm)],[fact_max__ext__compat]) ).
fof(f_3480_2,plain,
! [U_13476,U_13475,U_13474] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_13474,tc_HOL_Obool),tc_fun(U_13474,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_13474,tc_HOL_Obool),tc_fun(U_13474,tc_HOL_Obool),tc_fun(U_13474,tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_13474,U_13475)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_13474,tc_HOL_Obool),tc_fun(U_13474,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_13474,U_13476)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_13474,tc_HOL_Obool),tc_fun(U_13474,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13474,tc_HOL_Obool),tc_fun(U_13474,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13474,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_13474,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_13474,tc_HOL_Obool),tc_fun(U_13474,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(U_13474,U_13475)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13474,U_13474),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13474,U_13474,U_13474),U_13475),U_13476)),U_13475)) ),
inference(variable_rename,[status(thm)],[f_3480_1]) ).
cnf(f_3480_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_13474,tc_HOL_Obool),tc_fun(U_13474,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_13474,tc_HOL_Obool),tc_fun(U_13474,tc_HOL_Obool),tc_fun(U_13474,tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_13474,U_13475)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_13474,tc_HOL_Obool),tc_fun(U_13474,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_13474,U_13476)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_13474,tc_HOL_Obool),tc_fun(U_13474,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13474,tc_HOL_Obool),tc_fun(U_13474,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13474,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_13474,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_13474,tc_HOL_Obool),tc_fun(U_13474,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(U_13474,U_13475)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13474,U_13474),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13474,U_13474,U_13474),U_13475),U_13476)),U_13475)) ),
inference(clausify,[status(thm)],[f_3480_2]) ).
fof(f_3481_1,plain,
! [V_S_2,V_R_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_b,V_R_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2)) ),
inference(fof_nnf,[status(thm)],[fact_min__ext__compat]) ).
fof(f_3481_2,plain,
! [U_13479,U_13478,U_13477] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_13477,tc_HOL_Obool),tc_fun(U_13477,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_13477,tc_HOL_Obool),tc_fun(U_13477,tc_HOL_Obool),tc_fun(U_13477,tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_13477,U_13478)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_13477,tc_HOL_Obool),tc_fun(U_13477,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_13477,U_13479)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_13477,tc_HOL_Obool),tc_fun(U_13477,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13477,tc_HOL_Obool),tc_fun(U_13477,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13477,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_13477,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_13477,tc_HOL_Obool),tc_fun(U_13477,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(U_13477,U_13478)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13477,U_13477),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13477,U_13477,U_13477),U_13478),U_13479)),U_13478)) ),
inference(variable_rename,[status(thm)],[f_3481_1]) ).
cnf(f_3481_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_13477,tc_HOL_Obool),tc_fun(U_13477,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_13477,tc_HOL_Obool),tc_fun(U_13477,tc_HOL_Obool),tc_fun(U_13477,tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_13477,U_13478)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_13477,tc_HOL_Obool),tc_fun(U_13477,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_13477,U_13479)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_13477,tc_HOL_Obool),tc_fun(U_13477,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_13477,tc_HOL_Obool),tc_fun(U_13477,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13477,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_13477,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_13477,tc_HOL_Obool),tc_fun(U_13477,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(U_13477,U_13478)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13477,U_13477),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13477,U_13477,U_13477),U_13478),U_13479)),U_13478)) ),
inference(clausify,[status(thm)],[f_3481_2]) ).
fof(f_3482_1,plain,
! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2)),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2)),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_pred__comp__rel__comp__eq]) ).
fof(f_3482_2,plain,
! [U_13486,U_13485,U_13484,U_13483,U_13482,U_13481,U_13480] :
( ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13480,U_13481,U_13482,hAPP(hAPP(c_COMBC(U_13480,tc_fun(tc_prod(U_13480,U_13481),tc_HOL_Obool),tc_fun(U_13481,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13481,tc_fun(tc_fun(tc_prod(U_13480,U_13481),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13480,U_13481),tc_HOL_Obool),tc_fun(U_13481,tc_HOL_Obool)),U_13480),c_COMBC(U_13481,tc_fun(tc_prod(U_13480,U_13481),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13481,tc_prod(U_13480,U_13481)),tc_fun(U_13481,tc_fun(tc_fun(tc_prod(U_13480,U_13481),tc_HOL_Obool),tc_HOL_Obool)),U_13480),hAPP(c_COMBB(tc_prod(U_13480,U_13481),tc_fun(tc_fun(tc_prod(U_13480,U_13481),tc_HOL_Obool),tc_HOL_Obool),U_13481),c_member(tc_prod(U_13480,U_13481)))),c_Product__Type_OPair(U_13480,U_13481)))),U_13483),hAPP(hAPP(c_COMBC(U_13481,tc_fun(tc_prod(U_13481,U_13482),tc_HOL_Obool),tc_fun(U_13482,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13482,tc_fun(tc_fun(tc_prod(U_13481,U_13482),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13481,U_13482),tc_HOL_Obool),tc_fun(U_13482,tc_HOL_Obool)),U_13481),c_COMBC(U_13482,tc_fun(tc_prod(U_13481,U_13482),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13482,tc_prod(U_13481,U_13482)),tc_fun(U_13482,tc_fun(tc_fun(tc_prod(U_13481,U_13482),tc_HOL_Obool),tc_HOL_Obool)),U_13481),hAPP(c_COMBB(tc_prod(U_13481,U_13482),tc_fun(tc_fun(tc_prod(U_13481,U_13482),tc_HOL_Obool),tc_HOL_Obool),U_13482),c_member(tc_prod(U_13481,U_13482)))),c_Product__Type_OPair(U_13481,U_13482)))),U_13484)),U_13485),U_13486))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13480,U_13482)),hAPP(hAPP(c_Product__Type_OPair(U_13480,U_13482),U_13485),U_13486)),hAPP(hAPP(c_Relation_Orel__comp(U_13480,U_13481,U_13482),U_13483),U_13484))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13480,U_13482)),hAPP(hAPP(c_Product__Type_OPair(U_13480,U_13482),U_13485),U_13486)),hAPP(hAPP(c_Relation_Orel__comp(U_13480,U_13481,U_13482),U_13483),U_13484)))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13480,U_13481,U_13482,hAPP(hAPP(c_COMBC(U_13480,tc_fun(tc_prod(U_13480,U_13481),tc_HOL_Obool),tc_fun(U_13481,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13481,tc_fun(tc_fun(tc_prod(U_13480,U_13481),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13480,U_13481),tc_HOL_Obool),tc_fun(U_13481,tc_HOL_Obool)),U_13480),c_COMBC(U_13481,tc_fun(tc_prod(U_13480,U_13481),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13481,tc_prod(U_13480,U_13481)),tc_fun(U_13481,tc_fun(tc_fun(tc_prod(U_13480,U_13481),tc_HOL_Obool),tc_HOL_Obool)),U_13480),hAPP(c_COMBB(tc_prod(U_13480,U_13481),tc_fun(tc_fun(tc_prod(U_13480,U_13481),tc_HOL_Obool),tc_HOL_Obool),U_13481),c_member(tc_prod(U_13480,U_13481)))),c_Product__Type_OPair(U_13480,U_13481)))),U_13483),hAPP(hAPP(c_COMBC(U_13481,tc_fun(tc_prod(U_13481,U_13482),tc_HOL_Obool),tc_fun(U_13482,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13482,tc_fun(tc_fun(tc_prod(U_13481,U_13482),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13481,U_13482),tc_HOL_Obool),tc_fun(U_13482,tc_HOL_Obool)),U_13481),c_COMBC(U_13482,tc_fun(tc_prod(U_13481,U_13482),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13482,tc_prod(U_13481,U_13482)),tc_fun(U_13482,tc_fun(tc_fun(tc_prod(U_13481,U_13482),tc_HOL_Obool),tc_HOL_Obool)),U_13481),hAPP(c_COMBB(tc_prod(U_13481,U_13482),tc_fun(tc_fun(tc_prod(U_13481,U_13482),tc_HOL_Obool),tc_HOL_Obool),U_13482),c_member(tc_prod(U_13481,U_13482)))),c_Product__Type_OPair(U_13481,U_13482)))),U_13484)),U_13485),U_13486)) ) ),
inference(variable_rename,[status(thm)],[f_3482_1]) ).
fof(f_3482_3,plain,
( ! [U_13500,U_13498,U_13496,U_13494,U_13492,U_13490,U_13488] :
( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13488,U_13490,U_13492,hAPP(hAPP(c_COMBC(U_13488,tc_fun(tc_prod(U_13488,U_13490),tc_HOL_Obool),tc_fun(U_13490,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13490,tc_fun(tc_fun(tc_prod(U_13488,U_13490),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13488,U_13490),tc_HOL_Obool),tc_fun(U_13490,tc_HOL_Obool)),U_13488),c_COMBC(U_13490,tc_fun(tc_prod(U_13488,U_13490),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13490,tc_prod(U_13488,U_13490)),tc_fun(U_13490,tc_fun(tc_fun(tc_prod(U_13488,U_13490),tc_HOL_Obool),tc_HOL_Obool)),U_13488),hAPP(c_COMBB(tc_prod(U_13488,U_13490),tc_fun(tc_fun(tc_prod(U_13488,U_13490),tc_HOL_Obool),tc_HOL_Obool),U_13490),c_member(tc_prod(U_13488,U_13490)))),c_Product__Type_OPair(U_13488,U_13490)))),U_13494),hAPP(hAPP(c_COMBC(U_13490,tc_fun(tc_prod(U_13490,U_13492),tc_HOL_Obool),tc_fun(U_13492,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13492,tc_fun(tc_fun(tc_prod(U_13490,U_13492),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13490,U_13492),tc_HOL_Obool),tc_fun(U_13492,tc_HOL_Obool)),U_13490),c_COMBC(U_13492,tc_fun(tc_prod(U_13490,U_13492),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13492,tc_prod(U_13490,U_13492)),tc_fun(U_13492,tc_fun(tc_fun(tc_prod(U_13490,U_13492),tc_HOL_Obool),tc_HOL_Obool)),U_13490),hAPP(c_COMBB(tc_prod(U_13490,U_13492),tc_fun(tc_fun(tc_prod(U_13490,U_13492),tc_HOL_Obool),tc_HOL_Obool),U_13492),c_member(tc_prod(U_13490,U_13492)))),c_Product__Type_OPair(U_13490,U_13492)))),U_13496)),U_13498),U_13500))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13488,U_13492)),hAPP(hAPP(c_Product__Type_OPair(U_13488,U_13492),U_13498),U_13500)),hAPP(hAPP(c_Relation_Orel__comp(U_13488,U_13490,U_13492),U_13494),U_13496))) )
& ! [U_13499,U_13497,U_13495,U_13493,U_13491,U_13489,U_13487] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13487,U_13491)),hAPP(hAPP(c_Product__Type_OPair(U_13487,U_13491),U_13497),U_13499)),hAPP(hAPP(c_Relation_Orel__comp(U_13487,U_13489,U_13491),U_13493),U_13495)))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13487,U_13489,U_13491,hAPP(hAPP(c_COMBC(U_13487,tc_fun(tc_prod(U_13487,U_13489),tc_HOL_Obool),tc_fun(U_13489,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13489,tc_fun(tc_fun(tc_prod(U_13487,U_13489),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13487,U_13489),tc_HOL_Obool),tc_fun(U_13489,tc_HOL_Obool)),U_13487),c_COMBC(U_13489,tc_fun(tc_prod(U_13487,U_13489),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13489,tc_prod(U_13487,U_13489)),tc_fun(U_13489,tc_fun(tc_fun(tc_prod(U_13487,U_13489),tc_HOL_Obool),tc_HOL_Obool)),U_13487),hAPP(c_COMBB(tc_prod(U_13487,U_13489),tc_fun(tc_fun(tc_prod(U_13487,U_13489),tc_HOL_Obool),tc_HOL_Obool),U_13489),c_member(tc_prod(U_13487,U_13489)))),c_Product__Type_OPair(U_13487,U_13489)))),U_13493),hAPP(hAPP(c_COMBC(U_13489,tc_fun(tc_prod(U_13489,U_13491),tc_HOL_Obool),tc_fun(U_13491,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13491,tc_fun(tc_fun(tc_prod(U_13489,U_13491),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13489,U_13491),tc_HOL_Obool),tc_fun(U_13491,tc_HOL_Obool)),U_13489),c_COMBC(U_13491,tc_fun(tc_prod(U_13489,U_13491),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13491,tc_prod(U_13489,U_13491)),tc_fun(U_13491,tc_fun(tc_fun(tc_prod(U_13489,U_13491),tc_HOL_Obool),tc_HOL_Obool)),U_13489),hAPP(c_COMBB(tc_prod(U_13489,U_13491),tc_fun(tc_fun(tc_prod(U_13489,U_13491),tc_HOL_Obool),tc_HOL_Obool),U_13491),c_member(tc_prod(U_13489,U_13491)))),c_Product__Type_OPair(U_13489,U_13491)))),U_13495)),U_13497),U_13499)) ) ),
inference(miniscope,[status(thm)],[f_3482_2]) ).
cnf(f_3482_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13487,U_13491)),hAPP(hAPP(c_Product__Type_OPair(U_13487,U_13491),U_13497),U_13499)),hAPP(hAPP(c_Relation_Orel__comp(U_13487,U_13489,U_13491),U_13493),U_13495)))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13487,U_13489,U_13491,hAPP(hAPP(c_COMBC(U_13487,tc_fun(tc_prod(U_13487,U_13489),tc_HOL_Obool),tc_fun(U_13489,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13489,tc_fun(tc_fun(tc_prod(U_13487,U_13489),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13487,U_13489),tc_HOL_Obool),tc_fun(U_13489,tc_HOL_Obool)),U_13487),c_COMBC(U_13489,tc_fun(tc_prod(U_13487,U_13489),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13489,tc_prod(U_13487,U_13489)),tc_fun(U_13489,tc_fun(tc_fun(tc_prod(U_13487,U_13489),tc_HOL_Obool),tc_HOL_Obool)),U_13487),hAPP(c_COMBB(tc_prod(U_13487,U_13489),tc_fun(tc_fun(tc_prod(U_13487,U_13489),tc_HOL_Obool),tc_HOL_Obool),U_13489),c_member(tc_prod(U_13487,U_13489)))),c_Product__Type_OPair(U_13487,U_13489)))),U_13493),hAPP(hAPP(c_COMBC(U_13489,tc_fun(tc_prod(U_13489,U_13491),tc_HOL_Obool),tc_fun(U_13491,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13491,tc_fun(tc_fun(tc_prod(U_13489,U_13491),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13489,U_13491),tc_HOL_Obool),tc_fun(U_13491,tc_HOL_Obool)),U_13489),c_COMBC(U_13491,tc_fun(tc_prod(U_13489,U_13491),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13491,tc_prod(U_13489,U_13491)),tc_fun(U_13491,tc_fun(tc_fun(tc_prod(U_13489,U_13491),tc_HOL_Obool),tc_HOL_Obool)),U_13489),hAPP(c_COMBB(tc_prod(U_13489,U_13491),tc_fun(tc_fun(tc_prod(U_13489,U_13491),tc_HOL_Obool),tc_HOL_Obool),U_13491),c_member(tc_prod(U_13489,U_13491)))),c_Product__Type_OPair(U_13489,U_13491)))),U_13495)),U_13497),U_13499)) ),
inference(clausify,[status(thm)],[f_3482_3]) ).
cnf(f_3482_5,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13488,U_13490,U_13492,hAPP(hAPP(c_COMBC(U_13488,tc_fun(tc_prod(U_13488,U_13490),tc_HOL_Obool),tc_fun(U_13490,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13490,tc_fun(tc_fun(tc_prod(U_13488,U_13490),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13488,U_13490),tc_HOL_Obool),tc_fun(U_13490,tc_HOL_Obool)),U_13488),c_COMBC(U_13490,tc_fun(tc_prod(U_13488,U_13490),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13490,tc_prod(U_13488,U_13490)),tc_fun(U_13490,tc_fun(tc_fun(tc_prod(U_13488,U_13490),tc_HOL_Obool),tc_HOL_Obool)),U_13488),hAPP(c_COMBB(tc_prod(U_13488,U_13490),tc_fun(tc_fun(tc_prod(U_13488,U_13490),tc_HOL_Obool),tc_HOL_Obool),U_13490),c_member(tc_prod(U_13488,U_13490)))),c_Product__Type_OPair(U_13488,U_13490)))),U_13494),hAPP(hAPP(c_COMBC(U_13490,tc_fun(tc_prod(U_13490,U_13492),tc_HOL_Obool),tc_fun(U_13492,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13492,tc_fun(tc_fun(tc_prod(U_13490,U_13492),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13490,U_13492),tc_HOL_Obool),tc_fun(U_13492,tc_HOL_Obool)),U_13490),c_COMBC(U_13492,tc_fun(tc_prod(U_13490,U_13492),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13492,tc_prod(U_13490,U_13492)),tc_fun(U_13492,tc_fun(tc_fun(tc_prod(U_13490,U_13492),tc_HOL_Obool),tc_HOL_Obool)),U_13490),hAPP(c_COMBB(tc_prod(U_13490,U_13492),tc_fun(tc_fun(tc_prod(U_13490,U_13492),tc_HOL_Obool),tc_HOL_Obool),U_13492),c_member(tc_prod(U_13490,U_13492)))),c_Product__Type_OPair(U_13490,U_13492)))),U_13496)),U_13498),U_13500))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13488,U_13492)),hAPP(hAPP(c_Product__Type_OPair(U_13488,U_13492),U_13498),U_13500)),hAPP(hAPP(c_Relation_Orel__comp(U_13488,U_13490,U_13492),U_13494),U_13496))) ),
inference(clausify,[status(thm)],[f_3482_3]) ).
fof(f_3483_1,plain,
! [V_S_2,V_R_2,T_b] :
( c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
| ~ c_Wellfounded_Owf(T_b,V_R_2) ),
inference(fof_nnf,[status(thm)],[fact_reduction__pairI]) ).
fof(f_3483_2,plain,
! [U_13503,U_13502,U_13501] :
( c_FunDef_Oreduction__pair(U_13501,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_13501,U_13501),tc_HOL_Obool),tc_fun(tc_prod(U_13501,U_13501),tc_HOL_Obool)),U_13502),U_13503))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13501,U_13501),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13501,U_13501,U_13501),U_13502),U_13503)),U_13502))
| ~ c_Wellfounded_Owf(U_13501,U_13502) ),
inference(variable_rename,[status(thm)],[f_3483_1]) ).
cnf(f_3483_3,plain,
( c_FunDef_Oreduction__pair(U_13501,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_13501,U_13501),tc_HOL_Obool),tc_fun(tc_prod(U_13501,U_13501),tc_HOL_Obool)),U_13502),U_13503))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13501,U_13501),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13501,U_13501,U_13501),U_13502),U_13503)),U_13502))
| ~ c_Wellfounded_Owf(U_13501,U_13502) ),
inference(clausify,[status(thm)],[f_3483_2]) ).
fof(f_3484_1,plain,
! [V_P_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_P_2))),
inference(fof_nnf,[status(thm)],[fact_Range__Collect__split]) ).
fof(f_3484_2,plain,
! [U_13506,U_13505,U_13504] : hAPP(c_Relation_ORange(U_13504,U_13505),hAPP(c_Set_OCollect(tc_prod(U_13504,U_13505)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13504,U_13505,tc_HOL_Obool),U_13506))) = hAPP(c_Set_OCollect(U_13505),hAPP(hAPP(c_COMBB(tc_fun(U_13504,tc_HOL_Obool),tc_HOL_Obool,U_13505),c_HOL_OEx(U_13504)),hAPP(c_COMBC(U_13504,U_13505,tc_HOL_Obool),U_13506))),
inference(variable_rename,[status(thm)],[f_3484_1]) ).
cnf(f_3484_3,plain,
hAPP(c_Relation_ORange(U_13504,U_13505),hAPP(c_Set_OCollect(tc_prod(U_13504,U_13505)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13504,U_13505,tc_HOL_Obool),U_13506))) = hAPP(c_Set_OCollect(U_13505),hAPP(hAPP(c_COMBB(tc_fun(U_13504,tc_HOL_Obool),tc_HOL_Obool,U_13505),c_HOL_OEx(U_13504)),hAPP(c_COMBC(U_13504,U_13505,tc_HOL_Obool),U_13506))),
inference(clausify,[status(thm)],[f_3484_2]) ).
fof(f_3485_1,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(fof_nnf,[status(thm)],[fact_wf__less__than]) ).
cnf(f_3485_2,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(clausify,[status(thm)],[f_3485_1]) ).
fof(f_3486_1,plain,
! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
| ~ hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_pred__comp_Ointros]) ).
fof(f_3486_2,plain,
! [U_13514,U_13513,U_13512,U_13511,U_13510,U_13509,U_13508,U_13507] :
( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13512,U_13513,U_13514,U_13507,U_13510),U_13508),U_13511))
| ~ hBOOL(hAPP(hAPP(U_13510,U_13509),U_13511))
| ~ hBOOL(hAPP(hAPP(U_13507,U_13508),U_13509)) ),
inference(variable_rename,[status(thm)],[f_3486_1]) ).
cnf(f_3486_3,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13512,U_13513,U_13514,U_13507,U_13510),U_13508),U_13511))
| ~ hBOOL(hAPP(hAPP(U_13510,U_13509),U_13511))
| ~ hBOOL(hAPP(hAPP(U_13507,U_13508),U_13509)) ),
inference(clausify,[status(thm)],[f_3486_2]) ).
fof(f_3487_1,plain,
! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_wf__empty]) ).
fof(f_3487_2,plain,
! [U_13515] : c_Wellfounded_Owf(U_13515,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13515,U_13515),tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_3487_1]) ).
cnf(f_3487_3,plain,
c_Wellfounded_Owf(U_13515,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13515,U_13515),tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_3487_2]) ).
fof(f_3488_1,plain,
! [V_f_2,T_c,V_r_2,T_b] :
( c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2))
| ~ c_Wellfounded_Owf(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__inv__image]) ).
fof(f_3488_2,plain,
! [U_13519,U_13518,U_13517,U_13516] :
( c_Wellfounded_Owf(U_13518,hAPP(hAPP(c_Relation_Oinv__image(U_13516,U_13518),U_13517),U_13519))
| ~ c_Wellfounded_Owf(U_13516,U_13517) ),
inference(variable_rename,[status(thm)],[f_3488_1]) ).
cnf(f_3488_3,plain,
( c_Wellfounded_Owf(U_13518,hAPP(hAPP(c_Relation_Oinv__image(U_13516,U_13518),U_13517),U_13519))
| ~ c_Wellfounded_Owf(U_13516,U_13517) ),
inference(clausify,[status(thm)],[f_3488_2]) ).
fof(f_3489_1,plain,
! [V_rb_2,T_c,V_ra_2,T_b] :
( c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2))
| ~ c_Wellfounded_Owf(T_c,V_rb_2)
| ~ c_Wellfounded_Owf(T_b,V_ra_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__lex__prod]) ).
fof(f_3489_2,plain,
! [U_13523,U_13522,U_13521,U_13520] :
( c_Wellfounded_Owf(tc_prod(U_13520,U_13522),c_Wellfounded_Olex__prod(U_13520,U_13522,U_13521,U_13523))
| ~ c_Wellfounded_Owf(U_13522,U_13523)
| ~ c_Wellfounded_Owf(U_13520,U_13521) ),
inference(variable_rename,[status(thm)],[f_3489_1]) ).
cnf(f_3489_3,plain,
( c_Wellfounded_Owf(tc_prod(U_13520,U_13522),c_Wellfounded_Olex__prod(U_13520,U_13522,U_13521,U_13523))
| ~ c_Wellfounded_Owf(U_13522,U_13523)
| ~ c_Wellfounded_Owf(U_13520,U_13521) ),
inference(clausify,[status(thm)],[f_3489_2]) ).
fof(f_3490_1,plain,
! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)),
inference(fof_nnf,[status(thm)],[fact_wf__measure]) ).
fof(f_3490_2,plain,
! [U_13525,U_13524] : c_Wellfounded_Owf(U_13524,hAPP(c_Wellfounded_Omeasure(U_13524),U_13525)),
inference(variable_rename,[status(thm)],[f_3490_1]) ).
cnf(f_3490_3,plain,
c_Wellfounded_Owf(U_13524,hAPP(c_Wellfounded_Omeasure(U_13524),U_13525)),
inference(clausify,[status(thm)],[f_3490_2]) ).
fof(f_3491_1,plain,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_RangeI]) ).
fof(f_3491_2,plain,
! [U_13530,U_13529,U_13528,U_13527,U_13526] :
( hBOOL(hAPP(hAPP(c_member(U_13527),U_13529),hAPP(c_Relation_ORange(U_13526,U_13527),U_13530)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13526,U_13527)),hAPP(hAPP(c_Product__Type_OPair(U_13526,U_13527),U_13528),U_13529)),U_13530)) ),
inference(variable_rename,[status(thm)],[f_3491_1]) ).
cnf(f_3491_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_13527),U_13529),hAPP(c_Relation_ORange(U_13526,U_13527),U_13530)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13526,U_13527)),hAPP(hAPP(c_Product__Type_OPair(U_13526,U_13527),U_13528),U_13529)),U_13530)) ),
inference(clausify,[status(thm)],[f_3491_2]) ).
fof(f_3492_1,plain,
! [V_R_2,T_b] :
( ( c_Wellfounded_Owf(T_b,V_R_2)
| ~ c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) )
& ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2))
| ~ c_Wellfounded_Owf(T_b,V_R_2) ) ),
inference(fof_nnf,[status(thm)],[fact_wf__comp__self]) ).
fof(f_3492_2,plain,
! [U_13532,U_13531] :
( ( c_Wellfounded_Owf(U_13531,U_13532)
| ~ c_Wellfounded_Owf(U_13531,hAPP(hAPP(c_Relation_Orel__comp(U_13531,U_13531,U_13531),U_13532),U_13532)) )
& ( c_Wellfounded_Owf(U_13531,hAPP(hAPP(c_Relation_Orel__comp(U_13531,U_13531,U_13531),U_13532),U_13532))
| ~ c_Wellfounded_Owf(U_13531,U_13532) ) ),
inference(variable_rename,[status(thm)],[f_3492_1]) ).
fof(f_3492_3,plain,
( ! [U_13536,U_13534] :
( c_Wellfounded_Owf(U_13534,U_13536)
| ~ c_Wellfounded_Owf(U_13534,hAPP(hAPP(c_Relation_Orel__comp(U_13534,U_13534,U_13534),U_13536),U_13536)) )
& ! [U_13535,U_13533] :
( c_Wellfounded_Owf(U_13533,hAPP(hAPP(c_Relation_Orel__comp(U_13533,U_13533,U_13533),U_13535),U_13535))
| ~ c_Wellfounded_Owf(U_13533,U_13535) ) ),
inference(miniscope,[status(thm)],[f_3492_2]) ).
cnf(f_3492_4,plain,
( c_Wellfounded_Owf(U_13533,hAPP(hAPP(c_Relation_Orel__comp(U_13533,U_13533,U_13533),U_13535),U_13535))
| ~ c_Wellfounded_Owf(U_13533,U_13535) ),
inference(clausify,[status(thm)],[f_3492_3]) ).
cnf(f_3492_5,plain,
( c_Wellfounded_Owf(U_13534,U_13536)
| ~ c_Wellfounded_Owf(U_13534,hAPP(hAPP(c_Relation_Orel__comp(U_13534,U_13534,U_13534),U_13536),U_13536)) ),
inference(clausify,[status(thm)],[f_3492_3]) ).
fof(f_3493_1,plain,
! [V_A_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Range__Id__on]) ).
fof(f_3493_2,plain,
! [U_13538,U_13537] : hAPP(c_Relation_ORange(U_13537,U_13537),c_Relation_OId__on(U_13537,U_13538)) = U_13538,
inference(variable_rename,[status(thm)],[f_3493_1]) ).
cnf(f_3493_3,plain,
hAPP(c_Relation_ORange(U_13537,U_13537),c_Relation_OId__on(U_13537,U_13538)) = U_13538,
inference(clausify,[status(thm)],[f_3493_2]) ).
fof(f_3494_1,plain,
! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)),
inference(fof_nnf,[status(thm)],[fact_wf__finite__psubset]) ).
fof(f_3494_2,plain,
! [U_13539] : c_Wellfounded_Owf(tc_fun(U_13539,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_13539)),
inference(variable_rename,[status(thm)],[f_3494_1]) ).
cnf(f_3494_3,plain,
c_Wellfounded_Owf(tc_fun(U_13539,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_13539)),
inference(clausify,[status(thm)],[f_3494_2]) ).
fof(f_3495_1,plain,
! [V_f_2,V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))
| ~ c_Wellfounded_Owf(T_b,V_R_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__mlex]) ).
fof(f_3495_2,plain,
! [U_13542,U_13541,U_13540] :
( c_Wellfounded_Owf(U_13540,c_Wellfounded_Omlex__prod(U_13540,U_13542,U_13541))
| ~ c_Wellfounded_Owf(U_13540,U_13541) ),
inference(variable_rename,[status(thm)],[f_3495_1]) ).
cnf(f_3495_3,plain,
( c_Wellfounded_Owf(U_13540,c_Wellfounded_Omlex__prod(U_13540,U_13542,U_13541))
| ~ c_Wellfounded_Owf(U_13540,U_13541) ),
inference(clausify,[status(thm)],[f_3495_2]) ).
fof(f_3496_1,plain,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2))
| ~ c_Wellfounded_Owf(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_min__ext__wf]) ).
fof(f_3496_2,plain,
! [U_13544,U_13543] :
( c_Wellfounded_Owf(tc_fun(U_13543,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_13543,U_13544))
| ~ c_Wellfounded_Owf(U_13543,U_13544) ),
inference(variable_rename,[status(thm)],[f_3496_1]) ).
cnf(f_3496_3,plain,
( c_Wellfounded_Owf(tc_fun(U_13543,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_13543,U_13544))
| ~ c_Wellfounded_Owf(U_13543,U_13544) ),
inference(clausify,[status(thm)],[f_3496_2]) ).
fof(f_3497_1,plain,
! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a1_2),V_a3_2))
| ! [B_b] :
( ~ hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2))
| ~ hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) ) )
& ( ? [B_b] :
( hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2))
& hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) )
| ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a1_2),V_a3_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_pred__comp_Oequations]) ).
fof(f_3497_2,plain,
! [U_13553,U_13552,U_13551,U_13550,U_13549,U_13548,U_13547] :
( ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13547,U_13548,U_13549,U_13550,U_13551),U_13552),U_13553))
| ! [U_13546] :
( ~ hBOOL(hAPP(hAPP(U_13551,U_13546),U_13553))
| ~ hBOOL(hAPP(hAPP(U_13550,U_13552),U_13546)) ) )
& ( ? [U_13545] :
( hBOOL(hAPP(hAPP(U_13551,U_13545),U_13553))
& hBOOL(hAPP(hAPP(U_13550,U_13552),U_13545)) )
| ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13547,U_13548,U_13549,U_13550,U_13551),U_13552),U_13553)) ) ),
inference(variable_rename,[status(thm)],[f_3497_1]) ).
fof(f_3497_3,plain,
( ! [U_13567,U_13565,U_13563,U_13561] :
( ! [U_13559,U_13557,U_13555] : hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13555,U_13557,U_13559,U_13561,U_13563),U_13565),U_13567))
| ! [U_13546] :
( ~ hBOOL(hAPP(hAPP(U_13563,U_13546),U_13567))
| ~ hBOOL(hAPP(hAPP(U_13561,U_13565),U_13546)) ) )
& ! [U_13566,U_13564,U_13562,U_13560] :
( ! [U_13558,U_13556,U_13554] : ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13554,U_13556,U_13558,U_13560,U_13562),U_13564),U_13566))
| ? [U_13545] :
( hBOOL(hAPP(hAPP(U_13562,U_13545),U_13566))
& hBOOL(hAPP(hAPP(U_13560,U_13564),U_13545)) ) ) ),
inference(miniscope,[status(thm)],[f_3497_2]) ).
fof(f_3497_4,plain,
( ! [U_13567,U_13565,U_13563,U_13561] :
( ! [U_13559,U_13557,U_13555] : hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13555,U_13557,U_13559,U_13561,U_13563),U_13565),U_13567))
| ! [U_13546] :
( ~ hBOOL(hAPP(hAPP(U_13563,U_13546),U_13567))
| ~ hBOOL(hAPP(hAPP(U_13561,U_13565),U_13546)) ) )
& ! [U_13566,U_13564,U_13562,U_13560] :
( ! [U_13558,U_13556,U_13554] : ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13554,U_13556,U_13558,U_13560,U_13562),U_13564),U_13566))
| ( hBOOL(hAPP(hAPP(U_13562,sK321(U_13566,U_13564,U_13562,U_13560)),U_13566))
& hBOOL(hAPP(hAPP(U_13560,U_13564),sK321(U_13566,U_13564,U_13562,U_13560))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK321]),skolemize(U_13545,sK321(U_13566,U_13564,U_13562,U_13560))],[f_3497_3]) ).
cnf(f_3497_5,plain,
( hBOOL(hAPP(hAPP(U_13560,U_13564),sK321(U_13566,U_13564,U_13562,U_13560)))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13554,U_13556,U_13558,U_13560,U_13562),U_13564),U_13566)) ),
inference(clausify,[status(thm)],[f_3497_4]) ).
cnf(f_3497_6,plain,
( hBOOL(hAPP(hAPP(U_13562,sK321(U_13566,U_13564,U_13562,U_13560)),U_13566))
| ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13554,U_13556,U_13558,U_13560,U_13562),U_13564),U_13566)) ),
inference(clausify,[status(thm)],[f_3497_4]) ).
cnf(f_3497_7,plain,
( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_13555,U_13557,U_13559,U_13561,U_13563),U_13565),U_13567))
| ~ hBOOL(hAPP(hAPP(U_13563,U_13546),U_13567))
| ~ hBOOL(hAPP(hAPP(U_13561,U_13565),U_13546)) ),
inference(clausify,[status(thm)],[f_3497_4]) ).
fof(f_3498_1,plain,
! [V_p_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_p_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_p_2),V_r_2))
| ~ c_Wellfounded_Owf(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__subset]) ).
fof(f_3498_2,plain,
! [U_13570,U_13569,U_13568] :
( c_Wellfounded_Owf(U_13568,U_13570)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13568,U_13568),tc_HOL_Obool)),U_13570),U_13569))
| ~ c_Wellfounded_Owf(U_13568,U_13569) ),
inference(variable_rename,[status(thm)],[f_3498_1]) ).
cnf(f_3498_3,plain,
( c_Wellfounded_Owf(U_13568,U_13570)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13568,U_13568),tc_HOL_Obool)),U_13570),U_13569))
| ~ c_Wellfounded_Owf(U_13568,U_13569) ),
inference(clausify,[status(thm)],[f_3498_2]) ).
fof(f_3499_1,plain,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(fof_nnf,[status(thm)],[fact_wf__pair__less]) ).
cnf(f_3499_2,plain,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(clausify,[status(thm)],[f_3499_1]) ).
fof(f_3500_1,plain,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2))
| ~ c_Wellfounded_Owf(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_max__ext__wf]) ).
fof(f_3500_2,plain,
! [U_13572,U_13571] :
( c_Wellfounded_Owf(tc_fun(U_13571,tc_HOL_Obool),c_Wellfounded_Omax__ext(U_13571,U_13572))
| ~ c_Wellfounded_Owf(U_13571,U_13572) ),
inference(variable_rename,[status(thm)],[f_3500_1]) ).
cnf(f_3500_3,plain,
( c_Wellfounded_Owf(tc_fun(U_13571,tc_HOL_Obool),c_Wellfounded_Omax__ext(U_13571,U_13572))
| ~ c_Wellfounded_Owf(U_13571,U_13572) ),
inference(clausify,[status(thm)],[f_3500_2]) ).
fof(f_3501_1,plain,
! [V_r_H_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2))
| ~ c_Wellfounded_Owf(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__Int1]) ).
fof(f_3501_2,plain,
! [U_13575,U_13574,U_13573] :
( c_Wellfounded_Owf(U_13573,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13573,U_13573),tc_HOL_Obool)),U_13574),U_13575))
| ~ c_Wellfounded_Owf(U_13573,U_13574) ),
inference(variable_rename,[status(thm)],[f_3501_1]) ).
cnf(f_3501_3,plain,
( c_Wellfounded_Owf(U_13573,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13573,U_13573),tc_HOL_Obool)),U_13574),U_13575))
| ~ c_Wellfounded_Owf(U_13573,U_13574) ),
inference(clausify,[status(thm)],[f_3501_2]) ).
fof(f_3502_1,plain,
! [V_r_H_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2))
| ~ c_Wellfounded_Owf(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__Int2]) ).
fof(f_3502_2,plain,
! [U_13578,U_13577,U_13576] :
( c_Wellfounded_Owf(U_13576,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13576,U_13576),tc_HOL_Obool)),U_13578),U_13577))
| ~ c_Wellfounded_Owf(U_13576,U_13577) ),
inference(variable_rename,[status(thm)],[f_3502_1]) ).
cnf(f_3502_3,plain,
( c_Wellfounded_Owf(U_13576,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13576,U_13576),tc_HOL_Obool)),U_13578),U_13577))
| ~ c_Wellfounded_Owf(U_13576,U_13577) ),
inference(clausify,[status(thm)],[f_3502_2]) ).
fof(f_3503_1,plain,
! [V_a_2,V_r_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2))
| ~ c_Wellfounded_Owf(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__not__refl]) ).
fof(f_3503_2,plain,
! [U_13581,U_13580,U_13579] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13579,U_13579)),hAPP(hAPP(c_Product__Type_OPair(U_13579,U_13579),U_13581),U_13581)),U_13580))
| ~ c_Wellfounded_Owf(U_13579,U_13580) ),
inference(variable_rename,[status(thm)],[f_3503_1]) ).
cnf(f_3503_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13579,U_13579)),hAPP(hAPP(c_Product__Type_OPair(U_13579,U_13579),U_13581),U_13581)),U_13580))
| ~ c_Wellfounded_Owf(U_13579,U_13580) ),
inference(clausify,[status(thm)],[f_3503_2]) ).
fof(f_3504_1,plain,
! [V_x_2,V_a_2,V_r_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
| ~ c_Wellfounded_Owf(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__not__sym]) ).
fof(f_3504_2,plain,
! [U_13585,U_13584,U_13583,U_13582] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13582,U_13582)),hAPP(hAPP(c_Product__Type_OPair(U_13582,U_13582),U_13585),U_13584)),U_13583))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13582,U_13582)),hAPP(hAPP(c_Product__Type_OPair(U_13582,U_13582),U_13584),U_13585)),U_13583))
| ~ c_Wellfounded_Owf(U_13582,U_13583) ),
inference(variable_rename,[status(thm)],[f_3504_1]) ).
cnf(f_3504_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13582,U_13582)),hAPP(hAPP(c_Product__Type_OPair(U_13582,U_13582),U_13585),U_13584)),U_13583))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13582,U_13582)),hAPP(hAPP(c_Product__Type_OPair(U_13582,U_13582),U_13584),U_13585)),U_13583))
| ~ c_Wellfounded_Owf(U_13582,U_13583) ),
inference(clausify,[status(thm)],[f_3504_2]) ).
fof(f_3505_1,plain,
! [V_x_2,V_a_2,V_r_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
| ~ c_Wellfounded_Owf(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__asym]) ).
fof(f_3505_2,plain,
! [U_13589,U_13588,U_13587,U_13586] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13586,U_13586)),hAPP(hAPP(c_Product__Type_OPair(U_13586,U_13586),U_13589),U_13588)),U_13587))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13586,U_13586)),hAPP(hAPP(c_Product__Type_OPair(U_13586,U_13586),U_13588),U_13589)),U_13587))
| ~ c_Wellfounded_Owf(U_13586,U_13587) ),
inference(variable_rename,[status(thm)],[f_3505_1]) ).
cnf(f_3505_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13586,U_13586)),hAPP(hAPP(c_Product__Type_OPair(U_13586,U_13586),U_13589),U_13588)),U_13587))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13586,U_13586)),hAPP(hAPP(c_Product__Type_OPair(U_13586,U_13586),U_13588),U_13589)),U_13587))
| ~ c_Wellfounded_Owf(U_13586,U_13587) ),
inference(clausify,[status(thm)],[f_3505_2]) ).
fof(f_3506_1,plain,
! [V_a_2,V_r_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2))
| ~ c_Wellfounded_Owf(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__irrefl]) ).
fof(f_3506_2,plain,
! [U_13592,U_13591,U_13590] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13590,U_13590)),hAPP(hAPP(c_Product__Type_OPair(U_13590,U_13590),U_13592),U_13592)),U_13591))
| ~ c_Wellfounded_Owf(U_13590,U_13591) ),
inference(variable_rename,[status(thm)],[f_3506_1]) ).
cnf(f_3506_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13590,U_13590)),hAPP(hAPP(c_Product__Type_OPair(U_13590,U_13590),U_13592),U_13592)),U_13591))
| ~ c_Wellfounded_Owf(U_13590,U_13591) ),
inference(clausify,[status(thm)],[f_3506_2]) ).
fof(f_3507_1,plain,
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)))),
inference(fof_nnf,[status(thm)],[fact_wf__less]) ).
cnf(f_3507_2,plain,
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)))),
inference(clausify,[status(thm)],[f_3507_1]) ).
fof(f_3508_1,plain,
! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)),
inference(fof_nnf,[status(thm)],[fact_wf__int__ge__less__than2]) ).
fof(f_3508_2,plain,
! [U_13593] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(U_13593)),
inference(variable_rename,[status(thm)],[f_3508_1]) ).
cnf(f_3508_3,plain,
c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(U_13593)),
inference(clausify,[status(thm)],[f_3508_2]) ).
fof(f_3509_1,plain,
! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)),
inference(fof_nnf,[status(thm)],[fact_wf__int__ge__less__than]) ).
fof(f_3509_2,plain,
! [U_13594] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(U_13594)),
inference(variable_rename,[status(thm)],[f_3509_1]) ).
cnf(f_3509_3,plain,
c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(U_13594)),
inference(clausify,[status(thm)],[f_3509_2]) ).
fof(f_3510_1,plain,
! [V_x_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
| ~ c_Wellfounded_Owf(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_acc__wfD]) ).
fof(f_3510_2,plain,
! [U_13597,U_13596,U_13595] :
( hBOOL(hAPP(hAPP(c_member(U_13595),U_13597),c_Wellfounded_Oacc(U_13595,U_13596)))
| ~ c_Wellfounded_Owf(U_13595,U_13596) ),
inference(variable_rename,[status(thm)],[f_3510_1]) ).
cnf(f_3510_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_13595),U_13597),c_Wellfounded_Oacc(U_13595,U_13596)))
| ~ c_Wellfounded_Owf(U_13595,U_13596) ),
inference(clausify,[status(thm)],[f_3510_2]) ).
fof(f_3511_1,plain,
! [V_r_2,T_b] :
( ( c_Wellfounded_Owf(T_b,V_r_2)
| ? [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) )
& ( ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2)))
| ~ c_Wellfounded_Owf(T_b,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_wf__acc__iff]) ).
fof(f_3511_2,plain,
! [U_13601,U_13600] :
( ( c_Wellfounded_Owf(U_13600,U_13601)
| ? [U_13599] : ~ hBOOL(hAPP(hAPP(c_member(U_13600),U_13599),c_Wellfounded_Oacc(U_13600,U_13601))) )
& ( ! [U_13598] : hBOOL(hAPP(hAPP(c_member(U_13600),U_13598),c_Wellfounded_Oacc(U_13600,U_13601)))
| ~ c_Wellfounded_Owf(U_13600,U_13601) ) ),
inference(variable_rename,[status(thm)],[f_3511_1]) ).
fof(f_3511_3,plain,
( ! [U_13605,U_13603] :
( c_Wellfounded_Owf(U_13603,U_13605)
| ? [U_13599] : ~ hBOOL(hAPP(hAPP(c_member(U_13603),U_13599),c_Wellfounded_Oacc(U_13603,U_13605))) )
& ! [U_13604,U_13602] :
( ! [U_13598] : hBOOL(hAPP(hAPP(c_member(U_13602),U_13598),c_Wellfounded_Oacc(U_13602,U_13604)))
| ~ c_Wellfounded_Owf(U_13602,U_13604) ) ),
inference(miniscope,[status(thm)],[f_3511_2]) ).
fof(f_3511_4,plain,
( ! [U_13605,U_13603] :
( c_Wellfounded_Owf(U_13603,U_13605)
| ~ hBOOL(hAPP(hAPP(c_member(U_13603),sK322(U_13605,U_13603)),c_Wellfounded_Oacc(U_13603,U_13605))) )
& ! [U_13604,U_13602] :
( ! [U_13598] : hBOOL(hAPP(hAPP(c_member(U_13602),U_13598),c_Wellfounded_Oacc(U_13602,U_13604)))
| ~ c_Wellfounded_Owf(U_13602,U_13604) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK322]),skolemize(U_13599,sK322(U_13605,U_13603))],[f_3511_3]) ).
cnf(f_3511_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_13602),U_13598),c_Wellfounded_Oacc(U_13602,U_13604)))
| ~ c_Wellfounded_Owf(U_13602,U_13604) ),
inference(clausify,[status(thm)],[f_3511_4]) ).
cnf(f_3511_6,plain,
( c_Wellfounded_Owf(U_13603,U_13605)
| ~ hBOOL(hAPP(hAPP(c_member(U_13603),sK322(U_13605,U_13603)),c_Wellfounded_Oacc(U_13603,U_13605))) ),
inference(clausify,[status(thm)],[f_3511_4]) ).
fof(f_3512_1,plain,
! [V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,V_R_2)
| hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_wf__no__loop]) ).
fof(f_3512_2,plain,
! [U_13607,U_13606] :
( c_Wellfounded_Owf(U_13606,U_13607)
| hAPP(hAPP(c_Relation_Orel__comp(U_13606,U_13606,U_13606),U_13607),U_13607) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13606,U_13606),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_3512_1]) ).
cnf(f_3512_3,plain,
( c_Wellfounded_Owf(U_13606,U_13607)
| hAPP(hAPP(c_Relation_Orel__comp(U_13606,U_13606,U_13606),U_13607),U_13607) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13606,U_13606),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3512_2]) ).
fof(f_3513_1,plain,
! [V_S_2,V_R_2,T_b] :
( ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
| ~ c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_S_2),V_R_2))),V_S_2)) )
& ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_S_2),V_R_2))),V_S_2))
| ~ c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_wf__union__merge]) ).
fof(f_3513_2,plain,
! [U_13610,U_13609,U_13608] :
( ( c_Wellfounded_Owf(U_13608,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13608,U_13608),tc_HOL_Obool)),U_13609),U_13610))
| ~ c_Wellfounded_Owf(U_13608,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13608,U_13608),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13608,U_13608),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13608,U_13608,U_13608),U_13609),U_13609)),hAPP(hAPP(c_Relation_Orel__comp(U_13608,U_13608,U_13608),U_13610),U_13609))),U_13610)) )
& ( c_Wellfounded_Owf(U_13608,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13608,U_13608),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13608,U_13608),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13608,U_13608,U_13608),U_13609),U_13609)),hAPP(hAPP(c_Relation_Orel__comp(U_13608,U_13608,U_13608),U_13610),U_13609))),U_13610))
| ~ c_Wellfounded_Owf(U_13608,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13608,U_13608),tc_HOL_Obool)),U_13609),U_13610)) ) ),
inference(variable_rename,[status(thm)],[f_3513_1]) ).
fof(f_3513_3,plain,
( ! [U_13616,U_13614,U_13612] :
( c_Wellfounded_Owf(U_13612,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13612,U_13612),tc_HOL_Obool)),U_13614),U_13616))
| ~ c_Wellfounded_Owf(U_13612,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13612,U_13612),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13612,U_13612),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13612,U_13612,U_13612),U_13614),U_13614)),hAPP(hAPP(c_Relation_Orel__comp(U_13612,U_13612,U_13612),U_13616),U_13614))),U_13616)) )
& ! [U_13615,U_13613,U_13611] :
( c_Wellfounded_Owf(U_13611,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13611,U_13611),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13611,U_13611),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13611,U_13611,U_13611),U_13613),U_13613)),hAPP(hAPP(c_Relation_Orel__comp(U_13611,U_13611,U_13611),U_13615),U_13613))),U_13615))
| ~ c_Wellfounded_Owf(U_13611,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13611,U_13611),tc_HOL_Obool)),U_13613),U_13615)) ) ),
inference(miniscope,[status(thm)],[f_3513_2]) ).
cnf(f_3513_4,plain,
( c_Wellfounded_Owf(U_13611,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13611,U_13611),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13611,U_13611),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13611,U_13611,U_13611),U_13613),U_13613)),hAPP(hAPP(c_Relation_Orel__comp(U_13611,U_13611,U_13611),U_13615),U_13613))),U_13615))
| ~ c_Wellfounded_Owf(U_13611,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13611,U_13611),tc_HOL_Obool)),U_13613),U_13615)) ),
inference(clausify,[status(thm)],[f_3513_3]) ).
cnf(f_3513_5,plain,
( c_Wellfounded_Owf(U_13612,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13612,U_13612),tc_HOL_Obool)),U_13614),U_13616))
| ~ c_Wellfounded_Owf(U_13612,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13612,U_13612),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13612,U_13612),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13612,U_13612,U_13612),U_13614),U_13614)),hAPP(hAPP(c_Relation_Orel__comp(U_13612,U_13612,U_13612),U_13616),U_13614))),U_13616)) ),
inference(clausify,[status(thm)],[f_3513_3]) ).
fof(f_3514_1,plain,
! [T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Range__empty]) ).
fof(f_3514_2,plain,
! [U_13618,U_13617] : hAPP(c_Relation_ORange(U_13617,U_13618),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13617,U_13618),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13618,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3514_1]) ).
cnf(f_3514_3,plain,
hAPP(c_Relation_ORange(U_13617,U_13618),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13617,U_13618),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13618,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3514_2]) ).
fof(f_3515_1,plain,
! [V_r_2,T_b,T_c] :
( ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| V_r_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) )
& ( V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))
| hAPP(c_Relation_ORange(T_c,T_b),V_r_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_Range__empty__iff]) ).
fof(f_3515_2,plain,
! [U_13621,U_13620,U_13619] :
( ( hAPP(c_Relation_ORange(U_13619,U_13620),U_13621) = c_Orderings_Obot__class_Obot(tc_fun(U_13620,tc_HOL_Obool))
| U_13621 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13619,U_13620),tc_HOL_Obool)) )
& ( U_13621 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13619,U_13620),tc_HOL_Obool))
| hAPP(c_Relation_ORange(U_13619,U_13620),U_13621) != c_Orderings_Obot__class_Obot(tc_fun(U_13620,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3515_1]) ).
fof(f_3515_3,plain,
( ! [U_13627,U_13625,U_13623] :
( hAPP(c_Relation_ORange(U_13623,U_13625),U_13627) = c_Orderings_Obot__class_Obot(tc_fun(U_13625,tc_HOL_Obool))
| U_13627 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13623,U_13625),tc_HOL_Obool)) )
& ! [U_13626,U_13624,U_13622] :
( U_13626 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13622,U_13624),tc_HOL_Obool))
| hAPP(c_Relation_ORange(U_13622,U_13624),U_13626) != c_Orderings_Obot__class_Obot(tc_fun(U_13624,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_3515_2]) ).
cnf(f_3515_4,plain,
( U_13626 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13622,U_13624),tc_HOL_Obool))
| hAPP(c_Relation_ORange(U_13622,U_13624),U_13626) != c_Orderings_Obot__class_Obot(tc_fun(U_13624,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3515_3]) ).
cnf(f_3515_5,plain,
( hAPP(c_Relation_ORange(U_13623,U_13625),U_13627) = c_Orderings_Obot__class_Obot(tc_fun(U_13625,tc_HOL_Obool))
| U_13627 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13623,U_13625),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3515_3]) ).
fof(f_3516_1,plain,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Range__Un__eq]) ).
fof(f_3516_2,plain,
! [U_13631,U_13630,U_13629,U_13628] : hAPP(c_Relation_ORange(U_13628,U_13629),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13628,U_13629),tc_HOL_Obool)),U_13630),U_13631)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13629,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13628,U_13629),U_13630)),hAPP(c_Relation_ORange(U_13628,U_13629),U_13631)),
inference(variable_rename,[status(thm)],[f_3516_1]) ).
cnf(f_3516_3,plain,
hAPP(c_Relation_ORange(U_13628,U_13629),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13628,U_13629),tc_HOL_Obool)),U_13630),U_13631)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13629,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13628,U_13629),U_13630)),hAPP(c_Relation_ORange(U_13628,U_13629),U_13631)),
inference(clausify,[status(thm)],[f_3516_2]) ).
fof(f_3517_1,plain,
! [V_r_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__Range]) ).
fof(f_3517_2,plain,
! [U_13634,U_13633,U_13632] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13633),hAPP(c_Relation_ORange(U_13632,U_13633),U_13634)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13632,U_13633)),U_13634)) ),
inference(variable_rename,[status(thm)],[f_3517_1]) ).
cnf(f_3517_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13633),hAPP(c_Relation_ORange(U_13632,U_13633),U_13634)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13632,U_13633)),U_13634)) ),
inference(clausify,[status(thm)],[f_3517_2]) ).
fof(f_3518_1,plain,
! [V_R_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_b,c_Product__Type_Osnd(T_c,T_b)),V_R_2) = hAPP(c_Relation_ORange(T_c,T_b),V_R_2),
inference(fof_nnf,[status(thm)],[fact_snd__eq__Range]) ).
fof(f_3518_2,plain,
! [U_13637,U_13636,U_13635] : hAPP(c_Set_Oimage(tc_prod(U_13635,U_13636),U_13636,c_Product__Type_Osnd(U_13635,U_13636)),U_13637) = hAPP(c_Relation_ORange(U_13635,U_13636),U_13637),
inference(variable_rename,[status(thm)],[f_3518_1]) ).
cnf(f_3518_3,plain,
hAPP(c_Set_Oimage(tc_prod(U_13635,U_13636),U_13636,c_Product__Type_Osnd(U_13635,U_13636)),U_13637) = hAPP(c_Relation_ORange(U_13635,U_13636),U_13637),
inference(clausify,[status(thm)],[f_3518_2]) ).
fof(f_3519_1,plain,
! [V_r_2,T_b] :
( ( c_Wellfounded_Owf(T_b,V_r_2)
| ? [B_f] :
! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) )
& ( ! [B_f] :
? [B_i] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2))
| ~ c_Wellfounded_Owf(T_b,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_wf__iff__no__infinite__down__chain]) ).
fof(f_3519_2,plain,
! [U_13643,U_13642] :
( ( c_Wellfounded_Owf(U_13642,U_13643)
| ? [U_13641] :
! [U_13640] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13642,U_13642)),hAPP(hAPP(c_Product__Type_OPair(U_13642,U_13642),hAPP(U_13641,hAPP(c_Nat_OSuc,U_13640))),hAPP(U_13641,U_13640))),U_13643)) )
& ( ! [U_13639] :
? [U_13638] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13642,U_13642)),hAPP(hAPP(c_Product__Type_OPair(U_13642,U_13642),hAPP(U_13639,hAPP(c_Nat_OSuc,U_13638))),hAPP(U_13639,U_13638))),U_13643))
| ~ c_Wellfounded_Owf(U_13642,U_13643) ) ),
inference(variable_rename,[status(thm)],[f_3519_1]) ).
fof(f_3519_3,plain,
( ! [U_13647,U_13645] :
( c_Wellfounded_Owf(U_13645,U_13647)
| ? [U_13641] :
! [U_13640] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13645,U_13645)),hAPP(hAPP(c_Product__Type_OPair(U_13645,U_13645),hAPP(U_13641,hAPP(c_Nat_OSuc,U_13640))),hAPP(U_13641,U_13640))),U_13647)) )
& ! [U_13646,U_13644] :
( ! [U_13639] :
? [U_13638] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13644,U_13644)),hAPP(hAPP(c_Product__Type_OPair(U_13644,U_13644),hAPP(U_13639,hAPP(c_Nat_OSuc,U_13638))),hAPP(U_13639,U_13638))),U_13646))
| ~ c_Wellfounded_Owf(U_13644,U_13646) ) ),
inference(miniscope,[status(thm)],[f_3519_2]) ).
fof(f_3519_4,plain,
( ! [U_13647,U_13645] :
( c_Wellfounded_Owf(U_13645,U_13647)
| ? [U_13641] :
! [U_13640] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13645,U_13645)),hAPP(hAPP(c_Product__Type_OPair(U_13645,U_13645),hAPP(U_13641,hAPP(c_Nat_OSuc,U_13640))),hAPP(U_13641,U_13640))),U_13647)) )
& ! [U_13646,U_13644] :
( ! [U_13639] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13644,U_13644)),hAPP(hAPP(c_Product__Type_OPair(U_13644,U_13644),hAPP(U_13639,hAPP(c_Nat_OSuc,sK323(U_13646,U_13644,U_13639)))),hAPP(U_13639,sK323(U_13646,U_13644,U_13639)))),U_13646))
| ~ c_Wellfounded_Owf(U_13644,U_13646) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK323]),skolemize(U_13638,sK323(U_13646,U_13644,U_13639))],[f_3519_3]) ).
fof(f_3519_5,plain,
( ! [U_13647,U_13645] :
( c_Wellfounded_Owf(U_13645,U_13647)
| ! [U_13640] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13645,U_13645)),hAPP(hAPP(c_Product__Type_OPair(U_13645,U_13645),hAPP(sK324(U_13647,U_13645),hAPP(c_Nat_OSuc,U_13640))),hAPP(sK324(U_13647,U_13645),U_13640))),U_13647)) )
& ! [U_13646,U_13644] :
( ! [U_13639] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13644,U_13644)),hAPP(hAPP(c_Product__Type_OPair(U_13644,U_13644),hAPP(U_13639,hAPP(c_Nat_OSuc,sK323(U_13646,U_13644,U_13639)))),hAPP(U_13639,sK323(U_13646,U_13644,U_13639)))),U_13646))
| ~ c_Wellfounded_Owf(U_13644,U_13646) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK324]),skolemize(U_13641,sK324(U_13647,U_13645))],[f_3519_4]) ).
cnf(f_3519_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13644,U_13644)),hAPP(hAPP(c_Product__Type_OPair(U_13644,U_13644),hAPP(U_13639,hAPP(c_Nat_OSuc,sK323(U_13646,U_13644,U_13639)))),hAPP(U_13639,sK323(U_13646,U_13644,U_13639)))),U_13646))
| ~ c_Wellfounded_Owf(U_13644,U_13646) ),
inference(clausify,[status(thm)],[f_3519_5]) ).
cnf(f_3519_7,plain,
( c_Wellfounded_Owf(U_13645,U_13647)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_13645,U_13645)),hAPP(hAPP(c_Product__Type_OPair(U_13645,U_13645),hAPP(sK324(U_13647,U_13645),hAPP(c_Nat_OSuc,U_13640))),hAPP(sK324(U_13647,U_13645),U_13640))),U_13647)) ),
inference(clausify,[status(thm)],[f_3519_5]) ).
fof(f_3520_1,plain,
! [V_A_2,V_R_2,T_b] :
( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),V_A_2)))
| ~ c_Wellfounded_Owf(T_b,V_R_2) ),
inference(fof_nnf,[status(thm)],[fact_wfE__pf]) ).
fof(f_3520_2,plain,
! [U_13650,U_13649,U_13648] :
( U_13650 = c_Orderings_Obot__class_Obot(tc_fun(U_13648,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13648,tc_HOL_Obool)),U_13650),hAPP(c_Relation_OImage(U_13648,U_13648,U_13649),U_13650)))
| ~ c_Wellfounded_Owf(U_13648,U_13649) ),
inference(variable_rename,[status(thm)],[f_3520_1]) ).
cnf(f_3520_3,plain,
( U_13650 = c_Orderings_Obot__class_Obot(tc_fun(U_13648,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13648,tc_HOL_Obool)),U_13650),hAPP(c_Relation_OImage(U_13648,U_13648,U_13649),U_13650)))
| ~ c_Wellfounded_Owf(U_13648,U_13649) ),
inference(clausify,[status(thm)],[f_3520_2]) ).
fof(f_3521_1,plain,
! [V_S_2,V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
| ~ c_Wellfounded_Owf(T_b,V_S_2)
| ~ c_Wellfounded_Owf(T_b,V_R_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__union__compatible]) ).
fof(f_3521_2,plain,
! [U_13653,U_13652,U_13651] :
( c_Wellfounded_Owf(U_13651,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13651,U_13651),tc_HOL_Obool)),U_13652),U_13653))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13651,U_13651),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13651,U_13651,U_13651),U_13652),U_13653)),U_13652))
| ~ c_Wellfounded_Owf(U_13651,U_13653)
| ~ c_Wellfounded_Owf(U_13651,U_13652) ),
inference(variable_rename,[status(thm)],[f_3521_1]) ).
cnf(f_3521_3,plain,
( c_Wellfounded_Owf(U_13651,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13651,U_13651),tc_HOL_Obool)),U_13652),U_13653))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13651,U_13651),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13651,U_13651,U_13651),U_13652),U_13653)),U_13652))
| ~ c_Wellfounded_Owf(U_13651,U_13653)
| ~ c_Wellfounded_Owf(U_13651,U_13652) ),
inference(clausify,[status(thm)],[f_3521_2]) ).
fof(f_3522_1,plain,
! [V_r_2,T_c,V_a_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
| ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),V_a_2)),V_r_2)) )
& ( ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),V_a_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Range__iff]) ).
fof(f_3522_2,plain,
! [U_13659,U_13658,U_13657,U_13656] :
( ( hBOOL(hAPP(hAPP(c_member(U_13656),U_13657),hAPP(c_Relation_ORange(U_13658,U_13656),U_13659)))
| ! [U_13655] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13658,U_13656)),hAPP(hAPP(c_Product__Type_OPair(U_13658,U_13656),U_13655),U_13657)),U_13659)) )
& ( ? [U_13654] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13658,U_13656)),hAPP(hAPP(c_Product__Type_OPair(U_13658,U_13656),U_13654),U_13657)),U_13659))
| ~ hBOOL(hAPP(hAPP(c_member(U_13656),U_13657),hAPP(c_Relation_ORange(U_13658,U_13656),U_13659))) ) ),
inference(variable_rename,[status(thm)],[f_3522_1]) ).
fof(f_3522_3,plain,
( ! [U_13667,U_13665,U_13663,U_13661] :
( hBOOL(hAPP(hAPP(c_member(U_13661),U_13663),hAPP(c_Relation_ORange(U_13665,U_13661),U_13667)))
| ! [U_13655] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13665,U_13661)),hAPP(hAPP(c_Product__Type_OPair(U_13665,U_13661),U_13655),U_13663)),U_13667)) )
& ! [U_13666,U_13664,U_13662,U_13660] :
( ? [U_13654] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13664,U_13660)),hAPP(hAPP(c_Product__Type_OPair(U_13664,U_13660),U_13654),U_13662)),U_13666))
| ~ hBOOL(hAPP(hAPP(c_member(U_13660),U_13662),hAPP(c_Relation_ORange(U_13664,U_13660),U_13666))) ) ),
inference(miniscope,[status(thm)],[f_3522_2]) ).
fof(f_3522_4,plain,
( ! [U_13667,U_13665,U_13663,U_13661] :
( hBOOL(hAPP(hAPP(c_member(U_13661),U_13663),hAPP(c_Relation_ORange(U_13665,U_13661),U_13667)))
| ! [U_13655] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13665,U_13661)),hAPP(hAPP(c_Product__Type_OPair(U_13665,U_13661),U_13655),U_13663)),U_13667)) )
& ! [U_13666,U_13664,U_13662,U_13660] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13664,U_13660)),hAPP(hAPP(c_Product__Type_OPair(U_13664,U_13660),sK325(U_13666,U_13664,U_13662,U_13660)),U_13662)),U_13666))
| ~ hBOOL(hAPP(hAPP(c_member(U_13660),U_13662),hAPP(c_Relation_ORange(U_13664,U_13660),U_13666))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK325]),skolemize(U_13654,sK325(U_13666,U_13664,U_13662,U_13660))],[f_3522_3]) ).
cnf(f_3522_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13664,U_13660)),hAPP(hAPP(c_Product__Type_OPair(U_13664,U_13660),sK325(U_13666,U_13664,U_13662,U_13660)),U_13662)),U_13666))
| ~ hBOOL(hAPP(hAPP(c_member(U_13660),U_13662),hAPP(c_Relation_ORange(U_13664,U_13660),U_13666))) ),
inference(clausify,[status(thm)],[f_3522_4]) ).
cnf(f_3522_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_13661),U_13663),hAPP(c_Relation_ORange(U_13665,U_13661),U_13667)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13665,U_13661)),hAPP(hAPP(c_Product__Type_OPair(U_13665,U_13661),U_13655),U_13663)),U_13667)) ),
inference(clausify,[status(thm)],[f_3522_4]) ).
fof(f_3523_1,plain,
! [T_b] :
( c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_b))))
| ~ class_Orderings_Owellorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_wf]) ).
fof(f_3523_2,plain,
! [U_13668] :
( c_Wellfounded_Owf(U_13668,hAPP(c_Set_OCollect(tc_prod(U_13668,U_13668)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13668,U_13668,tc_HOL_Obool),c_Orderings_Oord__class_Oless(U_13668))))
| ~ class_Orderings_Owellorder(U_13668) ),
inference(variable_rename,[status(thm)],[f_3523_1]) ).
cnf(f_3523_3,plain,
( c_Wellfounded_Owf(U_13668,hAPP(c_Set_OCollect(tc_prod(U_13668,U_13668)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13668,U_13668,tc_HOL_Obool),c_Orderings_Oord__class_Oless(U_13668))))
| ~ class_Orderings_Owellorder(U_13668) ),
inference(clausify,[status(thm)],[f_3523_2]) ).
fof(f_3524_1,plain,
! [V_P_2,T_b] :
( ( c_FunDef_Oreduction__pair(T_b,V_P_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
| ~ c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
& c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)) )
| ~ c_FunDef_Oreduction__pair(T_b,V_P_2) ) ),
inference(fof_nnf,[status(thm)],[fact_reduction__pair__def]) ).
fof(f_3524_2,plain,
! [U_13670,U_13669] :
( ( c_FunDef_Oreduction__pair(U_13669,U_13670)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13669,U_13669),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13669,U_13669,U_13669),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13669,U_13669),tc_HOL_Obool),tc_fun(tc_prod(U_13669,U_13669),tc_HOL_Obool)),U_13670)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13669,U_13669),tc_HOL_Obool),tc_fun(tc_prod(U_13669,U_13669),tc_HOL_Obool)),U_13670))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13669,U_13669),tc_HOL_Obool),tc_fun(tc_prod(U_13669,U_13669),tc_HOL_Obool)),U_13670)))
| ~ c_Wellfounded_Owf(U_13669,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13669,U_13669),tc_HOL_Obool),tc_fun(tc_prod(U_13669,U_13669),tc_HOL_Obool)),U_13670)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13669,U_13669),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13669,U_13669,U_13669),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13669,U_13669),tc_HOL_Obool),tc_fun(tc_prod(U_13669,U_13669),tc_HOL_Obool)),U_13670)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13669,U_13669),tc_HOL_Obool),tc_fun(tc_prod(U_13669,U_13669),tc_HOL_Obool)),U_13670))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13669,U_13669),tc_HOL_Obool),tc_fun(tc_prod(U_13669,U_13669),tc_HOL_Obool)),U_13670)))
& c_Wellfounded_Owf(U_13669,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13669,U_13669),tc_HOL_Obool),tc_fun(tc_prod(U_13669,U_13669),tc_HOL_Obool)),U_13670)) )
| ~ c_FunDef_Oreduction__pair(U_13669,U_13670) ) ),
inference(variable_rename,[status(thm)],[f_3524_1]) ).
fof(f_3524_3,plain,
( ! [U_13674,U_13672] :
( c_FunDef_Oreduction__pair(U_13672,U_13674)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13672,U_13672),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13672,U_13672,U_13672),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13672,U_13672),tc_HOL_Obool),tc_fun(tc_prod(U_13672,U_13672),tc_HOL_Obool)),U_13674)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13672,U_13672),tc_HOL_Obool),tc_fun(tc_prod(U_13672,U_13672),tc_HOL_Obool)),U_13674))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13672,U_13672),tc_HOL_Obool),tc_fun(tc_prod(U_13672,U_13672),tc_HOL_Obool)),U_13674)))
| ~ c_Wellfounded_Owf(U_13672,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13672,U_13672),tc_HOL_Obool),tc_fun(tc_prod(U_13672,U_13672),tc_HOL_Obool)),U_13674)) )
& ! [U_13673,U_13671] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13671,U_13671),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13671,U_13671,U_13671),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13671,U_13671),tc_HOL_Obool),tc_fun(tc_prod(U_13671,U_13671),tc_HOL_Obool)),U_13673)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13671,U_13671),tc_HOL_Obool),tc_fun(tc_prod(U_13671,U_13671),tc_HOL_Obool)),U_13673))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13671,U_13671),tc_HOL_Obool),tc_fun(tc_prod(U_13671,U_13671),tc_HOL_Obool)),U_13673)))
& c_Wellfounded_Owf(U_13671,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13671,U_13671),tc_HOL_Obool),tc_fun(tc_prod(U_13671,U_13671),tc_HOL_Obool)),U_13673)) )
| ~ c_FunDef_Oreduction__pair(U_13671,U_13673) ) ),
inference(miniscope,[status(thm)],[f_3524_2]) ).
cnf(f_3524_4,plain,
( c_Wellfounded_Owf(U_13671,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13671,U_13671),tc_HOL_Obool),tc_fun(tc_prod(U_13671,U_13671),tc_HOL_Obool)),U_13673))
| ~ c_FunDef_Oreduction__pair(U_13671,U_13673) ),
inference(clausify,[status(thm)],[f_3524_3]) ).
cnf(f_3524_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13671,U_13671),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13671,U_13671,U_13671),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13671,U_13671),tc_HOL_Obool),tc_fun(tc_prod(U_13671,U_13671),tc_HOL_Obool)),U_13673)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13671,U_13671),tc_HOL_Obool),tc_fun(tc_prod(U_13671,U_13671),tc_HOL_Obool)),U_13673))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13671,U_13671),tc_HOL_Obool),tc_fun(tc_prod(U_13671,U_13671),tc_HOL_Obool)),U_13673)))
| ~ c_FunDef_Oreduction__pair(U_13671,U_13673) ),
inference(clausify,[status(thm)],[f_3524_3]) ).
cnf(f_3524_6,plain,
( c_FunDef_Oreduction__pair(U_13672,U_13674)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13672,U_13672),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_13672,U_13672,U_13672),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13672,U_13672),tc_HOL_Obool),tc_fun(tc_prod(U_13672,U_13672),tc_HOL_Obool)),U_13674)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13672,U_13672),tc_HOL_Obool),tc_fun(tc_prod(U_13672,U_13672),tc_HOL_Obool)),U_13674))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13672,U_13672),tc_HOL_Obool),tc_fun(tc_prod(U_13672,U_13672),tc_HOL_Obool)),U_13674)))
| ~ c_Wellfounded_Owf(U_13672,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13672,U_13672),tc_HOL_Obool),tc_fun(tc_prod(U_13672,U_13672),tc_HOL_Obool)),U_13674)) ),
inference(clausify,[status(thm)],[f_3524_3]) ).
fof(f_3525_1,plain,
! [V_S_2,V_R_2,V_P_2,T_b] :
( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
| ~ c_Wellfounded_Owf(T_b,V_S_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
| ~ c_FunDef_Oreduction__pair(T_b,V_P_2) ),
inference(fof_nnf,[status(thm)],[fact_reduction__pair__lemma]) ).
fof(f_3525_2,plain,
! [U_13678,U_13677,U_13676,U_13675] :
( c_Wellfounded_Owf(U_13675,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13675,U_13675),tc_HOL_Obool)),U_13677),U_13678))
| ~ c_Wellfounded_Owf(U_13675,U_13678)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13675,U_13675),tc_HOL_Obool)),U_13678),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13675,U_13675),tc_HOL_Obool),tc_fun(tc_prod(U_13675,U_13675),tc_HOL_Obool)),U_13676)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13675,U_13675),tc_HOL_Obool)),U_13677),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13675,U_13675),tc_HOL_Obool),tc_fun(tc_prod(U_13675,U_13675),tc_HOL_Obool)),U_13676)))
| ~ c_FunDef_Oreduction__pair(U_13675,U_13676) ),
inference(variable_rename,[status(thm)],[f_3525_1]) ).
cnf(f_3525_3,plain,
( c_Wellfounded_Owf(U_13675,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13675,U_13675),tc_HOL_Obool)),U_13677),U_13678))
| ~ c_Wellfounded_Owf(U_13675,U_13678)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13675,U_13675),tc_HOL_Obool)),U_13678),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_13675,U_13675),tc_HOL_Obool),tc_fun(tc_prod(U_13675,U_13675),tc_HOL_Obool)),U_13676)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13675,U_13675),tc_HOL_Obool)),U_13677),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_13675,U_13675),tc_HOL_Obool),tc_fun(tc_prod(U_13675,U_13675),tc_HOL_Obool)),U_13676)))
| ~ c_FunDef_Oreduction__pair(U_13675,U_13676) ),
inference(clausify,[status(thm)],[f_3525_2]) ).
fof(f_3526_1,plain,
! [V_r_2,V_b_2,V_a_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)),
inference(fof_nnf,[status(thm)],[fact_Range__insert]) ).
fof(f_3526_2,plain,
! [U_13683,U_13682,U_13681,U_13680,U_13679] : hAPP(c_Relation_ORange(U_13679,U_13680),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13679,U_13680)),hAPP(hAPP(c_Product__Type_OPair(U_13679,U_13680),U_13681),U_13682)),U_13683)) = hAPP(hAPP(c_Set_Oinsert(U_13680),U_13682),hAPP(c_Relation_ORange(U_13679,U_13680),U_13683)),
inference(variable_rename,[status(thm)],[f_3526_1]) ).
cnf(f_3526_3,plain,
hAPP(c_Relation_ORange(U_13679,U_13680),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13679,U_13680)),hAPP(hAPP(c_Product__Type_OPair(U_13679,U_13680),U_13681),U_13682)),U_13683)) = hAPP(hAPP(c_Set_Oinsert(U_13680),U_13682),hAPP(c_Relation_ORange(U_13679,U_13680),U_13683)),
inference(clausify,[status(thm)],[f_3526_2]) ).
fof(f_3527_1,plain,
! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_Range__Int__subset]) ).
fof(f_3527_2,plain,
! [U_13687,U_13686,U_13685,U_13684] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13684,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13685,U_13684),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13685,U_13684),tc_HOL_Obool)),U_13686),U_13687))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13684,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13685,U_13684),U_13686)),hAPP(c_Relation_ORange(U_13685,U_13684),U_13687)))),
inference(variable_rename,[status(thm)],[f_3527_1]) ).
cnf(f_3527_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13684,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13685,U_13684),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13685,U_13684),tc_HOL_Obool)),U_13686),U_13687))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13684,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13685,U_13684),U_13686)),hAPP(c_Relation_ORange(U_13685,U_13684),U_13687)))),
inference(clausify,[status(thm)],[f_3527_2]) ).
fof(f_3528_1,plain,
! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2))),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_Range__Diff__subset]) ).
fof(f_3528_2,plain,
! [U_13691,U_13690,U_13689,U_13688] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13688,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13688,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13689,U_13688),U_13690)),hAPP(c_Relation_ORange(U_13689,U_13688),U_13691))),hAPP(c_Relation_ORange(U_13689,U_13688),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13689,U_13688),tc_HOL_Obool)),U_13690),U_13691)))),
inference(variable_rename,[status(thm)],[f_3528_1]) ).
cnf(f_3528_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13688,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13688,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_13689,U_13688),U_13690)),hAPP(c_Relation_ORange(U_13689,U_13688),U_13691))),hAPP(c_Relation_ORange(U_13689,U_13688),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13689,U_13688),tc_HOL_Obool)),U_13690),U_13691)))),
inference(clausify,[status(thm)],[f_3528_2]) ).
fof(f_3529_1,plain,
! [V_f_2,T_c,V_r_2,T_b] :
( c_Wellfounded_Owf(T_c,hAPP(c_Set_Oimage(tc_prod(T_b,T_b),tc_prod(T_c,T_c),c_Product__Type_Omap__pair(T_b,T_c,T_b,T_c,V_f_2,V_f_2)),V_r_2))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
| ~ c_Wellfounded_Owf(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__map__pair__image]) ).
fof(f_3529_2,plain,
! [U_13695,U_13694,U_13693,U_13692] :
( c_Wellfounded_Owf(U_13694,hAPP(c_Set_Oimage(tc_prod(U_13692,U_13692),tc_prod(U_13694,U_13694),c_Product__Type_Omap__pair(U_13692,U_13694,U_13692,U_13694,U_13695,U_13695)),U_13693))
| ~ c_Fun_Oinj__on(U_13692,U_13694,U_13695,c_Orderings_Otop__class_Otop(tc_fun(U_13692,tc_HOL_Obool)))
| ~ c_Wellfounded_Owf(U_13692,U_13693) ),
inference(variable_rename,[status(thm)],[f_3529_1]) ).
cnf(f_3529_3,plain,
( c_Wellfounded_Owf(U_13694,hAPP(c_Set_Oimage(tc_prod(U_13692,U_13692),tc_prod(U_13694,U_13694),c_Product__Type_Omap__pair(U_13692,U_13694,U_13692,U_13694,U_13695,U_13695)),U_13693))
| ~ c_Fun_Oinj__on(U_13692,U_13694,U_13695,c_Orderings_Otop__class_Otop(tc_fun(U_13692,tc_HOL_Obool)))
| ~ c_Wellfounded_Owf(U_13692,U_13693) ),
inference(clausify,[status(thm)],[f_3529_2]) ).
fof(f_3530_1,plain,
! [V_x_2,V_r_2,T_c,T_b] :
( ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) )
& ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2)))
| ~ hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_RangeP__Range__eq]) ).
fof(f_3530_2,plain,
! [U_13699,U_13698,U_13697,U_13696] :
( ( hBOOL(hAPP(c_Predicate_ORangeP(U_13696,U_13697,hAPP(hAPP(c_COMBC(U_13696,tc_fun(tc_prod(U_13696,U_13697),tc_HOL_Obool),tc_fun(U_13697,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13697,tc_fun(tc_fun(tc_prod(U_13696,U_13697),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13696,U_13697),tc_HOL_Obool),tc_fun(U_13697,tc_HOL_Obool)),U_13696),c_COMBC(U_13697,tc_fun(tc_prod(U_13696,U_13697),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13697,tc_prod(U_13696,U_13697)),tc_fun(U_13697,tc_fun(tc_fun(tc_prod(U_13696,U_13697),tc_HOL_Obool),tc_HOL_Obool)),U_13696),hAPP(c_COMBB(tc_prod(U_13696,U_13697),tc_fun(tc_fun(tc_prod(U_13696,U_13697),tc_HOL_Obool),tc_HOL_Obool),U_13697),c_member(tc_prod(U_13696,U_13697)))),c_Product__Type_OPair(U_13696,U_13697)))),U_13698)),U_13699))
| ~ hBOOL(hAPP(hAPP(c_member(U_13697),U_13699),hAPP(c_Relation_ORange(U_13696,U_13697),U_13698))) )
& ( hBOOL(hAPP(hAPP(c_member(U_13697),U_13699),hAPP(c_Relation_ORange(U_13696,U_13697),U_13698)))
| ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13696,U_13697,hAPP(hAPP(c_COMBC(U_13696,tc_fun(tc_prod(U_13696,U_13697),tc_HOL_Obool),tc_fun(U_13697,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13697,tc_fun(tc_fun(tc_prod(U_13696,U_13697),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13696,U_13697),tc_HOL_Obool),tc_fun(U_13697,tc_HOL_Obool)),U_13696),c_COMBC(U_13697,tc_fun(tc_prod(U_13696,U_13697),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13697,tc_prod(U_13696,U_13697)),tc_fun(U_13697,tc_fun(tc_fun(tc_prod(U_13696,U_13697),tc_HOL_Obool),tc_HOL_Obool)),U_13696),hAPP(c_COMBB(tc_prod(U_13696,U_13697),tc_fun(tc_fun(tc_prod(U_13696,U_13697),tc_HOL_Obool),tc_HOL_Obool),U_13697),c_member(tc_prod(U_13696,U_13697)))),c_Product__Type_OPair(U_13696,U_13697)))),U_13698)),U_13699)) ) ),
inference(variable_rename,[status(thm)],[f_3530_1]) ).
fof(f_3530_3,plain,
( ! [U_13707,U_13705,U_13703,U_13701] :
( hBOOL(hAPP(c_Predicate_ORangeP(U_13701,U_13703,hAPP(hAPP(c_COMBC(U_13701,tc_fun(tc_prod(U_13701,U_13703),tc_HOL_Obool),tc_fun(U_13703,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13703,tc_fun(tc_fun(tc_prod(U_13701,U_13703),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13701,U_13703),tc_HOL_Obool),tc_fun(U_13703,tc_HOL_Obool)),U_13701),c_COMBC(U_13703,tc_fun(tc_prod(U_13701,U_13703),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13703,tc_prod(U_13701,U_13703)),tc_fun(U_13703,tc_fun(tc_fun(tc_prod(U_13701,U_13703),tc_HOL_Obool),tc_HOL_Obool)),U_13701),hAPP(c_COMBB(tc_prod(U_13701,U_13703),tc_fun(tc_fun(tc_prod(U_13701,U_13703),tc_HOL_Obool),tc_HOL_Obool),U_13703),c_member(tc_prod(U_13701,U_13703)))),c_Product__Type_OPair(U_13701,U_13703)))),U_13705)),U_13707))
| ~ hBOOL(hAPP(hAPP(c_member(U_13703),U_13707),hAPP(c_Relation_ORange(U_13701,U_13703),U_13705))) )
& ! [U_13706,U_13704,U_13702,U_13700] :
( hBOOL(hAPP(hAPP(c_member(U_13702),U_13706),hAPP(c_Relation_ORange(U_13700,U_13702),U_13704)))
| ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13700,U_13702,hAPP(hAPP(c_COMBC(U_13700,tc_fun(tc_prod(U_13700,U_13702),tc_HOL_Obool),tc_fun(U_13702,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13702,tc_fun(tc_fun(tc_prod(U_13700,U_13702),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13700,U_13702),tc_HOL_Obool),tc_fun(U_13702,tc_HOL_Obool)),U_13700),c_COMBC(U_13702,tc_fun(tc_prod(U_13700,U_13702),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13702,tc_prod(U_13700,U_13702)),tc_fun(U_13702,tc_fun(tc_fun(tc_prod(U_13700,U_13702),tc_HOL_Obool),tc_HOL_Obool)),U_13700),hAPP(c_COMBB(tc_prod(U_13700,U_13702),tc_fun(tc_fun(tc_prod(U_13700,U_13702),tc_HOL_Obool),tc_HOL_Obool),U_13702),c_member(tc_prod(U_13700,U_13702)))),c_Product__Type_OPair(U_13700,U_13702)))),U_13704)),U_13706)) ) ),
inference(miniscope,[status(thm)],[f_3530_2]) ).
cnf(f_3530_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_13702),U_13706),hAPP(c_Relation_ORange(U_13700,U_13702),U_13704)))
| ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13700,U_13702,hAPP(hAPP(c_COMBC(U_13700,tc_fun(tc_prod(U_13700,U_13702),tc_HOL_Obool),tc_fun(U_13702,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13702,tc_fun(tc_fun(tc_prod(U_13700,U_13702),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13700,U_13702),tc_HOL_Obool),tc_fun(U_13702,tc_HOL_Obool)),U_13700),c_COMBC(U_13702,tc_fun(tc_prod(U_13700,U_13702),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13702,tc_prod(U_13700,U_13702)),tc_fun(U_13702,tc_fun(tc_fun(tc_prod(U_13700,U_13702),tc_HOL_Obool),tc_HOL_Obool)),U_13700),hAPP(c_COMBB(tc_prod(U_13700,U_13702),tc_fun(tc_fun(tc_prod(U_13700,U_13702),tc_HOL_Obool),tc_HOL_Obool),U_13702),c_member(tc_prod(U_13700,U_13702)))),c_Product__Type_OPair(U_13700,U_13702)))),U_13704)),U_13706)) ),
inference(clausify,[status(thm)],[f_3530_3]) ).
cnf(f_3530_5,plain,
( hBOOL(hAPP(c_Predicate_ORangeP(U_13701,U_13703,hAPP(hAPP(c_COMBC(U_13701,tc_fun(tc_prod(U_13701,U_13703),tc_HOL_Obool),tc_fun(U_13703,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13703,tc_fun(tc_fun(tc_prod(U_13701,U_13703),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13701,U_13703),tc_HOL_Obool),tc_fun(U_13703,tc_HOL_Obool)),U_13701),c_COMBC(U_13703,tc_fun(tc_prod(U_13701,U_13703),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13703,tc_prod(U_13701,U_13703)),tc_fun(U_13703,tc_fun(tc_fun(tc_prod(U_13701,U_13703),tc_HOL_Obool),tc_HOL_Obool)),U_13701),hAPP(c_COMBB(tc_prod(U_13701,U_13703),tc_fun(tc_fun(tc_prod(U_13701,U_13703),tc_HOL_Obool),tc_HOL_Obool),U_13703),c_member(tc_prod(U_13701,U_13703)))),c_Product__Type_OPair(U_13701,U_13703)))),U_13705)),U_13707))
| ~ hBOOL(hAPP(hAPP(c_member(U_13703),U_13707),hAPP(c_Relation_ORange(U_13701,U_13703),U_13705))) ),
inference(clausify,[status(thm)],[f_3530_3]) ).
fof(f_3531_1,plain,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2))
| ~ c_Wellfounded_Owf(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__lenlex]) ).
fof(f_3531_2,plain,
! [U_13709,U_13708] :
( c_Wellfounded_Owf(tc_List_Olist(U_13708),c_List_Olenlex(U_13708,U_13709))
| ~ c_Wellfounded_Owf(U_13708,U_13709) ),
inference(variable_rename,[status(thm)],[f_3531_1]) ).
cnf(f_3531_3,plain,
( c_Wellfounded_Owf(tc_List_Olist(U_13708),c_List_Olenlex(U_13708,U_13709))
| ~ c_Wellfounded_Owf(U_13708,U_13709) ),
inference(clausify,[status(thm)],[f_3531_2]) ).
fof(f_3532_1,plain,
! [V_r_2,T_c,V_b_2,T_b] :
( ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_RangeE]) ).
fof(f_3532_2,plain,
! [U_13714,U_13713,U_13712,U_13711] :
( ? [U_13710] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13713,U_13711)),hAPP(hAPP(c_Product__Type_OPair(U_13713,U_13711),U_13710),U_13712)),U_13714))
| ~ hBOOL(hAPP(hAPP(c_member(U_13711),U_13712),hAPP(c_Relation_ORange(U_13713,U_13711),U_13714))) ),
inference(variable_rename,[status(thm)],[f_3532_1]) ).
fof(f_3532_3,plain,
! [U_13714,U_13713,U_13712,U_13711] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13713,U_13711)),hAPP(hAPP(c_Product__Type_OPair(U_13713,U_13711),sK326(U_13714,U_13713,U_13712,U_13711)),U_13712)),U_13714))
| ~ hBOOL(hAPP(hAPP(c_member(U_13711),U_13712),hAPP(c_Relation_ORange(U_13713,U_13711),U_13714))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK326]),skolemize(U_13710,sK326(U_13714,U_13713,U_13712,U_13711))],[f_3532_2]) ).
cnf(f_3532_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13713,U_13711)),hAPP(hAPP(c_Product__Type_OPair(U_13713,U_13711),sK326(U_13714,U_13713,U_13712,U_13711)),U_13712)),U_13714))
| ~ hBOOL(hAPP(hAPP(c_member(U_13711),U_13712),hAPP(c_Relation_ORange(U_13713,U_13711),U_13714))) ),
inference(clausify,[status(thm)],[f_3532_3]) ).
fof(f_3533_1,plain,
! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2))
| ~ hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_RangeP_Ointros]) ).
fof(f_3533_2,plain,
! [U_13719,U_13718,U_13717,U_13716,U_13715] :
( hBOOL(hAPP(c_Predicate_ORangeP(U_13718,U_13719,U_13715),U_13717))
| ~ hBOOL(hAPP(hAPP(U_13715,U_13716),U_13717)) ),
inference(variable_rename,[status(thm)],[f_3533_1]) ).
cnf(f_3533_3,plain,
( hBOOL(hAPP(c_Predicate_ORangeP(U_13718,U_13719,U_13715),U_13717))
| ~ hBOOL(hAPP(hAPP(U_13715,U_13716),U_13717)) ),
inference(clausify,[status(thm)],[f_3533_2]) ).
fof(f_3534_1,plain,
! [V_a2_2,V_r_2,T_c,T_b] :
( ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
| ! [B_a] : ~ hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) )
& ( ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2))
| ~ hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_RangeP_Oequations]) ).
fof(f_3534_2,plain,
! [U_13725,U_13724,U_13723,U_13722] :
( ( hBOOL(hAPP(c_Predicate_ORangeP(U_13722,U_13723,U_13724),U_13725))
| ! [U_13721] : ~ hBOOL(hAPP(hAPP(U_13724,U_13721),U_13725)) )
& ( ? [U_13720] : hBOOL(hAPP(hAPP(U_13724,U_13720),U_13725))
| ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13722,U_13723,U_13724),U_13725)) ) ),
inference(variable_rename,[status(thm)],[f_3534_1]) ).
fof(f_3534_3,plain,
( ! [U_13733,U_13731] :
( ! [U_13729,U_13727] : hBOOL(hAPP(c_Predicate_ORangeP(U_13727,U_13729,U_13731),U_13733))
| ! [U_13721] : ~ hBOOL(hAPP(hAPP(U_13731,U_13721),U_13733)) )
& ! [U_13732,U_13730] :
( ! [U_13728,U_13726] : ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13726,U_13728,U_13730),U_13732))
| ? [U_13720] : hBOOL(hAPP(hAPP(U_13730,U_13720),U_13732)) ) ),
inference(miniscope,[status(thm)],[f_3534_2]) ).
fof(f_3534_4,plain,
( ! [U_13733,U_13731] :
( ! [U_13729,U_13727] : hBOOL(hAPP(c_Predicate_ORangeP(U_13727,U_13729,U_13731),U_13733))
| ! [U_13721] : ~ hBOOL(hAPP(hAPP(U_13731,U_13721),U_13733)) )
& ! [U_13732,U_13730] :
( ! [U_13728,U_13726] : ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13726,U_13728,U_13730),U_13732))
| hBOOL(hAPP(hAPP(U_13730,sK327(U_13732,U_13730)),U_13732)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK327]),skolemize(U_13720,sK327(U_13732,U_13730))],[f_3534_3]) ).
cnf(f_3534_5,plain,
( ~ hBOOL(hAPP(c_Predicate_ORangeP(U_13726,U_13728,U_13730),U_13732))
| hBOOL(hAPP(hAPP(U_13730,sK327(U_13732,U_13730)),U_13732)) ),
inference(clausify,[status(thm)],[f_3534_4]) ).
cnf(f_3534_6,plain,
( hBOOL(hAPP(c_Predicate_ORangeP(U_13727,U_13729,U_13731),U_13733))
| ~ hBOOL(hAPP(hAPP(U_13731,U_13721),U_13733)) ),
inference(clausify,[status(thm)],[f_3534_4]) ).
fof(f_3535_1,plain,
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))),
inference(fof_nnf,[status(thm)],[fact_pred__nat__def]) ).
cnf(f_3535_2,plain,
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))),
inference(clausify,[status(thm)],[f_3535_1]) ).
fof(f_3536_1,plain,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2))
| ~ c_Wellfounded_Owf(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__lex]) ).
fof(f_3536_2,plain,
! [U_13735,U_13734] :
( c_Wellfounded_Owf(tc_List_Olist(U_13734),c_List_Olex(U_13734,U_13735))
| ~ c_Wellfounded_Owf(U_13734,U_13735) ),
inference(variable_rename,[status(thm)],[f_3536_1]) ).
cnf(f_3536_3,plain,
( c_Wellfounded_Owf(tc_List_Olist(U_13734),c_List_Olex(U_13734,U_13735))
| ~ c_Wellfounded_Owf(U_13734,U_13735) ),
inference(clausify,[status(thm)],[f_3536_2]) ).
fof(f_3537_1,plain,
! [V_na_2,V_r_2,T_b] :
( c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_na_2))
| ~ c_Wellfounded_Owf(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__lexn]) ).
fof(f_3537_2,plain,
! [U_13738,U_13737,U_13736] :
( c_Wellfounded_Owf(tc_List_Olist(U_13736),hAPP(c_List_Olexn(U_13736,U_13737),U_13738))
| ~ c_Wellfounded_Owf(U_13736,U_13737) ),
inference(variable_rename,[status(thm)],[f_3537_1]) ).
cnf(f_3537_3,plain,
( c_Wellfounded_Owf(tc_List_Olist(U_13736),hAPP(c_List_Olexn(U_13736,U_13737),U_13738))
| ~ c_Wellfounded_Owf(U_13736,U_13737) ),
inference(clausify,[status(thm)],[f_3537_2]) ).
fof(f_3538_1,plain,
! [V_r_2,T_b] : c_List_Olex(T_b,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_b,V_r_2)),
inference(fof_nnf,[status(thm)],[fact_lex__def]) ).
fof(f_3538_2,plain,
! [U_13740,U_13739] : c_List_Olex(U_13739,U_13740) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(U_13739),tc_List_Olist(U_13739)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(U_13739,U_13740)),
inference(variable_rename,[status(thm)],[f_3538_1]) ).
cnf(f_3538_3,plain,
c_List_Olex(U_13739,U_13740) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(U_13739),tc_List_Olist(U_13739)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(U_13739,U_13740)),
inference(clausify,[status(thm)],[f_3538_2]) ).
fof(f_3539_1,plain,
! [V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_lexn_Osimps_I1_J]) ).
fof(f_3539_2,plain,
! [U_13742,U_13741] : hAPP(c_List_Olexn(U_13741,U_13742),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(U_13741),tc_List_Olist(U_13741)),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3539_1]) ).
cnf(f_3539_3,plain,
hAPP(c_List_Olexn(U_13741,U_13742),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(U_13741),tc_List_Olist(U_13741)),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3539_2]) ).
fof(f_3540_1,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(fof_nnf,[status(thm)],[fact_wf__pred__nat]) ).
cnf(f_3540_2,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(clausify,[status(thm)],[f_3540_1]) ).
fof(f_3541_1,plain,
! [V_s_2,V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_s_2)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ c_Wellfounded_Owf(T_b,V_s_2)
| ~ c_Wellfounded_Owf(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__Un]) ).
fof(f_3541_2,plain,
! [U_13745,U_13744,U_13743] :
( c_Wellfounded_Owf(U_13743,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13743,U_13743),tc_HOL_Obool)),U_13744),U_13745))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13743,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13743,U_13743),U_13744)),hAPP(c_Relation_ORange(U_13743,U_13743),U_13745)) != c_Orderings_Obot__class_Obot(tc_fun(U_13743,tc_HOL_Obool))
| ~ c_Wellfounded_Owf(U_13743,U_13745)
| ~ c_Wellfounded_Owf(U_13743,U_13744) ),
inference(variable_rename,[status(thm)],[f_3541_1]) ).
cnf(f_3541_3,plain,
( c_Wellfounded_Owf(U_13743,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13743,U_13743),tc_HOL_Obool)),U_13744),U_13745))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13743,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13743,U_13743),U_13744)),hAPP(c_Relation_ORange(U_13743,U_13743),U_13745)) != c_Orderings_Obot__class_Obot(tc_fun(U_13743,tc_HOL_Obool))
| ~ c_Wellfounded_Owf(U_13743,U_13745)
| ~ c_Wellfounded_Owf(U_13743,U_13744) ),
inference(clausify,[status(thm)],[f_3541_2]) ).
fof(f_3542_1,plain,
! [T_b,V_R_2,T_c,V_P_2] :
( c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2))
| ? [B_x] :
( ~ c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x))
& hBOOL(hAPP(V_P_2,B_x)) ) ),
inference(fof_nnf,[status(thm)],[fact_wf__same__fst]) ).
fof(f_3542_2,plain,
! [U_13750,U_13749,U_13748,U_13747] :
( c_Wellfounded_Owf(tc_prod(U_13750,U_13748),c_Recdef_Osame__fst(U_13750,U_13748,U_13747,U_13749))
| ? [U_13746] :
( ~ c_Wellfounded_Owf(U_13748,hAPP(U_13749,U_13746))
& hBOOL(hAPP(U_13747,U_13746)) ) ),
inference(variable_rename,[status(thm)],[f_3542_1]) ).
fof(f_3542_3,plain,
! [U_13750,U_13749,U_13748,U_13747] :
( c_Wellfounded_Owf(tc_prod(U_13750,U_13748),c_Recdef_Osame__fst(U_13750,U_13748,U_13747,U_13749))
| ( ~ c_Wellfounded_Owf(U_13748,hAPP(U_13749,sK328(U_13750,U_13749,U_13748,U_13747)))
& hBOOL(hAPP(U_13747,sK328(U_13750,U_13749,U_13748,U_13747))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK328]),skolemize(U_13746,sK328(U_13750,U_13749,U_13748,U_13747))],[f_3542_2]) ).
cnf(f_3542_4,plain,
( hBOOL(hAPP(U_13747,sK328(U_13750,U_13749,U_13748,U_13747)))
| c_Wellfounded_Owf(tc_prod(U_13750,U_13748),c_Recdef_Osame__fst(U_13750,U_13748,U_13747,U_13749)) ),
inference(clausify,[status(thm)],[f_3542_3]) ).
cnf(f_3542_5,plain,
( ~ c_Wellfounded_Owf(U_13748,hAPP(U_13749,sK328(U_13750,U_13749,U_13748,U_13747)))
| c_Wellfounded_Owf(tc_prod(U_13750,U_13748),c_Recdef_Osame__fst(U_13750,U_13748,U_13747,U_13749)) ),
inference(clausify,[status(thm)],[f_3542_3]) ).
fof(f_3543_1,plain,
! [T_b,V_g_2,V_f_2,V_P_2] :
( c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2)))))
| ? [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)))
& hBOOL(hAPP(V_P_2,B_x)) ) ),
inference(fof_nnf,[status(thm)],[fact_wf__if__measure]) ).
fof(f_3543_2,plain,
! [U_13755,U_13754,U_13753,U_13752] :
( c_Wellfounded_Owf(U_13755,hAPP(c_Set_OCollect(tc_prod(U_13755,U_13755)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13755,U_13755,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13755,tc_HOL_Obool),tc_fun(U_13755,tc_HOL_Obool),U_13755),hAPP(c_COMBS(U_13755,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13755),c_fconj),U_13752))),hAPP(hAPP(c_COMBC(U_13755,tc_fun(U_13755,U_13755),tc_fun(U_13755,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13755,tc_HOL_Obool),tc_fun(tc_fun(U_13755,U_13755),tc_fun(U_13755,tc_HOL_Obool)),U_13755),c_COMBB(U_13755,tc_HOL_Obool,U_13755)),c_fequal)),U_13754)))))
| ? [U_13751] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_13753,hAPP(U_13754,U_13751))),hAPP(U_13753,U_13751)))
& hBOOL(hAPP(U_13752,U_13751)) ) ),
inference(variable_rename,[status(thm)],[f_3543_1]) ).
fof(f_3543_3,plain,
! [U_13755,U_13754,U_13753,U_13752] :
( c_Wellfounded_Owf(U_13755,hAPP(c_Set_OCollect(tc_prod(U_13755,U_13755)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13755,U_13755,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13755,tc_HOL_Obool),tc_fun(U_13755,tc_HOL_Obool),U_13755),hAPP(c_COMBS(U_13755,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13755),c_fconj),U_13752))),hAPP(hAPP(c_COMBC(U_13755,tc_fun(U_13755,U_13755),tc_fun(U_13755,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13755,tc_HOL_Obool),tc_fun(tc_fun(U_13755,U_13755),tc_fun(U_13755,tc_HOL_Obool)),U_13755),c_COMBB(U_13755,tc_HOL_Obool,U_13755)),c_fequal)),U_13754)))))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_13753,hAPP(U_13754,sK329(U_13755,U_13754,U_13753,U_13752)))),hAPP(U_13753,sK329(U_13755,U_13754,U_13753,U_13752))))
& hBOOL(hAPP(U_13752,sK329(U_13755,U_13754,U_13753,U_13752))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK329]),skolemize(U_13751,sK329(U_13755,U_13754,U_13753,U_13752))],[f_3543_2]) ).
cnf(f_3543_4,plain,
( hBOOL(hAPP(U_13752,sK329(U_13755,U_13754,U_13753,U_13752)))
| c_Wellfounded_Owf(U_13755,hAPP(c_Set_OCollect(tc_prod(U_13755,U_13755)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13755,U_13755,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13755,tc_HOL_Obool),tc_fun(U_13755,tc_HOL_Obool),U_13755),hAPP(c_COMBS(U_13755,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13755),c_fconj),U_13752))),hAPP(hAPP(c_COMBC(U_13755,tc_fun(U_13755,U_13755),tc_fun(U_13755,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13755,tc_HOL_Obool),tc_fun(tc_fun(U_13755,U_13755),tc_fun(U_13755,tc_HOL_Obool)),U_13755),c_COMBB(U_13755,tc_HOL_Obool,U_13755)),c_fequal)),U_13754))))) ),
inference(clausify,[status(thm)],[f_3543_3]) ).
cnf(f_3543_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_13753,hAPP(U_13754,sK329(U_13755,U_13754,U_13753,U_13752)))),hAPP(U_13753,sK329(U_13755,U_13754,U_13753,U_13752))))
| c_Wellfounded_Owf(U_13755,hAPP(c_Set_OCollect(tc_prod(U_13755,U_13755)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13755,U_13755,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_13755,tc_HOL_Obool),tc_fun(U_13755,tc_HOL_Obool),U_13755),hAPP(c_COMBS(U_13755,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13755),c_fconj),U_13752))),hAPP(hAPP(c_COMBC(U_13755,tc_fun(U_13755,U_13755),tc_fun(U_13755,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13755,tc_HOL_Obool),tc_fun(tc_fun(U_13755,U_13755),tc_fun(U_13755,tc_HOL_Obool)),U_13755),c_COMBB(U_13755,tc_HOL_Obool,U_13755)),c_fequal)),U_13754))))) ),
inference(clausify,[status(thm)],[f_3543_3]) ).
fof(f_3544_1,plain,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_DomainI]) ).
fof(f_3544_2,plain,
! [U_13760,U_13759,U_13758,U_13757,U_13756] :
( hBOOL(hAPP(hAPP(c_member(U_13756),U_13758),hAPP(c_Relation_ODomain(U_13756,U_13757),U_13760)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13756,U_13757)),hAPP(hAPP(c_Product__Type_OPair(U_13756,U_13757),U_13758),U_13759)),U_13760)) ),
inference(variable_rename,[status(thm)],[f_3544_1]) ).
cnf(f_3544_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_13756),U_13758),hAPP(c_Relation_ODomain(U_13756,U_13757),U_13760)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13756,U_13757)),hAPP(hAPP(c_Product__Type_OPair(U_13756,U_13757),U_13758),U_13759)),U_13760)) ),
inference(clausify,[status(thm)],[f_3544_2]) ).
fof(f_3545_1,plain,
! [V_A_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Domain__Id__on]) ).
fof(f_3545_2,plain,
! [U_13762,U_13761] : hAPP(c_Relation_ODomain(U_13761,U_13761),c_Relation_OId__on(U_13761,U_13762)) = U_13762,
inference(variable_rename,[status(thm)],[f_3545_1]) ).
cnf(f_3545_3,plain,
hAPP(c_Relation_ODomain(U_13761,U_13761),c_Relation_OId__on(U_13761,U_13762)) = U_13762,
inference(clausify,[status(thm)],[f_3545_2]) ).
fof(f_3546_1,plain,
! [V_r_2,T_c,T_b] :
( ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| V_r_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) )
& ( V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))
| hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_Domain__empty__iff]) ).
fof(f_3546_2,plain,
! [U_13765,U_13764,U_13763] :
( ( hAPP(c_Relation_ODomain(U_13763,U_13764),U_13765) = c_Orderings_Obot__class_Obot(tc_fun(U_13763,tc_HOL_Obool))
| U_13765 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13763,U_13764),tc_HOL_Obool)) )
& ( U_13765 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13763,U_13764),tc_HOL_Obool))
| hAPP(c_Relation_ODomain(U_13763,U_13764),U_13765) != c_Orderings_Obot__class_Obot(tc_fun(U_13763,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3546_1]) ).
fof(f_3546_3,plain,
( ! [U_13771,U_13769,U_13767] :
( hAPP(c_Relation_ODomain(U_13767,U_13769),U_13771) = c_Orderings_Obot__class_Obot(tc_fun(U_13767,tc_HOL_Obool))
| U_13771 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13767,U_13769),tc_HOL_Obool)) )
& ! [U_13770,U_13768,U_13766] :
( U_13770 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13766,U_13768),tc_HOL_Obool))
| hAPP(c_Relation_ODomain(U_13766,U_13768),U_13770) != c_Orderings_Obot__class_Obot(tc_fun(U_13766,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_3546_2]) ).
cnf(f_3546_4,plain,
( U_13770 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13766,U_13768),tc_HOL_Obool))
| hAPP(c_Relation_ODomain(U_13766,U_13768),U_13770) != c_Orderings_Obot__class_Obot(tc_fun(U_13766,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3546_3]) ).
cnf(f_3546_5,plain,
( hAPP(c_Relation_ODomain(U_13767,U_13769),U_13771) = c_Orderings_Obot__class_Obot(tc_fun(U_13767,tc_HOL_Obool))
| U_13771 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13767,U_13769),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3546_3]) ).
fof(f_3547_1,plain,
! [T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Domain__empty]) ).
fof(f_3547_2,plain,
! [U_13773,U_13772] : hAPP(c_Relation_ODomain(U_13772,U_13773),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13772,U_13773),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13772,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3547_1]) ).
cnf(f_3547_3,plain,
hAPP(c_Relation_ODomain(U_13772,U_13773),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13772,U_13773),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13772,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3547_2]) ).
fof(f_3548_1,plain,
! [V_s_2,V_r_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_s_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) ),
inference(fof_nnf,[status(thm)],[fact_Domain__mono]) ).
fof(f_3548_2,plain,
! [U_13777,U_13776,U_13775,U_13774] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13774,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13774,U_13775),U_13776)),hAPP(c_Relation_ODomain(U_13774,U_13775),U_13777)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13774,U_13775),tc_HOL_Obool)),U_13776),U_13777)) ),
inference(variable_rename,[status(thm)],[f_3548_1]) ).
cnf(f_3548_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13774,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13774,U_13775),U_13776)),hAPP(c_Relation_ODomain(U_13774,U_13775),U_13777)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13774,U_13775),tc_HOL_Obool)),U_13776),U_13777)) ),
inference(clausify,[status(thm)],[f_3548_2]) ).
fof(f_3549_1,plain,
! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Domain__Un__eq]) ).
fof(f_3549_2,plain,
! [U_13781,U_13780,U_13779,U_13778] : hAPP(c_Relation_ODomain(U_13778,U_13779),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13778,U_13779),tc_HOL_Obool)),U_13780),U_13781)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13778,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13778,U_13779),U_13780)),hAPP(c_Relation_ODomain(U_13778,U_13779),U_13781)),
inference(variable_rename,[status(thm)],[f_3549_1]) ).
cnf(f_3549_3,plain,
hAPP(c_Relation_ODomain(U_13778,U_13779),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_13778,U_13779),tc_HOL_Obool)),U_13780),U_13781)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13778,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13778,U_13779),U_13780)),hAPP(c_Relation_ODomain(U_13778,U_13779),U_13781)),
inference(clausify,[status(thm)],[f_3549_2]) ).
fof(f_3550_1,plain,
! [V_r_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__Domain]) ).
fof(f_3550_2,plain,
! [U_13784,U_13783,U_13782] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13782),hAPP(c_Relation_ODomain(U_13782,U_13783),U_13784)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13782,U_13783)),U_13784)) ),
inference(variable_rename,[status(thm)],[f_3550_1]) ).
cnf(f_3550_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13782),hAPP(c_Relation_ODomain(U_13782,U_13783),U_13784)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13782,U_13783)),U_13784)) ),
inference(clausify,[status(thm)],[f_3550_2]) ).
fof(f_3551_1,plain,
! [V_R_2,T_c,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),V_R_2) = hAPP(c_Relation_ODomain(T_b,T_c),V_R_2),
inference(fof_nnf,[status(thm)],[fact_fst__eq__Domain]) ).
fof(f_3551_2,plain,
! [U_13787,U_13786,U_13785] : hAPP(c_Set_Oimage(tc_prod(U_13785,U_13786),U_13785,c_Product__Type_Ofst(U_13785,U_13786)),U_13787) = hAPP(c_Relation_ODomain(U_13785,U_13786),U_13787),
inference(variable_rename,[status(thm)],[f_3551_1]) ).
cnf(f_3551_3,plain,
hAPP(c_Set_Oimage(tc_prod(U_13785,U_13786),U_13785,c_Product__Type_Ofst(U_13785,U_13786)),U_13787) = hAPP(c_Relation_ODomain(U_13785,U_13786),U_13787),
inference(clausify,[status(thm)],[f_3551_2]) ).
fof(f_3552_1,plain,
! [V_r_2,T_c,V_a_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
| ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) )
& ( ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_Domain__iff]) ).
fof(f_3552_2,plain,
! [U_13793,U_13792,U_13791,U_13790] :
( ( hBOOL(hAPP(hAPP(c_member(U_13790),U_13791),hAPP(c_Relation_ODomain(U_13790,U_13792),U_13793)))
| ! [U_13789] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13790,U_13792)),hAPP(hAPP(c_Product__Type_OPair(U_13790,U_13792),U_13791),U_13789)),U_13793)) )
& ( ? [U_13788] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13790,U_13792)),hAPP(hAPP(c_Product__Type_OPair(U_13790,U_13792),U_13791),U_13788)),U_13793))
| ~ hBOOL(hAPP(hAPP(c_member(U_13790),U_13791),hAPP(c_Relation_ODomain(U_13790,U_13792),U_13793))) ) ),
inference(variable_rename,[status(thm)],[f_3552_1]) ).
fof(f_3552_3,plain,
( ! [U_13801,U_13799,U_13797,U_13795] :
( hBOOL(hAPP(hAPP(c_member(U_13795),U_13797),hAPP(c_Relation_ODomain(U_13795,U_13799),U_13801)))
| ! [U_13789] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13795,U_13799)),hAPP(hAPP(c_Product__Type_OPair(U_13795,U_13799),U_13797),U_13789)),U_13801)) )
& ! [U_13800,U_13798,U_13796,U_13794] :
( ? [U_13788] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13794,U_13798)),hAPP(hAPP(c_Product__Type_OPair(U_13794,U_13798),U_13796),U_13788)),U_13800))
| ~ hBOOL(hAPP(hAPP(c_member(U_13794),U_13796),hAPP(c_Relation_ODomain(U_13794,U_13798),U_13800))) ) ),
inference(miniscope,[status(thm)],[f_3552_2]) ).
fof(f_3552_4,plain,
( ! [U_13801,U_13799,U_13797,U_13795] :
( hBOOL(hAPP(hAPP(c_member(U_13795),U_13797),hAPP(c_Relation_ODomain(U_13795,U_13799),U_13801)))
| ! [U_13789] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13795,U_13799)),hAPP(hAPP(c_Product__Type_OPair(U_13795,U_13799),U_13797),U_13789)),U_13801)) )
& ! [U_13800,U_13798,U_13796,U_13794] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13794,U_13798)),hAPP(hAPP(c_Product__Type_OPair(U_13794,U_13798),U_13796),sK330(U_13800,U_13798,U_13796,U_13794))),U_13800))
| ~ hBOOL(hAPP(hAPP(c_member(U_13794),U_13796),hAPP(c_Relation_ODomain(U_13794,U_13798),U_13800))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK330]),skolemize(U_13788,sK330(U_13800,U_13798,U_13796,U_13794))],[f_3552_3]) ).
cnf(f_3552_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13794,U_13798)),hAPP(hAPP(c_Product__Type_OPair(U_13794,U_13798),U_13796),sK330(U_13800,U_13798,U_13796,U_13794))),U_13800))
| ~ hBOOL(hAPP(hAPP(c_member(U_13794),U_13796),hAPP(c_Relation_ODomain(U_13794,U_13798),U_13800))) ),
inference(clausify,[status(thm)],[f_3552_4]) ).
cnf(f_3552_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_13795),U_13797),hAPP(c_Relation_ODomain(U_13795,U_13799),U_13801)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13795,U_13799)),hAPP(hAPP(c_Product__Type_OPair(U_13795,U_13799),U_13797),U_13789)),U_13801)) ),
inference(clausify,[status(thm)],[f_3552_4]) ).
fof(f_3553_1,plain,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),
inference(fof_nnf,[status(thm)],[fact_Domain__insert]) ).
fof(f_3553_2,plain,
! [U_13806,U_13805,U_13804,U_13803,U_13802] : hAPP(c_Relation_ODomain(U_13802,U_13803),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13802,U_13803)),hAPP(hAPP(c_Product__Type_OPair(U_13802,U_13803),U_13804),U_13805)),U_13806)) = hAPP(hAPP(c_Set_Oinsert(U_13802),U_13804),hAPP(c_Relation_ODomain(U_13802,U_13803),U_13806)),
inference(variable_rename,[status(thm)],[f_3553_1]) ).
cnf(f_3553_3,plain,
hAPP(c_Relation_ODomain(U_13802,U_13803),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_13802,U_13803)),hAPP(hAPP(c_Product__Type_OPair(U_13802,U_13803),U_13804),U_13805)),U_13806)) = hAPP(hAPP(c_Set_Oinsert(U_13802),U_13804),hAPP(c_Relation_ODomain(U_13802,U_13803),U_13806)),
inference(clausify,[status(thm)],[f_3553_2]) ).
fof(f_3554_1,plain,
! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_Domain__Int__subset]) ).
fof(f_3554_2,plain,
! [U_13810,U_13809,U_13808,U_13807] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13807,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13807,U_13808),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13807,U_13808),tc_HOL_Obool)),U_13809),U_13810))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13807,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13807,U_13808),U_13809)),hAPP(c_Relation_ODomain(U_13807,U_13808),U_13810)))),
inference(variable_rename,[status(thm)],[f_3554_1]) ).
cnf(f_3554_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13807,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13807,U_13808),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_13807,U_13808),tc_HOL_Obool)),U_13809),U_13810))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13807,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13807,U_13808),U_13809)),hAPP(c_Relation_ODomain(U_13807,U_13808),U_13810)))),
inference(clausify,[status(thm)],[f_3554_2]) ).
fof(f_3555_1,plain,
! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2))),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_Domain__Diff__subset]) ).
fof(f_3555_2,plain,
! [U_13814,U_13813,U_13812,U_13811] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13811,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13811,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13811,U_13812),U_13813)),hAPP(c_Relation_ODomain(U_13811,U_13812),U_13814))),hAPP(c_Relation_ODomain(U_13811,U_13812),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13811,U_13812),tc_HOL_Obool)),U_13813),U_13814)))),
inference(variable_rename,[status(thm)],[f_3555_1]) ).
cnf(f_3555_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13811,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13811,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13811,U_13812),U_13813)),hAPP(c_Relation_ODomain(U_13811,U_13812),U_13814))),hAPP(c_Relation_ODomain(U_13811,U_13812),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_13811,U_13812),tc_HOL_Obool)),U_13813),U_13814)))),
inference(clausify,[status(thm)],[f_3555_2]) ).
fof(f_3556_1,plain,
! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_r_2)),
inference(fof_nnf,[status(thm)],[fact_Field__def]) ).
fof(f_3556_2,plain,
! [U_13816,U_13815] : hAPP(c_Relation_OField(U_13815),U_13816) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13815,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13815,U_13815),U_13816)),hAPP(c_Relation_ORange(U_13815,U_13815),U_13816)),
inference(variable_rename,[status(thm)],[f_3556_1]) ).
cnf(f_3556_3,plain,
hAPP(c_Relation_OField(U_13815),U_13816) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13815,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_13815,U_13815),U_13816)),hAPP(c_Relation_ORange(U_13815,U_13815),U_13816)),
inference(clausify,[status(thm)],[f_3556_2]) ).
fof(f_3557_1,plain,
! [V_P_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_P_2)),
inference(fof_nnf,[status(thm)],[fact_Domain__Collect__split]) ).
fof(f_3557_2,plain,
! [U_13819,U_13818,U_13817] : hAPP(c_Relation_ODomain(U_13817,U_13818),hAPP(c_Set_OCollect(tc_prod(U_13817,U_13818)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13817,U_13818,tc_HOL_Obool),U_13819))) = hAPP(c_Set_OCollect(U_13817),hAPP(hAPP(c_COMBB(tc_fun(U_13818,tc_HOL_Obool),tc_HOL_Obool,U_13817),c_HOL_OEx(U_13818)),U_13819)),
inference(variable_rename,[status(thm)],[f_3557_1]) ).
cnf(f_3557_3,plain,
hAPP(c_Relation_ODomain(U_13817,U_13818),hAPP(c_Set_OCollect(tc_prod(U_13817,U_13818)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13817,U_13818,tc_HOL_Obool),U_13819))) = hAPP(c_Set_OCollect(U_13817),hAPP(hAPP(c_COMBB(tc_fun(U_13818,tc_HOL_Obool),tc_HOL_Obool,U_13817),c_HOL_OEx(U_13818)),U_13819)),
inference(clausify,[status(thm)],[f_3557_2]) ).
fof(f_3558_1,plain,
! [V_x_2,V_r_2,T_c,T_b] :
( ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) )
& ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
| ~ hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_r_2)),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_DomainP__Domain__eq]) ).
fof(f_3558_2,plain,
! [U_13823,U_13822,U_13821,U_13820] :
( ( hBOOL(hAPP(c_Predicate_ODomainP(U_13820,U_13821,hAPP(hAPP(c_COMBC(U_13820,tc_fun(tc_prod(U_13820,U_13821),tc_HOL_Obool),tc_fun(U_13821,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13821,tc_fun(tc_fun(tc_prod(U_13820,U_13821),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13820,U_13821),tc_HOL_Obool),tc_fun(U_13821,tc_HOL_Obool)),U_13820),c_COMBC(U_13821,tc_fun(tc_prod(U_13820,U_13821),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13821,tc_prod(U_13820,U_13821)),tc_fun(U_13821,tc_fun(tc_fun(tc_prod(U_13820,U_13821),tc_HOL_Obool),tc_HOL_Obool)),U_13820),hAPP(c_COMBB(tc_prod(U_13820,U_13821),tc_fun(tc_fun(tc_prod(U_13820,U_13821),tc_HOL_Obool),tc_HOL_Obool),U_13821),c_member(tc_prod(U_13820,U_13821)))),c_Product__Type_OPair(U_13820,U_13821)))),U_13822)),U_13823))
| ~ hBOOL(hAPP(hAPP(c_member(U_13820),U_13823),hAPP(c_Relation_ODomain(U_13820,U_13821),U_13822))) )
& ( hBOOL(hAPP(hAPP(c_member(U_13820),U_13823),hAPP(c_Relation_ODomain(U_13820,U_13821),U_13822)))
| ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13820,U_13821,hAPP(hAPP(c_COMBC(U_13820,tc_fun(tc_prod(U_13820,U_13821),tc_HOL_Obool),tc_fun(U_13821,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13821,tc_fun(tc_fun(tc_prod(U_13820,U_13821),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13820,U_13821),tc_HOL_Obool),tc_fun(U_13821,tc_HOL_Obool)),U_13820),c_COMBC(U_13821,tc_fun(tc_prod(U_13820,U_13821),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13821,tc_prod(U_13820,U_13821)),tc_fun(U_13821,tc_fun(tc_fun(tc_prod(U_13820,U_13821),tc_HOL_Obool),tc_HOL_Obool)),U_13820),hAPP(c_COMBB(tc_prod(U_13820,U_13821),tc_fun(tc_fun(tc_prod(U_13820,U_13821),tc_HOL_Obool),tc_HOL_Obool),U_13821),c_member(tc_prod(U_13820,U_13821)))),c_Product__Type_OPair(U_13820,U_13821)))),U_13822)),U_13823)) ) ),
inference(variable_rename,[status(thm)],[f_3558_1]) ).
fof(f_3558_3,plain,
( ! [U_13831,U_13829,U_13827,U_13825] :
( hBOOL(hAPP(c_Predicate_ODomainP(U_13825,U_13827,hAPP(hAPP(c_COMBC(U_13825,tc_fun(tc_prod(U_13825,U_13827),tc_HOL_Obool),tc_fun(U_13827,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13827,tc_fun(tc_fun(tc_prod(U_13825,U_13827),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13825,U_13827),tc_HOL_Obool),tc_fun(U_13827,tc_HOL_Obool)),U_13825),c_COMBC(U_13827,tc_fun(tc_prod(U_13825,U_13827),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13827,tc_prod(U_13825,U_13827)),tc_fun(U_13827,tc_fun(tc_fun(tc_prod(U_13825,U_13827),tc_HOL_Obool),tc_HOL_Obool)),U_13825),hAPP(c_COMBB(tc_prod(U_13825,U_13827),tc_fun(tc_fun(tc_prod(U_13825,U_13827),tc_HOL_Obool),tc_HOL_Obool),U_13827),c_member(tc_prod(U_13825,U_13827)))),c_Product__Type_OPair(U_13825,U_13827)))),U_13829)),U_13831))
| ~ hBOOL(hAPP(hAPP(c_member(U_13825),U_13831),hAPP(c_Relation_ODomain(U_13825,U_13827),U_13829))) )
& ! [U_13830,U_13828,U_13826,U_13824] :
( hBOOL(hAPP(hAPP(c_member(U_13824),U_13830),hAPP(c_Relation_ODomain(U_13824,U_13826),U_13828)))
| ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13824,U_13826,hAPP(hAPP(c_COMBC(U_13824,tc_fun(tc_prod(U_13824,U_13826),tc_HOL_Obool),tc_fun(U_13826,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13826,tc_fun(tc_fun(tc_prod(U_13824,U_13826),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13824,U_13826),tc_HOL_Obool),tc_fun(U_13826,tc_HOL_Obool)),U_13824),c_COMBC(U_13826,tc_fun(tc_prod(U_13824,U_13826),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13826,tc_prod(U_13824,U_13826)),tc_fun(U_13826,tc_fun(tc_fun(tc_prod(U_13824,U_13826),tc_HOL_Obool),tc_HOL_Obool)),U_13824),hAPP(c_COMBB(tc_prod(U_13824,U_13826),tc_fun(tc_fun(tc_prod(U_13824,U_13826),tc_HOL_Obool),tc_HOL_Obool),U_13826),c_member(tc_prod(U_13824,U_13826)))),c_Product__Type_OPair(U_13824,U_13826)))),U_13828)),U_13830)) ) ),
inference(miniscope,[status(thm)],[f_3558_2]) ).
cnf(f_3558_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_13824),U_13830),hAPP(c_Relation_ODomain(U_13824,U_13826),U_13828)))
| ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13824,U_13826,hAPP(hAPP(c_COMBC(U_13824,tc_fun(tc_prod(U_13824,U_13826),tc_HOL_Obool),tc_fun(U_13826,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13826,tc_fun(tc_fun(tc_prod(U_13824,U_13826),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13824,U_13826),tc_HOL_Obool),tc_fun(U_13826,tc_HOL_Obool)),U_13824),c_COMBC(U_13826,tc_fun(tc_prod(U_13824,U_13826),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13826,tc_prod(U_13824,U_13826)),tc_fun(U_13826,tc_fun(tc_fun(tc_prod(U_13824,U_13826),tc_HOL_Obool),tc_HOL_Obool)),U_13824),hAPP(c_COMBB(tc_prod(U_13824,U_13826),tc_fun(tc_fun(tc_prod(U_13824,U_13826),tc_HOL_Obool),tc_HOL_Obool),U_13826),c_member(tc_prod(U_13824,U_13826)))),c_Product__Type_OPair(U_13824,U_13826)))),U_13828)),U_13830)) ),
inference(clausify,[status(thm)],[f_3558_3]) ).
cnf(f_3558_5,plain,
( hBOOL(hAPP(c_Predicate_ODomainP(U_13825,U_13827,hAPP(hAPP(c_COMBC(U_13825,tc_fun(tc_prod(U_13825,U_13827),tc_HOL_Obool),tc_fun(U_13827,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13827,tc_fun(tc_fun(tc_prod(U_13825,U_13827),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13825,U_13827),tc_HOL_Obool),tc_fun(U_13827,tc_HOL_Obool)),U_13825),c_COMBC(U_13827,tc_fun(tc_prod(U_13825,U_13827),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13827,tc_prod(U_13825,U_13827)),tc_fun(U_13827,tc_fun(tc_fun(tc_prod(U_13825,U_13827),tc_HOL_Obool),tc_HOL_Obool)),U_13825),hAPP(c_COMBB(tc_prod(U_13825,U_13827),tc_fun(tc_fun(tc_prod(U_13825,U_13827),tc_HOL_Obool),tc_HOL_Obool),U_13827),c_member(tc_prod(U_13825,U_13827)))),c_Product__Type_OPair(U_13825,U_13827)))),U_13829)),U_13831))
| ~ hBOOL(hAPP(hAPP(c_member(U_13825),U_13831),hAPP(c_Relation_ODomain(U_13825,U_13827),U_13829))) ),
inference(clausify,[status(thm)],[f_3558_3]) ).
fof(f_3559_1,plain,
! [V_r_2,T_c,V_a_2,T_b] :
( ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_DomainE]) ).
fof(f_3559_2,plain,
! [U_13836,U_13835,U_13834,U_13833] :
( ? [U_13832] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_13833,U_13835)),hAPP(hAPP(c_Product__Type_OPair(U_13833,U_13835),U_13834),U_13832)),U_13836))
| ~ hBOOL(hAPP(hAPP(c_member(U_13833),U_13834),hAPP(c_Relation_ODomain(U_13833,U_13835),U_13836))) ),
inference(variable_rename,[status(thm)],[f_3559_1]) ).
fof(f_3559_3,plain,
! [U_13836,U_13835,U_13834,U_13833] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13833,U_13835)),hAPP(hAPP(c_Product__Type_OPair(U_13833,U_13835),U_13834),sK331(U_13836,U_13835,U_13834,U_13833))),U_13836))
| ~ hBOOL(hAPP(hAPP(c_member(U_13833),U_13834),hAPP(c_Relation_ODomain(U_13833,U_13835),U_13836))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK331]),skolemize(U_13832,sK331(U_13836,U_13835,U_13834,U_13833))],[f_3559_2]) ).
cnf(f_3559_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13833,U_13835)),hAPP(hAPP(c_Product__Type_OPair(U_13833,U_13835),U_13834),sK331(U_13836,U_13835,U_13834,U_13833))),U_13836))
| ~ hBOOL(hAPP(hAPP(c_member(U_13833),U_13834),hAPP(c_Relation_ODomain(U_13833,U_13835),U_13836))) ),
inference(clausify,[status(thm)],[f_3559_3]) ).
fof(f_3560_1,plain,
! [V_r_2,T_b] :
( ( c_Wellfounded_OwfP(T_b,V_r_2)
| ~ c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) )
& ( c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2)))
| ~ c_Wellfounded_OwfP(T_b,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_wfP__def]) ).
fof(f_3560_2,plain,
! [U_13838,U_13837] :
( ( c_Wellfounded_OwfP(U_13837,U_13838)
| ~ c_Wellfounded_Owf(U_13837,hAPP(c_Set_OCollect(tc_prod(U_13837,U_13837)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13837,U_13837,tc_HOL_Obool),U_13838))) )
& ( c_Wellfounded_Owf(U_13837,hAPP(c_Set_OCollect(tc_prod(U_13837,U_13837)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13837,U_13837,tc_HOL_Obool),U_13838)))
| ~ c_Wellfounded_OwfP(U_13837,U_13838) ) ),
inference(variable_rename,[status(thm)],[f_3560_1]) ).
fof(f_3560_3,plain,
( ! [U_13842,U_13840] :
( c_Wellfounded_OwfP(U_13840,U_13842)
| ~ c_Wellfounded_Owf(U_13840,hAPP(c_Set_OCollect(tc_prod(U_13840,U_13840)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13840,U_13840,tc_HOL_Obool),U_13842))) )
& ! [U_13841,U_13839] :
( c_Wellfounded_Owf(U_13839,hAPP(c_Set_OCollect(tc_prod(U_13839,U_13839)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13839,U_13839,tc_HOL_Obool),U_13841)))
| ~ c_Wellfounded_OwfP(U_13839,U_13841) ) ),
inference(miniscope,[status(thm)],[f_3560_2]) ).
cnf(f_3560_4,plain,
( c_Wellfounded_Owf(U_13839,hAPP(c_Set_OCollect(tc_prod(U_13839,U_13839)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13839,U_13839,tc_HOL_Obool),U_13841)))
| ~ c_Wellfounded_OwfP(U_13839,U_13841) ),
inference(clausify,[status(thm)],[f_3560_3]) ).
cnf(f_3560_5,plain,
( c_Wellfounded_OwfP(U_13840,U_13842)
| ~ c_Wellfounded_Owf(U_13840,hAPP(c_Set_OCollect(tc_prod(U_13840,U_13840)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13840,U_13840,tc_HOL_Obool),U_13842))) ),
inference(clausify,[status(thm)],[f_3560_3]) ).
fof(f_3561_1,plain,
! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2))
| ~ hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) ),
inference(fof_nnf,[status(thm)],[fact_DomainP_Ointros]) ).
fof(f_3561_2,plain,
! [U_13847,U_13846,U_13845,U_13844,U_13843] :
( hBOOL(hAPP(c_Predicate_ODomainP(U_13846,U_13847,U_13843),U_13844))
| ~ hBOOL(hAPP(hAPP(U_13843,U_13844),U_13845)) ),
inference(variable_rename,[status(thm)],[f_3561_1]) ).
cnf(f_3561_3,plain,
( hBOOL(hAPP(c_Predicate_ODomainP(U_13846,U_13847,U_13843),U_13844))
| ~ hBOOL(hAPP(hAPP(U_13843,U_13844),U_13845)) ),
inference(clausify,[status(thm)],[f_3561_2]) ).
fof(f_3562_1,plain,
! [T_b] : c_Wellfounded_OwfP(T_b,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse))),
inference(fof_nnf,[status(thm)],[fact_wfP__empty]) ).
fof(f_3562_2,plain,
! [U_13848] : c_Wellfounded_OwfP(U_13848,hAPP(c_COMBK(tc_fun(U_13848,tc_HOL_Obool),U_13848),hAPP(c_COMBK(tc_HOL_Obool,U_13848),c_fFalse))),
inference(variable_rename,[status(thm)],[f_3562_1]) ).
cnf(f_3562_3,plain,
c_Wellfounded_OwfP(U_13848,hAPP(c_COMBK(tc_fun(U_13848,tc_HOL_Obool),U_13848),hAPP(c_COMBK(tc_HOL_Obool,U_13848),c_fFalse))),
inference(clausify,[status(thm)],[f_3562_2]) ).
fof(f_3563_1,plain,
! [V_r_2,T_b] :
( ( c_Wellfounded_OwfP(T_b,V_r_2)
| ? [B_x1] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) )
& ( ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1))
| ~ c_Wellfounded_OwfP(T_b,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_wfP__accp__iff]) ).
fof(f_3563_2,plain,
! [U_13852,U_13851] :
( ( c_Wellfounded_OwfP(U_13851,U_13852)
| ? [U_13850] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13851,U_13852),U_13850)) )
& ( ! [U_13849] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_13851,U_13852),U_13849))
| ~ c_Wellfounded_OwfP(U_13851,U_13852) ) ),
inference(variable_rename,[status(thm)],[f_3563_1]) ).
fof(f_3563_3,plain,
( ! [U_13856,U_13854] :
( c_Wellfounded_OwfP(U_13854,U_13856)
| ? [U_13850] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13854,U_13856),U_13850)) )
& ! [U_13855,U_13853] :
( ! [U_13849] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_13853,U_13855),U_13849))
| ~ c_Wellfounded_OwfP(U_13853,U_13855) ) ),
inference(miniscope,[status(thm)],[f_3563_2]) ).
fof(f_3563_4,plain,
( ! [U_13856,U_13854] :
( c_Wellfounded_OwfP(U_13854,U_13856)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13854,U_13856),sK332(U_13856,U_13854))) )
& ! [U_13855,U_13853] :
( ! [U_13849] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_13853,U_13855),U_13849))
| ~ c_Wellfounded_OwfP(U_13853,U_13855) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK332]),skolemize(U_13850,sK332(U_13856,U_13854))],[f_3563_3]) ).
cnf(f_3563_5,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_13853,U_13855),U_13849))
| ~ c_Wellfounded_OwfP(U_13853,U_13855) ),
inference(clausify,[status(thm)],[f_3563_4]) ).
cnf(f_3563_6,plain,
( c_Wellfounded_OwfP(U_13854,U_13856)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_13854,U_13856),sK332(U_13856,U_13854))) ),
inference(clausify,[status(thm)],[f_3563_4]) ).
fof(f_3564_1,plain,
! [V_x_2,V_r_2,T_b] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2))
| ~ c_Wellfounded_OwfP(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_accp__wfPD]) ).
fof(f_3564_2,plain,
! [U_13859,U_13858,U_13857] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_13857,U_13858),U_13859))
| ~ c_Wellfounded_OwfP(U_13857,U_13858) ),
inference(variable_rename,[status(thm)],[f_3564_1]) ).
cnf(f_3564_3,plain,
( hBOOL(hAPP(c_Wellfounded_Oaccp(U_13857,U_13858),U_13859))
| ~ c_Wellfounded_OwfP(U_13857,U_13858) ),
inference(clausify,[status(thm)],[f_3564_2]) ).
fof(f_3565_1,plain,
! [V_p_2,V_r_2,T_b] :
( c_Wellfounded_OwfP(T_b,V_p_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_p_2),V_r_2))
| ~ c_Wellfounded_OwfP(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wfP__subset]) ).
fof(f_3565_2,plain,
! [U_13862,U_13861,U_13860] :
( c_Wellfounded_OwfP(U_13860,U_13862)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13860,tc_fun(U_13860,tc_HOL_Obool))),U_13862),U_13861))
| ~ c_Wellfounded_OwfP(U_13860,U_13861) ),
inference(variable_rename,[status(thm)],[f_3565_1]) ).
cnf(f_3565_3,plain,
( c_Wellfounded_OwfP(U_13860,U_13862)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13860,tc_fun(U_13860,tc_HOL_Obool))),U_13862),U_13861))
| ~ c_Wellfounded_OwfP(U_13860,U_13861) ),
inference(clausify,[status(thm)],[f_3565_2]) ).
fof(f_3566_1,plain,
! [V_a1_2,V_r_2,T_c,T_b] :
( ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
| ! [B_x1] : ~ hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) )
& ( ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1))
| ~ hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_DomainP_Oequations]) ).
fof(f_3566_2,plain,
! [U_13868,U_13867,U_13866,U_13865] :
( ( hBOOL(hAPP(c_Predicate_ODomainP(U_13865,U_13866,U_13867),U_13868))
| ! [U_13864] : ~ hBOOL(hAPP(hAPP(U_13867,U_13868),U_13864)) )
& ( ? [U_13863] : hBOOL(hAPP(hAPP(U_13867,U_13868),U_13863))
| ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13865,U_13866,U_13867),U_13868)) ) ),
inference(variable_rename,[status(thm)],[f_3566_1]) ).
fof(f_3566_3,plain,
( ! [U_13876,U_13874] :
( ! [U_13872,U_13870] : hBOOL(hAPP(c_Predicate_ODomainP(U_13870,U_13872,U_13874),U_13876))
| ! [U_13864] : ~ hBOOL(hAPP(hAPP(U_13874,U_13876),U_13864)) )
& ! [U_13875,U_13873] :
( ! [U_13871,U_13869] : ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13869,U_13871,U_13873),U_13875))
| ? [U_13863] : hBOOL(hAPP(hAPP(U_13873,U_13875),U_13863)) ) ),
inference(miniscope,[status(thm)],[f_3566_2]) ).
fof(f_3566_4,plain,
( ! [U_13876,U_13874] :
( ! [U_13872,U_13870] : hBOOL(hAPP(c_Predicate_ODomainP(U_13870,U_13872,U_13874),U_13876))
| ! [U_13864] : ~ hBOOL(hAPP(hAPP(U_13874,U_13876),U_13864)) )
& ! [U_13875,U_13873] :
( ! [U_13871,U_13869] : ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13869,U_13871,U_13873),U_13875))
| hBOOL(hAPP(hAPP(U_13873,U_13875),sK333(U_13875,U_13873))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK333]),skolemize(U_13863,sK333(U_13875,U_13873))],[f_3566_3]) ).
cnf(f_3566_5,plain,
( ~ hBOOL(hAPP(c_Predicate_ODomainP(U_13869,U_13871,U_13873),U_13875))
| hBOOL(hAPP(hAPP(U_13873,U_13875),sK333(U_13875,U_13873))) ),
inference(clausify,[status(thm)],[f_3566_4]) ).
cnf(f_3566_6,plain,
( hBOOL(hAPP(c_Predicate_ODomainP(U_13870,U_13872,U_13874),U_13876))
| ~ hBOOL(hAPP(hAPP(U_13874,U_13876),U_13864)) ),
inference(clausify,[status(thm)],[f_3566_4]) ).
fof(f_3567_1,plain,
! [V_R_2,T_b] :
( c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2))
| ~ c_Wellfounded_Owf(T_b,V_R_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__in__rel]) ).
fof(f_3567_2,plain,
! [U_13878,U_13877] :
( c_Wellfounded_OwfP(U_13877,c_FunDef_Oin__rel(U_13877,U_13877,U_13878))
| ~ c_Wellfounded_Owf(U_13877,U_13878) ),
inference(variable_rename,[status(thm)],[f_3567_1]) ).
cnf(f_3567_3,plain,
( c_Wellfounded_OwfP(U_13877,c_FunDef_Oin__rel(U_13877,U_13877,U_13878))
| ~ c_Wellfounded_Owf(U_13877,U_13878) ),
inference(clausify,[status(thm)],[f_3567_2]) ).
fof(f_3568_1,plain,
! [V_r_2,T_b] :
( ( c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2))
| ~ c_Wellfounded_Owf(T_b,V_r_2) )
& ( c_Wellfounded_Owf(T_b,V_r_2)
| ~ c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_wfP__wf__eq]) ).
fof(f_3568_2,plain,
! [U_13880,U_13879] :
( ( c_Wellfounded_OwfP(U_13879,hAPP(hAPP(c_COMBC(U_13879,tc_fun(tc_prod(U_13879,U_13879),tc_HOL_Obool),tc_fun(U_13879,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13879,tc_fun(tc_fun(tc_prod(U_13879,U_13879),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13879,U_13879),tc_HOL_Obool),tc_fun(U_13879,tc_HOL_Obool)),U_13879),c_COMBC(U_13879,tc_fun(tc_prod(U_13879,U_13879),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13879,tc_prod(U_13879,U_13879)),tc_fun(U_13879,tc_fun(tc_fun(tc_prod(U_13879,U_13879),tc_HOL_Obool),tc_HOL_Obool)),U_13879),hAPP(c_COMBB(tc_prod(U_13879,U_13879),tc_fun(tc_fun(tc_prod(U_13879,U_13879),tc_HOL_Obool),tc_HOL_Obool),U_13879),c_member(tc_prod(U_13879,U_13879)))),c_Product__Type_OPair(U_13879,U_13879)))),U_13880))
| ~ c_Wellfounded_Owf(U_13879,U_13880) )
& ( c_Wellfounded_Owf(U_13879,U_13880)
| ~ c_Wellfounded_OwfP(U_13879,hAPP(hAPP(c_COMBC(U_13879,tc_fun(tc_prod(U_13879,U_13879),tc_HOL_Obool),tc_fun(U_13879,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13879,tc_fun(tc_fun(tc_prod(U_13879,U_13879),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13879,U_13879),tc_HOL_Obool),tc_fun(U_13879,tc_HOL_Obool)),U_13879),c_COMBC(U_13879,tc_fun(tc_prod(U_13879,U_13879),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13879,tc_prod(U_13879,U_13879)),tc_fun(U_13879,tc_fun(tc_fun(tc_prod(U_13879,U_13879),tc_HOL_Obool),tc_HOL_Obool)),U_13879),hAPP(c_COMBB(tc_prod(U_13879,U_13879),tc_fun(tc_fun(tc_prod(U_13879,U_13879),tc_HOL_Obool),tc_HOL_Obool),U_13879),c_member(tc_prod(U_13879,U_13879)))),c_Product__Type_OPair(U_13879,U_13879)))),U_13880)) ) ),
inference(variable_rename,[status(thm)],[f_3568_1]) ).
fof(f_3568_3,plain,
( ! [U_13884,U_13882] :
( c_Wellfounded_OwfP(U_13882,hAPP(hAPP(c_COMBC(U_13882,tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_fun(U_13882,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13882,tc_fun(tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_fun(U_13882,tc_HOL_Obool)),U_13882),c_COMBC(U_13882,tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13882,tc_prod(U_13882,U_13882)),tc_fun(U_13882,tc_fun(tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_HOL_Obool)),U_13882),hAPP(c_COMBB(tc_prod(U_13882,U_13882),tc_fun(tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_HOL_Obool),U_13882),c_member(tc_prod(U_13882,U_13882)))),c_Product__Type_OPair(U_13882,U_13882)))),U_13884))
| ~ c_Wellfounded_Owf(U_13882,U_13884) )
& ! [U_13883,U_13881] :
( c_Wellfounded_Owf(U_13881,U_13883)
| ~ c_Wellfounded_OwfP(U_13881,hAPP(hAPP(c_COMBC(U_13881,tc_fun(tc_prod(U_13881,U_13881),tc_HOL_Obool),tc_fun(U_13881,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13881,tc_fun(tc_fun(tc_prod(U_13881,U_13881),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13881,U_13881),tc_HOL_Obool),tc_fun(U_13881,tc_HOL_Obool)),U_13881),c_COMBC(U_13881,tc_fun(tc_prod(U_13881,U_13881),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13881,tc_prod(U_13881,U_13881)),tc_fun(U_13881,tc_fun(tc_fun(tc_prod(U_13881,U_13881),tc_HOL_Obool),tc_HOL_Obool)),U_13881),hAPP(c_COMBB(tc_prod(U_13881,U_13881),tc_fun(tc_fun(tc_prod(U_13881,U_13881),tc_HOL_Obool),tc_HOL_Obool),U_13881),c_member(tc_prod(U_13881,U_13881)))),c_Product__Type_OPair(U_13881,U_13881)))),U_13883)) ) ),
inference(miniscope,[status(thm)],[f_3568_2]) ).
cnf(f_3568_4,plain,
( c_Wellfounded_Owf(U_13881,U_13883)
| ~ c_Wellfounded_OwfP(U_13881,hAPP(hAPP(c_COMBC(U_13881,tc_fun(tc_prod(U_13881,U_13881),tc_HOL_Obool),tc_fun(U_13881,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13881,tc_fun(tc_fun(tc_prod(U_13881,U_13881),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13881,U_13881),tc_HOL_Obool),tc_fun(U_13881,tc_HOL_Obool)),U_13881),c_COMBC(U_13881,tc_fun(tc_prod(U_13881,U_13881),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13881,tc_prod(U_13881,U_13881)),tc_fun(U_13881,tc_fun(tc_fun(tc_prod(U_13881,U_13881),tc_HOL_Obool),tc_HOL_Obool)),U_13881),hAPP(c_COMBB(tc_prod(U_13881,U_13881),tc_fun(tc_fun(tc_prod(U_13881,U_13881),tc_HOL_Obool),tc_HOL_Obool),U_13881),c_member(tc_prod(U_13881,U_13881)))),c_Product__Type_OPair(U_13881,U_13881)))),U_13883)) ),
inference(clausify,[status(thm)],[f_3568_3]) ).
cnf(f_3568_5,plain,
( c_Wellfounded_OwfP(U_13882,hAPP(hAPP(c_COMBC(U_13882,tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_fun(U_13882,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13882,tc_fun(tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_fun(U_13882,tc_HOL_Obool)),U_13882),c_COMBC(U_13882,tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13882,tc_prod(U_13882,U_13882)),tc_fun(U_13882,tc_fun(tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_HOL_Obool)),U_13882),hAPP(c_COMBB(tc_prod(U_13882,U_13882),tc_fun(tc_fun(tc_prod(U_13882,U_13882),tc_HOL_Obool),tc_HOL_Obool),U_13882),c_member(tc_prod(U_13882,U_13882)))),c_Product__Type_OPair(U_13882,U_13882)))),U_13884))
| ~ c_Wellfounded_Owf(U_13882,U_13884) ),
inference(clausify,[status(thm)],[f_3568_3]) ).
fof(f_3569_1,plain,
! [V_r_2,T_b] :
( c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2)))
| ~ c_Wellfounded_OwfP(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wfP__acyclicP]) ).
fof(f_3569_2,plain,
! [U_13886,U_13885] :
( c_Wellfounded_Oacyclic(U_13885,hAPP(c_Set_OCollect(tc_prod(U_13885,U_13885)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13885,U_13885,tc_HOL_Obool),U_13886)))
| ~ c_Wellfounded_OwfP(U_13885,U_13886) ),
inference(variable_rename,[status(thm)],[f_3569_1]) ).
cnf(f_3569_3,plain,
( c_Wellfounded_Oacyclic(U_13885,hAPP(c_Set_OCollect(tc_prod(U_13885,U_13885)),hAPP(c_Product__Type_Oprod_Oprod__case(U_13885,U_13885,tc_HOL_Obool),U_13886)))
| ~ c_Wellfounded_OwfP(U_13885,U_13886) ),
inference(clausify,[status(thm)],[f_3569_2]) ).
fof(f_3570_1,plain,
! [V_f_2,T_c,V_A_2,T_b] :
( ? [B_x] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_f_2,B_x))))))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_pigeonhole__infinite]) ).
fof(f_3570_2,plain,
! [U_13891,U_13890,U_13889,U_13888] :
( ? [U_13887] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13888),hAPP(c_Set_OCollect(U_13888),hAPP(hAPP(c_COMBS(U_13888,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13888),c_fconj),hAPP(hAPP(c_COMBC(U_13888,tc_fun(U_13888,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13888)),U_13889))),hAPP(hAPP(c_COMBC(U_13888,U_13890,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13890,tc_fun(U_13890,tc_HOL_Obool),U_13888),c_fequal),U_13891)),hAPP(U_13891,U_13887))))))
& hBOOL(hAPP(hAPP(c_member(U_13888),U_13887),U_13889)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13890),hAPP(c_Set_Oimage(U_13888,U_13890,U_13891),U_13889)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_13888),U_13889)) ),
inference(variable_rename,[status(thm)],[f_3570_1]) ).
fof(f_3570_3,plain,
! [U_13891,U_13890,U_13889,U_13888] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13888),hAPP(c_Set_OCollect(U_13888),hAPP(hAPP(c_COMBS(U_13888,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13888),c_fconj),hAPP(hAPP(c_COMBC(U_13888,tc_fun(U_13888,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13888)),U_13889))),hAPP(hAPP(c_COMBC(U_13888,U_13890,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13890,tc_fun(U_13890,tc_HOL_Obool),U_13888),c_fequal),U_13891)),hAPP(U_13891,sK334(U_13891,U_13890,U_13889,U_13888)))))))
& hBOOL(hAPP(hAPP(c_member(U_13888),sK334(U_13891,U_13890,U_13889,U_13888)),U_13889)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13890),hAPP(c_Set_Oimage(U_13888,U_13890,U_13891),U_13889)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_13888),U_13889)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK334]),skolemize(U_13887,sK334(U_13891,U_13890,U_13889,U_13888))],[f_3570_2]) ).
cnf(f_3570_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_13888),sK334(U_13891,U_13890,U_13889,U_13888)),U_13889))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13890),hAPP(c_Set_Oimage(U_13888,U_13890,U_13891),U_13889)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_13888),U_13889)) ),
inference(clausify,[status(thm)],[f_3570_3]) ).
cnf(f_3570_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13888),hAPP(c_Set_OCollect(U_13888),hAPP(hAPP(c_COMBS(U_13888,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13888),c_fconj),hAPP(hAPP(c_COMBC(U_13888,tc_fun(U_13888,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13888)),U_13889))),hAPP(hAPP(c_COMBC(U_13888,U_13890,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13890,tc_fun(U_13890,tc_HOL_Obool),U_13888),c_fequal),U_13891)),hAPP(U_13891,sK334(U_13891,U_13890,U_13889,U_13888)))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13890),hAPP(c_Set_Oimage(U_13888,U_13890,U_13891),U_13889)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_13888),U_13889)) ),
inference(clausify,[status(thm)],[f_3570_3]) ).
fof(f_3571_1,plain,
! [V_x_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))
& V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) ),
inference(fof_nnf,[status(thm)],[fact_Abs__Integ__cases]) ).
fof(f_3571_2,plain,
! [U_13893] :
? [U_13892] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13892),c_Int_OInteg))
& U_13893 = hAPP(c_Int_OAbs__Integ,U_13892) ),
inference(variable_rename,[status(thm)],[f_3571_1]) ).
fof(f_3571_3,plain,
! [U_13893] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK335(U_13893)),c_Int_OInteg))
& U_13893 = hAPP(c_Int_OAbs__Integ,sK335(U_13893)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK335]),skolemize(U_13892,sK335(U_13893))],[f_3571_2]) ).
cnf(f_3571_4,plain,
U_13893 = hAPP(c_Int_OAbs__Integ,sK335(U_13893)),
inference(clausify,[status(thm)],[f_3571_3]) ).
cnf(f_3571_5,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK335(U_13893)),c_Int_OInteg)),
inference(clausify,[status(thm)],[f_3571_3]) ).
fof(f_3572_1,plain,
! [V_r_2,V_s_2,T_b] :
( c_Wellfounded_Oacyclic(T_b,V_r_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
| ~ c_Wellfounded_Oacyclic(T_b,V_s_2) ),
inference(fof_nnf,[status(thm)],[fact_acyclic__subset]) ).
fof(f_3572_2,plain,
! [U_13896,U_13895,U_13894] :
( c_Wellfounded_Oacyclic(U_13894,U_13896)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13894,U_13894),tc_HOL_Obool)),U_13896),U_13895))
| ~ c_Wellfounded_Oacyclic(U_13894,U_13895) ),
inference(variable_rename,[status(thm)],[f_3572_1]) ).
cnf(f_3572_3,plain,
( c_Wellfounded_Oacyclic(U_13894,U_13896)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_13894,U_13894),tc_HOL_Obool)),U_13896),U_13895))
| ~ c_Wellfounded_Oacyclic(U_13894,U_13895) ),
inference(clausify,[status(thm)],[f_3572_2]) ).
fof(f_3573_1,plain,
! [V_r_2,T_b] :
( c_Wellfounded_Oacyclic(T_b,V_r_2)
| ~ c_Wellfounded_Owf(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__acyclic]) ).
fof(f_3573_2,plain,
! [U_13898,U_13897] :
( c_Wellfounded_Oacyclic(U_13897,U_13898)
| ~ c_Wellfounded_Owf(U_13897,U_13898) ),
inference(variable_rename,[status(thm)],[f_3573_1]) ).
cnf(f_3573_3,plain,
( c_Wellfounded_Oacyclic(U_13897,U_13898)
| ~ c_Wellfounded_Owf(U_13897,U_13898) ),
inference(clausify,[status(thm)],[f_3573_2]) ).
fof(f_3574_1,plain,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,V_r_2)
| ~ c_Wellfounded_Oacyclic(T_b,V_r_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf]) ).
fof(f_3574_2,plain,
! [U_13900,U_13899] :
( c_Wellfounded_Owf(U_13899,U_13900)
| ~ c_Wellfounded_Oacyclic(U_13899,U_13900)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13899,U_13899)),U_13900)) ),
inference(variable_rename,[status(thm)],[f_3574_1]) ).
cnf(f_3574_3,plain,
( c_Wellfounded_Owf(U_13899,U_13900)
| ~ c_Wellfounded_Oacyclic(U_13899,U_13900)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13899,U_13899)),U_13900)) ),
inference(clausify,[status(thm)],[f_3574_2]) ).
fof(f_3575_1,plain,
! [V_r_2,T_b] :
( ( ( c_Wellfounded_Owf(T_b,V_r_2)
| ~ c_Wellfounded_Oacyclic(T_b,V_r_2) )
& ( c_Wellfounded_Oacyclic(T_b,V_r_2)
| ~ c_Wellfounded_Owf(T_b,V_r_2) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_wf__iff__acyclic__if__finite]) ).
fof(f_3575_2,plain,
! [U_13902,U_13901] :
( ( ( c_Wellfounded_Owf(U_13901,U_13902)
| ~ c_Wellfounded_Oacyclic(U_13901,U_13902) )
& ( c_Wellfounded_Oacyclic(U_13901,U_13902)
| ~ c_Wellfounded_Owf(U_13901,U_13902) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13901,U_13901)),U_13902)) ),
inference(variable_rename,[status(thm)],[f_3575_1]) ).
cnf(f_3575_3,plain,
( c_Wellfounded_Oacyclic(U_13901,U_13902)
| ~ c_Wellfounded_Owf(U_13901,U_13902)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13901,U_13901)),U_13902)) ),
inference(clausify,[status(thm)],[f_3575_2]) ).
cnf(f_3575_4,plain,
( c_Wellfounded_Owf(U_13901,U_13902)
| ~ c_Wellfounded_Oacyclic(U_13901,U_13902)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13901,U_13901)),U_13902)) ),
inference(clausify,[status(thm)],[f_3575_2]) ).
fof(f_3576_1,plain,
! [V_r_2,T_b] :
( ( c_Nitpick_Owf_H(T_b,V_r_2)
| ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) )
| ~ c_Wellfounded_Oacyclic(T_b,V_r_2) )
& ( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) )
& c_Wellfounded_Oacyclic(T_b,V_r_2) )
| ~ c_Nitpick_Owf_H(T_b,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Owf_H__def]) ).
fof(f_3576_2,plain,
! [U_13904,U_13903] :
( ( c_Nitpick_Owf_H(U_13903,U_13904)
| ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13903,U_13903)),U_13904)) )
| ~ c_Wellfounded_Oacyclic(U_13903,U_13904) )
& ( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13903,U_13903)),U_13904)) )
& c_Wellfounded_Oacyclic(U_13903,U_13904) )
| ~ c_Nitpick_Owf_H(U_13903,U_13904) ) ),
inference(variable_rename,[status(thm)],[f_3576_1]) ).
fof(f_3576_3,plain,
( ! [U_13908,U_13906] :
( c_Nitpick_Owf_H(U_13906,U_13908)
| ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13906,U_13906)),U_13908)) )
| ~ c_Wellfounded_Oacyclic(U_13906,U_13908) )
& ! [U_13907,U_13905] :
( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13905,U_13905)),U_13907)) )
& c_Wellfounded_Oacyclic(U_13905,U_13907) )
| ~ c_Nitpick_Owf_H(U_13905,U_13907) ) ),
inference(miniscope,[status(thm)],[f_3576_2]) ).
cnf(f_3576_4,plain,
( c_Wellfounded_Oacyclic(U_13905,U_13907)
| ~ c_Nitpick_Owf_H(U_13905,U_13907) ),
inference(clausify,[status(thm)],[f_3576_3]) ).
cnf(f_3576_5,plain,
( c_Nitpick_Ounknown(tc_HOL_Obool)
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13905,U_13905)),U_13907))
| ~ c_Nitpick_Owf_H(U_13905,U_13907) ),
inference(clausify,[status(thm)],[f_3576_3]) ).
cnf(f_3576_6,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13906,U_13906)),U_13908))
| ~ c_Wellfounded_Oacyclic(U_13906,U_13908)
| c_Nitpick_Owf_H(U_13906,U_13908) ),
inference(clausify,[status(thm)],[f_3576_3]) ).
cnf(f_3576_7,plain,
( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
| ~ c_Wellfounded_Oacyclic(U_13906,U_13908)
| c_Nitpick_Owf_H(U_13906,U_13908) ),
inference(clausify,[status(thm)],[f_3576_3]) ).
fof(f_3577_1,plain,
! [V_x_2,V_P_2] :
( hBOOL(hAPP(V_P_2,V_x_2))
| ? [B_y] :
( ~ hBOOL(hAPP(V_P_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)) ) ),
inference(fof_nnf,[status(thm)],[fact_Abs__Integ__induct]) ).
fof(f_3577_2,plain,
! [U_13911,U_13910] :
( hBOOL(hAPP(U_13910,U_13911))
| ? [U_13909] :
( ~ hBOOL(hAPP(U_13910,hAPP(c_Int_OAbs__Integ,U_13909)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_13909),c_Int_OInteg)) ) ),
inference(variable_rename,[status(thm)],[f_3577_1]) ).
fof(f_3577_3,plain,
! [U_13911,U_13910] :
( hBOOL(hAPP(U_13910,U_13911))
| ( ~ hBOOL(hAPP(U_13910,hAPP(c_Int_OAbs__Integ,sK336(U_13911,U_13910))))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK336(U_13911,U_13910)),c_Int_OInteg)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK336]),skolemize(U_13909,sK336(U_13911,U_13910))],[f_3577_2]) ).
cnf(f_3577_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK336(U_13911,U_13910)),c_Int_OInteg))
| hBOOL(hAPP(U_13910,U_13911)) ),
inference(clausify,[status(thm)],[f_3577_3]) ).
cnf(f_3577_5,plain,
( ~ hBOOL(hAPP(U_13910,hAPP(c_Int_OAbs__Integ,sK336(U_13911,U_13910))))
| hBOOL(hAPP(U_13910,U_13911)) ),
inference(clausify,[status(thm)],[f_3577_3]) ).
fof(f_3578_1,plain,
! [V_B_2,T_c,V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
| ? [B_a] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__UN__I]) ).
fof(f_3578_2,plain,
! [U_13916,U_13915,U_13914,U_13913] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13915),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13913,tc_fun(U_13915,tc_HOL_Obool)),U_13914),U_13916)))
| ? [U_13912] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13915),hAPP(U_13916,U_13912)))
& hBOOL(hAPP(hAPP(c_member(U_13913),U_13912),U_13914)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13913),U_13914)) ),
inference(variable_rename,[status(thm)],[f_3578_1]) ).
fof(f_3578_3,plain,
! [U_13916,U_13915,U_13914,U_13913] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13915),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13913,tc_fun(U_13915,tc_HOL_Obool)),U_13914),U_13916)))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13915),hAPP(U_13916,sK337(U_13916,U_13915,U_13914,U_13913))))
& hBOOL(hAPP(hAPP(c_member(U_13913),sK337(U_13916,U_13915,U_13914,U_13913)),U_13914)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13913),U_13914)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK337]),skolemize(U_13912,sK337(U_13916,U_13915,U_13914,U_13913))],[f_3578_2]) ).
cnf(f_3578_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_13913),sK337(U_13916,U_13915,U_13914,U_13913)),U_13914))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_13915),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13913,tc_fun(U_13915,tc_HOL_Obool)),U_13914),U_13916)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13913),U_13914)) ),
inference(clausify,[status(thm)],[f_3578_3]) ).
cnf(f_3578_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13915),hAPP(U_13916,sK337(U_13916,U_13915,U_13914,U_13913))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_13915),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13913,tc_fun(U_13915,tc_HOL_Obool)),U_13914),U_13916)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13913),U_13914)) ),
inference(clausify,[status(thm)],[f_3578_3]) ).
fof(f_3579_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_3579_2,plain,
! [U_13919,U_13918] :
( 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_13919),U_13918)
| ? [U_13917] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_13919),U_13917))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_13917),U_13918)) ) ),
inference(variable_rename,[status(thm)],[f_3579_1]) ).
fof(f_3579_3,plain,
! [U_13919,U_13918] :
( 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_13919),U_13918)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_13919),sK338(U_13919,U_13918)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK338(U_13919,U_13918)),U_13918)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK338]),skolemize(U_13917,sK338(U_13919,U_13918))],[f_3579_2]) ).
cnf(f_3579_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK338(U_13919,U_13918)),U_13918))
| 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_13919),U_13918) ),
inference(clausify,[status(thm)],[f_3579_3]) ).
cnf(f_3579_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_13919),sK338(U_13919,U_13918)))
| 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_13919),U_13918) ),
inference(clausify,[status(thm)],[f_3579_3]) ).
fof(f_3580_1,plain,
! [T_b,V_r_2,T_c] :
( c_Wellfounded_OwfP(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))
| ? [B_i,B_j] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Predicate_ODomainP(T_c,T_c,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_c,T_c,hAPP(V_r_2,B_j))) != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
& hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) )
| ? [B_i] : ~ c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i)) ),
inference(fof_nnf,[status(thm)],[fact_wfP__SUP]) ).
fof(f_3580_2,plain,
! [U_13925,U_13924,U_13923] :
( c_Wellfounded_OwfP(U_13923,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13925,tc_fun(U_13923,tc_fun(U_13923,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13925,tc_HOL_Obool))),U_13924))
| ? [U_13922,U_13921] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13923,tc_HOL_Obool)),c_Predicate_ODomainP(U_13923,U_13923,hAPP(U_13924,U_13922))),c_Predicate_ORangeP(U_13923,U_13923,hAPP(U_13924,U_13921))) != c_Orderings_Obot__class_Obot(tc_fun(U_13923,tc_HOL_Obool))
& hAPP(U_13924,U_13922) != hAPP(U_13924,U_13921) )
| ? [U_13920] : ~ c_Wellfounded_OwfP(U_13923,hAPP(U_13924,U_13920)) ),
inference(variable_rename,[status(thm)],[f_3580_1]) ).
fof(f_3580_3,plain,
! [U_13925,U_13924,U_13923] :
( c_Wellfounded_OwfP(U_13923,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13925,tc_fun(U_13923,tc_fun(U_13923,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13925,tc_HOL_Obool))),U_13924))
| ? [U_13922,U_13921] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13923,tc_HOL_Obool)),c_Predicate_ODomainP(U_13923,U_13923,hAPP(U_13924,U_13922))),c_Predicate_ORangeP(U_13923,U_13923,hAPP(U_13924,U_13921))) != c_Orderings_Obot__class_Obot(tc_fun(U_13923,tc_HOL_Obool))
& hAPP(U_13924,U_13922) != hAPP(U_13924,U_13921) )
| ~ c_Wellfounded_OwfP(U_13923,hAPP(U_13924,sK339(U_13925,U_13924,U_13923))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK339]),skolemize(U_13920,sK339(U_13925,U_13924,U_13923))],[f_3580_2]) ).
fof(f_3580_4,plain,
! [U_13925,U_13924,U_13923] :
( c_Wellfounded_OwfP(U_13923,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13925,tc_fun(U_13923,tc_fun(U_13923,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13925,tc_HOL_Obool))),U_13924))
| ? [U_13921] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13923,tc_HOL_Obool)),c_Predicate_ODomainP(U_13923,U_13923,hAPP(U_13924,sK340(U_13925,U_13924,U_13923)))),c_Predicate_ORangeP(U_13923,U_13923,hAPP(U_13924,U_13921))) != c_Orderings_Obot__class_Obot(tc_fun(U_13923,tc_HOL_Obool))
& hAPP(U_13924,sK340(U_13925,U_13924,U_13923)) != hAPP(U_13924,U_13921) )
| ~ c_Wellfounded_OwfP(U_13923,hAPP(U_13924,sK339(U_13925,U_13924,U_13923))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK340]),skolemize(U_13922,sK340(U_13925,U_13924,U_13923))],[f_3580_3]) ).
fof(f_3580_5,plain,
! [U_13925,U_13924,U_13923] :
( c_Wellfounded_OwfP(U_13923,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13925,tc_fun(U_13923,tc_fun(U_13923,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13925,tc_HOL_Obool))),U_13924))
| ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13923,tc_HOL_Obool)),c_Predicate_ODomainP(U_13923,U_13923,hAPP(U_13924,sK340(U_13925,U_13924,U_13923)))),c_Predicate_ORangeP(U_13923,U_13923,hAPP(U_13924,sK341(U_13925,U_13924,U_13923)))) != c_Orderings_Obot__class_Obot(tc_fun(U_13923,tc_HOL_Obool))
& hAPP(U_13924,sK340(U_13925,U_13924,U_13923)) != hAPP(U_13924,sK341(U_13925,U_13924,U_13923)) )
| ~ c_Wellfounded_OwfP(U_13923,hAPP(U_13924,sK339(U_13925,U_13924,U_13923))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK341]),skolemize(U_13921,sK341(U_13925,U_13924,U_13923))],[f_3580_4]) ).
cnf(f_3580_6,plain,
( hAPP(U_13924,sK340(U_13925,U_13924,U_13923)) != hAPP(U_13924,sK341(U_13925,U_13924,U_13923))
| c_Wellfounded_OwfP(U_13923,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13925,tc_fun(U_13923,tc_fun(U_13923,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13925,tc_HOL_Obool))),U_13924))
| ~ c_Wellfounded_OwfP(U_13923,hAPP(U_13924,sK339(U_13925,U_13924,U_13923))) ),
inference(clausify,[status(thm)],[f_3580_5]) ).
cnf(f_3580_7,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13923,tc_HOL_Obool)),c_Predicate_ODomainP(U_13923,U_13923,hAPP(U_13924,sK340(U_13925,U_13924,U_13923)))),c_Predicate_ORangeP(U_13923,U_13923,hAPP(U_13924,sK341(U_13925,U_13924,U_13923)))) != c_Orderings_Obot__class_Obot(tc_fun(U_13923,tc_HOL_Obool))
| c_Wellfounded_OwfP(U_13923,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13925,tc_fun(U_13923,tc_fun(U_13923,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_13925,tc_HOL_Obool))),U_13924))
| ~ c_Wellfounded_OwfP(U_13923,hAPP(U_13924,sK339(U_13925,U_13924,U_13923))) ),
inference(clausify,[status(thm)],[f_3580_5]) ).
fof(f_3581_1,plain,
! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] :
( hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_c_2),V_p_2)))
| ? [B_a,B_b] :
( ~ hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b)))
& V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b) ) ),
inference(fof_nnf,[status(thm)],[fact_mem__splitI2]) ).
fof(f_3581_2,plain,
! [U_13933,U_13932,U_13931,U_13930,U_13929,U_13928] :
( hBOOL(hAPP(hAPP(c_member(U_13931),U_13932),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13929,U_13930,tc_fun(U_13931,tc_HOL_Obool)),U_13933),U_13928)))
| ? [U_13927,U_13926] :
( ~ hBOOL(hAPP(hAPP(c_member(U_13931),U_13932),hAPP(hAPP(U_13933,U_13927),U_13926)))
& U_13928 = hAPP(hAPP(c_Product__Type_OPair(U_13929,U_13930),U_13927),U_13926) ) ),
inference(variable_rename,[status(thm)],[f_3581_1]) ).
fof(f_3581_3,plain,
! [U_13933,U_13932,U_13931,U_13930,U_13929,U_13928] :
( hBOOL(hAPP(hAPP(c_member(U_13931),U_13932),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13929,U_13930,tc_fun(U_13931,tc_HOL_Obool)),U_13933),U_13928)))
| ? [U_13926] :
( ~ hBOOL(hAPP(hAPP(c_member(U_13931),U_13932),hAPP(hAPP(U_13933,sK342(U_13933,U_13932,U_13931,U_13930,U_13929,U_13928)),U_13926)))
& U_13928 = hAPP(hAPP(c_Product__Type_OPair(U_13929,U_13930),sK342(U_13933,U_13932,U_13931,U_13930,U_13929,U_13928)),U_13926) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK342]),skolemize(U_13927,sK342(U_13933,U_13932,U_13931,U_13930,U_13929,U_13928))],[f_3581_2]) ).
fof(f_3581_4,plain,
! [U_13933,U_13932,U_13931,U_13930,U_13929,U_13928] :
( hBOOL(hAPP(hAPP(c_member(U_13931),U_13932),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13929,U_13930,tc_fun(U_13931,tc_HOL_Obool)),U_13933),U_13928)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_13931),U_13932),hAPP(hAPP(U_13933,sK342(U_13933,U_13932,U_13931,U_13930,U_13929,U_13928)),sK343(U_13933,U_13932,U_13931,U_13930,U_13929,U_13928))))
& U_13928 = hAPP(hAPP(c_Product__Type_OPair(U_13929,U_13930),sK342(U_13933,U_13932,U_13931,U_13930,U_13929,U_13928)),sK343(U_13933,U_13932,U_13931,U_13930,U_13929,U_13928)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK343]),skolemize(U_13926,sK343(U_13933,U_13932,U_13931,U_13930,U_13929,U_13928))],[f_3581_3]) ).
cnf(f_3581_5,plain,
( U_13928 = hAPP(hAPP(c_Product__Type_OPair(U_13929,U_13930),sK342(U_13933,U_13932,U_13931,U_13930,U_13929,U_13928)),sK343(U_13933,U_13932,U_13931,U_13930,U_13929,U_13928))
| hBOOL(hAPP(hAPP(c_member(U_13931),U_13932),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13929,U_13930,tc_fun(U_13931,tc_HOL_Obool)),U_13933),U_13928))) ),
inference(clausify,[status(thm)],[f_3581_4]) ).
cnf(f_3581_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_13931),U_13932),hAPP(hAPP(U_13933,sK342(U_13933,U_13932,U_13931,U_13930,U_13929,U_13928)),sK343(U_13933,U_13932,U_13931,U_13930,U_13929,U_13928))))
| hBOOL(hAPP(hAPP(c_member(U_13931),U_13932),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13929,U_13930,tc_fun(U_13931,tc_HOL_Obool)),U_13933),U_13928))) ),
inference(clausify,[status(thm)],[f_3581_4]) ).
fof(f_3582_1,plain,
! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] :
( ? [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y)))
& V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),V_p_2))) ),
inference(fof_nnf,[status(thm)],[fact_mem__splitE]) ).
fof(f_3582_2,plain,
! [U_13941,U_13940,U_13939,U_13938,U_13937,U_13936] :
( ? [U_13935,U_13934] :
( hBOOL(hAPP(hAPP(c_member(U_13936),U_13937),hAPP(hAPP(U_13940,U_13935),U_13934)))
& U_13941 = hAPP(hAPP(c_Product__Type_OPair(U_13938,U_13939),U_13935),U_13934) )
| ~ hBOOL(hAPP(hAPP(c_member(U_13936),U_13937),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13938,U_13939,tc_fun(U_13936,tc_HOL_Obool)),U_13940),U_13941))) ),
inference(variable_rename,[status(thm)],[f_3582_1]) ).
fof(f_3582_3,plain,
! [U_13941,U_13940,U_13939,U_13938,U_13937,U_13936] :
( ? [U_13934] :
( hBOOL(hAPP(hAPP(c_member(U_13936),U_13937),hAPP(hAPP(U_13940,sK344(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936)),U_13934)))
& U_13941 = hAPP(hAPP(c_Product__Type_OPair(U_13938,U_13939),sK344(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936)),U_13934) )
| ~ hBOOL(hAPP(hAPP(c_member(U_13936),U_13937),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13938,U_13939,tc_fun(U_13936,tc_HOL_Obool)),U_13940),U_13941))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK344]),skolemize(U_13935,sK344(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936))],[f_3582_2]) ).
fof(f_3582_4,plain,
! [U_13941,U_13940,U_13939,U_13938,U_13937,U_13936] :
( ( hBOOL(hAPP(hAPP(c_member(U_13936),U_13937),hAPP(hAPP(U_13940,sK344(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936)),sK345(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936))))
& U_13941 = hAPP(hAPP(c_Product__Type_OPair(U_13938,U_13939),sK344(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936)),sK345(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_13936),U_13937),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13938,U_13939,tc_fun(U_13936,tc_HOL_Obool)),U_13940),U_13941))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK345]),skolemize(U_13934,sK345(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936))],[f_3582_3]) ).
cnf(f_3582_5,plain,
( U_13941 = hAPP(hAPP(c_Product__Type_OPair(U_13938,U_13939),sK344(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936)),sK345(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936))
| ~ hBOOL(hAPP(hAPP(c_member(U_13936),U_13937),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13938,U_13939,tc_fun(U_13936,tc_HOL_Obool)),U_13940),U_13941))) ),
inference(clausify,[status(thm)],[f_3582_4]) ).
cnf(f_3582_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_13936),U_13937),hAPP(hAPP(U_13940,sK344(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936)),sK345(U_13941,U_13940,U_13939,U_13938,U_13937,U_13936))))
| ~ hBOOL(hAPP(hAPP(c_member(U_13936),U_13937),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_13938,U_13939,tc_fun(U_13936,tc_HOL_Obool)),U_13940),U_13941))) ),
inference(clausify,[status(thm)],[f_3582_4]) ).
fof(f_3583_1,plain,
! [V_B_2,V_A_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,tc_prod(T_c,T_d),V_f_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,T_b,c_Product__Type_Ofst(T_c,T_d)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_d,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_d,T_b,c_Product__Type_Osnd(T_c,T_d)),V_f_2)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__Times]) ).
fof(f_3583_2,plain,
! [U_13947,U_13946,U_13945,U_13944,U_13943,U_13942] : hAPP(c_Set_Ovimage(U_13942,tc_prod(U_13943,U_13944),U_13945),hAPP(hAPP(c_Product__Type_OSigma(U_13943,U_13944),U_13946),hAPP(c_COMBK(tc_fun(U_13944,tc_HOL_Obool),U_13943),U_13947))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13942,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13942,U_13943,hAPP(c_Fun_Ocomp(tc_prod(U_13943,U_13944),U_13943,U_13942,c_Product__Type_Ofst(U_13943,U_13944)),U_13945)),U_13946)),hAPP(c_Set_Ovimage(U_13942,U_13944,hAPP(c_Fun_Ocomp(tc_prod(U_13943,U_13944),U_13944,U_13942,c_Product__Type_Osnd(U_13943,U_13944)),U_13945)),U_13947)),
inference(variable_rename,[status(thm)],[f_3583_1]) ).
cnf(f_3583_3,plain,
hAPP(c_Set_Ovimage(U_13942,tc_prod(U_13943,U_13944),U_13945),hAPP(hAPP(c_Product__Type_OSigma(U_13943,U_13944),U_13946),hAPP(c_COMBK(tc_fun(U_13944,tc_HOL_Obool),U_13943),U_13947))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13942,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_13942,U_13943,hAPP(c_Fun_Ocomp(tc_prod(U_13943,U_13944),U_13943,U_13942,c_Product__Type_Ofst(U_13943,U_13944)),U_13945)),U_13946)),hAPP(c_Set_Ovimage(U_13942,U_13944,hAPP(c_Fun_Ocomp(tc_prod(U_13943,U_13944),U_13944,U_13942,c_Product__Type_Osnd(U_13943,U_13944)),U_13945)),U_13947)),
inference(clausify,[status(thm)],[f_3583_2]) ).
fof(f_3584_1,plain,
! [V_g_2,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_g_2) = V_g_2,
inference(fof_nnf,[status(thm)],[fact_id__o]) ).
fof(f_3584_2,plain,
! [U_13950,U_13949,U_13948] : hAPP(c_Fun_Ocomp(U_13948,U_13948,U_13949,c_Fun_Oid(U_13948)),U_13950) = U_13950,
inference(variable_rename,[status(thm)],[f_3584_1]) ).
cnf(f_3584_3,plain,
hAPP(c_Fun_Ocomp(U_13948,U_13948,U_13949,c_Fun_Oid(U_13948)),U_13950) = U_13950,
inference(clausify,[status(thm)],[f_3584_2]) ).
fof(f_3585_1,plain,
! [V_f_2,T_c,T_b] : hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_f_2),c_Fun_Oid(T_b)) = V_f_2,
inference(fof_nnf,[status(thm)],[fact_o__id]) ).
fof(f_3585_2,plain,
! [U_13953,U_13952,U_13951] : hAPP(c_Fun_Ocomp(U_13951,U_13952,U_13951,U_13953),c_Fun_Oid(U_13951)) = U_13953,
inference(variable_rename,[status(thm)],[f_3585_1]) ).
cnf(f_3585_3,plain,
hAPP(c_Fun_Ocomp(U_13951,U_13952,U_13951,U_13953),c_Fun_Oid(U_13951)) = U_13953,
inference(clausify,[status(thm)],[f_3585_2]) ).
fof(f_3586_1,plain,
! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
( hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2)
| hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) != hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_c_2) ),
inference(fof_nnf,[status(thm)],[fact_o__eq__id__dest]) ).
fof(f_3586_2,plain,
! [U_13960,U_13959,U_13958,U_13957,U_13956,U_13955,U_13954] :
( hAPP(U_13957,hAPP(U_13958,U_13960)) = hAPP(U_13959,U_13960)
| hAPP(c_Fun_Ocomp(U_13954,U_13955,U_13956,U_13957),U_13958) != hAPP(c_Fun_Ocomp(U_13955,U_13955,U_13956,c_Fun_Oid(U_13955)),U_13959) ),
inference(variable_rename,[status(thm)],[f_3586_1]) ).
fof(f_3586_3,plain,
! [U_13960,U_13959,U_13958,U_13957] :
( ! [U_13956,U_13955,U_13954] : hAPP(c_Fun_Ocomp(U_13954,U_13955,U_13956,U_13957),U_13958) != hAPP(c_Fun_Ocomp(U_13955,U_13955,U_13956,c_Fun_Oid(U_13955)),U_13959)
| hAPP(U_13957,hAPP(U_13958,U_13960)) = hAPP(U_13959,U_13960) ),
inference(miniscope,[status(thm)],[f_3586_2]) ).
cnf(f_3586_4,plain,
( hAPP(c_Fun_Ocomp(U_13954,U_13955,U_13956,U_13957),U_13958) != hAPP(c_Fun_Ocomp(U_13955,U_13955,U_13956,c_Fun_Oid(U_13955)),U_13959)
| hAPP(U_13957,hAPP(U_13958,U_13960)) = hAPP(U_13959,U_13960) ),
inference(clausify,[status(thm)],[f_3586_3]) ).
fof(f_3587_1,plain,
! [V_x_2,V_f_2,T_c,T_b] :
( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2)
| ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__comp__idem]) ).
fof(f_3587_2,plain,
! [U_13964,U_13963,U_13962,U_13961] :
( hAPP(c_Fun_Ocomp(U_13962,U_13962,U_13962,hAPP(U_13963,U_13964)),hAPP(U_13963,U_13964)) = hAPP(U_13963,U_13964)
| ~ c_Finite__Set_Ofun__left__comm__idem(U_13961,U_13962,U_13963) ),
inference(variable_rename,[status(thm)],[f_3587_1]) ).
fof(f_3587_3,plain,
! [U_13964,U_13963,U_13962] :
( ! [U_13961] : ~ c_Finite__Set_Ofun__left__comm__idem(U_13961,U_13962,U_13963)
| hAPP(c_Fun_Ocomp(U_13962,U_13962,U_13962,hAPP(U_13963,U_13964)),hAPP(U_13963,U_13964)) = hAPP(U_13963,U_13964) ),
inference(miniscope,[status(thm)],[f_3587_2]) ).
cnf(f_3587_4,plain,
( ~ c_Finite__Set_Ofun__left__comm__idem(U_13961,U_13962,U_13963)
| hAPP(c_Fun_Ocomp(U_13962,U_13962,U_13962,hAPP(U_13963,U_13964)),hAPP(U_13963,U_13964)) = hAPP(U_13963,U_13964) ),
inference(clausify,[status(thm)],[f_3587_3]) ).
fof(f_3588_1,plain,
! [V_x_2,V_f_2,V_g_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_b,T_d,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_g_2),V_x_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__compose]) ).
fof(f_3588_2,plain,
! [U_13970,U_13969,U_13968,U_13967,U_13966,U_13965] : hAPP(c_Set_Ovimage(U_13965,U_13966,hAPP(c_Fun_Ocomp(U_13967,U_13966,U_13965,U_13968),U_13969)),U_13970) = hAPP(c_Set_Ovimage(U_13965,U_13967,U_13969),hAPP(c_Set_Ovimage(U_13967,U_13966,U_13968),U_13970)),
inference(variable_rename,[status(thm)],[f_3588_1]) ).
cnf(f_3588_3,plain,
hAPP(c_Set_Ovimage(U_13965,U_13966,hAPP(c_Fun_Ocomp(U_13967,U_13966,U_13965,U_13968),U_13969)),U_13970) = hAPP(c_Set_Ovimage(U_13965,U_13967,U_13969),hAPP(c_Set_Ovimage(U_13967,U_13966,U_13968),U_13970)),
inference(clausify,[status(thm)],[f_3588_2]) ).
fof(f_3589_1,plain,
! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)),
inference(fof_nnf,[status(thm)],[fact_o__def]) ).
fof(f_3589_2,plain,
! [U_13976,U_13975,U_13974,U_13973,U_13972,U_13971] : hAPP(hAPP(c_Fun_Ocomp(U_13971,U_13972,U_13973,U_13974),U_13975),U_13976) = hAPP(U_13974,hAPP(U_13975,U_13976)),
inference(variable_rename,[status(thm)],[f_3589_1]) ).
cnf(f_3589_3,plain,
hAPP(hAPP(c_Fun_Ocomp(U_13971,U_13972,U_13973,U_13974),U_13975),U_13976) = hAPP(U_13974,hAPP(U_13975,U_13976)),
inference(clausify,[status(thm)],[f_3589_2]) ).
fof(f_3590_1,plain,
! [V_h_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(c_Fun_Ocomp(T_e,T_d,T_b,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_h_2),
inference(fof_nnf,[status(thm)],[fact_o__assoc]) ).
fof(f_3590_2,plain,
! [U_13983,U_13982,U_13981,U_13980,U_13979,U_13978,U_13977] : hAPP(c_Fun_Ocomp(U_13977,U_13978,U_13979,U_13980),hAPP(c_Fun_Ocomp(U_13981,U_13977,U_13979,U_13982),U_13983)) = hAPP(c_Fun_Ocomp(U_13981,U_13978,U_13979,hAPP(c_Fun_Ocomp(U_13977,U_13978,U_13981,U_13980),U_13982)),U_13983),
inference(variable_rename,[status(thm)],[f_3590_1]) ).
cnf(f_3590_3,plain,
hAPP(c_Fun_Ocomp(U_13977,U_13978,U_13979,U_13980),hAPP(c_Fun_Ocomp(U_13981,U_13977,U_13979,U_13982),U_13983)) = hAPP(c_Fun_Ocomp(U_13981,U_13978,U_13979,hAPP(c_Fun_Ocomp(U_13977,U_13978,U_13981,U_13980),U_13982)),U_13983),
inference(clausify,[status(thm)],[f_3590_2]) ).
fof(f_3591_1,plain,
! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)),
inference(fof_nnf,[status(thm)],[fact_o__apply]) ).
fof(f_3591_2,plain,
! [U_13989,U_13988,U_13987,U_13986,U_13985,U_13984] : hAPP(hAPP(c_Fun_Ocomp(U_13984,U_13985,U_13986,U_13987),U_13988),U_13989) = hAPP(U_13987,hAPP(U_13988,U_13989)),
inference(variable_rename,[status(thm)],[f_3591_1]) ).
cnf(f_3591_3,plain,
hAPP(hAPP(c_Fun_Ocomp(U_13984,U_13985,U_13986,U_13987),U_13988),U_13989) = hAPP(U_13987,hAPP(U_13988,U_13989)),
inference(clausify,[status(thm)],[f_3591_2]) ).
fof(f_3592_1,plain,
! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
( hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2))
| hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) != hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2) ),
inference(fof_nnf,[status(thm)],[fact_o__eq__dest]) ).
fof(f_3592_2,plain,
! [U_13998,U_13997,U_13996,U_13995,U_13994,U_13993,U_13992,U_13991,U_13990] :
( hAPP(U_13993,hAPP(U_13994,U_13998)) = hAPP(U_13996,hAPP(U_13997,U_13998))
| hAPP(c_Fun_Ocomp(U_13990,U_13991,U_13992,U_13993),U_13994) != hAPP(c_Fun_Ocomp(U_13995,U_13991,U_13992,U_13996),U_13997) ),
inference(variable_rename,[status(thm)],[f_3592_1]) ).
fof(f_3592_3,plain,
! [U_13998,U_13997,U_13996,U_13995,U_13994,U_13993] :
( ! [U_13992,U_13991,U_13990] : hAPP(c_Fun_Ocomp(U_13990,U_13991,U_13992,U_13993),U_13994) != hAPP(c_Fun_Ocomp(U_13995,U_13991,U_13992,U_13996),U_13997)
| hAPP(U_13993,hAPP(U_13994,U_13998)) = hAPP(U_13996,hAPP(U_13997,U_13998)) ),
inference(miniscope,[status(thm)],[f_3592_2]) ).
cnf(f_3592_4,plain,
( hAPP(c_Fun_Ocomp(U_13990,U_13991,U_13992,U_13993),U_13994) != hAPP(c_Fun_Ocomp(U_13995,U_13991,U_13992,U_13996),U_13997)
| hAPP(U_13993,hAPP(U_13994,U_13998)) = hAPP(U_13996,hAPP(U_13997,U_13998)) ),
inference(clausify,[status(thm)],[f_3592_3]) ).
fof(f_3593_1,plain,
! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
( ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v))
| hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) != hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2) ),
inference(fof_nnf,[status(thm)],[fact_o__eq__elim]) ).
fof(f_3593_2,plain,
! [U_14007,U_14006,U_14005,U_14004,U_14003,U_14002,U_14001,U_14000] :
( ! [U_13999] : hAPP(U_14003,hAPP(U_14004,U_13999)) = hAPP(U_14006,hAPP(U_14007,U_13999))
| hAPP(c_Fun_Ocomp(U_14000,U_14001,U_14002,U_14003),U_14004) != hAPP(c_Fun_Ocomp(U_14005,U_14001,U_14002,U_14006),U_14007) ),
inference(variable_rename,[status(thm)],[f_3593_1]) ).
fof(f_3593_3,plain,
! [U_14007,U_14006,U_14005,U_14004,U_14003] :
( ! [U_14002,U_14001,U_14000] : hAPP(c_Fun_Ocomp(U_14000,U_14001,U_14002,U_14003),U_14004) != hAPP(c_Fun_Ocomp(U_14005,U_14001,U_14002,U_14006),U_14007)
| ! [U_13999] : hAPP(U_14003,hAPP(U_14004,U_13999)) = hAPP(U_14006,hAPP(U_14007,U_13999)) ),
inference(miniscope,[status(thm)],[f_3593_2]) ).
cnf(f_3593_4,plain,
( hAPP(c_Fun_Ocomp(U_14000,U_14001,U_14002,U_14003),U_14004) != hAPP(c_Fun_Ocomp(U_14005,U_14001,U_14002,U_14006),U_14007)
| hAPP(U_14003,hAPP(U_14004,U_13999)) = hAPP(U_14006,hAPP(U_14007,U_13999)) ),
inference(clausify,[status(thm)],[f_3593_3]) ).
fof(f_3594_1,plain,
! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_d,T_c,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_e,V_f_2),V_g_2)),V_x_2),
inference(fof_nnf,[status(thm)],[fact_apfst__compose]) ).
fof(f_3594_2,plain,
! [U_14014,U_14013,U_14012,U_14011,U_14010,U_14009,U_14008] : hAPP(c_Product__Type_Oapfst(U_14008,U_14009,U_14010,U_14011),hAPP(c_Product__Type_Oapfst(U_14012,U_14008,U_14010,U_14013),U_14014)) = hAPP(c_Product__Type_Oapfst(U_14012,U_14009,U_14010,hAPP(c_Fun_Ocomp(U_14008,U_14009,U_14012,U_14011),U_14013)),U_14014),
inference(variable_rename,[status(thm)],[f_3594_1]) ).
cnf(f_3594_3,plain,
hAPP(c_Product__Type_Oapfst(U_14008,U_14009,U_14010,U_14011),hAPP(c_Product__Type_Oapfst(U_14012,U_14008,U_14010,U_14013),U_14014)) = hAPP(c_Product__Type_Oapfst(U_14012,U_14009,U_14010,hAPP(c_Fun_Ocomp(U_14008,U_14009,U_14012,U_14011),U_14013)),U_14014),
inference(clausify,[status(thm)],[f_3594_2]) ).
fof(f_3595_1,plain,
! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_x_2),
inference(fof_nnf,[status(thm)],[fact_apsnd__compose]) ).
fof(f_3595_2,plain,
! [U_14021,U_14020,U_14019,U_14018,U_14017,U_14016,U_14015] : hAPP(c_Product__Type_Oapsnd(U_14015,U_14016,U_14017,U_14018),hAPP(c_Product__Type_Oapsnd(U_14019,U_14015,U_14017,U_14020),U_14021)) = hAPP(c_Product__Type_Oapsnd(U_14019,U_14016,U_14017,hAPP(c_Fun_Ocomp(U_14015,U_14016,U_14019,U_14018),U_14020)),U_14021),
inference(variable_rename,[status(thm)],[f_3595_1]) ).
cnf(f_3595_3,plain,
hAPP(c_Product__Type_Oapsnd(U_14015,U_14016,U_14017,U_14018),hAPP(c_Product__Type_Oapsnd(U_14019,U_14015,U_14017,U_14020),U_14021)) = hAPP(c_Product__Type_Oapsnd(U_14019,U_14016,U_14017,hAPP(c_Fun_Ocomp(U_14015,U_14016,U_14019,U_14018),U_14020)),U_14021),
inference(clausify,[status(thm)],[f_3595_2]) ).
fof(f_3596_1,plain,
! [T_f,T_e,T_d,T_b,T_c,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] :
( hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_e,T_b,T_f,V_f_H_2),V_g_H_2),V_x_H_2)
| 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)) ),
inference(fof_nnf,[status(thm)],[fact_comp__cong]) ).
fof(f_3596_2,plain,
! [U_14032,U_14031,U_14030,U_14029,U_14028,U_14027,U_14026,U_14025,U_14024,U_14023,U_14022] :
( hAPP(hAPP(c_Fun_Ocomp(U_14028,U_14029,U_14030,U_14022),U_14023),U_14024) = hAPP(hAPP(c_Fun_Ocomp(U_14031,U_14029,U_14032,U_14025),U_14026),U_14027)
| hAPP(U_14022,hAPP(U_14023,U_14024)) != hAPP(U_14025,hAPP(U_14026,U_14027)) ),
inference(variable_rename,[status(thm)],[f_3596_1]) ).
cnf(f_3596_3,plain,
( hAPP(hAPP(c_Fun_Ocomp(U_14028,U_14029,U_14030,U_14022),U_14023),U_14024) = hAPP(hAPP(c_Fun_Ocomp(U_14031,U_14029,U_14032,U_14025),U_14026),U_14027)
| hAPP(U_14022,hAPP(U_14023,U_14024)) != hAPP(U_14025,hAPP(U_14026,U_14027)) ),
inference(clausify,[status(thm)],[f_3596_2]) ).
fof(f_3597_1,plain,
! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),c_Fun_Ofun__upd(T_b,T_d,V_g_2,V_x_2,V_y_2)) = c_Fun_Ofun__upd(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2),V_x_2,hAPP(V_f_2,V_y_2)),
inference(fof_nnf,[status(thm)],[fact_fun__upd__comp]) ).
fof(f_3597_2,plain,
! [U_14039,U_14038,U_14037,U_14036,U_14035,U_14034,U_14033] : hAPP(c_Fun_Ocomp(U_14033,U_14034,U_14035,U_14036),c_Fun_Ofun__upd(U_14035,U_14033,U_14037,U_14038,U_14039)) = c_Fun_Ofun__upd(U_14035,U_14034,hAPP(c_Fun_Ocomp(U_14033,U_14034,U_14035,U_14036),U_14037),U_14038,hAPP(U_14036,U_14039)),
inference(variable_rename,[status(thm)],[f_3597_1]) ).
cnf(f_3597_3,plain,
hAPP(c_Fun_Ocomp(U_14033,U_14034,U_14035,U_14036),c_Fun_Ofun__upd(U_14035,U_14033,U_14037,U_14038,U_14039)) = c_Fun_Ofun__upd(U_14035,U_14034,hAPP(c_Fun_Ocomp(U_14033,U_14034,U_14035,U_14036),U_14037),U_14038,hAPP(U_14036,U_14039)),
inference(clausify,[status(thm)],[f_3597_2]) ).
fof(f_3598_1,plain,
! [V_x_2,V_f_2,V_c_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_f_2),V_x_2) = V_c_2,
inference(fof_nnf,[status(thm)],[fact_K__record__comp]) ).
fof(f_3598_2,plain,
! [U_14045,U_14044,U_14043,U_14042,U_14041,U_14040] : hAPP(hAPP(c_Fun_Ocomp(U_14040,U_14041,U_14042,hAPP(c_COMBK(U_14041,U_14040),U_14043)),U_14044),U_14045) = U_14043,
inference(variable_rename,[status(thm)],[f_3598_1]) ).
cnf(f_3598_3,plain,
hAPP(hAPP(c_Fun_Ocomp(U_14040,U_14041,U_14042,hAPP(c_COMBK(U_14041,U_14040),U_14043)),U_14044),U_14045) = U_14043,
inference(clausify,[status(thm)],[f_3598_2]) ).
fof(f_3599_1,plain,
! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
( hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2)
| hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) != V_c_2 ),
inference(fof_nnf,[status(thm)],[fact_o__eq__dest__lhs]) ).
fof(f_3599_2,plain,
! [U_14052,U_14051,U_14050,U_14049,U_14048,U_14047,U_14046] :
( hAPP(U_14049,hAPP(U_14050,U_14052)) = hAPP(U_14051,U_14052)
| hAPP(c_Fun_Ocomp(U_14046,U_14047,U_14048,U_14049),U_14050) != U_14051 ),
inference(variable_rename,[status(thm)],[f_3599_1]) ).
fof(f_3599_3,plain,
! [U_14052,U_14051,U_14050,U_14049] :
( ! [U_14048,U_14047,U_14046] : hAPP(c_Fun_Ocomp(U_14046,U_14047,U_14048,U_14049),U_14050) != U_14051
| hAPP(U_14049,hAPP(U_14050,U_14052)) = hAPP(U_14051,U_14052) ),
inference(miniscope,[status(thm)],[f_3599_2]) ).
cnf(f_3599_4,plain,
( hAPP(c_Fun_Ocomp(U_14046,U_14047,U_14048,U_14049),U_14050) != U_14051
| hAPP(U_14049,hAPP(U_14050,U_14052)) = hAPP(U_14051,U_14052) ),
inference(clausify,[status(thm)],[f_3599_3]) ).
fof(f_3600_1,plain,
! [V_prod_2,V_i_2,V_h_2,T_g,T_f,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_f,T_b,T_g,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_e,T_c,T_g,V_g_2),V_i_2)),V_prod_2),
inference(fof_nnf,[status(thm)],[fact_map__pair_Ocompositionality]) ).
fof(f_3600_2,plain,
! [U_14063,U_14062,U_14061,U_14060,U_14059,U_14058,U_14057,U_14056,U_14055,U_14054,U_14053] : hAPP(c_Product__Type_Omap__pair(U_14053,U_14054,U_14055,U_14056,U_14057,U_14058),hAPP(c_Product__Type_Omap__pair(U_14059,U_14053,U_14060,U_14055,U_14061,U_14062),U_14063)) = hAPP(c_Product__Type_Omap__pair(U_14059,U_14054,U_14060,U_14056,hAPP(c_Fun_Ocomp(U_14053,U_14054,U_14059,U_14057),U_14061),hAPP(c_Fun_Ocomp(U_14055,U_14056,U_14060,U_14058),U_14062)),U_14063),
inference(variable_rename,[status(thm)],[f_3600_1]) ).
cnf(f_3600_3,plain,
hAPP(c_Product__Type_Omap__pair(U_14053,U_14054,U_14055,U_14056,U_14057,U_14058),hAPP(c_Product__Type_Omap__pair(U_14059,U_14053,U_14060,U_14055,U_14061,U_14062),U_14063)) = hAPP(c_Product__Type_Omap__pair(U_14059,U_14054,U_14060,U_14056,hAPP(c_Fun_Ocomp(U_14053,U_14054,U_14059,U_14057),U_14061),hAPP(c_Fun_Ocomp(U_14055,U_14056,U_14060,U_14058),U_14062)),U_14063),
inference(clausify,[status(thm)],[f_3600_2]) ).
fof(f_3601_1,plain,
! [V_g2_2,V_g1_2,T_g,V_f2_2,V_f1_2,T_f,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_f2_2,V_g2_2)),
inference(fof_nnf,[status(thm)],[fact_map__pair__compose]) ).
fof(f_3601_2,plain,
! [U_14073,U_14072,U_14071,U_14070,U_14069,U_14068,U_14067,U_14066,U_14065,U_14064] : c_Product__Type_Omap__pair(U_14064,U_14065,U_14066,U_14067,hAPP(c_Fun_Ocomp(U_14068,U_14065,U_14064,U_14069),U_14070),hAPP(c_Fun_Ocomp(U_14071,U_14067,U_14066,U_14072),U_14073)) = hAPP(c_Fun_Ocomp(tc_prod(U_14068,U_14071),tc_prod(U_14065,U_14067),tc_prod(U_14064,U_14066),c_Product__Type_Omap__pair(U_14068,U_14065,U_14071,U_14067,U_14069,U_14072)),c_Product__Type_Omap__pair(U_14064,U_14068,U_14066,U_14071,U_14070,U_14073)),
inference(variable_rename,[status(thm)],[f_3601_1]) ).
cnf(f_3601_3,plain,
c_Product__Type_Omap__pair(U_14064,U_14065,U_14066,U_14067,hAPP(c_Fun_Ocomp(U_14068,U_14065,U_14064,U_14069),U_14070),hAPP(c_Fun_Ocomp(U_14071,U_14067,U_14066,U_14072),U_14073)) = hAPP(c_Fun_Ocomp(tc_prod(U_14068,U_14071),tc_prod(U_14065,U_14067),tc_prod(U_14064,U_14066),c_Product__Type_Omap__pair(U_14068,U_14065,U_14071,U_14067,U_14069,U_14072)),c_Product__Type_Omap__pair(U_14064,U_14068,U_14066,U_14071,U_14070,U_14073)),
inference(clausify,[status(thm)],[f_3601_2]) ).
fof(f_3602_1,plain,
! [V_i_2,V_h_2,V_g_2,V_f_2,T_c,T_b,T_e,T_d,T_g,T_f] : hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g_2),V_i_2)),
inference(fof_nnf,[status(thm)],[fact_map__pair_Ocomp]) ).
fof(f_3602_2,plain,
! [U_14083,U_14082,U_14081,U_14080,U_14079,U_14078,U_14077,U_14076,U_14075,U_14074] : hAPP(c_Fun_Ocomp(tc_prod(U_14074,U_14075),tc_prod(U_14076,U_14077),tc_prod(U_14078,U_14079),c_Product__Type_Omap__pair(U_14074,U_14076,U_14075,U_14077,U_14080,U_14081)),c_Product__Type_Omap__pair(U_14078,U_14074,U_14079,U_14075,U_14082,U_14083)) = c_Product__Type_Omap__pair(U_14078,U_14076,U_14079,U_14077,hAPP(c_Fun_Ocomp(U_14074,U_14076,U_14078,U_14080),U_14082),hAPP(c_Fun_Ocomp(U_14075,U_14077,U_14079,U_14081),U_14083)),
inference(variable_rename,[status(thm)],[f_3602_1]) ).
cnf(f_3602_3,plain,
hAPP(c_Fun_Ocomp(tc_prod(U_14074,U_14075),tc_prod(U_14076,U_14077),tc_prod(U_14078,U_14079),c_Product__Type_Omap__pair(U_14074,U_14076,U_14075,U_14077,U_14080,U_14081)),c_Product__Type_Omap__pair(U_14078,U_14074,U_14079,U_14075,U_14082,U_14083)) = c_Product__Type_Omap__pair(U_14078,U_14076,U_14079,U_14077,hAPP(c_Fun_Ocomp(U_14074,U_14076,U_14078,U_14080),U_14082),hAPP(c_Fun_Ocomp(U_14075,U_14077,U_14079,U_14081),U_14083)),
inference(clausify,[status(thm)],[f_3602_2]) ).
fof(f_3603_1,plain,
! [V_r_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_b,T_c,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),V_r_2)),
inference(fof_nnf,[status(thm)],[fact_image__compose]) ).
fof(f_3603_2,plain,
! [U_14089,U_14088,U_14087,U_14086,U_14085,U_14084] : hAPP(c_Set_Oimage(U_14084,U_14085,hAPP(c_Fun_Ocomp(U_14086,U_14085,U_14084,U_14087),U_14088)),U_14089) = hAPP(c_Set_Oimage(U_14086,U_14085,U_14087),hAPP(c_Set_Oimage(U_14084,U_14086,U_14088),U_14089)),
inference(variable_rename,[status(thm)],[f_3603_1]) ).
cnf(f_3603_3,plain,
hAPP(c_Set_Oimage(U_14084,U_14085,hAPP(c_Fun_Ocomp(U_14086,U_14085,U_14084,U_14087),U_14088)),U_14089) = hAPP(c_Set_Oimage(U_14086,U_14085,U_14087),hAPP(c_Set_Oimage(U_14084,U_14086,U_14088),U_14089)),
inference(clausify,[status(thm)],[f_3603_2]) ).
fof(f_3604_1,plain,
! [V_g_2,T_d,V_f_2,T_b,T_c] :
( hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
| hAPP(c_Set_Oimage(T_b,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
| hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_comp__surj]) ).
fof(f_3604_2,plain,
! [U_14094,U_14093,U_14092,U_14091,U_14090] :
( hAPP(c_Set_Oimage(U_14090,U_14093,hAPP(c_Fun_Ocomp(U_14091,U_14093,U_14090,U_14094),U_14092)),c_Orderings_Otop__class_Otop(tc_fun(U_14090,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_14093,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_14091,U_14093,U_14094),c_Orderings_Otop__class_Otop(tc_fun(U_14091,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14093,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_14090,U_14091,U_14092),c_Orderings_Otop__class_Otop(tc_fun(U_14090,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14091,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_3604_1]) ).
cnf(f_3604_3,plain,
( hAPP(c_Set_Oimage(U_14090,U_14093,hAPP(c_Fun_Ocomp(U_14091,U_14093,U_14090,U_14094),U_14092)),c_Orderings_Otop__class_Otop(tc_fun(U_14090,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_14093,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_14091,U_14093,U_14094),c_Orderings_Otop__class_Otop(tc_fun(U_14091,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14093,tc_HOL_Obool))
| hAPP(c_Set_Oimage(U_14090,U_14091,U_14092),c_Orderings_Otop__class_Otop(tc_fun(U_14090,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14091,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3604_2]) ).
fof(f_3605_1,plain,
! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2)
| ~ c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_H_2),V_f_2),V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__imageI2]) ).
fof(f_3605_2,plain,
! [U_14100,U_14099,U_14098,U_14097,U_14096,U_14095] :
( c_Fun_Oinj__on(U_14095,U_14097,U_14099,U_14100)
| ~ c_Fun_Oinj__on(U_14095,U_14096,hAPP(c_Fun_Ocomp(U_14097,U_14096,U_14095,U_14098),U_14099),U_14100) ),
inference(variable_rename,[status(thm)],[f_3605_1]) ).
cnf(f_3605_3,plain,
( c_Fun_Oinj__on(U_14095,U_14097,U_14099,U_14100)
| ~ c_Fun_Oinj__on(U_14095,U_14096,hAPP(c_Fun_Ocomp(U_14097,U_14096,U_14095,U_14098),U_14099),U_14100) ),
inference(clausify,[status(thm)],[f_3605_2]) ).
fof(f_3606_1,plain,
! [V_g_2,T_d,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
inference(fof_nnf,[status(thm)],[fact_inj__comp]) ).
fof(f_3606_2,plain,
! [U_14105,U_14104,U_14103,U_14102,U_14101] :
( c_Fun_Oinj__on(U_14104,U_14102,hAPP(c_Fun_Ocomp(U_14101,U_14102,U_14104,U_14103),U_14105),c_Orderings_Otop__class_Otop(tc_fun(U_14104,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(U_14104,U_14101,U_14105,c_Orderings_Otop__class_Otop(tc_fun(U_14104,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(U_14101,U_14102,U_14103,c_Orderings_Otop__class_Otop(tc_fun(U_14101,tc_HOL_Obool))) ),
inference(variable_rename,[status(thm)],[f_3606_1]) ).
cnf(f_3606_3,plain,
( c_Fun_Oinj__on(U_14104,U_14102,hAPP(c_Fun_Ocomp(U_14101,U_14102,U_14104,U_14103),U_14105),c_Orderings_Otop__class_Otop(tc_fun(U_14104,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(U_14104,U_14101,U_14105,c_Orderings_Otop__class_Otop(tc_fun(U_14104,tc_HOL_Obool)))
| ~ c_Fun_Oinj__on(U_14101,U_14102,U_14103,c_Orderings_Otop__class_Otop(tc_fun(U_14101,tc_HOL_Obool))) ),
inference(clausify,[status(thm)],[f_3606_2]) ).
fof(f_3607_1,plain,
! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
( c_Fun_Oinj__on(T_d,T_c,V_g_2,hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_A_2))
| ~ c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2),V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__imageI]) ).
fof(f_3607_2,plain,
! [U_14111,U_14110,U_14109,U_14108,U_14107,U_14106] :
( c_Fun_Oinj__on(U_14108,U_14107,U_14109,hAPP(c_Set_Oimage(U_14106,U_14108,U_14110),U_14111))
| ~ c_Fun_Oinj__on(U_14106,U_14107,hAPP(c_Fun_Ocomp(U_14108,U_14107,U_14106,U_14109),U_14110),U_14111) ),
inference(variable_rename,[status(thm)],[f_3607_1]) ).
cnf(f_3607_3,plain,
( c_Fun_Oinj__on(U_14108,U_14107,U_14109,hAPP(c_Set_Oimage(U_14106,U_14108,U_14110),U_14111))
| ~ c_Fun_Oinj__on(U_14106,U_14107,hAPP(c_Fun_Ocomp(U_14108,U_14107,U_14106,U_14109),U_14110),U_14111) ),
inference(clausify,[status(thm)],[f_3607_2]) ).
fof(f_3608_1,plain,
! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
( c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2)
| ~ c_Fun_Oinj__on(T_c,T_d,V_g_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_comp__inj__on]) ).
fof(f_3608_2,plain,
! [U_14117,U_14116,U_14115,U_14114,U_14113,U_14112] :
( c_Fun_Oinj__on(U_14112,U_14116,hAPP(c_Fun_Ocomp(U_14113,U_14116,U_14112,U_14117),U_14114),U_14115)
| ~ c_Fun_Oinj__on(U_14113,U_14116,U_14117,hAPP(c_Set_Oimage(U_14112,U_14113,U_14114),U_14115))
| ~ c_Fun_Oinj__on(U_14112,U_14113,U_14114,U_14115) ),
inference(variable_rename,[status(thm)],[f_3608_1]) ).
cnf(f_3608_3,plain,
( c_Fun_Oinj__on(U_14112,U_14116,hAPP(c_Fun_Ocomp(U_14113,U_14116,U_14112,U_14117),U_14114),U_14115)
| ~ c_Fun_Oinj__on(U_14113,U_14116,U_14117,hAPP(c_Set_Oimage(U_14112,U_14113,U_14114),U_14115))
| ~ c_Fun_Oinj__on(U_14112,U_14113,U_14114,U_14115) ),
inference(clausify,[status(thm)],[f_3608_2]) ).
fof(f_3609_1,plain,
! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
( ( ( c_Fun_Oinj__on(T_c,T_d,V_f_H_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
| ~ c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2) )
& ( c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2)
| ~ c_Fun_Oinj__on(T_c,T_d,V_f_H_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) )
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ),
inference(fof_nnf,[status(thm)],[fact_comp__inj__on__iff]) ).
fof(f_3609_2,plain,
! [U_14123,U_14122,U_14121,U_14120,U_14119,U_14118] :
( ( ( c_Fun_Oinj__on(U_14119,U_14122,U_14123,hAPP(c_Set_Oimage(U_14118,U_14119,U_14120),U_14121))
| ~ c_Fun_Oinj__on(U_14118,U_14122,hAPP(c_Fun_Ocomp(U_14119,U_14122,U_14118,U_14123),U_14120),U_14121) )
& ( c_Fun_Oinj__on(U_14118,U_14122,hAPP(c_Fun_Ocomp(U_14119,U_14122,U_14118,U_14123),U_14120),U_14121)
| ~ c_Fun_Oinj__on(U_14119,U_14122,U_14123,hAPP(c_Set_Oimage(U_14118,U_14119,U_14120),U_14121)) ) )
| ~ c_Fun_Oinj__on(U_14118,U_14119,U_14120,U_14121) ),
inference(variable_rename,[status(thm)],[f_3609_1]) ).
cnf(f_3609_3,plain,
( c_Fun_Oinj__on(U_14118,U_14122,hAPP(c_Fun_Ocomp(U_14119,U_14122,U_14118,U_14123),U_14120),U_14121)
| ~ c_Fun_Oinj__on(U_14119,U_14122,U_14123,hAPP(c_Set_Oimage(U_14118,U_14119,U_14120),U_14121))
| ~ c_Fun_Oinj__on(U_14118,U_14119,U_14120,U_14121) ),
inference(clausify,[status(thm)],[f_3609_2]) ).
cnf(f_3609_4,plain,
( c_Fun_Oinj__on(U_14119,U_14122,U_14123,hAPP(c_Set_Oimage(U_14118,U_14119,U_14120),U_14121))
| ~ c_Fun_Oinj__on(U_14118,U_14122,hAPP(c_Fun_Ocomp(U_14119,U_14122,U_14118,U_14123),U_14120),U_14121)
| ~ c_Fun_Oinj__on(U_14118,U_14119,U_14120,U_14121) ),
inference(clausify,[status(thm)],[f_3609_2]) ).
fof(f_3610_1,plain,
! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2)
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__reindex]) ).
fof(f_3610_2,plain,
! [U_14129,U_14128,U_14127,U_14126,U_14125,U_14124] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14126,U_14124),U_14129),hAPP(c_Set_Oimage(U_14125,U_14126,U_14127),U_14128)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14125,U_14124),hAPP(c_Fun_Ocomp(U_14126,U_14124,U_14125,U_14129),U_14127)),U_14128)
| ~ c_Fun_Oinj__on(U_14125,U_14126,U_14127,U_14128)
| ~ class_Groups_Ocomm__monoid__add(U_14124) ),
inference(variable_rename,[status(thm)],[f_3610_1]) ).
cnf(f_3610_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14126,U_14124),U_14129),hAPP(c_Set_Oimage(U_14125,U_14126,U_14127),U_14128)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14125,U_14124),hAPP(c_Fun_Ocomp(U_14126,U_14124,U_14125,U_14129),U_14127)),U_14128)
| ~ c_Fun_Oinj__on(U_14125,U_14126,U_14127,U_14128)
| ~ class_Groups_Ocomm__monoid__add(U_14124) ),
inference(clausify,[status(thm)],[f_3610_2]) ).
fof(f_3611_1,plain,
! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2)
| V_g_2 != hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
| V_B_2 != hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod__reindex__cong]) ).
fof(f_3611_2,plain,
! [U_14137,U_14136,U_14135,U_14134,U_14133,U_14132,U_14131,U_14130] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14132,U_14130),U_14137),U_14135) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14131,U_14130),U_14136),U_14134)
| U_14136 != hAPP(c_Fun_Ocomp(U_14132,U_14130,U_14131,U_14137),U_14133)
| U_14135 != hAPP(c_Set_Oimage(U_14131,U_14132,U_14133),U_14134)
| ~ c_Fun_Oinj__on(U_14131,U_14132,U_14133,U_14134)
| ~ class_Groups_Ocomm__monoid__mult(U_14130) ),
inference(variable_rename,[status(thm)],[f_3611_1]) ).
cnf(f_3611_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14132,U_14130),U_14137),U_14135) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14131,U_14130),U_14136),U_14134)
| U_14136 != hAPP(c_Fun_Ocomp(U_14132,U_14130,U_14131,U_14137),U_14133)
| U_14135 != hAPP(c_Set_Oimage(U_14131,U_14132,U_14133),U_14134)
| ~ c_Fun_Oinj__on(U_14131,U_14132,U_14133,U_14134)
| ~ class_Groups_Ocomm__monoid__mult(U_14130) ),
inference(clausify,[status(thm)],[f_3611_2]) ).
fof(f_3612_1,plain,
! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2)
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setprod__reindex]) ).
fof(f_3612_2,plain,
! [U_14143,U_14142,U_14141,U_14140,U_14139,U_14138] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14140,U_14138),U_14143),hAPP(c_Set_Oimage(U_14139,U_14140,U_14141),U_14142)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14139,U_14138),hAPP(c_Fun_Ocomp(U_14140,U_14138,U_14139,U_14143),U_14141)),U_14142)
| ~ c_Fun_Oinj__on(U_14139,U_14140,U_14141,U_14142)
| ~ class_Groups_Ocomm__monoid__mult(U_14138) ),
inference(variable_rename,[status(thm)],[f_3612_1]) ).
cnf(f_3612_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14140,U_14138),U_14143),hAPP(c_Set_Oimage(U_14139,U_14140,U_14141),U_14142)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14139,U_14138),hAPP(c_Fun_Ocomp(U_14140,U_14138,U_14139,U_14143),U_14141)),U_14142)
| ~ c_Fun_Oinj__on(U_14139,U_14140,U_14141,U_14142)
| ~ class_Groups_Ocomm__monoid__mult(U_14138) ),
inference(clausify,[status(thm)],[f_3612_2]) ).
fof(f_3613_1,plain,
! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2)
| ~ c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__add(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setsum_Oreindex]) ).
fof(f_3613_2,plain,
! [U_14148,U_14147,U_14146,U_14145,U_14144] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14145,U_14144),U_14148),hAPP(c_Set_Oimage(U_14145,U_14145,U_14147),U_14146)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14145,U_14144),hAPP(c_Fun_Ocomp(U_14145,U_14144,U_14145,U_14148),U_14147)),U_14146)
| ~ c_Fun_Oinj__on(U_14145,U_14145,U_14147,U_14146)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14145),U_14146))
| ~ class_Groups_Ocomm__monoid__add(U_14144) ),
inference(variable_rename,[status(thm)],[f_3613_1]) ).
cnf(f_3613_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14145,U_14144),U_14148),hAPP(c_Set_Oimage(U_14145,U_14145,U_14147),U_14146)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14145,U_14144),hAPP(c_Fun_Ocomp(U_14145,U_14144,U_14145,U_14148),U_14147)),U_14146)
| ~ c_Fun_Oinj__on(U_14145,U_14145,U_14147,U_14146)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14145),U_14146))
| ~ class_Groups_Ocomm__monoid__add(U_14144) ),
inference(clausify,[status(thm)],[f_3613_2]) ).
fof(f_3614_1,plain,
! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2)
| ~ c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod_Oreindex]) ).
fof(f_3614_2,plain,
! [U_14153,U_14152,U_14151,U_14150,U_14149] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14150,U_14149),U_14153),hAPP(c_Set_Oimage(U_14150,U_14150,U_14152),U_14151)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14150,U_14149),hAPP(c_Fun_Ocomp(U_14150,U_14149,U_14150,U_14153),U_14152)),U_14151)
| ~ c_Fun_Oinj__on(U_14150,U_14150,U_14152,U_14151)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14150),U_14151))
| ~ class_Groups_Ocomm__monoid__mult(U_14149) ),
inference(variable_rename,[status(thm)],[f_3614_1]) ).
cnf(f_3614_3,plain,
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14150,U_14149),U_14153),hAPP(c_Set_Oimage(U_14150,U_14150,U_14152),U_14151)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14150,U_14149),hAPP(c_Fun_Ocomp(U_14150,U_14149,U_14150,U_14153),U_14152)),U_14151)
| ~ c_Fun_Oinj__on(U_14150,U_14150,U_14152,U_14151)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14150),U_14151))
| ~ class_Groups_Ocomm__monoid__mult(U_14149) ),
inference(clausify,[status(thm)],[f_3614_2]) ).
fof(f_3615_1,plain,
! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
( hAPP(c_Fun_Othe__inv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Fun_Othe__inv__into(T_d,T_b,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))))
| ~ c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_the__inv__into__comp]) ).
fof(f_3615_2,plain,
! [U_14160,U_14159,U_14158,U_14157,U_14156,U_14155,U_14154] :
( hAPP(c_Fun_Othe__inv__into(U_14157,U_14155,U_14159,hAPP(c_Fun_Ocomp(U_14154,U_14155,U_14157,U_14156),U_14158)),U_14160) = hAPP(hAPP(c_Fun_Ocomp(U_14154,U_14157,U_14155,c_Fun_Othe__inv__into(U_14157,U_14154,U_14159,U_14158)),c_Fun_Othe__inv__into(U_14154,U_14155,hAPP(c_Set_Oimage(U_14157,U_14154,U_14158),U_14159),U_14156)),U_14160)
| ~ hBOOL(hAPP(hAPP(c_member(U_14155),U_14160),hAPP(c_Set_Oimage(U_14154,U_14155,U_14156),hAPP(c_Set_Oimage(U_14157,U_14154,U_14158),U_14159))))
| ~ c_Fun_Oinj__on(U_14157,U_14154,U_14158,U_14159)
| ~ c_Fun_Oinj__on(U_14154,U_14155,U_14156,hAPP(c_Set_Oimage(U_14157,U_14154,U_14158),U_14159)) ),
inference(variable_rename,[status(thm)],[f_3615_1]) ).
cnf(f_3615_3,plain,
( hAPP(c_Fun_Othe__inv__into(U_14157,U_14155,U_14159,hAPP(c_Fun_Ocomp(U_14154,U_14155,U_14157,U_14156),U_14158)),U_14160) = hAPP(hAPP(c_Fun_Ocomp(U_14154,U_14157,U_14155,c_Fun_Othe__inv__into(U_14157,U_14154,U_14159,U_14158)),c_Fun_Othe__inv__into(U_14154,U_14155,hAPP(c_Set_Oimage(U_14157,U_14154,U_14158),U_14159),U_14156)),U_14160)
| ~ hBOOL(hAPP(hAPP(c_member(U_14155),U_14160),hAPP(c_Set_Oimage(U_14154,U_14155,U_14156),hAPP(c_Set_Oimage(U_14157,U_14154,U_14158),U_14159))))
| ~ c_Fun_Oinj__on(U_14157,U_14154,U_14158,U_14159)
| ~ c_Fun_Oinj__on(U_14154,U_14155,U_14156,hAPP(c_Set_Oimage(U_14157,U_14154,U_14158),U_14159)) ),
inference(clausify,[status(thm)],[f_3615_2]) ).
fof(f_3616_1,plain,
! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,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(c_Set_Oimage(T_b,T_c,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_h_2)),V_z_2),V_A_2)
| ~ c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Oab__semigroup__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_fold__image__reindex]) ).
fof(f_3616_2,plain,
! [U_14167,U_14166,U_14165,U_14164,U_14163,U_14162,U_14161] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14161,U_14164,c_Groups_Otimes__class_Otimes(U_14161)),U_14166),U_14167),hAPP(c_Set_Oimage(U_14162,U_14164,U_14165),U_14163)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14161,U_14162,c_Groups_Otimes__class_Otimes(U_14161)),hAPP(c_Fun_Ocomp(U_14164,U_14161,U_14162,U_14166),U_14165)),U_14167),U_14163)
| ~ c_Fun_Oinj__on(U_14162,U_14164,U_14165,U_14163)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14162),U_14163))
| ~ class_Groups_Oab__semigroup__mult(U_14161) ),
inference(variable_rename,[status(thm)],[f_3616_1]) ).
cnf(f_3616_3,plain,
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14161,U_14164,c_Groups_Otimes__class_Otimes(U_14161)),U_14166),U_14167),hAPP(c_Set_Oimage(U_14162,U_14164,U_14165),U_14163)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14161,U_14162,c_Groups_Otimes__class_Otimes(U_14161)),hAPP(c_Fun_Ocomp(U_14164,U_14161,U_14162,U_14166),U_14165)),U_14167),U_14163)
| ~ c_Fun_Oinj__on(U_14162,U_14164,U_14165,U_14163)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14162),U_14163))
| ~ class_Groups_Oab__semigroup__mult(U_14161) ),
inference(clausify,[status(thm)],[f_3616_2]) ).
fof(f_3617_1,plain,
! [T_b] : c_Nitpick_Odenom(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Odenom__def]) ).
fof(f_3617_2,plain,
! [U_14168] : c_Nitpick_Odenom(U_14168) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14168,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14168)),
inference(variable_rename,[status(thm)],[f_3617_1]) ).
cnf(f_3617_3,plain,
c_Nitpick_Odenom(U_14168) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14168,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14168)),
inference(clausify,[status(thm)],[f_3617_2]) ).
fof(f_3618_1,plain,
! [T_b] : c_Nitpick_Onum(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)),
inference(fof_nnf,[status(thm)],[fact_Nitpick_Onum__def]) ).
fof(f_3618_2,plain,
! [U_14169] : c_Nitpick_Onum(U_14169) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14169,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14169)),
inference(variable_rename,[status(thm)],[f_3618_1]) ).
cnf(f_3618_3,plain,
c_Nitpick_Onum(U_14169) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_14169,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_14169)),
inference(clausify,[status(thm)],[f_3618_2]) ).
fof(f_3619_1,plain,
! [V_g_2,V_f_2,T_c,T_b,T_e,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_e),T_d,tc_prod(T_b,T_c),c_Product__Type_Ofst(T_d,T_e)),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,tc_prod(T_b,T_c),V_f_2),c_Product__Type_Ofst(T_b,T_c)),
inference(fof_nnf,[status(thm)],[fact_fst__comp__map__pair]) ).
fof(f_3619_2,plain,
! [U_14175,U_14174,U_14173,U_14172,U_14171,U_14170] : hAPP(c_Fun_Ocomp(tc_prod(U_14170,U_14171),U_14170,tc_prod(U_14172,U_14173),c_Product__Type_Ofst(U_14170,U_14171)),c_Product__Type_Omap__pair(U_14172,U_14170,U_14173,U_14171,U_14174,U_14175)) = hAPP(c_Fun_Ocomp(U_14172,U_14170,tc_prod(U_14172,U_14173),U_14174),c_Product__Type_Ofst(U_14172,U_14173)),
inference(variable_rename,[status(thm)],[f_3619_1]) ).
cnf(f_3619_3,plain,
hAPP(c_Fun_Ocomp(tc_prod(U_14170,U_14171),U_14170,tc_prod(U_14172,U_14173),c_Product__Type_Ofst(U_14170,U_14171)),c_Product__Type_Omap__pair(U_14172,U_14170,U_14173,U_14171,U_14174,U_14175)) = hAPP(c_Fun_Ocomp(U_14172,U_14170,tc_prod(U_14172,U_14173),U_14174),c_Product__Type_Ofst(U_14172,U_14173)),
inference(clausify,[status(thm)],[f_3619_2]) ).
fof(f_3620_1,plain,
! [V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_d),T_d,tc_prod(T_b,T_c),c_Product__Type_Osnd(T_e,T_d)),c_Product__Type_Omap__pair(T_b,T_e,T_c,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_d,tc_prod(T_b,T_c),V_g_2),c_Product__Type_Osnd(T_b,T_c)),
inference(fof_nnf,[status(thm)],[fact_snd__comp__map__pair]) ).
fof(f_3620_2,plain,
! [U_14181,U_14180,U_14179,U_14178,U_14177,U_14176] : hAPP(c_Fun_Ocomp(tc_prod(U_14176,U_14177),U_14177,tc_prod(U_14178,U_14179),c_Product__Type_Osnd(U_14176,U_14177)),c_Product__Type_Omap__pair(U_14178,U_14176,U_14179,U_14177,U_14180,U_14181)) = hAPP(c_Fun_Ocomp(U_14179,U_14177,tc_prod(U_14178,U_14179),U_14181),c_Product__Type_Osnd(U_14178,U_14179)),
inference(variable_rename,[status(thm)],[f_3620_1]) ).
cnf(f_3620_3,plain,
hAPP(c_Fun_Ocomp(tc_prod(U_14176,U_14177),U_14177,tc_prod(U_14178,U_14179),c_Product__Type_Osnd(U_14176,U_14177)),c_Product__Type_Omap__pair(U_14178,U_14176,U_14179,U_14177,U_14180,U_14181)) = hAPP(c_Fun_Ocomp(U_14179,U_14177,tc_prod(U_14178,U_14179),U_14181),c_Product__Type_Osnd(U_14178,U_14179)),
inference(clausify,[status(thm)],[f_3620_2]) ).
fof(f_3621_1,plain,
! [V_f_2,V_g_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_b,tc_HOL_Obool),T_c,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_g_2),
inference(fof_nnf,[status(thm)],[fact_UN__o]) ).
fof(f_3621_2,plain,
! [U_14187,U_14186,U_14185,U_14184,U_14183,U_14182] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14182,tc_fun(U_14183,tc_HOL_Obool)),U_14184),hAPP(c_Fun_Ocomp(U_14185,tc_fun(U_14183,tc_HOL_Obool),U_14182,U_14186),U_14187)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14185,tc_fun(U_14183,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14182,U_14185,U_14187),U_14184)),U_14186),
inference(variable_rename,[status(thm)],[f_3621_1]) ).
cnf(f_3621_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14182,tc_fun(U_14183,tc_HOL_Obool)),U_14184),hAPP(c_Fun_Ocomp(U_14185,tc_fun(U_14183,tc_HOL_Obool),U_14182,U_14186),U_14187)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14185,tc_fun(U_14183,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14182,U_14185,U_14187),U_14184)),U_14186),
inference(clausify,[status(thm)],[f_3621_2]) ).
fof(f_3622_1,plain,
! [V_x_2,V_g_2,V_f_2,T_e,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),hAPP(c_Fun_Ocomp(T_e,tc_fun(T_d,T_b),T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)),
inference(fof_nnf,[status(thm)],[fact_split__comp]) ).
fof(f_3622_2,plain,
! [U_14194,U_14193,U_14192,U_14191,U_14190,U_14189,U_14188] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14188,U_14189,U_14190),hAPP(c_Fun_Ocomp(U_14191,tc_fun(U_14189,U_14190),U_14188,U_14192),U_14193)),U_14194) = hAPP(hAPP(U_14192,hAPP(U_14193,hAPP(c_Product__Type_Ofst(U_14188,U_14189),U_14194))),hAPP(c_Product__Type_Osnd(U_14188,U_14189),U_14194)),
inference(variable_rename,[status(thm)],[f_3622_1]) ).
cnf(f_3622_3,plain,
hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_14188,U_14189,U_14190),hAPP(c_Fun_Ocomp(U_14191,tc_fun(U_14189,U_14190),U_14188,U_14192),U_14193)),U_14194) = hAPP(hAPP(U_14192,hAPP(U_14193,hAPP(c_Product__Type_Ofst(U_14188,U_14189),U_14194))),hAPP(c_Product__Type_Osnd(U_14188,U_14189),U_14194)),
inference(clausify,[status(thm)],[f_3622_2]) ).
fof(f_3623_1,plain,
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),
inference(fof_nnf,[status(thm)],[fact_number__of__code__numeral__def]) ).
cnf(f_3623_2,plain,
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),
inference(clausify,[status(thm)],[f_3623_1]) ).
fof(f_3624_1,plain,
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),
inference(fof_nnf,[status(thm)],[fact_int__of__def]) ).
cnf(f_3624_2,plain,
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),
inference(clausify,[status(thm)],[f_3624_1]) ).
fof(f_3625_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding_Oremove]) ).
fof(f_3625_2,plain,
! [U_14200,U_14199,U_14198,U_14197,U_14196,U_14195] :
( hAPP(U_14198,U_14199) = hAPP(c_Fun_Ocomp(U_14196,U_14196,U_14196,hAPP(U_14198,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14195,tc_HOL_Obool)),U_14199),hAPP(hAPP(c_Set_Oinsert(U_14195),U_14200),c_Orderings_Obot__class_Obot(tc_fun(U_14195,tc_HOL_Obool)))))),hAPP(U_14197,U_14200))
| ~ hBOOL(hAPP(hAPP(c_member(U_14195),U_14200),U_14199))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14195),U_14199))
| ~ c_Finite__Set_Ofolding(U_14195,U_14196,U_14197,U_14198) ),
inference(variable_rename,[status(thm)],[f_3625_1]) ).
cnf(f_3625_3,plain,
( hAPP(U_14198,U_14199) = hAPP(c_Fun_Ocomp(U_14196,U_14196,U_14196,hAPP(U_14198,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14195,tc_HOL_Obool)),U_14199),hAPP(hAPP(c_Set_Oinsert(U_14195),U_14200),c_Orderings_Obot__class_Obot(tc_fun(U_14195,tc_HOL_Obool)))))),hAPP(U_14197,U_14200))
| ~ hBOOL(hAPP(hAPP(c_member(U_14195),U_14200),U_14199))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14195),U_14199))
| ~ c_Finite__Set_Ofolding(U_14195,U_14196,U_14197,U_14198) ),
inference(clausify,[status(thm)],[f_3625_2]) ).
fof(f_3626_1,plain,
! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_c,T_b,T_c,V_g_2),V_h_2)),V_A_2)
| ~ c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image_Oreindex]) ).
fof(f_3626_2,plain,
! [U_14208,U_14207,U_14206,U_14205,U_14204,U_14203,U_14202,U_14201] :
( hAPP(hAPP(U_14205,U_14208),hAPP(c_Set_Oimage(U_14202,U_14202,U_14207),U_14206)) = hAPP(hAPP(U_14205,hAPP(c_Fun_Ocomp(U_14202,U_14201,U_14202,U_14208),U_14207)),U_14206)
| ~ c_Fun_Oinj__on(U_14202,U_14202,U_14207,U_14206)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14202),U_14206))
| ~ c_Finite__Set_Ofolding__image(U_14201,U_14202,U_14203,U_14204,U_14205) ),
inference(variable_rename,[status(thm)],[f_3626_1]) ).
cnf(f_3626_3,plain,
( hAPP(hAPP(U_14205,U_14208),hAPP(c_Set_Oimage(U_14202,U_14202,U_14207),U_14206)) = hAPP(hAPP(U_14205,hAPP(c_Fun_Ocomp(U_14202,U_14201,U_14202,U_14208),U_14207)),U_14206)
| ~ c_Fun_Oinj__on(U_14202,U_14202,U_14207,U_14206)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14202),U_14206))
| ~ c_Finite__Set_Ofolding__image(U_14201,U_14202,U_14203,U_14204,U_14205) ),
inference(clausify,[status(thm)],[f_3626_2]) ).
fof(f_3627_1,plain,
! [V_h_2,V_g_2,T_g,V_f_2,T_d,T_e,T_f,V_F_2,V_fa_2,T_c,T_b] :
( hAPP(c_Fun_Ocomp(T_f,T_e,T_d,V_f_2),hAPP(c_Fun_Ocomp(T_g,T_f,T_d,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_g,T_e,T_d,hAPP(c_Fun_Ocomp(T_f,T_e,T_g,V_f_2),V_g_2)),V_h_2)
| ~ c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comps_I1_J]) ).
fof(f_3627_2,plain,
! [U_14219,U_14218,U_14217,U_14216,U_14215,U_14214,U_14213,U_14212,U_14211,U_14210,U_14209] :
( hAPP(c_Fun_Ocomp(U_14213,U_14214,U_14215,U_14216),hAPP(c_Fun_Ocomp(U_14217,U_14213,U_14215,U_14218),U_14219)) = hAPP(c_Fun_Ocomp(U_14217,U_14214,U_14215,hAPP(c_Fun_Ocomp(U_14213,U_14214,U_14217,U_14216),U_14218)),U_14219)
| ~ c_Finite__Set_Ofolding(U_14209,U_14210,U_14211,U_14212) ),
inference(variable_rename,[status(thm)],[f_3627_1]) ).
fof(f_3627_3,plain,
( ! [U_14219,U_14218,U_14217,U_14216,U_14215,U_14214,U_14213] : hAPP(c_Fun_Ocomp(U_14213,U_14214,U_14215,U_14216),hAPP(c_Fun_Ocomp(U_14217,U_14213,U_14215,U_14218),U_14219)) = hAPP(c_Fun_Ocomp(U_14217,U_14214,U_14215,hAPP(c_Fun_Ocomp(U_14213,U_14214,U_14217,U_14216),U_14218)),U_14219)
| ! [U_14212,U_14211,U_14210,U_14209] : ~ c_Finite__Set_Ofolding(U_14209,U_14210,U_14211,U_14212) ),
inference(miniscope,[status(thm)],[f_3627_2]) ).
cnf(f_3627_4,plain,
( hAPP(c_Fun_Ocomp(U_14213,U_14214,U_14215,U_14216),hAPP(c_Fun_Ocomp(U_14217,U_14213,U_14215,U_14218),U_14219)) = hAPP(c_Fun_Ocomp(U_14217,U_14214,U_14215,hAPP(c_Fun_Ocomp(U_14213,U_14214,U_14217,U_14216),U_14218)),U_14219)
| ~ c_Finite__Set_Ofolding(U_14209,U_14210,U_14211,U_14212) ),
inference(clausify,[status(thm)],[f_3627_3]) ).
fof(f_3628_1,plain,
! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))
| ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp]) ).
fof(f_3628_2,plain,
! [U_14225,U_14224,U_14223,U_14222,U_14221,U_14220] :
( hAPP(c_Fun_Ocomp(U_14221,U_14221,U_14221,hAPP(U_14222,U_14224)),hAPP(U_14222,U_14225)) = hAPP(c_Fun_Ocomp(U_14221,U_14221,U_14221,hAPP(U_14222,U_14225)),hAPP(U_14222,U_14224))
| ~ c_Finite__Set_Ofolding(U_14220,U_14221,U_14222,U_14223) ),
inference(variable_rename,[status(thm)],[f_3628_1]) ).
fof(f_3628_3,plain,
! [U_14225,U_14224,U_14223,U_14222,U_14221] :
( ! [U_14220] : ~ c_Finite__Set_Ofolding(U_14220,U_14221,U_14222,U_14223)
| hAPP(c_Fun_Ocomp(U_14221,U_14221,U_14221,hAPP(U_14222,U_14224)),hAPP(U_14222,U_14225)) = hAPP(c_Fun_Ocomp(U_14221,U_14221,U_14221,hAPP(U_14222,U_14225)),hAPP(U_14222,U_14224)) ),
inference(miniscope,[status(thm)],[f_3628_2]) ).
cnf(f_3628_4,plain,
( ~ c_Finite__Set_Ofolding(U_14220,U_14221,U_14222,U_14223)
| hAPP(c_Fun_Ocomp(U_14221,U_14221,U_14221,hAPP(U_14222,U_14224)),hAPP(U_14222,U_14225)) = hAPP(c_Fun_Ocomp(U_14221,U_14221,U_14221,hAPP(U_14222,U_14225)),hAPP(U_14222,U_14224)) ),
inference(clausify,[status(thm)],[f_3628_3]) ).
fof(f_3629_1,plain,
! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
( hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),V_g_2))
| ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp]) ).
fof(f_3629_2,plain,
! [U_14233,U_14232,U_14231,U_14230,U_14229,U_14228,U_14227,U_14226] :
( hAPP(c_Fun_Ocomp(U_14227,U_14227,U_14230,hAPP(U_14228,U_14231)),hAPP(c_Fun_Ocomp(U_14227,U_14227,U_14230,hAPP(U_14228,U_14232)),U_14233)) = hAPP(c_Fun_Ocomp(U_14227,U_14227,U_14230,hAPP(U_14228,U_14232)),hAPP(c_Fun_Ocomp(U_14227,U_14227,U_14230,hAPP(U_14228,U_14231)),U_14233))
| ~ c_Finite__Set_Ofolding(U_14226,U_14227,U_14228,U_14229) ),
inference(variable_rename,[status(thm)],[f_3629_1]) ).
fof(f_3629_3,plain,
! [U_14233,U_14232,U_14231,U_14230,U_14229,U_14228,U_14227] :
( ! [U_14226] : ~ c_Finite__Set_Ofolding(U_14226,U_14227,U_14228,U_14229)
| hAPP(c_Fun_Ocomp(U_14227,U_14227,U_14230,hAPP(U_14228,U_14231)),hAPP(c_Fun_Ocomp(U_14227,U_14227,U_14230,hAPP(U_14228,U_14232)),U_14233)) = hAPP(c_Fun_Ocomp(U_14227,U_14227,U_14230,hAPP(U_14228,U_14232)),hAPP(c_Fun_Ocomp(U_14227,U_14227,U_14230,hAPP(U_14228,U_14231)),U_14233)) ),
inference(miniscope,[status(thm)],[f_3629_2]) ).
cnf(f_3629_4,plain,
( ~ c_Finite__Set_Ofolding(U_14226,U_14227,U_14228,U_14229)
| hAPP(c_Fun_Ocomp(U_14227,U_14227,U_14230,hAPP(U_14228,U_14231)),hAPP(c_Fun_Ocomp(U_14227,U_14227,U_14230,hAPP(U_14228,U_14232)),U_14233)) = hAPP(c_Fun_Ocomp(U_14227,U_14227,U_14230,hAPP(U_14228,U_14232)),hAPP(c_Fun_Ocomp(U_14227,U_14227,U_14230,hAPP(U_14228,U_14231)),U_14233)) ),
inference(clausify,[status(thm)],[f_3629_3]) ).
fof(f_3630_1,plain,
! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(V_f_2,hAPP(hAPP(V_F_2,V_g_2),V_A_2)),hAPP(hAPP(V_F_2,V_h_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image_Odistrib]) ).
fof(f_3630_2,plain,
! [U_14241,U_14240,U_14239,U_14238,U_14237,U_14236,U_14235,U_14234] :
( hAPP(hAPP(U_14238,hAPP(hAPP(c_COMBS(U_14235,U_14234,U_14234),hAPP(hAPP(c_COMBB(U_14234,tc_fun(U_14234,U_14234),U_14235),U_14236),U_14240)),U_14241)),U_14239) = hAPP(hAPP(U_14236,hAPP(hAPP(U_14238,U_14240),U_14239)),hAPP(hAPP(U_14238,U_14241),U_14239))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14235),U_14239))
| ~ c_Finite__Set_Ofolding__image(U_14234,U_14235,U_14236,U_14237,U_14238) ),
inference(variable_rename,[status(thm)],[f_3630_1]) ).
cnf(f_3630_3,plain,
( hAPP(hAPP(U_14238,hAPP(hAPP(c_COMBS(U_14235,U_14234,U_14234),hAPP(hAPP(c_COMBB(U_14234,tc_fun(U_14234,U_14234),U_14235),U_14236),U_14240)),U_14241)),U_14239) = hAPP(hAPP(U_14236,hAPP(hAPP(U_14238,U_14240),U_14239)),hAPP(hAPP(U_14238,U_14241),U_14239))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14235),U_14239))
| ~ c_Finite__Set_Ofolding__image(U_14234,U_14235,U_14236,U_14237,U_14238) ),
inference(clausify,[status(thm)],[f_3630_2]) ).
fof(f_3631_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H]) ).
fof(f_3631_2,plain,
! [U_14247,U_14246,U_14245,U_14244,U_14243,U_14242] :
( hAPP(c_Fun_Ocomp(U_14243,U_14243,U_14243,hAPP(U_14244,U_14247)),hAPP(U_14245,U_14246)) = hAPP(c_Fun_Ocomp(U_14243,U_14243,U_14243,hAPP(U_14245,U_14246)),hAPP(U_14244,U_14247))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14242),U_14246))
| ~ c_Finite__Set_Ofolding(U_14242,U_14243,U_14244,U_14245) ),
inference(variable_rename,[status(thm)],[f_3631_1]) ).
cnf(f_3631_3,plain,
( hAPP(c_Fun_Ocomp(U_14243,U_14243,U_14243,hAPP(U_14244,U_14247)),hAPP(U_14245,U_14246)) = hAPP(c_Fun_Ocomp(U_14243,U_14243,U_14243,hAPP(U_14245,U_14246)),hAPP(U_14244,U_14247))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14242),U_14246))
| ~ c_Finite__Set_Ofolding(U_14242,U_14243,U_14244,U_14245) ),
inference(clausify,[status(thm)],[f_3631_2]) ).
fof(f_3632_1,plain,
! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp_H]) ).
fof(f_3632_2,plain,
! [U_14255,U_14254,U_14253,U_14252,U_14251,U_14250,U_14249,U_14248] :
( hAPP(c_Fun_Ocomp(U_14249,U_14249,U_14253,hAPP(U_14250,U_14254)),hAPP(c_Fun_Ocomp(U_14249,U_14249,U_14253,hAPP(U_14251,U_14252)),U_14255)) = hAPP(c_Fun_Ocomp(U_14249,U_14249,U_14253,hAPP(U_14251,U_14252)),hAPP(c_Fun_Ocomp(U_14249,U_14249,U_14253,hAPP(U_14250,U_14254)),U_14255))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14248),U_14252))
| ~ c_Finite__Set_Ofolding(U_14248,U_14249,U_14250,U_14251) ),
inference(variable_rename,[status(thm)],[f_3632_1]) ).
cnf(f_3632_3,plain,
( hAPP(c_Fun_Ocomp(U_14249,U_14249,U_14253,hAPP(U_14250,U_14254)),hAPP(c_Fun_Ocomp(U_14249,U_14249,U_14253,hAPP(U_14251,U_14252)),U_14255)) = hAPP(c_Fun_Ocomp(U_14249,U_14249,U_14253,hAPP(U_14251,U_14252)),hAPP(c_Fun_Ocomp(U_14249,U_14249,U_14253,hAPP(U_14250,U_14254)),U_14255))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14248),U_14252))
| ~ c_Finite__Set_Ofolding(U_14248,U_14249,U_14250,U_14251) ),
inference(clausify,[status(thm)],[f_3632_2]) ).
fof(f_3633_1,plain,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H_H]) ).
fof(f_3633_2,plain,
! [U_14261,U_14260,U_14259,U_14258,U_14257,U_14256] :
( hAPP(c_Fun_Ocomp(U_14257,U_14257,U_14257,hAPP(U_14259,U_14261)),hAPP(U_14259,U_14260)) = hAPP(c_Fun_Ocomp(U_14257,U_14257,U_14257,hAPP(U_14259,U_14260)),hAPP(U_14259,U_14261))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14256),U_14261))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14256),U_14260))
| ~ c_Finite__Set_Ofolding(U_14256,U_14257,U_14258,U_14259) ),
inference(variable_rename,[status(thm)],[f_3633_1]) ).
cnf(f_3633_3,plain,
( hAPP(c_Fun_Ocomp(U_14257,U_14257,U_14257,hAPP(U_14259,U_14261)),hAPP(U_14259,U_14260)) = hAPP(c_Fun_Ocomp(U_14257,U_14257,U_14257,hAPP(U_14259,U_14260)),hAPP(U_14259,U_14261))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14256),U_14261))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14256),U_14260))
| ~ c_Finite__Set_Ofolding(U_14256,U_14257,U_14258,U_14259) ),
inference(clausify,[status(thm)],[f_3633_2]) ).
fof(f_3634_1,plain,
! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),V_g_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp_H_H]) ).
fof(f_3634_2,plain,
! [U_14269,U_14268,U_14267,U_14266,U_14265,U_14264,U_14263,U_14262] :
( hAPP(c_Fun_Ocomp(U_14263,U_14263,U_14268,hAPP(U_14265,U_14267)),hAPP(c_Fun_Ocomp(U_14263,U_14263,U_14268,hAPP(U_14265,U_14266)),U_14269)) = hAPP(c_Fun_Ocomp(U_14263,U_14263,U_14268,hAPP(U_14265,U_14266)),hAPP(c_Fun_Ocomp(U_14263,U_14263,U_14268,hAPP(U_14265,U_14267)),U_14269))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14262),U_14267))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14262),U_14266))
| ~ c_Finite__Set_Ofolding(U_14262,U_14263,U_14264,U_14265) ),
inference(variable_rename,[status(thm)],[f_3634_1]) ).
cnf(f_3634_3,plain,
( hAPP(c_Fun_Ocomp(U_14263,U_14263,U_14268,hAPP(U_14265,U_14267)),hAPP(c_Fun_Ocomp(U_14263,U_14263,U_14268,hAPP(U_14265,U_14266)),U_14269)) = hAPP(c_Fun_Ocomp(U_14263,U_14263,U_14268,hAPP(U_14265,U_14266)),hAPP(c_Fun_Ocomp(U_14263,U_14263,U_14268,hAPP(U_14265,U_14267)),U_14269))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14262),U_14267))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14262),U_14266))
| ~ c_Finite__Set_Ofolding(U_14262,U_14263,U_14264,U_14265) ),
inference(clausify,[status(thm)],[f_3634_2]) ).
fof(f_3635_1,plain,
! [V_F_2,V_f_2,T_c,T_b] :
( hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c)
| ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding_Oempty]) ).
fof(f_3635_2,plain,
! [U_14273,U_14272,U_14271,U_14270] :
( hAPP(U_14273,c_Orderings_Obot__class_Obot(tc_fun(U_14270,tc_HOL_Obool))) = c_Fun_Oid(U_14271)
| ~ c_Finite__Set_Ofolding(U_14270,U_14271,U_14272,U_14273) ),
inference(variable_rename,[status(thm)],[f_3635_1]) ).
cnf(f_3635_3,plain,
( hAPP(U_14273,c_Orderings_Obot__class_Obot(tc_fun(U_14270,tc_HOL_Obool))) = c_Fun_Oid(U_14271)
| ~ c_Finite__Set_Ofolding(U_14270,U_14271,U_14272,U_14273) ),
inference(clausify,[status(thm)],[f_3635_2]) ).
fof(f_3636_1,plain,
! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image_Oeq__fold]) ).
fof(f_3636_2,plain,
! [U_14280,U_14279,U_14278,U_14277,U_14276,U_14275,U_14274] :
( hAPP(hAPP(U_14278,U_14280),U_14279) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14274,U_14275,U_14276),U_14280),U_14277),U_14279)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14275),U_14279))
| ~ c_Finite__Set_Ofolding__image(U_14274,U_14275,U_14276,U_14277,U_14278) ),
inference(variable_rename,[status(thm)],[f_3636_1]) ).
cnf(f_3636_3,plain,
( hAPP(hAPP(U_14278,U_14280),U_14279) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14274,U_14275,U_14276),U_14280),U_14277),U_14279)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14275),U_14279))
| ~ c_Finite__Set_Ofolding__image(U_14274,U_14275,U_14276,U_14277,U_14278) ),
inference(clausify,[status(thm)],[f_3636_2]) ).
fof(f_3637_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding_Oinsert]) ).
fof(f_3637_2,plain,
! [U_14286,U_14285,U_14284,U_14283,U_14282,U_14281] :
( hAPP(U_14284,hAPP(hAPP(c_Set_Oinsert(U_14281),U_14286),U_14285)) = hAPP(c_Fun_Ocomp(U_14282,U_14282,U_14282,hAPP(U_14284,U_14285)),hAPP(U_14283,U_14286))
| hBOOL(hAPP(hAPP(c_member(U_14281),U_14286),U_14285))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14281),U_14285))
| ~ c_Finite__Set_Ofolding(U_14281,U_14282,U_14283,U_14284) ),
inference(variable_rename,[status(thm)],[f_3637_1]) ).
cnf(f_3637_3,plain,
( hAPP(U_14284,hAPP(hAPP(c_Set_Oinsert(U_14281),U_14286),U_14285)) = hAPP(c_Fun_Ocomp(U_14282,U_14282,U_14282,hAPP(U_14284,U_14285)),hAPP(U_14283,U_14286))
| hBOOL(hAPP(hAPP(c_member(U_14281),U_14286),U_14285))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14281),U_14285))
| ~ c_Finite__Set_Ofolding(U_14281,U_14282,U_14283,U_14284) ),
inference(clausify,[status(thm)],[f_3637_2]) ).
fof(f_3638_1,plain,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding_Ounion__inter]) ).
fof(f_3638_2,plain,
! [U_14292,U_14291,U_14290,U_14289,U_14288,U_14287] :
( hAPP(c_Fun_Ocomp(U_14288,U_14288,U_14288,hAPP(U_14290,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14287,tc_HOL_Obool)),U_14291),U_14292))),hAPP(U_14290,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14287,tc_HOL_Obool)),U_14291),U_14292))) = hAPP(c_Fun_Ocomp(U_14288,U_14288,U_14288,hAPP(U_14290,U_14291)),hAPP(U_14290,U_14292))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14287),U_14292))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14287),U_14291))
| ~ c_Finite__Set_Ofolding(U_14287,U_14288,U_14289,U_14290) ),
inference(variable_rename,[status(thm)],[f_3638_1]) ).
cnf(f_3638_3,plain,
( hAPP(c_Fun_Ocomp(U_14288,U_14288,U_14288,hAPP(U_14290,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14287,tc_HOL_Obool)),U_14291),U_14292))),hAPP(U_14290,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14287,tc_HOL_Obool)),U_14291),U_14292))) = hAPP(c_Fun_Ocomp(U_14288,U_14288,U_14288,hAPP(U_14290,U_14291)),hAPP(U_14290,U_14292))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14287),U_14292))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14287),U_14291))
| ~ c_Finite__Set_Ofolding(U_14287,U_14288,U_14289,U_14290) ),
inference(clausify,[status(thm)],[f_3638_2]) ).
fof(f_3639_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding_Oinsert__remove]) ).
fof(f_3639_2,plain,
! [U_14298,U_14297,U_14296,U_14295,U_14294,U_14293] :
( hAPP(U_14296,hAPP(hAPP(c_Set_Oinsert(U_14293),U_14298),U_14297)) = hAPP(c_Fun_Ocomp(U_14294,U_14294,U_14294,hAPP(U_14296,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14293,tc_HOL_Obool)),U_14297),hAPP(hAPP(c_Set_Oinsert(U_14293),U_14298),c_Orderings_Obot__class_Obot(tc_fun(U_14293,tc_HOL_Obool)))))),hAPP(U_14295,U_14298))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14293),U_14297))
| ~ c_Finite__Set_Ofolding(U_14293,U_14294,U_14295,U_14296) ),
inference(variable_rename,[status(thm)],[f_3639_1]) ).
cnf(f_3639_3,plain,
( hAPP(U_14296,hAPP(hAPP(c_Set_Oinsert(U_14293),U_14298),U_14297)) = hAPP(c_Fun_Ocomp(U_14294,U_14294,U_14294,hAPP(U_14296,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14293,tc_HOL_Obool)),U_14297),hAPP(hAPP(c_Set_Oinsert(U_14293),U_14298),c_Orderings_Obot__class_Obot(tc_fun(U_14293,tc_HOL_Obool)))))),hAPP(U_14295,U_14298))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14293),U_14297))
| ~ c_Finite__Set_Ofolding(U_14293,U_14294,U_14295,U_14296) ),
inference(clausify,[status(thm)],[f_3639_2]) ).
fof(f_3640_1,plain,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding_Ounion]) ).
fof(f_3640_2,plain,
! [U_14304,U_14303,U_14302,U_14301,U_14300,U_14299] :
( hAPP(U_14302,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14299,tc_HOL_Obool)),U_14303),U_14304)) = hAPP(c_Fun_Ocomp(U_14300,U_14300,U_14300,hAPP(U_14302,U_14303)),hAPP(U_14302,U_14304))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14299,tc_HOL_Obool)),U_14303),U_14304) != c_Orderings_Obot__class_Obot(tc_fun(U_14299,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14299),U_14304))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14299),U_14303))
| ~ c_Finite__Set_Ofolding(U_14299,U_14300,U_14301,U_14302) ),
inference(variable_rename,[status(thm)],[f_3640_1]) ).
cnf(f_3640_3,plain,
( hAPP(U_14302,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14299,tc_HOL_Obool)),U_14303),U_14304)) = hAPP(c_Fun_Ocomp(U_14300,U_14300,U_14300,hAPP(U_14302,U_14303)),hAPP(U_14302,U_14304))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14299,tc_HOL_Obool)),U_14303),U_14304) != c_Orderings_Obot__class_Obot(tc_fun(U_14299,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14299),U_14304))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14299),U_14303))
| ~ c_Finite__Set_Ofolding(U_14299,U_14300,U_14301,U_14302) ),
inference(clausify,[status(thm)],[f_3640_2]) ).
fof(f_3641_1,plain,
! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_S_2)
| ? [B_x] :
( ? [B_y] :
( hAPP(V_h_2,hAPP(V_f_2,B_x)) != c_Groups_Ozero__class_Ozero(T_d)
& hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
& B_x != B_y
& hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2)) )
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__reindex__nonzero]) ).
fof(f_3641_2,plain,
! [U_14312,U_14311,U_14310,U_14309,U_14308,U_14307] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14312,U_14307),U_14311),hAPP(c_Set_Oimage(U_14308,U_14312,U_14310),U_14309)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14308,U_14307),hAPP(c_Fun_Ocomp(U_14312,U_14307,U_14308,U_14311),U_14310)),U_14309)
| ? [U_14306] :
( ? [U_14305] :
( hAPP(U_14311,hAPP(U_14310,U_14306)) != c_Groups_Ozero__class_Ozero(U_14307)
& hAPP(U_14310,U_14306) = hAPP(U_14310,U_14305)
& U_14306 != U_14305
& hBOOL(hAPP(hAPP(c_member(U_14308),U_14305),U_14309)) )
& hBOOL(hAPP(hAPP(c_member(U_14308),U_14306),U_14309)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14308),U_14309))
| ~ class_Groups_Ocomm__monoid__add(U_14307) ),
inference(variable_rename,[status(thm)],[f_3641_1]) ).
fof(f_3641_3,plain,
! [U_14312,U_14311,U_14310,U_14309,U_14308,U_14307] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14312,U_14307),U_14311),hAPP(c_Set_Oimage(U_14308,U_14312,U_14310),U_14309)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14308,U_14307),hAPP(c_Fun_Ocomp(U_14312,U_14307,U_14308,U_14311),U_14310)),U_14309)
| ( ? [U_14305] :
( hAPP(U_14311,hAPP(U_14310,sK346(U_14312,U_14311,U_14310,U_14309,U_14308,U_14307))) != c_Groups_Ozero__class_Ozero(U_14307)
& hAPP(U_14310,sK346(U_14312,U_14311,U_14310,U_14309,U_14308,U_14307)) = hAPP(U_14310,U_14305)
& sK346(U_14312,U_14311,U_14310,U_14309,U_14308,U_14307) != U_14305
& hBOOL(hAPP(hAPP(c_member(U_14308),U_14305),U_14309)) )
& hBOOL(hAPP(hAPP(c_member(U_14308),sK346(U_14312,U_14311,U_14310,U_14309,U_14308,U_14307)),U_14309)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14308),U_14309))
| ~ class_Groups_Ocomm__monoid__add(U_14307) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK346]),skolemize(U_14306,sK346(U_14312,U_14311,U_14310,U_14309,U_14308,U_14307))],[f_3641_2]) ).
fof(f_3641_4,plain,
! [U_14312,U_14311,U_14310,U_14309,U_14308,U_14307] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14312,U_14307),U_14311),hAPP(c_Set_Oimage(U_14308,U_14312,U_14310),U_14309)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14308,U_14307),hAPP(c_Fun_Ocomp(U_14312,U_14307,U_14308,U_14311),U_14310)),U_14309)
| ( hAPP(U_14311,hAPP(U_14310,sK346(U_14312,U_14311,U_14310,U_14309,U_14308,U_14307))) != c_Groups_Ozero__class_Ozero(U_14307)
& hAPP(U_14310,sK346(U_14312,U_14311,U_14310,U_14309,U_14308,U_14307)) = hAPP(U_14310,sK347(U_14312,U_14311,U_14310,U_14309,U_14308,U_14307))
& sK346(U_14312,U_14311,U_14310,U_14309,U_14308,U_14307) != sK347(U_14312,U_14311,U_14310,U_14309,U_14308,U_14307)
& hBOOL(hAPP(hAPP(c_member(U_14308),sK347(U_14312,U_14311,U_14310,U_14309,U_14308,U_14307)),U_14309))
& hBOOL(hAPP(hAPP(c_member(U_14308),sK346(U_14312,U_14311,U_14310,U_14309,U_14308,U_14307)),U_14309)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14308),U_14309))
| ~ class_Groups_Ocomm__monoid__add(U_14307) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK347]),skolemize(U_14305,sK347(U_14312,U_14311,U_14310,U_14309,U_14308,U_14307))],[f_3641_3]) ).
cnf(f_3641_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_14308),sK346(U_14312,U_14311,U_14310,U_14309,U_14308,U_14307)),U_14309))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14312,U_14307),U_14311),hAPP(c_Set_Oimage(U_14308,U_14312,U_14310),U_14309)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14308,U_14307),hAPP(c_Fun_Ocomp(U_14312,U_14307,U_14308,U_14311),U_14310)),U_14309)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14308),U_14309))
| ~ class_Groups_Ocomm__monoid__add(U_14307) ),
inference(clausify,[status(thm)],[f_3641_4]) ).
cnf(f_3641_6,plain,
( hBOOL(hAPP(hAPP(c_member(U_14308),sK347(U_14312,U_14311,U_14310,U_14309,U_14308,U_14307)),U_14309))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14312,U_14307),U_14311),hAPP(c_Set_Oimage(U_14308,U_14312,U_14310),U_14309)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14308,U_14307),hAPP(c_Fun_Ocomp(U_14312,U_14307,U_14308,U_14311),U_14310)),U_14309)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14308),U_14309))
| ~ class_Groups_Ocomm__monoid__add(U_14307) ),
inference(clausify,[status(thm)],[f_3641_4]) ).
cnf(f_3641_7,plain,
( sK346(U_14312,U_14311,U_14310,U_14309,U_14308,U_14307) != sK347(U_14312,U_14311,U_14310,U_14309,U_14308,U_14307)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14312,U_14307),U_14311),hAPP(c_Set_Oimage(U_14308,U_14312,U_14310),U_14309)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14308,U_14307),hAPP(c_Fun_Ocomp(U_14312,U_14307,U_14308,U_14311),U_14310)),U_14309)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14308),U_14309))
| ~ class_Groups_Ocomm__monoid__add(U_14307) ),
inference(clausify,[status(thm)],[f_3641_4]) ).
cnf(f_3641_8,plain,
( hAPP(U_14310,sK346(U_14312,U_14311,U_14310,U_14309,U_14308,U_14307)) = hAPP(U_14310,sK347(U_14312,U_14311,U_14310,U_14309,U_14308,U_14307))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14312,U_14307),U_14311),hAPP(c_Set_Oimage(U_14308,U_14312,U_14310),U_14309)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14308,U_14307),hAPP(c_Fun_Ocomp(U_14312,U_14307,U_14308,U_14311),U_14310)),U_14309)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14308),U_14309))
| ~ class_Groups_Ocomm__monoid__add(U_14307) ),
inference(clausify,[status(thm)],[f_3641_4]) ).
cnf(f_3641_9,plain,
( hAPP(U_14311,hAPP(U_14310,sK346(U_14312,U_14311,U_14310,U_14309,U_14308,U_14307))) != c_Groups_Ozero__class_Ozero(U_14307)
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14312,U_14307),U_14311),hAPP(c_Set_Oimage(U_14308,U_14312,U_14310),U_14309)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14308,U_14307),hAPP(c_Fun_Ocomp(U_14312,U_14307,U_14308,U_14311),U_14310)),U_14309)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14308),U_14309))
| ~ class_Groups_Ocomm__monoid__add(U_14307) ),
inference(clausify,[status(thm)],[f_3641_4]) ).
fof(f_3642_1,plain,
! [V_P_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_P_2) = c_Random__Sequence_Obind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)),
inference(fof_nnf,[status(thm)],[fact_Random__Sequence_Omap__def]) ).
fof(f_3642_2,plain,
! [U_14316,U_14315,U_14314,U_14313] : c_Random__Sequence_Omap(U_14313,U_14314,U_14315,U_14316) = c_Random__Sequence_Obind(U_14313,U_14314,U_14316,hAPP(c_Fun_Ocomp(U_14314,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(U_14314)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),U_14313,c_Random__Sequence_Osingle(U_14314)),U_14315)),
inference(variable_rename,[status(thm)],[f_3642_1]) ).
cnf(f_3642_3,plain,
c_Random__Sequence_Omap(U_14313,U_14314,U_14315,U_14316) = c_Random__Sequence_Obind(U_14313,U_14314,U_14316,hAPP(c_Fun_Ocomp(U_14314,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(U_14314)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),U_14313,c_Random__Sequence_Osingle(U_14314)),U_14315)),
inference(clausify,[status(thm)],[f_3642_2]) ).
fof(f_3643_1,plain,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__idem_Ounion__idem]) ).
fof(f_3643_2,plain,
! [U_14322,U_14321,U_14320,U_14319,U_14318,U_14317] :
( hAPP(U_14320,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14317,tc_HOL_Obool)),U_14321),U_14322)) = hAPP(c_Fun_Ocomp(U_14318,U_14318,U_14318,hAPP(U_14320,U_14321)),hAPP(U_14320,U_14322))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14317),U_14322))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14317),U_14321))
| ~ c_Finite__Set_Ofolding__idem(U_14317,U_14318,U_14319,U_14320) ),
inference(variable_rename,[status(thm)],[f_3643_1]) ).
cnf(f_3643_3,plain,
( hAPP(U_14320,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14317,tc_HOL_Obool)),U_14321),U_14322)) = hAPP(c_Fun_Ocomp(U_14318,U_14318,U_14318,hAPP(U_14320,U_14321)),hAPP(U_14320,U_14322))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14317),U_14322))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14317),U_14321))
| ~ c_Finite__Set_Ofolding__idem(U_14317,U_14318,U_14319,U_14320) ),
inference(clausify,[status(thm)],[f_3643_2]) ).
fof(f_3644_1,plain,
! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__idem_Osubset__comp__idem]) ).
fof(f_3644_2,plain,
! [U_14328,U_14327,U_14326,U_14325,U_14324,U_14323] :
( hAPP(c_Fun_Ocomp(U_14324,U_14324,U_14324,hAPP(U_14326,U_14327)),hAPP(U_14326,U_14328)) = hAPP(U_14326,U_14327)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14323,tc_HOL_Obool)),U_14328),U_14327))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14323),U_14327))
| ~ c_Finite__Set_Ofolding__idem(U_14323,U_14324,U_14325,U_14326) ),
inference(variable_rename,[status(thm)],[f_3644_1]) ).
cnf(f_3644_3,plain,
( hAPP(c_Fun_Ocomp(U_14324,U_14324,U_14324,hAPP(U_14326,U_14327)),hAPP(U_14326,U_14328)) = hAPP(U_14326,U_14327)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14323,tc_HOL_Obool)),U_14328),U_14327))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14323),U_14327))
| ~ c_Finite__Set_Ofolding__idem(U_14323,U_14324,U_14325,U_14326) ),
inference(clausify,[status(thm)],[f_3644_2]) ).
fof(f_3645_1,plain,
! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2)
| ~ c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__comp]) ).
fof(f_3645_2,plain,
! [U_14333,U_14332,U_14331,U_14330,U_14329] :
( hAPP(c_Fun_Ocomp(U_14330,U_14330,U_14330,hAPP(U_14331,U_14333)),hAPP(U_14331,U_14333)) = hAPP(U_14331,U_14333)
| ~ c_Finite__Set_Ofolding__idem(U_14329,U_14330,U_14331,U_14332) ),
inference(variable_rename,[status(thm)],[f_3645_1]) ).
fof(f_3645_3,plain,
! [U_14333,U_14332,U_14331,U_14330] :
( ! [U_14329] : ~ c_Finite__Set_Ofolding__idem(U_14329,U_14330,U_14331,U_14332)
| hAPP(c_Fun_Ocomp(U_14330,U_14330,U_14330,hAPP(U_14331,U_14333)),hAPP(U_14331,U_14333)) = hAPP(U_14331,U_14333) ),
inference(miniscope,[status(thm)],[f_3645_2]) ).
cnf(f_3645_4,plain,
( ~ c_Finite__Set_Ofolding__idem(U_14329,U_14330,U_14331,U_14332)
| hAPP(c_Fun_Ocomp(U_14330,U_14330,U_14330,hAPP(U_14331,U_14333)),hAPP(U_14331,U_14333)) = hAPP(U_14331,U_14333) ),
inference(clausify,[status(thm)],[f_3645_3]) ).
fof(f_3646_1,plain,
! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
( hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)
| ~ c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__left__comp]) ).
fof(f_3646_2,plain,
! [U_14340,U_14339,U_14338,U_14337,U_14336,U_14335,U_14334] :
( hAPP(c_Fun_Ocomp(U_14335,U_14335,U_14338,hAPP(U_14336,U_14339)),hAPP(c_Fun_Ocomp(U_14335,U_14335,U_14338,hAPP(U_14336,U_14339)),U_14340)) = hAPP(c_Fun_Ocomp(U_14335,U_14335,U_14338,hAPP(U_14336,U_14339)),U_14340)
| ~ c_Finite__Set_Ofolding__idem(U_14334,U_14335,U_14336,U_14337) ),
inference(variable_rename,[status(thm)],[f_3646_1]) ).
fof(f_3646_3,plain,
! [U_14340,U_14339,U_14338,U_14337,U_14336,U_14335] :
( ! [U_14334] : ~ c_Finite__Set_Ofolding__idem(U_14334,U_14335,U_14336,U_14337)
| hAPP(c_Fun_Ocomp(U_14335,U_14335,U_14338,hAPP(U_14336,U_14339)),hAPP(c_Fun_Ocomp(U_14335,U_14335,U_14338,hAPP(U_14336,U_14339)),U_14340)) = hAPP(c_Fun_Ocomp(U_14335,U_14335,U_14338,hAPP(U_14336,U_14339)),U_14340) ),
inference(miniscope,[status(thm)],[f_3646_2]) ).
cnf(f_3646_4,plain,
( ~ c_Finite__Set_Ofolding__idem(U_14334,U_14335,U_14336,U_14337)
| hAPP(c_Fun_Ocomp(U_14335,U_14335,U_14338,hAPP(U_14336,U_14339)),hAPP(c_Fun_Ocomp(U_14335,U_14335,U_14338,hAPP(U_14336,U_14339)),U_14340)) = hAPP(c_Fun_Ocomp(U_14335,U_14335,U_14338,hAPP(U_14336,U_14339)),U_14340) ),
inference(clausify,[status(thm)],[f_3646_3]) ).
fof(f_3647_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__idem_Oin__comp__idem]) ).
fof(f_3647_2,plain,
! [U_14346,U_14345,U_14344,U_14343,U_14342,U_14341] :
( hAPP(c_Fun_Ocomp(U_14342,U_14342,U_14342,hAPP(U_14344,U_14345)),hAPP(U_14343,U_14346)) = hAPP(U_14344,U_14345)
| ~ hBOOL(hAPP(hAPP(c_member(U_14341),U_14346),U_14345))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14341),U_14345))
| ~ c_Finite__Set_Ofolding__idem(U_14341,U_14342,U_14343,U_14344) ),
inference(variable_rename,[status(thm)],[f_3647_1]) ).
cnf(f_3647_3,plain,
( hAPP(c_Fun_Ocomp(U_14342,U_14342,U_14342,hAPP(U_14344,U_14345)),hAPP(U_14343,U_14346)) = hAPP(U_14344,U_14345)
| ~ hBOOL(hAPP(hAPP(c_member(U_14341),U_14346),U_14345))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14341),U_14345))
| ~ c_Finite__Set_Ofolding__idem(U_14341,U_14342,U_14343,U_14344) ),
inference(clausify,[status(thm)],[f_3647_2]) ).
fof(f_3648_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__idem_Oinsert__idem]) ).
fof(f_3648_2,plain,
! [U_14352,U_14351,U_14350,U_14349,U_14348,U_14347] :
( hAPP(U_14350,hAPP(hAPP(c_Set_Oinsert(U_14347),U_14352),U_14351)) = hAPP(c_Fun_Ocomp(U_14348,U_14348,U_14348,hAPP(U_14350,U_14351)),hAPP(U_14349,U_14352))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14347),U_14351))
| ~ c_Finite__Set_Ofolding__idem(U_14347,U_14348,U_14349,U_14350) ),
inference(variable_rename,[status(thm)],[f_3648_1]) ).
cnf(f_3648_3,plain,
( hAPP(U_14350,hAPP(hAPP(c_Set_Oinsert(U_14347),U_14352),U_14351)) = hAPP(c_Fun_Ocomp(U_14348,U_14348,U_14348,hAPP(U_14350,U_14351)),hAPP(U_14349,U_14352))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14347),U_14351))
| ~ c_Finite__Set_Ofolding__idem(U_14347,U_14348,U_14349,U_14350) ),
inference(clausify,[status(thm)],[f_3648_2]) ).
fof(f_3649_1,plain,
! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2)
| ? [B_x] :
( hAPP(V_g_2,B_x) != hAPP(hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2),B_x)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| V_B_2 != hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
| ~ class_Groups_Ocomm__monoid__mult(T_d) ),
inference(fof_nnf,[status(thm)],[fact_strong__setprod__reindex__cong]) ).
fof(f_3649_2,plain,
! [U_14361,U_14360,U_14359,U_14358,U_14357,U_14356,U_14355,U_14354] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14356,U_14354),U_14361),U_14359) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14355,U_14354),U_14360),U_14358)
| ? [U_14353] :
( hAPP(U_14360,U_14353) != hAPP(hAPP(c_Fun_Ocomp(U_14356,U_14354,U_14355,U_14361),U_14357),U_14353)
& hBOOL(hAPP(hAPP(c_member(U_14355),U_14353),U_14358)) )
| U_14359 != hAPP(c_Set_Oimage(U_14355,U_14356,U_14357),U_14358)
| ~ c_Fun_Oinj__on(U_14355,U_14356,U_14357,U_14358)
| ~ class_Groups_Ocomm__monoid__mult(U_14354) ),
inference(variable_rename,[status(thm)],[f_3649_1]) ).
fof(f_3649_3,plain,
! [U_14361,U_14360,U_14359,U_14358,U_14357,U_14356,U_14355,U_14354] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14356,U_14354),U_14361),U_14359) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14355,U_14354),U_14360),U_14358)
| ( hAPP(U_14360,sK348(U_14361,U_14360,U_14359,U_14358,U_14357,U_14356,U_14355,U_14354)) != hAPP(hAPP(c_Fun_Ocomp(U_14356,U_14354,U_14355,U_14361),U_14357),sK348(U_14361,U_14360,U_14359,U_14358,U_14357,U_14356,U_14355,U_14354))
& hBOOL(hAPP(hAPP(c_member(U_14355),sK348(U_14361,U_14360,U_14359,U_14358,U_14357,U_14356,U_14355,U_14354)),U_14358)) )
| U_14359 != hAPP(c_Set_Oimage(U_14355,U_14356,U_14357),U_14358)
| ~ c_Fun_Oinj__on(U_14355,U_14356,U_14357,U_14358)
| ~ class_Groups_Ocomm__monoid__mult(U_14354) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK348]),skolemize(U_14353,sK348(U_14361,U_14360,U_14359,U_14358,U_14357,U_14356,U_14355,U_14354))],[f_3649_2]) ).
cnf(f_3649_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_14355),sK348(U_14361,U_14360,U_14359,U_14358,U_14357,U_14356,U_14355,U_14354)),U_14358))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14356,U_14354),U_14361),U_14359) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14355,U_14354),U_14360),U_14358)
| U_14359 != hAPP(c_Set_Oimage(U_14355,U_14356,U_14357),U_14358)
| ~ c_Fun_Oinj__on(U_14355,U_14356,U_14357,U_14358)
| ~ class_Groups_Ocomm__monoid__mult(U_14354) ),
inference(clausify,[status(thm)],[f_3649_3]) ).
cnf(f_3649_5,plain,
( hAPP(U_14360,sK348(U_14361,U_14360,U_14359,U_14358,U_14357,U_14356,U_14355,U_14354)) != hAPP(hAPP(c_Fun_Ocomp(U_14356,U_14354,U_14355,U_14361),U_14357),sK348(U_14361,U_14360,U_14359,U_14358,U_14357,U_14356,U_14355,U_14354))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14356,U_14354),U_14361),U_14359) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14355,U_14354),U_14360),U_14358)
| U_14359 != hAPP(c_Set_Oimage(U_14355,U_14356,U_14357),U_14358)
| ~ c_Fun_Oinj__on(U_14355,U_14356,U_14357,U_14358)
| ~ class_Groups_Ocomm__monoid__mult(U_14354) ),
inference(clausify,[status(thm)],[f_3649_3]) ).
fof(f_3650_1,plain,
! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)),
inference(fof_nnf,[status(thm)],[fact_neg__map__def]) ).
fof(f_3650_2,plain,
! [U_14365,U_14364,U_14363,U_14362] : c_New__Random__Sequence_Oneg__map(U_14362,U_14363,U_14364,U_14365) = c_New__Random__Sequence_Oneg__bind(U_14362,U_14363,U_14365,hAPP(c_Fun_Ocomp(U_14363,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(U_14363)))))),U_14362,c_New__Random__Sequence_Oneg__single(U_14363)),U_14364)),
inference(variable_rename,[status(thm)],[f_3650_1]) ).
cnf(f_3650_3,plain,
c_New__Random__Sequence_Oneg__map(U_14362,U_14363,U_14364,U_14365) = c_New__Random__Sequence_Oneg__bind(U_14362,U_14363,U_14365,hAPP(c_Fun_Ocomp(U_14363,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(U_14363)))))),U_14362,c_New__Random__Sequence_Oneg__single(U_14363)),U_14364)),
inference(clausify,[status(thm)],[f_3650_2]) ).
fof(f_3651_1,plain,
! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_b,V_x_2),
inference(fof_nnf,[status(thm)],[fact_neg__single__def]) ).
fof(f_3651_2,plain,
! [U_14370,U_14369,U_14368,U_14367,U_14366] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(U_14366),U_14367),U_14368),U_14369),U_14370) = c_New__DSequence_Oneg__single(U_14366,U_14367),
inference(variable_rename,[status(thm)],[f_3651_1]) ).
cnf(f_3651_3,plain,
hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(U_14366),U_14367),U_14368),U_14369),U_14370) = c_New__DSequence_Oneg__single(U_14366,U_14367),
inference(clausify,[status(thm)],[f_3651_2]) ).
fof(f_3652_1,plain,
! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)),
inference(fof_nnf,[status(thm)],[fact_pos__map__def]) ).
fof(f_3652_2,plain,
! [U_14374,U_14373,U_14372,U_14371] : c_New__Random__Sequence_Opos__map(U_14371,U_14372,U_14373,U_14374) = c_New__Random__Sequence_Opos__bind(U_14371,U_14372,U_14374,hAPP(c_Fun_Ocomp(U_14372,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(U_14372))))),U_14371,c_New__Random__Sequence_Opos__single(U_14372)),U_14373)),
inference(variable_rename,[status(thm)],[f_3652_1]) ).
cnf(f_3652_3,plain,
c_New__Random__Sequence_Opos__map(U_14371,U_14372,U_14373,U_14374) = c_New__Random__Sequence_Opos__bind(U_14371,U_14372,U_14374,hAPP(c_Fun_Ocomp(U_14372,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(U_14372))))),U_14371,c_New__Random__Sequence_Opos__single(U_14372)),U_14373)),
inference(clausify,[status(thm)],[f_3652_2]) ).
fof(f_3653_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_New__DSequence_Oneg__single__def]) ).
fof(f_3653_2,plain,
! [U_14377,U_14376,U_14375] : hAPP(c_New__DSequence_Oneg__single(U_14375,U_14376),U_14377) = c_Lazy__Sequence_Ohb__single(U_14375,U_14376),
inference(variable_rename,[status(thm)],[f_3653_1]) ).
cnf(f_3653_3,plain,
hAPP(c_New__DSequence_Oneg__single(U_14375,U_14376),U_14377) = c_Lazy__Sequence_Ohb__single(U_14375,U_14376),
inference(clausify,[status(thm)],[f_3653_2]) ).
fof(f_3654_1,plain,
! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_b,V_x_2),
inference(fof_nnf,[status(thm)],[fact_pos__single__def]) ).
fof(f_3654_2,plain,
! [U_14382,U_14381,U_14380,U_14379,U_14378] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(U_14378),U_14379),U_14380),U_14381),U_14382) = c_New__DSequence_Opos__single(U_14378,U_14379),
inference(variable_rename,[status(thm)],[f_3654_1]) ).
cnf(f_3654_3,plain,
hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(U_14378),U_14379),U_14380),U_14381),U_14382) = c_New__DSequence_Opos__single(U_14378,U_14379),
inference(clausify,[status(thm)],[f_3654_2]) ).
fof(f_3655_1,plain,
! [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),
inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__single__def]) ).
fof(f_3655_2,plain,
! [U_14385,U_14384,U_14383] : hAPP(c_New__DSequence_Opos__single(U_14383,U_14384),U_14385) = hAPP(c_Lazy__Sequence_Osingle(U_14383),U_14384),
inference(variable_rename,[status(thm)],[f_3655_1]) ).
cnf(f_3655_3,plain,
hAPP(c_New__DSequence_Opos__single(U_14383,U_14384),U_14385) = hAPP(c_Lazy__Sequence_Osingle(U_14383),U_14384),
inference(clausify,[status(thm)],[f_3655_2]) ).
fof(f_3656_1,plain,
! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))),
inference(fof_nnf,[status(thm)],[fact_Eps__split]) ).
fof(f_3656_2,plain,
! [U_14388,U_14387,U_14386] : c_Hilbert__Choice_OEps(tc_prod(U_14386,U_14387),hAPP(c_Product__Type_Oprod_Oprod__case(U_14386,U_14387,tc_HOL_Obool),U_14388)) = c_Hilbert__Choice_OEps(tc_prod(U_14386,U_14387),hAPP(hAPP(c_COMBS(tc_prod(U_14386,U_14387),U_14387,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14386,tc_fun(U_14387,tc_HOL_Obool),tc_prod(U_14386,U_14387)),U_14388),c_Product__Type_Ofst(U_14386,U_14387))),c_Product__Type_Osnd(U_14386,U_14387))),
inference(variable_rename,[status(thm)],[f_3656_1]) ).
cnf(f_3656_3,plain,
c_Hilbert__Choice_OEps(tc_prod(U_14386,U_14387),hAPP(c_Product__Type_Oprod_Oprod__case(U_14386,U_14387,tc_HOL_Obool),U_14388)) = c_Hilbert__Choice_OEps(tc_prod(U_14386,U_14387),hAPP(hAPP(c_COMBS(tc_prod(U_14386,U_14387),U_14387,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14386,tc_fun(U_14387,tc_HOL_Obool),tc_prod(U_14386,U_14387)),U_14388),c_Product__Type_Ofst(U_14386,U_14387))),c_Product__Type_Osnd(U_14386,U_14387))),
inference(clausify,[status(thm)],[f_3656_2]) ).
fof(f_3657_1,plain,
! [T_b,V_c_2,V_P_2] :
( hBOOL(hAPP(V_P_2,V_c_2))
| V_c_2 != c_Hilbert__Choice_OEps(T_b,V_P_2)
| ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ),
inference(fof_nnf,[status(thm)],[fact_exE__some]) ).
fof(f_3657_2,plain,
! [U_14392,U_14391,U_14390] :
( hBOOL(hAPP(U_14390,U_14391))
| U_14391 != c_Hilbert__Choice_OEps(U_14392,U_14390)
| ! [U_14389] : ~ hBOOL(hAPP(U_14390,U_14389)) ),
inference(variable_rename,[status(thm)],[f_3657_1]) ).
cnf(f_3657_3,plain,
( hBOOL(hAPP(U_14390,U_14391))
| U_14391 != c_Hilbert__Choice_OEps(U_14392,U_14390)
| ~ hBOOL(hAPP(U_14390,U_14389)) ),
inference(clausify,[status(thm)],[f_3657_2]) ).
fof(f_3658_1,plain,
! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2,
inference(fof_nnf,[status(thm)],[fact_some__sym__eq__trivial]) ).
fof(f_3658_2,plain,
! [U_14394,U_14393] : c_Hilbert__Choice_OEps(U_14393,hAPP(c_fequal,U_14394)) = U_14394,
inference(variable_rename,[status(thm)],[f_3658_1]) ).
cnf(f_3658_3,plain,
c_Hilbert__Choice_OEps(U_14393,hAPP(c_fequal,U_14394)) = U_14394,
inference(clausify,[status(thm)],[f_3658_2]) ).
fof(f_3659_1,plain,
! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2,
inference(fof_nnf,[status(thm)],[fact_some__eq__trivial]) ).
fof(f_3659_2,plain,
! [U_14396,U_14395] : c_Hilbert__Choice_OEps(U_14395,hAPP(hAPP(c_COMBC(U_14395,U_14395,tc_HOL_Obool),c_fequal),U_14396)) = U_14396,
inference(variable_rename,[status(thm)],[f_3659_1]) ).
cnf(f_3659_3,plain,
c_Hilbert__Choice_OEps(U_14395,hAPP(hAPP(c_COMBC(U_14395,U_14395,tc_HOL_Obool),c_fequal),U_14396)) = U_14396,
inference(clausify,[status(thm)],[f_3659_2]) ).
fof(f_3660_1,plain,
! [T_b,V_P_2] :
( ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
| ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) )
& ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
| ~ hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_some__eq__ex]) ).
fof(f_3660_2,plain,
! [U_14400,U_14399] :
( ( hBOOL(hAPP(U_14399,c_Hilbert__Choice_OEps(U_14400,U_14399)))
| ! [U_14398] : ~ hBOOL(hAPP(U_14399,U_14398)) )
& ( ? [U_14397] : hBOOL(hAPP(U_14399,U_14397))
| ~ hBOOL(hAPP(U_14399,c_Hilbert__Choice_OEps(U_14400,U_14399))) ) ),
inference(variable_rename,[status(thm)],[f_3660_1]) ).
fof(f_3660_3,plain,
( ! [U_14404,U_14402] :
( hBOOL(hAPP(U_14402,c_Hilbert__Choice_OEps(U_14404,U_14402)))
| ! [U_14398] : ~ hBOOL(hAPP(U_14402,U_14398)) )
& ! [U_14403,U_14401] :
( ? [U_14397] : hBOOL(hAPP(U_14401,U_14397))
| ~ hBOOL(hAPP(U_14401,c_Hilbert__Choice_OEps(U_14403,U_14401))) ) ),
inference(miniscope,[status(thm)],[f_3660_2]) ).
fof(f_3660_4,plain,
( ! [U_14404,U_14402] :
( hBOOL(hAPP(U_14402,c_Hilbert__Choice_OEps(U_14404,U_14402)))
| ! [U_14398] : ~ hBOOL(hAPP(U_14402,U_14398)) )
& ! [U_14403,U_14401] :
( hBOOL(hAPP(U_14401,sK349(U_14403,U_14401)))
| ~ hBOOL(hAPP(U_14401,c_Hilbert__Choice_OEps(U_14403,U_14401))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK349]),skolemize(U_14397,sK349(U_14403,U_14401))],[f_3660_3]) ).
cnf(f_3660_5,plain,
( hBOOL(hAPP(U_14401,sK349(U_14403,U_14401)))
| ~ hBOOL(hAPP(U_14401,c_Hilbert__Choice_OEps(U_14403,U_14401))) ),
inference(clausify,[status(thm)],[f_3660_4]) ).
cnf(f_3660_6,plain,
( hBOOL(hAPP(U_14402,c_Hilbert__Choice_OEps(U_14404,U_14402)))
| ~ hBOOL(hAPP(U_14402,U_14398)) ),
inference(clausify,[status(thm)],[f_3660_4]) ).
fof(f_3661_1,plain,
! [T_b,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
| ! [B_x1] : ~ hBOOL(hAPP(V_P_2,B_x1)) ),
inference(fof_nnf,[status(thm)],[fact_someI__ex]) ).
fof(f_3661_2,plain,
! [U_14407,U_14406] :
( hBOOL(hAPP(U_14406,c_Hilbert__Choice_OEps(U_14407,U_14406)))
| ! [U_14405] : ~ hBOOL(hAPP(U_14406,U_14405)) ),
inference(variable_rename,[status(thm)],[f_3661_1]) ).
cnf(f_3661_3,plain,
( hBOOL(hAPP(U_14406,c_Hilbert__Choice_OEps(U_14407,U_14406)))
| ~ hBOOL(hAPP(U_14406,U_14405)) ),
inference(clausify,[status(thm)],[f_3661_2]) ).
fof(f_3662_1,plain,
! [T_b,B_P] :
( hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P)))
| ! [B_x] : ~ hBOOL(hAPP(B_P,B_x)) ),
inference(fof_nnf,[status(thm)],[fact_tfl__some]) ).
fof(f_3662_2,plain,
! [U_14410,U_14409] :
( hBOOL(hAPP(U_14409,c_Hilbert__Choice_OEps(U_14410,U_14409)))
| ! [U_14408] : ~ hBOOL(hAPP(U_14409,U_14408)) ),
inference(variable_rename,[status(thm)],[f_3662_1]) ).
cnf(f_3662_3,plain,
( hBOOL(hAPP(U_14409,c_Hilbert__Choice_OEps(U_14410,U_14409)))
| ~ hBOOL(hAPP(U_14409,U_14408)) ),
inference(clausify,[status(thm)],[f_3662_2]) ).
fof(f_3663_1,plain,
! [T_b,V_x_2,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
| ~ hBOOL(hAPP(V_P_2,V_x_2)) ),
inference(fof_nnf,[status(thm)],[fact_someI]) ).
fof(f_3663_2,plain,
! [U_14413,U_14412,U_14411] :
( hBOOL(hAPP(U_14411,c_Hilbert__Choice_OEps(U_14413,U_14411)))
| ~ hBOOL(hAPP(U_14411,U_14412)) ),
inference(variable_rename,[status(thm)],[f_3663_1]) ).
cnf(f_3663_3,plain,
( hBOOL(hAPP(U_14411,c_Hilbert__Choice_OEps(U_14413,U_14411)))
| ~ hBOOL(hAPP(U_14411,U_14412)) ),
inference(clausify,[status(thm)],[f_3663_2]) ).
fof(f_3664_1,plain,
! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_P_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))),
inference(fof_nnf,[status(thm)],[fact_split__paired__Eps]) ).
fof(f_3664_2,plain,
! [U_14416,U_14415,U_14414] : c_Hilbert__Choice_OEps(tc_prod(U_14414,U_14415),U_14416) = c_Hilbert__Choice_OEps(tc_prod(U_14414,U_14415),hAPP(c_Product__Type_Oprod_Oprod__case(U_14414,U_14415,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14415,tc_prod(U_14414,U_14415)),tc_fun(U_14415,tc_HOL_Obool),U_14414),hAPP(c_COMBB(tc_prod(U_14414,U_14415),tc_HOL_Obool,U_14415),U_14416)),c_Product__Type_OPair(U_14414,U_14415)))),
inference(variable_rename,[status(thm)],[f_3664_1]) ).
cnf(f_3664_3,plain,
c_Hilbert__Choice_OEps(tc_prod(U_14414,U_14415),U_14416) = c_Hilbert__Choice_OEps(tc_prod(U_14414,U_14415),hAPP(c_Product__Type_Oprod_Oprod__case(U_14414,U_14415,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_14415,tc_prod(U_14414,U_14415)),tc_fun(U_14415,tc_HOL_Obool),U_14414),hAPP(c_COMBB(tc_prod(U_14414,U_14415),tc_HOL_Obool,U_14415),U_14416)),c_Product__Type_OPair(U_14414,U_14415)))),
inference(clausify,[status(thm)],[f_3664_2]) ).
fof(f_3665_1,plain,
! [V_y_2,V_x_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2),
inference(fof_nnf,[status(thm)],[fact_Eps__split__eq]) ).
fof(f_3665_2,plain,
! [U_14420,U_14419,U_14418,U_14417] : c_Hilbert__Choice_OEps(tc_prod(U_14417,U_14418),hAPP(c_Product__Type_Oprod_Oprod__case(U_14417,U_14418,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14417,tc_fun(U_14418,tc_HOL_Obool),tc_fun(U_14418,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14418,tc_HOL_Obool),tc_fun(U_14418,tc_HOL_Obool)),U_14417),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14418)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14417),c_fconj),hAPP(c_fequal,U_14419)))),hAPP(c_fequal,U_14420)))) = hAPP(hAPP(c_Product__Type_OPair(U_14417,U_14418),U_14419),U_14420),
inference(variable_rename,[status(thm)],[f_3665_1]) ).
cnf(f_3665_3,plain,
c_Hilbert__Choice_OEps(tc_prod(U_14417,U_14418),hAPP(c_Product__Type_Oprod_Oprod__case(U_14417,U_14418,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14417,tc_fun(U_14418,tc_HOL_Obool),tc_fun(U_14418,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14418,tc_HOL_Obool),tc_fun(U_14418,tc_HOL_Obool)),U_14417),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14418)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14417),c_fconj),hAPP(c_fequal,U_14419)))),hAPP(c_fequal,U_14420)))) = hAPP(hAPP(c_Product__Type_OPair(U_14417,U_14418),U_14419),U_14420),
inference(clausify,[status(thm)],[f_3665_2]) ).
fof(f_3666_1,plain,
! [V_R_2,T_b] :
( c_Wellfounded_Owf(T_b,V_R_2)
| ? [B_A] :
( B_A != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),B_A))) ) ),
inference(fof_nnf,[status(thm)],[fact_wfI__pf]) ).
fof(f_3666_2,plain,
! [U_14423,U_14422] :
( c_Wellfounded_Owf(U_14422,U_14423)
| ? [U_14421] :
( U_14421 != c_Orderings_Obot__class_Obot(tc_fun(U_14422,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14422,tc_HOL_Obool)),U_14421),hAPP(c_Relation_OImage(U_14422,U_14422,U_14423),U_14421))) ) ),
inference(variable_rename,[status(thm)],[f_3666_1]) ).
fof(f_3666_3,plain,
! [U_14423,U_14422] :
( c_Wellfounded_Owf(U_14422,U_14423)
| ( sK350(U_14423,U_14422) != c_Orderings_Obot__class_Obot(tc_fun(U_14422,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14422,tc_HOL_Obool)),sK350(U_14423,U_14422)),hAPP(c_Relation_OImage(U_14422,U_14422,U_14423),sK350(U_14423,U_14422)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK350]),skolemize(U_14421,sK350(U_14423,U_14422))],[f_3666_2]) ).
cnf(f_3666_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14422,tc_HOL_Obool)),sK350(U_14423,U_14422)),hAPP(c_Relation_OImage(U_14422,U_14422,U_14423),sK350(U_14423,U_14422))))
| c_Wellfounded_Owf(U_14422,U_14423) ),
inference(clausify,[status(thm)],[f_3666_3]) ).
cnf(f_3666_5,plain,
( sK350(U_14423,U_14422) != c_Orderings_Obot__class_Obot(tc_fun(U_14422,tc_HOL_Obool))
| c_Wellfounded_Owf(U_14422,U_14423) ),
inference(clausify,[status(thm)],[f_3666_3]) ).
fof(f_3667_1,plain,
! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_C_2),V_D_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_Sigma__mono]) ).
fof(f_3667_2,plain,
! [U_14430,U_14429,U_14428,U_14427,U_14426,U_14425] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14425,U_14428),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14425,U_14428),U_14426),U_14429)),hAPP(hAPP(c_Product__Type_OSigma(U_14425,U_14428),U_14427),U_14430)))
| ? [U_14424] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14428,tc_HOL_Obool)),hAPP(U_14429,U_14424)),hAPP(U_14430,U_14424)))
& hBOOL(hAPP(hAPP(c_member(U_14425),U_14424),U_14426)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14425,tc_HOL_Obool)),U_14426),U_14427)) ),
inference(variable_rename,[status(thm)],[f_3667_1]) ).
fof(f_3667_3,plain,
! [U_14430,U_14429,U_14428,U_14427,U_14426,U_14425] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14425,U_14428),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14425,U_14428),U_14426),U_14429)),hAPP(hAPP(c_Product__Type_OSigma(U_14425,U_14428),U_14427),U_14430)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14428,tc_HOL_Obool)),hAPP(U_14429,sK351(U_14430,U_14429,U_14428,U_14427,U_14426,U_14425))),hAPP(U_14430,sK351(U_14430,U_14429,U_14428,U_14427,U_14426,U_14425))))
& hBOOL(hAPP(hAPP(c_member(U_14425),sK351(U_14430,U_14429,U_14428,U_14427,U_14426,U_14425)),U_14426)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14425,tc_HOL_Obool)),U_14426),U_14427)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK351]),skolemize(U_14424,sK351(U_14430,U_14429,U_14428,U_14427,U_14426,U_14425))],[f_3667_2]) ).
cnf(f_3667_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_14425),sK351(U_14430,U_14429,U_14428,U_14427,U_14426,U_14425)),U_14426))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14425,U_14428),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14425,U_14428),U_14426),U_14429)),hAPP(hAPP(c_Product__Type_OSigma(U_14425,U_14428),U_14427),U_14430)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14425,tc_HOL_Obool)),U_14426),U_14427)) ),
inference(clausify,[status(thm)],[f_3667_3]) ).
cnf(f_3667_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14428,tc_HOL_Obool)),hAPP(U_14429,sK351(U_14430,U_14429,U_14428,U_14427,U_14426,U_14425))),hAPP(U_14430,sK351(U_14430,U_14429,U_14428,U_14427,U_14426,U_14425))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14425,U_14428),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14425,U_14428),U_14426),U_14429)),hAPP(hAPP(c_Product__Type_OSigma(U_14425,U_14428),U_14427),U_14430)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14425,tc_HOL_Obool)),U_14426),U_14427)) ),
inference(clausify,[status(thm)],[f_3667_3]) ).
fof(f_3668_1,plain,
! [V_R_2,V_x_2,T_b] :
( ? [B_z] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_x_2)),V_R_2)) )
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_not__acc__down]) ).
fof(f_3668_2,plain,
! [U_14434,U_14433,U_14432] :
( ? [U_14431] :
( ~ hBOOL(hAPP(hAPP(c_member(U_14432),U_14431),c_Wellfounded_Oacc(U_14432,U_14434)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_14432,U_14432)),hAPP(hAPP(c_Product__Type_OPair(U_14432,U_14432),U_14431),U_14433)),U_14434)) )
| hBOOL(hAPP(hAPP(c_member(U_14432),U_14433),c_Wellfounded_Oacc(U_14432,U_14434))) ),
inference(variable_rename,[status(thm)],[f_3668_1]) ).
fof(f_3668_3,plain,
! [U_14434,U_14433,U_14432] :
( ( ~ hBOOL(hAPP(hAPP(c_member(U_14432),sK352(U_14434,U_14433,U_14432)),c_Wellfounded_Oacc(U_14432,U_14434)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_14432,U_14432)),hAPP(hAPP(c_Product__Type_OPair(U_14432,U_14432),sK352(U_14434,U_14433,U_14432)),U_14433)),U_14434)) )
| hBOOL(hAPP(hAPP(c_member(U_14432),U_14433),c_Wellfounded_Oacc(U_14432,U_14434))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK352]),skolemize(U_14431,sK352(U_14434,U_14433,U_14432))],[f_3668_2]) ).
cnf(f_3668_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14432,U_14432)),hAPP(hAPP(c_Product__Type_OPair(U_14432,U_14432),sK352(U_14434,U_14433,U_14432)),U_14433)),U_14434))
| hBOOL(hAPP(hAPP(c_member(U_14432),U_14433),c_Wellfounded_Oacc(U_14432,U_14434))) ),
inference(clausify,[status(thm)],[f_3668_3]) ).
cnf(f_3668_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_14432),sK352(U_14434,U_14433,U_14432)),c_Wellfounded_Oacc(U_14432,U_14434)))
| hBOOL(hAPP(hAPP(c_member(U_14432),U_14433),c_Wellfounded_Oacc(U_14432,U_14434))) ),
inference(clausify,[status(thm)],[f_3668_3]) ).
fof(f_3669_1,plain,
! [V_r_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
| ? [B_y] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_x_2)),V_r_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_acc_OaccI]) ).
fof(f_3669_2,plain,
! [U_14438,U_14437,U_14436] :
( hBOOL(hAPP(hAPP(c_member(U_14436),U_14437),c_Wellfounded_Oacc(U_14436,U_14438)))
| ? [U_14435] :
( ~ hBOOL(hAPP(hAPP(c_member(U_14436),U_14435),c_Wellfounded_Oacc(U_14436,U_14438)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_14436,U_14436)),hAPP(hAPP(c_Product__Type_OPair(U_14436,U_14436),U_14435),U_14437)),U_14438)) ) ),
inference(variable_rename,[status(thm)],[f_3669_1]) ).
fof(f_3669_3,plain,
! [U_14438,U_14437,U_14436] :
( hBOOL(hAPP(hAPP(c_member(U_14436),U_14437),c_Wellfounded_Oacc(U_14436,U_14438)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_14436),sK353(U_14438,U_14437,U_14436)),c_Wellfounded_Oacc(U_14436,U_14438)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_14436,U_14436)),hAPP(hAPP(c_Product__Type_OPair(U_14436,U_14436),sK353(U_14438,U_14437,U_14436)),U_14437)),U_14438)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK353]),skolemize(U_14435,sK353(U_14438,U_14437,U_14436))],[f_3669_2]) ).
cnf(f_3669_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14436,U_14436)),hAPP(hAPP(c_Product__Type_OPair(U_14436,U_14436),sK353(U_14438,U_14437,U_14436)),U_14437)),U_14438))
| hBOOL(hAPP(hAPP(c_member(U_14436),U_14437),c_Wellfounded_Oacc(U_14436,U_14438))) ),
inference(clausify,[status(thm)],[f_3669_3]) ).
cnf(f_3669_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_14436),sK353(U_14438,U_14437,U_14436)),c_Wellfounded_Oacc(U_14436,U_14438)))
| hBOOL(hAPP(hAPP(c_member(U_14436),U_14437),c_Wellfounded_Oacc(U_14436,U_14438))) ),
inference(clausify,[status(thm)],[f_3669_3]) ).
fof(f_3670_1,plain,
! [V_f_2,V_S_2,T_b,T_c] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2) = c_Groups_Oone__class_Oone(T_c)
| ? [B_x] :
( hAPP(V_f_2,B_x) != c_Groups_Oone__class_Oone(T_c)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
| ~ class_Groups_Ocomm__monoid__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold__image__1]) ).
fof(f_3670_2,plain,
! [U_14443,U_14442,U_14441,U_14440] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14440,U_14441,c_Groups_Otimes__class_Otimes(U_14440)),U_14443),c_Groups_Oone__class_Oone(U_14440)),U_14442) = c_Groups_Oone__class_Oone(U_14440)
| ? [U_14439] :
( hAPP(U_14443,U_14439) != c_Groups_Oone__class_Oone(U_14440)
& hBOOL(hAPP(hAPP(c_member(U_14441),U_14439),U_14442)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14441),U_14442))
| ~ class_Groups_Ocomm__monoid__mult(U_14440) ),
inference(variable_rename,[status(thm)],[f_3670_1]) ).
fof(f_3670_3,plain,
! [U_14443,U_14442,U_14441,U_14440] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14440,U_14441,c_Groups_Otimes__class_Otimes(U_14440)),U_14443),c_Groups_Oone__class_Oone(U_14440)),U_14442) = c_Groups_Oone__class_Oone(U_14440)
| ( hAPP(U_14443,sK354(U_14443,U_14442,U_14441,U_14440)) != c_Groups_Oone__class_Oone(U_14440)
& hBOOL(hAPP(hAPP(c_member(U_14441),sK354(U_14443,U_14442,U_14441,U_14440)),U_14442)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14441),U_14442))
| ~ class_Groups_Ocomm__monoid__mult(U_14440) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK354]),skolemize(U_14439,sK354(U_14443,U_14442,U_14441,U_14440))],[f_3670_2]) ).
cnf(f_3670_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_14441),sK354(U_14443,U_14442,U_14441,U_14440)),U_14442))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14440,U_14441,c_Groups_Otimes__class_Otimes(U_14440)),U_14443),c_Groups_Oone__class_Oone(U_14440)),U_14442) = c_Groups_Oone__class_Oone(U_14440)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14441),U_14442))
| ~ class_Groups_Ocomm__monoid__mult(U_14440) ),
inference(clausify,[status(thm)],[f_3670_3]) ).
cnf(f_3670_5,plain,
( hAPP(U_14443,sK354(U_14443,U_14442,U_14441,U_14440)) != c_Groups_Oone__class_Oone(U_14440)
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14440,U_14441,c_Groups_Otimes__class_Otimes(U_14440)),U_14443),c_Groups_Oone__class_Oone(U_14440)),U_14442) = c_Groups_Oone__class_Oone(U_14440)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14441),U_14442))
| ~ class_Groups_Ocomm__monoid__mult(U_14440) ),
inference(clausify,[status(thm)],[f_3670_3]) ).
fof(f_3671_1,plain,
! [V_A_2,T_b] :
( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_card_Oneutral]) ).
fof(f_3671_2,plain,
! [U_14446,U_14445] :
( hAPP(c_Finite__Set_Ocard(U_14445),U_14446) = 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_14444] : hBOOL(hAPP(hAPP(c_member(U_14445),U_14444),U_14446)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14445),U_14446)) ),
inference(variable_rename,[status(thm)],[f_3671_1]) ).
fof(f_3671_3,plain,
! [U_14446,U_14445] :
( hAPP(c_Finite__Set_Ocard(U_14445),U_14446) = 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_14445),sK355(U_14446,U_14445)),U_14446)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14445),U_14446)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK355]),skolemize(U_14444,sK355(U_14446,U_14445))],[f_3671_2]) ).
cnf(f_3671_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_14445),sK355(U_14446,U_14445)),U_14446))
| hAPP(c_Finite__Set_Ocard(U_14445),U_14446) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14445),U_14446)) ),
inference(clausify,[status(thm)],[f_3671_3]) ).
cnf(f_3671_5,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Finite__Set_Ocard(U_14445),U_14446) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14445),U_14446)) ),
inference(clausify,[status(thm)],[f_3671_3]) ).
fof(f_3672_1,plain,
! [V_R_2,V_a2_2,V_a1_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
| ? [B_x] :
( ! [B_xa] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) )
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) )
| V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) )
& ( ( ! [B_x] :
( ? [B_xa] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2)) )
& V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_max__ext_Osimps]) ).
fof(f_3672_2,plain,
! [U_14454,U_14453,U_14452,U_14451] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14451,tc_HOL_Obool),tc_fun(U_14451,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14451,tc_HOL_Obool),tc_fun(U_14451,tc_HOL_Obool)),U_14452),U_14453)),c_Wellfounded_Omax__ext(U_14451,U_14454)))
| ? [U_14450] :
( ! [U_14449] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14451,U_14451)),hAPP(hAPP(c_Product__Type_OPair(U_14451,U_14451),U_14450),U_14449)),U_14454))
| ~ hBOOL(hAPP(hAPP(c_member(U_14451),U_14449),U_14453)) )
& hBOOL(hAPP(hAPP(c_member(U_14451),U_14450),U_14452)) )
| U_14453 = c_Orderings_Obot__class_Obot(tc_fun(U_14451,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14451),U_14453))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14451),U_14452)) )
& ( ( ! [U_14448] :
( ? [U_14447] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14451,U_14451)),hAPP(hAPP(c_Product__Type_OPair(U_14451,U_14451),U_14448),U_14447)),U_14454))
& hBOOL(hAPP(hAPP(c_member(U_14451),U_14447),U_14453)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_14451),U_14448),U_14452)) )
& U_14453 != c_Orderings_Obot__class_Obot(tc_fun(U_14451,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_14451),U_14453))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_14451),U_14452)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14451,tc_HOL_Obool),tc_fun(U_14451,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14451,tc_HOL_Obool),tc_fun(U_14451,tc_HOL_Obool)),U_14452),U_14453)),c_Wellfounded_Omax__ext(U_14451,U_14454))) ) ),
inference(variable_rename,[status(thm)],[f_3672_1]) ).
fof(f_3672_3,plain,
( ! [U_14462,U_14460,U_14458,U_14456] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14456,tc_HOL_Obool),tc_fun(U_14456,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14456,tc_HOL_Obool),tc_fun(U_14456,tc_HOL_Obool)),U_14458),U_14460)),c_Wellfounded_Omax__ext(U_14456,U_14462)))
| ? [U_14450] :
( ! [U_14449] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14456,U_14456)),hAPP(hAPP(c_Product__Type_OPair(U_14456,U_14456),U_14450),U_14449)),U_14462))
| ~ hBOOL(hAPP(hAPP(c_member(U_14456),U_14449),U_14460)) )
& hBOOL(hAPP(hAPP(c_member(U_14456),U_14450),U_14458)) )
| U_14460 = c_Orderings_Obot__class_Obot(tc_fun(U_14456,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14456),U_14460))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14456),U_14458)) )
& ! [U_14461,U_14459,U_14457,U_14455] :
( ( ! [U_14448] :
( ? [U_14447] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14455,U_14455)),hAPP(hAPP(c_Product__Type_OPair(U_14455,U_14455),U_14448),U_14447)),U_14461))
& hBOOL(hAPP(hAPP(c_member(U_14455),U_14447),U_14459)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_14455),U_14448),U_14457)) )
& U_14459 != c_Orderings_Obot__class_Obot(tc_fun(U_14455,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_14455),U_14459))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_14455),U_14457)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14455,tc_HOL_Obool),tc_fun(U_14455,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14455,tc_HOL_Obool),tc_fun(U_14455,tc_HOL_Obool)),U_14457),U_14459)),c_Wellfounded_Omax__ext(U_14455,U_14461))) ) ),
inference(miniscope,[status(thm)],[f_3672_2]) ).
fof(f_3672_4,plain,
( ! [U_14462,U_14460,U_14458,U_14456] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14456,tc_HOL_Obool),tc_fun(U_14456,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14456,tc_HOL_Obool),tc_fun(U_14456,tc_HOL_Obool)),U_14458),U_14460)),c_Wellfounded_Omax__ext(U_14456,U_14462)))
| ? [U_14450] :
( ! [U_14449] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14456,U_14456)),hAPP(hAPP(c_Product__Type_OPair(U_14456,U_14456),U_14450),U_14449)),U_14462))
| ~ hBOOL(hAPP(hAPP(c_member(U_14456),U_14449),U_14460)) )
& hBOOL(hAPP(hAPP(c_member(U_14456),U_14450),U_14458)) )
| U_14460 = c_Orderings_Obot__class_Obot(tc_fun(U_14456,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14456),U_14460))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14456),U_14458)) )
& ! [U_14461,U_14459,U_14457,U_14455] :
( ( ! [U_14448] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14455,U_14455)),hAPP(hAPP(c_Product__Type_OPair(U_14455,U_14455),U_14448),sK356(U_14461,U_14459,U_14457,U_14455,U_14448))),U_14461))
& hBOOL(hAPP(hAPP(c_member(U_14455),sK356(U_14461,U_14459,U_14457,U_14455,U_14448)),U_14459)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_14455),U_14448),U_14457)) )
& U_14459 != c_Orderings_Obot__class_Obot(tc_fun(U_14455,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_14455),U_14459))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_14455),U_14457)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14455,tc_HOL_Obool),tc_fun(U_14455,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14455,tc_HOL_Obool),tc_fun(U_14455,tc_HOL_Obool)),U_14457),U_14459)),c_Wellfounded_Omax__ext(U_14455,U_14461))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK356]),skolemize(U_14447,sK356(U_14461,U_14459,U_14457,U_14455,U_14448))],[f_3672_3]) ).
fof(f_3672_5,plain,
( ! [U_14462,U_14460,U_14458,U_14456] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14456,tc_HOL_Obool),tc_fun(U_14456,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14456,tc_HOL_Obool),tc_fun(U_14456,tc_HOL_Obool)),U_14458),U_14460)),c_Wellfounded_Omax__ext(U_14456,U_14462)))
| ( ! [U_14449] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14456,U_14456)),hAPP(hAPP(c_Product__Type_OPair(U_14456,U_14456),sK357(U_14462,U_14460,U_14458,U_14456)),U_14449)),U_14462))
| ~ hBOOL(hAPP(hAPP(c_member(U_14456),U_14449),U_14460)) )
& hBOOL(hAPP(hAPP(c_member(U_14456),sK357(U_14462,U_14460,U_14458,U_14456)),U_14458)) )
| U_14460 = c_Orderings_Obot__class_Obot(tc_fun(U_14456,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14456),U_14460))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14456),U_14458)) )
& ! [U_14461,U_14459,U_14457,U_14455] :
( ( ! [U_14448] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14455,U_14455)),hAPP(hAPP(c_Product__Type_OPair(U_14455,U_14455),U_14448),sK356(U_14461,U_14459,U_14457,U_14455,U_14448))),U_14461))
& hBOOL(hAPP(hAPP(c_member(U_14455),sK356(U_14461,U_14459,U_14457,U_14455,U_14448)),U_14459)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_14455),U_14448),U_14457)) )
& U_14459 != c_Orderings_Obot__class_Obot(tc_fun(U_14455,tc_HOL_Obool))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_14455),U_14459))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_14455),U_14457)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14455,tc_HOL_Obool),tc_fun(U_14455,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14455,tc_HOL_Obool),tc_fun(U_14455,tc_HOL_Obool)),U_14457),U_14459)),c_Wellfounded_Omax__ext(U_14455,U_14461))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK357]),skolemize(U_14450,sK357(U_14462,U_14460,U_14458,U_14456))],[f_3672_4]) ).
cnf(f_3672_6,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14455),U_14457))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14455,tc_HOL_Obool),tc_fun(U_14455,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14455,tc_HOL_Obool),tc_fun(U_14455,tc_HOL_Obool)),U_14457),U_14459)),c_Wellfounded_Omax__ext(U_14455,U_14461))) ),
inference(clausify,[status(thm)],[f_3672_5]) ).
cnf(f_3672_7,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14455),U_14459))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14455,tc_HOL_Obool),tc_fun(U_14455,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14455,tc_HOL_Obool),tc_fun(U_14455,tc_HOL_Obool)),U_14457),U_14459)),c_Wellfounded_Omax__ext(U_14455,U_14461))) ),
inference(clausify,[status(thm)],[f_3672_5]) ).
cnf(f_3672_8,plain,
( U_14459 != c_Orderings_Obot__class_Obot(tc_fun(U_14455,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14455,tc_HOL_Obool),tc_fun(U_14455,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14455,tc_HOL_Obool),tc_fun(U_14455,tc_HOL_Obool)),U_14457),U_14459)),c_Wellfounded_Omax__ext(U_14455,U_14461))) ),
inference(clausify,[status(thm)],[f_3672_5]) ).
cnf(f_3672_9,plain,
( hBOOL(hAPP(hAPP(c_member(U_14455),sK356(U_14461,U_14459,U_14457,U_14455,U_14448)),U_14459))
| ~ hBOOL(hAPP(hAPP(c_member(U_14455),U_14448),U_14457))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14455,tc_HOL_Obool),tc_fun(U_14455,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14455,tc_HOL_Obool),tc_fun(U_14455,tc_HOL_Obool)),U_14457),U_14459)),c_Wellfounded_Omax__ext(U_14455,U_14461))) ),
inference(clausify,[status(thm)],[f_3672_5]) ).
cnf(f_3672_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14455,U_14455)),hAPP(hAPP(c_Product__Type_OPair(U_14455,U_14455),U_14448),sK356(U_14461,U_14459,U_14457,U_14455,U_14448))),U_14461))
| ~ hBOOL(hAPP(hAPP(c_member(U_14455),U_14448),U_14457))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14455,tc_HOL_Obool),tc_fun(U_14455,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14455,tc_HOL_Obool),tc_fun(U_14455,tc_HOL_Obool)),U_14457),U_14459)),c_Wellfounded_Omax__ext(U_14455,U_14461))) ),
inference(clausify,[status(thm)],[f_3672_5]) ).
cnf(f_3672_11,plain,
( hBOOL(hAPP(hAPP(c_member(U_14456),sK357(U_14462,U_14460,U_14458,U_14456)),U_14458))
| U_14460 = c_Orderings_Obot__class_Obot(tc_fun(U_14456,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14456),U_14460))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14456),U_14458))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14456,tc_HOL_Obool),tc_fun(U_14456,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14456,tc_HOL_Obool),tc_fun(U_14456,tc_HOL_Obool)),U_14458),U_14460)),c_Wellfounded_Omax__ext(U_14456,U_14462))) ),
inference(clausify,[status(thm)],[f_3672_5]) ).
cnf(f_3672_12,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14456,U_14456)),hAPP(hAPP(c_Product__Type_OPair(U_14456,U_14456),sK357(U_14462,U_14460,U_14458,U_14456)),U_14449)),U_14462))
| ~ hBOOL(hAPP(hAPP(c_member(U_14456),U_14449),U_14460))
| U_14460 = c_Orderings_Obot__class_Obot(tc_fun(U_14456,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14456),U_14460))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14456),U_14458))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14456,tc_HOL_Obool),tc_fun(U_14456,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14456,tc_HOL_Obool),tc_fun(U_14456,tc_HOL_Obool)),U_14458),U_14460)),c_Wellfounded_Omax__ext(U_14456,U_14462))) ),
inference(clausify,[status(thm)],[f_3672_5]) ).
fof(f_3673_1,plain,
! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),V_z_2),V_A_2)
| ? [B_x] :
( hAPP(V_g_2,B_x) != hAPP(V_h_2,B_x)
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Oab__semigroup__mult(T_c) ),
inference(fof_nnf,[status(thm)],[fact_fold__image__cong]) ).
fof(f_3673_2,plain,
! [U_14469,U_14468,U_14467,U_14466,U_14465,U_14464] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14464,U_14465,c_Groups_Otimes__class_Otimes(U_14464)),U_14467),U_14469),U_14466) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14464,U_14465,c_Groups_Otimes__class_Otimes(U_14464)),U_14468),U_14469),U_14466)
| ? [U_14463] :
( hAPP(U_14467,U_14463) != hAPP(U_14468,U_14463)
& hBOOL(hAPP(hAPP(c_member(U_14465),U_14463),U_14466)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14465),U_14466))
| ~ class_Groups_Oab__semigroup__mult(U_14464) ),
inference(variable_rename,[status(thm)],[f_3673_1]) ).
fof(f_3673_3,plain,
! [U_14469,U_14468,U_14467,U_14466,U_14465,U_14464] :
( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14464,U_14465,c_Groups_Otimes__class_Otimes(U_14464)),U_14467),U_14469),U_14466) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14464,U_14465,c_Groups_Otimes__class_Otimes(U_14464)),U_14468),U_14469),U_14466)
| ( hAPP(U_14467,sK358(U_14469,U_14468,U_14467,U_14466,U_14465,U_14464)) != hAPP(U_14468,sK358(U_14469,U_14468,U_14467,U_14466,U_14465,U_14464))
& hBOOL(hAPP(hAPP(c_member(U_14465),sK358(U_14469,U_14468,U_14467,U_14466,U_14465,U_14464)),U_14466)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14465),U_14466))
| ~ class_Groups_Oab__semigroup__mult(U_14464) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK358]),skolemize(U_14463,sK358(U_14469,U_14468,U_14467,U_14466,U_14465,U_14464))],[f_3673_2]) ).
cnf(f_3673_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_14465),sK358(U_14469,U_14468,U_14467,U_14466,U_14465,U_14464)),U_14466))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14464,U_14465,c_Groups_Otimes__class_Otimes(U_14464)),U_14467),U_14469),U_14466) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14464,U_14465,c_Groups_Otimes__class_Otimes(U_14464)),U_14468),U_14469),U_14466)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14465),U_14466))
| ~ class_Groups_Oab__semigroup__mult(U_14464) ),
inference(clausify,[status(thm)],[f_3673_3]) ).
cnf(f_3673_5,plain,
( hAPP(U_14467,sK358(U_14469,U_14468,U_14467,U_14466,U_14465,U_14464)) != hAPP(U_14468,sK358(U_14469,U_14468,U_14467,U_14466,U_14465,U_14464))
| hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14464,U_14465,c_Groups_Otimes__class_Otimes(U_14464)),U_14467),U_14469),U_14466) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14464,U_14465,c_Groups_Otimes__class_Otimes(U_14464)),U_14468),U_14469),U_14466)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14465),U_14466))
| ~ class_Groups_Oab__semigroup__mult(U_14464) ),
inference(clausify,[status(thm)],[f_3673_3]) ).
fof(f_3674_1,plain,
! [V_g_2,V_f_2,V_A_2,V_B_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
| ~ class_Rings_Ocomm__semiring__1(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__dvd__setprod__subset2]) ).
fof(f_3674_2,plain,
! [U_14476,U_14475,U_14474,U_14473,U_14472,U_14471] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_14471),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14472,U_14471),U_14475),U_14474)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14472,U_14471),U_14476),U_14473)))
| ? [U_14470] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_14471),hAPP(U_14475,U_14470)),hAPP(U_14476,U_14470)))
& hBOOL(hAPP(hAPP(c_member(U_14472),U_14470),U_14474)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14472,tc_HOL_Obool)),U_14474),U_14473))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14472),U_14473))
| ~ class_Rings_Ocomm__semiring__1(U_14471) ),
inference(variable_rename,[status(thm)],[f_3674_1]) ).
fof(f_3674_3,plain,
! [U_14476,U_14475,U_14474,U_14473,U_14472,U_14471] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_14471),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14472,U_14471),U_14475),U_14474)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14472,U_14471),U_14476),U_14473)))
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_14471),hAPP(U_14475,sK359(U_14476,U_14475,U_14474,U_14473,U_14472,U_14471))),hAPP(U_14476,sK359(U_14476,U_14475,U_14474,U_14473,U_14472,U_14471))))
& hBOOL(hAPP(hAPP(c_member(U_14472),sK359(U_14476,U_14475,U_14474,U_14473,U_14472,U_14471)),U_14474)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14472,tc_HOL_Obool)),U_14474),U_14473))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14472),U_14473))
| ~ class_Rings_Ocomm__semiring__1(U_14471) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK359]),skolemize(U_14470,sK359(U_14476,U_14475,U_14474,U_14473,U_14472,U_14471))],[f_3674_2]) ).
cnf(f_3674_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_14472),sK359(U_14476,U_14475,U_14474,U_14473,U_14472,U_14471)),U_14474))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_14471),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14472,U_14471),U_14475),U_14474)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14472,U_14471),U_14476),U_14473)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14472,tc_HOL_Obool)),U_14474),U_14473))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14472),U_14473))
| ~ class_Rings_Ocomm__semiring__1(U_14471) ),
inference(clausify,[status(thm)],[f_3674_3]) ).
cnf(f_3674_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_14471),hAPP(U_14475,sK359(U_14476,U_14475,U_14474,U_14473,U_14472,U_14471))),hAPP(U_14476,sK359(U_14476,U_14475,U_14474,U_14473,U_14472,U_14471))))
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_14471),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14472,U_14471),U_14475),U_14474)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14472,U_14471),U_14476),U_14473)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14472,tc_HOL_Obool)),U_14474),U_14473))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14472),U_14473))
| ~ class_Rings_Ocomm__semiring__1(U_14471) ),
inference(clausify,[status(thm)],[f_3674_3]) ).
fof(f_3675_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ? [B_y] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max__eqI]) ).
fof(f_3675_2,plain,
! [U_14480,U_14479,U_14478] :
( c_Big__Operators_Olinorder__class_OMax(U_14478,U_14479) = U_14480
| ~ hBOOL(hAPP(hAPP(c_member(U_14478),U_14480),U_14479))
| ? [U_14477] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14478),U_14477),U_14480))
& hBOOL(hAPP(hAPP(c_member(U_14478),U_14477),U_14479)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14478),U_14479))
| ~ class_Orderings_Olinorder(U_14478) ),
inference(variable_rename,[status(thm)],[f_3675_1]) ).
fof(f_3675_3,plain,
! [U_14480,U_14479,U_14478] :
( c_Big__Operators_Olinorder__class_OMax(U_14478,U_14479) = U_14480
| ~ hBOOL(hAPP(hAPP(c_member(U_14478),U_14480),U_14479))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14478),sK360(U_14480,U_14479,U_14478)),U_14480))
& hBOOL(hAPP(hAPP(c_member(U_14478),sK360(U_14480,U_14479,U_14478)),U_14479)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14478),U_14479))
| ~ class_Orderings_Olinorder(U_14478) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK360]),skolemize(U_14477,sK360(U_14480,U_14479,U_14478))],[f_3675_2]) ).
cnf(f_3675_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_14478),sK360(U_14480,U_14479,U_14478)),U_14479))
| c_Big__Operators_Olinorder__class_OMax(U_14478,U_14479) = U_14480
| ~ hBOOL(hAPP(hAPP(c_member(U_14478),U_14480),U_14479))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14478),U_14479))
| ~ class_Orderings_Olinorder(U_14478) ),
inference(clausify,[status(thm)],[f_3675_3]) ).
cnf(f_3675_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14478),sK360(U_14480,U_14479,U_14478)),U_14480))
| c_Big__Operators_Olinorder__class_OMax(U_14478,U_14479) = U_14480
| ~ hBOOL(hAPP(hAPP(c_member(U_14478),U_14480),U_14479))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14478),U_14479))
| ~ class_Orderings_Olinorder(U_14478) ),
inference(clausify,[status(thm)],[f_3675_3]) ).
fof(f_3676_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ? [B_y] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y))
& hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min__eqI]) ).
fof(f_3676_2,plain,
! [U_14484,U_14483,U_14482] :
( c_Big__Operators_Olinorder__class_OMin(U_14482,U_14483) = U_14484
| ~ hBOOL(hAPP(hAPP(c_member(U_14482),U_14484),U_14483))
| ? [U_14481] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14482),U_14484),U_14481))
& hBOOL(hAPP(hAPP(c_member(U_14482),U_14481),U_14483)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14482),U_14483))
| ~ class_Orderings_Olinorder(U_14482) ),
inference(variable_rename,[status(thm)],[f_3676_1]) ).
fof(f_3676_3,plain,
! [U_14484,U_14483,U_14482] :
( c_Big__Operators_Olinorder__class_OMin(U_14482,U_14483) = U_14484
| ~ hBOOL(hAPP(hAPP(c_member(U_14482),U_14484),U_14483))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14482),U_14484),sK361(U_14484,U_14483,U_14482)))
& hBOOL(hAPP(hAPP(c_member(U_14482),sK361(U_14484,U_14483,U_14482)),U_14483)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14482),U_14483))
| ~ class_Orderings_Olinorder(U_14482) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK361]),skolemize(U_14481,sK361(U_14484,U_14483,U_14482))],[f_3676_2]) ).
cnf(f_3676_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_14482),sK361(U_14484,U_14483,U_14482)),U_14483))
| c_Big__Operators_Olinorder__class_OMin(U_14482,U_14483) = U_14484
| ~ hBOOL(hAPP(hAPP(c_member(U_14482),U_14484),U_14483))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14482),U_14483))
| ~ class_Orderings_Olinorder(U_14482) ),
inference(clausify,[status(thm)],[f_3676_3]) ).
cnf(f_3676_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14482),U_14484),sK361(U_14484,U_14483,U_14482)))
| c_Big__Operators_Olinorder__class_OMin(U_14482,U_14483) = U_14484
| ~ hBOOL(hAPP(hAPP(c_member(U_14482),U_14484),U_14483))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14482),U_14483))
| ~ class_Orderings_Olinorder(U_14482) ),
inference(clausify,[status(thm)],[f_3676_3]) ).
fof(f_3677_1,plain,
! [V_f_2,V_r_2,T_b] :
( ? [B_k] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2))
| ~ c_Wellfounded_Owf(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__no__infinite__down__chainE]) ).
fof(f_3677_2,plain,
! [U_14488,U_14487,U_14486] :
( ? [U_14485] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14486,U_14486)),hAPP(hAPP(c_Product__Type_OPair(U_14486,U_14486),hAPP(U_14488,hAPP(c_Nat_OSuc,U_14485))),hAPP(U_14488,U_14485))),U_14487))
| ~ c_Wellfounded_Owf(U_14486,U_14487) ),
inference(variable_rename,[status(thm)],[f_3677_1]) ).
fof(f_3677_3,plain,
! [U_14488,U_14487,U_14486] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14486,U_14486)),hAPP(hAPP(c_Product__Type_OPair(U_14486,U_14486),hAPP(U_14488,hAPP(c_Nat_OSuc,sK362(U_14488,U_14487,U_14486)))),hAPP(U_14488,sK362(U_14488,U_14487,U_14486)))),U_14487))
| ~ c_Wellfounded_Owf(U_14486,U_14487) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK362]),skolemize(U_14485,sK362(U_14488,U_14487,U_14486))],[f_3677_2]) ).
cnf(f_3677_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14486,U_14486)),hAPP(hAPP(c_Product__Type_OPair(U_14486,U_14486),hAPP(U_14488,hAPP(c_Nat_OSuc,sK362(U_14488,U_14487,U_14486)))),hAPP(U_14488,sK362(U_14488,U_14487,U_14486)))),U_14487))
| ~ c_Wellfounded_Owf(U_14486,U_14487) ),
inference(clausify,[status(thm)],[f_3677_3]) ).
fof(f_3678_1,plain,
! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_g_2),V_A_2)
| ? [B_a] :
( hAPP(V_g_2,B_a) != hAPP(V_h_2,hAPP(V_f_2,B_a))
& hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2)) )
| V_B_2 != hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
| ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
| ~ class_Groups_Ocomm__monoid__add(T_d) ),
inference(fof_nnf,[status(thm)],[fact_setsum__reindex__cong]) ).
fof(f_3678_2,plain,
! [U_14497,U_14496,U_14495,U_14494,U_14493,U_14492,U_14491,U_14490] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14492,U_14490),U_14497),U_14495) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14491,U_14490),U_14496),U_14494)
| ? [U_14489] :
( hAPP(U_14496,U_14489) != hAPP(U_14497,hAPP(U_14493,U_14489))
& hBOOL(hAPP(hAPP(c_member(U_14491),U_14489),U_14494)) )
| U_14495 != hAPP(c_Set_Oimage(U_14491,U_14492,U_14493),U_14494)
| ~ c_Fun_Oinj__on(U_14491,U_14492,U_14493,U_14494)
| ~ class_Groups_Ocomm__monoid__add(U_14490) ),
inference(variable_rename,[status(thm)],[f_3678_1]) ).
fof(f_3678_3,plain,
! [U_14497,U_14496,U_14495,U_14494,U_14493,U_14492,U_14491,U_14490] :
( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14492,U_14490),U_14497),U_14495) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14491,U_14490),U_14496),U_14494)
| ( hAPP(U_14496,sK363(U_14497,U_14496,U_14495,U_14494,U_14493,U_14492,U_14491,U_14490)) != hAPP(U_14497,hAPP(U_14493,sK363(U_14497,U_14496,U_14495,U_14494,U_14493,U_14492,U_14491,U_14490)))
& hBOOL(hAPP(hAPP(c_member(U_14491),sK363(U_14497,U_14496,U_14495,U_14494,U_14493,U_14492,U_14491,U_14490)),U_14494)) )
| U_14495 != hAPP(c_Set_Oimage(U_14491,U_14492,U_14493),U_14494)
| ~ c_Fun_Oinj__on(U_14491,U_14492,U_14493,U_14494)
| ~ class_Groups_Ocomm__monoid__add(U_14490) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK363]),skolemize(U_14489,sK363(U_14497,U_14496,U_14495,U_14494,U_14493,U_14492,U_14491,U_14490))],[f_3678_2]) ).
cnf(f_3678_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_14491),sK363(U_14497,U_14496,U_14495,U_14494,U_14493,U_14492,U_14491,U_14490)),U_14494))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14492,U_14490),U_14497),U_14495) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14491,U_14490),U_14496),U_14494)
| U_14495 != hAPP(c_Set_Oimage(U_14491,U_14492,U_14493),U_14494)
| ~ c_Fun_Oinj__on(U_14491,U_14492,U_14493,U_14494)
| ~ class_Groups_Ocomm__monoid__add(U_14490) ),
inference(clausify,[status(thm)],[f_3678_3]) ).
cnf(f_3678_5,plain,
( hAPP(U_14496,sK363(U_14497,U_14496,U_14495,U_14494,U_14493,U_14492,U_14491,U_14490)) != hAPP(U_14497,hAPP(U_14493,sK363(U_14497,U_14496,U_14495,U_14494,U_14493,U_14492,U_14491,U_14490)))
| hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14492,U_14490),U_14497),U_14495) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14491,U_14490),U_14496),U_14494)
| U_14495 != hAPP(c_Set_Oimage(U_14491,U_14492,U_14493),U_14494)
| ~ c_Fun_Oinj__on(U_14491,U_14492,U_14493,U_14494)
| ~ class_Groups_Ocomm__monoid__add(U_14490) ),
inference(clausify,[status(thm)],[f_3678_3]) ).
fof(f_3679_1,plain,
! [V_na_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_na_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_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_na_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_na_2)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq]) ).
fof(f_3679_2,plain,
! [U_14499,U_14498] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14498),U_14499)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14498),U_14499)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14498),U_14499))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14498),U_14499)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
inference(variable_rename,[status(thm)],[f_3679_1]) ).
fof(f_3679_3,plain,
( ! [U_14503,U_14501] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14501),U_14503)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14501),U_14503)) )
& ! [U_14502,U_14500] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14500),U_14502))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14500),U_14502)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
inference(miniscope,[status(thm)],[f_3679_2]) ).
cnf(f_3679_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14500),U_14502))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14500),U_14502)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
inference(clausify,[status(thm)],[f_3679_3]) ).
cnf(f_3679_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14501),U_14503)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_14501),U_14503)) ),
inference(clausify,[status(thm)],[f_3679_3]) ).
fof(f_3680_1,plain,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2))
| ~ c_Wellfounded_Owf(T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_wf__trancl]) ).
fof(f_3680_2,plain,
! [U_14505,U_14504] :
( c_Wellfounded_Owf(U_14504,c_Transitive__Closure_Otrancl(U_14504,U_14505))
| ~ c_Wellfounded_Owf(U_14504,U_14505) ),
inference(variable_rename,[status(thm)],[f_3680_1]) ).
cnf(f_3680_3,plain,
( c_Wellfounded_Owf(U_14504,c_Transitive__Closure_Otrancl(U_14504,U_14505))
| ~ c_Wellfounded_Owf(U_14504,U_14505) ),
inference(clausify,[status(thm)],[f_3680_2]) ).
fof(f_3681_1,plain,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(fof_nnf,[status(thm)],[fact_less__than__def]) ).
cnf(f_3681_2,plain,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(clausify,[status(thm)],[f_3681_1]) ).
fof(f_3682_1,plain,
! [V_r_2,T_b] :
( ( c_Wellfounded_Oacyclic(T_b,V_r_2)
| ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) )
& ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ c_Wellfounded_Oacyclic(T_b,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_acyclic__def]) ).
fof(f_3682_2,plain,
! [U_14509,U_14508] :
( ( c_Wellfounded_Oacyclic(U_14508,U_14509)
| ? [U_14507] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14508,U_14508)),hAPP(hAPP(c_Product__Type_OPair(U_14508,U_14508),U_14507),U_14507)),c_Transitive__Closure_Otrancl(U_14508,U_14509))) )
& ( ! [U_14506] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14508,U_14508)),hAPP(hAPP(c_Product__Type_OPair(U_14508,U_14508),U_14506),U_14506)),c_Transitive__Closure_Otrancl(U_14508,U_14509)))
| ~ c_Wellfounded_Oacyclic(U_14508,U_14509) ) ),
inference(variable_rename,[status(thm)],[f_3682_1]) ).
fof(f_3682_3,plain,
( ! [U_14513,U_14511] :
( c_Wellfounded_Oacyclic(U_14511,U_14513)
| ? [U_14507] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14511,U_14511)),hAPP(hAPP(c_Product__Type_OPair(U_14511,U_14511),U_14507),U_14507)),c_Transitive__Closure_Otrancl(U_14511,U_14513))) )
& ! [U_14512,U_14510] :
( ! [U_14506] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14510,U_14510)),hAPP(hAPP(c_Product__Type_OPair(U_14510,U_14510),U_14506),U_14506)),c_Transitive__Closure_Otrancl(U_14510,U_14512)))
| ~ c_Wellfounded_Oacyclic(U_14510,U_14512) ) ),
inference(miniscope,[status(thm)],[f_3682_2]) ).
fof(f_3682_4,plain,
( ! [U_14513,U_14511] :
( c_Wellfounded_Oacyclic(U_14511,U_14513)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_14511,U_14511)),hAPP(hAPP(c_Product__Type_OPair(U_14511,U_14511),sK364(U_14513,U_14511)),sK364(U_14513,U_14511))),c_Transitive__Closure_Otrancl(U_14511,U_14513))) )
& ! [U_14512,U_14510] :
( ! [U_14506] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14510,U_14510)),hAPP(hAPP(c_Product__Type_OPair(U_14510,U_14510),U_14506),U_14506)),c_Transitive__Closure_Otrancl(U_14510,U_14512)))
| ~ c_Wellfounded_Oacyclic(U_14510,U_14512) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK364]),skolemize(U_14507,sK364(U_14513,U_14511))],[f_3682_3]) ).
cnf(f_3682_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14510,U_14510)),hAPP(hAPP(c_Product__Type_OPair(U_14510,U_14510),U_14506),U_14506)),c_Transitive__Closure_Otrancl(U_14510,U_14512)))
| ~ c_Wellfounded_Oacyclic(U_14510,U_14512) ),
inference(clausify,[status(thm)],[f_3682_4]) ).
cnf(f_3682_6,plain,
( c_Wellfounded_Oacyclic(U_14511,U_14513)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_14511,U_14511)),hAPP(hAPP(c_Product__Type_OPair(U_14511,U_14511),sK364(U_14513,U_14511)),sK364(U_14513,U_14511))),c_Transitive__Closure_Otrancl(U_14511,U_14513))) ),
inference(clausify,[status(thm)],[f_3682_4]) ).
fof(f_3683_1,plain,
! [V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_trancl_Or__into__trancl]) ).
fof(f_3683_2,plain,
! [U_14517,U_14516,U_14515,U_14514] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14514,U_14514)),hAPP(hAPP(c_Product__Type_OPair(U_14514,U_14514),U_14515),U_14516)),c_Transitive__Closure_Otrancl(U_14514,U_14517)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14514,U_14514)),hAPP(hAPP(c_Product__Type_OPair(U_14514,U_14514),U_14515),U_14516)),U_14517)) ),
inference(variable_rename,[status(thm)],[f_3683_1]) ).
cnf(f_3683_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14514,U_14514)),hAPP(hAPP(c_Product__Type_OPair(U_14514,U_14514),U_14515),U_14516)),c_Transitive__Closure_Otrancl(U_14514,U_14517)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14514,U_14514)),hAPP(hAPP(c_Product__Type_OPair(U_14514,U_14514),U_14515),U_14516)),U_14517)) ),
inference(clausify,[status(thm)],[f_3683_2]) ).
fof(f_3684_1,plain,
! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_Relation_OField(T_b),V_r_2))))),
inference(fof_nnf,[status(thm)],[fact_trancl__subset__Field2]) ).
fof(f_3684_2,plain,
! [U_14519,U_14518] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14518,U_14518),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14518,U_14519)),hAPP(hAPP(c_Product__Type_OSigma(U_14518,U_14518),hAPP(c_Relation_OField(U_14518),U_14519)),hAPP(c_COMBK(tc_fun(U_14518,tc_HOL_Obool),U_14518),hAPP(c_Relation_OField(U_14518),U_14519))))),
inference(variable_rename,[status(thm)],[f_3684_1]) ).
cnf(f_3684_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14518,U_14518),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14518,U_14519)),hAPP(hAPP(c_Product__Type_OSigma(U_14518,U_14518),hAPP(c_Relation_OField(U_14518),U_14519)),hAPP(c_COMBK(tc_fun(U_14518,tc_HOL_Obool),U_14518),hAPP(c_Relation_OField(U_14518),U_14519))))),
inference(clausify,[status(thm)],[f_3684_2]) ).
fof(f_3685_1,plain,
! [V_r_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_r__into__trancl_H]) ).
fof(f_3685_2,plain,
! [U_14522,U_14521,U_14520] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14520,U_14520)),U_14521),c_Transitive__Closure_Otrancl(U_14520,U_14522)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14520,U_14520)),U_14521),U_14522)) ),
inference(variable_rename,[status(thm)],[f_3685_1]) ).
cnf(f_3685_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14520,U_14520)),U_14521),c_Transitive__Closure_Otrancl(U_14520,U_14522)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14520,U_14520)),U_14521),U_14522)) ),
inference(clausify,[status(thm)],[f_3685_2]) ).
fof(f_3686_1,plain,
! [T_b] : c_Transitive__Closure_Otrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_trancl__empty]) ).
fof(f_3686_2,plain,
! [U_14523] : c_Transitive__Closure_Otrancl(U_14523,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14523,U_14523),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14523,U_14523),tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3686_1]) ).
cnf(f_3686_3,plain,
c_Transitive__Closure_Otrancl(U_14523,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14523,U_14523),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14523,U_14523),tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3686_2]) ).
fof(f_3687_1,plain,
! [V_r_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_b),V_r_2),
inference(fof_nnf,[status(thm)],[fact_trancl__domain]) ).
fof(f_3687_2,plain,
! [U_14525,U_14524] : hAPP(c_Relation_ODomain(U_14524,U_14524),c_Transitive__Closure_Otrancl(U_14524,U_14525)) = hAPP(c_Relation_ODomain(U_14524,U_14524),U_14525),
inference(variable_rename,[status(thm)],[f_3687_1]) ).
cnf(f_3687_3,plain,
hAPP(c_Relation_ODomain(U_14524,U_14524),c_Transitive__Closure_Otrancl(U_14524,U_14525)) = hAPP(c_Relation_ODomain(U_14524,U_14524),U_14525),
inference(clausify,[status(thm)],[f_3687_2]) ).
fof(f_3688_1,plain,
! [V_r_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ORange(T_b,T_b),V_r_2),
inference(fof_nnf,[status(thm)],[fact_trancl__range]) ).
fof(f_3688_2,plain,
! [U_14527,U_14526] : hAPP(c_Relation_ORange(U_14526,U_14526),c_Transitive__Closure_Otrancl(U_14526,U_14527)) = hAPP(c_Relation_ORange(U_14526,U_14526),U_14527),
inference(variable_rename,[status(thm)],[f_3688_1]) ).
cnf(f_3688_3,plain,
hAPP(c_Relation_ORange(U_14526,U_14526),c_Transitive__Closure_Otrancl(U_14526,U_14527)) = hAPP(c_Relation_ORange(U_14526,U_14526),U_14527),
inference(clausify,[status(thm)],[f_3688_2]) ).
fof(f_3689_1,plain,
! [V_r_2,T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__trancl]) ).
fof(f_3689_2,plain,
! [U_14529,U_14528] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14528,U_14528)),c_Transitive__Closure_Otrancl(U_14528,U_14529)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14528,U_14528)),U_14529)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14528,U_14528)),U_14529))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14528,U_14528)),c_Transitive__Closure_Otrancl(U_14528,U_14529))) ) ),
inference(variable_rename,[status(thm)],[f_3689_1]) ).
fof(f_3689_3,plain,
( ! [U_14533,U_14531] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14531,U_14531)),c_Transitive__Closure_Otrancl(U_14531,U_14533)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14531,U_14531)),U_14533)) )
& ! [U_14532,U_14530] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14530,U_14530)),U_14532))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14530,U_14530)),c_Transitive__Closure_Otrancl(U_14530,U_14532))) ) ),
inference(miniscope,[status(thm)],[f_3689_2]) ).
cnf(f_3689_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14530,U_14530)),U_14532))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14530,U_14530)),c_Transitive__Closure_Otrancl(U_14530,U_14532))) ),
inference(clausify,[status(thm)],[f_3689_3]) ).
cnf(f_3689_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14531,U_14531)),c_Transitive__Closure_Otrancl(U_14531,U_14533)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14531,U_14531)),U_14533)) ),
inference(clausify,[status(thm)],[f_3689_3]) ).
fof(f_3690_1,plain,
! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_R_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_R_2)) ),
inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl]) ).
fof(f_3690_2,plain,
! [U_14538,U_14537,U_14536,U_14535,U_14534] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14534,U_14534)),hAPP(hAPP(c_Product__Type_OPair(U_14534,U_14534),U_14535),U_14538)),c_Transitive__Closure_Otrancl(U_14534,U_14537)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14534,U_14534)),hAPP(hAPP(c_Product__Type_OPair(U_14534,U_14534),U_14536),U_14538)),U_14537))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14534,U_14534)),hAPP(hAPP(c_Product__Type_OPair(U_14534,U_14534),U_14535),U_14536)),U_14537)) ),
inference(variable_rename,[status(thm)],[f_3690_1]) ).
cnf(f_3690_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14534,U_14534)),hAPP(hAPP(c_Product__Type_OPair(U_14534,U_14534),U_14535),U_14538)),c_Transitive__Closure_Otrancl(U_14534,U_14537)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14534,U_14534)),hAPP(hAPP(c_Product__Type_OPair(U_14534,U_14534),U_14536),U_14538)),U_14537))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14534,U_14534)),hAPP(hAPP(c_Product__Type_OPair(U_14534,U_14534),U_14535),U_14536)),U_14537)) ),
inference(clausify,[status(thm)],[f_3690_2]) ).
fof(f_3691_1,plain,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_trancl__into__trancl2]) ).
fof(f_3691_2,plain,
! [U_14543,U_14542,U_14541,U_14540,U_14539] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14539,U_14539)),hAPP(hAPP(c_Product__Type_OPair(U_14539,U_14539),U_14540),U_14543)),c_Transitive__Closure_Otrancl(U_14539,U_14542)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14539,U_14539)),hAPP(hAPP(c_Product__Type_OPair(U_14539,U_14539),U_14541),U_14543)),c_Transitive__Closure_Otrancl(U_14539,U_14542)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14539,U_14539)),hAPP(hAPP(c_Product__Type_OPair(U_14539,U_14539),U_14540),U_14541)),U_14542)) ),
inference(variable_rename,[status(thm)],[f_3691_1]) ).
cnf(f_3691_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14539,U_14539)),hAPP(hAPP(c_Product__Type_OPair(U_14539,U_14539),U_14540),U_14543)),c_Transitive__Closure_Otrancl(U_14539,U_14542)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14539,U_14539)),hAPP(hAPP(c_Product__Type_OPair(U_14539,U_14539),U_14541),U_14543)),c_Transitive__Closure_Otrancl(U_14539,U_14542)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14539,U_14539)),hAPP(hAPP(c_Product__Type_OPair(U_14539,U_14539),U_14540),U_14541)),U_14542)) ),
inference(clausify,[status(thm)],[f_3691_2]) ).
fof(f_3692_1,plain,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_Transitive__Closure_Otrancl__into__trancl]) ).
fof(f_3692_2,plain,
! [U_14548,U_14547,U_14546,U_14545,U_14544] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14544,U_14544)),hAPP(hAPP(c_Product__Type_OPair(U_14544,U_14544),U_14545),U_14548)),c_Transitive__Closure_Otrancl(U_14544,U_14547)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14544,U_14544)),hAPP(hAPP(c_Product__Type_OPair(U_14544,U_14544),U_14546),U_14548)),U_14547))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14544,U_14544)),hAPP(hAPP(c_Product__Type_OPair(U_14544,U_14544),U_14545),U_14546)),c_Transitive__Closure_Otrancl(U_14544,U_14547))) ),
inference(variable_rename,[status(thm)],[f_3692_1]) ).
cnf(f_3692_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14544,U_14544)),hAPP(hAPP(c_Product__Type_OPair(U_14544,U_14544),U_14545),U_14548)),c_Transitive__Closure_Otrancl(U_14544,U_14547)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14544,U_14544)),hAPP(hAPP(c_Product__Type_OPair(U_14544,U_14544),U_14546),U_14548)),U_14547))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14544,U_14544)),hAPP(hAPP(c_Product__Type_OPair(U_14544,U_14544),U_14545),U_14546)),c_Transitive__Closure_Otrancl(U_14544,U_14547))) ),
inference(clausify,[status(thm)],[f_3692_2]) ).
fof(f_3693_1,plain,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_trancl__trans]) ).
fof(f_3693_2,plain,
! [U_14553,U_14552,U_14551,U_14550,U_14549] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14549,U_14549)),hAPP(hAPP(c_Product__Type_OPair(U_14549,U_14549),U_14550),U_14553)),c_Transitive__Closure_Otrancl(U_14549,U_14552)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14549,U_14549)),hAPP(hAPP(c_Product__Type_OPair(U_14549,U_14549),U_14551),U_14553)),c_Transitive__Closure_Otrancl(U_14549,U_14552)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14549,U_14549)),hAPP(hAPP(c_Product__Type_OPair(U_14549,U_14549),U_14550),U_14551)),c_Transitive__Closure_Otrancl(U_14549,U_14552))) ),
inference(variable_rename,[status(thm)],[f_3693_1]) ).
cnf(f_3693_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14549,U_14549)),hAPP(hAPP(c_Product__Type_OPair(U_14549,U_14549),U_14550),U_14553)),c_Transitive__Closure_Otrancl(U_14549,U_14552)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14549,U_14549)),hAPP(hAPP(c_Product__Type_OPair(U_14549,U_14549),U_14551),U_14553)),c_Transitive__Closure_Otrancl(U_14549,U_14552)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14549,U_14549)),hAPP(hAPP(c_Product__Type_OPair(U_14549,U_14549),U_14550),U_14551)),c_Transitive__Closure_Otrancl(U_14549,U_14552))) ),
inference(clausify,[status(thm)],[f_3693_2]) ).
fof(f_3694_1,plain,
! [V_s_2,V_r_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_trancl__mono]) ).
fof(f_3694_2,plain,
! [U_14557,U_14556,U_14555,U_14554] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14554,U_14554)),U_14555),c_Transitive__Closure_Otrancl(U_14554,U_14557)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14554,U_14554),tc_HOL_Obool)),U_14556),U_14557))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14554,U_14554)),U_14555),c_Transitive__Closure_Otrancl(U_14554,U_14556))) ),
inference(variable_rename,[status(thm)],[f_3694_1]) ).
cnf(f_3694_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14554,U_14554)),U_14555),c_Transitive__Closure_Otrancl(U_14554,U_14557)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14554,U_14554),tc_HOL_Obool)),U_14556),U_14557))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14554,U_14554)),U_14555),c_Transitive__Closure_Otrancl(U_14554,U_14556))) ),
inference(clausify,[status(thm)],[f_3694_2]) ).
fof(f_3695_1,plain,
! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_r_2)),
inference(fof_nnf,[status(thm)],[fact_trancl__unfold]) ).
fof(f_3695_2,plain,
! [U_14559,U_14558] : c_Transitive__Closure_Otrancl(U_14558,U_14559) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14558,U_14558),tc_HOL_Obool)),U_14559),hAPP(hAPP(c_Relation_Orel__comp(U_14558,U_14558,U_14558),c_Transitive__Closure_Otrancl(U_14558,U_14559)),U_14559)),
inference(variable_rename,[status(thm)],[f_3695_1]) ).
cnf(f_3695_3,plain,
c_Transitive__Closure_Otrancl(U_14558,U_14559) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14558,U_14558),tc_HOL_Obool)),U_14559),hAPP(hAPP(c_Relation_Orel__comp(U_14558,U_14558,U_14558),c_Transitive__Closure_Otrancl(U_14558,U_14559)),U_14559)),
inference(clausify,[status(thm)],[f_3695_2]) ).
fof(f_3696_1,plain,
! [V_A_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ),
inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma]) ).
fof(f_3696_2,plain,
! [U_14562,U_14561,U_14560] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14560,U_14560),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14560,U_14561)),hAPP(hAPP(c_Product__Type_OSigma(U_14560,U_14560),U_14562),hAPP(c_COMBK(tc_fun(U_14560,tc_HOL_Obool),U_14560),U_14562))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14560,U_14560),tc_HOL_Obool)),U_14561),hAPP(hAPP(c_Product__Type_OSigma(U_14560,U_14560),U_14562),hAPP(c_COMBK(tc_fun(U_14560,tc_HOL_Obool),U_14560),U_14562)))) ),
inference(variable_rename,[status(thm)],[f_3696_1]) ).
cnf(f_3696_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14560,U_14560),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14560,U_14561)),hAPP(hAPP(c_Product__Type_OSigma(U_14560,U_14560),U_14562),hAPP(c_COMBK(tc_fun(U_14560,tc_HOL_Obool),U_14560),U_14562))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14560,U_14560),tc_HOL_Obool)),U_14561),hAPP(hAPP(c_Product__Type_OSigma(U_14560,U_14560),U_14562),hAPP(c_COMBK(tc_fun(U_14560,tc_HOL_Obool),U_14560),U_14562)))) ),
inference(clausify,[status(thm)],[f_3696_2]) ).
fof(f_3697_1,plain,
! [V_s_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ),
inference(fof_nnf,[status(thm)],[fact_trancl__Int__subset]) ).
fof(f_3697_2,plain,
! [U_14565,U_14564,U_14563] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14563,U_14563),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14563,U_14564)),U_14565))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14563,U_14563),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14563,U_14563,U_14563),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14563,U_14563),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14563,U_14564)),U_14565)),U_14564)),U_14565))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14563,U_14563),tc_HOL_Obool)),U_14564),U_14565)) ),
inference(variable_rename,[status(thm)],[f_3697_1]) ).
cnf(f_3697_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14563,U_14563),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14563,U_14564)),U_14565))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14563,U_14563),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14563,U_14563,U_14563),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14563,U_14563),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14563,U_14564)),U_14565)),U_14564)),U_14565))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14563,U_14563),tc_HOL_Obool)),U_14564),U_14565)) ),
inference(clausify,[status(thm)],[f_3697_2]) ).
fof(f_3698_1,plain,
! [V_r_2,V_x_2,V_y_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBC(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),V_y_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b))),hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))))),
inference(fof_nnf,[status(thm)],[fact_trancl__insert]) ).
fof(f_3698_2,plain,
! [U_14569,U_14568,U_14567,U_14566] : c_Transitive__Closure_Otrancl(U_14566,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14566,U_14566)),hAPP(hAPP(c_Product__Type_OPair(U_14566,U_14566),U_14567),U_14568)),U_14569)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14566,U_14566),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14566,U_14569)),hAPP(c_Set_OCollect(tc_prod(U_14566,U_14566)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14566,U_14566,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14566,tc_fun(U_14566,tc_HOL_Obool),tc_fun(U_14566,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14566,tc_HOL_Obool),tc_fun(U_14566,tc_HOL_Obool)),U_14566),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14566)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14566),c_fconj),hAPP(hAPP(c_COMBC(U_14566,tc_fun(tc_prod(U_14566,U_14566),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_14566,U_14566),tc_fun(tc_fun(tc_prod(U_14566,U_14566),tc_HOL_Obool),tc_HOL_Obool),U_14566),c_member(tc_prod(U_14566,U_14566))),hAPP(hAPP(c_COMBC(U_14566,U_14566,tc_prod(U_14566,U_14566)),c_Product__Type_OPair(U_14566,U_14566)),U_14567))),c_Transitive__Closure_Ortrancl(U_14566,U_14569))))),hAPP(hAPP(c_COMBC(U_14566,tc_fun(tc_prod(U_14566,U_14566),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_14566,U_14566),tc_fun(tc_fun(tc_prod(U_14566,U_14566),tc_HOL_Obool),tc_HOL_Obool),U_14566),c_member(tc_prod(U_14566,U_14566))),hAPP(c_Product__Type_OPair(U_14566,U_14566),U_14568))),c_Transitive__Closure_Ortrancl(U_14566,U_14569)))))),
inference(variable_rename,[status(thm)],[f_3698_1]) ).
cnf(f_3698_3,plain,
c_Transitive__Closure_Otrancl(U_14566,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14566,U_14566)),hAPP(hAPP(c_Product__Type_OPair(U_14566,U_14566),U_14567),U_14568)),U_14569)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14566,U_14566),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14566,U_14569)),hAPP(c_Set_OCollect(tc_prod(U_14566,U_14566)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14566,U_14566,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14566,tc_fun(U_14566,tc_HOL_Obool),tc_fun(U_14566,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14566,tc_HOL_Obool),tc_fun(U_14566,tc_HOL_Obool)),U_14566),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14566)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14566),c_fconj),hAPP(hAPP(c_COMBC(U_14566,tc_fun(tc_prod(U_14566,U_14566),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_14566,U_14566),tc_fun(tc_fun(tc_prod(U_14566,U_14566),tc_HOL_Obool),tc_HOL_Obool),U_14566),c_member(tc_prod(U_14566,U_14566))),hAPP(hAPP(c_COMBC(U_14566,U_14566,tc_prod(U_14566,U_14566)),c_Product__Type_OPair(U_14566,U_14566)),U_14567))),c_Transitive__Closure_Ortrancl(U_14566,U_14569))))),hAPP(hAPP(c_COMBC(U_14566,tc_fun(tc_prod(U_14566,U_14566),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_14566,U_14566),tc_fun(tc_fun(tc_prod(U_14566,U_14566),tc_HOL_Obool),tc_HOL_Obool),U_14566),c_member(tc_prod(U_14566,U_14566))),hAPP(c_Product__Type_OPair(U_14566,U_14566),U_14568))),c_Transitive__Closure_Ortrancl(U_14566,U_14569)))))),
inference(clausify,[status(thm)],[f_3698_2]) ).
fof(f_3699_1,plain,
! [V_y_2,V_x_2,V_r_2,T_b] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),c_fequal),V_x_2),V_y_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),c_fequal),V_x_2),V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_reflcl__set__eq]) ).
fof(f_3699_2,plain,
! [U_14573,U_14572,U_14571,U_14570] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14570,tc_fun(U_14570,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14570,tc_fun(tc_prod(U_14570,U_14570),tc_HOL_Obool),tc_fun(U_14570,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14570,tc_fun(tc_fun(tc_prod(U_14570,U_14570),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14570,U_14570),tc_HOL_Obool),tc_fun(U_14570,tc_HOL_Obool)),U_14570),c_COMBC(U_14570,tc_fun(tc_prod(U_14570,U_14570),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14570,tc_prod(U_14570,U_14570)),tc_fun(U_14570,tc_fun(tc_fun(tc_prod(U_14570,U_14570),tc_HOL_Obool),tc_HOL_Obool)),U_14570),hAPP(c_COMBB(tc_prod(U_14570,U_14570),tc_fun(tc_fun(tc_prod(U_14570,U_14570),tc_HOL_Obool),tc_HOL_Obool),U_14570),c_member(tc_prod(U_14570,U_14570)))),c_Product__Type_OPair(U_14570,U_14570)))),U_14571)),c_fequal),U_14572),U_14573))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14570,U_14570)),hAPP(hAPP(c_Product__Type_OPair(U_14570,U_14570),U_14572),U_14573)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14570,U_14570),tc_HOL_Obool)),U_14571),c_Relation_OId(U_14570)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14570,U_14570)),hAPP(hAPP(c_Product__Type_OPair(U_14570,U_14570),U_14572),U_14573)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14570,U_14570),tc_HOL_Obool)),U_14571),c_Relation_OId(U_14570))))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14570,tc_fun(U_14570,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14570,tc_fun(tc_prod(U_14570,U_14570),tc_HOL_Obool),tc_fun(U_14570,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14570,tc_fun(tc_fun(tc_prod(U_14570,U_14570),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14570,U_14570),tc_HOL_Obool),tc_fun(U_14570,tc_HOL_Obool)),U_14570),c_COMBC(U_14570,tc_fun(tc_prod(U_14570,U_14570),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14570,tc_prod(U_14570,U_14570)),tc_fun(U_14570,tc_fun(tc_fun(tc_prod(U_14570,U_14570),tc_HOL_Obool),tc_HOL_Obool)),U_14570),hAPP(c_COMBB(tc_prod(U_14570,U_14570),tc_fun(tc_fun(tc_prod(U_14570,U_14570),tc_HOL_Obool),tc_HOL_Obool),U_14570),c_member(tc_prod(U_14570,U_14570)))),c_Product__Type_OPair(U_14570,U_14570)))),U_14571)),c_fequal),U_14572),U_14573)) ) ),
inference(variable_rename,[status(thm)],[f_3699_1]) ).
fof(f_3699_3,plain,
( ! [U_14581,U_14579,U_14577,U_14575] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14575,tc_fun(U_14575,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14575,tc_fun(tc_prod(U_14575,U_14575),tc_HOL_Obool),tc_fun(U_14575,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14575,tc_fun(tc_fun(tc_prod(U_14575,U_14575),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14575,U_14575),tc_HOL_Obool),tc_fun(U_14575,tc_HOL_Obool)),U_14575),c_COMBC(U_14575,tc_fun(tc_prod(U_14575,U_14575),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14575,tc_prod(U_14575,U_14575)),tc_fun(U_14575,tc_fun(tc_fun(tc_prod(U_14575,U_14575),tc_HOL_Obool),tc_HOL_Obool)),U_14575),hAPP(c_COMBB(tc_prod(U_14575,U_14575),tc_fun(tc_fun(tc_prod(U_14575,U_14575),tc_HOL_Obool),tc_HOL_Obool),U_14575),c_member(tc_prod(U_14575,U_14575)))),c_Product__Type_OPair(U_14575,U_14575)))),U_14577)),c_fequal),U_14579),U_14581))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14575,U_14575)),hAPP(hAPP(c_Product__Type_OPair(U_14575,U_14575),U_14579),U_14581)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14575,U_14575),tc_HOL_Obool)),U_14577),c_Relation_OId(U_14575)))) )
& ! [U_14580,U_14578,U_14576,U_14574] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14574,U_14574)),hAPP(hAPP(c_Product__Type_OPair(U_14574,U_14574),U_14578),U_14580)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14574,U_14574),tc_HOL_Obool)),U_14576),c_Relation_OId(U_14574))))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14574,tc_fun(U_14574,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14574,tc_fun(tc_prod(U_14574,U_14574),tc_HOL_Obool),tc_fun(U_14574,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14574,tc_fun(tc_fun(tc_prod(U_14574,U_14574),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14574,U_14574),tc_HOL_Obool),tc_fun(U_14574,tc_HOL_Obool)),U_14574),c_COMBC(U_14574,tc_fun(tc_prod(U_14574,U_14574),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14574,tc_prod(U_14574,U_14574)),tc_fun(U_14574,tc_fun(tc_fun(tc_prod(U_14574,U_14574),tc_HOL_Obool),tc_HOL_Obool)),U_14574),hAPP(c_COMBB(tc_prod(U_14574,U_14574),tc_fun(tc_fun(tc_prod(U_14574,U_14574),tc_HOL_Obool),tc_HOL_Obool),U_14574),c_member(tc_prod(U_14574,U_14574)))),c_Product__Type_OPair(U_14574,U_14574)))),U_14576)),c_fequal),U_14578),U_14580)) ) ),
inference(miniscope,[status(thm)],[f_3699_2]) ).
cnf(f_3699_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14574,U_14574)),hAPP(hAPP(c_Product__Type_OPair(U_14574,U_14574),U_14578),U_14580)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14574,U_14574),tc_HOL_Obool)),U_14576),c_Relation_OId(U_14574))))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14574,tc_fun(U_14574,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14574,tc_fun(tc_prod(U_14574,U_14574),tc_HOL_Obool),tc_fun(U_14574,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14574,tc_fun(tc_fun(tc_prod(U_14574,U_14574),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14574,U_14574),tc_HOL_Obool),tc_fun(U_14574,tc_HOL_Obool)),U_14574),c_COMBC(U_14574,tc_fun(tc_prod(U_14574,U_14574),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14574,tc_prod(U_14574,U_14574)),tc_fun(U_14574,tc_fun(tc_fun(tc_prod(U_14574,U_14574),tc_HOL_Obool),tc_HOL_Obool)),U_14574),hAPP(c_COMBB(tc_prod(U_14574,U_14574),tc_fun(tc_fun(tc_prod(U_14574,U_14574),tc_HOL_Obool),tc_HOL_Obool),U_14574),c_member(tc_prod(U_14574,U_14574)))),c_Product__Type_OPair(U_14574,U_14574)))),U_14576)),c_fequal),U_14578),U_14580)) ),
inference(clausify,[status(thm)],[f_3699_3]) ).
cnf(f_3699_5,plain,
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14575,tc_fun(U_14575,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_14575,tc_fun(tc_prod(U_14575,U_14575),tc_HOL_Obool),tc_fun(U_14575,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14575,tc_fun(tc_fun(tc_prod(U_14575,U_14575),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14575,U_14575),tc_HOL_Obool),tc_fun(U_14575,tc_HOL_Obool)),U_14575),c_COMBC(U_14575,tc_fun(tc_prod(U_14575,U_14575),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14575,tc_prod(U_14575,U_14575)),tc_fun(U_14575,tc_fun(tc_fun(tc_prod(U_14575,U_14575),tc_HOL_Obool),tc_HOL_Obool)),U_14575),hAPP(c_COMBB(tc_prod(U_14575,U_14575),tc_fun(tc_fun(tc_prod(U_14575,U_14575),tc_HOL_Obool),tc_HOL_Obool),U_14575),c_member(tc_prod(U_14575,U_14575)))),c_Product__Type_OPair(U_14575,U_14575)))),U_14577)),c_fequal),U_14579),U_14581))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14575,U_14575)),hAPP(hAPP(c_Product__Type_OPair(U_14575,U_14575),U_14579),U_14581)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14575,U_14575),tc_HOL_Obool)),U_14577),c_Relation_OId(U_14575)))) ),
inference(clausify,[status(thm)],[f_3699_3]) ).
fof(f_3700_1,plain,
! [V_r_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_r__into__rtrancl]) ).
fof(f_3700_2,plain,
! [U_14584,U_14583,U_14582] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14582,U_14582)),U_14583),c_Transitive__Closure_Ortrancl(U_14582,U_14584)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14582,U_14582)),U_14583),U_14584)) ),
inference(variable_rename,[status(thm)],[f_3700_1]) ).
cnf(f_3700_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14582,U_14582)),U_14583),c_Transitive__Closure_Ortrancl(U_14582,U_14584)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14582,U_14582)),U_14583),U_14584)) ),
inference(clausify,[status(thm)],[f_3700_2]) ).
fof(f_3701_1,plain,
! [V_r_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))),
inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__refl]) ).
fof(f_3701_2,plain,
! [U_14587,U_14586,U_14585] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14585,U_14585)),hAPP(hAPP(c_Product__Type_OPair(U_14585,U_14585),U_14586),U_14586)),c_Transitive__Closure_Ortrancl(U_14585,U_14587))),
inference(variable_rename,[status(thm)],[f_3701_1]) ).
cnf(f_3701_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(U_14585,U_14585)),hAPP(hAPP(c_Product__Type_OPair(U_14585,U_14585),U_14586),U_14586)),c_Transitive__Closure_Ortrancl(U_14585,U_14587))),
inference(clausify,[status(thm)],[f_3701_2]) ).
fof(f_3702_1,plain,
! [V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Relation_OId(T_b))),
inference(fof_nnf,[status(thm)],[fact_IdI]) ).
fof(f_3702_2,plain,
! [U_14589,U_14588] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14588,U_14588)),hAPP(hAPP(c_Product__Type_OPair(U_14588,U_14588),U_14589),U_14589)),c_Relation_OId(U_14588))),
inference(variable_rename,[status(thm)],[f_3702_1]) ).
cnf(f_3702_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(U_14588,U_14588)),hAPP(hAPP(c_Product__Type_OPair(U_14588,U_14588),U_14589),U_14589)),c_Relation_OId(U_14588))),
inference(clausify,[status(thm)],[f_3702_2]) ).
fof(f_3703_1,plain,
! [V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_trancl__into__rtrancl]) ).
fof(f_3703_2,plain,
! [U_14593,U_14592,U_14591,U_14590] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14590,U_14590)),hAPP(hAPP(c_Product__Type_OPair(U_14590,U_14590),U_14591),U_14592)),c_Transitive__Closure_Ortrancl(U_14590,U_14593)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14590,U_14590)),hAPP(hAPP(c_Product__Type_OPair(U_14590,U_14590),U_14591),U_14592)),c_Transitive__Closure_Otrancl(U_14590,U_14593))) ),
inference(variable_rename,[status(thm)],[f_3703_1]) ).
cnf(f_3703_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14590,U_14590)),hAPP(hAPP(c_Product__Type_OPair(U_14590,U_14590),U_14591),U_14592)),c_Transitive__Closure_Ortrancl(U_14590,U_14593)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14590,U_14590)),hAPP(hAPP(c_Product__Type_OPair(U_14590,U_14590),U_14591),U_14592)),c_Transitive__Closure_Otrancl(U_14590,U_14593))) ),
inference(clausify,[status(thm)],[f_3703_2]) ).
fof(f_3704_1,plain,
! [V_R_2,T_b] : c_Transitive__Closure_Otrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
inference(fof_nnf,[status(thm)],[fact_rtrancl__trancl__absorb]) ).
fof(f_3704_2,plain,
! [U_14595,U_14594] : c_Transitive__Closure_Otrancl(U_14594,c_Transitive__Closure_Ortrancl(U_14594,U_14595)) = c_Transitive__Closure_Ortrancl(U_14594,U_14595),
inference(variable_rename,[status(thm)],[f_3704_1]) ).
cnf(f_3704_3,plain,
c_Transitive__Closure_Otrancl(U_14594,c_Transitive__Closure_Ortrancl(U_14594,U_14595)) = c_Transitive__Closure_Ortrancl(U_14594,U_14595),
inference(clausify,[status(thm)],[f_3704_2]) ).
fof(f_3705_1,plain,
! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Otrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
inference(fof_nnf,[status(thm)],[fact_trancl__rtrancl__absorb]) ).
fof(f_3705_2,plain,
! [U_14597,U_14596] : c_Transitive__Closure_Ortrancl(U_14596,c_Transitive__Closure_Otrancl(U_14596,U_14597)) = c_Transitive__Closure_Ortrancl(U_14596,U_14597),
inference(variable_rename,[status(thm)],[f_3705_1]) ).
cnf(f_3705_3,plain,
c_Transitive__Closure_Ortrancl(U_14596,c_Transitive__Closure_Otrancl(U_14596,U_14597)) = c_Transitive__Closure_Ortrancl(U_14596,U_14597),
inference(clausify,[status(thm)],[f_3705_2]) ).
fof(f_3706_1,plain,
! [V_r_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
inference(fof_nnf,[status(thm)],[fact_reflcl__trancl]) ).
fof(f_3706_2,plain,
! [U_14599,U_14598] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14598,U_14598),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14598,U_14599)),c_Relation_OId(U_14598)) = c_Transitive__Closure_Ortrancl(U_14598,U_14599),
inference(variable_rename,[status(thm)],[f_3706_1]) ).
cnf(f_3706_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14598,U_14598),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14598,U_14599)),c_Relation_OId(U_14598)) = c_Transitive__Closure_Ortrancl(U_14598,U_14599),
inference(clausify,[status(thm)],[f_3706_2]) ).
fof(f_3707_1,plain,
! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
inference(fof_nnf,[status(thm)],[fact_trancl__reflcl]) ).
fof(f_3707_2,plain,
! [U_14601,U_14600] : c_Transitive__Closure_Otrancl(U_14600,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14600,U_14600),tc_HOL_Obool)),U_14601),c_Relation_OId(U_14600))) = c_Transitive__Closure_Ortrancl(U_14600,U_14601),
inference(variable_rename,[status(thm)],[f_3707_1]) ).
cnf(f_3707_3,plain,
c_Transitive__Closure_Otrancl(U_14600,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14600,U_14600),tc_HOL_Obool)),U_14601),c_Relation_OId(U_14600))) = c_Transitive__Closure_Ortrancl(U_14600,U_14601),
inference(clausify,[status(thm)],[f_3707_2]) ).
fof(f_3708_1,plain,
! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
inference(fof_nnf,[status(thm)],[fact_trancl__unfold__left]) ).
fof(f_3708_2,plain,
! [U_14603,U_14602] : c_Transitive__Closure_Otrancl(U_14602,U_14603) = hAPP(hAPP(c_Relation_Orel__comp(U_14602,U_14602,U_14602),U_14603),c_Transitive__Closure_Ortrancl(U_14602,U_14603)),
inference(variable_rename,[status(thm)],[f_3708_1]) ).
cnf(f_3708_3,plain,
c_Transitive__Closure_Otrancl(U_14602,U_14603) = hAPP(hAPP(c_Relation_Orel__comp(U_14602,U_14602,U_14602),U_14603),c_Transitive__Closure_Ortrancl(U_14602,U_14603)),
inference(clausify,[status(thm)],[f_3708_2]) ).
fof(f_3709_1,plain,
! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2),
inference(fof_nnf,[status(thm)],[fact_trancl__unfold__right]) ).
fof(f_3709_2,plain,
! [U_14605,U_14604] : c_Transitive__Closure_Otrancl(U_14604,U_14605) = hAPP(hAPP(c_Relation_Orel__comp(U_14604,U_14604,U_14604),c_Transitive__Closure_Ortrancl(U_14604,U_14605)),U_14605),
inference(variable_rename,[status(thm)],[f_3709_1]) ).
cnf(f_3709_3,plain,
c_Transitive__Closure_Otrancl(U_14604,U_14605) = hAPP(hAPP(c_Relation_Orel__comp(U_14604,U_14604,U_14604),c_Transitive__Closure_Ortrancl(U_14604,U_14605)),U_14605),
inference(clausify,[status(thm)],[f_3709_2]) ).
fof(f_3710_1,plain,
! [V_r_2,V_s_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),V_s_2)) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__Int__subset]) ).
fof(f_3710_2,plain,
! [U_14608,U_14607,U_14606] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14606,U_14606),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14606,U_14608)),U_14607))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14606,U_14606),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14606,U_14606,U_14606),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14606,U_14606),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14606,U_14608)),U_14607)),U_14608)),U_14607))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14606,U_14606),tc_HOL_Obool)),c_Relation_OId(U_14606)),U_14607)) ),
inference(variable_rename,[status(thm)],[f_3710_1]) ).
cnf(f_3710_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14606,U_14606),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14606,U_14608)),U_14607))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14606,U_14606),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14606,U_14606,U_14606),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14606,U_14606),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14606,U_14608)),U_14607)),U_14608)),U_14607))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14606,U_14606),tc_HOL_Obool)),c_Relation_OId(U_14606)),U_14607)) ),
inference(clausify,[status(thm)],[f_3710_2]) ).
fof(f_3711_1,plain,
! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2)),
inference(fof_nnf,[status(thm)],[fact_rtrancl__unfold]) ).
fof(f_3711_2,plain,
! [U_14610,U_14609] : c_Transitive__Closure_Ortrancl(U_14609,U_14610) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14609,U_14609),tc_HOL_Obool)),c_Relation_OId(U_14609)),hAPP(hAPP(c_Relation_Orel__comp(U_14609,U_14609,U_14609),c_Transitive__Closure_Ortrancl(U_14609,U_14610)),U_14610)),
inference(variable_rename,[status(thm)],[f_3711_1]) ).
cnf(f_3711_3,plain,
c_Transitive__Closure_Ortrancl(U_14609,U_14610) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14609,U_14609),tc_HOL_Obool)),c_Relation_OId(U_14609)),hAPP(hAPP(c_Relation_Orel__comp(U_14609,U_14609,U_14609),c_Transitive__Closure_Ortrancl(U_14609,U_14610)),U_14610)),
inference(clausify,[status(thm)],[f_3711_2]) ).
fof(f_3712_1,plain,
! [V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
inference(fof_nnf,[status(thm)],[fact_rtrancl__idemp__self__comp]) ).
fof(f_3712_2,plain,
! [U_14612,U_14611] : hAPP(hAPP(c_Relation_Orel__comp(U_14611,U_14611,U_14611),c_Transitive__Closure_Ortrancl(U_14611,U_14612)),c_Transitive__Closure_Ortrancl(U_14611,U_14612)) = c_Transitive__Closure_Ortrancl(U_14611,U_14612),
inference(variable_rename,[status(thm)],[f_3712_1]) ).
cnf(f_3712_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_14611,U_14611,U_14611),c_Transitive__Closure_Ortrancl(U_14611,U_14612)),c_Transitive__Closure_Ortrancl(U_14611,U_14612)) = c_Transitive__Closure_Ortrancl(U_14611,U_14612),
inference(clausify,[status(thm)],[f_3712_2]) ).
fof(f_3713_1,plain,
! [V_r_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2),
inference(fof_nnf,[status(thm)],[fact_r__comp__rtrancl__eq]) ).
fof(f_3713_2,plain,
! [U_14614,U_14613] : hAPP(hAPP(c_Relation_Orel__comp(U_14613,U_14613,U_14613),U_14614),c_Transitive__Closure_Ortrancl(U_14613,U_14614)) = hAPP(hAPP(c_Relation_Orel__comp(U_14613,U_14613,U_14613),c_Transitive__Closure_Ortrancl(U_14613,U_14614)),U_14614),
inference(variable_rename,[status(thm)],[f_3713_1]) ).
cnf(f_3713_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_14613,U_14613,U_14613),U_14614),c_Transitive__Closure_Ortrancl(U_14613,U_14614)) = hAPP(hAPP(c_Relation_Orel__comp(U_14613,U_14613,U_14613),c_Transitive__Closure_Ortrancl(U_14613,U_14614)),U_14614),
inference(clausify,[status(thm)],[f_3713_2]) ).
fof(f_3714_1,plain,
! [V_X_2,V_r_2,T_b] :
( hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),V_X_2)),V_X_2)) ),
inference(fof_nnf,[status(thm)],[fact_Image__closed__trancl]) ).
fof(f_3714_2,plain,
! [U_14617,U_14616,U_14615] :
( hAPP(c_Relation_OImage(U_14615,U_14615,c_Transitive__Closure_Ortrancl(U_14615,U_14616)),U_14617) = U_14617
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14615,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14615,U_14615,U_14616),U_14617)),U_14617)) ),
inference(variable_rename,[status(thm)],[f_3714_1]) ).
cnf(f_3714_3,plain,
( hAPP(c_Relation_OImage(U_14615,U_14615,c_Transitive__Closure_Ortrancl(U_14615,U_14616)),U_14617) = U_14617
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14615,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14615,U_14615,U_14616),U_14617)),U_14617)) ),
inference(clausify,[status(thm)],[f_3714_2]) ).
fof(f_3715_1,plain,
! [V_s_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__mono]) ).
fof(f_3715_2,plain,
! [U_14620,U_14619,U_14618] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14618,U_14618),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14618,U_14619)),c_Transitive__Closure_Ortrancl(U_14618,U_14620)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14618,U_14618),tc_HOL_Obool)),U_14619),U_14620)) ),
inference(variable_rename,[status(thm)],[f_3715_1]) ).
cnf(f_3715_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14618,U_14618),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14618,U_14619)),c_Transitive__Closure_Ortrancl(U_14618,U_14620)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14618,U_14618),tc_HOL_Obool)),U_14619),U_14620)) ),
inference(clausify,[status(thm)],[f_3715_2]) ).
fof(f_3716_1,plain,
! [V_S_2,V_R_2,T_b] :
( c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__subset]) ).
fof(f_3716_2,plain,
! [U_14623,U_14622,U_14621] :
( c_Transitive__Closure_Ortrancl(U_14621,U_14623) = c_Transitive__Closure_Ortrancl(U_14621,U_14622)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14621,U_14621),tc_HOL_Obool)),U_14623),c_Transitive__Closure_Ortrancl(U_14621,U_14622)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14621,U_14621),tc_HOL_Obool)),U_14622),U_14623)) ),
inference(variable_rename,[status(thm)],[f_3716_1]) ).
cnf(f_3716_3,plain,
( c_Transitive__Closure_Ortrancl(U_14621,U_14623) = c_Transitive__Closure_Ortrancl(U_14621,U_14622)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14621,U_14621),tc_HOL_Obool)),U_14623),c_Transitive__Closure_Ortrancl(U_14621,U_14622)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14621,U_14621),tc_HOL_Obool)),U_14622),U_14623)) ),
inference(clausify,[status(thm)],[f_3716_2]) ).
fof(f_3717_1,plain,
! [V_s_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__subset__rtrancl]) ).
fof(f_3717_2,plain,
! [U_14626,U_14625,U_14624] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14624,U_14624),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14624,U_14625)),c_Transitive__Closure_Ortrancl(U_14624,U_14626)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14624,U_14624),tc_HOL_Obool)),U_14625),c_Transitive__Closure_Ortrancl(U_14624,U_14626))) ),
inference(variable_rename,[status(thm)],[f_3717_1]) ).
cnf(f_3717_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14624,U_14624),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14624,U_14625)),c_Transitive__Closure_Ortrancl(U_14624,U_14626)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14624,U_14624),tc_HOL_Obool)),U_14625),c_Transitive__Closure_Ortrancl(U_14624,U_14626))) ),
inference(clausify,[status(thm)],[f_3717_2]) ).
fof(f_3718_1,plain,
! [V_S_2,V_R_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))),
inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__subset]) ).
fof(f_3718_2,plain,
! [U_14629,U_14628,U_14627] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14627,U_14627),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14627,U_14627),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14627,U_14628)),c_Transitive__Closure_Ortrancl(U_14627,U_14629))),c_Transitive__Closure_Ortrancl(U_14627,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14627,U_14627),tc_HOL_Obool)),U_14628),U_14629)))),
inference(variable_rename,[status(thm)],[f_3718_1]) ).
cnf(f_3718_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14627,U_14627),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14627,U_14627),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14627,U_14628)),c_Transitive__Closure_Ortrancl(U_14627,U_14629))),c_Transitive__Closure_Ortrancl(U_14627,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14627,U_14627),tc_HOL_Obool)),U_14628),U_14629)))),
inference(clausify,[status(thm)],[f_3718_2]) ).
fof(f_3719_1,plain,
! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
inference(fof_nnf,[status(thm)],[fact_rtrancl__reflcl]) ).
fof(f_3719_2,plain,
! [U_14631,U_14630] : c_Transitive__Closure_Ortrancl(U_14630,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14630,U_14630),tc_HOL_Obool)),U_14631),c_Relation_OId(U_14630))) = c_Transitive__Closure_Ortrancl(U_14630,U_14631),
inference(variable_rename,[status(thm)],[f_3719_1]) ).
cnf(f_3719_3,plain,
c_Transitive__Closure_Ortrancl(U_14630,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14630,U_14630),tc_HOL_Obool)),U_14631),c_Relation_OId(U_14630))) = c_Transitive__Closure_Ortrancl(U_14630,U_14631),
inference(clausify,[status(thm)],[f_3719_2]) ).
fof(f_3720_1,plain,
! [V_S_2,V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) = c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),
inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__rtrancl]) ).
fof(f_3720_2,plain,
! [U_14634,U_14633,U_14632] : c_Transitive__Closure_Ortrancl(U_14632,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14632,U_14632),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14632,U_14633)),c_Transitive__Closure_Ortrancl(U_14632,U_14634))) = c_Transitive__Closure_Ortrancl(U_14632,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14632,U_14632),tc_HOL_Obool)),U_14633),U_14634)),
inference(variable_rename,[status(thm)],[f_3720_1]) ).
cnf(f_3720_3,plain,
c_Transitive__Closure_Ortrancl(U_14632,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14632,U_14632),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14632,U_14633)),c_Transitive__Closure_Ortrancl(U_14632,U_14634))) = c_Transitive__Closure_Ortrancl(U_14632,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14632,U_14632),tc_HOL_Obool)),U_14633),U_14634)),
inference(clausify,[status(thm)],[f_3720_2]) ).
fof(f_3721_1,plain,
! [V_R_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2),
inference(fof_nnf,[status(thm)],[fact_rtrancl__reflcl__absorb]) ).
fof(f_3721_2,plain,
! [U_14636,U_14635] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14635,U_14635),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14635,U_14636)),c_Relation_OId(U_14635)) = c_Transitive__Closure_Ortrancl(U_14635,U_14636),
inference(variable_rename,[status(thm)],[f_3721_1]) ).
cnf(f_3721_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14635,U_14635),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14635,U_14636)),c_Relation_OId(U_14635)) = c_Transitive__Closure_Ortrancl(U_14635,U_14636),
inference(clausify,[status(thm)],[f_3721_2]) ).
fof(f_3722_1,plain,
! [V_R_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Range__rtrancl]) ).
fof(f_3722_2,plain,
! [U_14638,U_14637] : hAPP(c_Relation_ORange(U_14637,U_14637),c_Transitive__Closure_Ortrancl(U_14637,U_14638)) = c_Orderings_Otop__class_Otop(tc_fun(U_14637,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3722_1]) ).
cnf(f_3722_3,plain,
hAPP(c_Relation_ORange(U_14637,U_14637),c_Transitive__Closure_Ortrancl(U_14637,U_14638)) = c_Orderings_Otop__class_Otop(tc_fun(U_14637,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3722_2]) ).
fof(f_3723_1,plain,
! [V_S_2,V_R_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2)))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_in__rtrancl__UnI]) ).
fof(f_3723_2,plain,
! [U_14642,U_14641,U_14640,U_14639] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14639,U_14639)),U_14640),c_Transitive__Closure_Ortrancl(U_14639,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14639,U_14639),tc_HOL_Obool)),U_14641),U_14642))))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14639,U_14639)),U_14640),c_Transitive__Closure_Ortrancl(U_14639,U_14642)))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14639,U_14639)),U_14640),c_Transitive__Closure_Ortrancl(U_14639,U_14641))) ) ),
inference(variable_rename,[status(thm)],[f_3723_1]) ).
cnf(f_3723_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14639,U_14639)),U_14640),c_Transitive__Closure_Ortrancl(U_14639,U_14641)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_14639,U_14639)),U_14640),c_Transitive__Closure_Ortrancl(U_14639,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14639,U_14639),tc_HOL_Obool)),U_14641),U_14642)))) ),
inference(clausify,[status(thm)],[f_3723_2]) ).
cnf(f_3723_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14639,U_14639)),U_14640),c_Transitive__Closure_Ortrancl(U_14639,U_14642)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_14639,U_14639)),U_14640),c_Transitive__Closure_Ortrancl(U_14639,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14639,U_14639),tc_HOL_Obool)),U_14641),U_14642)))) ),
inference(clausify,[status(thm)],[f_3723_2]) ).
fof(f_3724_1,plain,
! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
inference(fof_nnf,[status(thm)],[fact_rtrancl__r__diff__Id]) ).
fof(f_3724_2,plain,
! [U_14644,U_14643] : c_Transitive__Closure_Ortrancl(U_14643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14643,U_14643),tc_HOL_Obool)),U_14644),c_Relation_OId(U_14643))) = c_Transitive__Closure_Ortrancl(U_14643,U_14644),
inference(variable_rename,[status(thm)],[f_3724_1]) ).
cnf(f_3724_3,plain,
c_Transitive__Closure_Ortrancl(U_14643,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14643,U_14643),tc_HOL_Obool)),U_14644),c_Relation_OId(U_14643))) = c_Transitive__Closure_Ortrancl(U_14643,U_14644),
inference(clausify,[status(thm)],[f_3724_2]) ).
fof(f_3725_1,plain,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__into__rtrancl]) ).
fof(f_3725_2,plain,
! [U_14649,U_14648,U_14647,U_14646,U_14645] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14645,U_14645)),hAPP(hAPP(c_Product__Type_OPair(U_14645,U_14645),U_14646),U_14649)),c_Transitive__Closure_Ortrancl(U_14645,U_14648)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14645,U_14645)),hAPP(hAPP(c_Product__Type_OPair(U_14645,U_14645),U_14647),U_14649)),c_Transitive__Closure_Ortrancl(U_14645,U_14648)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14645,U_14645)),hAPP(hAPP(c_Product__Type_OPair(U_14645,U_14645),U_14646),U_14647)),U_14648)) ),
inference(variable_rename,[status(thm)],[f_3725_1]) ).
cnf(f_3725_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14645,U_14645)),hAPP(hAPP(c_Product__Type_OPair(U_14645,U_14645),U_14646),U_14649)),c_Transitive__Closure_Ortrancl(U_14645,U_14648)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14645,U_14645)),hAPP(hAPP(c_Product__Type_OPair(U_14645,U_14645),U_14647),U_14649)),c_Transitive__Closure_Ortrancl(U_14645,U_14648)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14645,U_14645)),hAPP(hAPP(c_Product__Type_OPair(U_14645,U_14645),U_14646),U_14647)),U_14648)) ),
inference(clausify,[status(thm)],[f_3725_2]) ).
fof(f_3726_1,plain,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__into__rtrancl]) ).
fof(f_3726_2,plain,
! [U_14654,U_14653,U_14652,U_14651,U_14650] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14650,U_14650)),hAPP(hAPP(c_Product__Type_OPair(U_14650,U_14650),U_14651),U_14654)),c_Transitive__Closure_Ortrancl(U_14650,U_14653)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14650,U_14650)),hAPP(hAPP(c_Product__Type_OPair(U_14650,U_14650),U_14652),U_14654)),U_14653))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14650,U_14650)),hAPP(hAPP(c_Product__Type_OPair(U_14650,U_14650),U_14651),U_14652)),c_Transitive__Closure_Ortrancl(U_14650,U_14653))) ),
inference(variable_rename,[status(thm)],[f_3726_1]) ).
cnf(f_3726_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14650,U_14650)),hAPP(hAPP(c_Product__Type_OPair(U_14650,U_14650),U_14651),U_14654)),c_Transitive__Closure_Ortrancl(U_14650,U_14653)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14650,U_14650)),hAPP(hAPP(c_Product__Type_OPair(U_14650,U_14650),U_14652),U_14654)),U_14653))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14650,U_14650)),hAPP(hAPP(c_Product__Type_OPair(U_14650,U_14650),U_14651),U_14652)),c_Transitive__Closure_Ortrancl(U_14650,U_14653))) ),
inference(clausify,[status(thm)],[f_3726_2]) ).
fof(f_3727_1,plain,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__trans]) ).
fof(f_3727_2,plain,
! [U_14659,U_14658,U_14657,U_14656,U_14655] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14655,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14655,U_14655),U_14656),U_14659)),c_Transitive__Closure_Ortrancl(U_14655,U_14658)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14655,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14655,U_14655),U_14657),U_14659)),c_Transitive__Closure_Ortrancl(U_14655,U_14658)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14655,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14655,U_14655),U_14656),U_14657)),c_Transitive__Closure_Ortrancl(U_14655,U_14658))) ),
inference(variable_rename,[status(thm)],[f_3727_1]) ).
cnf(f_3727_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14655,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14655,U_14655),U_14656),U_14659)),c_Transitive__Closure_Ortrancl(U_14655,U_14658)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14655,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14655,U_14655),U_14657),U_14659)),c_Transitive__Closure_Ortrancl(U_14655,U_14658)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14655,U_14655)),hAPP(hAPP(c_Product__Type_OPair(U_14655,U_14655),U_14656),U_14657)),c_Transitive__Closure_Ortrancl(U_14655,U_14658))) ),
inference(clausify,[status(thm)],[f_3727_2]) ).
fof(f_3728_1,plain,
! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
inference(fof_nnf,[status(thm)],[fact_refl__rtrancl]) ).
fof(f_3728_2,plain,
! [U_14661,U_14660] : c_Relation_Orefl__on(U_14660,c_Orderings_Otop__class_Otop(tc_fun(U_14660,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14660,U_14661)),
inference(variable_rename,[status(thm)],[f_3728_1]) ).
cnf(f_3728_3,plain,
c_Relation_Orefl__on(U_14660,c_Orderings_Otop__class_Otop(tc_fun(U_14660,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_14660,U_14661)),
inference(clausify,[status(thm)],[f_3728_2]) ).
fof(f_3729_1,plain,
! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
inference(fof_nnf,[status(thm)],[fact_rtrancl__idemp]) ).
fof(f_3729_2,plain,
! [U_14663,U_14662] : c_Transitive__Closure_Ortrancl(U_14662,c_Transitive__Closure_Ortrancl(U_14662,U_14663)) = c_Transitive__Closure_Ortrancl(U_14662,U_14663),
inference(variable_rename,[status(thm)],[f_3729_1]) ).
cnf(f_3729_3,plain,
c_Transitive__Closure_Ortrancl(U_14662,c_Transitive__Closure_Ortrancl(U_14662,U_14663)) = c_Transitive__Closure_Ortrancl(U_14662,U_14663),
inference(clausify,[status(thm)],[f_3729_2]) ).
fof(f_3730_1,plain,
! [V_R_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Domain__rtrancl]) ).
fof(f_3730_2,plain,
! [U_14665,U_14664] : hAPP(c_Relation_ODomain(U_14664,U_14664),c_Transitive__Closure_Ortrancl(U_14664,U_14665)) = c_Orderings_Otop__class_Otop(tc_fun(U_14664,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3730_1]) ).
cnf(f_3730_3,plain,
hAPP(c_Relation_ODomain(U_14664,U_14664),c_Transitive__Closure_Ortrancl(U_14664,U_14665)) = c_Orderings_Otop__class_Otop(tc_fun(U_14664,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3730_2]) ).
fof(f_3731_1,plain,
! [T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Relation_OId(T_b),
inference(fof_nnf,[status(thm)],[fact_rtrancl__empty]) ).
fof(f_3731_2,plain,
! [U_14666] : c_Transitive__Closure_Ortrancl(U_14666,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14666,U_14666),tc_HOL_Obool))) = c_Relation_OId(U_14666),
inference(variable_rename,[status(thm)],[f_3731_1]) ).
cnf(f_3731_3,plain,
c_Transitive__Closure_Ortrancl(U_14666,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14666,U_14666),tc_HOL_Obool))) = c_Relation_OId(U_14666),
inference(clausify,[status(thm)],[f_3731_2]) ).
fof(f_3732_1,plain,
! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Image__Id]) ).
fof(f_3732_2,plain,
! [U_14668,U_14667] : hAPP(c_Relation_OImage(U_14667,U_14667,c_Relation_OId(U_14667)),U_14668) = U_14668,
inference(variable_rename,[status(thm)],[f_3732_1]) ).
cnf(f_3732_3,plain,
hAPP(c_Relation_OImage(U_14667,U_14667,c_Relation_OId(U_14667)),U_14668) = U_14668,
inference(clausify,[status(thm)],[f_3732_2]) ).
fof(f_3733_1,plain,
! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_c),V_R_2),c_Relation_OId(T_c)) = V_R_2,
inference(fof_nnf,[status(thm)],[fact_R__O__Id]) ).
fof(f_3733_2,plain,
! [U_14671,U_14670,U_14669] : hAPP(hAPP(c_Relation_Orel__comp(U_14669,U_14670,U_14670),U_14671),c_Relation_OId(U_14670)) = U_14671,
inference(variable_rename,[status(thm)],[f_3733_1]) ).
cnf(f_3733_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_14669,U_14670,U_14670),U_14671),c_Relation_OId(U_14670)) = U_14671,
inference(clausify,[status(thm)],[f_3733_2]) ).
fof(f_3734_1,plain,
! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_c),c_Relation_OId(T_b)),V_R_2) = V_R_2,
inference(fof_nnf,[status(thm)],[fact_Id__O__R]) ).
fof(f_3734_2,plain,
! [U_14674,U_14673,U_14672] : hAPP(hAPP(c_Relation_Orel__comp(U_14672,U_14672,U_14673),c_Relation_OId(U_14672)),U_14674) = U_14674,
inference(variable_rename,[status(thm)],[f_3734_1]) ).
cnf(f_3734_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_14672,U_14672,U_14673),c_Relation_OId(U_14672)),U_14674) = U_14674,
inference(clausify,[status(thm)],[f_3734_2]) ).
fof(f_3735_1,plain,
! [V_b_2,V_a_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b)))
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b))) ) ),
inference(fof_nnf,[status(thm)],[fact_pair__in__Id__conv]) ).
fof(f_3735_2,plain,
! [U_14677,U_14676,U_14675] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14675,U_14675)),hAPP(hAPP(c_Product__Type_OPair(U_14675,U_14675),U_14676),U_14677)),c_Relation_OId(U_14675)))
| U_14676 != U_14677 )
& ( U_14676 = U_14677
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14675,U_14675)),hAPP(hAPP(c_Product__Type_OPair(U_14675,U_14675),U_14676),U_14677)),c_Relation_OId(U_14675))) ) ),
inference(variable_rename,[status(thm)],[f_3735_1]) ).
fof(f_3735_3,plain,
( ! [U_14683,U_14681] :
( ! [U_14679] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14679,U_14679)),hAPP(hAPP(c_Product__Type_OPair(U_14679,U_14679),U_14681),U_14683)),c_Relation_OId(U_14679)))
| U_14681 != U_14683 )
& ! [U_14682,U_14680] :
( ! [U_14678] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14678,U_14678)),hAPP(hAPP(c_Product__Type_OPair(U_14678,U_14678),U_14680),U_14682)),c_Relation_OId(U_14678)))
| U_14680 = U_14682 ) ),
inference(miniscope,[status(thm)],[f_3735_2]) ).
cnf(f_3735_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14678,U_14678)),hAPP(hAPP(c_Product__Type_OPair(U_14678,U_14678),U_14680),U_14682)),c_Relation_OId(U_14678)))
| U_14680 = U_14682 ),
inference(clausify,[status(thm)],[f_3735_3]) ).
cnf(f_3735_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14679,U_14679)),hAPP(hAPP(c_Product__Type_OPair(U_14679,U_14679),U_14681),U_14683)),c_Relation_OId(U_14679)))
| U_14681 != U_14683 ),
inference(clausify,[status(thm)],[f_3735_3]) ).
fof(f_3736_1,plain,
! [V_R_2,V_y_2,V_x_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
| V_x_2 = V_y_2 )
& V_x_2 != V_y_2 ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
& V_x_2 != V_y_2 )
| V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__eq__or__trancl]) ).
fof(f_3736_2,plain,
! [U_14687,U_14686,U_14685,U_14684] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14684,U_14684)),hAPP(hAPP(c_Product__Type_OPair(U_14684,U_14684),U_14685),U_14686)),c_Transitive__Closure_Ortrancl(U_14684,U_14687)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14684,U_14684)),hAPP(hAPP(c_Product__Type_OPair(U_14684,U_14684),U_14685),U_14686)),c_Transitive__Closure_Otrancl(U_14684,U_14687)))
| U_14685 = U_14686 )
& U_14685 != U_14686 ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14684,U_14684)),hAPP(hAPP(c_Product__Type_OPair(U_14684,U_14684),U_14685),U_14686)),c_Transitive__Closure_Otrancl(U_14684,U_14687)))
& U_14685 != U_14686 )
| U_14685 = U_14686
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14684,U_14684)),hAPP(hAPP(c_Product__Type_OPair(U_14684,U_14684),U_14685),U_14686)),c_Transitive__Closure_Ortrancl(U_14684,U_14687))) ) ),
inference(variable_rename,[status(thm)],[f_3736_1]) ).
fof(f_3736_3,plain,
( ! [U_14695,U_14693,U_14691,U_14689] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14689,U_14689)),hAPP(hAPP(c_Product__Type_OPair(U_14689,U_14689),U_14691),U_14693)),c_Transitive__Closure_Ortrancl(U_14689,U_14695)))
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14689,U_14689)),hAPP(hAPP(c_Product__Type_OPair(U_14689,U_14689),U_14691),U_14693)),c_Transitive__Closure_Otrancl(U_14689,U_14695)))
| U_14691 = U_14693 )
& U_14691 != U_14693 ) )
& ! [U_14694,U_14692,U_14690,U_14688] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14688,U_14688)),hAPP(hAPP(c_Product__Type_OPair(U_14688,U_14688),U_14690),U_14692)),c_Transitive__Closure_Otrancl(U_14688,U_14694)))
& U_14690 != U_14692 )
| U_14690 = U_14692
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14688,U_14688)),hAPP(hAPP(c_Product__Type_OPair(U_14688,U_14688),U_14690),U_14692)),c_Transitive__Closure_Ortrancl(U_14688,U_14694))) ) ),
inference(miniscope,[status(thm)],[f_3736_2]) ).
cnf(f_3736_4,plain,
( U_14690 != U_14692
| U_14690 = U_14692
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14688,U_14688)),hAPP(hAPP(c_Product__Type_OPair(U_14688,U_14688),U_14690),U_14692)),c_Transitive__Closure_Ortrancl(U_14688,U_14694))) ),
inference(clausify,[status(thm)],[f_3736_3]) ).
cnf(f_3736_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14688,U_14688)),hAPP(hAPP(c_Product__Type_OPair(U_14688,U_14688),U_14690),U_14692)),c_Transitive__Closure_Otrancl(U_14688,U_14694)))
| U_14690 = U_14692
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14688,U_14688)),hAPP(hAPP(c_Product__Type_OPair(U_14688,U_14688),U_14690),U_14692)),c_Transitive__Closure_Ortrancl(U_14688,U_14694))) ),
inference(clausify,[status(thm)],[f_3736_3]) ).
cnf(f_3736_6,plain,
( U_14691 != U_14693
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_14689,U_14689)),hAPP(hAPP(c_Product__Type_OPair(U_14689,U_14689),U_14691),U_14693)),c_Transitive__Closure_Ortrancl(U_14689,U_14695))) ),
inference(clausify,[status(thm)],[f_3736_3]) ).
cnf(f_3736_7,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14689,U_14689)),hAPP(hAPP(c_Product__Type_OPair(U_14689,U_14689),U_14691),U_14693)),c_Transitive__Closure_Otrancl(U_14689,U_14695)))
| U_14691 = U_14693
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_14689,U_14689)),hAPP(hAPP(c_Product__Type_OPair(U_14689,U_14689),U_14691),U_14693)),c_Transitive__Closure_Ortrancl(U_14689,U_14695))) ),
inference(clausify,[status(thm)],[f_3736_3]) ).
fof(f_3737_1,plain,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl2]) ).
fof(f_3737_2,plain,
! [U_14700,U_14699,U_14698,U_14697,U_14696] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14696,U_14696)),hAPP(hAPP(c_Product__Type_OPair(U_14696,U_14696),U_14697),U_14700)),c_Transitive__Closure_Otrancl(U_14696,U_14699)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14696,U_14696)),hAPP(hAPP(c_Product__Type_OPair(U_14696,U_14696),U_14698),U_14700)),c_Transitive__Closure_Ortrancl(U_14696,U_14699)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14696,U_14696)),hAPP(hAPP(c_Product__Type_OPair(U_14696,U_14696),U_14697),U_14698)),U_14699)) ),
inference(variable_rename,[status(thm)],[f_3737_1]) ).
cnf(f_3737_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14696,U_14696)),hAPP(hAPP(c_Product__Type_OPair(U_14696,U_14696),U_14697),U_14700)),c_Transitive__Closure_Otrancl(U_14696,U_14699)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14696,U_14696)),hAPP(hAPP(c_Product__Type_OPair(U_14696,U_14696),U_14698),U_14700)),c_Transitive__Closure_Ortrancl(U_14696,U_14699)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14696,U_14696)),hAPP(hAPP(c_Product__Type_OPair(U_14696,U_14696),U_14697),U_14698)),U_14699)) ),
inference(clausify,[status(thm)],[f_3737_2]) ).
fof(f_3738_1,plain,
! [V_R_2,V_b_2,V_a_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
& V_a_2 != V_b_2 )
| V_a_2 = V_b_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_rtranclD]) ).
fof(f_3738_2,plain,
! [U_14704,U_14703,U_14702,U_14701] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14701,U_14701)),hAPP(hAPP(c_Product__Type_OPair(U_14701,U_14701),U_14702),U_14703)),c_Transitive__Closure_Otrancl(U_14701,U_14704)))
& U_14702 != U_14703 )
| U_14702 = U_14703
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14701,U_14701)),hAPP(hAPP(c_Product__Type_OPair(U_14701,U_14701),U_14702),U_14703)),c_Transitive__Closure_Ortrancl(U_14701,U_14704))) ),
inference(variable_rename,[status(thm)],[f_3738_1]) ).
cnf(f_3738_3,plain,
( U_14702 != U_14703
| U_14702 = U_14703
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14701,U_14701)),hAPP(hAPP(c_Product__Type_OPair(U_14701,U_14701),U_14702),U_14703)),c_Transitive__Closure_Ortrancl(U_14701,U_14704))) ),
inference(clausify,[status(thm)],[f_3738_2]) ).
cnf(f_3738_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14701,U_14701)),hAPP(hAPP(c_Product__Type_OPair(U_14701,U_14701),U_14702),U_14703)),c_Transitive__Closure_Otrancl(U_14701,U_14704)))
| U_14702 = U_14703
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14701,U_14701)),hAPP(hAPP(c_Product__Type_OPair(U_14701,U_14701),U_14702),U_14703)),c_Transitive__Closure_Ortrancl(U_14701,U_14704))) ),
inference(clausify,[status(thm)],[f_3738_2]) ).
fof(f_3739_1,plain,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl1]) ).
fof(f_3739_2,plain,
! [U_14709,U_14708,U_14707,U_14706,U_14705] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14705,U_14705)),hAPP(hAPP(c_Product__Type_OPair(U_14705,U_14705),U_14706),U_14709)),c_Transitive__Closure_Otrancl(U_14705,U_14708)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14705,U_14705)),hAPP(hAPP(c_Product__Type_OPair(U_14705,U_14705),U_14707),U_14709)),U_14708))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14705,U_14705)),hAPP(hAPP(c_Product__Type_OPair(U_14705,U_14705),U_14706),U_14707)),c_Transitive__Closure_Ortrancl(U_14705,U_14708))) ),
inference(variable_rename,[status(thm)],[f_3739_1]) ).
cnf(f_3739_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14705,U_14705)),hAPP(hAPP(c_Product__Type_OPair(U_14705,U_14705),U_14706),U_14709)),c_Transitive__Closure_Otrancl(U_14705,U_14708)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14705,U_14705)),hAPP(hAPP(c_Product__Type_OPair(U_14705,U_14705),U_14707),U_14709)),U_14708))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14705,U_14705)),hAPP(hAPP(c_Product__Type_OPair(U_14705,U_14705),U_14706),U_14707)),c_Transitive__Closure_Ortrancl(U_14705,U_14708))) ),
inference(clausify,[status(thm)],[f_3739_2]) ).
fof(f_3740_1,plain,
! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_trancl__rtrancl__trancl]) ).
fof(f_3740_2,plain,
! [U_14714,U_14713,U_14712,U_14711,U_14710] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14710,U_14710)),hAPP(hAPP(c_Product__Type_OPair(U_14710,U_14710),U_14711),U_14714)),c_Transitive__Closure_Otrancl(U_14710,U_14713)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14710,U_14710)),hAPP(hAPP(c_Product__Type_OPair(U_14710,U_14710),U_14712),U_14714)),c_Transitive__Closure_Ortrancl(U_14710,U_14713)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14710,U_14710)),hAPP(hAPP(c_Product__Type_OPair(U_14710,U_14710),U_14711),U_14712)),c_Transitive__Closure_Otrancl(U_14710,U_14713))) ),
inference(variable_rename,[status(thm)],[f_3740_1]) ).
cnf(f_3740_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14710,U_14710)),hAPP(hAPP(c_Product__Type_OPair(U_14710,U_14710),U_14711),U_14714)),c_Transitive__Closure_Otrancl(U_14710,U_14713)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14710,U_14710)),hAPP(hAPP(c_Product__Type_OPair(U_14710,U_14710),U_14712),U_14714)),c_Transitive__Closure_Ortrancl(U_14710,U_14713)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14710,U_14710)),hAPP(hAPP(c_Product__Type_OPair(U_14710,U_14710),U_14711),U_14712)),c_Transitive__Closure_Otrancl(U_14710,U_14713))) ),
inference(clausify,[status(thm)],[f_3740_2]) ).
fof(f_3741_1,plain,
! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__trancl__trancl]) ).
fof(f_3741_2,plain,
! [U_14719,U_14718,U_14717,U_14716,U_14715] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14715,U_14715)),hAPP(hAPP(c_Product__Type_OPair(U_14715,U_14715),U_14716),U_14719)),c_Transitive__Closure_Otrancl(U_14715,U_14718)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14715,U_14715)),hAPP(hAPP(c_Product__Type_OPair(U_14715,U_14715),U_14717),U_14719)),c_Transitive__Closure_Otrancl(U_14715,U_14718)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14715,U_14715)),hAPP(hAPP(c_Product__Type_OPair(U_14715,U_14715),U_14716),U_14717)),c_Transitive__Closure_Ortrancl(U_14715,U_14718))) ),
inference(variable_rename,[status(thm)],[f_3741_1]) ).
cnf(f_3741_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14715,U_14715)),hAPP(hAPP(c_Product__Type_OPair(U_14715,U_14715),U_14716),U_14719)),c_Transitive__Closure_Otrancl(U_14715,U_14718)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14715,U_14715)),hAPP(hAPP(c_Product__Type_OPair(U_14715,U_14715),U_14717),U_14719)),c_Transitive__Closure_Otrancl(U_14715,U_14718)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14715,U_14715)),hAPP(hAPP(c_Product__Type_OPair(U_14715,U_14715),U_14716),U_14717)),c_Transitive__Closure_Ortrancl(U_14715,U_14718))) ),
inference(clausify,[status(thm)],[f_3741_2]) ).
fof(f_3742_1,plain,
! [T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Domain__Id]) ).
fof(f_3742_2,plain,
! [U_14720] : hAPP(c_Relation_ODomain(U_14720,U_14720),c_Relation_OId(U_14720)) = c_Orderings_Otop__class_Otop(tc_fun(U_14720,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3742_1]) ).
cnf(f_3742_3,plain,
hAPP(c_Relation_ODomain(U_14720,U_14720),c_Relation_OId(U_14720)) = c_Orderings_Otop__class_Otop(tc_fun(U_14720,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3742_2]) ).
fof(f_3743_1,plain,
! [T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Range__Id]) ).
fof(f_3743_2,plain,
! [U_14721] : hAPP(c_Relation_ORange(U_14721,U_14721),c_Relation_OId(U_14721)) = c_Orderings_Otop__class_Otop(tc_fun(U_14721,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3743_1]) ).
cnf(f_3743_3,plain,
hAPP(c_Relation_ORange(U_14721,U_14721),c_Relation_OId(U_14721)) = c_Orderings_Otop__class_Otop(tc_fun(U_14721,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3743_2]) ).
fof(f_3744_1,plain,
! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Relation_OId(T_b)),
inference(fof_nnf,[status(thm)],[fact_refl__Id]) ).
fof(f_3744_2,plain,
! [U_14722] : c_Relation_Orefl__on(U_14722,c_Orderings_Otop__class_Otop(tc_fun(U_14722,tc_HOL_Obool)),c_Relation_OId(U_14722)),
inference(variable_rename,[status(thm)],[f_3744_1]) ).
cnf(f_3744_3,plain,
c_Relation_Orefl__on(U_14722,c_Orderings_Otop__class_Otop(tc_fun(U_14722,tc_HOL_Obool)),c_Relation_OId(U_14722)),
inference(clausify,[status(thm)],[f_3744_2]) ).
fof(f_3745_1,plain,
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))),
inference(fof_nnf,[status(thm)],[fact_pair__leq__def]) ).
cnf(f_3745_2,plain,
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))),
inference(clausify,[status(thm)],[f_3745_1]) ).
fof(f_3746_1,plain,
! [V_y_2,V_R_2,V_x_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) )
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_Not__Domain__rtrancl]) ).
fof(f_3746_2,plain,
! [U_14726,U_14725,U_14724,U_14723] :
( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14723,U_14723)),hAPP(hAPP(c_Product__Type_OPair(U_14723,U_14723),U_14724),U_14726)),c_Transitive__Closure_Ortrancl(U_14723,U_14725)))
| U_14724 != U_14726 )
& ( U_14724 = U_14726
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14723,U_14723)),hAPP(hAPP(c_Product__Type_OPair(U_14723,U_14723),U_14724),U_14726)),c_Transitive__Closure_Ortrancl(U_14723,U_14725))) ) )
| hBOOL(hAPP(hAPP(c_member(U_14723),U_14724),hAPP(c_Relation_ODomain(U_14723,U_14723),U_14725))) ),
inference(variable_rename,[status(thm)],[f_3746_1]) ).
cnf(f_3746_3,plain,
( U_14724 = U_14726
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14723,U_14723)),hAPP(hAPP(c_Product__Type_OPair(U_14723,U_14723),U_14724),U_14726)),c_Transitive__Closure_Ortrancl(U_14723,U_14725)))
| hBOOL(hAPP(hAPP(c_member(U_14723),U_14724),hAPP(c_Relation_ODomain(U_14723,U_14723),U_14725))) ),
inference(clausify,[status(thm)],[f_3746_2]) ).
cnf(f_3746_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14723,U_14723)),hAPP(hAPP(c_Product__Type_OPair(U_14723,U_14723),U_14724),U_14726)),c_Transitive__Closure_Ortrancl(U_14723,U_14725)))
| U_14724 != U_14726
| hBOOL(hAPP(hAPP(c_member(U_14723),U_14724),hAPP(c_Relation_ODomain(U_14723,U_14723),U_14725))) ),
inference(clausify,[status(thm)],[f_3746_2]) ).
fof(f_3747_1,plain,
! [V_b_2,V_r_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_acc__downwards]) ).
fof(f_3747_2,plain,
! [U_14730,U_14729,U_14728,U_14727] :
( hBOOL(hAPP(hAPP(c_member(U_14727),U_14730),c_Wellfounded_Oacc(U_14727,U_14729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14727,U_14727)),hAPP(hAPP(c_Product__Type_OPair(U_14727,U_14727),U_14730),U_14728)),c_Transitive__Closure_Ortrancl(U_14727,U_14729)))
| ~ hBOOL(hAPP(hAPP(c_member(U_14727),U_14728),c_Wellfounded_Oacc(U_14727,U_14729))) ),
inference(variable_rename,[status(thm)],[f_3747_1]) ).
cnf(f_3747_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_14727),U_14730),c_Wellfounded_Oacc(U_14727,U_14729)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14727,U_14727)),hAPP(hAPP(c_Product__Type_OPair(U_14727,U_14727),U_14730),U_14728)),c_Transitive__Closure_Ortrancl(U_14727,U_14729)))
| ~ hBOOL(hAPP(hAPP(c_member(U_14727),U_14728),c_Wellfounded_Oacc(U_14727,U_14729))) ),
inference(clausify,[status(thm)],[f_3747_2]) ).
fof(f_3748_1,plain,
! [V_r_2,V_a_2,V_b_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_acc__downwards__aux]) ).
fof(f_3748_2,plain,
! [U_14734,U_14733,U_14732,U_14731] :
( hBOOL(hAPP(hAPP(c_member(U_14731),U_14732),c_Wellfounded_Oacc(U_14731,U_14734)))
| ~ hBOOL(hAPP(hAPP(c_member(U_14731),U_14733),c_Wellfounded_Oacc(U_14731,U_14734)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14731,U_14731)),hAPP(hAPP(c_Product__Type_OPair(U_14731,U_14731),U_14732),U_14733)),c_Transitive__Closure_Ortrancl(U_14731,U_14734))) ),
inference(variable_rename,[status(thm)],[f_3748_1]) ).
cnf(f_3748_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_14731),U_14732),c_Wellfounded_Oacc(U_14731,U_14734)))
| ~ hBOOL(hAPP(hAPP(c_member(U_14731),U_14733),c_Wellfounded_Oacc(U_14731,U_14734)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14731,U_14731)),hAPP(hAPP(c_Product__Type_OPair(U_14731,U_14731),U_14732),U_14733)),c_Transitive__Closure_Ortrancl(U_14731,U_14734))) ),
inference(clausify,[status(thm)],[f_3748_2]) ).
fof(f_3749_1,plain,
! [V_r_2,V_x_2,V_y_2,T_b] :
( ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ c_Wellfounded_Owf(T_b,V_r_2) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
& c_Wellfounded_Owf(T_b,V_r_2) )
| ~ c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_wf__insert]) ).
fof(f_3749_2,plain,
! [U_14738,U_14737,U_14736,U_14735] :
( ( c_Wellfounded_Owf(U_14735,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14735,U_14735)),hAPP(hAPP(c_Product__Type_OPair(U_14735,U_14735),U_14736),U_14737)),U_14738))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_14735,U_14735)),hAPP(hAPP(c_Product__Type_OPair(U_14735,U_14735),U_14737),U_14736)),c_Transitive__Closure_Ortrancl(U_14735,U_14738)))
| ~ c_Wellfounded_Owf(U_14735,U_14738) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14735,U_14735)),hAPP(hAPP(c_Product__Type_OPair(U_14735,U_14735),U_14737),U_14736)),c_Transitive__Closure_Ortrancl(U_14735,U_14738)))
& c_Wellfounded_Owf(U_14735,U_14738) )
| ~ c_Wellfounded_Owf(U_14735,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14735,U_14735)),hAPP(hAPP(c_Product__Type_OPair(U_14735,U_14735),U_14736),U_14737)),U_14738)) ) ),
inference(variable_rename,[status(thm)],[f_3749_1]) ).
fof(f_3749_3,plain,
( ! [U_14746,U_14744,U_14742,U_14740] :
( c_Wellfounded_Owf(U_14740,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14740,U_14740)),hAPP(hAPP(c_Product__Type_OPair(U_14740,U_14740),U_14742),U_14744)),U_14746))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_14740,U_14740)),hAPP(hAPP(c_Product__Type_OPair(U_14740,U_14740),U_14744),U_14742)),c_Transitive__Closure_Ortrancl(U_14740,U_14746)))
| ~ c_Wellfounded_Owf(U_14740,U_14746) )
& ! [U_14745,U_14743,U_14741,U_14739] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14739,U_14739)),hAPP(hAPP(c_Product__Type_OPair(U_14739,U_14739),U_14743),U_14741)),c_Transitive__Closure_Ortrancl(U_14739,U_14745)))
& c_Wellfounded_Owf(U_14739,U_14745) )
| ~ c_Wellfounded_Owf(U_14739,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14739,U_14739)),hAPP(hAPP(c_Product__Type_OPair(U_14739,U_14739),U_14741),U_14743)),U_14745)) ) ),
inference(miniscope,[status(thm)],[f_3749_2]) ).
cnf(f_3749_4,plain,
( c_Wellfounded_Owf(U_14739,U_14745)
| ~ c_Wellfounded_Owf(U_14739,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14739,U_14739)),hAPP(hAPP(c_Product__Type_OPair(U_14739,U_14739),U_14741),U_14743)),U_14745)) ),
inference(clausify,[status(thm)],[f_3749_3]) ).
cnf(f_3749_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14739,U_14739)),hAPP(hAPP(c_Product__Type_OPair(U_14739,U_14739),U_14743),U_14741)),c_Transitive__Closure_Ortrancl(U_14739,U_14745)))
| ~ c_Wellfounded_Owf(U_14739,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14739,U_14739)),hAPP(hAPP(c_Product__Type_OPair(U_14739,U_14739),U_14741),U_14743)),U_14745)) ),
inference(clausify,[status(thm)],[f_3749_3]) ).
cnf(f_3749_6,plain,
( c_Wellfounded_Owf(U_14740,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14740,U_14740)),hAPP(hAPP(c_Product__Type_OPair(U_14740,U_14740),U_14742),U_14744)),U_14746))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_14740,U_14740)),hAPP(hAPP(c_Product__Type_OPair(U_14740,U_14740),U_14744),U_14742)),c_Transitive__Closure_Ortrancl(U_14740,U_14746)))
| ~ c_Wellfounded_Owf(U_14740,U_14746) ),
inference(clausify,[status(thm)],[f_3749_3]) ).
fof(f_3750_1,plain,
! [V_r_2,V_x_2,V_y_2,T_b] :
( ( c_Wellfounded_Oacyclic(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ c_Wellfounded_Oacyclic(T_b,V_r_2) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
& c_Wellfounded_Oacyclic(T_b,V_r_2) )
| ~ c_Wellfounded_Oacyclic(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_acyclic__insert]) ).
fof(f_3750_2,plain,
! [U_14750,U_14749,U_14748,U_14747] :
( ( c_Wellfounded_Oacyclic(U_14747,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14747,U_14747)),hAPP(hAPP(c_Product__Type_OPair(U_14747,U_14747),U_14748),U_14749)),U_14750))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_14747,U_14747)),hAPP(hAPP(c_Product__Type_OPair(U_14747,U_14747),U_14749),U_14748)),c_Transitive__Closure_Ortrancl(U_14747,U_14750)))
| ~ c_Wellfounded_Oacyclic(U_14747,U_14750) )
& ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14747,U_14747)),hAPP(hAPP(c_Product__Type_OPair(U_14747,U_14747),U_14749),U_14748)),c_Transitive__Closure_Ortrancl(U_14747,U_14750)))
& c_Wellfounded_Oacyclic(U_14747,U_14750) )
| ~ c_Wellfounded_Oacyclic(U_14747,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14747,U_14747)),hAPP(hAPP(c_Product__Type_OPair(U_14747,U_14747),U_14748),U_14749)),U_14750)) ) ),
inference(variable_rename,[status(thm)],[f_3750_1]) ).
fof(f_3750_3,plain,
( ! [U_14758,U_14756,U_14754,U_14752] :
( c_Wellfounded_Oacyclic(U_14752,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14752,U_14752)),hAPP(hAPP(c_Product__Type_OPair(U_14752,U_14752),U_14754),U_14756)),U_14758))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_14752,U_14752)),hAPP(hAPP(c_Product__Type_OPair(U_14752,U_14752),U_14756),U_14754)),c_Transitive__Closure_Ortrancl(U_14752,U_14758)))
| ~ c_Wellfounded_Oacyclic(U_14752,U_14758) )
& ! [U_14757,U_14755,U_14753,U_14751] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14751,U_14751)),hAPP(hAPP(c_Product__Type_OPair(U_14751,U_14751),U_14755),U_14753)),c_Transitive__Closure_Ortrancl(U_14751,U_14757)))
& c_Wellfounded_Oacyclic(U_14751,U_14757) )
| ~ c_Wellfounded_Oacyclic(U_14751,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14751,U_14751)),hAPP(hAPP(c_Product__Type_OPair(U_14751,U_14751),U_14753),U_14755)),U_14757)) ) ),
inference(miniscope,[status(thm)],[f_3750_2]) ).
cnf(f_3750_4,plain,
( c_Wellfounded_Oacyclic(U_14751,U_14757)
| ~ c_Wellfounded_Oacyclic(U_14751,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14751,U_14751)),hAPP(hAPP(c_Product__Type_OPair(U_14751,U_14751),U_14753),U_14755)),U_14757)) ),
inference(clausify,[status(thm)],[f_3750_3]) ).
cnf(f_3750_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14751,U_14751)),hAPP(hAPP(c_Product__Type_OPair(U_14751,U_14751),U_14755),U_14753)),c_Transitive__Closure_Ortrancl(U_14751,U_14757)))
| ~ c_Wellfounded_Oacyclic(U_14751,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14751,U_14751)),hAPP(hAPP(c_Product__Type_OPair(U_14751,U_14751),U_14753),U_14755)),U_14757)) ),
inference(clausify,[status(thm)],[f_3750_3]) ).
cnf(f_3750_6,plain,
( c_Wellfounded_Oacyclic(U_14752,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14752,U_14752)),hAPP(hAPP(c_Product__Type_OPair(U_14752,U_14752),U_14754),U_14756)),U_14758))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_14752,U_14752)),hAPP(hAPP(c_Product__Type_OPair(U_14752,U_14752),U_14756),U_14754)),c_Transitive__Closure_Ortrancl(U_14752,U_14758)))
| ~ c_Wellfounded_Oacyclic(U_14752,U_14758) ),
inference(clausify,[status(thm)],[f_3750_3]) ).
fof(f_3751_1,plain,
! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))),
inference(fof_nnf,[status(thm)],[fact_refl__reflcl]) ).
fof(f_3751_2,plain,
! [U_14760,U_14759] : c_Relation_Orefl__on(U_14759,c_Orderings_Otop__class_Otop(tc_fun(U_14759,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14759,U_14759),tc_HOL_Obool)),U_14760),c_Relation_OId(U_14759))),
inference(variable_rename,[status(thm)],[f_3751_1]) ).
cnf(f_3751_3,plain,
c_Relation_Orefl__on(U_14759,c_Orderings_Otop__class_Otop(tc_fun(U_14759,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14759,U_14759),tc_HOL_Obool)),U_14760),c_Relation_OId(U_14759))),
inference(clausify,[status(thm)],[f_3751_2]) ).
fof(f_3752_1,plain,
! [T_b] : c_Relation_OId(T_b) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_b),tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),tc_prod(T_b,T_b)),c_COMBB(tc_prod(T_b,T_b),tc_HOL_Obool,T_b)),c_fequal)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))))),
inference(fof_nnf,[status(thm)],[fact_Id__def]) ).
fof(f_3752_2,plain,
! [U_14761] : c_Relation_OId(U_14761) = hAPP(c_Set_OCollect(tc_prod(U_14761,U_14761)),hAPP(hAPP(c_COMBB(tc_fun(U_14761,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_14761,U_14761)),c_HOL_OEx(U_14761)),hAPP(hAPP(c_COMBC(tc_prod(U_14761,U_14761),tc_fun(U_14761,tc_prod(U_14761,U_14761)),tc_fun(U_14761,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14761,U_14761),tc_HOL_Obool),tc_fun(tc_fun(U_14761,tc_prod(U_14761,U_14761)),tc_fun(U_14761,tc_HOL_Obool)),tc_prod(U_14761,U_14761)),c_COMBB(tc_prod(U_14761,U_14761),tc_HOL_Obool,U_14761)),c_fequal)),hAPP(hAPP(c_COMBS(U_14761,U_14761,tc_prod(U_14761,U_14761)),c_Product__Type_OPair(U_14761,U_14761)),c_COMBI(U_14761))))),
inference(variable_rename,[status(thm)],[f_3752_1]) ).
cnf(f_3752_3,plain,
c_Relation_OId(U_14761) = hAPP(c_Set_OCollect(tc_prod(U_14761,U_14761)),hAPP(hAPP(c_COMBB(tc_fun(U_14761,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_14761,U_14761)),c_HOL_OEx(U_14761)),hAPP(hAPP(c_COMBC(tc_prod(U_14761,U_14761),tc_fun(U_14761,tc_prod(U_14761,U_14761)),tc_fun(U_14761,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14761,U_14761),tc_HOL_Obool),tc_fun(tc_fun(U_14761,tc_prod(U_14761,U_14761)),tc_fun(U_14761,tc_HOL_Obool)),tc_prod(U_14761,U_14761)),c_COMBB(tc_prod(U_14761,U_14761),tc_HOL_Obool,U_14761)),c_fequal)),hAPP(hAPP(c_COMBS(U_14761,U_14761,tc_prod(U_14761,U_14761)),c_Product__Type_OPair(U_14761,U_14761)),c_COMBI(U_14761))))),
inference(clausify,[status(thm)],[f_3752_2]) ).
fof(f_3753_1,plain,
! [V_r_2,T_b] : c_Relation_Oirrefl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))),
inference(fof_nnf,[status(thm)],[fact_irrefl__diff__Id]) ).
fof(f_3753_2,plain,
! [U_14763,U_14762] : c_Relation_Oirrefl(U_14762,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14762,U_14762),tc_HOL_Obool)),U_14763),c_Relation_OId(U_14762))),
inference(variable_rename,[status(thm)],[f_3753_1]) ).
cnf(f_3753_3,plain,
c_Relation_Oirrefl(U_14762,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14762,U_14762),tc_HOL_Obool)),U_14763),c_Relation_OId(U_14762))),
inference(clausify,[status(thm)],[f_3753_2]) ).
fof(f_3754_1,plain,
! [V_na_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_na_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_na_2)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_na_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_na_2)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
inference(fof_nnf,[status(thm)],[fact_pred__nat__trancl__eq__le]) ).
fof(f_3754_2,plain,
! [U_14765,U_14764] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14764),U_14765)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14764),U_14765)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14764),U_14765))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14764),U_14765)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
inference(variable_rename,[status(thm)],[f_3754_1]) ).
fof(f_3754_3,plain,
( ! [U_14769,U_14767] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14767),U_14769)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14767),U_14769)) )
& ! [U_14768,U_14766] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14766),U_14768))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14766),U_14768)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
inference(miniscope,[status(thm)],[f_3754_2]) ).
cnf(f_3754_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14766),U_14768))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14766),U_14768)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
inference(clausify,[status(thm)],[f_3754_3]) ).
cnf(f_3754_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_14767),U_14769)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_14767),U_14769)) ),
inference(clausify,[status(thm)],[f_3754_3]) ).
fof(f_3755_1,plain,
! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| V_a_2 = V_b_2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma__aux]) ).
fof(f_3755_2,plain,
! [U_14774,U_14773,U_14772,U_14771,U_14770] :
( hBOOL(hAPP(hAPP(c_member(U_14770),U_14771),U_14774))
| U_14771 = U_14772
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14770,U_14770),tc_HOL_Obool)),U_14773),hAPP(hAPP(c_Product__Type_OSigma(U_14770,U_14770),U_14774),hAPP(c_COMBK(tc_fun(U_14770,tc_HOL_Obool),U_14770),U_14774))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14770,U_14770)),hAPP(hAPP(c_Product__Type_OPair(U_14770,U_14770),U_14771),U_14772)),c_Transitive__Closure_Ortrancl(U_14770,U_14773))) ),
inference(variable_rename,[status(thm)],[f_3755_1]) ).
cnf(f_3755_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_14770),U_14771),U_14774))
| U_14771 = U_14772
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14770,U_14770),tc_HOL_Obool)),U_14773),hAPP(hAPP(c_Product__Type_OSigma(U_14770,U_14770),U_14774),hAPP(c_COMBK(tc_fun(U_14770,tc_HOL_Obool),U_14770),U_14774))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14770,U_14770)),hAPP(hAPP(c_Product__Type_OPair(U_14770,U_14770),U_14771),U_14772)),c_Transitive__Closure_Ortrancl(U_14770,U_14773))) ),
inference(clausify,[status(thm)],[f_3755_2]) ).
fof(f_3756_1,plain,
! [V_x_2,V_r_2,T_b] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_irrefl__tranclI]) ).
fof(f_3756_2,plain,
! [U_14777,U_14776,U_14775] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),U_14777),U_14777)),c_Transitive__Closure_Otrancl(U_14775,U_14776)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14775,U_14775),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14775,U_14775),U_14776)),c_Transitive__Closure_Ortrancl(U_14775,U_14776)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14775,U_14775),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_3756_1]) ).
cnf(f_3756_3,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14775,U_14775)),hAPP(hAPP(c_Product__Type_OPair(U_14775,U_14775),U_14777),U_14777)),c_Transitive__Closure_Otrancl(U_14775,U_14776)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14775,U_14775),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14775,U_14775),U_14776)),c_Transitive__Closure_Ortrancl(U_14775,U_14776)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14775,U_14775),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3756_2]) ).
fof(f_3757_1,plain,
! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))),hAPP(V_f_2,V_i_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ? [B_i] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_sequence__trans]) ).
fof(f_3757_2,plain,
! [U_14783,U_14782,U_14781,U_14780,U_14779] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),hAPP(U_14780,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14782),U_14783))),hAPP(U_14780,U_14782))),c_Transitive__Closure_Ortrancl(U_14779,U_14781)))
| ? [U_14778] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),hAPP(U_14780,hAPP(c_Nat_OSuc,U_14778))),hAPP(U_14780,U_14778))),c_Transitive__Closure_Ortrancl(U_14779,U_14781))) ),
inference(variable_rename,[status(thm)],[f_3757_1]) ).
fof(f_3757_3,plain,
! [U_14783,U_14782,U_14781,U_14780,U_14779] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),hAPP(U_14780,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14782),U_14783))),hAPP(U_14780,U_14782))),c_Transitive__Closure_Ortrancl(U_14779,U_14781)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),hAPP(U_14780,hAPP(c_Nat_OSuc,sK365(U_14783,U_14782,U_14781,U_14780,U_14779)))),hAPP(U_14780,sK365(U_14783,U_14782,U_14781,U_14780,U_14779)))),c_Transitive__Closure_Ortrancl(U_14779,U_14781))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK365]),skolemize(U_14778,sK365(U_14783,U_14782,U_14781,U_14780,U_14779))],[f_3757_2]) ).
cnf(f_3757_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),hAPP(U_14780,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14782),U_14783))),hAPP(U_14780,U_14782))),c_Transitive__Closure_Ortrancl(U_14779,U_14781)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14779,U_14779)),hAPP(hAPP(c_Product__Type_OPair(U_14779,U_14779),hAPP(U_14780,hAPP(c_Nat_OSuc,sK365(U_14783,U_14782,U_14781,U_14780,U_14779)))),hAPP(U_14780,sK365(U_14783,U_14782,U_14781,U_14780,U_14779)))),c_Transitive__Closure_Ortrancl(U_14779,U_14781))) ),
inference(clausify,[status(thm)],[f_3757_3]) ).
fof(f_3758_1,plain,
! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),
inference(fof_nnf,[status(thm)],[fact_rtrancl__converse]) ).
fof(f_3758_2,plain,
! [U_14785,U_14784] : c_Transitive__Closure_Ortrancl(U_14784,hAPP(c_Relation_Oconverse(U_14784,U_14784),U_14785)) = hAPP(c_Relation_Oconverse(U_14784,U_14784),c_Transitive__Closure_Ortrancl(U_14784,U_14785)),
inference(variable_rename,[status(thm)],[f_3758_1]) ).
cnf(f_3758_3,plain,
c_Transitive__Closure_Ortrancl(U_14784,hAPP(c_Relation_Oconverse(U_14784,U_14784),U_14785)) = hAPP(c_Relation_Oconverse(U_14784,U_14784),c_Transitive__Closure_Ortrancl(U_14784,U_14785)),
inference(clausify,[status(thm)],[f_3758_2]) ).
fof(f_3759_1,plain,
! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b),
inference(fof_nnf,[status(thm)],[fact_converse__Id]) ).
fof(f_3759_2,plain,
! [U_14786] : hAPP(c_Relation_Oconverse(U_14786,U_14786),c_Relation_OId(U_14786)) = c_Relation_OId(U_14786),
inference(variable_rename,[status(thm)],[f_3759_1]) ).
cnf(f_3759_3,plain,
hAPP(c_Relation_Oconverse(U_14786,U_14786),c_Relation_OId(U_14786)) = c_Relation_OId(U_14786),
inference(clausify,[status(thm)],[f_3759_2]) ).
fof(f_3760_1,plain,
! [V_s_2,V_r_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_b),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(c_Relation_Oconverse(T_d,T_b),V_s_2)),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2)),
inference(fof_nnf,[status(thm)],[fact_converse__rel__comp]) ).
fof(f_3760_2,plain,
! [U_14791,U_14790,U_14789,U_14788,U_14787] : hAPP(c_Relation_Oconverse(U_14787,U_14788),hAPP(hAPP(c_Relation_Orel__comp(U_14787,U_14789,U_14788),U_14790),U_14791)) = hAPP(hAPP(c_Relation_Orel__comp(U_14788,U_14789,U_14787),hAPP(c_Relation_Oconverse(U_14789,U_14788),U_14791)),hAPP(c_Relation_Oconverse(U_14787,U_14789),U_14790)),
inference(variable_rename,[status(thm)],[f_3760_1]) ).
cnf(f_3760_3,plain,
hAPP(c_Relation_Oconverse(U_14787,U_14788),hAPP(hAPP(c_Relation_Orel__comp(U_14787,U_14789,U_14788),U_14790),U_14791)) = hAPP(hAPP(c_Relation_Orel__comp(U_14788,U_14789,U_14787),hAPP(c_Relation_Oconverse(U_14789,U_14788),U_14791)),hAPP(c_Relation_Oconverse(U_14787,U_14789),U_14790)),
inference(clausify,[status(thm)],[f_3760_2]) ).
fof(f_3761_1,plain,
! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)),
inference(fof_nnf,[status(thm)],[fact_converse__Un]) ).
fof(f_3761_2,plain,
! [U_14795,U_14794,U_14793,U_14792] : hAPP(c_Relation_Oconverse(U_14792,U_14793),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14792,U_14793),tc_HOL_Obool)),U_14794),U_14795)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14793,U_14792),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14792,U_14793),U_14794)),hAPP(c_Relation_Oconverse(U_14792,U_14793),U_14795)),
inference(variable_rename,[status(thm)],[f_3761_1]) ).
cnf(f_3761_3,plain,
hAPP(c_Relation_Oconverse(U_14792,U_14793),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14792,U_14793),tc_HOL_Obool)),U_14794),U_14795)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14793,U_14792),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14792,U_14793),U_14794)),hAPP(c_Relation_Oconverse(U_14792,U_14793),U_14795)),
inference(clausify,[status(thm)],[f_3761_2]) ).
fof(f_3762_1,plain,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_converseD]) ).
fof(f_3762_2,plain,
! [U_14800,U_14799,U_14798,U_14797,U_14796] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14797,U_14796)),hAPP(hAPP(c_Product__Type_OPair(U_14797,U_14796),U_14799),U_14798)),U_14800))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14796,U_14797)),hAPP(hAPP(c_Product__Type_OPair(U_14796,U_14797),U_14798),U_14799)),hAPP(c_Relation_Oconverse(U_14797,U_14796),U_14800))) ),
inference(variable_rename,[status(thm)],[f_3762_1]) ).
cnf(f_3762_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14797,U_14796)),hAPP(hAPP(c_Product__Type_OPair(U_14797,U_14796),U_14799),U_14798)),U_14800))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14796,U_14797)),hAPP(hAPP(c_Product__Type_OPair(U_14796,U_14797),U_14798),U_14799)),hAPP(c_Relation_Oconverse(U_14797,U_14796),U_14800))) ),
inference(clausify,[status(thm)],[f_3762_2]) ).
fof(f_3763_1,plain,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_converseI]) ).
fof(f_3763_2,plain,
! [U_14805,U_14804,U_14803,U_14802,U_14801] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14802,U_14801)),hAPP(hAPP(c_Product__Type_OPair(U_14802,U_14801),U_14804),U_14803)),hAPP(c_Relation_Oconverse(U_14801,U_14802),U_14805)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14801,U_14802)),hAPP(hAPP(c_Product__Type_OPair(U_14801,U_14802),U_14803),U_14804)),U_14805)) ),
inference(variable_rename,[status(thm)],[f_3763_1]) ).
cnf(f_3763_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14802,U_14801)),hAPP(hAPP(c_Product__Type_OPair(U_14802,U_14801),U_14804),U_14803)),hAPP(c_Relation_Oconverse(U_14801,U_14802),U_14805)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14801,U_14802)),hAPP(hAPP(c_Product__Type_OPair(U_14801,U_14802),U_14803),U_14804)),U_14805)) ),
inference(clausify,[status(thm)],[f_3763_2]) ).
fof(f_3764_1,plain,
! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_converse__iff]) ).
fof(f_3764_2,plain,
! [U_14810,U_14809,U_14808,U_14807,U_14806] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14806,U_14807)),hAPP(hAPP(c_Product__Type_OPair(U_14806,U_14807),U_14808),U_14809)),hAPP(c_Relation_Oconverse(U_14807,U_14806),U_14810)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14807,U_14806)),hAPP(hAPP(c_Product__Type_OPair(U_14807,U_14806),U_14809),U_14808)),U_14810)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14807,U_14806)),hAPP(hAPP(c_Product__Type_OPair(U_14807,U_14806),U_14809),U_14808)),U_14810))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14806,U_14807)),hAPP(hAPP(c_Product__Type_OPair(U_14806,U_14807),U_14808),U_14809)),hAPP(c_Relation_Oconverse(U_14807,U_14806),U_14810))) ) ),
inference(variable_rename,[status(thm)],[f_3764_1]) ).
fof(f_3764_3,plain,
( ! [U_14820,U_14818,U_14816,U_14814,U_14812] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14812,U_14814)),hAPP(hAPP(c_Product__Type_OPair(U_14812,U_14814),U_14816),U_14818)),hAPP(c_Relation_Oconverse(U_14814,U_14812),U_14820)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14814,U_14812)),hAPP(hAPP(c_Product__Type_OPair(U_14814,U_14812),U_14818),U_14816)),U_14820)) )
& ! [U_14819,U_14817,U_14815,U_14813,U_14811] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14813,U_14811)),hAPP(hAPP(c_Product__Type_OPair(U_14813,U_14811),U_14817),U_14815)),U_14819))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14811,U_14813)),hAPP(hAPP(c_Product__Type_OPair(U_14811,U_14813),U_14815),U_14817)),hAPP(c_Relation_Oconverse(U_14813,U_14811),U_14819))) ) ),
inference(miniscope,[status(thm)],[f_3764_2]) ).
cnf(f_3764_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14813,U_14811)),hAPP(hAPP(c_Product__Type_OPair(U_14813,U_14811),U_14817),U_14815)),U_14819))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14811,U_14813)),hAPP(hAPP(c_Product__Type_OPair(U_14811,U_14813),U_14815),U_14817)),hAPP(c_Relation_Oconverse(U_14813,U_14811),U_14819))) ),
inference(clausify,[status(thm)],[f_3764_3]) ).
cnf(f_3764_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14812,U_14814)),hAPP(hAPP(c_Product__Type_OPair(U_14812,U_14814),U_14816),U_14818)),hAPP(c_Relation_Oconverse(U_14814,U_14812),U_14820)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14814,U_14812)),hAPP(hAPP(c_Product__Type_OPair(U_14814,U_14812),U_14818),U_14816)),U_14820)) ),
inference(clausify,[status(thm)],[f_3764_3]) ).
fof(f_3765_1,plain,
! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)),
inference(fof_nnf,[status(thm)],[fact_converse__INTER]) ).
fof(f_3765_2,plain,
! [U_14825,U_14824,U_14823,U_14822,U_14821] : hAPP(c_Relation_Oconverse(U_14821,U_14822),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14823,tc_fun(tc_prod(U_14821,U_14822),tc_HOL_Obool)),U_14824),U_14825)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14823,tc_fun(tc_prod(U_14822,U_14821),tc_HOL_Obool)),U_14824),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14821,U_14822),tc_HOL_Obool),tc_fun(tc_prod(U_14822,U_14821),tc_HOL_Obool),U_14823),c_Relation_Oconverse(U_14821,U_14822)),U_14825)),
inference(variable_rename,[status(thm)],[f_3765_1]) ).
cnf(f_3765_3,plain,
hAPP(c_Relation_Oconverse(U_14821,U_14822),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14823,tc_fun(tc_prod(U_14821,U_14822),tc_HOL_Obool)),U_14824),U_14825)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14823,tc_fun(tc_prod(U_14822,U_14821),tc_HOL_Obool)),U_14824),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14821,U_14822),tc_HOL_Obool),tc_fun(tc_prod(U_14822,U_14821),tc_HOL_Obool),U_14823),c_Relation_Oconverse(U_14821,U_14822)),U_14825)),
inference(clausify,[status(thm)],[f_3765_2]) ).
fof(f_3766_1,plain,
! [V_r_2,T_c,T_b] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__converse]) ).
fof(f_3766_2,plain,
! [U_14828,U_14827,U_14826] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14826,U_14827)),hAPP(c_Relation_Oconverse(U_14827,U_14826),U_14828)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14827,U_14826)),U_14828)) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14827,U_14826)),U_14828))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14826,U_14827)),hAPP(c_Relation_Oconverse(U_14827,U_14826),U_14828))) ) ),
inference(variable_rename,[status(thm)],[f_3766_1]) ).
fof(f_3766_3,plain,
( ! [U_14834,U_14832,U_14830] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14830,U_14832)),hAPP(c_Relation_Oconverse(U_14832,U_14830),U_14834)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14832,U_14830)),U_14834)) )
& ! [U_14833,U_14831,U_14829] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14831,U_14829)),U_14833))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14829,U_14831)),hAPP(c_Relation_Oconverse(U_14831,U_14829),U_14833))) ) ),
inference(miniscope,[status(thm)],[f_3766_2]) ).
cnf(f_3766_4,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14831,U_14829)),U_14833))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14829,U_14831)),hAPP(c_Relation_Oconverse(U_14831,U_14829),U_14833))) ),
inference(clausify,[status(thm)],[f_3766_3]) ).
cnf(f_3766_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14830,U_14832)),hAPP(c_Relation_Oconverse(U_14832,U_14830),U_14834)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14832,U_14830)),U_14834)) ),
inference(clausify,[status(thm)],[f_3766_3]) ).
fof(f_3767_1,plain,
! [V_r_2,V_A_2,T_b] :
( ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
| ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) )
& ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
| ~ c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_refl__on__converse]) ).
fof(f_3767_2,plain,
! [U_14837,U_14836,U_14835] :
( ( c_Relation_Orefl__on(U_14835,U_14836,hAPP(c_Relation_Oconverse(U_14835,U_14835),U_14837))
| ~ c_Relation_Orefl__on(U_14835,U_14836,U_14837) )
& ( c_Relation_Orefl__on(U_14835,U_14836,U_14837)
| ~ c_Relation_Orefl__on(U_14835,U_14836,hAPP(c_Relation_Oconverse(U_14835,U_14835),U_14837)) ) ),
inference(variable_rename,[status(thm)],[f_3767_1]) ).
fof(f_3767_3,plain,
( ! [U_14843,U_14841,U_14839] :
( c_Relation_Orefl__on(U_14839,U_14841,hAPP(c_Relation_Oconverse(U_14839,U_14839),U_14843))
| ~ c_Relation_Orefl__on(U_14839,U_14841,U_14843) )
& ! [U_14842,U_14840,U_14838] :
( c_Relation_Orefl__on(U_14838,U_14840,U_14842)
| ~ c_Relation_Orefl__on(U_14838,U_14840,hAPP(c_Relation_Oconverse(U_14838,U_14838),U_14842)) ) ),
inference(miniscope,[status(thm)],[f_3767_2]) ).
cnf(f_3767_4,plain,
( c_Relation_Orefl__on(U_14838,U_14840,U_14842)
| ~ c_Relation_Orefl__on(U_14838,U_14840,hAPP(c_Relation_Oconverse(U_14838,U_14838),U_14842)) ),
inference(clausify,[status(thm)],[f_3767_3]) ).
cnf(f_3767_5,plain,
( c_Relation_Orefl__on(U_14839,U_14841,hAPP(c_Relation_Oconverse(U_14839,U_14839),U_14843))
| ~ c_Relation_Orefl__on(U_14839,U_14841,U_14843) ),
inference(clausify,[status(thm)],[f_3767_3]) ).
fof(f_3768_1,plain,
! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)),
inference(fof_nnf,[status(thm)],[fact_converse__Int]) ).
fof(f_3768_2,plain,
! [U_14847,U_14846,U_14845,U_14844] : hAPP(c_Relation_Oconverse(U_14844,U_14845),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14844,U_14845),tc_HOL_Obool)),U_14846),U_14847)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14845,U_14844),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14844,U_14845),U_14846)),hAPP(c_Relation_Oconverse(U_14844,U_14845),U_14847)),
inference(variable_rename,[status(thm)],[f_3768_1]) ).
cnf(f_3768_3,plain,
hAPP(c_Relation_Oconverse(U_14844,U_14845),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14844,U_14845),tc_HOL_Obool)),U_14846),U_14847)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14845,U_14844),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_14844,U_14845),U_14846)),hAPP(c_Relation_Oconverse(U_14844,U_14845),U_14847)),
inference(clausify,[status(thm)],[f_3768_2]) ).
fof(f_3769_1,plain,
! [V_f_2,V_R_2,T_c,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_c),V_R_2)),V_f_2),
inference(fof_nnf,[status(thm)],[fact_converse__inv__image]) ).
fof(f_3769_2,plain,
! [U_14851,U_14850,U_14849,U_14848] : hAPP(c_Relation_Oconverse(U_14848,U_14848),hAPP(hAPP(c_Relation_Oinv__image(U_14849,U_14848),U_14850),U_14851)) = hAPP(hAPP(c_Relation_Oinv__image(U_14849,U_14848),hAPP(c_Relation_Oconverse(U_14849,U_14849),U_14850)),U_14851),
inference(variable_rename,[status(thm)],[f_3769_1]) ).
cnf(f_3769_3,plain,
hAPP(c_Relation_Oconverse(U_14848,U_14848),hAPP(hAPP(c_Relation_Oinv__image(U_14849,U_14848),U_14850),U_14851)) = hAPP(hAPP(c_Relation_Oinv__image(U_14849,U_14848),hAPP(c_Relation_Oconverse(U_14849,U_14849),U_14850)),U_14851),
inference(clausify,[status(thm)],[f_3769_2]) ).
fof(f_3770_1,plain,
! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = V_r_2,
inference(fof_nnf,[status(thm)],[fact_converse__converse]) ).
fof(f_3770_2,plain,
! [U_14854,U_14853,U_14852] : hAPP(c_Relation_Oconverse(U_14852,U_14853),hAPP(c_Relation_Oconverse(U_14853,U_14852),U_14854)) = U_14854,
inference(variable_rename,[status(thm)],[f_3770_1]) ).
cnf(f_3770_3,plain,
hAPP(c_Relation_Oconverse(U_14852,U_14853),hAPP(c_Relation_Oconverse(U_14853,U_14852),U_14854)) = U_14854,
inference(clausify,[status(thm)],[f_3770_2]) ).
fof(f_3771_1,plain,
! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_OField(T_b),V_r_2),
inference(fof_nnf,[status(thm)],[fact_Field__converse]) ).
fof(f_3771_2,plain,
! [U_14856,U_14855] : hAPP(c_Relation_OField(U_14855),hAPP(c_Relation_Oconverse(U_14855,U_14855),U_14856)) = hAPP(c_Relation_OField(U_14855),U_14856),
inference(variable_rename,[status(thm)],[f_3771_1]) ).
cnf(f_3771_3,plain,
hAPP(c_Relation_OField(U_14855),hAPP(c_Relation_Oconverse(U_14855,U_14855),U_14856)) = hAPP(c_Relation_OField(U_14855),U_14856),
inference(clausify,[status(thm)],[f_3771_2]) ).
fof(f_3772_1,plain,
! [V_A_2,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = c_Relation_OId__on(T_b,V_A_2),
inference(fof_nnf,[status(thm)],[fact_converse__Id__on]) ).
fof(f_3772_2,plain,
! [U_14858,U_14857] : hAPP(c_Relation_Oconverse(U_14857,U_14857),c_Relation_OId__on(U_14857,U_14858)) = c_Relation_OId__on(U_14857,U_14858),
inference(variable_rename,[status(thm)],[f_3772_1]) ).
cnf(f_3772_3,plain,
hAPP(c_Relation_Oconverse(U_14857,U_14857),c_Relation_OId__on(U_14857,U_14858)) = c_Relation_OId__on(U_14857,U_14858),
inference(clausify,[status(thm)],[f_3772_2]) ).
fof(f_3773_1,plain,
! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)),
inference(fof_nnf,[status(thm)],[fact_converse__UNION]) ).
fof(f_3773_2,plain,
! [U_14863,U_14862,U_14861,U_14860,U_14859] : hAPP(c_Relation_Oconverse(U_14859,U_14860),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14861,tc_fun(tc_prod(U_14859,U_14860),tc_HOL_Obool)),U_14862),U_14863)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14861,tc_fun(tc_prod(U_14860,U_14859),tc_HOL_Obool)),U_14862),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14859,U_14860),tc_HOL_Obool),tc_fun(tc_prod(U_14860,U_14859),tc_HOL_Obool),U_14861),c_Relation_Oconverse(U_14859,U_14860)),U_14863)),
inference(variable_rename,[status(thm)],[f_3773_1]) ).
cnf(f_3773_3,plain,
hAPP(c_Relation_Oconverse(U_14859,U_14860),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14861,tc_fun(tc_prod(U_14859,U_14860),tc_HOL_Obool)),U_14862),U_14863)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14861,tc_fun(tc_prod(U_14860,U_14859),tc_HOL_Obool)),U_14862),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14859,U_14860),tc_HOL_Obool),tc_fun(tc_prod(U_14860,U_14859),tc_HOL_Obool),U_14861),c_Relation_Oconverse(U_14859,U_14860)),U_14863)),
inference(clausify,[status(thm)],[f_3773_2]) ).
fof(f_3774_1,plain,
! [V_r_2,T_b] :
( ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
| ~ c_Wellfounded_Oacyclic(T_b,V_r_2) )
& ( c_Wellfounded_Oacyclic(T_b,V_r_2)
| ~ c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_acyclic__converse]) ).
fof(f_3774_2,plain,
! [U_14865,U_14864] :
( ( c_Wellfounded_Oacyclic(U_14864,hAPP(c_Relation_Oconverse(U_14864,U_14864),U_14865))
| ~ c_Wellfounded_Oacyclic(U_14864,U_14865) )
& ( c_Wellfounded_Oacyclic(U_14864,U_14865)
| ~ c_Wellfounded_Oacyclic(U_14864,hAPP(c_Relation_Oconverse(U_14864,U_14864),U_14865)) ) ),
inference(variable_rename,[status(thm)],[f_3774_1]) ).
fof(f_3774_3,plain,
( ! [U_14869,U_14867] :
( c_Wellfounded_Oacyclic(U_14867,hAPP(c_Relation_Oconverse(U_14867,U_14867),U_14869))
| ~ c_Wellfounded_Oacyclic(U_14867,U_14869) )
& ! [U_14868,U_14866] :
( c_Wellfounded_Oacyclic(U_14866,U_14868)
| ~ c_Wellfounded_Oacyclic(U_14866,hAPP(c_Relation_Oconverse(U_14866,U_14866),U_14868)) ) ),
inference(miniscope,[status(thm)],[f_3774_2]) ).
cnf(f_3774_4,plain,
( c_Wellfounded_Oacyclic(U_14866,U_14868)
| ~ c_Wellfounded_Oacyclic(U_14866,hAPP(c_Relation_Oconverse(U_14866,U_14866),U_14868)) ),
inference(clausify,[status(thm)],[f_3774_3]) ).
cnf(f_3774_5,plain,
( c_Wellfounded_Oacyclic(U_14867,hAPP(c_Relation_Oconverse(U_14867,U_14867),U_14869))
| ~ c_Wellfounded_Oacyclic(U_14867,U_14869) ),
inference(clausify,[status(thm)],[f_3774_3]) ).
fof(f_3775_1,plain,
! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),
inference(fof_nnf,[status(thm)],[fact_trancl__converse]) ).
fof(f_3775_2,plain,
! [U_14871,U_14870] : c_Transitive__Closure_Otrancl(U_14870,hAPP(c_Relation_Oconverse(U_14870,U_14870),U_14871)) = hAPP(c_Relation_Oconverse(U_14870,U_14870),c_Transitive__Closure_Otrancl(U_14870,U_14871)),
inference(variable_rename,[status(thm)],[f_3775_1]) ).
cnf(f_3775_3,plain,
c_Transitive__Closure_Otrancl(U_14870,hAPP(c_Relation_Oconverse(U_14870,U_14870),U_14871)) = hAPP(c_Relation_Oconverse(U_14870,U_14870),c_Transitive__Closure_Otrancl(U_14870,U_14871)),
inference(clausify,[status(thm)],[f_3775_2]) ).
fof(f_3776_1,plain,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
| ~ c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_wf__converse__trancl]) ).
fof(f_3776_2,plain,
! [U_14873,U_14872] :
( c_Wellfounded_Owf(U_14872,hAPP(c_Relation_Oconverse(U_14872,U_14872),c_Transitive__Closure_Otrancl(U_14872,U_14873)))
| ~ c_Wellfounded_Owf(U_14872,hAPP(c_Relation_Oconverse(U_14872,U_14872),U_14873)) ),
inference(variable_rename,[status(thm)],[f_3776_1]) ).
cnf(f_3776_3,plain,
( c_Wellfounded_Owf(U_14872,hAPP(c_Relation_Oconverse(U_14872,U_14872),c_Transitive__Closure_Otrancl(U_14872,U_14873)))
| ~ c_Wellfounded_Owf(U_14872,hAPP(c_Relation_Oconverse(U_14872,U_14872),U_14873)) ),
inference(clausify,[status(thm)],[f_3776_2]) ).
fof(f_3777_1,plain,
! [V_r_2,V_A_2,T_b] :
( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2
| ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_equiv__comp__eq]) ).
fof(f_3777_2,plain,
! [U_14876,U_14875,U_14874] :
( hAPP(hAPP(c_Relation_Orel__comp(U_14874,U_14874,U_14874),hAPP(c_Relation_Oconverse(U_14874,U_14874),U_14876)),U_14876) = U_14876
| ~ c_Equiv__Relations_Oequiv(U_14874,U_14875,U_14876) ),
inference(variable_rename,[status(thm)],[f_3777_1]) ).
cnf(f_3777_3,plain,
( hAPP(hAPP(c_Relation_Orel__comp(U_14874,U_14874,U_14874),hAPP(c_Relation_Oconverse(U_14874,U_14874),U_14876)),U_14876) = U_14876
| ~ c_Equiv__Relations_Oequiv(U_14874,U_14875,U_14876) ),
inference(clausify,[status(thm)],[f_3777_2]) ).
fof(f_3778_1,plain,
! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),
inference(fof_nnf,[status(thm)],[fact_Range__def]) ).
fof(f_3778_2,plain,
! [U_14879,U_14878,U_14877] : hAPP(c_Relation_ORange(U_14877,U_14878),U_14879) = hAPP(c_Relation_ODomain(U_14878,U_14877),hAPP(c_Relation_Oconverse(U_14877,U_14878),U_14879)),
inference(variable_rename,[status(thm)],[f_3778_1]) ).
cnf(f_3778_3,plain,
hAPP(c_Relation_ORange(U_14877,U_14878),U_14879) = hAPP(c_Relation_ODomain(U_14878,U_14877),hAPP(c_Relation_Oconverse(U_14877,U_14878),U_14879)),
inference(clausify,[status(thm)],[f_3778_2]) ).
fof(f_3779_1,plain,
! [V_r_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) = hAPP(c_Relation_ORange(T_c,T_b),V_r_2),
inference(fof_nnf,[status(thm)],[fact_Domain__converse]) ).
fof(f_3779_2,plain,
! [U_14882,U_14881,U_14880] : hAPP(c_Relation_ODomain(U_14880,U_14881),hAPP(c_Relation_Oconverse(U_14881,U_14880),U_14882)) = hAPP(c_Relation_ORange(U_14881,U_14880),U_14882),
inference(variable_rename,[status(thm)],[f_3779_1]) ).
cnf(f_3779_3,plain,
hAPP(c_Relation_ODomain(U_14880,U_14881),hAPP(c_Relation_Oconverse(U_14881,U_14880),U_14882)) = hAPP(c_Relation_ORange(U_14881,U_14880),U_14882),
inference(clausify,[status(thm)],[f_3779_2]) ).
fof(f_3780_1,plain,
! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_c),V_r_2),
inference(fof_nnf,[status(thm)],[fact_Range__converse]) ).
fof(f_3780_2,plain,
! [U_14885,U_14884,U_14883] : hAPP(c_Relation_ORange(U_14883,U_14884),hAPP(c_Relation_Oconverse(U_14884,U_14883),U_14885)) = hAPP(c_Relation_ODomain(U_14884,U_14883),U_14885),
inference(variable_rename,[status(thm)],[f_3780_1]) ).
cnf(f_3780_3,plain,
hAPP(c_Relation_ORange(U_14883,U_14884),hAPP(c_Relation_Oconverse(U_14884,U_14883),U_14885)) = hAPP(c_Relation_ODomain(U_14884,U_14883),U_14885),
inference(clausify,[status(thm)],[f_3780_2]) ).
fof(f_3781_1,plain,
! [V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__converseD]) ).
fof(f_3781_2,plain,
! [U_14889,U_14888,U_14887,U_14886] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14886,U_14886)),hAPP(hAPP(c_Product__Type_OPair(U_14886,U_14886),U_14888),U_14887)),c_Transitive__Closure_Ortrancl(U_14886,U_14889)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14886,U_14886)),hAPP(hAPP(c_Product__Type_OPair(U_14886,U_14886),U_14887),U_14888)),c_Transitive__Closure_Ortrancl(U_14886,hAPP(c_Relation_Oconverse(U_14886,U_14886),U_14889)))) ),
inference(variable_rename,[status(thm)],[f_3781_1]) ).
cnf(f_3781_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14886,U_14886)),hAPP(hAPP(c_Product__Type_OPair(U_14886,U_14886),U_14888),U_14887)),c_Transitive__Closure_Ortrancl(U_14886,U_14889)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14886,U_14886)),hAPP(hAPP(c_Product__Type_OPair(U_14886,U_14886),U_14887),U_14888)),c_Transitive__Closure_Ortrancl(U_14886,hAPP(c_Relation_Oconverse(U_14886,U_14886),U_14889)))) ),
inference(clausify,[status(thm)],[f_3781_2]) ).
fof(f_3782_1,plain,
! [V_r_2,V_x_2,V_y_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__converseI]) ).
fof(f_3782_2,plain,
! [U_14893,U_14892,U_14891,U_14890] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14890,U_14890)),hAPP(hAPP(c_Product__Type_OPair(U_14890,U_14890),U_14892),U_14891)),c_Transitive__Closure_Ortrancl(U_14890,hAPP(c_Relation_Oconverse(U_14890,U_14890),U_14893))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14890,U_14890)),hAPP(hAPP(c_Product__Type_OPair(U_14890,U_14890),U_14891),U_14892)),c_Transitive__Closure_Ortrancl(U_14890,U_14893))) ),
inference(variable_rename,[status(thm)],[f_3782_1]) ).
cnf(f_3782_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14890,U_14890)),hAPP(hAPP(c_Product__Type_OPair(U_14890,U_14890),U_14892),U_14891)),c_Transitive__Closure_Ortrancl(U_14890,hAPP(c_Relation_Oconverse(U_14890,U_14890),U_14893))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14890,U_14890)),hAPP(hAPP(c_Product__Type_OPair(U_14890,U_14890),U_14891),U_14892)),c_Transitive__Closure_Ortrancl(U_14890,U_14893))) ),
inference(clausify,[status(thm)],[f_3782_2]) ).
fof(f_3783_1,plain,
! [V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ),
inference(fof_nnf,[status(thm)],[fact_trancl__converseD]) ).
fof(f_3783_2,plain,
! [U_14897,U_14896,U_14895,U_14894] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14894,U_14894)),hAPP(hAPP(c_Product__Type_OPair(U_14894,U_14894),U_14895),U_14896)),hAPP(c_Relation_Oconverse(U_14894,U_14894),c_Transitive__Closure_Otrancl(U_14894,U_14897))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14894,U_14894)),hAPP(hAPP(c_Product__Type_OPair(U_14894,U_14894),U_14895),U_14896)),c_Transitive__Closure_Otrancl(U_14894,hAPP(c_Relation_Oconverse(U_14894,U_14894),U_14897)))) ),
inference(variable_rename,[status(thm)],[f_3783_1]) ).
cnf(f_3783_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14894,U_14894)),hAPP(hAPP(c_Product__Type_OPair(U_14894,U_14894),U_14895),U_14896)),hAPP(c_Relation_Oconverse(U_14894,U_14894),c_Transitive__Closure_Otrancl(U_14894,U_14897))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14894,U_14894)),hAPP(hAPP(c_Product__Type_OPair(U_14894,U_14894),U_14895),U_14896)),c_Transitive__Closure_Otrancl(U_14894,hAPP(c_Relation_Oconverse(U_14894,U_14894),U_14897)))) ),
inference(clausify,[status(thm)],[f_3783_2]) ).
fof(f_3784_1,plain,
! [V_r_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) ),
inference(fof_nnf,[status(thm)],[fact_trancl__converseI]) ).
fof(f_3784_2,plain,
! [U_14901,U_14900,U_14899,U_14898] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14898,U_14898)),hAPP(hAPP(c_Product__Type_OPair(U_14898,U_14898),U_14899),U_14900)),c_Transitive__Closure_Otrancl(U_14898,hAPP(c_Relation_Oconverse(U_14898,U_14898),U_14901))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14898,U_14898)),hAPP(hAPP(c_Product__Type_OPair(U_14898,U_14898),U_14899),U_14900)),hAPP(c_Relation_Oconverse(U_14898,U_14898),c_Transitive__Closure_Otrancl(U_14898,U_14901)))) ),
inference(variable_rename,[status(thm)],[f_3784_1]) ).
cnf(f_3784_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14898,U_14898)),hAPP(hAPP(c_Product__Type_OPair(U_14898,U_14898),U_14899),U_14900)),c_Transitive__Closure_Otrancl(U_14898,hAPP(c_Relation_Oconverse(U_14898,U_14898),U_14901))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14898,U_14898)),hAPP(hAPP(c_Product__Type_OPair(U_14898,U_14898),U_14899),U_14900)),hAPP(c_Relation_Oconverse(U_14898,U_14898),c_Transitive__Closure_Otrancl(U_14898,U_14901)))) ),
inference(clausify,[status(thm)],[f_3784_2]) ).
fof(f_3785_1,plain,
! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)),V_B_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Image__subset__eq]) ).
fof(f_3785_2,plain,
! [U_14906,U_14905,U_14904,U_14903,U_14902] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14902,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14903,U_14902,U_14904),U_14905)),U_14906))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14903,tc_HOL_Obool)),U_14905),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14903,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14902,U_14903,hAPP(c_Relation_Oconverse(U_14903,U_14902),U_14904)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14902,tc_HOL_Obool)),U_14906))))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14903,tc_HOL_Obool)),U_14905),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14903,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14902,U_14903,hAPP(c_Relation_Oconverse(U_14903,U_14902),U_14904)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14902,tc_HOL_Obool)),U_14906)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14902,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14903,U_14902,U_14904),U_14905)),U_14906)) ) ),
inference(variable_rename,[status(thm)],[f_3785_1]) ).
fof(f_3785_3,plain,
( ! [U_14916,U_14914,U_14912,U_14910,U_14908] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14908,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14910,U_14908,U_14912),U_14914)),U_14916))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14910,tc_HOL_Obool)),U_14914),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14910,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14908,U_14910,hAPP(c_Relation_Oconverse(U_14910,U_14908),U_14912)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14908,tc_HOL_Obool)),U_14916))))) )
& ! [U_14915,U_14913,U_14911,U_14909,U_14907] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14909,tc_HOL_Obool)),U_14913),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14909,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14907,U_14909,hAPP(c_Relation_Oconverse(U_14909,U_14907),U_14911)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14907,tc_HOL_Obool)),U_14915)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14907,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14909,U_14907,U_14911),U_14913)),U_14915)) ) ),
inference(miniscope,[status(thm)],[f_3785_2]) ).
cnf(f_3785_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14909,tc_HOL_Obool)),U_14913),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14909,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14907,U_14909,hAPP(c_Relation_Oconverse(U_14909,U_14907),U_14911)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14907,tc_HOL_Obool)),U_14915)))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14907,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14909,U_14907,U_14911),U_14913)),U_14915)) ),
inference(clausify,[status(thm)],[f_3785_3]) ).
cnf(f_3785_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14908,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14910,U_14908,U_14912),U_14914)),U_14916))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14910,tc_HOL_Obool)),U_14914),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14910,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14908,U_14910,hAPP(c_Relation_Oconverse(U_14910,U_14908),U_14912)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14908,tc_HOL_Obool)),U_14916))))) ),
inference(clausify,[status(thm)],[f_3785_3]) ).
fof(f_3786_1,plain,
! [V_r_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2)))
| ~ c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_refl__on__comp__subset]) ).
fof(f_3786_2,plain,
! [U_14919,U_14918,U_14917] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14917,U_14917),tc_HOL_Obool)),U_14919),hAPP(hAPP(c_Relation_Orel__comp(U_14917,U_14917,U_14917),hAPP(c_Relation_Oconverse(U_14917,U_14917),U_14919)),U_14919)))
| ~ c_Relation_Orefl__on(U_14917,U_14918,U_14919) ),
inference(variable_rename,[status(thm)],[f_3786_1]) ).
cnf(f_3786_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14917,U_14917),tc_HOL_Obool)),U_14919),hAPP(hAPP(c_Relation_Orel__comp(U_14917,U_14917,U_14917),hAPP(c_Relation_Oconverse(U_14917,U_14917),U_14919)),U_14919)))
| ~ c_Relation_Orefl__on(U_14917,U_14918,U_14919) ),
inference(clausify,[status(thm)],[f_3786_2]) ).
fof(f_3787_1,plain,
! [V_A_2,V_r_2,T_b] :
( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
| hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) != V_A_2
| hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) != V_r_2 ),
inference(fof_nnf,[status(thm)],[fact_comp__equivI]) ).
fof(f_3787_2,plain,
! [U_14922,U_14921,U_14920] :
( c_Equiv__Relations_Oequiv(U_14920,U_14922,U_14921)
| hAPP(c_Relation_ODomain(U_14920,U_14920),U_14921) != U_14922
| hAPP(hAPP(c_Relation_Orel__comp(U_14920,U_14920,U_14920),hAPP(c_Relation_Oconverse(U_14920,U_14920),U_14921)),U_14921) != U_14921 ),
inference(variable_rename,[status(thm)],[f_3787_1]) ).
cnf(f_3787_3,plain,
( c_Equiv__Relations_Oequiv(U_14920,U_14922,U_14921)
| hAPP(c_Relation_ODomain(U_14920,U_14920),U_14921) != U_14922
| hAPP(hAPP(c_Relation_Orel__comp(U_14920,U_14920,U_14920),hAPP(c_Relation_Oconverse(U_14920,U_14920),U_14921)),U_14921) != U_14921 ),
inference(clausify,[status(thm)],[f_3787_2]) ).
fof(f_3788_1,plain,
! [V_r_2,T_b] :
( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
| ~ c_Wellfounded_Oacyclic(T_b,V_r_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf__converse]) ).
fof(f_3788_2,plain,
! [U_14924,U_14923] :
( c_Wellfounded_Owf(U_14923,hAPP(c_Relation_Oconverse(U_14923,U_14923),U_14924))
| ~ c_Wellfounded_Oacyclic(U_14923,U_14924)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14923,U_14923)),U_14924)) ),
inference(variable_rename,[status(thm)],[f_3788_1]) ).
cnf(f_3788_3,plain,
( c_Wellfounded_Owf(U_14923,hAPP(c_Relation_Oconverse(U_14923,U_14923),U_14924))
| ~ c_Wellfounded_Oacyclic(U_14923,U_14924)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14923,U_14923)),U_14924)) ),
inference(clausify,[status(thm)],[f_3788_2]) ).
fof(f_3789_1,plain,
! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_b)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_c,T_b)))),hAPP(c_COMBC(T_c,T_b,tc_prod(T_c,T_b)),c_Product__Type_OPair(T_c,T_b))))),V_r_2))),
inference(fof_nnf,[status(thm)],[fact_converse__def]) ).
fof(f_3789_2,plain,
! [U_14927,U_14926,U_14925] : hAPP(c_Relation_Oconverse(U_14925,U_14926),U_14927) = hAPP(c_Set_OCollect(tc_prod(U_14926,U_14925)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14926,U_14925,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14926,tc_fun(tc_prod(U_14925,U_14926),tc_HOL_Obool),tc_fun(U_14925,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14925,tc_fun(tc_fun(tc_prod(U_14925,U_14926),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14925,U_14926),tc_HOL_Obool),tc_fun(U_14925,tc_HOL_Obool)),U_14926),c_COMBC(U_14925,tc_fun(tc_prod(U_14925,U_14926),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14925,tc_prod(U_14925,U_14926)),tc_fun(U_14925,tc_fun(tc_fun(tc_prod(U_14925,U_14926),tc_HOL_Obool),tc_HOL_Obool)),U_14926),hAPP(c_COMBB(tc_prod(U_14925,U_14926),tc_fun(tc_fun(tc_prod(U_14925,U_14926),tc_HOL_Obool),tc_HOL_Obool),U_14925),c_member(tc_prod(U_14925,U_14926)))),hAPP(c_COMBC(U_14925,U_14926,tc_prod(U_14925,U_14926)),c_Product__Type_OPair(U_14925,U_14926))))),U_14927))),
inference(variable_rename,[status(thm)],[f_3789_1]) ).
cnf(f_3789_3,plain,
hAPP(c_Relation_Oconverse(U_14925,U_14926),U_14927) = hAPP(c_Set_OCollect(tc_prod(U_14926,U_14925)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14926,U_14925,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14926,tc_fun(tc_prod(U_14925,U_14926),tc_HOL_Obool),tc_fun(U_14925,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14925,tc_fun(tc_fun(tc_prod(U_14925,U_14926),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14925,U_14926),tc_HOL_Obool),tc_fun(U_14925,tc_HOL_Obool)),U_14926),c_COMBC(U_14925,tc_fun(tc_prod(U_14925,U_14926),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14925,tc_prod(U_14925,U_14926)),tc_fun(U_14925,tc_fun(tc_fun(tc_prod(U_14925,U_14926),tc_HOL_Obool),tc_HOL_Obool)),U_14926),hAPP(c_COMBB(tc_prod(U_14925,U_14926),tc_fun(tc_fun(tc_prod(U_14925,U_14926),tc_HOL_Obool),tc_HOL_Obool),U_14925),c_member(tc_prod(U_14925,U_14926)))),hAPP(c_COMBC(U_14925,U_14926,tc_prod(U_14925,U_14926)),c_Product__Type_OPair(U_14925,U_14926))))),U_14927))),
inference(clausify,[status(thm)],[f_3789_2]) ).
fof(f_3790_1,plain,
! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
( hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
| ~ c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) ),
inference(fof_nnf,[status(thm)],[fact_Image__INT__eq]) ).
fof(f_3790_2,plain,
! [U_14933,U_14932,U_14931,U_14930,U_14929,U_14928] :
( hAPP(c_Relation_OImage(U_14929,U_14928,U_14930),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14932,tc_fun(U_14929,tc_HOL_Obool)),U_14931),U_14933)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14932,tc_fun(U_14928,tc_HOL_Obool)),U_14931),hAPP(hAPP(c_COMBB(tc_fun(U_14929,tc_HOL_Obool),tc_fun(U_14928,tc_HOL_Obool),U_14932),c_Relation_OImage(U_14929,U_14928,U_14930)),U_14933))
| U_14931 = c_Orderings_Obot__class_Obot(tc_fun(U_14932,tc_HOL_Obool))
| ~ c_Relation_Osingle__valued(U_14928,U_14929,hAPP(c_Relation_Oconverse(U_14929,U_14928),U_14930)) ),
inference(variable_rename,[status(thm)],[f_3790_1]) ).
cnf(f_3790_3,plain,
( hAPP(c_Relation_OImage(U_14929,U_14928,U_14930),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14932,tc_fun(U_14929,tc_HOL_Obool)),U_14931),U_14933)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_14932,tc_fun(U_14928,tc_HOL_Obool)),U_14931),hAPP(hAPP(c_COMBB(tc_fun(U_14929,tc_HOL_Obool),tc_fun(U_14928,tc_HOL_Obool),U_14932),c_Relation_OImage(U_14929,U_14928,U_14930)),U_14933))
| U_14931 = c_Orderings_Obot__class_Obot(tc_fun(U_14932,tc_HOL_Obool))
| ~ c_Relation_Osingle__valued(U_14928,U_14929,hAPP(c_Relation_Oconverse(U_14929,U_14928),U_14930)) ),
inference(clausify,[status(thm)],[f_3790_2]) ).
fof(f_3791_1,plain,
! [V_r_2,V_A_2,T_b] :
( ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
| ~ c_Relation_Ototal__on(T_b,V_A_2,V_r_2) )
& ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
| ~ c_Relation_Ototal__on(T_b,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ) ),
inference(fof_nnf,[status(thm)],[fact_total__on__diff__Id]) ).
fof(f_3791_2,plain,
! [U_14936,U_14935,U_14934] :
( ( c_Relation_Ototal__on(U_14934,U_14935,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14934,U_14934),tc_HOL_Obool)),U_14936),c_Relation_OId(U_14934)))
| ~ c_Relation_Ototal__on(U_14934,U_14935,U_14936) )
& ( c_Relation_Ototal__on(U_14934,U_14935,U_14936)
| ~ c_Relation_Ototal__on(U_14934,U_14935,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14934,U_14934),tc_HOL_Obool)),U_14936),c_Relation_OId(U_14934))) ) ),
inference(variable_rename,[status(thm)],[f_3791_1]) ).
fof(f_3791_3,plain,
( ! [U_14942,U_14940,U_14938] :
( c_Relation_Ototal__on(U_14938,U_14940,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14938,U_14938),tc_HOL_Obool)),U_14942),c_Relation_OId(U_14938)))
| ~ c_Relation_Ototal__on(U_14938,U_14940,U_14942) )
& ! [U_14941,U_14939,U_14937] :
( c_Relation_Ototal__on(U_14937,U_14939,U_14941)
| ~ c_Relation_Ototal__on(U_14937,U_14939,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14937,U_14937),tc_HOL_Obool)),U_14941),c_Relation_OId(U_14937))) ) ),
inference(miniscope,[status(thm)],[f_3791_2]) ).
cnf(f_3791_4,plain,
( c_Relation_Ototal__on(U_14937,U_14939,U_14941)
| ~ c_Relation_Ototal__on(U_14937,U_14939,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14937,U_14937),tc_HOL_Obool)),U_14941),c_Relation_OId(U_14937))) ),
inference(clausify,[status(thm)],[f_3791_3]) ).
cnf(f_3791_5,plain,
( c_Relation_Ototal__on(U_14938,U_14940,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14938,U_14938),tc_HOL_Obool)),U_14942),c_Relation_OId(U_14938)))
| ~ c_Relation_Ototal__on(U_14938,U_14940,U_14942) ),
inference(clausify,[status(thm)],[f_3791_3]) ).
fof(f_3792_1,plain,
! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)),
inference(fof_nnf,[status(thm)],[fact_single__valued__Id]) ).
fof(f_3792_2,plain,
! [U_14943] : c_Relation_Osingle__valued(U_14943,U_14943,c_Relation_OId(U_14943)),
inference(variable_rename,[status(thm)],[f_3792_1]) ).
cnf(f_3792_3,plain,
c_Relation_Osingle__valued(U_14943,U_14943,c_Relation_OId(U_14943)),
inference(clausify,[status(thm)],[f_3792_2]) ).
fof(f_3793_1,plain,
! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),
inference(fof_nnf,[status(thm)],[fact_single__valued__Id__on]) ).
fof(f_3793_2,plain,
! [U_14945,U_14944] : c_Relation_Osingle__valued(U_14944,U_14944,c_Relation_OId__on(U_14944,U_14945)),
inference(variable_rename,[status(thm)],[f_3793_1]) ).
cnf(f_3793_3,plain,
c_Relation_Osingle__valued(U_14944,U_14944,c_Relation_OId__on(U_14944,U_14945)),
inference(clausify,[status(thm)],[f_3793_2]) ).
fof(f_3794_1,plain,
! [V_s_2,V_r_2,T_c,T_b] :
( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
| ~ c_Relation_Osingle__valued(T_b,T_c,V_s_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2)) ),
inference(fof_nnf,[status(thm)],[fact_single__valued__subset]) ).
fof(f_3794_2,plain,
! [U_14949,U_14948,U_14947,U_14946] :
( c_Relation_Osingle__valued(U_14946,U_14947,U_14948)
| ~ c_Relation_Osingle__valued(U_14946,U_14947,U_14949)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14946,U_14947),tc_HOL_Obool)),U_14948),U_14949)) ),
inference(variable_rename,[status(thm)],[f_3794_1]) ).
cnf(f_3794_3,plain,
( c_Relation_Osingle__valued(U_14946,U_14947,U_14948)
| ~ c_Relation_Osingle__valued(U_14946,U_14947,U_14949)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14946,U_14947),tc_HOL_Obool)),U_14948),U_14949)) ),
inference(clausify,[status(thm)],[f_3794_2]) ).
fof(f_3795_1,plain,
! [V_s_2,T_d,V_r_2,T_c,T_b] :
( c_Relation_Osingle__valued(T_b,T_d,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))
| ~ c_Relation_Osingle__valued(T_c,T_d,V_s_2)
| ~ c_Relation_Osingle__valued(T_b,T_c,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_single__valued__rel__comp]) ).
fof(f_3795_2,plain,
! [U_14954,U_14953,U_14952,U_14951,U_14950] :
( c_Relation_Osingle__valued(U_14950,U_14953,hAPP(hAPP(c_Relation_Orel__comp(U_14950,U_14951,U_14953),U_14952),U_14954))
| ~ c_Relation_Osingle__valued(U_14951,U_14953,U_14954)
| ~ c_Relation_Osingle__valued(U_14950,U_14951,U_14952) ),
inference(variable_rename,[status(thm)],[f_3795_1]) ).
cnf(f_3795_3,plain,
( c_Relation_Osingle__valued(U_14950,U_14953,hAPP(hAPP(c_Relation_Orel__comp(U_14950,U_14951,U_14953),U_14952),U_14954))
| ~ c_Relation_Osingle__valued(U_14951,U_14953,U_14954)
| ~ c_Relation_Osingle__valued(U_14950,U_14951,U_14952) ),
inference(clausify,[status(thm)],[f_3795_2]) ).
fof(f_3796_1,plain,
! [V_r_2,T_b] : c_Relation_Ototal__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_r_2),
inference(fof_nnf,[status(thm)],[fact_total__on__empty]) ).
fof(f_3796_2,plain,
! [U_14956,U_14955] : c_Relation_Ototal__on(U_14955,c_Orderings_Obot__class_Obot(tc_fun(U_14955,tc_HOL_Obool)),U_14956),
inference(variable_rename,[status(thm)],[f_3796_1]) ).
cnf(f_3796_3,plain,
c_Relation_Ototal__on(U_14955,c_Orderings_Obot__class_Obot(tc_fun(U_14955,tc_HOL_Obool)),U_14956),
inference(clausify,[status(thm)],[f_3796_2]) ).
fof(f_3797_1,plain,
! [V_r_2,V_A_2,T_b] :
( ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
| ~ c_Relation_Ototal__on(T_b,V_A_2,V_r_2) )
& ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
| ~ c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_total__on__converse]) ).
fof(f_3797_2,plain,
! [U_14959,U_14958,U_14957] :
( ( c_Relation_Ototal__on(U_14957,U_14958,hAPP(c_Relation_Oconverse(U_14957,U_14957),U_14959))
| ~ c_Relation_Ototal__on(U_14957,U_14958,U_14959) )
& ( c_Relation_Ototal__on(U_14957,U_14958,U_14959)
| ~ c_Relation_Ototal__on(U_14957,U_14958,hAPP(c_Relation_Oconverse(U_14957,U_14957),U_14959)) ) ),
inference(variable_rename,[status(thm)],[f_3797_1]) ).
fof(f_3797_3,plain,
( ! [U_14965,U_14963,U_14961] :
( c_Relation_Ototal__on(U_14961,U_14963,hAPP(c_Relation_Oconverse(U_14961,U_14961),U_14965))
| ~ c_Relation_Ototal__on(U_14961,U_14963,U_14965) )
& ! [U_14964,U_14962,U_14960] :
( c_Relation_Ototal__on(U_14960,U_14962,U_14964)
| ~ c_Relation_Ototal__on(U_14960,U_14962,hAPP(c_Relation_Oconverse(U_14960,U_14960),U_14964)) ) ),
inference(miniscope,[status(thm)],[f_3797_2]) ).
cnf(f_3797_4,plain,
( c_Relation_Ototal__on(U_14960,U_14962,U_14964)
| ~ c_Relation_Ototal__on(U_14960,U_14962,hAPP(c_Relation_Oconverse(U_14960,U_14960),U_14964)) ),
inference(clausify,[status(thm)],[f_3797_3]) ).
cnf(f_3797_5,plain,
( c_Relation_Ototal__on(U_14961,U_14963,hAPP(c_Relation_Oconverse(U_14961,U_14961),U_14965))
| ~ c_Relation_Ototal__on(U_14961,U_14963,U_14965) ),
inference(clausify,[status(thm)],[f_3797_3]) ).
fof(f_3798_1,plain,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
( V_y_2 = V_z_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_z_2)),V_r_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),V_r_2))
| ~ c_Relation_Osingle__valued(T_b,T_c,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_single__valuedD]) ).
fof(f_3798_2,plain,
! [U_14971,U_14970,U_14969,U_14968,U_14967,U_14966] :
( U_14970 = U_14971
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14966,U_14967)),hAPP(hAPP(c_Product__Type_OPair(U_14966,U_14967),U_14969),U_14971)),U_14968))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14966,U_14967)),hAPP(hAPP(c_Product__Type_OPair(U_14966,U_14967),U_14969),U_14970)),U_14968))
| ~ c_Relation_Osingle__valued(U_14966,U_14967,U_14968) ),
inference(variable_rename,[status(thm)],[f_3798_1]) ).
cnf(f_3798_3,plain,
( U_14970 = U_14971
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14966,U_14967)),hAPP(hAPP(c_Product__Type_OPair(U_14966,U_14967),U_14969),U_14971)),U_14968))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14966,U_14967)),hAPP(hAPP(c_Product__Type_OPair(U_14966,U_14967),U_14969),U_14970)),U_14968))
| ~ c_Relation_Osingle__valued(U_14966,U_14967,U_14968) ),
inference(clausify,[status(thm)],[f_3798_2]) ).
fof(f_3799_1,plain,
! [V_r_2,T_c,T_b] :
( ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
| ? [B_x,B_y] :
( ? [B_z] :
( B_y != B_z
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)),V_r_2)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)),V_r_2)) ) )
& ( ! [B_x,B_y] :
( ! [B_z] :
( B_y = B_z
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)),V_r_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)),V_r_2)) )
| ~ c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_single__valued__def]) ).
fof(f_3799_2,plain,
! [U_14980,U_14979,U_14978] :
( ( c_Relation_Osingle__valued(U_14978,U_14979,U_14980)
| ? [U_14977,U_14976] :
( ? [U_14975] :
( U_14976 != U_14975
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_14978,U_14979)),hAPP(hAPP(c_Product__Type_OPair(U_14978,U_14979),U_14977),U_14975)),U_14980)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_14978,U_14979)),hAPP(hAPP(c_Product__Type_OPair(U_14978,U_14979),U_14977),U_14976)),U_14980)) ) )
& ( ! [U_14974,U_14973] :
( ! [U_14972] :
( U_14973 = U_14972
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14978,U_14979)),hAPP(hAPP(c_Product__Type_OPair(U_14978,U_14979),U_14974),U_14972)),U_14980)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14978,U_14979)),hAPP(hAPP(c_Product__Type_OPair(U_14978,U_14979),U_14974),U_14973)),U_14980)) )
| ~ c_Relation_Osingle__valued(U_14978,U_14979,U_14980) ) ),
inference(variable_rename,[status(thm)],[f_3799_1]) ).
fof(f_3799_3,plain,
( ! [U_14986,U_14984,U_14982] :
( c_Relation_Osingle__valued(U_14982,U_14984,U_14986)
| ? [U_14977,U_14976] :
( ? [U_14975] :
( U_14976 != U_14975
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_14982,U_14984)),hAPP(hAPP(c_Product__Type_OPair(U_14982,U_14984),U_14977),U_14975)),U_14986)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_14982,U_14984)),hAPP(hAPP(c_Product__Type_OPair(U_14982,U_14984),U_14977),U_14976)),U_14986)) ) )
& ! [U_14985,U_14983,U_14981] :
( ! [U_14974,U_14973] :
( ! [U_14972] :
( U_14973 = U_14972
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14981,U_14983)),hAPP(hAPP(c_Product__Type_OPair(U_14981,U_14983),U_14974),U_14972)),U_14985)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14981,U_14983)),hAPP(hAPP(c_Product__Type_OPair(U_14981,U_14983),U_14974),U_14973)),U_14985)) )
| ~ c_Relation_Osingle__valued(U_14981,U_14983,U_14985) ) ),
inference(miniscope,[status(thm)],[f_3799_2]) ).
fof(f_3799_4,plain,
( ! [U_14986,U_14984,U_14982] :
( c_Relation_Osingle__valued(U_14982,U_14984,U_14986)
| ? [U_14976] :
( ? [U_14975] :
( U_14976 != U_14975
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_14982,U_14984)),hAPP(hAPP(c_Product__Type_OPair(U_14982,U_14984),sK366(U_14986,U_14984,U_14982)),U_14975)),U_14986)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_14982,U_14984)),hAPP(hAPP(c_Product__Type_OPair(U_14982,U_14984),sK366(U_14986,U_14984,U_14982)),U_14976)),U_14986)) ) )
& ! [U_14985,U_14983,U_14981] :
( ! [U_14974,U_14973] :
( ! [U_14972] :
( U_14973 = U_14972
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14981,U_14983)),hAPP(hAPP(c_Product__Type_OPair(U_14981,U_14983),U_14974),U_14972)),U_14985)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14981,U_14983)),hAPP(hAPP(c_Product__Type_OPair(U_14981,U_14983),U_14974),U_14973)),U_14985)) )
| ~ c_Relation_Osingle__valued(U_14981,U_14983,U_14985) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK366]),skolemize(U_14977,sK366(U_14986,U_14984,U_14982))],[f_3799_3]) ).
fof(f_3799_5,plain,
( ! [U_14986,U_14984,U_14982] :
( c_Relation_Osingle__valued(U_14982,U_14984,U_14986)
| ( ? [U_14975] :
( sK367(U_14986,U_14984,U_14982) != U_14975
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_14982,U_14984)),hAPP(hAPP(c_Product__Type_OPair(U_14982,U_14984),sK366(U_14986,U_14984,U_14982)),U_14975)),U_14986)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_14982,U_14984)),hAPP(hAPP(c_Product__Type_OPair(U_14982,U_14984),sK366(U_14986,U_14984,U_14982)),sK367(U_14986,U_14984,U_14982))),U_14986)) ) )
& ! [U_14985,U_14983,U_14981] :
( ! [U_14974,U_14973] :
( ! [U_14972] :
( U_14973 = U_14972
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14981,U_14983)),hAPP(hAPP(c_Product__Type_OPair(U_14981,U_14983),U_14974),U_14972)),U_14985)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14981,U_14983)),hAPP(hAPP(c_Product__Type_OPair(U_14981,U_14983),U_14974),U_14973)),U_14985)) )
| ~ c_Relation_Osingle__valued(U_14981,U_14983,U_14985) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK367]),skolemize(U_14976,sK367(U_14986,U_14984,U_14982))],[f_3799_4]) ).
fof(f_3799_6,plain,
( ! [U_14986,U_14984,U_14982] :
( c_Relation_Osingle__valued(U_14982,U_14984,U_14986)
| ( sK367(U_14986,U_14984,U_14982) != sK368(U_14986,U_14984,U_14982)
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_14982,U_14984)),hAPP(hAPP(c_Product__Type_OPair(U_14982,U_14984),sK366(U_14986,U_14984,U_14982)),sK368(U_14986,U_14984,U_14982))),U_14986))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_14982,U_14984)),hAPP(hAPP(c_Product__Type_OPair(U_14982,U_14984),sK366(U_14986,U_14984,U_14982)),sK367(U_14986,U_14984,U_14982))),U_14986)) ) )
& ! [U_14985,U_14983,U_14981] :
( ! [U_14974,U_14973] :
( ! [U_14972] :
( U_14973 = U_14972
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14981,U_14983)),hAPP(hAPP(c_Product__Type_OPair(U_14981,U_14983),U_14974),U_14972)),U_14985)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14981,U_14983)),hAPP(hAPP(c_Product__Type_OPair(U_14981,U_14983),U_14974),U_14973)),U_14985)) )
| ~ c_Relation_Osingle__valued(U_14981,U_14983,U_14985) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK368]),skolemize(U_14975,sK368(U_14986,U_14984,U_14982))],[f_3799_5]) ).
cnf(f_3799_7,plain,
( U_14973 = U_14972
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14981,U_14983)),hAPP(hAPP(c_Product__Type_OPair(U_14981,U_14983),U_14974),U_14972)),U_14985))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14981,U_14983)),hAPP(hAPP(c_Product__Type_OPair(U_14981,U_14983),U_14974),U_14973)),U_14985))
| ~ c_Relation_Osingle__valued(U_14981,U_14983,U_14985) ),
inference(clausify,[status(thm)],[f_3799_6]) ).
cnf(f_3799_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14982,U_14984)),hAPP(hAPP(c_Product__Type_OPair(U_14982,U_14984),sK366(U_14986,U_14984,U_14982)),sK367(U_14986,U_14984,U_14982))),U_14986))
| c_Relation_Osingle__valued(U_14982,U_14984,U_14986) ),
inference(clausify,[status(thm)],[f_3799_6]) ).
cnf(f_3799_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14982,U_14984)),hAPP(hAPP(c_Product__Type_OPair(U_14982,U_14984),sK366(U_14986,U_14984,U_14982)),sK368(U_14986,U_14984,U_14982))),U_14986))
| c_Relation_Osingle__valued(U_14982,U_14984,U_14986) ),
inference(clausify,[status(thm)],[f_3799_6]) ).
cnf(f_3799_10,plain,
( sK367(U_14986,U_14984,U_14982) != sK368(U_14986,U_14984,U_14982)
| c_Relation_Osingle__valued(U_14982,U_14984,U_14986) ),
inference(clausify,[status(thm)],[f_3799_6]) ).
fof(f_3800_1,plain,
! [V_r_2,V_A_2,T_b] :
( ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
| ? [B_x] :
( ? [B_xa] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_xa),B_x)),V_r_2))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2))
& B_x != B_xa
& hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ! [B_x] :
( ! [B_xa] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_xa),B_x)),V_r_2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2))
| B_x = B_xa
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_total__on__def]) ).
fof(f_3800_2,plain,
! [U_14993,U_14992,U_14991] :
( ( c_Relation_Ototal__on(U_14991,U_14992,U_14993)
| ? [U_14990] :
( ? [U_14989] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14991,U_14991)),hAPP(hAPP(c_Product__Type_OPair(U_14991,U_14991),U_14989),U_14990)),U_14993))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14991,U_14991)),hAPP(hAPP(c_Product__Type_OPair(U_14991,U_14991),U_14990),U_14989)),U_14993))
& U_14990 != U_14989
& hBOOL(hAPP(hAPP(c_member(U_14991),U_14989),U_14992)) )
& hBOOL(hAPP(hAPP(c_member(U_14991),U_14990),U_14992)) ) )
& ( ! [U_14988] :
( ! [U_14987] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14991,U_14991)),hAPP(hAPP(c_Product__Type_OPair(U_14991,U_14991),U_14987),U_14988)),U_14993))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_14991,U_14991)),hAPP(hAPP(c_Product__Type_OPair(U_14991,U_14991),U_14988),U_14987)),U_14993))
| U_14988 = U_14987
| ~ hBOOL(hAPP(hAPP(c_member(U_14991),U_14987),U_14992)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_14991),U_14988),U_14992)) )
| ~ c_Relation_Ototal__on(U_14991,U_14992,U_14993) ) ),
inference(variable_rename,[status(thm)],[f_3800_1]) ).
fof(f_3800_3,plain,
( ! [U_14999,U_14997,U_14995] :
( c_Relation_Ototal__on(U_14995,U_14997,U_14999)
| ? [U_14990] :
( ? [U_14989] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14995,U_14995)),hAPP(hAPP(c_Product__Type_OPair(U_14995,U_14995),U_14989),U_14990)),U_14999))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14995,U_14995)),hAPP(hAPP(c_Product__Type_OPair(U_14995,U_14995),U_14990),U_14989)),U_14999))
& U_14990 != U_14989
& hBOOL(hAPP(hAPP(c_member(U_14995),U_14989),U_14997)) )
& hBOOL(hAPP(hAPP(c_member(U_14995),U_14990),U_14997)) ) )
& ! [U_14998,U_14996,U_14994] :
( ! [U_14988] :
( ! [U_14987] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14994,U_14994)),hAPP(hAPP(c_Product__Type_OPair(U_14994,U_14994),U_14987),U_14988)),U_14998))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_14994,U_14994)),hAPP(hAPP(c_Product__Type_OPair(U_14994,U_14994),U_14988),U_14987)),U_14998))
| U_14988 = U_14987
| ~ hBOOL(hAPP(hAPP(c_member(U_14994),U_14987),U_14996)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_14994),U_14988),U_14996)) )
| ~ c_Relation_Ototal__on(U_14994,U_14996,U_14998) ) ),
inference(miniscope,[status(thm)],[f_3800_2]) ).
fof(f_3800_4,plain,
( ! [U_14999,U_14997,U_14995] :
( c_Relation_Ototal__on(U_14995,U_14997,U_14999)
| ( ? [U_14989] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14995,U_14995)),hAPP(hAPP(c_Product__Type_OPair(U_14995,U_14995),U_14989),sK369(U_14999,U_14997,U_14995))),U_14999))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14995,U_14995)),hAPP(hAPP(c_Product__Type_OPair(U_14995,U_14995),sK369(U_14999,U_14997,U_14995)),U_14989)),U_14999))
& sK369(U_14999,U_14997,U_14995) != U_14989
& hBOOL(hAPP(hAPP(c_member(U_14995),U_14989),U_14997)) )
& hBOOL(hAPP(hAPP(c_member(U_14995),sK369(U_14999,U_14997,U_14995)),U_14997)) ) )
& ! [U_14998,U_14996,U_14994] :
( ! [U_14988] :
( ! [U_14987] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14994,U_14994)),hAPP(hAPP(c_Product__Type_OPair(U_14994,U_14994),U_14987),U_14988)),U_14998))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_14994,U_14994)),hAPP(hAPP(c_Product__Type_OPair(U_14994,U_14994),U_14988),U_14987)),U_14998))
| U_14988 = U_14987
| ~ hBOOL(hAPP(hAPP(c_member(U_14994),U_14987),U_14996)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_14994),U_14988),U_14996)) )
| ~ c_Relation_Ototal__on(U_14994,U_14996,U_14998) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK369]),skolemize(U_14990,sK369(U_14999,U_14997,U_14995))],[f_3800_3]) ).
fof(f_3800_5,plain,
( ! [U_14999,U_14997,U_14995] :
( c_Relation_Ototal__on(U_14995,U_14997,U_14999)
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14995,U_14995)),hAPP(hAPP(c_Product__Type_OPair(U_14995,U_14995),sK370(U_14999,U_14997,U_14995)),sK369(U_14999,U_14997,U_14995))),U_14999))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14995,U_14995)),hAPP(hAPP(c_Product__Type_OPair(U_14995,U_14995),sK369(U_14999,U_14997,U_14995)),sK370(U_14999,U_14997,U_14995))),U_14999))
& sK369(U_14999,U_14997,U_14995) != sK370(U_14999,U_14997,U_14995)
& hBOOL(hAPP(hAPP(c_member(U_14995),sK370(U_14999,U_14997,U_14995)),U_14997))
& hBOOL(hAPP(hAPP(c_member(U_14995),sK369(U_14999,U_14997,U_14995)),U_14997)) ) )
& ! [U_14998,U_14996,U_14994] :
( ! [U_14988] :
( ! [U_14987] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14994,U_14994)),hAPP(hAPP(c_Product__Type_OPair(U_14994,U_14994),U_14987),U_14988)),U_14998))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_14994,U_14994)),hAPP(hAPP(c_Product__Type_OPair(U_14994,U_14994),U_14988),U_14987)),U_14998))
| U_14988 = U_14987
| ~ hBOOL(hAPP(hAPP(c_member(U_14994),U_14987),U_14996)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_14994),U_14988),U_14996)) )
| ~ c_Relation_Ototal__on(U_14994,U_14996,U_14998) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK370]),skolemize(U_14989,sK370(U_14999,U_14997,U_14995))],[f_3800_4]) ).
cnf(f_3800_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14994,U_14994)),hAPP(hAPP(c_Product__Type_OPair(U_14994,U_14994),U_14987),U_14988)),U_14998))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_14994,U_14994)),hAPP(hAPP(c_Product__Type_OPair(U_14994,U_14994),U_14988),U_14987)),U_14998))
| U_14988 = U_14987
| ~ hBOOL(hAPP(hAPP(c_member(U_14994),U_14987),U_14996))
| ~ hBOOL(hAPP(hAPP(c_member(U_14994),U_14988),U_14996))
| ~ c_Relation_Ototal__on(U_14994,U_14996,U_14998) ),
inference(clausify,[status(thm)],[f_3800_5]) ).
cnf(f_3800_7,plain,
( hBOOL(hAPP(hAPP(c_member(U_14995),sK369(U_14999,U_14997,U_14995)),U_14997))
| c_Relation_Ototal__on(U_14995,U_14997,U_14999) ),
inference(clausify,[status(thm)],[f_3800_5]) ).
cnf(f_3800_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_14995),sK370(U_14999,U_14997,U_14995)),U_14997))
| c_Relation_Ototal__on(U_14995,U_14997,U_14999) ),
inference(clausify,[status(thm)],[f_3800_5]) ).
cnf(f_3800_9,plain,
( sK369(U_14999,U_14997,U_14995) != sK370(U_14999,U_14997,U_14995)
| c_Relation_Ototal__on(U_14995,U_14997,U_14999) ),
inference(clausify,[status(thm)],[f_3800_5]) ).
cnf(f_3800_10,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14995,U_14995)),hAPP(hAPP(c_Product__Type_OPair(U_14995,U_14995),sK369(U_14999,U_14997,U_14995)),sK370(U_14999,U_14997,U_14995))),U_14999))
| c_Relation_Ototal__on(U_14995,U_14997,U_14999) ),
inference(clausify,[status(thm)],[f_3800_5]) ).
cnf(f_3800_11,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14995,U_14995)),hAPP(hAPP(c_Product__Type_OPair(U_14995,U_14995),sK370(U_14999,U_14997,U_14995)),sK369(U_14999,U_14997,U_14995))),U_14999))
| c_Relation_Ototal__on(U_14995,U_14997,U_14999) ),
inference(clausify,[status(thm)],[f_3800_5]) ).
fof(f_3801_1,plain,
! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
| ~ c_Relation_Osingle__valued(T_b,T_b,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_single__valued__confluent]) ).
fof(f_3801_2,plain,
! [U_15004,U_15003,U_15002,U_15001,U_15000] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15000,U_15000)),hAPP(hAPP(c_Product__Type_OPair(U_15000,U_15000),U_15004),U_15003)),c_Transitive__Closure_Ortrancl(U_15000,U_15001)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_15000,U_15000)),hAPP(hAPP(c_Product__Type_OPair(U_15000,U_15000),U_15003),U_15004)),c_Transitive__Closure_Ortrancl(U_15000,U_15001)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15000,U_15000)),hAPP(hAPP(c_Product__Type_OPair(U_15000,U_15000),U_15002),U_15004)),c_Transitive__Closure_Ortrancl(U_15000,U_15001)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15000,U_15000)),hAPP(hAPP(c_Product__Type_OPair(U_15000,U_15000),U_15002),U_15003)),c_Transitive__Closure_Ortrancl(U_15000,U_15001)))
| ~ c_Relation_Osingle__valued(U_15000,U_15000,U_15001) ),
inference(variable_rename,[status(thm)],[f_3801_1]) ).
cnf(f_3801_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15000,U_15000)),hAPP(hAPP(c_Product__Type_OPair(U_15000,U_15000),U_15004),U_15003)),c_Transitive__Closure_Ortrancl(U_15000,U_15001)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_15000,U_15000)),hAPP(hAPP(c_Product__Type_OPair(U_15000,U_15000),U_15003),U_15004)),c_Transitive__Closure_Ortrancl(U_15000,U_15001)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15000,U_15000)),hAPP(hAPP(c_Product__Type_OPair(U_15000,U_15000),U_15002),U_15004)),c_Transitive__Closure_Ortrancl(U_15000,U_15001)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15000,U_15000)),hAPP(hAPP(c_Product__Type_OPair(U_15000,U_15000),U_15002),U_15003)),c_Transitive__Closure_Ortrancl(U_15000,U_15001)))
| ~ c_Relation_Osingle__valued(U_15000,U_15000,U_15001) ),
inference(clausify,[status(thm)],[f_3801_2]) ).
fof(f_3802_1,plain,
! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
( hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2))
| ~ c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2)) ),
inference(fof_nnf,[status(thm)],[fact_Image__Int__eq]) ).
fof(f_3802_2,plain,
! [U_15009,U_15008,U_15007,U_15006,U_15005] :
( hAPP(c_Relation_OImage(U_15006,U_15005,U_15007),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15006,tc_HOL_Obool)),U_15008),U_15009)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15005,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15006,U_15005,U_15007),U_15008)),hAPP(c_Relation_OImage(U_15006,U_15005,U_15007),U_15009))
| ~ c_Relation_Osingle__valued(U_15005,U_15006,hAPP(c_Relation_Oconverse(U_15006,U_15005),U_15007)) ),
inference(variable_rename,[status(thm)],[f_3802_1]) ).
cnf(f_3802_3,plain,
( hAPP(c_Relation_OImage(U_15006,U_15005,U_15007),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15006,tc_HOL_Obool)),U_15008),U_15009)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15005,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15006,U_15005,U_15007),U_15008)),hAPP(c_Relation_OImage(U_15006,U_15005,U_15007),U_15009))
| ~ c_Relation_Osingle__valued(U_15005,U_15006,hAPP(c_Relation_Oconverse(U_15006,U_15005),U_15007)) ),
inference(clausify,[status(thm)],[f_3802_2]) ).
fof(f_3803_1,plain,
! [V_R_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__imp__UN__rel__pow]) ).
fof(f_3803_2,plain,
! [U_15012,U_15011,U_15010] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15010,U_15010)),U_15011),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_15010,U_15010),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(U_15010,U_15010),tc_HOL_Obool),tc_fun(tc_prod(U_15010,U_15010),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_15010,U_15010),tc_HOL_Obool)),U_15012))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15010,U_15010)),U_15011),c_Transitive__Closure_Ortrancl(U_15010,U_15012))) ),
inference(variable_rename,[status(thm)],[f_3803_1]) ).
cnf(f_3803_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15010,U_15010)),U_15011),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_15010,U_15010),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(U_15010,U_15010),tc_HOL_Obool),tc_fun(tc_prod(U_15010,U_15010),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_15010,U_15010),tc_HOL_Obool)),U_15012))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15010,U_15010)),U_15011),c_Transitive__Closure_Ortrancl(U_15010,U_15012))) ),
inference(clausify,[status(thm)],[f_3803_2]) ).
fof(f_3804_1,plain,
! [V_r_2,T_b] :
( c_Wellfounded_Oacyclic(T_b,V_r_2)
| ? [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_acyclicI]) ).
fof(f_3804_2,plain,
! [U_15015,U_15014] :
( c_Wellfounded_Oacyclic(U_15014,U_15015)
| ? [U_15013] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15014,U_15014)),hAPP(hAPP(c_Product__Type_OPair(U_15014,U_15014),U_15013),U_15013)),c_Transitive__Closure_Otrancl(U_15014,U_15015))) ),
inference(variable_rename,[status(thm)],[f_3804_1]) ).
fof(f_3804_3,plain,
! [U_15015,U_15014] :
( c_Wellfounded_Oacyclic(U_15014,U_15015)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_15014,U_15014)),hAPP(hAPP(c_Product__Type_OPair(U_15014,U_15014),sK371(U_15015,U_15014)),sK371(U_15015,U_15014))),c_Transitive__Closure_Otrancl(U_15014,U_15015))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK371]),skolemize(U_15013,sK371(U_15015,U_15014))],[f_3804_2]) ).
cnf(f_3804_4,plain,
( c_Wellfounded_Oacyclic(U_15014,U_15015)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_15014,U_15014)),hAPP(hAPP(c_Product__Type_OPair(U_15014,U_15014),sK371(U_15015,U_15014)),sK371(U_15015,U_15014))),c_Transitive__Closure_Otrancl(U_15014,U_15015))) ),
inference(clausify,[status(thm)],[f_3804_3]) ).
fof(f_3805_1,plain,
! [V_na_2,V_R_2,T_b] :
( c_Relation_Osingle__valued(T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2))
| ~ c_Relation_Osingle__valued(T_b,T_b,V_R_2) ),
inference(fof_nnf,[status(thm)],[fact_single__valued__rel__pow]) ).
fof(f_3805_2,plain,
! [U_15018,U_15017,U_15016] :
( c_Relation_Osingle__valued(U_15016,U_15016,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15016,U_15016),tc_HOL_Obool),U_15018),U_15017))
| ~ c_Relation_Osingle__valued(U_15016,U_15016,U_15017) ),
inference(variable_rename,[status(thm)],[f_3805_1]) ).
cnf(f_3805_3,plain,
( c_Relation_Osingle__valued(U_15016,U_15016,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15016,U_15016),tc_HOL_Obool),U_15018),U_15017))
| ~ c_Relation_Osingle__valued(U_15016,U_15016,U_15017) ),
inference(clausify,[status(thm)],[f_3805_2]) ).
fof(f_3806_1,plain,
! [V_f_2,V_m_2,V_na_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_na_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_na_2)),V_f_2),
inference(fof_nnf,[status(thm)],[fact_funpow__mult]) ).
fof(f_3806_2,plain,
! [U_15022,U_15021,U_15020,U_15019] : hAPP(hAPP(c_Nat_Ocompow(U_15019,U_15019),U_15020),hAPP(hAPP(c_Nat_Ocompow(U_15019,U_15019),U_15021),U_15022)) = hAPP(hAPP(c_Nat_Ocompow(U_15019,U_15019),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_15021),U_15020)),U_15022),
inference(variable_rename,[status(thm)],[f_3806_1]) ).
cnf(f_3806_3,plain,
hAPP(hAPP(c_Nat_Ocompow(U_15019,U_15019),U_15020),hAPP(hAPP(c_Nat_Ocompow(U_15019,U_15019),U_15021),U_15022)) = hAPP(hAPP(c_Nat_Ocompow(U_15019,U_15019),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_15021),U_15020)),U_15022),
inference(clausify,[status(thm)],[f_3806_2]) ).
fof(f_3807_1,plain,
! [V_x_2,V_na_2,T_b,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_na_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_na_2),V_f_2),hAPP(V_f_2,V_x_2)),
inference(fof_nnf,[status(thm)],[fact_funpow__swap1]) ).
fof(f_3807_2,plain,
! [U_15026,U_15025,U_15024,U_15023] : hAPP(U_15023,hAPP(hAPP(hAPP(c_Nat_Ocompow(U_15024,U_15024),U_15025),U_15023),U_15026)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(U_15024,U_15024),U_15025),U_15023),hAPP(U_15023,U_15026)),
inference(variable_rename,[status(thm)],[f_3807_1]) ).
cnf(f_3807_3,plain,
hAPP(U_15023,hAPP(hAPP(hAPP(c_Nat_Ocompow(U_15024,U_15024),U_15025),U_15023),U_15026)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(U_15024,U_15024),U_15025),U_15023),hAPP(U_15023,U_15026)),
inference(clausify,[status(thm)],[f_3807_2]) ).
fof(f_3808_1,plain,
! [V_R_2,V_na_2,T_b] :
( c_Wellfounded_Owf(T_b,V_R_2)
| ~ c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)) ),
inference(fof_nnf,[status(thm)],[fact_wf__exp]) ).
fof(f_3808_2,plain,
! [U_15029,U_15028,U_15027] :
( c_Wellfounded_Owf(U_15027,U_15029)
| ~ c_Wellfounded_Owf(U_15027,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15027,U_15027),tc_HOL_Obool),U_15028),U_15029)) ),
inference(variable_rename,[status(thm)],[f_3808_1]) ).
cnf(f_3808_3,plain,
( c_Wellfounded_Owf(U_15027,U_15029)
| ~ c_Wellfounded_Owf(U_15027,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15027,U_15027),tc_HOL_Obool),U_15028),U_15029)) ),
inference(clausify,[status(thm)],[f_3808_2]) ).
fof(f_3809_1,plain,
! [V_f_2,V_na_2,T_c,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),V_na_2),c_Fun_Ocomp(T_c,T_c,T_b,V_f_2)) = c_Fun_Ocomp(T_c,T_c,T_b,hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_na_2),V_f_2)),
inference(fof_nnf,[status(thm)],[fact_comp__funpow]) ).
fof(f_3809_2,plain,
! [U_15033,U_15032,U_15031,U_15030] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(U_15030,U_15031),tc_fun(U_15030,U_15031)),U_15032),c_Fun_Ocomp(U_15031,U_15031,U_15030,U_15033)) = c_Fun_Ocomp(U_15031,U_15031,U_15030,hAPP(hAPP(c_Nat_Ocompow(U_15031,U_15031),U_15032),U_15033)),
inference(variable_rename,[status(thm)],[f_3809_1]) ).
cnf(f_3809_3,plain,
hAPP(hAPP(c_Nat_Ocompow(tc_fun(U_15030,U_15031),tc_fun(U_15030,U_15031)),U_15032),c_Fun_Ocomp(U_15031,U_15031,U_15030,U_15033)) = c_Fun_Ocomp(U_15031,U_15031,U_15030,hAPP(hAPP(c_Nat_Ocompow(U_15031,U_15031),U_15032),U_15033)),
inference(clausify,[status(thm)],[f_3809_2]) ).
fof(f_3810_1,plain,
! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2,
inference(fof_nnf,[status(thm)],[fact_rel__pow__1]) ).
fof(f_3810_2,plain,
! [U_15035,U_15034] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15034,U_15034),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_15035) = U_15035,
inference(variable_rename,[status(thm)],[f_3810_1]) ).
cnf(f_3810_3,plain,
hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15034,U_15034),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_15035) = U_15035,
inference(clausify,[status(thm)],[f_3810_2]) ).
fof(f_3811_1,plain,
! [V_na_2,V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)),V_R_2),
inference(fof_nnf,[status(thm)],[fact_rel__pow__commute]) ).
fof(f_3811_2,plain,
! [U_15038,U_15037,U_15036] : hAPP(hAPP(c_Relation_Orel__comp(U_15036,U_15036,U_15036),U_15037),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15036,U_15036),tc_HOL_Obool),U_15038),U_15037)) = hAPP(hAPP(c_Relation_Orel__comp(U_15036,U_15036,U_15036),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15036,U_15036),tc_HOL_Obool),U_15038),U_15037)),U_15037),
inference(variable_rename,[status(thm)],[f_3811_1]) ).
cnf(f_3811_3,plain,
hAPP(hAPP(c_Relation_Orel__comp(U_15036,U_15036,U_15036),U_15037),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15036,U_15036),tc_HOL_Obool),U_15038),U_15037)) = hAPP(hAPP(c_Relation_Orel__comp(U_15036,U_15036,U_15036),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15036,U_15036),tc_HOL_Obool),U_15038),U_15037)),U_15037),
inference(clausify,[status(thm)],[f_3811_2]) ).
fof(f_3812_1,plain,
! [V_R_2,V_p_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
| ! [B_n] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) )
& ( ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__power]) ).
fof(f_3812_2,plain,
! [U_15043,U_15042,U_15041] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15041,U_15041)),U_15042),c_Transitive__Closure_Ortrancl(U_15041,U_15043)))
| ! [U_15040] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15041,U_15041)),U_15042),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15041,U_15041),tc_HOL_Obool),U_15040),U_15043))) )
& ( ? [U_15039] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15041,U_15041)),U_15042),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15041,U_15041),tc_HOL_Obool),U_15039),U_15043)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15041,U_15041)),U_15042),c_Transitive__Closure_Ortrancl(U_15041,U_15043))) ) ),
inference(variable_rename,[status(thm)],[f_3812_1]) ).
fof(f_3812_3,plain,
( ! [U_15049,U_15047,U_15045] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15045,U_15045)),U_15047),c_Transitive__Closure_Ortrancl(U_15045,U_15049)))
| ! [U_15040] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15045,U_15045)),U_15047),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15045,U_15045),tc_HOL_Obool),U_15040),U_15049))) )
& ! [U_15048,U_15046,U_15044] :
( ? [U_15039] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15044,U_15044)),U_15046),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15044,U_15044),tc_HOL_Obool),U_15039),U_15048)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15044,U_15044)),U_15046),c_Transitive__Closure_Ortrancl(U_15044,U_15048))) ) ),
inference(miniscope,[status(thm)],[f_3812_2]) ).
fof(f_3812_4,plain,
( ! [U_15049,U_15047,U_15045] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15045,U_15045)),U_15047),c_Transitive__Closure_Ortrancl(U_15045,U_15049)))
| ! [U_15040] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15045,U_15045)),U_15047),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15045,U_15045),tc_HOL_Obool),U_15040),U_15049))) )
& ! [U_15048,U_15046,U_15044] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15044,U_15044)),U_15046),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15044,U_15044),tc_HOL_Obool),sK372(U_15048,U_15046,U_15044)),U_15048)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15044,U_15044)),U_15046),c_Transitive__Closure_Ortrancl(U_15044,U_15048))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK372]),skolemize(U_15039,sK372(U_15048,U_15046,U_15044))],[f_3812_3]) ).
cnf(f_3812_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15044,U_15044)),U_15046),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15044,U_15044),tc_HOL_Obool),sK372(U_15048,U_15046,U_15044)),U_15048)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15044,U_15044)),U_15046),c_Transitive__Closure_Ortrancl(U_15044,U_15048))) ),
inference(clausify,[status(thm)],[f_3812_4]) ).
cnf(f_3812_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15045,U_15045)),U_15047),c_Transitive__Closure_Ortrancl(U_15045,U_15049)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15045,U_15045)),U_15047),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15045,U_15045),tc_HOL_Obool),U_15040),U_15049))) ),
inference(clausify,[status(thm)],[f_3812_4]) ).
fof(f_3813_1,plain,
! [V_R_2,V_na_2,V_p_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_rel__pow__imp__rtrancl]) ).
fof(f_3813_2,plain,
! [U_15053,U_15052,U_15051,U_15050] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15050,U_15050)),U_15051),c_Transitive__Closure_Ortrancl(U_15050,U_15053)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15050,U_15050)),U_15051),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15050,U_15050),tc_HOL_Obool),U_15052),U_15053))) ),
inference(variable_rename,[status(thm)],[f_3813_1]) ).
cnf(f_3813_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15050,U_15050)),U_15051),c_Transitive__Closure_Ortrancl(U_15050,U_15053)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15050,U_15050)),U_15051),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15050,U_15050),tc_HOL_Obool),U_15052),U_15053))) ),
inference(clausify,[status(thm)],[f_3813_2]) ).
fof(f_3814_1,plain,
! [V_R_2,V_na_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_na_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)),V_R_2),
inference(fof_nnf,[status(thm)],[fact_relpow_Osimps_I2_J]) ).
fof(f_3814_2,plain,
! [U_15056,U_15055,U_15054] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15054,U_15054),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15055)),U_15056) = hAPP(hAPP(c_Relation_Orel__comp(U_15054,U_15054,U_15054),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15054,U_15054),tc_HOL_Obool),U_15055),U_15056)),U_15056),
inference(variable_rename,[status(thm)],[f_3814_1]) ).
cnf(f_3814_3,plain,
hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15054,U_15054),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15055)),U_15056) = hAPP(hAPP(c_Relation_Orel__comp(U_15054,U_15054,U_15054),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15054,U_15054),tc_HOL_Obool),U_15055),U_15056)),U_15056),
inference(clausify,[status(thm)],[f_3814_2]) ).
fof(f_3815_1,plain,
! [V_R_2,V_na_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)),
inference(fof_nnf,[status(thm)],[fact_rel__pow__add]) ).
fof(f_3815_2,plain,
! [U_15060,U_15059,U_15058,U_15057] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15057,U_15057),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_15058),U_15059)),U_15060) = hAPP(hAPP(c_Relation_Orel__comp(U_15057,U_15057,U_15057),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15057,U_15057),tc_HOL_Obool),U_15058),U_15060)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15057,U_15057),tc_HOL_Obool),U_15059),U_15060)),
inference(variable_rename,[status(thm)],[f_3815_1]) ).
cnf(f_3815_3,plain,
hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15057,U_15057),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_15058),U_15059)),U_15060) = hAPP(hAPP(c_Relation_Orel__comp(U_15057,U_15057,U_15057),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15057,U_15057),tc_HOL_Obool),U_15058),U_15060)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15057,U_15057),tc_HOL_Obool),U_15059),U_15060)),
inference(clausify,[status(thm)],[f_3815_2]) ).
fof(f_3816_1,plain,
! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_b),
inference(fof_nnf,[status(thm)],[fact_relpow_Osimps_I1_J]) ).
fof(f_3816_2,plain,
! [U_15062,U_15061] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15061,U_15061),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15062) = c_Relation_OId(U_15061),
inference(variable_rename,[status(thm)],[f_3816_1]) ).
cnf(f_3816_3,plain,
hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15061,U_15061),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15062) = c_Relation_OId(U_15061),
inference(clausify,[status(thm)],[f_3816_2]) ).
fof(f_3817_1,plain,
! [V_R_2,V_y_2,V_x_2,T_b] :
( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_rel__pow__0__E]) ).
fof(f_3817_2,plain,
! [U_15066,U_15065,U_15064,U_15063] :
( U_15064 = U_15065
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15063,U_15063)),hAPP(hAPP(c_Product__Type_OPair(U_15063,U_15063),U_15064),U_15065)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15063,U_15063),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15066))) ),
inference(variable_rename,[status(thm)],[f_3817_1]) ).
fof(f_3817_3,plain,
! [U_15066,U_15065,U_15064] :
( ! [U_15063] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15063,U_15063)),hAPP(hAPP(c_Product__Type_OPair(U_15063,U_15063),U_15064),U_15065)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15063,U_15063),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15066)))
| U_15064 = U_15065 ),
inference(miniscope,[status(thm)],[f_3817_2]) ).
cnf(f_3817_4,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15063,U_15063)),hAPP(hAPP(c_Product__Type_OPair(U_15063,U_15063),U_15064),U_15065)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15063,U_15063),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15066)))
| U_15064 = U_15065 ),
inference(clausify,[status(thm)],[f_3817_3]) ).
fof(f_3818_1,plain,
! [V_R_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))),
inference(fof_nnf,[status(thm)],[fact_rel__pow__0__I]) ).
fof(f_3818_2,plain,
! [U_15069,U_15068,U_15067] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_15067,U_15067)),hAPP(hAPP(c_Product__Type_OPair(U_15067,U_15067),U_15068),U_15068)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15067,U_15067),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15069))),
inference(variable_rename,[status(thm)],[f_3818_1]) ).
cnf(f_3818_3,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(U_15067,U_15067)),hAPP(hAPP(c_Product__Type_OPair(U_15067,U_15067),U_15068),U_15068)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15067,U_15067),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15069))),
inference(clausify,[status(thm)],[f_3818_2]) ).
fof(f_3819_1,plain,
! [V_z_2,V_R_2,V_na_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_na_2)),V_R_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_R_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__I]) ).
fof(f_3819_2,plain,
! [U_15075,U_15074,U_15073,U_15072,U_15071,U_15070] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15070,U_15070)),hAPP(hAPP(c_Product__Type_OPair(U_15070,U_15070),U_15071),U_15075)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15070,U_15070),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15073)),U_15074)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15070,U_15070)),hAPP(hAPP(c_Product__Type_OPair(U_15070,U_15070),U_15072),U_15075)),U_15074))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15070,U_15070)),hAPP(hAPP(c_Product__Type_OPair(U_15070,U_15070),U_15071),U_15072)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15070,U_15070),tc_HOL_Obool),U_15073),U_15074))) ),
inference(variable_rename,[status(thm)],[f_3819_1]) ).
cnf(f_3819_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15070,U_15070)),hAPP(hAPP(c_Product__Type_OPair(U_15070,U_15070),U_15071),U_15075)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15070,U_15070),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15073)),U_15074)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15070,U_15070)),hAPP(hAPP(c_Product__Type_OPair(U_15070,U_15070),U_15072),U_15075)),U_15074))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15070,U_15070)),hAPP(hAPP(c_Product__Type_OPair(U_15070,U_15070),U_15071),U_15072)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15070,U_15070),tc_HOL_Obool),U_15073),U_15074))) ),
inference(clausify,[status(thm)],[f_3819_2]) ).
fof(f_3820_1,plain,
! [V_na_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_na_2)),V_R_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2)) ),
inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__I2]) ).
fof(f_3820_2,plain,
! [U_15081,U_15080,U_15079,U_15078,U_15077,U_15076] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15076,U_15076)),hAPP(hAPP(c_Product__Type_OPair(U_15076,U_15076),U_15077),U_15080)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15076,U_15076),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15081)),U_15079)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15076,U_15076)),hAPP(hAPP(c_Product__Type_OPair(U_15076,U_15076),U_15078),U_15080)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15076,U_15076),tc_HOL_Obool),U_15081),U_15079)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15076,U_15076)),hAPP(hAPP(c_Product__Type_OPair(U_15076,U_15076),U_15077),U_15078)),U_15079)) ),
inference(variable_rename,[status(thm)],[f_3820_1]) ).
cnf(f_3820_3,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15076,U_15076)),hAPP(hAPP(c_Product__Type_OPair(U_15076,U_15076),U_15077),U_15080)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15076,U_15076),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15081)),U_15079)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15076,U_15076)),hAPP(hAPP(c_Product__Type_OPair(U_15076,U_15076),U_15078),U_15080)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15076,U_15076),tc_HOL_Obool),U_15081),U_15079)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15076,U_15076)),hAPP(hAPP(c_Product__Type_OPair(U_15076,U_15076),U_15077),U_15078)),U_15079)) ),
inference(clausify,[status(thm)],[f_3820_2]) ).
fof(f_3821_1,plain,
! [V_f_2,V_na_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(c_Nat_OSuc,V_na_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_na_2),V_f_2)),
inference(fof_nnf,[status(thm)],[fact_funpow_Osimps_I2_J]) ).
fof(f_3821_2,plain,
! [U_15084,U_15083,U_15082] : hAPP(hAPP(c_Nat_Ocompow(U_15082,U_15082),hAPP(c_Nat_OSuc,U_15083)),U_15084) = hAPP(c_Fun_Ocomp(U_15082,U_15082,U_15082,U_15084),hAPP(hAPP(c_Nat_Ocompow(U_15082,U_15082),U_15083),U_15084)),
inference(variable_rename,[status(thm)],[f_3821_1]) ).
cnf(f_3821_3,plain,
hAPP(hAPP(c_Nat_Ocompow(U_15082,U_15082),hAPP(c_Nat_OSuc,U_15083)),U_15084) = hAPP(c_Fun_Ocomp(U_15082,U_15082,U_15082,U_15084),hAPP(hAPP(c_Nat_Ocompow(U_15082,U_15082),U_15083),U_15084)),
inference(clausify,[status(thm)],[f_3821_2]) ).
fof(f_3822_1,plain,
! [V_f_2,V_na_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_na_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_na_2),V_f_2)),
inference(fof_nnf,[status(thm)],[fact_funpow__add]) ).
fof(f_3822_2,plain,
! [U_15088,U_15087,U_15086,U_15085] : hAPP(hAPP(c_Nat_Ocompow(U_15085,U_15085),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_15086),U_15087)),U_15088) = hAPP(c_Fun_Ocomp(U_15085,U_15085,U_15085,hAPP(hAPP(c_Nat_Ocompow(U_15085,U_15085),U_15086),U_15088)),hAPP(hAPP(c_Nat_Ocompow(U_15085,U_15085),U_15087),U_15088)),
inference(variable_rename,[status(thm)],[f_3822_1]) ).
cnf(f_3822_3,plain,
hAPP(hAPP(c_Nat_Ocompow(U_15085,U_15085),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_15086),U_15087)),U_15088) = hAPP(c_Fun_Ocomp(U_15085,U_15085,U_15085,hAPP(hAPP(c_Nat_Ocompow(U_15085,U_15085),U_15086),U_15088)),hAPP(hAPP(c_Nat_Ocompow(U_15085,U_15085),U_15087),U_15088)),
inference(clausify,[status(thm)],[f_3822_2]) ).
fof(f_3823_1,plain,
! [V_f_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_b),
inference(fof_nnf,[status(thm)],[fact_funpow_Osimps_I1_J]) ).
fof(f_3823_2,plain,
! [U_15090,U_15089] : hAPP(hAPP(c_Nat_Ocompow(U_15089,U_15089),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15090) = c_Fun_Oid(U_15089),
inference(variable_rename,[status(thm)],[f_3823_1]) ).
cnf(f_3823_3,plain,
hAPP(hAPP(c_Nat_Ocompow(U_15089,U_15089),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15090) = c_Fun_Oid(U_15089),
inference(clausify,[status(thm)],[f_3823_2]) ).
fof(f_3824_1,plain,
! [V_R_2,V_p_2,T_b] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
| ! [B_n] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) ) )
& ( ? [B_n] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_trancl__power]) ).
fof(f_3824_2,plain,
! [U_15095,U_15094,U_15093] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15093,U_15093)),U_15094),c_Transitive__Closure_Otrancl(U_15093,U_15095)))
| ! [U_15092] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15093,U_15093)),U_15094),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15093,U_15093),tc_HOL_Obool),U_15092),U_15095)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15092)) ) )
& ( ? [U_15091] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15093,U_15093)),U_15094),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15093,U_15093),tc_HOL_Obool),U_15091),U_15095)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15091)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15093,U_15093)),U_15094),c_Transitive__Closure_Otrancl(U_15093,U_15095))) ) ),
inference(variable_rename,[status(thm)],[f_3824_1]) ).
fof(f_3824_3,plain,
( ! [U_15101,U_15099,U_15097] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15097,U_15097)),U_15099),c_Transitive__Closure_Otrancl(U_15097,U_15101)))
| ! [U_15092] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15097,U_15097)),U_15099),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15097,U_15097),tc_HOL_Obool),U_15092),U_15101)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15092)) ) )
& ! [U_15100,U_15098,U_15096] :
( ? [U_15091] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15096,U_15096)),U_15098),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15096,U_15096),tc_HOL_Obool),U_15091),U_15100)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15091)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15096,U_15096)),U_15098),c_Transitive__Closure_Otrancl(U_15096,U_15100))) ) ),
inference(miniscope,[status(thm)],[f_3824_2]) ).
fof(f_3824_4,plain,
( ! [U_15101,U_15099,U_15097] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15097,U_15097)),U_15099),c_Transitive__Closure_Otrancl(U_15097,U_15101)))
| ! [U_15092] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15097,U_15097)),U_15099),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15097,U_15097),tc_HOL_Obool),U_15092),U_15101)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15092)) ) )
& ! [U_15100,U_15098,U_15096] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15096,U_15096)),U_15098),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15096,U_15096),tc_HOL_Obool),sK373(U_15100,U_15098,U_15096)),U_15100)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK373(U_15100,U_15098,U_15096))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15096,U_15096)),U_15098),c_Transitive__Closure_Otrancl(U_15096,U_15100))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK373]),skolemize(U_15091,sK373(U_15100,U_15098,U_15096))],[f_3824_3]) ).
cnf(f_3824_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK373(U_15100,U_15098,U_15096)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15096,U_15096)),U_15098),c_Transitive__Closure_Otrancl(U_15096,U_15100))) ),
inference(clausify,[status(thm)],[f_3824_4]) ).
cnf(f_3824_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15096,U_15096)),U_15098),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15096,U_15096),tc_HOL_Obool),sK373(U_15100,U_15098,U_15096)),U_15100)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15096,U_15096)),U_15098),c_Transitive__Closure_Otrancl(U_15096,U_15100))) ),
inference(clausify,[status(thm)],[f_3824_4]) ).
cnf(f_3824_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15097,U_15097)),U_15099),c_Transitive__Closure_Otrancl(U_15097,U_15101)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15097,U_15097)),U_15099),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15097,U_15097),tc_HOL_Obool),U_15092),U_15101)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_15092)) ),
inference(clausify,[status(thm)],[f_3824_4]) ).
fof(f_3825_1,plain,
! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)),
inference(fof_nnf,[status(thm)],[fact_rtrancl__is__UN__rel__pow]) ).
fof(f_3825_2,plain,
! [U_15103,U_15102] : c_Transitive__Closure_Ortrancl(U_15102,U_15103) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_15102,U_15102),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(U_15102,U_15102),tc_HOL_Obool),tc_fun(tc_prod(U_15102,U_15102),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_15102,U_15102),tc_HOL_Obool)),U_15103)),
inference(variable_rename,[status(thm)],[f_3825_1]) ).
cnf(f_3825_3,plain,
c_Transitive__Closure_Ortrancl(U_15102,U_15103) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_15102,U_15102),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(U_15102,U_15102),tc_HOL_Obool),tc_fun(tc_prod(U_15102,U_15102),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_15102,U_15102),tc_HOL_Obool)),U_15103)),
inference(clausify,[status(thm)],[f_3825_2]) ).
fof(f_3826_1,plain,
! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b),
inference(fof_nnf,[status(thm)],[fact_funpow__code__def]) ).
fof(f_3826_2,plain,
! [U_15104] : c_Nat_Ofunpow(U_15104) = c_Nat_Ocompow(U_15104,U_15104),
inference(variable_rename,[status(thm)],[f_3826_1]) ).
cnf(f_3826_3,plain,
c_Nat_Ofunpow(U_15104) = c_Nat_Ocompow(U_15104,U_15104),
inference(clausify,[status(thm)],[f_3826_2]) ).
fof(f_3827_1,plain,
! [V_R_2,V_na_2,V_z_2,V_x_2,T_b] :
( ? [B_y,B_m] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2)))
& V_na_2 = hAPP(c_Nat_OSuc,B_m) )
| ( V_x_2 = V_z_2
& V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_rel__pow__E]) ).
fof(f_3827_2,plain,
! [U_15111,U_15110,U_15109,U_15108,U_15107] :
( ? [U_15106,U_15105] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15107,U_15107)),hAPP(hAPP(c_Product__Type_OPair(U_15107,U_15107),U_15106),U_15109)),U_15111))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15107,U_15107)),hAPP(hAPP(c_Product__Type_OPair(U_15107,U_15107),U_15108),U_15106)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15107,U_15107),tc_HOL_Obool),U_15105),U_15111)))
& U_15110 = hAPP(c_Nat_OSuc,U_15105) )
| ( U_15108 = U_15109
& U_15110 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15107,U_15107)),hAPP(hAPP(c_Product__Type_OPair(U_15107,U_15107),U_15108),U_15109)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15107,U_15107),tc_HOL_Obool),U_15110),U_15111))) ),
inference(variable_rename,[status(thm)],[f_3827_1]) ).
fof(f_3827_3,plain,
! [U_15111,U_15110,U_15109,U_15108,U_15107] :
( ? [U_15105] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15107,U_15107)),hAPP(hAPP(c_Product__Type_OPair(U_15107,U_15107),sK374(U_15111,U_15110,U_15109,U_15108,U_15107)),U_15109)),U_15111))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15107,U_15107)),hAPP(hAPP(c_Product__Type_OPair(U_15107,U_15107),U_15108),sK374(U_15111,U_15110,U_15109,U_15108,U_15107))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15107,U_15107),tc_HOL_Obool),U_15105),U_15111)))
& U_15110 = hAPP(c_Nat_OSuc,U_15105) )
| ( U_15108 = U_15109
& U_15110 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15107,U_15107)),hAPP(hAPP(c_Product__Type_OPair(U_15107,U_15107),U_15108),U_15109)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15107,U_15107),tc_HOL_Obool),U_15110),U_15111))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK374]),skolemize(U_15106,sK374(U_15111,U_15110,U_15109,U_15108,U_15107))],[f_3827_2]) ).
fof(f_3827_4,plain,
! [U_15111,U_15110,U_15109,U_15108,U_15107] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15107,U_15107)),hAPP(hAPP(c_Product__Type_OPair(U_15107,U_15107),sK374(U_15111,U_15110,U_15109,U_15108,U_15107)),U_15109)),U_15111))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15107,U_15107)),hAPP(hAPP(c_Product__Type_OPair(U_15107,U_15107),U_15108),sK374(U_15111,U_15110,U_15109,U_15108,U_15107))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15107,U_15107),tc_HOL_Obool),sK375(U_15111,U_15110,U_15109,U_15108,U_15107)),U_15111)))
& U_15110 = hAPP(c_Nat_OSuc,sK375(U_15111,U_15110,U_15109,U_15108,U_15107)) )
| ( U_15108 = U_15109
& U_15110 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15107,U_15107)),hAPP(hAPP(c_Product__Type_OPair(U_15107,U_15107),U_15108),U_15109)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15107,U_15107),tc_HOL_Obool),U_15110),U_15111))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK375]),skolemize(U_15105,sK375(U_15111,U_15110,U_15109,U_15108,U_15107))],[f_3827_3]) ).
cnf(f_3827_5,plain,
( U_15110 = hAPP(c_Nat_OSuc,sK375(U_15111,U_15110,U_15109,U_15108,U_15107))
| U_15110 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15107,U_15107)),hAPP(hAPP(c_Product__Type_OPair(U_15107,U_15107),U_15108),U_15109)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15107,U_15107),tc_HOL_Obool),U_15110),U_15111))) ),
inference(clausify,[status(thm)],[f_3827_4]) ).
cnf(f_3827_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15107,U_15107)),hAPP(hAPP(c_Product__Type_OPair(U_15107,U_15107),U_15108),sK374(U_15111,U_15110,U_15109,U_15108,U_15107))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15107,U_15107),tc_HOL_Obool),sK375(U_15111,U_15110,U_15109,U_15108,U_15107)),U_15111)))
| U_15110 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15107,U_15107)),hAPP(hAPP(c_Product__Type_OPair(U_15107,U_15107),U_15108),U_15109)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15107,U_15107),tc_HOL_Obool),U_15110),U_15111))) ),
inference(clausify,[status(thm)],[f_3827_4]) ).
cnf(f_3827_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15107,U_15107)),hAPP(hAPP(c_Product__Type_OPair(U_15107,U_15107),sK374(U_15111,U_15110,U_15109,U_15108,U_15107)),U_15109)),U_15111))
| U_15110 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15107,U_15107)),hAPP(hAPP(c_Product__Type_OPair(U_15107,U_15107),U_15108),U_15109)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15107,U_15107),tc_HOL_Obool),U_15110),U_15111))) ),
inference(clausify,[status(thm)],[f_3827_4]) ).
cnf(f_3827_8,plain,
( U_15110 = hAPP(c_Nat_OSuc,sK375(U_15111,U_15110,U_15109,U_15108,U_15107))
| U_15108 = U_15109
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15107,U_15107)),hAPP(hAPP(c_Product__Type_OPair(U_15107,U_15107),U_15108),U_15109)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15107,U_15107),tc_HOL_Obool),U_15110),U_15111))) ),
inference(clausify,[status(thm)],[f_3827_4]) ).
cnf(f_3827_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15107,U_15107)),hAPP(hAPP(c_Product__Type_OPair(U_15107,U_15107),U_15108),sK374(U_15111,U_15110,U_15109,U_15108,U_15107))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15107,U_15107),tc_HOL_Obool),sK375(U_15111,U_15110,U_15109,U_15108,U_15107)),U_15111)))
| U_15108 = U_15109
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15107,U_15107)),hAPP(hAPP(c_Product__Type_OPair(U_15107,U_15107),U_15108),U_15109)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15107,U_15107),tc_HOL_Obool),U_15110),U_15111))) ),
inference(clausify,[status(thm)],[f_3827_4]) ).
cnf(f_3827_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15107,U_15107)),hAPP(hAPP(c_Product__Type_OPair(U_15107,U_15107),sK374(U_15111,U_15110,U_15109,U_15108,U_15107)),U_15109)),U_15111))
| U_15108 = U_15109
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15107,U_15107)),hAPP(hAPP(c_Product__Type_OPair(U_15107,U_15107),U_15108),U_15109)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15107,U_15107),tc_HOL_Obool),U_15110),U_15111))) ),
inference(clausify,[status(thm)],[f_3827_4]) ).
fof(f_3828_1,plain,
! [V_R_2,V_na_2,V_z_2,V_x_2,T_b] :
( ? [B_y,B_m] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
& V_na_2 = hAPP(c_Nat_OSuc,B_m) )
| ( V_x_2 = V_z_2
& V_na_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_rel__pow__E2]) ).
fof(f_3828_2,plain,
! [U_15118,U_15117,U_15116,U_15115,U_15114] :
( ? [U_15113,U_15112] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),U_15113),U_15116)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15114,U_15114),tc_HOL_Obool),U_15112),U_15118)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),U_15115),U_15113)),U_15118))
& U_15117 = hAPP(c_Nat_OSuc,U_15112) )
| ( U_15115 = U_15116
& U_15117 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),U_15115),U_15116)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15114,U_15114),tc_HOL_Obool),U_15117),U_15118))) ),
inference(variable_rename,[status(thm)],[f_3828_1]) ).
fof(f_3828_3,plain,
! [U_15118,U_15117,U_15116,U_15115,U_15114] :
( ? [U_15112] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),sK376(U_15118,U_15117,U_15116,U_15115,U_15114)),U_15116)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15114,U_15114),tc_HOL_Obool),U_15112),U_15118)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),U_15115),sK376(U_15118,U_15117,U_15116,U_15115,U_15114))),U_15118))
& U_15117 = hAPP(c_Nat_OSuc,U_15112) )
| ( U_15115 = U_15116
& U_15117 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),U_15115),U_15116)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15114,U_15114),tc_HOL_Obool),U_15117),U_15118))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK376]),skolemize(U_15113,sK376(U_15118,U_15117,U_15116,U_15115,U_15114))],[f_3828_2]) ).
fof(f_3828_4,plain,
! [U_15118,U_15117,U_15116,U_15115,U_15114] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),sK376(U_15118,U_15117,U_15116,U_15115,U_15114)),U_15116)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15114,U_15114),tc_HOL_Obool),sK377(U_15118,U_15117,U_15116,U_15115,U_15114)),U_15118)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),U_15115),sK376(U_15118,U_15117,U_15116,U_15115,U_15114))),U_15118))
& U_15117 = hAPP(c_Nat_OSuc,sK377(U_15118,U_15117,U_15116,U_15115,U_15114)) )
| ( U_15115 = U_15116
& U_15117 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),U_15115),U_15116)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15114,U_15114),tc_HOL_Obool),U_15117),U_15118))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK377]),skolemize(U_15112,sK377(U_15118,U_15117,U_15116,U_15115,U_15114))],[f_3828_3]) ).
cnf(f_3828_5,plain,
( U_15117 = hAPP(c_Nat_OSuc,sK377(U_15118,U_15117,U_15116,U_15115,U_15114))
| U_15117 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),U_15115),U_15116)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15114,U_15114),tc_HOL_Obool),U_15117),U_15118))) ),
inference(clausify,[status(thm)],[f_3828_4]) ).
cnf(f_3828_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),U_15115),sK376(U_15118,U_15117,U_15116,U_15115,U_15114))),U_15118))
| U_15117 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),U_15115),U_15116)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15114,U_15114),tc_HOL_Obool),U_15117),U_15118))) ),
inference(clausify,[status(thm)],[f_3828_4]) ).
cnf(f_3828_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),sK376(U_15118,U_15117,U_15116,U_15115,U_15114)),U_15116)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15114,U_15114),tc_HOL_Obool),sK377(U_15118,U_15117,U_15116,U_15115,U_15114)),U_15118)))
| U_15117 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),U_15115),U_15116)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15114,U_15114),tc_HOL_Obool),U_15117),U_15118))) ),
inference(clausify,[status(thm)],[f_3828_4]) ).
cnf(f_3828_8,plain,
( U_15117 = hAPP(c_Nat_OSuc,sK377(U_15118,U_15117,U_15116,U_15115,U_15114))
| U_15115 = U_15116
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),U_15115),U_15116)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15114,U_15114),tc_HOL_Obool),U_15117),U_15118))) ),
inference(clausify,[status(thm)],[f_3828_4]) ).
cnf(f_3828_9,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),U_15115),sK376(U_15118,U_15117,U_15116,U_15115,U_15114))),U_15118))
| U_15115 = U_15116
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),U_15115),U_15116)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15114,U_15114),tc_HOL_Obool),U_15117),U_15118))) ),
inference(clausify,[status(thm)],[f_3828_4]) ).
cnf(f_3828_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),sK376(U_15118,U_15117,U_15116,U_15115,U_15114)),U_15116)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15114,U_15114),tc_HOL_Obool),sK377(U_15118,U_15117,U_15116,U_15115,U_15114)),U_15118)))
| U_15115 = U_15116
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15114,U_15114)),hAPP(hAPP(c_Product__Type_OPair(U_15114,U_15114),U_15115),U_15116)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15114,U_15114),tc_HOL_Obool),U_15117),U_15118))) ),
inference(clausify,[status(thm)],[f_3828_4]) ).
fof(f_3829_1,plain,
! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
| ? [B_x] :
( ? [B_y] :
( B_x != B_y
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_Q_2)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2)))) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separatorE]) ).
fof(f_3829_2,plain,
! [U_15125,U_15124,U_15123,U_15122,U_15121] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15121,U_15121)),hAPP(hAPP(c_Product__Type_OPair(U_15121,U_15121),U_15122),U_15123)),c_Transitive__Closure_Ortrancl(U_15121,U_15124)))
| ? [U_15120] :
( ? [U_15119] :
( U_15120 != U_15119
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15121,U_15121)),hAPP(hAPP(c_Product__Type_OPair(U_15121,U_15121),U_15120),U_15119)),U_15125)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15121,U_15121)),hAPP(hAPP(c_Product__Type_OPair(U_15121,U_15121),U_15122),U_15120)),c_Transitive__Closure_Ortrancl(U_15121,U_15124))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15121,U_15121)),hAPP(hAPP(c_Product__Type_OPair(U_15121,U_15121),U_15122),U_15123)),c_Transitive__Closure_Ortrancl(U_15121,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15121,U_15121),tc_HOL_Obool)),U_15124),U_15125)))) ),
inference(variable_rename,[status(thm)],[f_3829_1]) ).
fof(f_3829_3,plain,
! [U_15125,U_15124,U_15123,U_15122,U_15121] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15121,U_15121)),hAPP(hAPP(c_Product__Type_OPair(U_15121,U_15121),U_15122),U_15123)),c_Transitive__Closure_Ortrancl(U_15121,U_15124)))
| ( ? [U_15119] :
( sK378(U_15125,U_15124,U_15123,U_15122,U_15121) != U_15119
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15121,U_15121)),hAPP(hAPP(c_Product__Type_OPair(U_15121,U_15121),sK378(U_15125,U_15124,U_15123,U_15122,U_15121)),U_15119)),U_15125)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15121,U_15121)),hAPP(hAPP(c_Product__Type_OPair(U_15121,U_15121),U_15122),sK378(U_15125,U_15124,U_15123,U_15122,U_15121))),c_Transitive__Closure_Ortrancl(U_15121,U_15124))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15121,U_15121)),hAPP(hAPP(c_Product__Type_OPair(U_15121,U_15121),U_15122),U_15123)),c_Transitive__Closure_Ortrancl(U_15121,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15121,U_15121),tc_HOL_Obool)),U_15124),U_15125)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK378]),skolemize(U_15120,sK378(U_15125,U_15124,U_15123,U_15122,U_15121))],[f_3829_2]) ).
fof(f_3829_4,plain,
! [U_15125,U_15124,U_15123,U_15122,U_15121] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15121,U_15121)),hAPP(hAPP(c_Product__Type_OPair(U_15121,U_15121),U_15122),U_15123)),c_Transitive__Closure_Ortrancl(U_15121,U_15124)))
| ( sK378(U_15125,U_15124,U_15123,U_15122,U_15121) != sK379(U_15125,U_15124,U_15123,U_15122,U_15121)
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15121,U_15121)),hAPP(hAPP(c_Product__Type_OPair(U_15121,U_15121),sK378(U_15125,U_15124,U_15123,U_15122,U_15121)),sK379(U_15125,U_15124,U_15123,U_15122,U_15121))),U_15125))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15121,U_15121)),hAPP(hAPP(c_Product__Type_OPair(U_15121,U_15121),U_15122),sK378(U_15125,U_15124,U_15123,U_15122,U_15121))),c_Transitive__Closure_Ortrancl(U_15121,U_15124))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15121,U_15121)),hAPP(hAPP(c_Product__Type_OPair(U_15121,U_15121),U_15122),U_15123)),c_Transitive__Closure_Ortrancl(U_15121,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15121,U_15121),tc_HOL_Obool)),U_15124),U_15125)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK379]),skolemize(U_15119,sK379(U_15125,U_15124,U_15123,U_15122,U_15121))],[f_3829_3]) ).
cnf(f_3829_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15121,U_15121)),hAPP(hAPP(c_Product__Type_OPair(U_15121,U_15121),U_15122),sK378(U_15125,U_15124,U_15123,U_15122,U_15121))),c_Transitive__Closure_Ortrancl(U_15121,U_15124)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_15121,U_15121)),hAPP(hAPP(c_Product__Type_OPair(U_15121,U_15121),U_15122),U_15123)),c_Transitive__Closure_Ortrancl(U_15121,U_15124)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15121,U_15121)),hAPP(hAPP(c_Product__Type_OPair(U_15121,U_15121),U_15122),U_15123)),c_Transitive__Closure_Ortrancl(U_15121,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15121,U_15121),tc_HOL_Obool)),U_15124),U_15125)))) ),
inference(clausify,[status(thm)],[f_3829_4]) ).
cnf(f_3829_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15121,U_15121)),hAPP(hAPP(c_Product__Type_OPair(U_15121,U_15121),sK378(U_15125,U_15124,U_15123,U_15122,U_15121)),sK379(U_15125,U_15124,U_15123,U_15122,U_15121))),U_15125))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_15121,U_15121)),hAPP(hAPP(c_Product__Type_OPair(U_15121,U_15121),U_15122),U_15123)),c_Transitive__Closure_Ortrancl(U_15121,U_15124)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15121,U_15121)),hAPP(hAPP(c_Product__Type_OPair(U_15121,U_15121),U_15122),U_15123)),c_Transitive__Closure_Ortrancl(U_15121,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15121,U_15121),tc_HOL_Obool)),U_15124),U_15125)))) ),
inference(clausify,[status(thm)],[f_3829_4]) ).
cnf(f_3829_7,plain,
( sK378(U_15125,U_15124,U_15123,U_15122,U_15121) != sK379(U_15125,U_15124,U_15123,U_15122,U_15121)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_15121,U_15121)),hAPP(hAPP(c_Product__Type_OPair(U_15121,U_15121),U_15122),U_15123)),c_Transitive__Closure_Ortrancl(U_15121,U_15124)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15121,U_15121)),hAPP(hAPP(c_Product__Type_OPair(U_15121,U_15121),U_15122),U_15123)),c_Transitive__Closure_Ortrancl(U_15121,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15121,U_15121),tc_HOL_Obool)),U_15124),U_15125)))) ),
inference(clausify,[status(thm)],[f_3829_4]) ).
fof(f_3830_1,plain,
! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
| ? [B_x] :
( ? [B_y] :
( B_y != B_x
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_Q_2)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2)))) ),
inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separator__converseE]) ).
fof(f_3830_2,plain,
! [U_15132,U_15131,U_15130,U_15129,U_15128] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15128,U_15128)),hAPP(hAPP(c_Product__Type_OPair(U_15128,U_15128),U_15129),U_15130)),c_Transitive__Closure_Ortrancl(U_15128,U_15131)))
| ? [U_15127] :
( ? [U_15126] :
( U_15126 != U_15127
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15128,U_15128)),hAPP(hAPP(c_Product__Type_OPair(U_15128,U_15128),U_15126),U_15127)),U_15132)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15128,U_15128)),hAPP(hAPP(c_Product__Type_OPair(U_15128,U_15128),U_15127),U_15130)),c_Transitive__Closure_Ortrancl(U_15128,U_15131))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15128,U_15128)),hAPP(hAPP(c_Product__Type_OPair(U_15128,U_15128),U_15129),U_15130)),c_Transitive__Closure_Ortrancl(U_15128,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15128,U_15128),tc_HOL_Obool)),U_15131),U_15132)))) ),
inference(variable_rename,[status(thm)],[f_3830_1]) ).
fof(f_3830_3,plain,
! [U_15132,U_15131,U_15130,U_15129,U_15128] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15128,U_15128)),hAPP(hAPP(c_Product__Type_OPair(U_15128,U_15128),U_15129),U_15130)),c_Transitive__Closure_Ortrancl(U_15128,U_15131)))
| ( ? [U_15126] :
( U_15126 != sK380(U_15132,U_15131,U_15130,U_15129,U_15128)
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15128,U_15128)),hAPP(hAPP(c_Product__Type_OPair(U_15128,U_15128),U_15126),sK380(U_15132,U_15131,U_15130,U_15129,U_15128))),U_15132)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15128,U_15128)),hAPP(hAPP(c_Product__Type_OPair(U_15128,U_15128),sK380(U_15132,U_15131,U_15130,U_15129,U_15128)),U_15130)),c_Transitive__Closure_Ortrancl(U_15128,U_15131))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15128,U_15128)),hAPP(hAPP(c_Product__Type_OPair(U_15128,U_15128),U_15129),U_15130)),c_Transitive__Closure_Ortrancl(U_15128,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15128,U_15128),tc_HOL_Obool)),U_15131),U_15132)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK380]),skolemize(U_15127,sK380(U_15132,U_15131,U_15130,U_15129,U_15128))],[f_3830_2]) ).
fof(f_3830_4,plain,
! [U_15132,U_15131,U_15130,U_15129,U_15128] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15128,U_15128)),hAPP(hAPP(c_Product__Type_OPair(U_15128,U_15128),U_15129),U_15130)),c_Transitive__Closure_Ortrancl(U_15128,U_15131)))
| ( sK381(U_15132,U_15131,U_15130,U_15129,U_15128) != sK380(U_15132,U_15131,U_15130,U_15129,U_15128)
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15128,U_15128)),hAPP(hAPP(c_Product__Type_OPair(U_15128,U_15128),sK381(U_15132,U_15131,U_15130,U_15129,U_15128)),sK380(U_15132,U_15131,U_15130,U_15129,U_15128))),U_15132))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15128,U_15128)),hAPP(hAPP(c_Product__Type_OPair(U_15128,U_15128),sK380(U_15132,U_15131,U_15130,U_15129,U_15128)),U_15130)),c_Transitive__Closure_Ortrancl(U_15128,U_15131))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15128,U_15128)),hAPP(hAPP(c_Product__Type_OPair(U_15128,U_15128),U_15129),U_15130)),c_Transitive__Closure_Ortrancl(U_15128,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15128,U_15128),tc_HOL_Obool)),U_15131),U_15132)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK381]),skolemize(U_15126,sK381(U_15132,U_15131,U_15130,U_15129,U_15128))],[f_3830_3]) ).
cnf(f_3830_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15128,U_15128)),hAPP(hAPP(c_Product__Type_OPair(U_15128,U_15128),sK380(U_15132,U_15131,U_15130,U_15129,U_15128)),U_15130)),c_Transitive__Closure_Ortrancl(U_15128,U_15131)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_15128,U_15128)),hAPP(hAPP(c_Product__Type_OPair(U_15128,U_15128),U_15129),U_15130)),c_Transitive__Closure_Ortrancl(U_15128,U_15131)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15128,U_15128)),hAPP(hAPP(c_Product__Type_OPair(U_15128,U_15128),U_15129),U_15130)),c_Transitive__Closure_Ortrancl(U_15128,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15128,U_15128),tc_HOL_Obool)),U_15131),U_15132)))) ),
inference(clausify,[status(thm)],[f_3830_4]) ).
cnf(f_3830_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15128,U_15128)),hAPP(hAPP(c_Product__Type_OPair(U_15128,U_15128),sK381(U_15132,U_15131,U_15130,U_15129,U_15128)),sK380(U_15132,U_15131,U_15130,U_15129,U_15128))),U_15132))
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_15128,U_15128)),hAPP(hAPP(c_Product__Type_OPair(U_15128,U_15128),U_15129),U_15130)),c_Transitive__Closure_Ortrancl(U_15128,U_15131)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15128,U_15128)),hAPP(hAPP(c_Product__Type_OPair(U_15128,U_15128),U_15129),U_15130)),c_Transitive__Closure_Ortrancl(U_15128,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15128,U_15128),tc_HOL_Obool)),U_15131),U_15132)))) ),
inference(clausify,[status(thm)],[f_3830_4]) ).
cnf(f_3830_7,plain,
( sK381(U_15132,U_15131,U_15130,U_15129,U_15128) != sK380(U_15132,U_15131,U_15130,U_15129,U_15128)
| hBOOL(hAPP(hAPP(c_member(tc_prod(U_15128,U_15128)),hAPP(hAPP(c_Product__Type_OPair(U_15128,U_15128),U_15129),U_15130)),c_Transitive__Closure_Ortrancl(U_15128,U_15131)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15128,U_15128)),hAPP(hAPP(c_Product__Type_OPair(U_15128,U_15128),U_15129),U_15130)),c_Transitive__Closure_Ortrancl(U_15128,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15128,U_15128),tc_HOL_Obool)),U_15131),U_15132)))) ),
inference(clausify,[status(thm)],[f_3830_4]) ).
fof(f_3831_1,plain,
! [V_R_2,V_na_2,V_z_2,V_x_2,T_b] :
( ? [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_na_2)),V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__E]) ).
fof(f_3831_2,plain,
! [U_15138,U_15137,U_15136,U_15135,U_15134] :
( ? [U_15133] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15134,U_15134)),hAPP(hAPP(c_Product__Type_OPair(U_15134,U_15134),U_15133),U_15136)),U_15138))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15134,U_15134)),hAPP(hAPP(c_Product__Type_OPair(U_15134,U_15134),U_15135),U_15133)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15134,U_15134),tc_HOL_Obool),U_15137),U_15138))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15134,U_15134)),hAPP(hAPP(c_Product__Type_OPair(U_15134,U_15134),U_15135),U_15136)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15134,U_15134),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15137)),U_15138))) ),
inference(variable_rename,[status(thm)],[f_3831_1]) ).
fof(f_3831_3,plain,
! [U_15138,U_15137,U_15136,U_15135,U_15134] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15134,U_15134)),hAPP(hAPP(c_Product__Type_OPair(U_15134,U_15134),sK382(U_15138,U_15137,U_15136,U_15135,U_15134)),U_15136)),U_15138))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15134,U_15134)),hAPP(hAPP(c_Product__Type_OPair(U_15134,U_15134),U_15135),sK382(U_15138,U_15137,U_15136,U_15135,U_15134))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15134,U_15134),tc_HOL_Obool),U_15137),U_15138))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15134,U_15134)),hAPP(hAPP(c_Product__Type_OPair(U_15134,U_15134),U_15135),U_15136)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15134,U_15134),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15137)),U_15138))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK382]),skolemize(U_15133,sK382(U_15138,U_15137,U_15136,U_15135,U_15134))],[f_3831_2]) ).
cnf(f_3831_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15134,U_15134)),hAPP(hAPP(c_Product__Type_OPair(U_15134,U_15134),U_15135),sK382(U_15138,U_15137,U_15136,U_15135,U_15134))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15134,U_15134),tc_HOL_Obool),U_15137),U_15138)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15134,U_15134)),hAPP(hAPP(c_Product__Type_OPair(U_15134,U_15134),U_15135),U_15136)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15134,U_15134),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15137)),U_15138))) ),
inference(clausify,[status(thm)],[f_3831_3]) ).
cnf(f_3831_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15134,U_15134)),hAPP(hAPP(c_Product__Type_OPair(U_15134,U_15134),sK382(U_15138,U_15137,U_15136,U_15135,U_15134)),U_15136)),U_15138))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15134,U_15134)),hAPP(hAPP(c_Product__Type_OPair(U_15134,U_15134),U_15135),U_15136)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15134,U_15134),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15137)),U_15138))) ),
inference(clausify,[status(thm)],[f_3831_3]) ).
fof(f_3832_1,plain,
! [V_R_2,V_na_2,V_z_2,V_x_2,T_b] :
( ? [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_na_2)),V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__D2]) ).
fof(f_3832_2,plain,
! [U_15144,U_15143,U_15142,U_15141,U_15140] :
( ? [U_15139] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15140,U_15140)),hAPP(hAPP(c_Product__Type_OPair(U_15140,U_15140),U_15139),U_15142)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15140,U_15140),tc_HOL_Obool),U_15143),U_15144)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15140,U_15140)),hAPP(hAPP(c_Product__Type_OPair(U_15140,U_15140),U_15141),U_15139)),U_15144)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15140,U_15140)),hAPP(hAPP(c_Product__Type_OPair(U_15140,U_15140),U_15141),U_15142)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15140,U_15140),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15143)),U_15144))) ),
inference(variable_rename,[status(thm)],[f_3832_1]) ).
fof(f_3832_3,plain,
! [U_15144,U_15143,U_15142,U_15141,U_15140] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15140,U_15140)),hAPP(hAPP(c_Product__Type_OPair(U_15140,U_15140),sK383(U_15144,U_15143,U_15142,U_15141,U_15140)),U_15142)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15140,U_15140),tc_HOL_Obool),U_15143),U_15144)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15140,U_15140)),hAPP(hAPP(c_Product__Type_OPair(U_15140,U_15140),U_15141),sK383(U_15144,U_15143,U_15142,U_15141,U_15140))),U_15144)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15140,U_15140)),hAPP(hAPP(c_Product__Type_OPair(U_15140,U_15140),U_15141),U_15142)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15140,U_15140),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15143)),U_15144))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK383]),skolemize(U_15139,sK383(U_15144,U_15143,U_15142,U_15141,U_15140))],[f_3832_2]) ).
cnf(f_3832_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15140,U_15140)),hAPP(hAPP(c_Product__Type_OPair(U_15140,U_15140),U_15141),sK383(U_15144,U_15143,U_15142,U_15141,U_15140))),U_15144))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15140,U_15140)),hAPP(hAPP(c_Product__Type_OPair(U_15140,U_15140),U_15141),U_15142)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15140,U_15140),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15143)),U_15144))) ),
inference(clausify,[status(thm)],[f_3832_3]) ).
cnf(f_3832_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15140,U_15140)),hAPP(hAPP(c_Product__Type_OPair(U_15140,U_15140),sK383(U_15144,U_15143,U_15142,U_15141,U_15140)),U_15142)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15140,U_15140),tc_HOL_Obool),U_15143),U_15144)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15140,U_15140)),hAPP(hAPP(c_Product__Type_OPair(U_15140,U_15140),U_15141),U_15142)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15140,U_15140),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15143)),U_15144))) ),
inference(clausify,[status(thm)],[f_3832_3]) ).
fof(f_3833_1,plain,
! [V_R_2,V_na_2,V_z_2,V_x_2,T_b] :
( ? [B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_na_2),V_R_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_na_2)),V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__E2]) ).
fof(f_3833_2,plain,
! [U_15150,U_15149,U_15148,U_15147,U_15146] :
( ? [U_15145] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15146,U_15146)),hAPP(hAPP(c_Product__Type_OPair(U_15146,U_15146),U_15145),U_15148)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15146,U_15146),tc_HOL_Obool),U_15149),U_15150)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15146,U_15146)),hAPP(hAPP(c_Product__Type_OPair(U_15146,U_15146),U_15147),U_15145)),U_15150)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15146,U_15146)),hAPP(hAPP(c_Product__Type_OPair(U_15146,U_15146),U_15147),U_15148)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15146,U_15146),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15149)),U_15150))) ),
inference(variable_rename,[status(thm)],[f_3833_1]) ).
fof(f_3833_3,plain,
! [U_15150,U_15149,U_15148,U_15147,U_15146] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15146,U_15146)),hAPP(hAPP(c_Product__Type_OPair(U_15146,U_15146),sK384(U_15150,U_15149,U_15148,U_15147,U_15146)),U_15148)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15146,U_15146),tc_HOL_Obool),U_15149),U_15150)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15146,U_15146)),hAPP(hAPP(c_Product__Type_OPair(U_15146,U_15146),U_15147),sK384(U_15150,U_15149,U_15148,U_15147,U_15146))),U_15150)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15146,U_15146)),hAPP(hAPP(c_Product__Type_OPair(U_15146,U_15146),U_15147),U_15148)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15146,U_15146),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15149)),U_15150))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK384]),skolemize(U_15145,sK384(U_15150,U_15149,U_15148,U_15147,U_15146))],[f_3833_2]) ).
cnf(f_3833_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15146,U_15146)),hAPP(hAPP(c_Product__Type_OPair(U_15146,U_15146),U_15147),sK384(U_15150,U_15149,U_15148,U_15147,U_15146))),U_15150))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15146,U_15146)),hAPP(hAPP(c_Product__Type_OPair(U_15146,U_15146),U_15147),U_15148)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15146,U_15146),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15149)),U_15150))) ),
inference(clausify,[status(thm)],[f_3833_3]) ).
cnf(f_3833_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15146,U_15146)),hAPP(hAPP(c_Product__Type_OPair(U_15146,U_15146),sK384(U_15150,U_15149,U_15148,U_15147,U_15146)),U_15148)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15146,U_15146),tc_HOL_Obool),U_15149),U_15150)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15146,U_15146)),hAPP(hAPP(c_Product__Type_OPair(U_15146,U_15146),U_15147),U_15148)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15146,U_15146),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15149)),U_15150))) ),
inference(clausify,[status(thm)],[f_3833_3]) ).
fof(f_3834_1,plain,
! [V_R_2,V_y_2,V_x_2,T_b] :
( ? [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),V_R_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_tranclD]) ).
fof(f_3834_2,plain,
! [U_15155,U_15154,U_15153,U_15152] :
( ? [U_15151] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15152,U_15152)),hAPP(hAPP(c_Product__Type_OPair(U_15152,U_15152),U_15151),U_15154)),c_Transitive__Closure_Ortrancl(U_15152,U_15155)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15152,U_15152)),hAPP(hAPP(c_Product__Type_OPair(U_15152,U_15152),U_15153),U_15151)),U_15155)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15152,U_15152)),hAPP(hAPP(c_Product__Type_OPair(U_15152,U_15152),U_15153),U_15154)),c_Transitive__Closure_Otrancl(U_15152,U_15155))) ),
inference(variable_rename,[status(thm)],[f_3834_1]) ).
fof(f_3834_3,plain,
! [U_15155,U_15154,U_15153,U_15152] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15152,U_15152)),hAPP(hAPP(c_Product__Type_OPair(U_15152,U_15152),sK385(U_15155,U_15154,U_15153,U_15152)),U_15154)),c_Transitive__Closure_Ortrancl(U_15152,U_15155)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15152,U_15152)),hAPP(hAPP(c_Product__Type_OPair(U_15152,U_15152),U_15153),sK385(U_15155,U_15154,U_15153,U_15152))),U_15155)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15152,U_15152)),hAPP(hAPP(c_Product__Type_OPair(U_15152,U_15152),U_15153),U_15154)),c_Transitive__Closure_Otrancl(U_15152,U_15155))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK385]),skolemize(U_15151,sK385(U_15155,U_15154,U_15153,U_15152))],[f_3834_2]) ).
cnf(f_3834_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15152,U_15152)),hAPP(hAPP(c_Product__Type_OPair(U_15152,U_15152),U_15153),sK385(U_15155,U_15154,U_15153,U_15152))),U_15155))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15152,U_15152)),hAPP(hAPP(c_Product__Type_OPair(U_15152,U_15152),U_15153),U_15154)),c_Transitive__Closure_Otrancl(U_15152,U_15155))) ),
inference(clausify,[status(thm)],[f_3834_3]) ).
cnf(f_3834_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15152,U_15152)),hAPP(hAPP(c_Product__Type_OPair(U_15152,U_15152),sK385(U_15155,U_15154,U_15153,U_15152)),U_15154)),c_Transitive__Closure_Ortrancl(U_15152,U_15155)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15152,U_15152)),hAPP(hAPP(c_Product__Type_OPair(U_15152,U_15152),U_15153),U_15154)),c_Transitive__Closure_Otrancl(U_15152,U_15155))) ),
inference(clausify,[status(thm)],[f_3834_3]) ).
fof(f_3835_1,plain,
! [V_R_2,V_y_2,V_x_2,T_b] :
( ? [B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),V_R_2))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ),
inference(fof_nnf,[status(thm)],[fact_tranclD2]) ).
fof(f_3835_2,plain,
! [U_15160,U_15159,U_15158,U_15157] :
( ? [U_15156] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15157,U_15157)),hAPP(hAPP(c_Product__Type_OPair(U_15157,U_15157),U_15156),U_15159)),U_15160))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15157,U_15157)),hAPP(hAPP(c_Product__Type_OPair(U_15157,U_15157),U_15158),U_15156)),c_Transitive__Closure_Ortrancl(U_15157,U_15160))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15157,U_15157)),hAPP(hAPP(c_Product__Type_OPair(U_15157,U_15157),U_15158),U_15159)),c_Transitive__Closure_Otrancl(U_15157,U_15160))) ),
inference(variable_rename,[status(thm)],[f_3835_1]) ).
fof(f_3835_3,plain,
! [U_15160,U_15159,U_15158,U_15157] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15157,U_15157)),hAPP(hAPP(c_Product__Type_OPair(U_15157,U_15157),sK386(U_15160,U_15159,U_15158,U_15157)),U_15159)),U_15160))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15157,U_15157)),hAPP(hAPP(c_Product__Type_OPair(U_15157,U_15157),U_15158),sK386(U_15160,U_15159,U_15158,U_15157))),c_Transitive__Closure_Ortrancl(U_15157,U_15160))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15157,U_15157)),hAPP(hAPP(c_Product__Type_OPair(U_15157,U_15157),U_15158),U_15159)),c_Transitive__Closure_Otrancl(U_15157,U_15160))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK386]),skolemize(U_15156,sK386(U_15160,U_15159,U_15158,U_15157))],[f_3835_2]) ).
cnf(f_3835_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15157,U_15157)),hAPP(hAPP(c_Product__Type_OPair(U_15157,U_15157),U_15158),sK386(U_15160,U_15159,U_15158,U_15157))),c_Transitive__Closure_Ortrancl(U_15157,U_15160)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15157,U_15157)),hAPP(hAPP(c_Product__Type_OPair(U_15157,U_15157),U_15158),U_15159)),c_Transitive__Closure_Otrancl(U_15157,U_15160))) ),
inference(clausify,[status(thm)],[f_3835_3]) ).
cnf(f_3835_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15157,U_15157)),hAPP(hAPP(c_Product__Type_OPair(U_15157,U_15157),sK386(U_15160,U_15159,U_15158,U_15157)),U_15159)),U_15160))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15157,U_15157)),hAPP(hAPP(c_Product__Type_OPair(U_15157,U_15157),U_15158),U_15159)),c_Transitive__Closure_Otrancl(U_15157,U_15160))) ),
inference(clausify,[status(thm)],[f_3835_3]) ).
fof(f_3836_1,plain,
! [V_p_2,T_b] :
( ? [B_x] : V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b))) ),
inference(fof_nnf,[status(thm)],[fact_IdE]) ).
fof(f_3836_2,plain,
! [U_15163,U_15162] :
( ? [U_15161] : U_15163 = hAPP(hAPP(c_Product__Type_OPair(U_15162,U_15162),U_15161),U_15161)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15162,U_15162)),U_15163),c_Relation_OId(U_15162))) ),
inference(variable_rename,[status(thm)],[f_3836_1]) ).
fof(f_3836_3,plain,
! [U_15163,U_15162] :
( U_15163 = hAPP(hAPP(c_Product__Type_OPair(U_15162,U_15162),sK387(U_15163,U_15162)),sK387(U_15163,U_15162))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15162,U_15162)),U_15163),c_Relation_OId(U_15162))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK387]),skolemize(U_15161,sK387(U_15163,U_15162))],[f_3836_2]) ).
cnf(f_3836_4,plain,
( U_15163 = hAPP(hAPP(c_Product__Type_OPair(U_15162,U_15162),sK387(U_15163,U_15162)),sK387(U_15163,U_15162))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15162,U_15162)),U_15163),c_Relation_OId(U_15162))) ),
inference(clausify,[status(thm)],[f_3836_3]) ).
fof(f_3837_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold_H]) ).
fof(f_3837_2,plain,
! [U_15166,U_15165,U_15164] :
( c_Big__Operators_Olattice_OSup__fin(U_15164,c_Orderings_Oord__class_Omax(U_15164),hAPP(hAPP(c_Set_Oinsert(U_15164),U_15166),U_15165)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15164,U_15164,c_Orderings_Oord__class_Omax(U_15164)),U_15166),U_15165)
| hBOOL(hAPP(hAPP(c_member(U_15164),U_15166),U_15165))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15164),U_15165))
| ~ class_Orderings_Olinorder(U_15164) ),
inference(variable_rename,[status(thm)],[f_3837_1]) ).
cnf(f_3837_3,plain,
( c_Big__Operators_Olattice_OSup__fin(U_15164,c_Orderings_Oord__class_Omax(U_15164),hAPP(hAPP(c_Set_Oinsert(U_15164),U_15166),U_15165)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15164,U_15164,c_Orderings_Oord__class_Omax(U_15164)),U_15166),U_15165)
| hBOOL(hAPP(hAPP(c_member(U_15164),U_15166),U_15165))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15164),U_15165))
| ~ class_Orderings_Olinorder(U_15164) ),
inference(clausify,[status(thm)],[f_3837_2]) ).
fof(f_3838_1,plain,
! [V_g_2,V_f_2,T_c,T_b] : hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_c,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),
inference(fof_nnf,[status(thm)],[fact_fold__image__def]) ).
fof(f_3838_2,plain,
! [U_15170,U_15169,U_15168,U_15167] : hAPP(c_Finite__Set_Ofold__image(U_15167,U_15168,U_15169),U_15170) = c_Finite__Set_Ofold(U_15168,U_15167,hAPP(hAPP(c_COMBB(U_15167,tc_fun(U_15167,U_15167),U_15168),U_15169),U_15170)),
inference(variable_rename,[status(thm)],[f_3838_1]) ).
cnf(f_3838_3,plain,
hAPP(c_Finite__Set_Ofold__image(U_15167,U_15168,U_15169),U_15170) = c_Finite__Set_Ofold(U_15168,U_15167,hAPP(hAPP(c_COMBB(U_15167,tc_fun(U_15167,U_15167),U_15168),U_15169),U_15170)),
inference(clausify,[status(thm)],[f_3838_2]) ).
fof(f_3839_1,plain,
! [V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2,
inference(fof_nnf,[status(thm)],[fact_fold__empty]) ).
fof(f_3839_2,plain,
! [U_15174,U_15173,U_15172,U_15171] : hAPP(hAPP(c_Finite__Set_Ofold(U_15171,U_15172,U_15173),U_15174),c_Orderings_Obot__class_Obot(tc_fun(U_15171,tc_HOL_Obool))) = U_15174,
inference(variable_rename,[status(thm)],[f_3839_1]) ).
cnf(f_3839_3,plain,
hAPP(hAPP(c_Finite__Set_Ofold(U_15171,U_15172,U_15173),U_15174),c_Orderings_Obot__class_Obot(tc_fun(U_15171,tc_HOL_Obool))) = U_15174,
inference(clausify,[status(thm)],[f_3839_2]) ).
fof(f_3840_1,plain,
! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_s_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding_Oeq__fold]) ).
fof(f_3840_2,plain,
! [U_15180,U_15179,U_15178,U_15177,U_15176,U_15175] :
( hAPP(hAPP(U_15178,U_15179),U_15180) = hAPP(hAPP(c_Finite__Set_Ofold(U_15175,U_15176,U_15177),U_15180),U_15179)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15175),U_15179))
| ~ c_Finite__Set_Ofolding(U_15175,U_15176,U_15177,U_15178) ),
inference(variable_rename,[status(thm)],[f_3840_1]) ).
cnf(f_3840_3,plain,
( hAPP(hAPP(U_15178,U_15179),U_15180) = hAPP(hAPP(c_Finite__Set_Ofold(U_15175,U_15176,U_15177),U_15180),U_15179)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15175),U_15179))
| ~ c_Finite__Set_Ofolding(U_15175,U_15176,U_15177,U_15178) ),
inference(clausify,[status(thm)],[f_3840_2]) ).
fof(f_3841_1,plain,
! [V_A_2,V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold__graph(T_c,T_b,V_f_2,V_z_2,V_A_2)),
inference(fof_nnf,[status(thm)],[fact_fold__def]) ).
fof(f_3841_2,plain,
! [U_15185,U_15184,U_15183,U_15182,U_15181] : hAPP(hAPP(c_Finite__Set_Ofold(U_15181,U_15182,U_15183),U_15184),U_15185) = c_HOL_OThe(U_15182,c_Finite__Set_Ofold__graph(U_15181,U_15182,U_15183,U_15184,U_15185)),
inference(variable_rename,[status(thm)],[f_3841_1]) ).
cnf(f_3841_3,plain,
hAPP(hAPP(c_Finite__Set_Ofold(U_15181,U_15182,U_15183),U_15184),U_15185) = c_HOL_OThe(U_15182,c_Finite__Set_Ofold__graph(U_15181,U_15182,U_15183,U_15184,U_15185)),
inference(clausify,[status(thm)],[f_3841_2]) ).
fof(f_3842_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),V_B_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_union__fold__insert]) ).
fof(f_3842_2,plain,
! [U_15188,U_15187,U_15186] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15186,tc_HOL_Obool)),U_15187),U_15188) = hAPP(hAPP(c_Finite__Set_Ofold(U_15186,tc_fun(U_15186,tc_HOL_Obool),c_Set_Oinsert(U_15186)),U_15188),U_15187)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15186),U_15187)) ),
inference(variable_rename,[status(thm)],[f_3842_1]) ).
cnf(f_3842_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15186,tc_HOL_Obool)),U_15187),U_15188) = hAPP(hAPP(c_Finite__Set_Ofold(U_15186,tc_fun(U_15186,tc_HOL_Obool),c_Set_Oinsert(U_15186)),U_15188),U_15187)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15186),U_15187)) ),
inference(clausify,[status(thm)],[f_3842_2]) ).
fof(f_3843_1,plain,
! [V_a_2,V_b_2,V_A_2,T_b] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Osemilattice__sup(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold__sup__insert]) ).
fof(f_3843_2,plain,
! [U_15192,U_15191,U_15190,U_15189] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_15189,U_15189,c_Lattices_Osemilattice__sup__class_Osup(U_15189)),U_15191),hAPP(hAPP(c_Set_Oinsert(U_15189),U_15192),U_15190)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15189),U_15192),hAPP(hAPP(c_Finite__Set_Ofold(U_15189,U_15189,c_Lattices_Osemilattice__sup__class_Osup(U_15189)),U_15191),U_15190))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15189),U_15190))
| ~ class_Lattices_Osemilattice__sup(U_15189) ),
inference(variable_rename,[status(thm)],[f_3843_1]) ).
cnf(f_3843_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_15189,U_15189,c_Lattices_Osemilattice__sup__class_Osup(U_15189)),U_15191),hAPP(hAPP(c_Set_Oinsert(U_15189),U_15192),U_15190)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15189),U_15192),hAPP(hAPP(c_Finite__Set_Ofold(U_15189,U_15189,c_Lattices_Osemilattice__sup__class_Osup(U_15189)),U_15191),U_15190))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15189),U_15190))
| ~ class_Lattices_Osemilattice__sup(U_15189) ),
inference(clausify,[status(thm)],[f_3843_2]) ).
fof(f_3844_1,plain,
! [V_a_2,V_b_2,V_A_2,T_b] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Osemilattice__inf(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold__inf__insert]) ).
fof(f_3844_2,plain,
! [U_15196,U_15195,U_15194,U_15193] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_15193,U_15193,c_Lattices_Osemilattice__inf__class_Oinf(U_15193)),U_15195),hAPP(hAPP(c_Set_Oinsert(U_15193),U_15196),U_15194)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15193),U_15196),hAPP(hAPP(c_Finite__Set_Ofold(U_15193,U_15193,c_Lattices_Osemilattice__inf__class_Oinf(U_15193)),U_15195),U_15194))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15193),U_15194))
| ~ class_Lattices_Osemilattice__inf(U_15193) ),
inference(variable_rename,[status(thm)],[f_3844_1]) ).
cnf(f_3844_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_15193,U_15193,c_Lattices_Osemilattice__inf__class_Oinf(U_15193)),U_15195),hAPP(hAPP(c_Set_Oinsert(U_15193),U_15196),U_15194)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15193),U_15196),hAPP(hAPP(c_Finite__Set_Ofold(U_15193,U_15193,c_Lattices_Osemilattice__inf__class_Oinf(U_15193)),U_15195),U_15194))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15193),U_15194))
| ~ class_Lattices_Osemilattice__inf(U_15193) ),
inference(clausify,[status(thm)],[f_3844_2]) ).
fof(f_3845_1,plain,
! [V_a_2,V_b_2,V_A_2,T_b] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__insert]) ).
fof(f_3845_2,plain,
! [U_15200,U_15199,U_15198,U_15197] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_15197,U_15197,c_Orderings_Oord__class_Omin(U_15197)),U_15199),hAPP(hAPP(c_Set_Oinsert(U_15197),U_15200),U_15198)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15197),U_15200),hAPP(hAPP(c_Finite__Set_Ofold(U_15197,U_15197,c_Orderings_Oord__class_Omin(U_15197)),U_15199),U_15198))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15197),U_15198))
| ~ class_Orderings_Olinorder(U_15197) ),
inference(variable_rename,[status(thm)],[f_3845_1]) ).
cnf(f_3845_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_15197,U_15197,c_Orderings_Oord__class_Omin(U_15197)),U_15199),hAPP(hAPP(c_Set_Oinsert(U_15197),U_15200),U_15198)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15197),U_15200),hAPP(hAPP(c_Finite__Set_Ofold(U_15197,U_15197,c_Orderings_Oord__class_Omin(U_15197)),U_15199),U_15198))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15197),U_15198))
| ~ class_Orderings_Olinorder(U_15197) ),
inference(clausify,[status(thm)],[f_3845_2]) ).
fof(f_3846_1,plain,
! [V_a_2,V_b_2,V_A_2,T_b] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__insert]) ).
fof(f_3846_2,plain,
! [U_15204,U_15203,U_15202,U_15201] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_15201,U_15201,c_Orderings_Oord__class_Omax(U_15201)),U_15203),hAPP(hAPP(c_Set_Oinsert(U_15201),U_15204),U_15202)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15201),U_15204),hAPP(hAPP(c_Finite__Set_Ofold(U_15201,U_15201,c_Orderings_Oord__class_Omax(U_15201)),U_15203),U_15202))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15201),U_15202))
| ~ class_Orderings_Olinorder(U_15201) ),
inference(variable_rename,[status(thm)],[f_3846_1]) ).
cnf(f_3846_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_15201,U_15201,c_Orderings_Oord__class_Omax(U_15201)),U_15203),hAPP(hAPP(c_Set_Oinsert(U_15201),U_15204),U_15202)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15201),U_15204),hAPP(hAPP(c_Finite__Set_Ofold(U_15201,U_15201,c_Orderings_Oord__class_Omax(U_15201)),U_15203),U_15202))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15201),U_15202))
| ~ class_Orderings_Olinorder(U_15201) ),
inference(clausify,[status(thm)],[f_3846_2]) ).
fof(f_3847_1,plain,
! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem2]) ).
fof(f_3847_2,plain,
! [U_15210,U_15209,U_15208,U_15207,U_15206,U_15205] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_15205,U_15206,U_15207),U_15209),hAPP(hAPP(c_Set_Oinsert(U_15205),U_15210),U_15208)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15205,U_15206,U_15207),hAPP(hAPP(U_15207,U_15210),U_15209)),U_15208)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15205),U_15208))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_15205,U_15206,U_15207) ),
inference(variable_rename,[status(thm)],[f_3847_1]) ).
cnf(f_3847_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_15205,U_15206,U_15207),U_15209),hAPP(hAPP(c_Set_Oinsert(U_15205),U_15210),U_15208)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15205,U_15206,U_15207),hAPP(hAPP(U_15207,U_15210),U_15209)),U_15208)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15205),U_15208))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_15205,U_15206,U_15207) ),
inference(clausify,[status(thm)],[f_3847_2]) ).
fof(f_3848_1,plain,
! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem]) ).
fof(f_3848_2,plain,
! [U_15216,U_15215,U_15214,U_15213,U_15212,U_15211] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_15211,U_15212,U_15213),U_15215),hAPP(hAPP(c_Set_Oinsert(U_15211),U_15216),U_15214)) = hAPP(hAPP(U_15213,U_15216),hAPP(hAPP(c_Finite__Set_Ofold(U_15211,U_15212,U_15213),U_15215),U_15214))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15211),U_15214))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_15211,U_15212,U_15213) ),
inference(variable_rename,[status(thm)],[f_3848_1]) ).
cnf(f_3848_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_15211,U_15212,U_15213),U_15215),hAPP(hAPP(c_Set_Oinsert(U_15211),U_15216),U_15214)) = hAPP(hAPP(U_15213,U_15216),hAPP(hAPP(c_Finite__Set_Ofold(U_15211,U_15212,U_15213),U_15215),U_15214))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15211),U_15214))
| ~ c_Finite__Set_Ofun__left__comm__idem(U_15211,U_15212,U_15213) ),
inference(clausify,[status(thm)],[f_3848_2]) ).
fof(f_3849_1,plain,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),V_B_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_sup__SUPR__fold__sup]) ).
fof(f_3849_2,plain,
! [U_15221,U_15220,U_15219,U_15218,U_15217] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15217),U_15220),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15218,U_15217),U_15219),U_15221)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15218,U_15217,hAPP(hAPP(c_COMBB(U_15217,tc_fun(U_15217,U_15217),U_15218),c_Lattices_Osemilattice__sup__class_Osup(U_15217)),U_15221)),U_15220),U_15219)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15218),U_15219))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15217) ),
inference(variable_rename,[status(thm)],[f_3849_1]) ).
cnf(f_3849_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15217),U_15220),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15218,U_15217),U_15219),U_15221)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15218,U_15217,hAPP(hAPP(c_COMBB(U_15217,tc_fun(U_15217,U_15217),U_15218),c_Lattices_Osemilattice__sup__class_Osup(U_15217)),U_15221)),U_15220),U_15219)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15218),U_15219))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15217) ),
inference(clausify,[status(thm)],[f_3849_2]) ).
fof(f_3850_1,plain,
! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),V_B_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_inf__INFI__fold__inf]) ).
fof(f_3850_2,plain,
! [U_15226,U_15225,U_15224,U_15223,U_15222] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15222),U_15225),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15223,U_15222),U_15224),U_15226)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15223,U_15222,hAPP(hAPP(c_COMBB(U_15222,tc_fun(U_15222,U_15222),U_15223),c_Lattices_Osemilattice__inf__class_Oinf(U_15222)),U_15226)),U_15225),U_15224)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15223),U_15224))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15222) ),
inference(variable_rename,[status(thm)],[f_3850_1]) ).
cnf(f_3850_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15222),U_15225),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15223,U_15222),U_15224),U_15226)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15223,U_15222,hAPP(hAPP(c_COMBB(U_15222,tc_fun(U_15222,U_15222),U_15223),c_Lattices_Osemilattice__inf__class_Oinf(U_15222)),U_15226)),U_15225),U_15224)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15223),U_15224))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15222) ),
inference(clausify,[status(thm)],[f_3850_2]) ).
fof(f_3851_1,plain,
! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_a_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oeq__fold__idem_H]) ).
fof(f_3851_2,plain,
! [U_15231,U_15230,U_15229,U_15228,U_15227] :
( hAPP(U_15229,hAPP(hAPP(c_Set_Oinsert(U_15227),U_15231),U_15230)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15227,U_15227,U_15228),U_15231),U_15230)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15227),U_15230))
| ~ c_Finite__Set_Ofolding__one__idem(U_15227,U_15228,U_15229) ),
inference(variable_rename,[status(thm)],[f_3851_1]) ).
cnf(f_3851_3,plain,
( hAPP(U_15229,hAPP(hAPP(c_Set_Oinsert(U_15227),U_15231),U_15230)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15227,U_15227,U_15228),U_15231),U_15230)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15227),U_15230))
| ~ c_Finite__Set_Ofolding__one__idem(U_15227,U_15228,U_15229) ),
inference(clausify,[status(thm)],[f_3851_2]) ).
fof(f_3852_1,plain,
! [V_b_2,V_a_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Osemilattice__sup(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sup__le__fold__sup]) ).
fof(f_3852_2,plain,
! [U_15235,U_15234,U_15233,U_15232] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15232),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15232),U_15234),U_15235)),hAPP(hAPP(c_Finite__Set_Ofold(U_15232,U_15232,c_Lattices_Osemilattice__sup__class_Osup(U_15232)),U_15235),U_15233)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15232),U_15234),U_15233))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15232),U_15233))
| ~ class_Lattices_Osemilattice__sup(U_15232) ),
inference(variable_rename,[status(thm)],[f_3852_1]) ).
cnf(f_3852_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15232),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15232),U_15234),U_15235)),hAPP(hAPP(c_Finite__Set_Ofold(U_15232,U_15232,c_Lattices_Osemilattice__sup__class_Osup(U_15232)),U_15235),U_15233)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15232),U_15234),U_15233))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15232),U_15233))
| ~ class_Lattices_Osemilattice__sup(U_15232) ),
inference(clausify,[status(thm)],[f_3852_2]) ).
fof(f_3853_1,plain,
! [V_b_2,V_a_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Osemilattice__inf(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold__inf__le__inf]) ).
fof(f_3853_2,plain,
! [U_15239,U_15238,U_15237,U_15236] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15236),hAPP(hAPP(c_Finite__Set_Ofold(U_15236,U_15236,c_Lattices_Osemilattice__inf__class_Oinf(U_15236)),U_15239),U_15237)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15236),U_15238),U_15239)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15236),U_15238),U_15237))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15236),U_15237))
| ~ class_Lattices_Osemilattice__inf(U_15236) ),
inference(variable_rename,[status(thm)],[f_3853_1]) ).
cnf(f_3853_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15236),hAPP(hAPP(c_Finite__Set_Ofold(U_15236,U_15236,c_Lattices_Osemilattice__inf__class_Oinf(U_15236)),U_15239),U_15237)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15236),U_15238),U_15239)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15236),U_15238),U_15237))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15236),U_15237))
| ~ class_Lattices_Osemilattice__inf(U_15236) ),
inference(clausify,[status(thm)],[f_3853_2]) ).
fof(f_3854_1,plain,
! [V_b_2,V_a_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),V_b_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__le__inf]) ).
fof(f_3854_2,plain,
! [U_15243,U_15242,U_15241,U_15240] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15240),hAPP(hAPP(c_Finite__Set_Ofold(U_15240,U_15240,c_Orderings_Oord__class_Omin(U_15240)),U_15243),U_15241)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15240),U_15242),U_15243)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15240),U_15242),U_15241))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15240),U_15241))
| ~ class_Orderings_Olinorder(U_15240) ),
inference(variable_rename,[status(thm)],[f_3854_1]) ).
cnf(f_3854_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15240),hAPP(hAPP(c_Finite__Set_Ofold(U_15240,U_15240,c_Orderings_Oord__class_Omin(U_15240)),U_15243),U_15241)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15240),U_15242),U_15243)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15240),U_15242),U_15241))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15240),U_15241))
| ~ class_Orderings_Olinorder(U_15240) ),
inference(clausify,[status(thm)],[f_3854_2]) ).
fof(f_3855_1,plain,
! [V_b_2,V_a_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Osup__le__fold__sup]) ).
fof(f_3855_2,plain,
! [U_15247,U_15246,U_15245,U_15244] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15244),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15244),U_15246),U_15247)),hAPP(hAPP(c_Finite__Set_Ofold(U_15244,U_15244,c_Orderings_Oord__class_Omax(U_15244)),U_15247),U_15245)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15244),U_15246),U_15245))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15244),U_15245))
| ~ class_Orderings_Olinorder(U_15244) ),
inference(variable_rename,[status(thm)],[f_3855_1]) ).
cnf(f_3855_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15244),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15244),U_15246),U_15247)),hAPP(hAPP(c_Finite__Set_Ofold(U_15244,U_15244,c_Orderings_Oord__class_Omax(U_15244)),U_15247),U_15245)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15244),U_15246),U_15245))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15244),U_15245))
| ~ class_Orderings_Olinorder(U_15244) ),
inference(clausify,[status(thm)],[f_3855_2]) ).
fof(f_3856_1,plain,
! [V_a_2,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__eq__fold__idem]) ).
fof(f_3856_2,plain,
! [U_15250,U_15249,U_15248] :
( hAPP(c_Finite__Set_Ofold1(U_15248,c_Groups_Otimes__class_Otimes(U_15248)),hAPP(hAPP(c_Set_Oinsert(U_15248),U_15250),U_15249)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15248,U_15248,c_Groups_Otimes__class_Otimes(U_15248)),U_15250),U_15249)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15248),U_15249))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_15248) ),
inference(variable_rename,[status(thm)],[f_3856_1]) ).
cnf(f_3856_3,plain,
( hAPP(c_Finite__Set_Ofold1(U_15248,c_Groups_Otimes__class_Otimes(U_15248)),hAPP(hAPP(c_Set_Oinsert(U_15248),U_15250),U_15249)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15248,U_15248,c_Groups_Otimes__class_Otimes(U_15248)),U_15250),U_15249)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15248),U_15249))
| ~ class_Lattices_Oab__semigroup__idem__mult(U_15248) ),
inference(clausify,[status(thm)],[f_3856_2]) ).
fof(f_3857_1,plain,
! [V_a_2,V_A_2,T_b] :
( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_a_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oeq__fold__idem_H]) ).
fof(f_3857_2,plain,
! [U_15253,U_15252,U_15251] :
( c_Big__Operators_Olattice__class_OSup__fin(U_15251,hAPP(hAPP(c_Set_Oinsert(U_15251),U_15253),U_15252)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15251,U_15251,c_Lattices_Osemilattice__sup__class_Osup(U_15251)),U_15253),U_15252)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15251),U_15252))
| ~ class_Lattices_Olattice(U_15251) ),
inference(variable_rename,[status(thm)],[f_3857_1]) ).
cnf(f_3857_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_15251,hAPP(hAPP(c_Set_Oinsert(U_15251),U_15253),U_15252)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15251,U_15251,c_Lattices_Osemilattice__sup__class_Osup(U_15251)),U_15253),U_15252)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15251),U_15252))
| ~ class_Lattices_Olattice(U_15251) ),
inference(clausify,[status(thm)],[f_3857_2]) ).
fof(f_3858_1,plain,
! [V_a_2,V_A_2,T_b] :
( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_a_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oeq__fold__idem_H]) ).
fof(f_3858_2,plain,
! [U_15256,U_15255,U_15254] :
( c_Big__Operators_Olattice__class_OInf__fin(U_15254,hAPP(hAPP(c_Set_Oinsert(U_15254),U_15256),U_15255)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15254,U_15254,c_Lattices_Osemilattice__inf__class_Oinf(U_15254)),U_15256),U_15255)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15254),U_15255))
| ~ class_Lattices_Olattice(U_15254) ),
inference(variable_rename,[status(thm)],[f_3858_1]) ).
cnf(f_3858_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_15254,hAPP(hAPP(c_Set_Oinsert(U_15254),U_15256),U_15255)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15254,U_15254,c_Lattices_Osemilattice__inf__class_Oinf(U_15254)),U_15256),U_15255)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15254),U_15255))
| ~ class_Lattices_Olattice(U_15254) ),
inference(clausify,[status(thm)],[f_3858_2]) ).
fof(f_3859_1,plain,
! [V_a_2,V_A_2,T_b] :
( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oeq__fold__idem_H]) ).
fof(f_3859_2,plain,
! [U_15259,U_15258,U_15257] :
( c_Big__Operators_Olinorder__class_OMin(U_15257,hAPP(hAPP(c_Set_Oinsert(U_15257),U_15259),U_15258)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15257,U_15257,c_Orderings_Oord__class_Omin(U_15257)),U_15259),U_15258)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15257),U_15258))
| ~ class_Orderings_Olinorder(U_15257) ),
inference(variable_rename,[status(thm)],[f_3859_1]) ).
cnf(f_3859_3,plain,
( c_Big__Operators_Olinorder__class_OMin(U_15257,hAPP(hAPP(c_Set_Oinsert(U_15257),U_15259),U_15258)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15257,U_15257,c_Orderings_Oord__class_Omin(U_15257)),U_15259),U_15258)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15257),U_15258))
| ~ class_Orderings_Olinorder(U_15257) ),
inference(clausify,[status(thm)],[f_3859_2]) ).
fof(f_3860_1,plain,
! [V_a_2,V_A_2,T_b] :
( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oeq__fold__idem_H]) ).
fof(f_3860_2,plain,
! [U_15262,U_15261,U_15260] :
( c_Big__Operators_Olinorder__class_OMax(U_15260,hAPP(hAPP(c_Set_Oinsert(U_15260),U_15262),U_15261)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15260,U_15260,c_Orderings_Oord__class_Omax(U_15260)),U_15262),U_15261)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15260),U_15261))
| ~ class_Orderings_Olinorder(U_15260) ),
inference(variable_rename,[status(thm)],[f_3860_1]) ).
cnf(f_3860_3,plain,
( c_Big__Operators_Olinorder__class_OMax(U_15260,hAPP(hAPP(c_Set_Oinsert(U_15260),U_15262),U_15261)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15260,U_15260,c_Orderings_Oord__class_Omax(U_15260)),U_15262),U_15261)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15260),U_15261))
| ~ class_Orderings_Olinorder(U_15260) ),
inference(clausify,[status(thm)],[f_3860_2]) ).
fof(f_3861_1,plain,
! [V_a_2,V_A_2,T_b] :
( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold__idem_H]) ).
fof(f_3861_2,plain,
! [U_15265,U_15264,U_15263] :
( c_Big__Operators_Olattice_OInf__fin(U_15263,c_Orderings_Oord__class_Omin(U_15263),hAPP(hAPP(c_Set_Oinsert(U_15263),U_15265),U_15264)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15263,U_15263,c_Orderings_Oord__class_Omin(U_15263)),U_15265),U_15264)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15263),U_15264))
| ~ class_Orderings_Olinorder(U_15263) ),
inference(variable_rename,[status(thm)],[f_3861_1]) ).
cnf(f_3861_3,plain,
( c_Big__Operators_Olattice_OInf__fin(U_15263,c_Orderings_Oord__class_Omin(U_15263),hAPP(hAPP(c_Set_Oinsert(U_15263),U_15265),U_15264)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15263,U_15263,c_Orderings_Oord__class_Omin(U_15263)),U_15265),U_15264)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15263),U_15264))
| ~ class_Orderings_Olinorder(U_15263) ),
inference(clausify,[status(thm)],[f_3861_2]) ).
fof(f_3862_1,plain,
! [V_a_2,V_A_2,T_b] :
( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold__idem_H]) ).
fof(f_3862_2,plain,
! [U_15268,U_15267,U_15266] :
( c_Big__Operators_Olattice_OSup__fin(U_15266,c_Orderings_Oord__class_Omax(U_15266),hAPP(hAPP(c_Set_Oinsert(U_15266),U_15268),U_15267)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15266,U_15266,c_Orderings_Oord__class_Omax(U_15266)),U_15268),U_15267)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15266),U_15267))
| ~ class_Orderings_Olinorder(U_15266) ),
inference(variable_rename,[status(thm)],[f_3862_1]) ).
cnf(f_3862_3,plain,
( c_Big__Operators_Olattice_OSup__fin(U_15266,c_Orderings_Oord__class_Omax(U_15266),hAPP(hAPP(c_Set_Oinsert(U_15266),U_15268),U_15267)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15266,U_15266,c_Orderings_Oord__class_Omax(U_15266)),U_15268),U_15267)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15266),U_15267))
| ~ class_Orderings_Olinorder(U_15266) ),
inference(clausify,[status(thm)],[f_3862_2]) ).
fof(f_3863_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_minus__fold__remove]) ).
fof(f_3863_2,plain,
! [U_15271,U_15270,U_15269] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15269,tc_HOL_Obool)),U_15271),U_15270) = hAPP(hAPP(c_Finite__Set_Ofold(U_15269,tc_fun(U_15269,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15269,tc_HOL_Obool),tc_fun(tc_fun(U_15269,tc_HOL_Obool),tc_fun(U_15269,tc_HOL_Obool)),U_15269),hAPP(c_COMBC(tc_fun(U_15269,tc_HOL_Obool),tc_fun(U_15269,tc_HOL_Obool),tc_fun(U_15269,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_15269,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_15269,tc_fun(U_15269,tc_HOL_Obool),tc_fun(U_15269,tc_HOL_Obool)),c_Set_Oinsert(U_15269)),c_Orderings_Obot__class_Obot(tc_fun(U_15269,tc_HOL_Obool))))),U_15271),U_15270)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15269),U_15270)) ),
inference(variable_rename,[status(thm)],[f_3863_1]) ).
cnf(f_3863_3,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15269,tc_HOL_Obool)),U_15271),U_15270) = hAPP(hAPP(c_Finite__Set_Ofold(U_15269,tc_fun(U_15269,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15269,tc_HOL_Obool),tc_fun(tc_fun(U_15269,tc_HOL_Obool),tc_fun(U_15269,tc_HOL_Obool)),U_15269),hAPP(c_COMBC(tc_fun(U_15269,tc_HOL_Obool),tc_fun(U_15269,tc_HOL_Obool),tc_fun(U_15269,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_15269,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_15269,tc_fun(U_15269,tc_HOL_Obool),tc_fun(U_15269,tc_HOL_Obool)),c_Set_Oinsert(U_15269)),c_Orderings_Obot__class_Obot(tc_fun(U_15269,tc_HOL_Obool))))),U_15271),U_15270)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15269),U_15270)) ),
inference(clausify,[status(thm)],[f_3863_2]) ).
fof(f_3864_1,plain,
! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_x_2),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__one_Oeq__fold_H]) ).
fof(f_3864_2,plain,
! [U_15276,U_15275,U_15274,U_15273,U_15272] :
( hAPP(U_15274,hAPP(hAPP(c_Set_Oinsert(U_15272),U_15276),U_15275)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15272,U_15272,U_15273),U_15276),U_15275)
| hBOOL(hAPP(hAPP(c_member(U_15272),U_15276),U_15275))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15272),U_15275))
| ~ c_Finite__Set_Ofolding__one(U_15272,U_15273,U_15274) ),
inference(variable_rename,[status(thm)],[f_3864_1]) ).
cnf(f_3864_3,plain,
( hAPP(U_15274,hAPP(hAPP(c_Set_Oinsert(U_15272),U_15276),U_15275)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15272,U_15272,U_15273),U_15276),U_15275)
| hBOOL(hAPP(hAPP(c_member(U_15272),U_15276),U_15275))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15272),U_15275))
| ~ c_Finite__Set_Ofolding__one(U_15272,U_15273,U_15274) ),
inference(clausify,[status(thm)],[f_3864_2]) ).
fof(f_3865_1,plain,
! [V_f_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(T_c)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_SUPR__fold__sup]) ).
fof(f_3865_2,plain,
! [U_15280,U_15279,U_15278,U_15277] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15278,U_15277),U_15279),U_15280) = hAPP(hAPP(c_Finite__Set_Ofold(U_15278,U_15277,hAPP(hAPP(c_COMBB(U_15277,tc_fun(U_15277,U_15277),U_15278),c_Lattices_Osemilattice__sup__class_Osup(U_15277)),U_15280)),c_Orderings_Obot__class_Obot(U_15277)),U_15279)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15278),U_15279))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15277) ),
inference(variable_rename,[status(thm)],[f_3865_1]) ).
cnf(f_3865_3,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15278,U_15277),U_15279),U_15280) = hAPP(hAPP(c_Finite__Set_Ofold(U_15278,U_15277,hAPP(hAPP(c_COMBB(U_15277,tc_fun(U_15277,U_15277),U_15278),c_Lattices_Osemilattice__sup__class_Osup(U_15277)),U_15280)),c_Orderings_Obot__class_Obot(U_15277)),U_15279)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15278),U_15279))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15277) ),
inference(clausify,[status(thm)],[f_3865_2]) ).
fof(f_3866_1,plain,
! [V_f_2,V_A_2,T_b,T_c] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),c_Orderings_Otop__class_Otop(T_c)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_c) ),
inference(fof_nnf,[status(thm)],[fact_INFI__fold__inf]) ).
fof(f_3866_2,plain,
! [U_15284,U_15283,U_15282,U_15281] :
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15282,U_15281),U_15283),U_15284) = hAPP(hAPP(c_Finite__Set_Ofold(U_15282,U_15281,hAPP(hAPP(c_COMBB(U_15281,tc_fun(U_15281,U_15281),U_15282),c_Lattices_Osemilattice__inf__class_Oinf(U_15281)),U_15284)),c_Orderings_Otop__class_Otop(U_15281)),U_15283)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15282),U_15283))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15281) ),
inference(variable_rename,[status(thm)],[f_3866_1]) ).
cnf(f_3866_3,plain,
( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15282,U_15281),U_15283),U_15284) = hAPP(hAPP(c_Finite__Set_Ofold(U_15282,U_15281,hAPP(hAPP(c_COMBB(U_15281,tc_fun(U_15281,U_15281),U_15282),c_Lattices_Osemilattice__inf__class_Oinf(U_15281)),U_15284)),c_Orderings_Otop__class_Otop(U_15281)),U_15283)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15282),U_15283))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15281) ),
inference(clausify,[status(thm)],[f_3866_2]) ).
fof(f_3867_1,plain,
! [V_a_2,V_A_2,T_b] :
( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Groups_Oab__semigroup__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold1__eq__fold]) ).
fof(f_3867_2,plain,
! [U_15287,U_15286,U_15285] :
( hAPP(c_Finite__Set_Ofold1(U_15285,c_Groups_Otimes__class_Otimes(U_15285)),hAPP(hAPP(c_Set_Oinsert(U_15285),U_15287),U_15286)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15285,U_15285,c_Groups_Otimes__class_Otimes(U_15285)),U_15287),U_15286)
| hBOOL(hAPP(hAPP(c_member(U_15285),U_15287),U_15286))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15285),U_15286))
| ~ class_Groups_Oab__semigroup__mult(U_15285) ),
inference(variable_rename,[status(thm)],[f_3867_1]) ).
cnf(f_3867_3,plain,
( hAPP(c_Finite__Set_Ofold1(U_15285,c_Groups_Otimes__class_Otimes(U_15285)),hAPP(hAPP(c_Set_Oinsert(U_15285),U_15287),U_15286)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15285,U_15285,c_Groups_Otimes__class_Otimes(U_15285)),U_15287),U_15286)
| hBOOL(hAPP(hAPP(c_member(U_15285),U_15287),U_15286))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15285),U_15286))
| ~ class_Groups_Oab__semigroup__mult(U_15285) ),
inference(clausify,[status(thm)],[f_3867_2]) ).
fof(f_3868_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_x_2),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oeq__fold_H]) ).
fof(f_3868_2,plain,
! [U_15290,U_15289,U_15288] :
( c_Big__Operators_Olattice__class_OSup__fin(U_15288,hAPP(hAPP(c_Set_Oinsert(U_15288),U_15290),U_15289)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15288,U_15288,c_Lattices_Osemilattice__sup__class_Osup(U_15288)),U_15290),U_15289)
| hBOOL(hAPP(hAPP(c_member(U_15288),U_15290),U_15289))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15288),U_15289))
| ~ class_Lattices_Olattice(U_15288) ),
inference(variable_rename,[status(thm)],[f_3868_1]) ).
cnf(f_3868_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_15288,hAPP(hAPP(c_Set_Oinsert(U_15288),U_15290),U_15289)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15288,U_15288,c_Lattices_Osemilattice__sup__class_Osup(U_15288)),U_15290),U_15289)
| hBOOL(hAPP(hAPP(c_member(U_15288),U_15290),U_15289))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15288),U_15289))
| ~ class_Lattices_Olattice(U_15288) ),
inference(clausify,[status(thm)],[f_3868_2]) ).
fof(f_3869_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_x_2),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Olattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oeq__fold_H]) ).
fof(f_3869_2,plain,
! [U_15293,U_15292,U_15291] :
( c_Big__Operators_Olattice__class_OInf__fin(U_15291,hAPP(hAPP(c_Set_Oinsert(U_15291),U_15293),U_15292)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15291,U_15291,c_Lattices_Osemilattice__inf__class_Oinf(U_15291)),U_15293),U_15292)
| hBOOL(hAPP(hAPP(c_member(U_15291),U_15293),U_15292))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15291),U_15292))
| ~ class_Lattices_Olattice(U_15291) ),
inference(variable_rename,[status(thm)],[f_3869_1]) ).
cnf(f_3869_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_15291,hAPP(hAPP(c_Set_Oinsert(U_15291),U_15293),U_15292)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15291,U_15291,c_Lattices_Osemilattice__inf__class_Oinf(U_15291)),U_15293),U_15292)
| hBOOL(hAPP(hAPP(c_member(U_15291),U_15293),U_15292))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15291),U_15292))
| ~ class_Lattices_Olattice(U_15291) ),
inference(clausify,[status(thm)],[f_3869_2]) ).
fof(f_3870_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Min_Oeq__fold_H]) ).
fof(f_3870_2,plain,
! [U_15296,U_15295,U_15294] :
( c_Big__Operators_Olinorder__class_OMin(U_15294,hAPP(hAPP(c_Set_Oinsert(U_15294),U_15296),U_15295)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15294,U_15294,c_Orderings_Oord__class_Omin(U_15294)),U_15296),U_15295)
| hBOOL(hAPP(hAPP(c_member(U_15294),U_15296),U_15295))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15294),U_15295))
| ~ class_Orderings_Olinorder(U_15294) ),
inference(variable_rename,[status(thm)],[f_3870_1]) ).
cnf(f_3870_3,plain,
( c_Big__Operators_Olinorder__class_OMin(U_15294,hAPP(hAPP(c_Set_Oinsert(U_15294),U_15296),U_15295)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15294,U_15294,c_Orderings_Oord__class_Omin(U_15294)),U_15296),U_15295)
| hBOOL(hAPP(hAPP(c_member(U_15294),U_15296),U_15295))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15294),U_15295))
| ~ class_Orderings_Olinorder(U_15294) ),
inference(clausify,[status(thm)],[f_3870_2]) ).
fof(f_3871_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Max_Oeq__fold_H]) ).
fof(f_3871_2,plain,
! [U_15299,U_15298,U_15297] :
( c_Big__Operators_Olinorder__class_OMax(U_15297,hAPP(hAPP(c_Set_Oinsert(U_15297),U_15299),U_15298)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15297,U_15297,c_Orderings_Oord__class_Omax(U_15297)),U_15299),U_15298)
| hBOOL(hAPP(hAPP(c_member(U_15297),U_15299),U_15298))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15297),U_15298))
| ~ class_Orderings_Olinorder(U_15297) ),
inference(variable_rename,[status(thm)],[f_3871_1]) ).
cnf(f_3871_3,plain,
( c_Big__Operators_Olinorder__class_OMax(U_15297,hAPP(hAPP(c_Set_Oinsert(U_15297),U_15299),U_15298)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15297,U_15297,c_Orderings_Oord__class_Omax(U_15297)),U_15299),U_15298)
| hBOOL(hAPP(hAPP(c_member(U_15297),U_15299),U_15298))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15297),U_15298))
| ~ class_Orderings_Olinorder(U_15297) ),
inference(clausify,[status(thm)],[f_3871_2]) ).
fof(f_3872_1,plain,
! [V_x_2,V_A_2,T_b] :
( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold_H]) ).
fof(f_3872_2,plain,
! [U_15302,U_15301,U_15300] :
( c_Big__Operators_Olattice_OInf__fin(U_15300,c_Orderings_Oord__class_Omin(U_15300),hAPP(hAPP(c_Set_Oinsert(U_15300),U_15302),U_15301)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15300,U_15300,c_Orderings_Oord__class_Omin(U_15300)),U_15302),U_15301)
| hBOOL(hAPP(hAPP(c_member(U_15300),U_15302),U_15301))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15300),U_15301))
| ~ class_Orderings_Olinorder(U_15300) ),
inference(variable_rename,[status(thm)],[f_3872_1]) ).
cnf(f_3872_3,plain,
( c_Big__Operators_Olattice_OInf__fin(U_15300,c_Orderings_Oord__class_Omin(U_15300),hAPP(hAPP(c_Set_Oinsert(U_15300),U_15302),U_15301)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15300,U_15300,c_Orderings_Oord__class_Omin(U_15300)),U_15302),U_15301)
| hBOOL(hAPP(hAPP(c_member(U_15300),U_15302),U_15301))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15300),U_15301))
| ~ class_Orderings_Olinorder(U_15300) ),
inference(clausify,[status(thm)],[f_3872_2]) ).
fof(f_3873_1,plain,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__rec]) ).
fof(f_3873_2,plain,
! [U_15308,U_15307,U_15306,U_15305,U_15304,U_15303] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_15303,U_15304,U_15305),U_15308),U_15306) = hAPP(hAPP(U_15305,U_15307),hAPP(hAPP(c_Finite__Set_Ofold(U_15303,U_15304,U_15305),U_15308),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15303,tc_HOL_Obool)),U_15306),hAPP(hAPP(c_Set_Oinsert(U_15303),U_15307),c_Orderings_Obot__class_Obot(tc_fun(U_15303,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_15303),U_15307),U_15306))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15303),U_15306))
| ~ c_Finite__Set_Ofun__left__comm(U_15303,U_15304,U_15305) ),
inference(variable_rename,[status(thm)],[f_3873_1]) ).
cnf(f_3873_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_15303,U_15304,U_15305),U_15308),U_15306) = hAPP(hAPP(U_15305,U_15307),hAPP(hAPP(c_Finite__Set_Ofold(U_15303,U_15304,U_15305),U_15308),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15303,tc_HOL_Obool)),U_15306),hAPP(hAPP(c_Set_Oinsert(U_15303),U_15307),c_Orderings_Obot__class_Obot(tc_fun(U_15303,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(U_15303),U_15307),U_15306))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15303),U_15306))
| ~ c_Finite__Set_Ofun__left__comm(U_15303,U_15304,U_15305) ),
inference(clausify,[status(thm)],[f_3873_2]) ).
fof(f_3874_1,plain,
! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert__remove]) ).
fof(f_3874_2,plain,
! [U_15314,U_15313,U_15312,U_15311,U_15310,U_15309] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_15309,U_15310,U_15311),U_15313),hAPP(hAPP(c_Set_Oinsert(U_15309),U_15314),U_15312)) = hAPP(hAPP(U_15311,U_15314),hAPP(hAPP(c_Finite__Set_Ofold(U_15309,U_15310,U_15311),U_15313),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15309,tc_HOL_Obool)),U_15312),hAPP(hAPP(c_Set_Oinsert(U_15309),U_15314),c_Orderings_Obot__class_Obot(tc_fun(U_15309,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15309),U_15312))
| ~ c_Finite__Set_Ofun__left__comm(U_15309,U_15310,U_15311) ),
inference(variable_rename,[status(thm)],[f_3874_1]) ).
cnf(f_3874_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_15309,U_15310,U_15311),U_15313),hAPP(hAPP(c_Set_Oinsert(U_15309),U_15314),U_15312)) = hAPP(hAPP(U_15311,U_15314),hAPP(hAPP(c_Finite__Set_Ofold(U_15309,U_15310,U_15311),U_15313),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15309,tc_HOL_Obool)),U_15312),hAPP(hAPP(c_Set_Oinsert(U_15309),U_15314),c_Orderings_Obot__class_Obot(tc_fun(U_15309,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15309),U_15312))
| ~ c_Finite__Set_Ofun__left__comm(U_15309,U_15310,U_15311) ),
inference(clausify,[status(thm)],[f_3874_2]) ).
fof(f_3875_1,plain,
! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
( hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__comp__comm]) ).
fof(f_3875_2,plain,
! [U_15319,U_15318,U_15317,U_15316,U_15315] :
( hAPP(c_Fun_Ocomp(U_15316,U_15316,U_15316,hAPP(U_15317,U_15318)),hAPP(U_15317,U_15319)) = hAPP(c_Fun_Ocomp(U_15316,U_15316,U_15316,hAPP(U_15317,U_15319)),hAPP(U_15317,U_15318))
| ~ c_Finite__Set_Ofun__left__comm(U_15315,U_15316,U_15317) ),
inference(variable_rename,[status(thm)],[f_3875_1]) ).
fof(f_3875_3,plain,
! [U_15319,U_15318,U_15317,U_15316] :
( ! [U_15315] : ~ c_Finite__Set_Ofun__left__comm(U_15315,U_15316,U_15317)
| hAPP(c_Fun_Ocomp(U_15316,U_15316,U_15316,hAPP(U_15317,U_15318)),hAPP(U_15317,U_15319)) = hAPP(c_Fun_Ocomp(U_15316,U_15316,U_15316,hAPP(U_15317,U_15319)),hAPP(U_15317,U_15318)) ),
inference(miniscope,[status(thm)],[f_3875_2]) ).
cnf(f_3875_4,plain,
( ~ c_Finite__Set_Ofun__left__comm(U_15315,U_15316,U_15317)
| hAPP(c_Fun_Ocomp(U_15316,U_15316,U_15316,hAPP(U_15317,U_15318)),hAPP(U_15317,U_15319)) = hAPP(c_Fun_Ocomp(U_15316,U_15316,U_15316,hAPP(U_15317,U_15319)),hAPP(U_15317,U_15318)) ),
inference(clausify,[status(thm)],[f_3875_3]) ).
fof(f_3876_1,plain,
! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
( V_y_2 = V_x_2
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__determ]) ).
fof(f_3876_2,plain,
! [U_15326,U_15325,U_15324,U_15323,U_15322,U_15321,U_15320] :
( U_15326 = U_15325
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15320,U_15321,U_15322,U_15323,U_15324),U_15326))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15320,U_15321,U_15322,U_15323,U_15324),U_15325))
| ~ c_Finite__Set_Ofun__left__comm(U_15320,U_15321,U_15322) ),
inference(variable_rename,[status(thm)],[f_3876_1]) ).
cnf(f_3876_3,plain,
( U_15326 = U_15325
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15320,U_15321,U_15322,U_15323,U_15324),U_15326))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15320,U_15321,U_15322,U_15323,U_15324),U_15325))
| ~ c_Finite__Set_Ofun__left__comm(U_15320,U_15321,U_15322) ),
inference(clausify,[status(thm)],[f_3876_2]) ).
fof(f_3877_1,plain,
! [T_b] :
( c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b))
| ~ class_Groups_Oab__semigroup__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm]) ).
fof(f_3877_2,plain,
! [U_15327] :
( c_Finite__Set_Ofun__left__comm(U_15327,U_15327,c_Groups_Otimes__class_Otimes(U_15327))
| ~ class_Groups_Oab__semigroup__mult(U_15327) ),
inference(variable_rename,[status(thm)],[f_3877_1]) ).
cnf(f_3877_3,plain,
( c_Finite__Set_Ofun__left__comm(U_15327,U_15327,c_Groups_Otimes__class_Otimes(U_15327))
| ~ class_Groups_Oab__semigroup__mult(U_15327) ),
inference(clausify,[status(thm)],[f_3877_2]) ).
fof(f_3878_1,plain,
! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_y_2),V_z_2)) = hAPP(hAPP(V_f_2,V_y_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm]) ).
fof(f_3878_2,plain,
! [U_15333,U_15332,U_15331,U_15330,U_15329,U_15328] :
( hAPP(hAPP(U_15330,U_15331),hAPP(hAPP(U_15330,U_15332),U_15333)) = hAPP(hAPP(U_15330,U_15332),hAPP(hAPP(U_15330,U_15331),U_15333))
| ~ c_Finite__Set_Ofun__left__comm(U_15328,U_15329,U_15330) ),
inference(variable_rename,[status(thm)],[f_3878_1]) ).
fof(f_3878_3,plain,
! [U_15333,U_15332,U_15331,U_15330] :
( ! [U_15329,U_15328] : ~ c_Finite__Set_Ofun__left__comm(U_15328,U_15329,U_15330)
| hAPP(hAPP(U_15330,U_15331),hAPP(hAPP(U_15330,U_15332),U_15333)) = hAPP(hAPP(U_15330,U_15332),hAPP(hAPP(U_15330,U_15331),U_15333)) ),
inference(miniscope,[status(thm)],[f_3878_2]) ).
cnf(f_3878_4,plain,
( ~ c_Finite__Set_Ofun__left__comm(U_15328,U_15329,U_15330)
| hAPP(hAPP(U_15330,U_15331),hAPP(hAPP(U_15330,U_15332),U_15333)) = hAPP(hAPP(U_15330,U_15332),hAPP(hAPP(U_15330,U_15331),U_15333)) ),
inference(clausify,[status(thm)],[f_3878_3]) ).
fof(f_3879_1,plain,
! [V_g_2,T_d,V_f_2,T_c,T_b] :
( c_Finite__Set_Ofun__left__comm(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm__apply]) ).
fof(f_3879_2,plain,
! [U_15338,U_15337,U_15336,U_15335,U_15334] :
( c_Finite__Set_Ofun__left__comm(U_15337,U_15335,hAPP(hAPP(c_COMBB(U_15334,tc_fun(U_15335,U_15335),U_15337),U_15336),U_15338))
| ~ c_Finite__Set_Ofun__left__comm(U_15334,U_15335,U_15336) ),
inference(variable_rename,[status(thm)],[f_3879_1]) ).
cnf(f_3879_3,plain,
( c_Finite__Set_Ofun__left__comm(U_15337,U_15335,hAPP(hAPP(c_COMBB(U_15334,tc_fun(U_15335,U_15335),U_15337),U_15336),U_15338))
| ~ c_Finite__Set_Ofun__left__comm(U_15334,U_15335,U_15336) ),
inference(clausify,[status(thm)],[f_3879_2]) ).
fof(f_3880_1,plain,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__fun__comm]) ).
fof(f_3880_2,plain,
! [U_15344,U_15343,U_15342,U_15341,U_15340,U_15339] :
( hAPP(hAPP(U_15341,U_15343),hAPP(hAPP(c_Finite__Set_Ofold(U_15339,U_15340,U_15341),U_15344),U_15342)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15339,U_15340,U_15341),hAPP(hAPP(U_15341,U_15343),U_15344)),U_15342)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15339),U_15342))
| ~ c_Finite__Set_Ofun__left__comm(U_15339,U_15340,U_15341) ),
inference(variable_rename,[status(thm)],[f_3880_1]) ).
cnf(f_3880_3,plain,
( hAPP(hAPP(U_15341,U_15343),hAPP(hAPP(c_Finite__Set_Ofold(U_15339,U_15340,U_15341),U_15344),U_15342)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15339,U_15340,U_15341),hAPP(hAPP(U_15341,U_15343),U_15344)),U_15342)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15339),U_15342))
| ~ c_Finite__Set_Ofun__left__comm(U_15339,U_15340,U_15341) ),
inference(clausify,[status(thm)],[f_3880_2]) ).
fof(f_3881_1,plain,
! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__equality]) ).
fof(f_3881_2,plain,
! [U_15350,U_15349,U_15348,U_15347,U_15346,U_15345] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_15345,U_15346,U_15347),U_15348),U_15349) = U_15350
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15345,U_15346,U_15347,U_15348,U_15349),U_15350))
| ~ c_Finite__Set_Ofun__left__comm(U_15345,U_15346,U_15347) ),
inference(variable_rename,[status(thm)],[f_3881_1]) ).
cnf(f_3881_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_15345,U_15346,U_15347),U_15348),U_15349) = U_15350
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15345,U_15346,U_15347,U_15348,U_15349),U_15350))
| ~ c_Finite__Set_Ofun__left__comm(U_15345,U_15346,U_15347) ),
inference(clausify,[status(thm)],[f_3881_2]) ).
fof(f_3882_1,plain,
! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__fold]) ).
fof(f_3882_2,plain,
! [U_15355,U_15354,U_15353,U_15352,U_15351] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15351,U_15352,U_15353,U_15355,U_15354),hAPP(hAPP(c_Finite__Set_Ofold(U_15351,U_15352,U_15353),U_15355),U_15354)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15351),U_15354))
| ~ c_Finite__Set_Ofun__left__comm(U_15351,U_15352,U_15353) ),
inference(variable_rename,[status(thm)],[f_3882_1]) ).
cnf(f_3882_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15351,U_15352,U_15353,U_15355,U_15354),hAPP(hAPP(c_Finite__Set_Ofold(U_15351,U_15352,U_15353),U_15355),U_15354)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15351),U_15354))
| ~ c_Finite__Set_Ofun__left__comm(U_15351,U_15352,U_15353) ),
inference(clausify,[status(thm)],[f_3882_2]) ).
fof(f_3883_1,plain,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2)
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert2]) ).
fof(f_3883_2,plain,
! [U_15361,U_15360,U_15359,U_15358,U_15357,U_15356] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_15356,U_15357,U_15358),U_15361),hAPP(hAPP(c_Set_Oinsert(U_15356),U_15360),U_15359)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15356,U_15357,U_15358),hAPP(hAPP(U_15358,U_15360),U_15361)),U_15359)
| hBOOL(hAPP(hAPP(c_member(U_15356),U_15360),U_15359))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15356),U_15359))
| ~ c_Finite__Set_Ofun__left__comm(U_15356,U_15357,U_15358) ),
inference(variable_rename,[status(thm)],[f_3883_1]) ).
cnf(f_3883_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_15356,U_15357,U_15358),U_15361),hAPP(hAPP(c_Set_Oinsert(U_15356),U_15360),U_15359)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15356,U_15357,U_15358),hAPP(hAPP(U_15358,U_15360),U_15361)),U_15359)
| hBOOL(hAPP(hAPP(c_member(U_15356),U_15360),U_15359))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15356),U_15359))
| ~ c_Finite__Set_Ofun__left__comm(U_15356,U_15357,U_15358) ),
inference(clausify,[status(thm)],[f_3883_2]) ).
fof(f_3884_1,plain,
! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert]) ).
fof(f_3884_2,plain,
! [U_15367,U_15366,U_15365,U_15364,U_15363,U_15362] :
( hAPP(hAPP(c_Finite__Set_Ofold(U_15362,U_15363,U_15364),U_15367),hAPP(hAPP(c_Set_Oinsert(U_15362),U_15366),U_15365)) = hAPP(hAPP(U_15364,U_15366),hAPP(hAPP(c_Finite__Set_Ofold(U_15362,U_15363,U_15364),U_15367),U_15365))
| hBOOL(hAPP(hAPP(c_member(U_15362),U_15366),U_15365))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15362),U_15365))
| ~ c_Finite__Set_Ofun__left__comm(U_15362,U_15363,U_15364) ),
inference(variable_rename,[status(thm)],[f_3884_1]) ).
cnf(f_3884_3,plain,
( hAPP(hAPP(c_Finite__Set_Ofold(U_15362,U_15363,U_15364),U_15367),hAPP(hAPP(c_Set_Oinsert(U_15362),U_15366),U_15365)) = hAPP(hAPP(U_15364,U_15366),hAPP(hAPP(c_Finite__Set_Ofold(U_15362,U_15363,U_15364),U_15367),U_15365))
| hBOOL(hAPP(hAPP(c_member(U_15362),U_15366),U_15365))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15362),U_15365))
| ~ c_Finite__Set_Ofun__left__comm(U_15362,U_15363,U_15364) ),
inference(clausify,[status(thm)],[f_3884_2]) ).
fof(f_3885_1,plain,
! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
( ? [B_y_H] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),B_y_H))
& V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE__aux]) ).
fof(f_3885_2,plain,
! [U_15375,U_15374,U_15373,U_15372,U_15371,U_15370,U_15369] :
( ? [U_15368] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15369,U_15370,U_15371,U_15372,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15369,tc_HOL_Obool)),U_15373),hAPP(hAPP(c_Set_Oinsert(U_15369),U_15375),c_Orderings_Obot__class_Obot(tc_fun(U_15369,tc_HOL_Obool))))),U_15368))
& U_15374 = hAPP(hAPP(U_15371,U_15375),U_15368) )
| ~ hBOOL(hAPP(hAPP(c_member(U_15369),U_15375),U_15373))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15369,U_15370,U_15371,U_15372,U_15373),U_15374))
| ~ c_Finite__Set_Ofun__left__comm(U_15369,U_15370,U_15371) ),
inference(variable_rename,[status(thm)],[f_3885_1]) ).
fof(f_3885_3,plain,
! [U_15375,U_15374,U_15373,U_15372,U_15371,U_15370,U_15369] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15369,U_15370,U_15371,U_15372,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15369,tc_HOL_Obool)),U_15373),hAPP(hAPP(c_Set_Oinsert(U_15369),U_15375),c_Orderings_Obot__class_Obot(tc_fun(U_15369,tc_HOL_Obool))))),sK388(U_15375,U_15374,U_15373,U_15372,U_15371,U_15370,U_15369)))
& U_15374 = hAPP(hAPP(U_15371,U_15375),sK388(U_15375,U_15374,U_15373,U_15372,U_15371,U_15370,U_15369)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_15369),U_15375),U_15373))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15369,U_15370,U_15371,U_15372,U_15373),U_15374))
| ~ c_Finite__Set_Ofun__left__comm(U_15369,U_15370,U_15371) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK388]),skolemize(U_15368,sK388(U_15375,U_15374,U_15373,U_15372,U_15371,U_15370,U_15369))],[f_3885_2]) ).
cnf(f_3885_4,plain,
( U_15374 = hAPP(hAPP(U_15371,U_15375),sK388(U_15375,U_15374,U_15373,U_15372,U_15371,U_15370,U_15369))
| ~ hBOOL(hAPP(hAPP(c_member(U_15369),U_15375),U_15373))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15369,U_15370,U_15371,U_15372,U_15373),U_15374))
| ~ c_Finite__Set_Ofun__left__comm(U_15369,U_15370,U_15371) ),
inference(clausify,[status(thm)],[f_3885_3]) ).
cnf(f_3885_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15369,U_15370,U_15371,U_15372,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15369,tc_HOL_Obool)),U_15373),hAPP(hAPP(c_Set_Oinsert(U_15369),U_15375),c_Orderings_Obot__class_Obot(tc_fun(U_15369,tc_HOL_Obool))))),sK388(U_15375,U_15374,U_15373,U_15372,U_15371,U_15370,U_15369)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15369),U_15375),U_15373))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15369,U_15370,U_15371,U_15372,U_15373),U_15374))
| ~ c_Finite__Set_Ofun__left__comm(U_15369,U_15370,U_15371) ),
inference(clausify,[status(thm)],[f_3885_3]) ).
fof(f_3886_1,plain,
! [V_A_2,T_b] :
( c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),c_Orderings_Otop__class_Otop(T_b)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fold__inf]) ).
fof(f_3886_2,plain,
! [U_15377,U_15376] :
( c_Complete__Lattice_OInf__class_OInf(U_15376,U_15377) = hAPP(hAPP(c_Finite__Set_Ofold(U_15376,U_15376,c_Lattices_Osemilattice__inf__class_Oinf(U_15376)),c_Orderings_Otop__class_Otop(U_15376)),U_15377)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15376),U_15377))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15376) ),
inference(variable_rename,[status(thm)],[f_3886_1]) ).
cnf(f_3886_3,plain,
( c_Complete__Lattice_OInf__class_OInf(U_15376,U_15377) = hAPP(hAPP(c_Finite__Set_Ofold(U_15376,U_15376,c_Lattices_Osemilattice__inf__class_Oinf(U_15376)),c_Orderings_Otop__class_Otop(U_15376)),U_15377)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15376),U_15377))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15376) ),
inference(clausify,[status(thm)],[f_3886_2]) ).
fof(f_3887_1,plain,
! [V_M_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2)))
| ! [B_x] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_finite__Inter]) ).
fof(f_3887_2,plain,
! [U_15380,U_15379] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15379),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15379,tc_HOL_Obool),U_15380)))
| ! [U_15378] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15379),U_15378))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_15379,tc_HOL_Obool)),U_15378),U_15380)) ) ),
inference(variable_rename,[status(thm)],[f_3887_1]) ).
cnf(f_3887_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15379),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15379,tc_HOL_Obool),U_15380)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15379),U_15378))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_15379,tc_HOL_Obool)),U_15378),U_15380)) ),
inference(clausify,[status(thm)],[f_3887_2]) ).
fof(f_3888_1,plain,
! [V_X_2,V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ),
inference(fof_nnf,[status(thm)],[fact_InterD]) ).
fof(f_3888_2,plain,
! [U_15384,U_15383,U_15382,U_15381] :
( hBOOL(hAPP(hAPP(c_member(U_15381),U_15382),U_15384))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_15381,tc_HOL_Obool)),U_15384),U_15383))
| ~ hBOOL(hAPP(hAPP(c_member(U_15381),U_15382),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15381,tc_HOL_Obool),U_15383))) ),
inference(variable_rename,[status(thm)],[f_3888_1]) ).
cnf(f_3888_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_15381),U_15382),U_15384))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_15381,tc_HOL_Obool)),U_15384),U_15383))
| ~ hBOOL(hAPP(hAPP(c_member(U_15381),U_15382),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15381,tc_HOL_Obool),U_15383))) ),
inference(clausify,[status(thm)],[f_3888_2]) ).
fof(f_3889_1,plain,
! [V_X_2,V_C_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ),
inference(fof_nnf,[status(thm)],[fact_InterE]) ).
fof(f_3889_2,plain,
! [U_15388,U_15387,U_15386,U_15385] :
( hBOOL(hAPP(hAPP(c_member(U_15385),U_15386),U_15388))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_15385,tc_HOL_Obool)),U_15388),U_15387))
| ~ hBOOL(hAPP(hAPP(c_member(U_15385),U_15386),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15385,tc_HOL_Obool),U_15387))) ),
inference(variable_rename,[status(thm)],[f_3889_1]) ).
cnf(f_3889_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_15385),U_15386),U_15388))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_15385,tc_HOL_Obool)),U_15388),U_15387))
| ~ hBOOL(hAPP(hAPP(c_member(U_15385),U_15386),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15385,tc_HOL_Obool),U_15387))) ),
inference(clausify,[status(thm)],[f_3889_2]) ).
fof(f_3890_1,plain,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Inter__lower]) ).
fof(f_3890_2,plain,
! [U_15391,U_15390,U_15389] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15389,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15389,tc_HOL_Obool),U_15391)),U_15390))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_15389,tc_HOL_Obool)),U_15390),U_15391)) ),
inference(variable_rename,[status(thm)],[f_3890_1]) ).
cnf(f_3890_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15389,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15389,tc_HOL_Obool),U_15391)),U_15390))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_15389,tc_HOL_Obool)),U_15390),U_15391)) ),
inference(clausify,[status(thm)],[f_3890_2]) ).
fof(f_3891_1,plain,
! [V_A_2,V_b_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__Inf__iff]) ).
fof(f_3891_2,plain,
! [U_15396,U_15395,U_15394] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15394),U_15395),c_Complete__Lattice_OInf__class_OInf(U_15394,U_15396)))
| ? [U_15393] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15394),U_15395),U_15393))
& hBOOL(hAPP(hAPP(c_member(U_15394),U_15393),U_15396)) ) )
& ( ! [U_15392] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15394),U_15395),U_15392))
| ~ hBOOL(hAPP(hAPP(c_member(U_15394),U_15392),U_15396)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15394),U_15395),c_Complete__Lattice_OInf__class_OInf(U_15394,U_15396))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15394) ),
inference(variable_rename,[status(thm)],[f_3891_1]) ).
fof(f_3891_3,plain,
! [U_15396,U_15395,U_15394] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15394),U_15395),c_Complete__Lattice_OInf__class_OInf(U_15394,U_15396)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15394),U_15395),sK389(U_15396,U_15395,U_15394)))
& hBOOL(hAPP(hAPP(c_member(U_15394),sK389(U_15396,U_15395,U_15394)),U_15396)) ) )
& ( ! [U_15392] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15394),U_15395),U_15392))
| ~ hBOOL(hAPP(hAPP(c_member(U_15394),U_15392),U_15396)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15394),U_15395),c_Complete__Lattice_OInf__class_OInf(U_15394,U_15396))) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15394) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK389]),skolemize(U_15393,sK389(U_15396,U_15395,U_15394))],[f_3891_2]) ).
cnf(f_3891_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15394),U_15395),U_15392))
| ~ hBOOL(hAPP(hAPP(c_member(U_15394),U_15392),U_15396))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15394),U_15395),c_Complete__Lattice_OInf__class_OInf(U_15394,U_15396)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15394) ),
inference(clausify,[status(thm)],[f_3891_3]) ).
cnf(f_3891_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_15394),sK389(U_15396,U_15395,U_15394)),U_15396))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15394),U_15395),c_Complete__Lattice_OInf__class_OInf(U_15394,U_15396)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15394) ),
inference(clausify,[status(thm)],[f_3891_3]) ).
cnf(f_3891_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15394),U_15395),sK389(U_15396,U_15395,U_15394)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15394),U_15395),c_Complete__Lattice_OInf__class_OInf(U_15394,U_15396)))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15394) ),
inference(clausify,[status(thm)],[f_3891_3]) ).
fof(f_3892_1,plain,
! [V_a_2,V_S_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2)) ) )
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__less__iff]) ).
fof(f_3892_2,plain,
! [U_15401,U_15400,U_15399] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15399),c_Complete__Lattice_OInf__class_OInf(U_15399,U_15400)),U_15401))
| ! [U_15398] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15399),U_15398),U_15401))
| ~ hBOOL(hAPP(hAPP(c_member(U_15399),U_15398),U_15400)) ) )
& ( ? [U_15397] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15399),U_15397),U_15401))
& hBOOL(hAPP(hAPP(c_member(U_15399),U_15397),U_15400)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15399),c_Complete__Lattice_OInf__class_OInf(U_15399,U_15400)),U_15401)) ) )
| ~ class_Orderings_Olinorder(U_15399)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15399) ),
inference(variable_rename,[status(thm)],[f_3892_1]) ).
fof(f_3892_3,plain,
! [U_15401,U_15400,U_15399] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15399),c_Complete__Lattice_OInf__class_OInf(U_15399,U_15400)),U_15401))
| ! [U_15398] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15399),U_15398),U_15401))
| ~ hBOOL(hAPP(hAPP(c_member(U_15399),U_15398),U_15400)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15399),sK390(U_15401,U_15400,U_15399)),U_15401))
& hBOOL(hAPP(hAPP(c_member(U_15399),sK390(U_15401,U_15400,U_15399)),U_15400)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15399),c_Complete__Lattice_OInf__class_OInf(U_15399,U_15400)),U_15401)) ) )
| ~ class_Orderings_Olinorder(U_15399)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15399) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK390]),skolemize(U_15397,sK390(U_15401,U_15400,U_15399))],[f_3892_2]) ).
cnf(f_3892_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_15399),sK390(U_15401,U_15400,U_15399)),U_15400))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15399),c_Complete__Lattice_OInf__class_OInf(U_15399,U_15400)),U_15401))
| ~ class_Orderings_Olinorder(U_15399)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15399) ),
inference(clausify,[status(thm)],[f_3892_3]) ).
cnf(f_3892_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15399),sK390(U_15401,U_15400,U_15399)),U_15401))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15399),c_Complete__Lattice_OInf__class_OInf(U_15399,U_15400)),U_15401))
| ~ class_Orderings_Olinorder(U_15399)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15399) ),
inference(clausify,[status(thm)],[f_3892_3]) ).
cnf(f_3892_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15399),c_Complete__Lattice_OInf__class_OInf(U_15399,U_15400)),U_15401))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15399),U_15398),U_15401))
| ~ hBOOL(hAPP(hAPP(c_member(U_15399),U_15398),U_15400))
| ~ class_Orderings_Olinorder(U_15399)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15399) ),
inference(clausify,[status(thm)],[f_3892_3]) ).
fof(f_3893_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Un__Inter]) ).
fof(f_3893_2,plain,
! [U_15404,U_15403,U_15402] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15402,tc_HOL_Obool)),U_15403),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15402,tc_HOL_Obool),U_15404)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_15402,tc_HOL_Obool),tc_fun(U_15402,tc_HOL_Obool)),U_15404),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15402,tc_HOL_Obool)),U_15403)),
inference(variable_rename,[status(thm)],[f_3893_1]) ).
cnf(f_3893_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15402,tc_HOL_Obool)),U_15403),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15402,tc_HOL_Obool),U_15404)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_15402,tc_HOL_Obool),tc_fun(U_15402,tc_HOL_Obool)),U_15404),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15402,tc_HOL_Obool)),U_15403)),
inference(clausify,[status(thm)],[f_3893_2]) ).
fof(f_3894_1,plain,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Inter__anti__mono]) ).
fof(f_3894_2,plain,
! [U_15407,U_15406,U_15405] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15405,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15405,tc_HOL_Obool),U_15407)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15405,tc_HOL_Obool),U_15406)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_15405,tc_HOL_Obool),tc_HOL_Obool)),U_15406),U_15407)) ),
inference(variable_rename,[status(thm)],[f_3894_1]) ).
cnf(f_3894_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15405,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15405,tc_HOL_Obool),U_15407)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15405,tc_HOL_Obool),U_15406)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_15405,tc_HOL_Obool),tc_HOL_Obool)),U_15406),U_15407)) ),
inference(clausify,[status(thm)],[f_3894_2]) ).
fof(f_3895_1,plain,
! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Inter__empty]) ).
fof(f_3895_2,plain,
! [U_15408] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15408,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_15408,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_15408,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3895_1]) ).
cnf(f_3895_3,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15408,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_15408,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_15408,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3895_2]) ).
fof(f_3896_1,plain,
! [V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))),
inference(fof_nnf,[status(thm)],[fact_Inter__eq]) ).
fof(f_3896_2,plain,
! [U_15410,U_15409] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15409,tc_HOL_Obool),U_15410) = hAPP(c_Set_OCollect(U_15409),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_15409,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_15409),c_HOL_OAll(tc_fun(U_15409,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_15409,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_15409,tc_HOL_Obool),tc_HOL_Obool),U_15409),hAPP(c_COMBS(tc_fun(U_15409,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(U_15409,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(U_15409,tc_HOL_Obool),tc_fun(tc_fun(U_15409,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_15409,tc_HOL_Obool))),U_15410)))),c_member(U_15409)))),
inference(variable_rename,[status(thm)],[f_3896_1]) ).
cnf(f_3896_3,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15409,tc_HOL_Obool),U_15410) = hAPP(c_Set_OCollect(U_15409),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_15409,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_15409),c_HOL_OAll(tc_fun(U_15409,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_15409,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_15409,tc_HOL_Obool),tc_HOL_Obool),U_15409),hAPP(c_COMBS(tc_fun(U_15409,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(U_15409,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(U_15409,tc_HOL_Obool),tc_fun(tc_fun(U_15409,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_15409,tc_HOL_Obool))),U_15410)))),c_member(U_15409)))),
inference(clausify,[status(thm)],[f_3896_2]) ).
fof(f_3897_1,plain,
! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Inter__insert]) ).
fof(f_3897_2,plain,
! [U_15413,U_15412,U_15411] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15411,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_15411,tc_HOL_Obool)),U_15412),U_15413)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15411,tc_HOL_Obool)),U_15412),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15411,tc_HOL_Obool),U_15413)),
inference(variable_rename,[status(thm)],[f_3897_1]) ).
cnf(f_3897_3,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15411,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_15411,tc_HOL_Obool)),U_15412),U_15413)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15411,tc_HOL_Obool)),U_15412),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15411,tc_HOL_Obool),U_15413)),
inference(clausify,[status(thm)],[f_3897_2]) ).
fof(f_3898_1,plain,
! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Inter__UNIV]) ).
fof(f_3898_2,plain,
! [U_15414] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15414,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_15414,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_15414,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3898_1]) ).
cnf(f_3898_3,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15414,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_15414,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_15414,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3898_2]) ).
fof(f_3899_1,plain,
! [V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)),V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__lower]) ).
fof(f_3899_2,plain,
! [U_15417,U_15416,U_15415] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15415),c_Complete__Lattice_OInf__class_OInf(U_15415,U_15417)),U_15416))
| ~ hBOOL(hAPP(hAPP(c_member(U_15415),U_15416),U_15417))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15415) ),
inference(variable_rename,[status(thm)],[f_3899_1]) ).
cnf(f_3899_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15415),c_Complete__Lattice_OInf__class_OInf(U_15415,U_15417)),U_15416))
| ~ hBOOL(hAPP(hAPP(c_member(U_15415),U_15416),U_15417))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15415) ),
inference(clausify,[status(thm)],[f_3899_2]) ).
fof(f_3900_1,plain,
! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Inter__Un__distrib]) ).
fof(f_3900_2,plain,
! [U_15420,U_15419,U_15418] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15418,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_15418,tc_HOL_Obool),tc_HOL_Obool)),U_15419),U_15420)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15418,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15418,tc_HOL_Obool),U_15419)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15418,tc_HOL_Obool),U_15420)),
inference(variable_rename,[status(thm)],[f_3900_1]) ).
cnf(f_3900_3,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15418,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_15418,tc_HOL_Obool),tc_HOL_Obool)),U_15419),U_15420)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15418,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15418,tc_HOL_Obool),U_15419)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15418,tc_HOL_Obool),U_15420)),
inference(clausify,[status(thm)],[f_3900_2]) ).
fof(f_3901_1,plain,
! [V_a_2,T_b] :
( c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__singleton]) ).
fof(f_3901_2,plain,
! [U_15422,U_15421] :
( c_Complete__Lattice_OInf__class_OInf(U_15421,hAPP(hAPP(c_Set_Oinsert(U_15421),U_15422),c_Orderings_Obot__class_Obot(tc_fun(U_15421,tc_HOL_Obool)))) = U_15422
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15421) ),
inference(variable_rename,[status(thm)],[f_3901_1]) ).
cnf(f_3901_3,plain,
( c_Complete__Lattice_OInf__class_OInf(U_15421,hAPP(hAPP(c_Set_Oinsert(U_15421),U_15422),c_Orderings_Obot__class_Obot(tc_fun(U_15421,tc_HOL_Obool)))) = U_15422
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15421) ),
inference(clausify,[status(thm)],[f_3901_2]) ).
fof(f_3902_1,plain,
! [T_b] :
( c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__empty]) ).
fof(f_3902_2,plain,
! [U_15423] :
( c_Complete__Lattice_OInf__class_OInf(U_15423,c_Orderings_Obot__class_Obot(tc_fun(U_15423,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_15423)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15423) ),
inference(variable_rename,[status(thm)],[f_3902_1]) ).
cnf(f_3902_3,plain,
( c_Complete__Lattice_OInf__class_OInf(U_15423,c_Orderings_Obot__class_Obot(tc_fun(U_15423,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_15423)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15423) ),
inference(clausify,[status(thm)],[f_3902_2]) ).
fof(f_3903_1,plain,
! [T_b] :
( c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__UNIV]) ).
fof(f_3903_2,plain,
! [U_15424] :
( c_Complete__Lattice_OInf__class_OInf(U_15424,c_Orderings_Otop__class_Otop(tc_fun(U_15424,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_15424)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15424) ),
inference(variable_rename,[status(thm)],[f_3903_1]) ).
cnf(f_3903_3,plain,
( c_Complete__Lattice_OInf__class_OInf(U_15424,c_Orderings_Otop__class_Otop(tc_fun(U_15424,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_15424)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15424) ),
inference(clausify,[status(thm)],[f_3903_2]) ).
fof(f_3904_1,plain,
! [V_A_2,V_a_2,T_b] :
( c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__insert]) ).
fof(f_3904_2,plain,
! [U_15427,U_15426,U_15425] :
( c_Complete__Lattice_OInf__class_OInf(U_15425,hAPP(hAPP(c_Set_Oinsert(U_15425),U_15426),U_15427)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15425),U_15426),c_Complete__Lattice_OInf__class_OInf(U_15425,U_15427))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15425) ),
inference(variable_rename,[status(thm)],[f_3904_1]) ).
cnf(f_3904_3,plain,
( c_Complete__Lattice_OInf__class_OInf(U_15425,hAPP(hAPP(c_Set_Oinsert(U_15425),U_15426),U_15427)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15425),U_15426),c_Complete__Lattice_OInf__class_OInf(U_15425,U_15427))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15425) ),
inference(clausify,[status(thm)],[f_3904_2]) ).
fof(f_3905_1,plain,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_INTER__eq__Inter__image]) ).
fof(f_3905_2,plain,
! [U_15431,U_15430,U_15429,U_15428] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15428,tc_fun(U_15429,tc_HOL_Obool)),U_15430),U_15431) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15429,tc_HOL_Obool),hAPP(c_Set_Oimage(U_15428,tc_fun(U_15429,tc_HOL_Obool),U_15431),U_15430)),
inference(variable_rename,[status(thm)],[f_3905_1]) ).
cnf(f_3905_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15428,tc_fun(U_15429,tc_HOL_Obool)),U_15430),U_15431) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15429,tc_HOL_Obool),hAPP(c_Set_Oimage(U_15428,tc_fun(U_15429,tc_HOL_Obool),U_15431),U_15430)),
inference(clausify,[status(thm)],[f_3905_2]) ).
fof(f_3906_1,plain,
! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
inference(fof_nnf,[status(thm)],[fact_Inter__image__eq]) ).
fof(f_3906_2,plain,
! [U_15435,U_15434,U_15433,U_15432] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15432,tc_HOL_Obool),hAPP(c_Set_Oimage(U_15433,tc_fun(U_15432,tc_HOL_Obool),U_15434),U_15435)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15433,tc_fun(U_15432,tc_HOL_Obool)),U_15435),U_15434),
inference(variable_rename,[status(thm)],[f_3906_1]) ).
cnf(f_3906_3,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15432,tc_HOL_Obool),hAPP(c_Set_Oimage(U_15433,tc_fun(U_15432,tc_HOL_Obool),U_15434),U_15435)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15433,tc_fun(U_15432,tc_HOL_Obool)),U_15435),U_15434),
inference(clausify,[status(thm)],[f_3906_2]) ).
fof(f_3907_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))),
inference(fof_nnf,[status(thm)],[fact_Int__eq__Inter]) ).
fof(f_3907_2,plain,
! [U_15438,U_15437,U_15436] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15436,tc_HOL_Obool)),U_15437),U_15438) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15436,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_15436,tc_HOL_Obool)),U_15437),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_15436,tc_HOL_Obool)),U_15438),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_15436,tc_HOL_Obool),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_3907_1]) ).
cnf(f_3907_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15436,tc_HOL_Obool)),U_15437),U_15438) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15436,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_15436,tc_HOL_Obool)),U_15437),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_15436,tc_HOL_Obool)),U_15438),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_15436,tc_HOL_Obool),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_3907_2]) ).
fof(f_3908_1,plain,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))),
inference(fof_nnf,[status(thm)],[fact_Int__Inter__image]) ).
fof(f_3908_2,plain,
! [U_15443,U_15442,U_15441,U_15440,U_15439] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15439,tc_fun(U_15440,tc_HOL_Obool)),U_15441),hAPP(hAPP(c_COMBS(U_15439,tc_fun(U_15440,tc_HOL_Obool),tc_fun(U_15440,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15440,tc_HOL_Obool),tc_fun(tc_fun(U_15440,tc_HOL_Obool),tc_fun(U_15440,tc_HOL_Obool)),U_15439),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15440,tc_HOL_Obool))),U_15442)),U_15443)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15440,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15440,tc_HOL_Obool),hAPP(c_Set_Oimage(U_15439,tc_fun(U_15440,tc_HOL_Obool),U_15442),U_15441))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15440,tc_HOL_Obool),hAPP(c_Set_Oimage(U_15439,tc_fun(U_15440,tc_HOL_Obool),U_15443),U_15441))),
inference(variable_rename,[status(thm)],[f_3908_1]) ).
cnf(f_3908_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15439,tc_fun(U_15440,tc_HOL_Obool)),U_15441),hAPP(hAPP(c_COMBS(U_15439,tc_fun(U_15440,tc_HOL_Obool),tc_fun(U_15440,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15440,tc_HOL_Obool),tc_fun(tc_fun(U_15440,tc_HOL_Obool),tc_fun(U_15440,tc_HOL_Obool)),U_15439),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15440,tc_HOL_Obool))),U_15442)),U_15443)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15440,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15440,tc_HOL_Obool),hAPP(c_Set_Oimage(U_15439,tc_fun(U_15440,tc_HOL_Obool),U_15442),U_15441))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15440,tc_HOL_Obool),hAPP(c_Set_Oimage(U_15439,tc_fun(U_15440,tc_HOL_Obool),U_15443),U_15441))),
inference(clausify,[status(thm)],[f_3908_2]) ).
fof(f_3909_1,plain,
! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_Inter__Un__subset]) ).
fof(f_3909_2,plain,
! [U_15446,U_15445,U_15444] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15444,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15444,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15444,tc_HOL_Obool),U_15445)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15444,tc_HOL_Obool),U_15446))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15444,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_15444,tc_HOL_Obool),tc_HOL_Obool)),U_15445),U_15446)))),
inference(variable_rename,[status(thm)],[f_3909_1]) ).
cnf(f_3909_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15444,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15444,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15444,tc_HOL_Obool),U_15445)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15444,tc_HOL_Obool),U_15446))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15444,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_15444,tc_HOL_Obool),tc_HOL_Obool)),U_15445),U_15446)))),
inference(clausify,[status(thm)],[f_3909_2]) ).
fof(f_3910_1,plain,
! [V_b_2,V_a_2,T_b] :
( c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__binary]) ).
fof(f_3910_2,plain,
! [U_15449,U_15448,U_15447] :
( c_Complete__Lattice_OInf__class_OInf(U_15447,hAPP(hAPP(c_Set_Oinsert(U_15447),U_15448),hAPP(hAPP(c_Set_Oinsert(U_15447),U_15449),c_Orderings_Obot__class_Obot(tc_fun(U_15447,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15447),U_15448),U_15449)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15447) ),
inference(variable_rename,[status(thm)],[f_3910_1]) ).
cnf(f_3910_3,plain,
( c_Complete__Lattice_OInf__class_OInf(U_15447,hAPP(hAPP(c_Set_Oinsert(U_15447),U_15448),hAPP(hAPP(c_Set_Oinsert(U_15447),U_15449),c_Orderings_Obot__class_Obot(tc_fun(U_15447,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15447),U_15448),U_15449)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15447) ),
inference(clausify,[status(thm)],[f_3910_2]) ).
fof(f_3911_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_B_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__Inf__fold__inf]) ).
fof(f_3911_2,plain,
! [U_15452,U_15451,U_15450] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15450),U_15452),c_Complete__Lattice_OInf__class_OInf(U_15450,U_15451)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15450,U_15450,c_Lattices_Osemilattice__inf__class_Oinf(U_15450)),U_15452),U_15451)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15450),U_15451))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15450) ),
inference(variable_rename,[status(thm)],[f_3911_1]) ).
cnf(f_3911_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15450),U_15452),c_Complete__Lattice_OInf__class_OInf(U_15450,U_15451)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15450,U_15450,c_Lattices_Osemilattice__inf__class_Oinf(U_15450)),U_15452),U_15451)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15450),U_15451))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15450) ),
inference(clausify,[status(thm)],[f_3911_2]) ).
fof(f_3912_1,plain,
! [V_A_2,T_b] :
( c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__fin__Inf]) ).
fof(f_3912_2,plain,
! [U_15454,U_15453] :
( c_Big__Operators_Olattice__class_OInf__fin(U_15453,U_15454) = c_Complete__Lattice_OInf__class_OInf(U_15453,U_15454)
| U_15454 = c_Orderings_Obot__class_Obot(tc_fun(U_15453,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15453),U_15454))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15453) ),
inference(variable_rename,[status(thm)],[f_3912_1]) ).
cnf(f_3912_3,plain,
( c_Big__Operators_Olattice__class_OInf__fin(U_15453,U_15454) = c_Complete__Lattice_OInf__class_OInf(U_15453,U_15454)
| U_15454 = c_Orderings_Obot__class_Obot(tc_fun(U_15453,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15453),U_15454))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15453) ),
inference(clausify,[status(thm)],[f_3912_2]) ).
fof(f_3913_1,plain,
! [V_A_2,T_b] :
( c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_b)))))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Inf__Sup]) ).
fof(f_3913_2,plain,
! [U_15456,U_15455] :
( c_Complete__Lattice_OInf__class_OInf(U_15455,U_15456) = c_Complete__Lattice_OSup__class_OSup(U_15455,hAPP(c_Set_OCollect(U_15455),hAPP(hAPP(c_COMBB(tc_fun(U_15455,tc_HOL_Obool),tc_HOL_Obool,U_15455),c_HOL_OAll(U_15455)),hAPP(hAPP(c_COMBB(tc_fun(U_15455,tc_HOL_Obool),tc_fun(U_15455,tc_HOL_Obool),U_15455),hAPP(c_COMBS(U_15455,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15455),c_fimplies),hAPP(hAPP(c_COMBC(U_15455,tc_fun(U_15455,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15455)),U_15456)))),c_Orderings_Oord__class_Oless__eq(U_15455)))))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15455) ),
inference(variable_rename,[status(thm)],[f_3913_1]) ).
cnf(f_3913_3,plain,
( c_Complete__Lattice_OInf__class_OInf(U_15455,U_15456) = c_Complete__Lattice_OSup__class_OSup(U_15455,hAPP(c_Set_OCollect(U_15455),hAPP(hAPP(c_COMBB(tc_fun(U_15455,tc_HOL_Obool),tc_HOL_Obool,U_15455),c_HOL_OAll(U_15455)),hAPP(hAPP(c_COMBB(tc_fun(U_15455,tc_HOL_Obool),tc_fun(U_15455,tc_HOL_Obool),U_15455),hAPP(c_COMBS(U_15455,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15455),c_fimplies),hAPP(hAPP(c_COMBC(U_15455,tc_fun(U_15455,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15455)),U_15456)))),c_Orderings_Oord__class_Oless__eq(U_15455)))))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15455) ),
inference(clausify,[status(thm)],[f_3913_2]) ).
fof(f_3914_1,plain,
! [V_A_2,T_b] :
( c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))))))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__Inf]) ).
fof(f_3914_2,plain,
! [U_15458,U_15457] :
( c_Complete__Lattice_OSup__class_OSup(U_15457,U_15458) = c_Complete__Lattice_OInf__class_OInf(U_15457,hAPP(c_Set_OCollect(U_15457),hAPP(hAPP(c_COMBB(tc_fun(U_15457,tc_HOL_Obool),tc_HOL_Obool,U_15457),c_HOL_OAll(U_15457)),hAPP(hAPP(c_COMBB(tc_fun(U_15457,tc_HOL_Obool),tc_fun(U_15457,tc_HOL_Obool),U_15457),hAPP(c_COMBS(U_15457,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15457),c_fimplies),hAPP(hAPP(c_COMBC(U_15457,tc_fun(U_15457,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15457)),U_15458)))),hAPP(c_COMBC(U_15457,U_15457,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_15457))))))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15457) ),
inference(variable_rename,[status(thm)],[f_3914_1]) ).
cnf(f_3914_3,plain,
( c_Complete__Lattice_OSup__class_OSup(U_15457,U_15458) = c_Complete__Lattice_OInf__class_OInf(U_15457,hAPP(c_Set_OCollect(U_15457),hAPP(hAPP(c_COMBB(tc_fun(U_15457,tc_HOL_Obool),tc_HOL_Obool,U_15457),c_HOL_OAll(U_15457)),hAPP(hAPP(c_COMBB(tc_fun(U_15457,tc_HOL_Obool),tc_fun(U_15457,tc_HOL_Obool),U_15457),hAPP(c_COMBS(U_15457,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15457),c_fimplies),hAPP(hAPP(c_COMBC(U_15457,tc_fun(U_15457,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15457)),U_15458)))),hAPP(c_COMBC(U_15457,U_15457,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_15457))))))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15457) ),
inference(clausify,[status(thm)],[f_3914_2]) ).
fof(f_3915_1,plain,
! [V_A_2,V_C_2,V_X_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_UnionI]) ).
fof(f_3915_2,plain,
! [U_15462,U_15461,U_15460,U_15459] :
( hBOOL(hAPP(hAPP(c_member(U_15459),U_15462),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15459,tc_HOL_Obool),U_15461)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15459),U_15462),U_15460))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_15459,tc_HOL_Obool)),U_15460),U_15461)) ),
inference(variable_rename,[status(thm)],[f_3915_1]) ).
cnf(f_3915_3,plain,
( hBOOL(hAPP(hAPP(c_member(U_15459),U_15462),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15459,tc_HOL_Obool),U_15461)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15459),U_15462),U_15460))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_15459,tc_HOL_Obool)),U_15460),U_15461)) ),
inference(clausify,[status(thm)],[f_3915_2]) ).
fof(f_3916_1,plain,
! [V_S_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_Inter__def]) ).
fof(f_3916_2,plain,
! [U_15464,U_15463] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15463,tc_HOL_Obool),U_15464) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_15463,tc_HOL_Obool),tc_fun(U_15463,tc_HOL_Obool)),U_15464),c_COMBI(tc_fun(U_15463,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_3916_1]) ).
cnf(f_3916_3,plain,
c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15463,tc_HOL_Obool),U_15464) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_15463,tc_HOL_Obool),tc_fun(U_15463,tc_HOL_Obool)),U_15464),c_COMBI(tc_fun(U_15463,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_3916_2]) ).
fof(f_3917_1,plain,
! [V_S_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_c,T_b,V_f_2)),
inference(fof_nnf,[status(thm)],[fact_image__Union]) ).
fof(f_3917_2,plain,
! [U_15468,U_15467,U_15466,U_15465] : hAPP(c_Set_Oimage(U_15465,U_15466,U_15467),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15465,tc_HOL_Obool),U_15468)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_15465,tc_HOL_Obool),tc_fun(U_15466,tc_HOL_Obool)),U_15468),c_Set_Oimage(U_15465,U_15466,U_15467)),
inference(variable_rename,[status(thm)],[f_3917_1]) ).
cnf(f_3917_3,plain,
hAPP(c_Set_Oimage(U_15465,U_15466,U_15467),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15465,tc_HOL_Obool),U_15468)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_15465,tc_HOL_Obool),tc_fun(U_15466,tc_HOL_Obool)),U_15468),c_Set_Oimage(U_15465,U_15466,U_15467)),
inference(clausify,[status(thm)],[f_3917_2]) ).
fof(f_3918_1,plain,
! [V_S_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_b,T_c)),
inference(fof_nnf,[status(thm)],[fact_Domain__Union]) ).
fof(f_3918_2,plain,
! [U_15471,U_15470,U_15469] : hAPP(c_Relation_ODomain(U_15469,U_15470),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_15469,U_15470),tc_HOL_Obool),U_15471)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_15469,U_15470),tc_HOL_Obool),tc_fun(U_15469,tc_HOL_Obool)),U_15471),c_Relation_ODomain(U_15469,U_15470)),
inference(variable_rename,[status(thm)],[f_3918_1]) ).
cnf(f_3918_3,plain,
hAPP(c_Relation_ODomain(U_15469,U_15470),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_15469,U_15470),tc_HOL_Obool),U_15471)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_15469,U_15470),tc_HOL_Obool),tc_fun(U_15469,tc_HOL_Obool)),U_15471),c_Relation_ODomain(U_15469,U_15470)),
inference(clausify,[status(thm)],[f_3918_2]) ).
fof(f_3919_1,plain,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_UN__simps_I8_J]) ).
fof(f_3919_2,plain,
! [U_15475,U_15474,U_15473,U_15472] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15472,tc_fun(U_15473,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15472,tc_HOL_Obool),U_15474)),U_15475) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_15472,tc_HOL_Obool),tc_fun(U_15473,tc_HOL_Obool)),U_15474),hAPP(hAPP(c_COMBC(tc_fun(U_15472,tc_HOL_Obool),tc_fun(U_15472,tc_fun(U_15473,tc_HOL_Obool)),tc_fun(U_15473,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15472,tc_fun(U_15473,tc_HOL_Obool))),U_15475)),
inference(variable_rename,[status(thm)],[f_3919_1]) ).
cnf(f_3919_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15472,tc_fun(U_15473,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15472,tc_HOL_Obool),U_15474)),U_15475) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_15472,tc_HOL_Obool),tc_fun(U_15473,tc_HOL_Obool)),U_15474),hAPP(hAPP(c_COMBC(tc_fun(U_15472,tc_HOL_Obool),tc_fun(U_15472,tc_fun(U_15473,tc_HOL_Obool)),tc_fun(U_15473,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15472,tc_fun(U_15473,tc_HOL_Obool))),U_15475)),
inference(clausify,[status(thm)],[f_3919_2]) ).
fof(f_3920_1,plain,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2),
inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I8_J]) ).
fof(f_3920_2,plain,
! [U_15479,U_15478,U_15477,U_15476] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_15476,tc_HOL_Obool),tc_fun(U_15477,tc_HOL_Obool)),U_15478),hAPP(hAPP(c_COMBC(tc_fun(U_15476,tc_HOL_Obool),tc_fun(U_15476,tc_fun(U_15477,tc_HOL_Obool)),tc_fun(U_15477,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15476,tc_fun(U_15477,tc_HOL_Obool))),U_15479)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15476,tc_fun(U_15477,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15476,tc_HOL_Obool),U_15478)),U_15479),
inference(variable_rename,[status(thm)],[f_3920_1]) ).
cnf(f_3920_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_15476,tc_HOL_Obool),tc_fun(U_15477,tc_HOL_Obool)),U_15478),hAPP(hAPP(c_COMBC(tc_fun(U_15476,tc_HOL_Obool),tc_fun(U_15476,tc_fun(U_15477,tc_HOL_Obool)),tc_fun(U_15477,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15476,tc_fun(U_15477,tc_HOL_Obool))),U_15479)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15476,tc_fun(U_15477,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15476,tc_HOL_Obool),U_15478)),U_15479),
inference(clausify,[status(thm)],[f_3920_2]) ).
fof(f_3921_1,plain,
! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Int__Union2]) ).
fof(f_3921_2,plain,
! [U_15482,U_15481,U_15480] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15480,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15480,tc_HOL_Obool),U_15481)),U_15482) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_15480,tc_HOL_Obool),tc_fun(U_15480,tc_HOL_Obool)),U_15481),hAPP(hAPP(c_COMBC(tc_fun(U_15480,tc_HOL_Obool),tc_fun(U_15480,tc_HOL_Obool),tc_fun(U_15480,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15480,tc_HOL_Obool))),U_15482)),
inference(variable_rename,[status(thm)],[f_3921_1]) ).
cnf(f_3921_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15480,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15480,tc_HOL_Obool),U_15481)),U_15482) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_15480,tc_HOL_Obool),tc_fun(U_15480,tc_HOL_Obool)),U_15481),hAPP(hAPP(c_COMBC(tc_fun(U_15480,tc_HOL_Obool),tc_fun(U_15480,tc_HOL_Obool),tc_fun(U_15480,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15480,tc_HOL_Obool))),U_15482)),
inference(clausify,[status(thm)],[f_3921_2]) ).
fof(f_3922_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_Int__Union]) ).
fof(f_3922_2,plain,
! [U_15485,U_15484,U_15483] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15483,tc_HOL_Obool)),U_15484),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15483,tc_HOL_Obool),U_15485)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_15483,tc_HOL_Obool),tc_fun(U_15483,tc_HOL_Obool)),U_15485),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15483,tc_HOL_Obool)),U_15484)),
inference(variable_rename,[status(thm)],[f_3922_1]) ).
cnf(f_3922_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15483,tc_HOL_Obool)),U_15484),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15483,tc_HOL_Obool),U_15485)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_15483,tc_HOL_Obool),tc_fun(U_15483,tc_HOL_Obool)),U_15485),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15483,tc_HOL_Obool)),U_15484)),
inference(clausify,[status(thm)],[f_3922_2]) ).
fof(f_3923_1,plain,
! [V_B_2,V_X_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Product__Type_OSigma(T_b,T_c)),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Sigma__Union]) ).
fof(f_3923_2,plain,
! [U_15489,U_15488,U_15487,U_15486] : hAPP(hAPP(c_Product__Type_OSigma(U_15486,U_15487),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15486,tc_HOL_Obool),U_15488)),U_15489) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_15486,tc_HOL_Obool),tc_fun(tc_prod(U_15486,U_15487),tc_HOL_Obool)),U_15488),hAPP(hAPP(c_COMBC(tc_fun(U_15486,tc_HOL_Obool),tc_fun(U_15486,tc_fun(U_15487,tc_HOL_Obool)),tc_fun(tc_prod(U_15486,U_15487),tc_HOL_Obool)),c_Product__Type_OSigma(U_15486,U_15487)),U_15489)),
inference(variable_rename,[status(thm)],[f_3923_1]) ).
cnf(f_3923_3,plain,
hAPP(hAPP(c_Product__Type_OSigma(U_15486,U_15487),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15486,tc_HOL_Obool),U_15488)),U_15489) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_15486,tc_HOL_Obool),tc_fun(tc_prod(U_15486,U_15487),tc_HOL_Obool)),U_15488),hAPP(hAPP(c_COMBC(tc_fun(U_15486,tc_HOL_Obool),tc_fun(U_15486,tc_fun(U_15487,tc_HOL_Obool)),tc_fun(tc_prod(U_15486,U_15487),tc_HOL_Obool)),c_Product__Type_OSigma(U_15486,U_15487)),U_15489)),
inference(clausify,[status(thm)],[f_3923_2]) ).
fof(f_3924_1,plain,
! [V_S_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_c,T_b)),
inference(fof_nnf,[status(thm)],[fact_Range__Union]) ).
fof(f_3924_2,plain,
! [U_15492,U_15491,U_15490] : hAPP(c_Relation_ORange(U_15490,U_15491),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_15490,U_15491),tc_HOL_Obool),U_15492)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_15490,U_15491),tc_HOL_Obool),tc_fun(U_15491,tc_HOL_Obool)),U_15492),c_Relation_ORange(U_15490,U_15491)),
inference(variable_rename,[status(thm)],[f_3924_1]) ).
cnf(f_3924_3,plain,
hAPP(c_Relation_ORange(U_15490,U_15491),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_15490,U_15491),tc_HOL_Obool),U_15492)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_15490,U_15491),tc_HOL_Obool),tc_fun(U_15491,tc_HOL_Obool)),U_15492),c_Relation_ORange(U_15490,U_15491)),
inference(clausify,[status(thm)],[f_3924_2]) ).
fof(f_3925_1,plain,
! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_b,T_c,V_f_2)),
inference(fof_nnf,[status(thm)],[fact_vimage__Union]) ).
fof(f_3925_2,plain,
! [U_15496,U_15495,U_15494,U_15493] : hAPP(c_Set_Ovimage(U_15493,U_15494,U_15495),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15494,tc_HOL_Obool),U_15496)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_15494,tc_HOL_Obool),tc_fun(U_15493,tc_HOL_Obool)),U_15496),c_Set_Ovimage(U_15493,U_15494,U_15495)),
inference(variable_rename,[status(thm)],[f_3925_1]) ).
cnf(f_3925_3,plain,
hAPP(c_Set_Ovimage(U_15493,U_15494,U_15495),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15494,tc_HOL_Obool),U_15496)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_15494,tc_HOL_Obool),tc_fun(U_15493,tc_HOL_Obool)),U_15496),c_Set_Ovimage(U_15493,U_15494,U_15495)),
inference(clausify,[status(thm)],[f_3925_2]) ).
fof(f_3926_1,plain,
! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Union__empty]) ).
fof(f_3926_2,plain,
! [U_15497] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15497,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_15497,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_15497,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3926_1]) ).
cnf(f_3926_3,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15497,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_15497,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_15497,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3926_2]) ).
fof(f_3927_1,plain,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Union__mono]) ).
fof(f_3927_2,plain,
! [U_15500,U_15499,U_15498] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15498,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15498,tc_HOL_Obool),U_15499)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15498,tc_HOL_Obool),U_15500)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_15498,tc_HOL_Obool),tc_HOL_Obool)),U_15499),U_15500)) ),
inference(variable_rename,[status(thm)],[f_3927_1]) ).
cnf(f_3927_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15498,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15498,tc_HOL_Obool),U_15499)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15498,tc_HOL_Obool),U_15500)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_15498,tc_HOL_Obool),tc_HOL_Obool)),U_15499),U_15500)) ),
inference(clausify,[status(thm)],[f_3927_2]) ).
fof(f_3928_1,plain,
! [V_A_2,V_C_2,T_b] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ? [B_x] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2)) ) )
& ( ! [B_x] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(fof_nnf,[status(thm)],[fact_Union__disjoint]) ).
fof(f_3928_2,plain,
! [U_15505,U_15504,U_15503] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15503,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15503,tc_HOL_Obool),U_15504)),U_15505) = c_Orderings_Obot__class_Obot(tc_fun(U_15503,tc_HOL_Obool))
| ? [U_15502] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15503,tc_HOL_Obool)),U_15502),U_15505) != c_Orderings_Obot__class_Obot(tc_fun(U_15503,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15503,tc_HOL_Obool)),U_15502),U_15504)) ) )
& ( ! [U_15501] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15503,tc_HOL_Obool)),U_15501),U_15505) = c_Orderings_Obot__class_Obot(tc_fun(U_15503,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_15503,tc_HOL_Obool)),U_15501),U_15504)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15503,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15503,tc_HOL_Obool),U_15504)),U_15505) != c_Orderings_Obot__class_Obot(tc_fun(U_15503,tc_HOL_Obool)) ) ),
inference(variable_rename,[status(thm)],[f_3928_1]) ).
fof(f_3928_3,plain,
( ! [U_15511,U_15509,U_15507] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15507,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15507,tc_HOL_Obool),U_15509)),U_15511) = c_Orderings_Obot__class_Obot(tc_fun(U_15507,tc_HOL_Obool))
| ? [U_15502] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15507,tc_HOL_Obool)),U_15502),U_15511) != c_Orderings_Obot__class_Obot(tc_fun(U_15507,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15507,tc_HOL_Obool)),U_15502),U_15509)) ) )
& ! [U_15510,U_15508,U_15506] :
( ! [U_15501] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15506,tc_HOL_Obool)),U_15501),U_15510) = c_Orderings_Obot__class_Obot(tc_fun(U_15506,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_15506,tc_HOL_Obool)),U_15501),U_15508)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15506,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15506,tc_HOL_Obool),U_15508)),U_15510) != c_Orderings_Obot__class_Obot(tc_fun(U_15506,tc_HOL_Obool)) ) ),
inference(miniscope,[status(thm)],[f_3928_2]) ).
fof(f_3928_4,plain,
( ! [U_15511,U_15509,U_15507] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15507,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15507,tc_HOL_Obool),U_15509)),U_15511) = c_Orderings_Obot__class_Obot(tc_fun(U_15507,tc_HOL_Obool))
| ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15507,tc_HOL_Obool)),sK391(U_15511,U_15509,U_15507)),U_15511) != c_Orderings_Obot__class_Obot(tc_fun(U_15507,tc_HOL_Obool))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15507,tc_HOL_Obool)),sK391(U_15511,U_15509,U_15507)),U_15509)) ) )
& ! [U_15510,U_15508,U_15506] :
( ! [U_15501] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15506,tc_HOL_Obool)),U_15501),U_15510) = c_Orderings_Obot__class_Obot(tc_fun(U_15506,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_15506,tc_HOL_Obool)),U_15501),U_15508)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15506,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15506,tc_HOL_Obool),U_15508)),U_15510) != c_Orderings_Obot__class_Obot(tc_fun(U_15506,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK391]),skolemize(U_15502,sK391(U_15511,U_15509,U_15507))],[f_3928_3]) ).
cnf(f_3928_5,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15506,tc_HOL_Obool)),U_15501),U_15510) = c_Orderings_Obot__class_Obot(tc_fun(U_15506,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_15506,tc_HOL_Obool)),U_15501),U_15508))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15506,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15506,tc_HOL_Obool),U_15508)),U_15510) != c_Orderings_Obot__class_Obot(tc_fun(U_15506,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3928_4]) ).
cnf(f_3928_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_15507,tc_HOL_Obool)),sK391(U_15511,U_15509,U_15507)),U_15509))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15507,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15507,tc_HOL_Obool),U_15509)),U_15511) = c_Orderings_Obot__class_Obot(tc_fun(U_15507,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3928_4]) ).
cnf(f_3928_7,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15507,tc_HOL_Obool)),sK391(U_15511,U_15509,U_15507)),U_15511) != c_Orderings_Obot__class_Obot(tc_fun(U_15507,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15507,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15507,tc_HOL_Obool),U_15509)),U_15511) = c_Orderings_Obot__class_Obot(tc_fun(U_15507,tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3928_4]) ).
fof(f_3929_1,plain,
! [V_R_2,T_b] : hAPP(c_Relation_OField(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Relation_OField(T_b)),V_R_2)),
inference(fof_nnf,[status(thm)],[fact_Field__Union]) ).
fof(f_3929_2,plain,
! [U_15513,U_15512] : hAPP(c_Relation_OField(U_15512),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_15512,U_15512),tc_HOL_Obool),U_15513)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15512,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(U_15512,U_15512),tc_HOL_Obool),tc_fun(U_15512,tc_HOL_Obool),c_Relation_OField(U_15512)),U_15513)),
inference(variable_rename,[status(thm)],[f_3929_1]) ).
cnf(f_3929_3,plain,
hAPP(c_Relation_OField(U_15512),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_15512,U_15512),tc_HOL_Obool),U_15513)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15512,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(U_15512,U_15512),tc_HOL_Obool),tc_fun(U_15512,tc_HOL_Obool),c_Relation_OField(U_15512)),U_15513)),
inference(clausify,[status(thm)],[f_3929_2]) ).
fof(f_3930_1,plain,
! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OPow(T_b),V_A_2)) = V_A_2,
inference(fof_nnf,[status(thm)],[fact_Union__Pow__eq]) ).
fof(f_3930_2,plain,
! [U_15515,U_15514] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15514,tc_HOL_Obool),hAPP(c_Set_OPow(U_15514),U_15515)) = U_15515,
inference(variable_rename,[status(thm)],[f_3930_1]) ).
cnf(f_3930_3,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15514,tc_HOL_Obool),hAPP(c_Set_OPow(U_15514),U_15515)) = U_15515,
inference(clausify,[status(thm)],[f_3930_2]) ).
fof(f_3931_1,plain,
! [V_S_2,V_a_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
| ! [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) ) )
& ( ? [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2))) ) )
| ~ class_Orderings_Olinorder(T_b)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__Sup__iff]) ).
fof(f_3931_2,plain,
! [U_15520,U_15519,U_15518] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15518),U_15519),c_Complete__Lattice_OSup__class_OSup(U_15518,U_15520)))
| ! [U_15517] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15518),U_15519),U_15517))
| ~ hBOOL(hAPP(hAPP(c_member(U_15518),U_15517),U_15520)) ) )
& ( ? [U_15516] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15518),U_15519),U_15516))
& hBOOL(hAPP(hAPP(c_member(U_15518),U_15516),U_15520)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15518),U_15519),c_Complete__Lattice_OSup__class_OSup(U_15518,U_15520))) ) )
| ~ class_Orderings_Olinorder(U_15518)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15518) ),
inference(variable_rename,[status(thm)],[f_3931_1]) ).
fof(f_3931_3,plain,
! [U_15520,U_15519,U_15518] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15518),U_15519),c_Complete__Lattice_OSup__class_OSup(U_15518,U_15520)))
| ! [U_15517] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15518),U_15519),U_15517))
| ~ hBOOL(hAPP(hAPP(c_member(U_15518),U_15517),U_15520)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15518),U_15519),sK392(U_15520,U_15519,U_15518)))
& hBOOL(hAPP(hAPP(c_member(U_15518),sK392(U_15520,U_15519,U_15518)),U_15520)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15518),U_15519),c_Complete__Lattice_OSup__class_OSup(U_15518,U_15520))) ) )
| ~ class_Orderings_Olinorder(U_15518)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15518) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK392]),skolemize(U_15516,sK392(U_15520,U_15519,U_15518))],[f_3931_2]) ).
cnf(f_3931_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_15518),sK392(U_15520,U_15519,U_15518)),U_15520))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15518),U_15519),c_Complete__Lattice_OSup__class_OSup(U_15518,U_15520)))
| ~ class_Orderings_Olinorder(U_15518)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15518) ),
inference(clausify,[status(thm)],[f_3931_3]) ).
cnf(f_3931_5,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15518),U_15519),sK392(U_15520,U_15519,U_15518)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15518),U_15519),c_Complete__Lattice_OSup__class_OSup(U_15518,U_15520)))
| ~ class_Orderings_Olinorder(U_15518)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15518) ),
inference(clausify,[status(thm)],[f_3931_3]) ).
cnf(f_3931_6,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15518),U_15519),c_Complete__Lattice_OSup__class_OSup(U_15518,U_15520)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15518),U_15519),U_15517))
| ~ hBOOL(hAPP(hAPP(c_member(U_15518),U_15517),U_15520))
| ~ class_Orderings_Olinorder(U_15518)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15518) ),
inference(clausify,[status(thm)],[f_3931_3]) ).
fof(f_3932_1,plain,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2),
inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I8_J]) ).
fof(f_3932_2,plain,
! [U_15524,U_15523,U_15522,U_15521] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_15521,tc_HOL_Obool),tc_fun(U_15522,tc_HOL_Obool)),U_15523),hAPP(hAPP(c_COMBC(tc_fun(U_15521,tc_HOL_Obool),tc_fun(U_15521,tc_fun(U_15522,tc_HOL_Obool)),tc_fun(U_15522,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15521,tc_fun(U_15522,tc_HOL_Obool))),U_15524)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15521,tc_fun(U_15522,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15521,tc_HOL_Obool),U_15523)),U_15524),
inference(variable_rename,[status(thm)],[f_3932_1]) ).
cnf(f_3932_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_15521,tc_HOL_Obool),tc_fun(U_15522,tc_HOL_Obool)),U_15523),hAPP(hAPP(c_COMBC(tc_fun(U_15521,tc_HOL_Obool),tc_fun(U_15521,tc_fun(U_15522,tc_HOL_Obool)),tc_fun(U_15522,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15521,tc_fun(U_15522,tc_HOL_Obool))),U_15524)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15521,tc_fun(U_15522,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15521,tc_HOL_Obool),U_15523)),U_15524),
inference(clausify,[status(thm)],[f_3932_2]) ).
fof(f_3933_1,plain,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_INT__simps_I8_J]) ).
fof(f_3933_2,plain,
! [U_15528,U_15527,U_15526,U_15525] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15525,tc_fun(U_15526,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15525,tc_HOL_Obool),U_15527)),U_15528) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_15525,tc_HOL_Obool),tc_fun(U_15526,tc_HOL_Obool)),U_15527),hAPP(hAPP(c_COMBC(tc_fun(U_15525,tc_HOL_Obool),tc_fun(U_15525,tc_fun(U_15526,tc_HOL_Obool)),tc_fun(U_15526,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15525,tc_fun(U_15526,tc_HOL_Obool))),U_15528)),
inference(variable_rename,[status(thm)],[f_3933_1]) ).
cnf(f_3933_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15525,tc_fun(U_15526,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15525,tc_HOL_Obool),U_15527)),U_15528) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_15525,tc_HOL_Obool),tc_fun(U_15526,tc_HOL_Obool)),U_15527),hAPP(hAPP(c_COMBC(tc_fun(U_15525,tc_HOL_Obool),tc_fun(U_15525,tc_fun(U_15526,tc_HOL_Obool)),tc_fun(U_15526,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_15525,tc_fun(U_15526,tc_HOL_Obool))),U_15528)),
inference(clausify,[status(thm)],[f_3933_2]) ).
fof(f_3934_1,plain,
! [V_b_2,V_A_2,T_b] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_b_2))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
& ( ! [B_x] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_b_2)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__le__iff]) ).
fof(f_3934_2,plain,
! [U_15533,U_15532,U_15531] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15531),c_Complete__Lattice_OSup__class_OSup(U_15531,U_15532)),U_15533))
| ? [U_15530] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15531),U_15530),U_15533))
& hBOOL(hAPP(hAPP(c_member(U_15531),U_15530),U_15532)) ) )
& ( ! [U_15529] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15531),U_15529),U_15533))
| ~ hBOOL(hAPP(hAPP(c_member(U_15531),U_15529),U_15532)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15531),c_Complete__Lattice_OSup__class_OSup(U_15531,U_15532)),U_15533)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15531) ),
inference(variable_rename,[status(thm)],[f_3934_1]) ).
fof(f_3934_3,plain,
! [U_15533,U_15532,U_15531] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15531),c_Complete__Lattice_OSup__class_OSup(U_15531,U_15532)),U_15533))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15531),sK393(U_15533,U_15532,U_15531)),U_15533))
& hBOOL(hAPP(hAPP(c_member(U_15531),sK393(U_15533,U_15532,U_15531)),U_15532)) ) )
& ( ! [U_15529] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15531),U_15529),U_15533))
| ~ hBOOL(hAPP(hAPP(c_member(U_15531),U_15529),U_15532)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15531),c_Complete__Lattice_OSup__class_OSup(U_15531,U_15532)),U_15533)) ) )
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15531) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK393]),skolemize(U_15530,sK393(U_15533,U_15532,U_15531))],[f_3934_2]) ).
cnf(f_3934_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15531),U_15529),U_15533))
| ~ hBOOL(hAPP(hAPP(c_member(U_15531),U_15529),U_15532))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15531),c_Complete__Lattice_OSup__class_OSup(U_15531,U_15532)),U_15533))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15531) ),
inference(clausify,[status(thm)],[f_3934_3]) ).
cnf(f_3934_5,plain,
( hBOOL(hAPP(hAPP(c_member(U_15531),sK393(U_15533,U_15532,U_15531)),U_15532))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15531),c_Complete__Lattice_OSup__class_OSup(U_15531,U_15532)),U_15533))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15531) ),
inference(clausify,[status(thm)],[f_3934_3]) ).
cnf(f_3934_6,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15531),sK393(U_15533,U_15532,U_15531)),U_15533))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15531),c_Complete__Lattice_OSup__class_OSup(U_15531,U_15532)),U_15533))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15531) ),
inference(clausify,[status(thm)],[f_3934_3]) ).
fof(f_3935_1,plain,
! [V_A_2,V_B_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_Union__upper]) ).
fof(f_3935_2,plain,
! [U_15536,U_15535,U_15534] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15534,tc_HOL_Obool)),U_15535),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15534,tc_HOL_Obool),U_15536)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_15534,tc_HOL_Obool)),U_15535),U_15536)) ),
inference(variable_rename,[status(thm)],[f_3935_1]) ).
cnf(f_3935_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15534,tc_HOL_Obool)),U_15535),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15534,tc_HOL_Obool),U_15536)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_15534,tc_HOL_Obool)),U_15535),U_15536)) ),
inference(clausify,[status(thm)],[f_3935_2]) ).
fof(f_3936_1,plain,
! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Union__insert]) ).
fof(f_3936_2,plain,
! [U_15539,U_15538,U_15537] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15537,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_15537,tc_HOL_Obool)),U_15538),U_15539)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15537,tc_HOL_Obool)),U_15538),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15537,tc_HOL_Obool),U_15539)),
inference(variable_rename,[status(thm)],[f_3936_1]) ).
cnf(f_3936_3,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15537,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_15537,tc_HOL_Obool)),U_15538),U_15539)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15537,tc_HOL_Obool)),U_15538),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15537,tc_HOL_Obool),U_15539)),
inference(clausify,[status(thm)],[f_3936_2]) ).
fof(f_3937_1,plain,
! [V_r_2,V_A_2,T_b] :
( c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = V_A_2
| ~ c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ),
inference(fof_nnf,[status(thm)],[fact_Union__quotient]) ).
fof(f_3937_2,plain,
! [U_15542,U_15541,U_15540] :
( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15540,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_15540),U_15541),U_15542)) = U_15541
| ~ c_Equiv__Relations_Oequiv(U_15540,U_15541,U_15542) ),
inference(variable_rename,[status(thm)],[f_3937_1]) ).
cnf(f_3937_3,plain,
( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15540,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_15540),U_15541),U_15542)) = U_15541
| ~ c_Equiv__Relations_Oequiv(U_15540,U_15541,U_15542) ),
inference(clausify,[status(thm)],[f_3937_2]) ).
fof(f_3938_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ),
inference(fof_nnf,[status(thm)],[fact_finite__UnionD]) ).
fof(f_3938_2,plain,
! [U_15544,U_15543] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_15543,tc_HOL_Obool)),U_15544))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15543),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15543,tc_HOL_Obool),U_15544))) ),
inference(variable_rename,[status(thm)],[f_3938_1]) ).
cnf(f_3938_3,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_15543,tc_HOL_Obool)),U_15544))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15543),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15543,tc_HOL_Obool),U_15544))) ),
inference(clausify,[status(thm)],[f_3938_2]) ).
fof(f_3939_1,plain,
! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))),
inference(fof_nnf,[status(thm)],[fact_subset__Pow__Union]) ).
fof(f_3939_2,plain,
! [U_15546,U_15545] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_15545,tc_HOL_Obool),tc_HOL_Obool)),U_15546),hAPP(c_Set_OPow(U_15545),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15545,tc_HOL_Obool),U_15546)))),
inference(variable_rename,[status(thm)],[f_3939_1]) ).
cnf(f_3939_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_15545,tc_HOL_Obool),tc_HOL_Obool)),U_15546),hAPP(c_Set_OPow(U_15545),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15545,tc_HOL_Obool),U_15546)))),
inference(clausify,[status(thm)],[f_3939_2]) ).
fof(f_3940_1,plain,
! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
inference(fof_nnf,[status(thm)],[fact_Union__UNIV]) ).
fof(f_3940_2,plain,
! [U_15547] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15547,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_15547,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_15547,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[f_3940_1]) ).
cnf(f_3940_3,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15547,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_15547,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_15547,tc_HOL_Obool)),
inference(clausify,[status(thm)],[f_3940_2]) ).
fof(f_3941_1,plain,
! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),
inference(fof_nnf,[status(thm)],[fact_Union__Un__distrib]) ).
fof(f_3941_2,plain,
! [U_15550,U_15549,U_15548] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15548,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_15548,tc_HOL_Obool),tc_HOL_Obool)),U_15549),U_15550)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15548,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15548,tc_HOL_Obool),U_15549)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15548,tc_HOL_Obool),U_15550)),
inference(variable_rename,[status(thm)],[f_3941_1]) ).
cnf(f_3941_3,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15548,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_15548,tc_HOL_Obool),tc_HOL_Obool)),U_15549),U_15550)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15548,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15548,tc_HOL_Obool),U_15549)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15548,tc_HOL_Obool),U_15550)),
inference(clausify,[status(thm)],[f_3941_2]) ).
fof(f_3942_1,plain,
! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)),
inference(fof_nnf,[status(thm)],[fact_UNION__eq__Union__image]) ).
fof(f_3942_2,plain,
! [U_15554,U_15553,U_15552,U_15551] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15551,tc_fun(U_15552,tc_HOL_Obool)),U_15553),U_15554) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15552,tc_HOL_Obool),hAPP(c_Set_Oimage(U_15551,tc_fun(U_15552,tc_HOL_Obool),U_15554),U_15553)),
inference(variable_rename,[status(thm)],[f_3942_1]) ).
cnf(f_3942_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15551,tc_fun(U_15552,tc_HOL_Obool)),U_15553),U_15554) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15552,tc_HOL_Obool),hAPP(c_Set_Oimage(U_15551,tc_fun(U_15552,tc_HOL_Obool),U_15554),U_15553)),
inference(clausify,[status(thm)],[f_3942_2]) ).
fof(f_3943_1,plain,
! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
inference(fof_nnf,[status(thm)],[fact_Union__image__eq]) ).
fof(f_3943_2,plain,
! [U_15558,U_15557,U_15556,U_15555] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15555,tc_HOL_Obool),hAPP(c_Set_Oimage(U_15556,tc_fun(U_15555,tc_HOL_Obool),U_15557),U_15558)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15556,tc_fun(U_15555,tc_HOL_Obool)),U_15558),U_15557),
inference(variable_rename,[status(thm)],[f_3943_1]) ).
cnf(f_3943_3,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15555,tc_HOL_Obool),hAPP(c_Set_Oimage(U_15556,tc_fun(U_15555,tc_HOL_Obool),U_15557),U_15558)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15556,tc_fun(U_15555,tc_HOL_Obool)),U_15558),U_15557),
inference(clausify,[status(thm)],[f_3943_2]) ).
fof(f_3944_1,plain,
! [V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__upper]) ).
fof(f_3944_2,plain,
! [U_15561,U_15560,U_15559] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15559),U_15560),c_Complete__Lattice_OSup__class_OSup(U_15559,U_15561)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15559),U_15560),U_15561))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15559) ),
inference(variable_rename,[status(thm)],[f_3944_1]) ).
cnf(f_3944_3,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15559),U_15560),c_Complete__Lattice_OSup__class_OSup(U_15559,U_15561)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15559),U_15560),U_15561))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15559) ),
inference(clausify,[status(thm)],[f_3944_2]) ).
fof(f_3945_1,plain,
! [T_b] :
( c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__empty]) ).
fof(f_3945_2,plain,
! [U_15562] :
( c_Complete__Lattice_OSup__class_OSup(U_15562,c_Orderings_Obot__class_Obot(tc_fun(U_15562,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_15562)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15562) ),
inference(variable_rename,[status(thm)],[f_3945_1]) ).
cnf(f_3945_3,plain,
( c_Complete__Lattice_OSup__class_OSup(U_15562,c_Orderings_Obot__class_Obot(tc_fun(U_15562,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_15562)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15562) ),
inference(clausify,[status(thm)],[f_3945_2]) ).
fof(f_3946_1,plain,
! [V_a_2,T_b] :
( c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__singleton]) ).
fof(f_3946_2,plain,
! [U_15564,U_15563] :
( c_Complete__Lattice_OSup__class_OSup(U_15563,hAPP(hAPP(c_Set_Oinsert(U_15563),U_15564),c_Orderings_Obot__class_Obot(tc_fun(U_15563,tc_HOL_Obool)))) = U_15564
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15563) ),
inference(variable_rename,[status(thm)],[f_3946_1]) ).
cnf(f_3946_3,plain,
( c_Complete__Lattice_OSup__class_OSup(U_15563,hAPP(hAPP(c_Set_Oinsert(U_15563),U_15564),c_Orderings_Obot__class_Obot(tc_fun(U_15563,tc_HOL_Obool)))) = U_15564
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15563) ),
inference(clausify,[status(thm)],[f_3946_2]) ).
fof(f_3947_1,plain,
! [V_A_2,V_a_2,T_b] :
( c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__insert]) ).
fof(f_3947_2,plain,
! [U_15567,U_15566,U_15565] :
( c_Complete__Lattice_OSup__class_OSup(U_15565,hAPP(hAPP(c_Set_Oinsert(U_15565),U_15566),U_15567)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15565),U_15566),c_Complete__Lattice_OSup__class_OSup(U_15565,U_15567))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15565) ),
inference(variable_rename,[status(thm)],[f_3947_1]) ).
cnf(f_3947_3,plain,
( c_Complete__Lattice_OSup__class_OSup(U_15565,hAPP(hAPP(c_Set_Oinsert(U_15565),U_15566),U_15567)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15565),U_15566),c_Complete__Lattice_OSup__class_OSup(U_15565,U_15567))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15565) ),
inference(clausify,[status(thm)],[f_3947_2]) ).
fof(f_3948_1,plain,
! [T_b] :
( c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__UNIV]) ).
fof(f_3948_2,plain,
! [U_15568] :
( c_Complete__Lattice_OSup__class_OSup(U_15568,c_Orderings_Otop__class_Otop(tc_fun(U_15568,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_15568)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15568) ),
inference(variable_rename,[status(thm)],[f_3948_1]) ).
cnf(f_3948_3,plain,
( c_Complete__Lattice_OSup__class_OSup(U_15568,c_Orderings_Otop__class_Otop(tc_fun(U_15568,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_15568)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15568) ),
inference(clausify,[status(thm)],[f_3948_2]) ).
fof(f_3949_1,plain,
! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))),
inference(fof_nnf,[status(thm)],[fact_Un__eq__Union]) ).
fof(f_3949_2,plain,
! [U_15571,U_15570,U_15569] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15569,tc_HOL_Obool)),U_15570),U_15571) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15569,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_15569,tc_HOL_Obool)),U_15570),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_15569,tc_HOL_Obool)),U_15571),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_15569,tc_HOL_Obool),tc_HOL_Obool))))),
inference(variable_rename,[status(thm)],[f_3949_1]) ).
cnf(f_3949_3,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15569,tc_HOL_Obool)),U_15570),U_15571) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15569,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_15569,tc_HOL_Obool)),U_15570),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_15569,tc_HOL_Obool)),U_15571),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_15569,tc_HOL_Obool),tc_HOL_Obool))))),
inference(clausify,[status(thm)],[f_3949_2]) ).
fof(f_3950_1,plain,
! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))),
inference(fof_nnf,[status(thm)],[fact_Un__Union__image]) ).
fof(f_3950_2,plain,
! [U_15576,U_15575,U_15574,U_15573,U_15572] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15572,tc_fun(U_15573,tc_HOL_Obool)),U_15574),hAPP(hAPP(c_COMBS(U_15572,tc_fun(U_15573,tc_HOL_Obool),tc_fun(U_15573,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15573,tc_HOL_Obool),tc_fun(tc_fun(U_15573,tc_HOL_Obool),tc_fun(U_15573,tc_HOL_Obool)),U_15572),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15573,tc_HOL_Obool))),U_15575)),U_15576)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15573,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15573,tc_HOL_Obool),hAPP(c_Set_Oimage(U_15572,tc_fun(U_15573,tc_HOL_Obool),U_15575),U_15574))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15573,tc_HOL_Obool),hAPP(c_Set_Oimage(U_15572,tc_fun(U_15573,tc_HOL_Obool),U_15576),U_15574))),
inference(variable_rename,[status(thm)],[f_3950_1]) ).
cnf(f_3950_3,plain,
hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15572,tc_fun(U_15573,tc_HOL_Obool)),U_15574),hAPP(hAPP(c_COMBS(U_15572,tc_fun(U_15573,tc_HOL_Obool),tc_fun(U_15573,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15573,tc_HOL_Obool),tc_fun(tc_fun(U_15573,tc_HOL_Obool),tc_fun(U_15573,tc_HOL_Obool)),U_15572),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15573,tc_HOL_Obool))),U_15575)),U_15576)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15573,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15573,tc_HOL_Obool),hAPP(c_Set_Oimage(U_15572,tc_fun(U_15573,tc_HOL_Obool),U_15575),U_15574))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15573,tc_HOL_Obool),hAPP(c_Set_Oimage(U_15572,tc_fun(U_15573,tc_HOL_Obool),U_15576),U_15574))),
inference(clausify,[status(thm)],[f_3950_2]) ).
fof(f_3951_1,plain,
! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)))),
inference(fof_nnf,[status(thm)],[fact_Union__Int__subset]) ).
fof(f_3951_2,plain,
! [U_15579,U_15578,U_15577] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15577,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15577,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_15577,tc_HOL_Obool),tc_HOL_Obool)),U_15578),U_15579))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15577,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15577,tc_HOL_Obool),U_15578)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15577,tc_HOL_Obool),U_15579)))),
inference(variable_rename,[status(thm)],[f_3951_1]) ).
cnf(f_3951_3,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15577,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15577,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_15577,tc_HOL_Obool),tc_HOL_Obool)),U_15578),U_15579))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15577,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15577,tc_HOL_Obool),U_15578)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15577,tc_HOL_Obool),U_15579)))),
inference(clausify,[status(thm)],[f_3951_2]) ).
fof(f_3952_1,plain,
! [V_b_2,V_a_2,T_b] :
( c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__binary]) ).
fof(f_3952_2,plain,
! [U_15582,U_15581,U_15580] :
( c_Complete__Lattice_OSup__class_OSup(U_15580,hAPP(hAPP(c_Set_Oinsert(U_15580),U_15581),hAPP(hAPP(c_Set_Oinsert(U_15580),U_15582),c_Orderings_Obot__class_Obot(tc_fun(U_15580,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15580),U_15581),U_15582)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15580) ),
inference(variable_rename,[status(thm)],[f_3952_1]) ).
cnf(f_3952_3,plain,
( c_Complete__Lattice_OSup__class_OSup(U_15580,hAPP(hAPP(c_Set_Oinsert(U_15580),U_15581),hAPP(hAPP(c_Set_Oinsert(U_15580),U_15582),c_Orderings_Obot__class_Obot(tc_fun(U_15580,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15580),U_15581),U_15582)
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15580) ),
inference(clausify,[status(thm)],[f_3952_2]) ).
fof(f_3953_1,plain,
! [V_B_2,V_A_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_B_2),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_sup__Sup__fold__sup]) ).
fof(f_3953_2,plain,
! [U_15585,U_15584,U_15583] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15583),U_15585),c_Complete__Lattice_OSup__class_OSup(U_15583,U_15584)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15583,U_15583,c_Lattices_Osemilattice__sup__class_Osup(U_15583)),U_15585),U_15584)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15583),U_15584))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15583) ),
inference(variable_rename,[status(thm)],[f_3953_1]) ).
cnf(f_3953_3,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15583),U_15585),c_Complete__Lattice_OSup__class_OSup(U_15583,U_15584)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15583,U_15583,c_Lattices_Osemilattice__sup__class_Osup(U_15583)),U_15585),U_15584)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15583),U_15584))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15583) ),
inference(clausify,[status(thm)],[f_3953_2]) ).
fof(f_3954_1,plain,
! [V_A_2,T_b] :
( c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fin__Sup]) ).
fof(f_3954_2,plain,
! [U_15587,U_15586] :
( c_Big__Operators_Olattice__class_OSup__fin(U_15586,U_15587) = c_Complete__Lattice_OSup__class_OSup(U_15586,U_15587)
| U_15587 = c_Orderings_Obot__class_Obot(tc_fun(U_15586,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15586),U_15587))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15586) ),
inference(variable_rename,[status(thm)],[f_3954_1]) ).
cnf(f_3954_3,plain,
( c_Big__Operators_Olattice__class_OSup__fin(U_15586,U_15587) = c_Complete__Lattice_OSup__class_OSup(U_15586,U_15587)
| U_15587 = c_Orderings_Obot__class_Obot(tc_fun(U_15586,tc_HOL_Obool))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15586),U_15587))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15586) ),
inference(clausify,[status(thm)],[f_3954_2]) ).
fof(f_3955_1,plain,
! [V_A_2,T_b] :
( c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),c_Orderings_Obot__class_Obot(T_b)),V_A_2)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Complete__Lattice_Ocomplete__lattice(T_b) ),
inference(fof_nnf,[status(thm)],[fact_Sup__fold__sup]) ).
fof(f_3955_2,plain,
! [U_15589,U_15588] :
( c_Complete__Lattice_OSup__class_OSup(U_15588,U_15589) = hAPP(hAPP(c_Finite__Set_Ofold(U_15588,U_15588,c_Lattices_Osemilattice__sup__class_Osup(U_15588)),c_Orderings_Obot__class_Obot(U_15588)),U_15589)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15588),U_15589))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15588) ),
inference(variable_rename,[status(thm)],[f_3955_1]) ).
cnf(f_3955_3,plain,
( c_Complete__Lattice_OSup__class_OSup(U_15588,U_15589) = hAPP(hAPP(c_Finite__Set_Ofold(U_15588,U_15588,c_Lattices_Osemilattice__sup__class_Osup(U_15588)),c_Orderings_Obot__class_Obot(U_15588)),U_15589)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15588),U_15589))
| ~ class_Complete__Lattice_Ocomplete__lattice(U_15588) ),
inference(clausify,[status(thm)],[f_3955_2]) ).
fof(f_3956_1,plain,
! [V_f_2,T_c,T_b,V_S_2] :
( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2))
| ? [B_A] :
( ~ c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A)
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2)) )
| V_S_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(fof_nnf,[status(thm)],[fact_inj__on__Inter]) ).
fof(f_3956_2,plain,
! [U_15594,U_15593,U_15592,U_15591] :
( c_Fun_Oinj__on(U_15592,U_15593,U_15594,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15592,tc_HOL_Obool),U_15591))
| ? [U_15590] :
( ~ c_Fun_Oinj__on(U_15592,U_15593,U_15594,U_15590)
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15592,tc_HOL_Obool)),U_15590),U_15591)) )
| U_15591 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_15592,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[f_3956_1]) ).
fof(f_3956_3,plain,
! [U_15594,U_15593,U_15592,U_15591] :
( c_Fun_Oinj__on(U_15592,U_15593,U_15594,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15592,tc_HOL_Obool),U_15591))
| ( ~ c_Fun_Oinj__on(U_15592,U_15593,U_15594,sK394(U_15594,U_15593,U_15592,U_15591))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15592,tc_HOL_Obool)),sK394(U_15594,U_15593,U_15592,U_15591)),U_15591)) )
| U_15591 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_15592,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK394]),skolemize(U_15590,sK394(U_15594,U_15593,U_15592,U_15591))],[f_3956_2]) ).
cnf(f_3956_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_15592,tc_HOL_Obool)),sK394(U_15594,U_15593,U_15592,U_15591)),U_15591))
| c_Fun_Oinj__on(U_15592,U_15593,U_15594,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15592,tc_HOL_Obool),U_15591))
| U_15591 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_15592,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3956_3]) ).
cnf(f_3956_5,plain,
( ~ c_Fun_Oinj__on(U_15592,U_15593,U_15594,sK394(U_15594,U_15593,U_15592,U_15591))
| c_Fun_Oinj__on(U_15592,U_15593,U_15594,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15592,tc_HOL_Obool),U_15591))
| U_15591 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_15592,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3956_3]) ).
fof(f_3957_1,plain,
! [V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2))
| V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
| ? [B_X] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2))
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Inter__subset]) ).
fof(f_3957_2,plain,
! [U_15598,U_15597,U_15596] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15596,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15596,tc_HOL_Obool),U_15597)),U_15598))
| U_15597 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_15596,tc_HOL_Obool),tc_HOL_Obool))
| ? [U_15595] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15596,tc_HOL_Obool)),U_15595),U_15598))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15596,tc_HOL_Obool)),U_15595),U_15597)) ) ),
inference(variable_rename,[status(thm)],[f_3957_1]) ).
fof(f_3957_3,plain,
! [U_15598,U_15597,U_15596] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15596,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15596,tc_HOL_Obool),U_15597)),U_15598))
| U_15597 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_15596,tc_HOL_Obool),tc_HOL_Obool))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15596,tc_HOL_Obool)),sK395(U_15598,U_15597,U_15596)),U_15598))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15596,tc_HOL_Obool)),sK395(U_15598,U_15597,U_15596)),U_15597)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK395]),skolemize(U_15595,sK395(U_15598,U_15597,U_15596))],[f_3957_2]) ).
cnf(f_3957_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_15596,tc_HOL_Obool)),sK395(U_15598,U_15597,U_15596)),U_15597))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15596,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15596,tc_HOL_Obool),U_15597)),U_15598))
| U_15597 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_15596,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3957_3]) ).
cnf(f_3957_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15596,tc_HOL_Obool)),sK395(U_15598,U_15597,U_15596)),U_15598))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15596,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15596,tc_HOL_Obool),U_15597)),U_15598))
| U_15597 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_15596,tc_HOL_Obool),tc_HOL_Obool)) ),
inference(clausify,[status(thm)],[f_3957_3]) ).
fof(f_3958_1,plain,
! [V_S_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))),
inference(fof_nnf,[status(thm)],[fact_Union__def]) ).
fof(f_3958_2,plain,
! [U_15600,U_15599] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15599,tc_HOL_Obool),U_15600) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_15599,tc_HOL_Obool),tc_fun(U_15599,tc_HOL_Obool)),U_15600),c_COMBI(tc_fun(U_15599,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[f_3958_1]) ).
cnf(f_3958_3,plain,
c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15599,tc_HOL_Obool),U_15600) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_15599,tc_HOL_Obool),tc_fun(U_15599,tc_HOL_Obool)),U_15600),c_COMBI(tc_fun(U_15599,tc_HOL_Obool))),
inference(clausify,[status(thm)],[f_3958_2]) ).
fof(f_3959_1,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
| ? [B_M] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M))
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__Union]) ).
fof(f_3959_2,plain,
! [U_15603,U_15602] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15602),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15602,tc_HOL_Obool),U_15603)))
| ? [U_15601] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15602),U_15601))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15602,tc_HOL_Obool)),U_15601),U_15603)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_15602,tc_HOL_Obool)),U_15603)) ),
inference(variable_rename,[status(thm)],[f_3959_1]) ).
fof(f_3959_3,plain,
! [U_15603,U_15602] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15602),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15602,tc_HOL_Obool),U_15603)))
| ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15602),sK396(U_15603,U_15602)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15602,tc_HOL_Obool)),sK396(U_15603,U_15602)),U_15603)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_15602,tc_HOL_Obool)),U_15603)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK396]),skolemize(U_15601,sK396(U_15603,U_15602))],[f_3959_2]) ).
cnf(f_3959_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_15602,tc_HOL_Obool)),sK396(U_15603,U_15602)),U_15603))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_15602),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15602,tc_HOL_Obool),U_15603)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_15602,tc_HOL_Obool)),U_15603)) ),
inference(clausify,[status(thm)],[f_3959_3]) ).
cnf(f_3959_5,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15602),sK396(U_15603,U_15602)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(U_15602),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15602,tc_HOL_Obool),U_15603)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_15602,tc_HOL_Obool)),U_15603)) ),
inference(clausify,[status(thm)],[f_3959_3]) ).
fof(f_3960_1,plain,
! [V_F_2,V_x_2,T_b] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ? [B_x] :
( ? [B_xa] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),B_xa) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& B_x != B_xa
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_insert__partition]) ).
fof(f_3960_2,plain,
! [U_15608,U_15607,U_15606] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15606,tc_HOL_Obool)),U_15607),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15606,tc_HOL_Obool),U_15608)) = c_Orderings_Obot__class_Obot(tc_fun(U_15606,tc_HOL_Obool))
| ? [U_15605] :
( ? [U_15604] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15606,tc_HOL_Obool)),U_15605),U_15604) != c_Orderings_Obot__class_Obot(tc_fun(U_15606,tc_HOL_Obool))
& U_15605 != U_15604
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15606,tc_HOL_Obool)),U_15604),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_15606,tc_HOL_Obool)),U_15607),U_15608))) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15606,tc_HOL_Obool)),U_15605),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_15606,tc_HOL_Obool)),U_15607),U_15608))) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_15606,tc_HOL_Obool)),U_15607),U_15608)) ),
inference(variable_rename,[status(thm)],[f_3960_1]) ).
fof(f_3960_3,plain,
! [U_15608,U_15607,U_15606] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15606,tc_HOL_Obool)),U_15607),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15606,tc_HOL_Obool),U_15608)) = c_Orderings_Obot__class_Obot(tc_fun(U_15606,tc_HOL_Obool))
| ( ? [U_15604] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15606,tc_HOL_Obool)),sK397(U_15608,U_15607,U_15606)),U_15604) != c_Orderings_Obot__class_Obot(tc_fun(U_15606,tc_HOL_Obool))
& sK397(U_15608,U_15607,U_15606) != U_15604
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15606,tc_HOL_Obool)),U_15604),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_15606,tc_HOL_Obool)),U_15607),U_15608))) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15606,tc_HOL_Obool)),sK397(U_15608,U_15607,U_15606)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_15606,tc_HOL_Obool)),U_15607),U_15608))) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_15606,tc_HOL_Obool)),U_15607),U_15608)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK397]),skolemize(U_15605,sK397(U_15608,U_15607,U_15606))],[f_3960_2]) ).
fof(f_3960_4,plain,
! [U_15608,U_15607,U_15606] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15606,tc_HOL_Obool)),U_15607),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15606,tc_HOL_Obool),U_15608)) = c_Orderings_Obot__class_Obot(tc_fun(U_15606,tc_HOL_Obool))
| ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15606,tc_HOL_Obool)),sK397(U_15608,U_15607,U_15606)),sK398(U_15608,U_15607,U_15606)) != c_Orderings_Obot__class_Obot(tc_fun(U_15606,tc_HOL_Obool))
& sK397(U_15608,U_15607,U_15606) != sK398(U_15608,U_15607,U_15606)
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15606,tc_HOL_Obool)),sK398(U_15608,U_15607,U_15606)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_15606,tc_HOL_Obool)),U_15607),U_15608)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15606,tc_HOL_Obool)),sK397(U_15608,U_15607,U_15606)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_15606,tc_HOL_Obool)),U_15607),U_15608))) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_15606,tc_HOL_Obool)),U_15607),U_15608)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK398]),skolemize(U_15604,sK398(U_15608,U_15607,U_15606))],[f_3960_3]) ).
cnf(f_3960_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_15606,tc_HOL_Obool)),sK397(U_15608,U_15607,U_15606)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_15606,tc_HOL_Obool)),U_15607),U_15608)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15606,tc_HOL_Obool)),U_15607),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15606,tc_HOL_Obool),U_15608)) = c_Orderings_Obot__class_Obot(tc_fun(U_15606,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_15606,tc_HOL_Obool)),U_15607),U_15608)) ),
inference(clausify,[status(thm)],[f_3960_4]) ).
cnf(f_3960_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_15606,tc_HOL_Obool)),sK398(U_15608,U_15607,U_15606)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_15606,tc_HOL_Obool)),U_15607),U_15608)))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15606,tc_HOL_Obool)),U_15607),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15606,tc_HOL_Obool),U_15608)) = c_Orderings_Obot__class_Obot(tc_fun(U_15606,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_15606,tc_HOL_Obool)),U_15607),U_15608)) ),
inference(clausify,[status(thm)],[f_3960_4]) ).
cnf(f_3960_7,plain,
( sK397(U_15608,U_15607,U_15606) != sK398(U_15608,U_15607,U_15606)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15606,tc_HOL_Obool)),U_15607),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15606,tc_HOL_Obool),U_15608)) = c_Orderings_Obot__class_Obot(tc_fun(U_15606,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_15606,tc_HOL_Obool)),U_15607),U_15608)) ),
inference(clausify,[status(thm)],[f_3960_4]) ).
cnf(f_3960_8,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15606,tc_HOL_Obool)),sK397(U_15608,U_15607,U_15606)),sK398(U_15608,U_15607,U_15606)) != c_Orderings_Obot__class_Obot(tc_fun(U_15606,tc_HOL_Obool))
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15606,tc_HOL_Obool)),U_15607),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15606,tc_HOL_Obool),U_15608)) = c_Orderings_Obot__class_Obot(tc_fun(U_15606,tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_15606,tc_HOL_Obool)),U_15607),U_15608)) ),
inference(clausify,[status(thm)],[f_3960_4]) ).
fof(f_3961_1,plain,
! [V_k_2,V_C_2,T_b] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))
| ? [B_c1] :
( ? [B_c2] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_c1),B_c2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
& B_c1 != B_c2
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2)) )
| ? [B_c] :
( hAPP(c_Finite__Set_Ocard(T_b),B_c) != V_k_2
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) ),
inference(fof_nnf,[status(thm)],[fact_card__partition]) ).
fof(f_3961_2,plain,
! [U_15614,U_15613,U_15612] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_15614),hAPP(c_Finite__Set_Ocard(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) = hAPP(c_Finite__Set_Ocard(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613))
| ? [U_15611] :
( ? [U_15610] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15612,tc_HOL_Obool)),U_15611),U_15610) != c_Orderings_Obot__class_Obot(tc_fun(U_15612,tc_HOL_Obool))
& U_15611 != U_15610
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15612,tc_HOL_Obool)),U_15610),U_15613)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15612,tc_HOL_Obool)),U_15611),U_15613)) )
| ? [U_15609] :
( hAPP(c_Finite__Set_Ocard(U_15612),U_15609) != U_15614
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15612,tc_HOL_Obool)),U_15609),U_15613)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) ),
inference(variable_rename,[status(thm)],[f_3961_1]) ).
fof(f_3961_3,plain,
! [U_15614,U_15613,U_15612] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_15614),hAPP(c_Finite__Set_Ocard(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) = hAPP(c_Finite__Set_Ocard(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613))
| ? [U_15611] :
( ? [U_15610] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15612,tc_HOL_Obool)),U_15611),U_15610) != c_Orderings_Obot__class_Obot(tc_fun(U_15612,tc_HOL_Obool))
& U_15611 != U_15610
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15612,tc_HOL_Obool)),U_15610),U_15613)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15612,tc_HOL_Obool)),U_15611),U_15613)) )
| ( hAPP(c_Finite__Set_Ocard(U_15612),sK399(U_15614,U_15613,U_15612)) != U_15614
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15612,tc_HOL_Obool)),sK399(U_15614,U_15613,U_15612)),U_15613)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK399]),skolemize(U_15609,sK399(U_15614,U_15613,U_15612))],[f_3961_2]) ).
fof(f_3961_4,plain,
! [U_15614,U_15613,U_15612] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_15614),hAPP(c_Finite__Set_Ocard(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) = hAPP(c_Finite__Set_Ocard(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613))
| ( ? [U_15610] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15612,tc_HOL_Obool)),sK400(U_15614,U_15613,U_15612)),U_15610) != c_Orderings_Obot__class_Obot(tc_fun(U_15612,tc_HOL_Obool))
& sK400(U_15614,U_15613,U_15612) != U_15610
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15612,tc_HOL_Obool)),U_15610),U_15613)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15612,tc_HOL_Obool)),sK400(U_15614,U_15613,U_15612)),U_15613)) )
| ( hAPP(c_Finite__Set_Ocard(U_15612),sK399(U_15614,U_15613,U_15612)) != U_15614
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15612,tc_HOL_Obool)),sK399(U_15614,U_15613,U_15612)),U_15613)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK400]),skolemize(U_15611,sK400(U_15614,U_15613,U_15612))],[f_3961_3]) ).
fof(f_3961_5,plain,
! [U_15614,U_15613,U_15612] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_15614),hAPP(c_Finite__Set_Ocard(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) = hAPP(c_Finite__Set_Ocard(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613))
| ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15612,tc_HOL_Obool)),sK400(U_15614,U_15613,U_15612)),sK401(U_15614,U_15613,U_15612)) != c_Orderings_Obot__class_Obot(tc_fun(U_15612,tc_HOL_Obool))
& sK400(U_15614,U_15613,U_15612) != sK401(U_15614,U_15613,U_15612)
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15612,tc_HOL_Obool)),sK401(U_15614,U_15613,U_15612)),U_15613))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15612,tc_HOL_Obool)),sK400(U_15614,U_15613,U_15612)),U_15613)) )
| ( hAPP(c_Finite__Set_Ocard(U_15612),sK399(U_15614,U_15613,U_15612)) != U_15614
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15612,tc_HOL_Obool)),sK399(U_15614,U_15613,U_15612)),U_15613)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK401]),skolemize(U_15610,sK401(U_15614,U_15613,U_15612))],[f_3961_4]) ).
cnf(f_3961_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_15612,tc_HOL_Obool)),sK400(U_15614,U_15613,U_15612)),U_15613))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_15614),hAPP(c_Finite__Set_Ocard(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) = hAPP(c_Finite__Set_Ocard(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_15612,tc_HOL_Obool)),sK399(U_15614,U_15613,U_15612)),U_15613))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) ),
inference(clausify,[status(thm)],[f_3961_5]) ).
cnf(f_3961_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_15612,tc_HOL_Obool)),sK401(U_15614,U_15613,U_15612)),U_15613))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_15614),hAPP(c_Finite__Set_Ocard(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) = hAPP(c_Finite__Set_Ocard(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_15612,tc_HOL_Obool)),sK399(U_15614,U_15613,U_15612)),U_15613))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) ),
inference(clausify,[status(thm)],[f_3961_5]) ).
cnf(f_3961_8,plain,
( sK400(U_15614,U_15613,U_15612) != sK401(U_15614,U_15613,U_15612)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_15614),hAPP(c_Finite__Set_Ocard(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) = hAPP(c_Finite__Set_Ocard(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_15612,tc_HOL_Obool)),sK399(U_15614,U_15613,U_15612)),U_15613))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) ),
inference(clausify,[status(thm)],[f_3961_5]) ).
cnf(f_3961_9,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15612,tc_HOL_Obool)),sK400(U_15614,U_15613,U_15612)),sK401(U_15614,U_15613,U_15612)) != c_Orderings_Obot__class_Obot(tc_fun(U_15612,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_15614),hAPP(c_Finite__Set_Ocard(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) = hAPP(c_Finite__Set_Ocard(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613))
| hBOOL(hAPP(hAPP(c_member(tc_fun(U_15612,tc_HOL_Obool)),sK399(U_15614,U_15613,U_15612)),U_15613))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) ),
inference(clausify,[status(thm)],[f_3961_5]) ).
cnf(f_3961_10,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_15612,tc_HOL_Obool)),sK400(U_15614,U_15613,U_15612)),U_15613))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_15614),hAPP(c_Finite__Set_Ocard(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) = hAPP(c_Finite__Set_Ocard(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613))
| hAPP(c_Finite__Set_Ocard(U_15612),sK399(U_15614,U_15613,U_15612)) != U_15614
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) ),
inference(clausify,[status(thm)],[f_3961_5]) ).
cnf(f_3961_11,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_15612,tc_HOL_Obool)),sK401(U_15614,U_15613,U_15612)),U_15613))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_15614),hAPP(c_Finite__Set_Ocard(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) = hAPP(c_Finite__Set_Ocard(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613))
| hAPP(c_Finite__Set_Ocard(U_15612),sK399(U_15614,U_15613,U_15612)) != U_15614
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) ),
inference(clausify,[status(thm)],[f_3961_5]) ).
cnf(f_3961_12,plain,
( sK400(U_15614,U_15613,U_15612) != sK401(U_15614,U_15613,U_15612)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_15614),hAPP(c_Finite__Set_Ocard(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) = hAPP(c_Finite__Set_Ocard(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613))
| hAPP(c_Finite__Set_Ocard(U_15612),sK399(U_15614,U_15613,U_15612)) != U_15614
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) ),
inference(clausify,[status(thm)],[f_3961_5]) ).
cnf(f_3961_13,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15612,tc_HOL_Obool)),sK400(U_15614,U_15613,U_15612)),sK401(U_15614,U_15613,U_15612)) != c_Orderings_Obot__class_Obot(tc_fun(U_15612,tc_HOL_Obool))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_15614),hAPP(c_Finite__Set_Ocard(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) = hAPP(c_Finite__Set_Ocard(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613))
| hAPP(c_Finite__Set_Ocard(U_15612),sK399(U_15614,U_15613,U_15612)) != U_15614
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15612),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15612,tc_HOL_Obool),U_15613)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_15612,tc_HOL_Obool)),U_15613)) ),
inference(clausify,[status(thm)],[f_3961_5]) ).
fof(f_3962_1,plain,
! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
( ? [B_y] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y))
& V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) )
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_v_2))
| ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE]) ).
fof(f_3962_2,plain,
! [U_15622,U_15621,U_15620,U_15619,U_15618,U_15617,U_15616] :
( ? [U_15615] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15616,U_15617,U_15618,U_15619,U_15621),U_15615))
& U_15622 = hAPP(hAPP(U_15618,U_15620),U_15615) )
| hBOOL(hAPP(hAPP(c_member(U_15616),U_15620),U_15621))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15616,U_15617,U_15618,U_15619,hAPP(hAPP(c_Set_Oinsert(U_15616),U_15620),U_15621)),U_15622))
| ~ c_Finite__Set_Ofun__left__comm(U_15616,U_15617,U_15618) ),
inference(variable_rename,[status(thm)],[f_3962_1]) ).
fof(f_3962_3,plain,
! [U_15622,U_15621,U_15620,U_15619,U_15618,U_15617,U_15616] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15616,U_15617,U_15618,U_15619,U_15621),sK402(U_15622,U_15621,U_15620,U_15619,U_15618,U_15617,U_15616)))
& U_15622 = hAPP(hAPP(U_15618,U_15620),sK402(U_15622,U_15621,U_15620,U_15619,U_15618,U_15617,U_15616)) )
| hBOOL(hAPP(hAPP(c_member(U_15616),U_15620),U_15621))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15616,U_15617,U_15618,U_15619,hAPP(hAPP(c_Set_Oinsert(U_15616),U_15620),U_15621)),U_15622))
| ~ c_Finite__Set_Ofun__left__comm(U_15616,U_15617,U_15618) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK402]),skolemize(U_15615,sK402(U_15622,U_15621,U_15620,U_15619,U_15618,U_15617,U_15616))],[f_3962_2]) ).
cnf(f_3962_4,plain,
( U_15622 = hAPP(hAPP(U_15618,U_15620),sK402(U_15622,U_15621,U_15620,U_15619,U_15618,U_15617,U_15616))
| hBOOL(hAPP(hAPP(c_member(U_15616),U_15620),U_15621))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15616,U_15617,U_15618,U_15619,hAPP(hAPP(c_Set_Oinsert(U_15616),U_15620),U_15621)),U_15622))
| ~ c_Finite__Set_Ofun__left__comm(U_15616,U_15617,U_15618) ),
inference(clausify,[status(thm)],[f_3962_3]) ).
cnf(f_3962_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15616,U_15617,U_15618,U_15619,U_15621),sK402(U_15622,U_15621,U_15620,U_15619,U_15618,U_15617,U_15616)))
| hBOOL(hAPP(hAPP(c_member(U_15616),U_15620),U_15621))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_15616,U_15617,U_15618,U_15619,hAPP(hAPP(c_Set_Oinsert(U_15616),U_15620),U_15621)),U_15622))
| ~ c_Finite__Set_Ofun__left__comm(U_15616,U_15617,U_15618) ),
inference(clausify,[status(thm)],[f_3962_3]) ).
fof(f_3963_1,plain,
! [V_c_2,V_b_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_c_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__le__sup]) ).
fof(f_3963_2,plain,
! [U_15627,U_15626,U_15625,U_15624] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15624),hAPP(hAPP(c_Finite__Set_Ofold(U_15624,U_15624,c_Orderings_Oord__class_Omax(U_15624)),U_15627),U_15625)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15624),U_15626),U_15627)))
| ? [U_15623] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15624),U_15623),U_15626))
& hBOOL(hAPP(hAPP(c_member(U_15624),U_15623),U_15625)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15624),U_15625))
| ~ class_Orderings_Olinorder(U_15624) ),
inference(variable_rename,[status(thm)],[f_3963_1]) ).
fof(f_3963_3,plain,
! [U_15627,U_15626,U_15625,U_15624] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15624),hAPP(hAPP(c_Finite__Set_Ofold(U_15624,U_15624,c_Orderings_Oord__class_Omax(U_15624)),U_15627),U_15625)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15624),U_15626),U_15627)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15624),sK403(U_15627,U_15626,U_15625,U_15624)),U_15626))
& hBOOL(hAPP(hAPP(c_member(U_15624),sK403(U_15627,U_15626,U_15625,U_15624)),U_15625)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15624),U_15625))
| ~ class_Orderings_Olinorder(U_15624) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK403]),skolemize(U_15623,sK403(U_15627,U_15626,U_15625,U_15624))],[f_3963_2]) ).
cnf(f_3963_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_15624),sK403(U_15627,U_15626,U_15625,U_15624)),U_15625))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15624),hAPP(hAPP(c_Finite__Set_Ofold(U_15624,U_15624,c_Orderings_Oord__class_Omax(U_15624)),U_15627),U_15625)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15624),U_15626),U_15627)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15624),U_15625))
| ~ class_Orderings_Olinorder(U_15624) ),
inference(clausify,[status(thm)],[f_3963_3]) ).
cnf(f_3963_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15624),sK403(U_15627,U_15626,U_15625,U_15624)),U_15626))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15624),hAPP(hAPP(c_Finite__Set_Ofold(U_15624,U_15624,c_Orderings_Oord__class_Omax(U_15624)),U_15627),U_15625)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15624),U_15626),U_15627)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15624),U_15625))
| ~ class_Orderings_Olinorder(U_15624) ),
inference(clausify,[status(thm)],[f_3963_3]) ).
fof(f_3964_1,plain,
! [V_c_2,V_b_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_c_2),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Orderings_Olinorder(T_b) ),
inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le__fold__inf]) ).
fof(f_3964_2,plain,
! [U_15632,U_15631,U_15630,U_15629] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15629),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15629),U_15631),U_15632)),hAPP(hAPP(c_Finite__Set_Ofold(U_15629,U_15629,c_Orderings_Oord__class_Omin(U_15629)),U_15632),U_15630)))
| ? [U_15628] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15629),U_15631),U_15628))
& hBOOL(hAPP(hAPP(c_member(U_15629),U_15628),U_15630)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15629),U_15630))
| ~ class_Orderings_Olinorder(U_15629) ),
inference(variable_rename,[status(thm)],[f_3964_1]) ).
fof(f_3964_3,plain,
! [U_15632,U_15631,U_15630,U_15629] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15629),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15629),U_15631),U_15632)),hAPP(hAPP(c_Finite__Set_Ofold(U_15629,U_15629,c_Orderings_Oord__class_Omin(U_15629)),U_15632),U_15630)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15629),U_15631),sK404(U_15632,U_15631,U_15630,U_15629)))
& hBOOL(hAPP(hAPP(c_member(U_15629),sK404(U_15632,U_15631,U_15630,U_15629)),U_15630)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15629),U_15630))
| ~ class_Orderings_Olinorder(U_15629) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK404]),skolemize(U_15628,sK404(U_15632,U_15631,U_15630,U_15629))],[f_3964_2]) ).
cnf(f_3964_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_15629),sK404(U_15632,U_15631,U_15630,U_15629)),U_15630))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15629),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15629),U_15631),U_15632)),hAPP(hAPP(c_Finite__Set_Ofold(U_15629,U_15629,c_Orderings_Oord__class_Omin(U_15629)),U_15632),U_15630)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15629),U_15630))
| ~ class_Orderings_Olinorder(U_15629) ),
inference(clausify,[status(thm)],[f_3964_3]) ).
cnf(f_3964_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15629),U_15631),sK404(U_15632,U_15631,U_15630,U_15629)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15629),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15629),U_15631),U_15632)),hAPP(hAPP(c_Finite__Set_Ofold(U_15629,U_15629,c_Orderings_Oord__class_Omin(U_15629)),U_15632),U_15630)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15629),U_15630))
| ~ class_Orderings_Olinorder(U_15629) ),
inference(clausify,[status(thm)],[f_3964_3]) ).
fof(f_3965_1,plain,
! [V_A_2,V_C_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
| ? [B_X] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
& hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_InterI]) ).
fof(f_3965_2,plain,
! [U_15636,U_15635,U_15634] :
( hBOOL(hAPP(hAPP(c_member(U_15634),U_15636),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15634,tc_HOL_Obool),U_15635)))
| ? [U_15633] :
( ~ hBOOL(hAPP(hAPP(c_member(U_15634),U_15636),U_15633))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15634,tc_HOL_Obool)),U_15633),U_15635)) ) ),
inference(variable_rename,[status(thm)],[f_3965_1]) ).
fof(f_3965_3,plain,
! [U_15636,U_15635,U_15634] :
( hBOOL(hAPP(hAPP(c_member(U_15634),U_15636),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15634,tc_HOL_Obool),U_15635)))
| ( ~ hBOOL(hAPP(hAPP(c_member(U_15634),U_15636),sK405(U_15636,U_15635,U_15634)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(U_15634,tc_HOL_Obool)),sK405(U_15636,U_15635,U_15634)),U_15635)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK405]),skolemize(U_15633,sK405(U_15636,U_15635,U_15634))],[f_3965_2]) ).
cnf(f_3965_4,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_15634,tc_HOL_Obool)),sK405(U_15636,U_15635,U_15634)),U_15635))
| hBOOL(hAPP(hAPP(c_member(U_15634),U_15636),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15634,tc_HOL_Obool),U_15635))) ),
inference(clausify,[status(thm)],[f_3965_3]) ).
cnf(f_3965_5,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_15634),U_15636),sK405(U_15636,U_15635,U_15634)))
| hBOOL(hAPP(hAPP(c_member(U_15634),U_15636),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_15634,tc_HOL_Obool),U_15635))) ),
inference(clausify,[status(thm)],[f_3965_3]) ).
fof(f_3966_1,plain,
! [V_c_2,V_b_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_c_2),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Osemilattice__inf(T_b) ),
inference(fof_nnf,[status(thm)],[fact_inf__le__fold__inf]) ).
fof(f_3966_2,plain,
! [U_15641,U_15640,U_15639,U_15638] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15638),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15638),U_15640),U_15641)),hAPP(hAPP(c_Finite__Set_Ofold(U_15638,U_15638,c_Lattices_Osemilattice__inf__class_Oinf(U_15638)),U_15641),U_15639)))
| ? [U_15637] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15638),U_15640),U_15637))
& hBOOL(hAPP(hAPP(c_member(U_15638),U_15637),U_15639)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15638),U_15639))
| ~ class_Lattices_Osemilattice__inf(U_15638) ),
inference(variable_rename,[status(thm)],[f_3966_1]) ).
fof(f_3966_3,plain,
! [U_15641,U_15640,U_15639,U_15638] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15638),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15638),U_15640),U_15641)),hAPP(hAPP(c_Finite__Set_Ofold(U_15638,U_15638,c_Lattices_Osemilattice__inf__class_Oinf(U_15638)),U_15641),U_15639)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15638),U_15640),sK406(U_15641,U_15640,U_15639,U_15638)))
& hBOOL(hAPP(hAPP(c_member(U_15638),sK406(U_15641,U_15640,U_15639,U_15638)),U_15639)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15638),U_15639))
| ~ class_Lattices_Osemilattice__inf(U_15638) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK406]),skolemize(U_15637,sK406(U_15641,U_15640,U_15639,U_15638))],[f_3966_2]) ).
cnf(f_3966_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_15638),sK406(U_15641,U_15640,U_15639,U_15638)),U_15639))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15638),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15638),U_15640),U_15641)),hAPP(hAPP(c_Finite__Set_Ofold(U_15638,U_15638,c_Lattices_Osemilattice__inf__class_Oinf(U_15638)),U_15641),U_15639)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15638),U_15639))
| ~ class_Lattices_Osemilattice__inf(U_15638) ),
inference(clausify,[status(thm)],[f_3966_3]) ).
cnf(f_3966_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15638),U_15640),sK406(U_15641,U_15640,U_15639,U_15638)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15638),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15638),U_15640),U_15641)),hAPP(hAPP(c_Finite__Set_Ofold(U_15638,U_15638,c_Lattices_Osemilattice__inf__class_Oinf(U_15638)),U_15641),U_15639)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15638),U_15639))
| ~ class_Lattices_Osemilattice__inf(U_15638) ),
inference(clausify,[status(thm)],[f_3966_3]) ).
fof(f_3967_1,plain,
! [V_c_2,V_b_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_c_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Lattices_Osemilattice__sup(T_b) ),
inference(fof_nnf,[status(thm)],[fact_fold__sup__le__sup]) ).
fof(f_3967_2,plain,
! [U_15646,U_15645,U_15644,U_15643] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15643),hAPP(hAPP(c_Finite__Set_Ofold(U_15643,U_15643,c_Lattices_Osemilattice__sup__class_Osup(U_15643)),U_15646),U_15644)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15643),U_15645),U_15646)))
| ? [U_15642] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15643),U_15642),U_15645))
& hBOOL(hAPP(hAPP(c_member(U_15643),U_15642),U_15644)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15643),U_15644))
| ~ class_Lattices_Osemilattice__sup(U_15643) ),
inference(variable_rename,[status(thm)],[f_3967_1]) ).
fof(f_3967_3,plain,
! [U_15646,U_15645,U_15644,U_15643] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15643),hAPP(hAPP(c_Finite__Set_Ofold(U_15643,U_15643,c_Lattices_Osemilattice__sup__class_Osup(U_15643)),U_15646),U_15644)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15643),U_15645),U_15646)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15643),sK407(U_15646,U_15645,U_15644,U_15643)),U_15645))
& hBOOL(hAPP(hAPP(c_member(U_15643),sK407(U_15646,U_15645,U_15644,U_15643)),U_15644)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15643),U_15644))
| ~ class_Lattices_Osemilattice__sup(U_15643) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK407]),skolemize(U_15642,sK407(U_15646,U_15645,U_15644,U_15643))],[f_3967_2]) ).
cnf(f_3967_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_15643),sK407(U_15646,U_15645,U_15644,U_15643)),U_15644))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15643),hAPP(hAPP(c_Finite__Set_Ofold(U_15643,U_15643,c_Lattices_Osemilattice__sup__class_Osup(U_15643)),U_15646),U_15644)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15643),U_15645),U_15646)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15643),U_15644))
| ~ class_Lattices_Osemilattice__sup(U_15643) ),
inference(clausify,[status(thm)],[f_3967_3]) ).
cnf(f_3967_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15643),sK407(U_15646,U_15645,U_15644,U_15643)),U_15645))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15643),hAPP(hAPP(c_Finite__Set_Ofold(U_15643,U_15643,c_Lattices_Osemilattice__sup__class_Osup(U_15643)),U_15646),U_15644)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15643),U_15645),U_15646)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15643),U_15644))
| ~ class_Lattices_Osemilattice__sup(U_15643) ),
inference(clausify,[status(thm)],[f_3967_3]) ).
fof(f_3968_1,plain,
! [V_r_2,T_b] :
( ( c_Wellfounded_Owf(T_b,V_r_2)
| ? [B_Q] :
( ! [B_x] :
( ? [B_y] :
( hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) )
& ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) ) )
& ( ! [B_Q] :
( ? [B_x] :
( ! [B_y] :
( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) )
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) )
| ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q)) )
| ~ c_Wellfounded_Owf(T_b,V_r_2) ) ),
inference(fof_nnf,[status(thm)],[fact_wf__eq__minimal]) ).
fof(f_3968_2,plain,
! [U_15656,U_15655] :
( ( c_Wellfounded_Owf(U_15655,U_15656)
| ? [U_15654] :
( ! [U_15653] :
( ? [U_15652] :
( hBOOL(hAPP(hAPP(c_member(U_15655),U_15652),U_15654))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15655,U_15655)),hAPP(hAPP(c_Product__Type_OPair(U_15655,U_15655),U_15652),U_15653)),U_15656)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_15655),U_15653),U_15654)) )
& ? [U_15651] : hBOOL(hAPP(hAPP(c_member(U_15655),U_15651),U_15654)) ) )
& ( ! [U_15650] :
( ? [U_15649] :
( ! [U_15648] :
( ~ hBOOL(hAPP(hAPP(c_member(U_15655),U_15648),U_15650))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15655,U_15655)),hAPP(hAPP(c_Product__Type_OPair(U_15655,U_15655),U_15648),U_15649)),U_15656)) )
& hBOOL(hAPP(hAPP(c_member(U_15655),U_15649),U_15650)) )
| ! [U_15647] : ~ hBOOL(hAPP(hAPP(c_member(U_15655),U_15647),U_15650)) )
| ~ c_Wellfounded_Owf(U_15655,U_15656) ) ),
inference(variable_rename,[status(thm)],[f_3968_1]) ).
fof(f_3968_3,plain,
( ! [U_15660,U_15658] :
( c_Wellfounded_Owf(U_15658,U_15660)
| ? [U_15654] :
( ! [U_15653] :
( ? [U_15652] :
( hBOOL(hAPP(hAPP(c_member(U_15658),U_15652),U_15654))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15658,U_15658)),hAPP(hAPP(c_Product__Type_OPair(U_15658,U_15658),U_15652),U_15653)),U_15660)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_15658),U_15653),U_15654)) )
& ? [U_15651] : hBOOL(hAPP(hAPP(c_member(U_15658),U_15651),U_15654)) ) )
& ! [U_15659,U_15657] :
( ! [U_15650] :
( ? [U_15649] :
( ! [U_15648] :
( ~ hBOOL(hAPP(hAPP(c_member(U_15657),U_15648),U_15650))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15657,U_15657)),hAPP(hAPP(c_Product__Type_OPair(U_15657,U_15657),U_15648),U_15649)),U_15659)) )
& hBOOL(hAPP(hAPP(c_member(U_15657),U_15649),U_15650)) )
| ! [U_15647] : ~ hBOOL(hAPP(hAPP(c_member(U_15657),U_15647),U_15650)) )
| ~ c_Wellfounded_Owf(U_15657,U_15659) ) ),
inference(miniscope,[status(thm)],[f_3968_2]) ).
fof(f_3968_4,plain,
( ! [U_15660,U_15658] :
( c_Wellfounded_Owf(U_15658,U_15660)
| ? [U_15654] :
( ! [U_15653] :
( ? [U_15652] :
( hBOOL(hAPP(hAPP(c_member(U_15658),U_15652),U_15654))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15658,U_15658)),hAPP(hAPP(c_Product__Type_OPair(U_15658,U_15658),U_15652),U_15653)),U_15660)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_15658),U_15653),U_15654)) )
& ? [U_15651] : hBOOL(hAPP(hAPP(c_member(U_15658),U_15651),U_15654)) ) )
& ! [U_15659,U_15657] :
( ! [U_15650] :
( ( ! [U_15648] :
( ~ hBOOL(hAPP(hAPP(c_member(U_15657),U_15648),U_15650))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15657,U_15657)),hAPP(hAPP(c_Product__Type_OPair(U_15657,U_15657),U_15648),sK408(U_15659,U_15657,U_15650))),U_15659)) )
& hBOOL(hAPP(hAPP(c_member(U_15657),sK408(U_15659,U_15657,U_15650)),U_15650)) )
| ! [U_15647] : ~ hBOOL(hAPP(hAPP(c_member(U_15657),U_15647),U_15650)) )
| ~ c_Wellfounded_Owf(U_15657,U_15659) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK408]),skolemize(U_15649,sK408(U_15659,U_15657,U_15650))],[f_3968_3]) ).
fof(f_3968_5,plain,
( ! [U_15660,U_15658] :
( c_Wellfounded_Owf(U_15658,U_15660)
| ( ! [U_15653] :
( ? [U_15652] :
( hBOOL(hAPP(hAPP(c_member(U_15658),U_15652),sK409(U_15660,U_15658)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15658,U_15658)),hAPP(hAPP(c_Product__Type_OPair(U_15658,U_15658),U_15652),U_15653)),U_15660)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_15658),U_15653),sK409(U_15660,U_15658))) )
& ? [U_15651] : hBOOL(hAPP(hAPP(c_member(U_15658),U_15651),sK409(U_15660,U_15658))) ) )
& ! [U_15659,U_15657] :
( ! [U_15650] :
( ( ! [U_15648] :
( ~ hBOOL(hAPP(hAPP(c_member(U_15657),U_15648),U_15650))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15657,U_15657)),hAPP(hAPP(c_Product__Type_OPair(U_15657,U_15657),U_15648),sK408(U_15659,U_15657,U_15650))),U_15659)) )
& hBOOL(hAPP(hAPP(c_member(U_15657),sK408(U_15659,U_15657,U_15650)),U_15650)) )
| ! [U_15647] : ~ hBOOL(hAPP(hAPP(c_member(U_15657),U_15647),U_15650)) )
| ~ c_Wellfounded_Owf(U_15657,U_15659) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK409]),skolemize(U_15654,sK409(U_15660,U_15658))],[f_3968_4]) ).
fof(f_3968_6,plain,
( ! [U_15660,U_15658] :
( c_Wellfounded_Owf(U_15658,U_15660)
| ( ! [U_15653] :
( ? [U_15652] :
( hBOOL(hAPP(hAPP(c_member(U_15658),U_15652),sK409(U_15660,U_15658)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15658,U_15658)),hAPP(hAPP(c_Product__Type_OPair(U_15658,U_15658),U_15652),U_15653)),U_15660)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_15658),U_15653),sK409(U_15660,U_15658))) )
& hBOOL(hAPP(hAPP(c_member(U_15658),sK410(U_15660,U_15658)),sK409(U_15660,U_15658))) ) )
& ! [U_15659,U_15657] :
( ! [U_15650] :
( ( ! [U_15648] :
( ~ hBOOL(hAPP(hAPP(c_member(U_15657),U_15648),U_15650))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15657,U_15657)),hAPP(hAPP(c_Product__Type_OPair(U_15657,U_15657),U_15648),sK408(U_15659,U_15657,U_15650))),U_15659)) )
& hBOOL(hAPP(hAPP(c_member(U_15657),sK408(U_15659,U_15657,U_15650)),U_15650)) )
| ! [U_15647] : ~ hBOOL(hAPP(hAPP(c_member(U_15657),U_15647),U_15650)) )
| ~ c_Wellfounded_Owf(U_15657,U_15659) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK410]),skolemize(U_15651,sK410(U_15660,U_15658))],[f_3968_5]) ).
fof(f_3968_7,plain,
( ! [U_15660,U_15658] :
( c_Wellfounded_Owf(U_15658,U_15660)
| ( ! [U_15653] :
( ( hBOOL(hAPP(hAPP(c_member(U_15658),sK411(U_15660,U_15658,U_15653)),sK409(U_15660,U_15658)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15658,U_15658)),hAPP(hAPP(c_Product__Type_OPair(U_15658,U_15658),sK411(U_15660,U_15658,U_15653)),U_15653)),U_15660)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_15658),U_15653),sK409(U_15660,U_15658))) )
& hBOOL(hAPP(hAPP(c_member(U_15658),sK410(U_15660,U_15658)),sK409(U_15660,U_15658))) ) )
& ! [U_15659,U_15657] :
( ! [U_15650] :
( ( ! [U_15648] :
( ~ hBOOL(hAPP(hAPP(c_member(U_15657),U_15648),U_15650))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15657,U_15657)),hAPP(hAPP(c_Product__Type_OPair(U_15657,U_15657),U_15648),sK408(U_15659,U_15657,U_15650))),U_15659)) )
& hBOOL(hAPP(hAPP(c_member(U_15657),sK408(U_15659,U_15657,U_15650)),U_15650)) )
| ! [U_15647] : ~ hBOOL(hAPP(hAPP(c_member(U_15657),U_15647),U_15650)) )
| ~ c_Wellfounded_Owf(U_15657,U_15659) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK411]),skolemize(U_15652,sK411(U_15660,U_15658,U_15653))],[f_3968_6]) ).
cnf(f_3968_8,plain,
( hBOOL(hAPP(hAPP(c_member(U_15657),sK408(U_15659,U_15657,U_15650)),U_15650))
| ~ hBOOL(hAPP(hAPP(c_member(U_15657),U_15647),U_15650))
| ~ c_Wellfounded_Owf(U_15657,U_15659) ),
inference(clausify,[status(thm)],[f_3968_7]) ).
cnf(f_3968_9,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_15657),U_15648),U_15650))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15657,U_15657)),hAPP(hAPP(c_Product__Type_OPair(U_15657,U_15657),U_15648),sK408(U_15659,U_15657,U_15650))),U_15659))
| ~ hBOOL(hAPP(hAPP(c_member(U_15657),U_15647),U_15650))
| ~ c_Wellfounded_Owf(U_15657,U_15659) ),
inference(clausify,[status(thm)],[f_3968_7]) ).
cnf(f_3968_10,plain,
( hBOOL(hAPP(hAPP(c_member(U_15658),sK410(U_15660,U_15658)),sK409(U_15660,U_15658)))
| c_Wellfounded_Owf(U_15658,U_15660) ),
inference(clausify,[status(thm)],[f_3968_7]) ).
cnf(f_3968_11,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15658,U_15658)),hAPP(hAPP(c_Product__Type_OPair(U_15658,U_15658),sK411(U_15660,U_15658,U_15653)),U_15653)),U_15660))
| ~ hBOOL(hAPP(hAPP(c_member(U_15658),U_15653),sK409(U_15660,U_15658)))
| c_Wellfounded_Owf(U_15658,U_15660) ),
inference(clausify,[status(thm)],[f_3968_7]) ).
cnf(f_3968_12,plain,
( hBOOL(hAPP(hAPP(c_member(U_15658),sK411(U_15660,U_15658,U_15653)),sK409(U_15660,U_15658)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15658),U_15653),sK409(U_15660,U_15658)))
| c_Wellfounded_Owf(U_15658,U_15660) ),
inference(clausify,[status(thm)],[f_3968_7]) ).
fof(f_3969_1,plain,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(V_f_2,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Ounion__idem]) ).
fof(f_3969_2,plain,
! [U_15668,U_15667,U_15666,U_15665,U_15664,U_15663,U_15662,U_15661] :
( hAPP(U_15666,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15662,tc_HOL_Obool)),U_15667),U_15668)) = hAPP(hAPP(U_15663,hAPP(U_15666,U_15667)),hAPP(U_15666,U_15668))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15662),U_15668))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15662),U_15667))
| ~ c_Finite__Set_Ofolding__image__simple__idem(U_15661,U_15662,U_15663,U_15664,U_15665,U_15666) ),
inference(variable_rename,[status(thm)],[f_3969_1]) ).
fof(f_3969_3,plain,
! [U_15668,U_15667,U_15666,U_15665,U_15664,U_15663,U_15662] :
( ! [U_15661] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_15661,U_15662,U_15663,U_15664,U_15665,U_15666)
| hAPP(U_15666,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15662,tc_HOL_Obool)),U_15667),U_15668)) = hAPP(hAPP(U_15663,hAPP(U_15666,U_15667)),hAPP(U_15666,U_15668))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15662),U_15668))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15662),U_15667)) ),
inference(miniscope,[status(thm)],[f_3969_2]) ).
cnf(f_3969_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_15661,U_15662,U_15663,U_15664,U_15665,U_15666)
| hAPP(U_15666,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15662,tc_HOL_Obool)),U_15667),U_15668)) = hAPP(hAPP(U_15663,hAPP(U_15666,U_15667)),hAPP(U_15666,U_15668))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15662),U_15668))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15662),U_15667)) ),
inference(clausify,[status(thm)],[f_3969_3]) ).
fof(f_3970_1,plain,
! [V_P_H_2,V_P_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_2)) = hAPP(c_Set_OCollect(tc_Int_Oint),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),V_P_H_2))
| ? [B_x] :
( ( ( ~ hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(V_P_H_2,B_x)) )
| ( ~ hBOOL(hAPP(V_P_H_2,B_x))
& hBOOL(hAPP(V_P_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__nat__int__set__cong]) ).
fof(f_3970_2,plain,
! [U_15671,U_15670] :
( 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_15670)) = 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_15671))
| ? [U_15669] :
( ( ( ~ hBOOL(hAPP(U_15670,U_15669))
& hBOOL(hAPP(U_15671,U_15669)) )
| ( ~ hBOOL(hAPP(U_15671,U_15669))
& hBOOL(hAPP(U_15670,U_15669)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_15669)) ) ),
inference(variable_rename,[status(thm)],[f_3970_1]) ).
fof(f_3970_3,plain,
! [U_15671,U_15670] :
( 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_15670)) = 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_15671))
| ( ( ( ~ hBOOL(hAPP(U_15670,sK412(U_15671,U_15670)))
& hBOOL(hAPP(U_15671,sK412(U_15671,U_15670))) )
| ( ~ hBOOL(hAPP(U_15671,sK412(U_15671,U_15670)))
& hBOOL(hAPP(U_15670,sK412(U_15671,U_15670))) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK412(U_15671,U_15670))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK412]),skolemize(U_15669,sK412(U_15671,U_15670))],[f_3970_2]) ).
cnf(f_3970_4,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK412(U_15671,U_15670)))
| 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_15670)) = 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_15671)) ),
inference(clausify,[status(thm)],[f_3970_3]) ).
cnf(f_3970_5,plain,
( hBOOL(hAPP(U_15671,sK412(U_15671,U_15670)))
| hBOOL(hAPP(U_15670,sK412(U_15671,U_15670)))
| 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_15670)) = 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_15671)) ),
inference(clausify,[status(thm)],[f_3970_3]) ).
cnf(f_3970_6,plain,
( ~ hBOOL(hAPP(U_15670,sK412(U_15671,U_15670)))
| hBOOL(hAPP(U_15670,sK412(U_15671,U_15670)))
| 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_15670)) = 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_15671)) ),
inference(clausify,[status(thm)],[f_3970_3]) ).
cnf(f_3970_7,plain,
( hBOOL(hAPP(U_15671,sK412(U_15671,U_15670)))
| ~ hBOOL(hAPP(U_15671,sK412(U_15671,U_15670)))
| 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_15670)) = 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_15671)) ),
inference(clausify,[status(thm)],[f_3970_3]) ).
cnf(f_3970_8,plain,
( ~ hBOOL(hAPP(U_15670,sK412(U_15671,U_15670)))
| ~ hBOOL(hAPP(U_15671,sK412(U_15671,U_15670)))
| 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_15670)) = 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_15671)) ),
inference(clausify,[status(thm)],[f_3970_3]) ).
fof(f_3971_1,plain,
! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2
| ~ c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oidem]) ).
fof(f_3971_2,plain,
! [U_15678,U_15677,U_15676,U_15675,U_15674,U_15673,U_15672] :
( hAPP(hAPP(U_15674,U_15678),U_15678) = U_15678
| ~ c_Finite__Set_Ofolding__image__simple__idem(U_15672,U_15673,U_15674,U_15675,U_15676,U_15677) ),
inference(variable_rename,[status(thm)],[f_3971_1]) ).
fof(f_3971_3,plain,
! [U_15678,U_15677,U_15676,U_15675,U_15674] :
( ! [U_15673,U_15672] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_15672,U_15673,U_15674,U_15675,U_15676,U_15677)
| hAPP(hAPP(U_15674,U_15678),U_15678) = U_15678 ),
inference(miniscope,[status(thm)],[f_3971_2]) ).
cnf(f_3971_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_15672,U_15673,U_15674,U_15675,U_15676,U_15677)
| hAPP(hAPP(U_15674,U_15678),U_15678) = U_15678 ),
inference(clausify,[status(thm)],[f_3971_3]) ).
fof(f_3972_1,plain,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oin__idem]) ).
fof(f_3972_2,plain,
! [U_15686,U_15685,U_15684,U_15683,U_15682,U_15681,U_15680,U_15679] :
( hAPP(hAPP(U_15681,hAPP(U_15683,U_15686)),hAPP(U_15684,U_15685)) = hAPP(U_15684,U_15685)
| ~ hBOOL(hAPP(hAPP(c_member(U_15680),U_15686),U_15685))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15680),U_15685))
| ~ c_Finite__Set_Ofolding__image__simple__idem(U_15679,U_15680,U_15681,U_15682,U_15683,U_15684) ),
inference(variable_rename,[status(thm)],[f_3972_1]) ).
fof(f_3972_3,plain,
! [U_15686,U_15685,U_15684,U_15683,U_15682,U_15681,U_15680] :
( ! [U_15679] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_15679,U_15680,U_15681,U_15682,U_15683,U_15684)
| hAPP(hAPP(U_15681,hAPP(U_15683,U_15686)),hAPP(U_15684,U_15685)) = hAPP(U_15684,U_15685)
| ~ hBOOL(hAPP(hAPP(c_member(U_15680),U_15686),U_15685))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15680),U_15685)) ),
inference(miniscope,[status(thm)],[f_3972_2]) ).
cnf(f_3972_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_15679,U_15680,U_15681,U_15682,U_15683,U_15684)
| hAPP(hAPP(U_15681,hAPP(U_15683,U_15686)),hAPP(U_15684,U_15685)) = hAPP(U_15684,U_15685)
| ~ hBOOL(hAPP(hAPP(c_member(U_15680),U_15686),U_15685))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15680),U_15685)) ),
inference(clausify,[status(thm)],[f_3972_3]) ).
fof(f_3973_1,plain,
! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,hAPP(V_g_2,V_x_2)),hAPP(V_F_2,V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oinsert__idem]) ).
fof(f_3973_2,plain,
! [U_15694,U_15693,U_15692,U_15691,U_15690,U_15689,U_15688,U_15687] :
( hAPP(U_15692,hAPP(hAPP(c_Set_Oinsert(U_15688),U_15694),U_15693)) = hAPP(hAPP(U_15689,hAPP(U_15691,U_15694)),hAPP(U_15692,U_15693))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15688),U_15693))
| ~ c_Finite__Set_Ofolding__image__simple__idem(U_15687,U_15688,U_15689,U_15690,U_15691,U_15692) ),
inference(variable_rename,[status(thm)],[f_3973_1]) ).
fof(f_3973_3,plain,
! [U_15694,U_15693,U_15692,U_15691,U_15690,U_15689,U_15688] :
( ! [U_15687] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_15687,U_15688,U_15689,U_15690,U_15691,U_15692)
| hAPP(U_15692,hAPP(hAPP(c_Set_Oinsert(U_15688),U_15694),U_15693)) = hAPP(hAPP(U_15689,hAPP(U_15691,U_15694)),hAPP(U_15692,U_15693))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15688),U_15693)) ),
inference(miniscope,[status(thm)],[f_3973_2]) ).
cnf(f_3973_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_15687,U_15688,U_15689,U_15690,U_15691,U_15692)
| hAPP(U_15692,hAPP(hAPP(c_Set_Oinsert(U_15688),U_15694),U_15693)) = hAPP(hAPP(U_15689,hAPP(U_15691,U_15694)),hAPP(U_15692,U_15693))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15688),U_15693)) ),
inference(clausify,[status(thm)],[f_3973_3]) ).
fof(f_3974_1,plain,
! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
( hAPP(hAPP(V_f_2,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
| ~ c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2) ),
inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Osubset__idem]) ).
fof(f_3974_2,plain,
! [U_15702,U_15701,U_15700,U_15699,U_15698,U_15697,U_15696,U_15695] :
( hAPP(hAPP(U_15697,hAPP(U_15700,U_15702)),hAPP(U_15700,U_15701)) = hAPP(U_15700,U_15701)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15696,tc_HOL_Obool)),U_15702),U_15701))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15696),U_15701))
| ~ c_Finite__Set_Ofolding__image__simple__idem(U_15695,U_15696,U_15697,U_15698,U_15699,U_15700) ),
inference(variable_rename,[status(thm)],[f_3974_1]) ).
fof(f_3974_3,plain,
! [U_15702,U_15701,U_15700,U_15699,U_15698,U_15697,U_15696] :
( ! [U_15695] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_15695,U_15696,U_15697,U_15698,U_15699,U_15700)
| hAPP(hAPP(U_15697,hAPP(U_15700,U_15702)),hAPP(U_15700,U_15701)) = hAPP(U_15700,U_15701)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15696,tc_HOL_Obool)),U_15702),U_15701))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15696),U_15701)) ),
inference(miniscope,[status(thm)],[f_3974_2]) ).
cnf(f_3974_4,plain,
( ~ c_Finite__Set_Ofolding__image__simple__idem(U_15695,U_15696,U_15697,U_15698,U_15699,U_15700)
| hAPP(hAPP(U_15697,hAPP(U_15700,U_15702)),hAPP(U_15700,U_15701)) = hAPP(U_15700,U_15701)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15696,tc_HOL_Obool)),U_15702),U_15701))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15696),U_15701)) ),
inference(clausify,[status(thm)],[f_3974_3]) ).
fof(f_3975_1,plain,
! [V_Q_2,V_P_2,V_B_2,V_A_2,T_b] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Q_2))))
| ? [B_x] :
( ~ hBOOL(hAPP(V_Q_2,B_x))
& hBOOL(hAPP(V_P_2,B_x))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ),
inference(fof_nnf,[status(thm)],[fact_Int__Collect__mono]) ).
fof(f_3975_2,plain,
! [U_15708,U_15707,U_15706,U_15705,U_15704] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15704,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15704,tc_HOL_Obool)),U_15705),hAPP(c_Set_OCollect(U_15704),U_15707))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15704,tc_HOL_Obool)),U_15706),hAPP(c_Set_OCollect(U_15704),U_15708))))
| ? [U_15703] :
( ~ hBOOL(hAPP(U_15708,U_15703))
& hBOOL(hAPP(U_15707,U_15703))
& hBOOL(hAPP(hAPP(c_member(U_15704),U_15703),U_15705)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15704,tc_HOL_Obool)),U_15705),U_15706)) ),
inference(variable_rename,[status(thm)],[f_3975_1]) ).
fof(f_3975_3,plain,
! [U_15708,U_15707,U_15706,U_15705,U_15704] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15704,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15704,tc_HOL_Obool)),U_15705),hAPP(c_Set_OCollect(U_15704),U_15707))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15704,tc_HOL_Obool)),U_15706),hAPP(c_Set_OCollect(U_15704),U_15708))))
| ( ~ hBOOL(hAPP(U_15708,sK413(U_15708,U_15707,U_15706,U_15705,U_15704)))
& hBOOL(hAPP(U_15707,sK413(U_15708,U_15707,U_15706,U_15705,U_15704)))
& hBOOL(hAPP(hAPP(c_member(U_15704),sK413(U_15708,U_15707,U_15706,U_15705,U_15704)),U_15705)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15704,tc_HOL_Obool)),U_15705),U_15706)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK413]),skolemize(U_15703,sK413(U_15708,U_15707,U_15706,U_15705,U_15704))],[f_3975_2]) ).
cnf(f_3975_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_15704),sK413(U_15708,U_15707,U_15706,U_15705,U_15704)),U_15705))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15704,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15704,tc_HOL_Obool)),U_15705),hAPP(c_Set_OCollect(U_15704),U_15707))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15704,tc_HOL_Obool)),U_15706),hAPP(c_Set_OCollect(U_15704),U_15708))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15704,tc_HOL_Obool)),U_15705),U_15706)) ),
inference(clausify,[status(thm)],[f_3975_3]) ).
cnf(f_3975_5,plain,
( hBOOL(hAPP(U_15707,sK413(U_15708,U_15707,U_15706,U_15705,U_15704)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15704,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15704,tc_HOL_Obool)),U_15705),hAPP(c_Set_OCollect(U_15704),U_15707))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15704,tc_HOL_Obool)),U_15706),hAPP(c_Set_OCollect(U_15704),U_15708))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15704,tc_HOL_Obool)),U_15705),U_15706)) ),
inference(clausify,[status(thm)],[f_3975_3]) ).
cnf(f_3975_6,plain,
( ~ hBOOL(hAPP(U_15708,sK413(U_15708,U_15707,U_15706,U_15705,U_15704)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15704,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15704,tc_HOL_Obool)),U_15705),hAPP(c_Set_OCollect(U_15704),U_15707))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15704,tc_HOL_Obool)),U_15706),hAPP(c_Set_OCollect(U_15704),U_15708))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15704,tc_HOL_Obool)),U_15705),U_15706)) ),
inference(clausify,[status(thm)],[f_3975_3]) ).
fof(f_3976_1,plain,
! [V_C_2,V_A_2,T_b] :
( ? [B_X] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
& hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ),
inference(fof_nnf,[status(thm)],[fact_UnionE]) ).
fof(f_3976_2,plain,
! [U_15712,U_15711,U_15710] :
( ? [U_15709] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_15710,tc_HOL_Obool)),U_15709),U_15712))
& hBOOL(hAPP(hAPP(c_member(U_15710),U_15711),U_15709)) )
| ~ hBOOL(hAPP(hAPP(c_member(U_15710),U_15711),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15710,tc_HOL_Obool),U_15712))) ),
inference(variable_rename,[status(thm)],[f_3976_1]) ).
fof(f_3976_3,plain,
! [U_15712,U_15711,U_15710] :
( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_15710,tc_HOL_Obool)),sK414(U_15712,U_15711,U_15710)),U_15712))
& hBOOL(hAPP(hAPP(c_member(U_15710),U_15711),sK414(U_15712,U_15711,U_15710))) )
| ~ hBOOL(hAPP(hAPP(c_member(U_15710),U_15711),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15710,tc_HOL_Obool),U_15712))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK414]),skolemize(U_15709,sK414(U_15712,U_15711,U_15710))],[f_3976_2]) ).
cnf(f_3976_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_15710),U_15711),sK414(U_15712,U_15711,U_15710)))
| ~ hBOOL(hAPP(hAPP(c_member(U_15710),U_15711),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15710,tc_HOL_Obool),U_15712))) ),
inference(clausify,[status(thm)],[f_3976_3]) ).
cnf(f_3976_5,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(U_15710,tc_HOL_Obool)),sK414(U_15712,U_15711,U_15710)),U_15712))
| ~ hBOOL(hAPP(hAPP(c_member(U_15710),U_15711),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_15710,tc_HOL_Obool),U_15712))) ),
inference(clausify,[status(thm)],[f_3976_3]) ).
fof(f_3977_1,plain,
! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
( ? [B_x,B_y,B_z] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_y),B_z)),V_s_2))
& hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),B_x),B_y)),V_r_2))
& V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2))) ),
inference(fof_nnf,[status(thm)],[fact_rel__compE]) ).
fof(f_3977_2,plain,
! [U_15721,U_15720,U_15719,U_15718,U_15717,U_15716] :
( ? [U_15715,U_15714,U_15713] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15719,U_15717)),hAPP(hAPP(c_Product__Type_OPair(U_15719,U_15717),U_15714),U_15713)),U_15721))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15716,U_15719)),hAPP(hAPP(c_Product__Type_OPair(U_15716,U_15719),U_15715),U_15714)),U_15720))
& U_15718 = hAPP(hAPP(c_Product__Type_OPair(U_15716,U_15717),U_15715),U_15713) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15716,U_15717)),U_15718),hAPP(hAPP(c_Relation_Orel__comp(U_15716,U_15719,U_15717),U_15720),U_15721))) ),
inference(variable_rename,[status(thm)],[f_3977_1]) ).
fof(f_3977_3,plain,
! [U_15721,U_15720,U_15719,U_15718,U_15717,U_15716] :
( ? [U_15714,U_15713] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15719,U_15717)),hAPP(hAPP(c_Product__Type_OPair(U_15719,U_15717),U_15714),U_15713)),U_15721))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15716,U_15719)),hAPP(hAPP(c_Product__Type_OPair(U_15716,U_15719),sK415(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716)),U_15714)),U_15720))
& U_15718 = hAPP(hAPP(c_Product__Type_OPair(U_15716,U_15717),sK415(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716)),U_15713) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15716,U_15717)),U_15718),hAPP(hAPP(c_Relation_Orel__comp(U_15716,U_15719,U_15717),U_15720),U_15721))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK415]),skolemize(U_15715,sK415(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716))],[f_3977_2]) ).
fof(f_3977_4,plain,
! [U_15721,U_15720,U_15719,U_15718,U_15717,U_15716] :
( ? [U_15713] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15719,U_15717)),hAPP(hAPP(c_Product__Type_OPair(U_15719,U_15717),sK416(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716)),U_15713)),U_15721))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15716,U_15719)),hAPP(hAPP(c_Product__Type_OPair(U_15716,U_15719),sK415(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716)),sK416(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716))),U_15720))
& U_15718 = hAPP(hAPP(c_Product__Type_OPair(U_15716,U_15717),sK415(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716)),U_15713) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15716,U_15717)),U_15718),hAPP(hAPP(c_Relation_Orel__comp(U_15716,U_15719,U_15717),U_15720),U_15721))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK416]),skolemize(U_15714,sK416(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716))],[f_3977_3]) ).
fof(f_3977_5,plain,
! [U_15721,U_15720,U_15719,U_15718,U_15717,U_15716] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15719,U_15717)),hAPP(hAPP(c_Product__Type_OPair(U_15719,U_15717),sK416(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716)),sK417(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716))),U_15721))
& hBOOL(hAPP(hAPP(c_member(tc_prod(U_15716,U_15719)),hAPP(hAPP(c_Product__Type_OPair(U_15716,U_15719),sK415(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716)),sK416(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716))),U_15720))
& U_15718 = hAPP(hAPP(c_Product__Type_OPair(U_15716,U_15717),sK415(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716)),sK417(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15716,U_15717)),U_15718),hAPP(hAPP(c_Relation_Orel__comp(U_15716,U_15719,U_15717),U_15720),U_15721))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK417]),skolemize(U_15713,sK417(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716))],[f_3977_4]) ).
cnf(f_3977_6,plain,
( U_15718 = hAPP(hAPP(c_Product__Type_OPair(U_15716,U_15717),sK415(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716)),sK417(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15716,U_15717)),U_15718),hAPP(hAPP(c_Relation_Orel__comp(U_15716,U_15719,U_15717),U_15720),U_15721))) ),
inference(clausify,[status(thm)],[f_3977_5]) ).
cnf(f_3977_7,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15716,U_15719)),hAPP(hAPP(c_Product__Type_OPair(U_15716,U_15719),sK415(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716)),sK416(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716))),U_15720))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15716,U_15717)),U_15718),hAPP(hAPP(c_Relation_Orel__comp(U_15716,U_15719,U_15717),U_15720),U_15721))) ),
inference(clausify,[status(thm)],[f_3977_5]) ).
cnf(f_3977_8,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15719,U_15717)),hAPP(hAPP(c_Product__Type_OPair(U_15719,U_15717),sK416(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716)),sK417(U_15721,U_15720,U_15719,U_15718,U_15717,U_15716))),U_15721))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15716,U_15717)),U_15718),hAPP(hAPP(c_Relation_Orel__comp(U_15716,U_15719,U_15717),U_15720),U_15721))) ),
inference(clausify,[status(thm)],[f_3977_5]) ).
fof(f_3978_1,plain,
! [V_r_2,V_yx_2,T_c,T_b] :
( ? [B_x,B_y] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),B_y)),V_r_2))
& V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_yx_2),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))) ),
inference(fof_nnf,[status(thm)],[fact_converseE]) ).
fof(f_3978_2,plain,
! [U_15727,U_15726,U_15725,U_15724] :
( ? [U_15723,U_15722] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15725,U_15724)),hAPP(hAPP(c_Product__Type_OPair(U_15725,U_15724),U_15723),U_15722)),U_15727))
& U_15726 = hAPP(hAPP(c_Product__Type_OPair(U_15724,U_15725),U_15722),U_15723) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15724,U_15725)),U_15726),hAPP(c_Relation_Oconverse(U_15725,U_15724),U_15727))) ),
inference(variable_rename,[status(thm)],[f_3978_1]) ).
fof(f_3978_3,plain,
! [U_15727,U_15726,U_15725,U_15724] :
( ? [U_15722] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15725,U_15724)),hAPP(hAPP(c_Product__Type_OPair(U_15725,U_15724),sK418(U_15727,U_15726,U_15725,U_15724)),U_15722)),U_15727))
& U_15726 = hAPP(hAPP(c_Product__Type_OPair(U_15724,U_15725),U_15722),sK418(U_15727,U_15726,U_15725,U_15724)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15724,U_15725)),U_15726),hAPP(c_Relation_Oconverse(U_15725,U_15724),U_15727))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK418]),skolemize(U_15723,sK418(U_15727,U_15726,U_15725,U_15724))],[f_3978_2]) ).
fof(f_3978_4,plain,
! [U_15727,U_15726,U_15725,U_15724] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15725,U_15724)),hAPP(hAPP(c_Product__Type_OPair(U_15725,U_15724),sK418(U_15727,U_15726,U_15725,U_15724)),sK419(U_15727,U_15726,U_15725,U_15724))),U_15727))
& U_15726 = hAPP(hAPP(c_Product__Type_OPair(U_15724,U_15725),sK419(U_15727,U_15726,U_15725,U_15724)),sK418(U_15727,U_15726,U_15725,U_15724)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15724,U_15725)),U_15726),hAPP(c_Relation_Oconverse(U_15725,U_15724),U_15727))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK419]),skolemize(U_15722,sK419(U_15727,U_15726,U_15725,U_15724))],[f_3978_3]) ).
cnf(f_3978_5,plain,
( U_15726 = hAPP(hAPP(c_Product__Type_OPair(U_15724,U_15725),sK419(U_15727,U_15726,U_15725,U_15724)),sK418(U_15727,U_15726,U_15725,U_15724))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15724,U_15725)),U_15726),hAPP(c_Relation_Oconverse(U_15725,U_15724),U_15727))) ),
inference(clausify,[status(thm)],[f_3978_4]) ).
cnf(f_3978_6,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15725,U_15724)),hAPP(hAPP(c_Product__Type_OPair(U_15725,U_15724),sK418(U_15727,U_15726,U_15725,U_15724)),sK419(U_15727,U_15726,U_15725,U_15724))),U_15727))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15724,U_15725)),U_15726),hAPP(c_Relation_Oconverse(U_15725,U_15724),U_15727))) ),
inference(clausify,[status(thm)],[f_3978_4]) ).
fof(f_3979_1,plain,
! [V_f_2,V_A_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ class_Rings_Olinordered__semidom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__pos]) ).
fof(f_3979_2,plain,
! [U_15732,U_15731,U_15730,U_15729] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15729),c_Groups_Ozero__class_Ozero(U_15729)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15730,U_15729),U_15732),U_15731)))
| ? [U_15728] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15729),c_Groups_Ozero__class_Ozero(U_15729)),hAPP(U_15732,U_15728)))
& hBOOL(hAPP(hAPP(c_member(U_15730),U_15728),U_15731)) )
| ~ class_Rings_Olinordered__semidom(U_15729) ),
inference(variable_rename,[status(thm)],[f_3979_1]) ).
fof(f_3979_3,plain,
! [U_15732,U_15731,U_15730,U_15729] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15729),c_Groups_Ozero__class_Ozero(U_15729)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15730,U_15729),U_15732),U_15731)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15729),c_Groups_Ozero__class_Ozero(U_15729)),hAPP(U_15732,sK420(U_15732,U_15731,U_15730,U_15729))))
& hBOOL(hAPP(hAPP(c_member(U_15730),sK420(U_15732,U_15731,U_15730,U_15729)),U_15731)) )
| ~ class_Rings_Olinordered__semidom(U_15729) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK420]),skolemize(U_15728,sK420(U_15732,U_15731,U_15730,U_15729))],[f_3979_2]) ).
cnf(f_3979_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_15730),sK420(U_15732,U_15731,U_15730,U_15729)),U_15731))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15729),c_Groups_Ozero__class_Ozero(U_15729)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15730,U_15729),U_15732),U_15731)))
| ~ class_Rings_Olinordered__semidom(U_15729) ),
inference(clausify,[status(thm)],[f_3979_3]) ).
cnf(f_3979_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15729),c_Groups_Ozero__class_Ozero(U_15729)),hAPP(U_15732,sK420(U_15732,U_15731,U_15730,U_15729))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15729),c_Groups_Ozero__class_Ozero(U_15729)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15730,U_15729),U_15732),U_15731)))
| ~ class_Rings_Olinordered__semidom(U_15729) ),
inference(clausify,[status(thm)],[f_3979_3]) ).
fof(f_3980_1,plain,
! [V_f_2,V_A_2,T_b,T_c] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)))
| ? [B_x] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x)))
& hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
| ~ class_Rings_Olinordered__semidom(T_c) ),
inference(fof_nnf,[status(thm)],[fact_setprod__nonneg]) ).
fof(f_3980_2,plain,
! [U_15737,U_15736,U_15735,U_15734] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15734),c_Groups_Ozero__class_Ozero(U_15734)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15735,U_15734),U_15737),U_15736)))
| ? [U_15733] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15734),c_Groups_Ozero__class_Ozero(U_15734)),hAPP(U_15737,U_15733)))
& hBOOL(hAPP(hAPP(c_member(U_15735),U_15733),U_15736)) )
| ~ class_Rings_Olinordered__semidom(U_15734) ),
inference(variable_rename,[status(thm)],[f_3980_1]) ).
fof(f_3980_3,plain,
! [U_15737,U_15736,U_15735,U_15734] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15734),c_Groups_Ozero__class_Ozero(U_15734)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15735,U_15734),U_15737),U_15736)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15734),c_Groups_Ozero__class_Ozero(U_15734)),hAPP(U_15737,sK421(U_15737,U_15736,U_15735,U_15734))))
& hBOOL(hAPP(hAPP(c_member(U_15735),sK421(U_15737,U_15736,U_15735,U_15734)),U_15736)) )
| ~ class_Rings_Olinordered__semidom(U_15734) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK421]),skolemize(U_15733,sK421(U_15737,U_15736,U_15735,U_15734))],[f_3980_2]) ).
cnf(f_3980_4,plain,
( hBOOL(hAPP(hAPP(c_member(U_15735),sK421(U_15737,U_15736,U_15735,U_15734)),U_15736))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15734),c_Groups_Ozero__class_Ozero(U_15734)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15735,U_15734),U_15737),U_15736)))
| ~ class_Rings_Olinordered__semidom(U_15734) ),
inference(clausify,[status(thm)],[f_3980_3]) ).
cnf(f_3980_5,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15734),c_Groups_Ozero__class_Ozero(U_15734)),hAPP(U_15737,sK421(U_15737,U_15736,U_15735,U_15734))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15734),c_Groups_Ozero__class_Ozero(U_15734)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15735,U_15734),U_15737),U_15736)))
| ~ class_Rings_Olinordered__semidom(U_15734) ),
inference(clausify,[status(thm)],[f_3980_3]) ).
fof(f_3981_1,plain,
! [V_u_2,V_f_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),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))))
| ? [B_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n))) ),
inference(fof_nnf,[status(thm)],[fact_finite__less__ub]) ).
fof(f_3981_2,plain,
! [U_15740,U_15739] :
( 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)),U_15739)),U_15740))))
| ? [U_15738] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15738),hAPP(U_15739,U_15738))) ),
inference(variable_rename,[status(thm)],[f_3981_1]) ).
fof(f_3981_3,plain,
! [U_15740,U_15739] :
( 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)),U_15739)),U_15740))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK422(U_15740,U_15739)),hAPP(U_15739,sK422(U_15740,U_15739)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK422]),skolemize(U_15738,sK422(U_15740,U_15739))],[f_3981_2]) ).
cnf(f_3981_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),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)),U_15739)),U_15740))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK422(U_15740,U_15739)),hAPP(U_15739,sK422(U_15740,U_15739)))) ),
inference(clausify,[status(thm)],[f_3981_3]) ).
fof(f_3982_1,plain,
! [V_P_2,V_F_2,T_b] :
( hBOOL(hAPP(V_P_2,V_F_2))
| ? [B_x,B_F] :
( ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F)))
& hBOOL(hAPP(V_P_2,B_F))
& ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
& hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F)) )
| ~ hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ),
inference(fof_nnf,[status(thm)],[fact_finite__induct]) ).
fof(f_3982_2,plain,
! [U_15745,U_15744,U_15743] :
( hBOOL(hAPP(U_15745,U_15744))
| ? [U_15742,U_15741] :
( ~ hBOOL(hAPP(U_15745,hAPP(hAPP(c_Set_Oinsert(U_15743),U_15742),U_15741)))
& hBOOL(hAPP(U_15745,U_15741))
& ~ hBOOL(hAPP(hAPP(c_member(U_15743),U_15742),U_15741))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_15743),U_15741)) )
| ~ hBOOL(hAPP(U_15745,c_Orderings_Obot__class_Obot(tc_fun(U_15743,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15743),U_15744)) ),
inference(variable_rename,[status(thm)],[f_3982_1]) ).
fof(f_3982_3,plain,
! [U_15745,U_15744,U_15743] :
( hBOOL(hAPP(U_15745,U_15744))
| ? [U_15741] :
( ~ hBOOL(hAPP(U_15745,hAPP(hAPP(c_Set_Oinsert(U_15743),sK423(U_15745,U_15744,U_15743)),U_15741)))
& hBOOL(hAPP(U_15745,U_15741))
& ~ hBOOL(hAPP(hAPP(c_member(U_15743),sK423(U_15745,U_15744,U_15743)),U_15741))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_15743),U_15741)) )
| ~ hBOOL(hAPP(U_15745,c_Orderings_Obot__class_Obot(tc_fun(U_15743,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15743),U_15744)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK423]),skolemize(U_15742,sK423(U_15745,U_15744,U_15743))],[f_3982_2]) ).
fof(f_3982_4,plain,
! [U_15745,U_15744,U_15743] :
( hBOOL(hAPP(U_15745,U_15744))
| ( ~ hBOOL(hAPP(U_15745,hAPP(hAPP(c_Set_Oinsert(U_15743),sK423(U_15745,U_15744,U_15743)),sK424(U_15745,U_15744,U_15743))))
& hBOOL(hAPP(U_15745,sK424(U_15745,U_15744,U_15743)))
& ~ hBOOL(hAPP(hAPP(c_member(U_15743),sK423(U_15745,U_15744,U_15743)),sK424(U_15745,U_15744,U_15743)))
& hBOOL(hAPP(c_Finite__Set_Ofinite(U_15743),sK424(U_15745,U_15744,U_15743))) )
| ~ hBOOL(hAPP(U_15745,c_Orderings_Obot__class_Obot(tc_fun(U_15743,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15743),U_15744)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK424]),skolemize(U_15741,sK424(U_15745,U_15744,U_15743))],[f_3982_3]) ).
cnf(f_3982_5,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15743),sK424(U_15745,U_15744,U_15743)))
| hBOOL(hAPP(U_15745,U_15744))
| ~ hBOOL(hAPP(U_15745,c_Orderings_Obot__class_Obot(tc_fun(U_15743,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15743),U_15744)) ),
inference(clausify,[status(thm)],[f_3982_4]) ).
cnf(f_3982_6,plain,
( ~ hBOOL(hAPP(hAPP(c_member(U_15743),sK423(U_15745,U_15744,U_15743)),sK424(U_15745,U_15744,U_15743)))
| hBOOL(hAPP(U_15745,U_15744))
| ~ hBOOL(hAPP(U_15745,c_Orderings_Obot__class_Obot(tc_fun(U_15743,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15743),U_15744)) ),
inference(clausify,[status(thm)],[f_3982_4]) ).
cnf(f_3982_7,plain,
( hBOOL(hAPP(U_15745,sK424(U_15745,U_15744,U_15743)))
| hBOOL(hAPP(U_15745,U_15744))
| ~ hBOOL(hAPP(U_15745,c_Orderings_Obot__class_Obot(tc_fun(U_15743,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15743),U_15744)) ),
inference(clausify,[status(thm)],[f_3982_4]) ).
cnf(f_3982_8,plain,
( ~ hBOOL(hAPP(U_15745,hAPP(hAPP(c_Set_Oinsert(U_15743),sK423(U_15745,U_15744,U_15743)),sK424(U_15745,U_15744,U_15743))))
| hBOOL(hAPP(U_15745,U_15744))
| ~ hBOOL(hAPP(U_15745,c_Orderings_Obot__class_Obot(tc_fun(U_15743,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15743),U_15744)) ),
inference(clausify,[status(thm)],[f_3982_4]) ).
fof(f_3983_1,plain,
! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_b),c_Wellfounded_Oless__than,c_List_Olex(T_b,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_b))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_COMBI(tc_List_Olist(T_b)))),
inference(fof_nnf,[status(thm)],[fact_lenlex__def]) ).
fof(f_3983_2,plain,
! [U_15747,U_15746] : c_List_Olenlex(U_15746,U_15747) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(U_15746)),tc_List_Olist(U_15746)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(U_15746),c_Wellfounded_Oless__than,c_List_Olex(U_15746,U_15747))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15746),tc_List_Olist(U_15746),tc_prod(tc_Nat_Onat,tc_List_Olist(U_15746))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(U_15746),tc_prod(tc_Nat_Onat,tc_List_Olist(U_15746))),tc_List_Olist(U_15746)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(U_15746))),c_Nat_Osize__class_Osize(tc_List_Olist(U_15746)))),c_COMBI(tc_List_Olist(U_15746)))),
inference(variable_rename,[status(thm)],[f_3983_1]) ).
cnf(f_3983_3,plain,
c_List_Olenlex(U_15746,U_15747) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(U_15746)),tc_List_Olist(U_15746)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(U_15746),c_Wellfounded_Oless__than,c_List_Olex(U_15746,U_15747))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_15746),tc_List_Olist(U_15746),tc_prod(tc_Nat_Onat,tc_List_Olist(U_15746))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(U_15746),tc_prod(tc_Nat_Onat,tc_List_Olist(U_15746))),tc_List_Olist(U_15746)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(U_15746))),c_Nat_Osize__class_Osize(tc_List_Olist(U_15746)))),c_COMBI(tc_List_Olist(U_15746)))),
inference(clausify,[status(thm)],[f_3983_2]) ).
fof(f_3984_1,plain,
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))),
inference(fof_nnf,[status(thm)],[fact_measure__function__int]) ).
cnf(f_3984_2,plain,
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))),
inference(clausify,[status(thm)],[f_3984_1]) ).
fof(f_3985_1,plain,
! [T_c,V_f_2,T_b] :
( c_FunDef_Ois__measure(tc_prod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_c,T_b)),V_f_2),c_Product__Type_Osnd(T_c,T_b)))
| ~ c_FunDef_Ois__measure(T_b,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_measure__snd]) ).
fof(f_3985_2,plain,
! [U_15750,U_15749,U_15748] :
( c_FunDef_Ois__measure(tc_prod(U_15750,U_15748),hAPP(hAPP(c_COMBB(U_15748,tc_Nat_Onat,tc_prod(U_15750,U_15748)),U_15749),c_Product__Type_Osnd(U_15750,U_15748)))
| ~ c_FunDef_Ois__measure(U_15748,U_15749) ),
inference(variable_rename,[status(thm)],[f_3985_1]) ).
cnf(f_3985_3,plain,
( c_FunDef_Ois__measure(tc_prod(U_15750,U_15748),hAPP(hAPP(c_COMBB(U_15748,tc_Nat_Onat,tc_prod(U_15750,U_15748)),U_15749),c_Product__Type_Osnd(U_15750,U_15748)))
| ~ c_FunDef_Ois__measure(U_15748,U_15749) ),
inference(clausify,[status(thm)],[f_3985_2]) ).
fof(f_3986_1,plain,
! [T_c,V_f_2,T_b] :
( c_FunDef_Ois__measure(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_b,T_c)),V_f_2),c_Product__Type_Ofst(T_b,T_c)))
| ~ c_FunDef_Ois__measure(T_b,V_f_2) ),
inference(fof_nnf,[status(thm)],[fact_measure__fst]) ).
fof(f_3986_2,plain,
! [U_15753,U_15752,U_15751] :
( c_FunDef_Ois__measure(tc_prod(U_15751,U_15753),hAPP(hAPP(c_COMBB(U_15751,tc_Nat_Onat,tc_prod(U_15751,U_15753)),U_15752),c_Product__Type_Ofst(U_15751,U_15753)))
| ~ c_FunDef_Ois__measure(U_15751,U_15752) ),
inference(variable_rename,[status(thm)],[f_3986_1]) ).
cnf(f_3986_3,plain,
( c_FunDef_Ois__measure(tc_prod(U_15751,U_15753),hAPP(hAPP(c_COMBB(U_15751,tc_Nat_Onat,tc_prod(U_15751,U_15753)),U_15752),c_Product__Type_Ofst(U_15751,U_15753)))
| ~ c_FunDef_Ois__measure(U_15751,U_15752) ),
inference(clausify,[status(thm)],[f_3986_2]) ).
fof(f_3987_1,plain,
! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2),
inference(fof_nnf,[status(thm)],[fact_is__measure_Osimps]) ).
fof(f_3987_2,plain,
! [U_15755,U_15754] : c_FunDef_Ois__measure(U_15754,U_15755),
inference(variable_rename,[status(thm)],[f_3987_1]) ).
cnf(f_3987_3,plain,
c_FunDef_Ois__measure(U_15754,U_15755),
inference(clausify,[status(thm)],[f_3987_2]) ).
fof(f_3988_1,plain,
! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2),
inference(fof_nnf,[status(thm)],[fact_is__measure_Oequations]) ).
fof(f_3988_2,plain,
! [U_15757,U_15756] : c_FunDef_Ois__measure(U_15756,U_15757),
inference(variable_rename,[status(thm)],[f_3988_1]) ).
cnf(f_3988_3,plain,
c_FunDef_Ois__measure(U_15756,U_15757),
inference(clausify,[status(thm)],[f_3988_2]) ).
fof(f_3989_1,plain,
! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2),
inference(fof_nnf,[status(thm)],[fact_is__measure_Ointros]) ).
fof(f_3989_2,plain,
! [U_15759,U_15758] : c_FunDef_Ois__measure(U_15758,U_15759),
inference(variable_rename,[status(thm)],[f_3989_1]) ).
cnf(f_3989_3,plain,
c_FunDef_Ois__measure(U_15758,U_15759),
inference(clausify,[status(thm)],[f_3989_2]) ).
fof(f_3990_1,plain,
! [V_ys,V_xs,T_a] :
( V_xs != V_ys
| 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) ),
inference(fof_nnf,[status(thm)],[fact_neq__if__length__neq]) ).
fof(f_3990_2,plain,
! [U_15762,U_15761,U_15760] :
( U_15761 != U_15762
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15760)),U_15761) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15760)),U_15762) ),
inference(variable_rename,[status(thm)],[f_3990_1]) ).
fof(f_3990_3,plain,
! [U_15762,U_15761] :
( ! [U_15760] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15760)),U_15761) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15760)),U_15762)
| U_15761 != U_15762 ),
inference(miniscope,[status(thm)],[f_3990_2]) ).
cnf(f_3990_4,plain,
( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15760)),U_15761) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15760)),U_15762)
| U_15761 != U_15762 ),
inference(clausify,[status(thm)],[f_3990_3]) ).
fof(f_3991_1,plain,
! [V_na_2,V_r_2,V_ys_2,V_xs_2,T_b] :
( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_na_2
& hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_na_2 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_b,V_r_2),V_na_2))) ),
inference(fof_nnf,[status(thm)],[fact_lexn__length]) ).
fof(f_3991_2,plain,
! [U_15767,U_15766,U_15765,U_15764,U_15763] :
( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_15763)),U_15765) = U_15767
&